Evaluation of methods for the rapid extraction of the ......trial extraction techniques are better suited to study rapid extraction of the auditory brainstem response (ABR) compared

Evaluation of methodsfor the rapid extraction of theAuditory Brainstem Response

from underlying Electroencephalogram

Anjula C. De Silva

Bachelor of Science (Electrical Engineering)

Thesis as the requirement of

Doctor of Philosophy

Sensory Neuroscience Laboratory

Swinburne University of Technology

2011

Coordinating Supervisor: Dr. Mark A. Schier

Associate Supervisor: A/Prof. David J.T. Liley

Authorship

I hereby declare that this submission is my own work. The content in this thesis has not

been previously submitted for a degree or diploma in Swinburne University of Technology

or in any other higher educational institute. To the best of my knowledge and belief,

the thesis contains no material previously published or written by another person except

where due references are made.

Signature: ............

Date: .................

Journal articles

Material for the following article was extracted from this thesis.

• DE SILVA, A. C. & SINCLAIR, N. C. & LILEY, D. T. J. 2012. Limitations in the

rapid extraction of evoked potentials using parametric modelling. IEEE Transac-

tions in Biomedical Engineering, accepted on January 21, 2012.

• DE SILVA, A. C. & SCHIER, M. A. 2011. Evaluation of wavelet techniques in rapid

extraction of ABR variations from underlying EEG. Physiological Measurement, 32,

1747-1761.

Conference proceedings

Following conference papers have been prepared in support of this thesis.

• DE SILVA, A. C. & SCHIER, M. A. 2009. A Feasibility Study of Commercially Avail-

able Audio Transducers in ABR Studies.13th International Conference on Biomedical

Engineering, Singapore.

• DE SILVA, A. C. & SCHIER, M. A. 2010. Effectiveness of wavelet filtering in rapid

extraction of ABR from underlying EEG. Biosignal 2010, Berlin.

Abstract

The single trial or rapid extraction of evoked potentials (EPs) has previously been applied

to middle and late latency evoked potentials with the aim of accurately tracking a variety

of central nervous system processes. Because the evoked ‘far fields’ are expected to be

largely independent of the overlying ‘near field’ EEG noise, it can be argued that single

trial extraction techniques are better suited to study rapid extraction of the auditory

brainstem response (ABR) compared with the other EPs with cortical origin. However,

methods have not been systematically studied to extract variations in the early ABR

largely due to the inherent low signal to noise ratio in single trials. Therefore, this thesis

aims to systematically analyse the denoising and time-scale variation tracking of the ABR

using autoregression with an exogenous input (ARX) and wavelet methods.

Rapid extraction of the ABR could reduce clinical test trial times, as a non-invasive

tool for long-term patient monitoring systems with enhanced patient comfort and for

real-time sensory identification applications in brain-computer interfacing. The literature

revealed that, time-series modelling using ARX and wavelet denoising techniques have a

potential to extract the ABR. These findings are further strengthened by the existence

of commercial devices using ARX modelling for monitoring depth of anaesthesia and the

encouraging results reported with wavelets in EP studies.

The dissertation initially presents the analysis conducted to adopt ARX modelling to

extract simulated ABRs. This includes a systematic evaluation of the ARX model and

its modified algorithm; the robust evoked potential estimator (REPE), for their feasibility

and limitations when used in the presence of known variations of ABR latency and signal

to noise ratio. Results revealed superior performance with ARX modelling in extracted

morphology (with a mean correlation coefficient of 0.84 (SD = 0.02)) and latency tracking

(with a mean square error of 0.18 (SD = 0.02)) compared to the robust evoked potential

estimator with a mean correlation coefficient of 0.63 (SD = 0.06) and a mean square error

of 0.35 (SD = 0.06). Verification of these simulated results with actual ABRs concluded;

while ARX modelling is capable of extracting time-scale varying features of a signal only

at relatively high SNRs of > −20 dB.

In a separate study, wavelet denoising methods were analysed as a rapid extraction

system by initially applying them to simulated ABRs followed by application to ABRs

recorded from human participants. The previously reported latency-intensity curve of the

ABR wave V was used as the reference to determine the variation tracking capability of

these wavelet methods. The application of the wavelet methods to the recorded ABRs

required validation of threshold functions and time-windows as an integral part of this

research. To arrive at more accurate results, the wavelet study was extended to observe

the effect of shift-variant discrete wavelet transform and the shift-invariant stationary

wavelet transform with the tested wavelet methods.

It was revealed that the cyclic-shift-tree-denoising wavelet method with the discrete

wavelet transform is the most effective since it produce significantly lower MSEs com-

pared to other methods (p < 0.01) and producing an optimum mean square error of 0.18

(SD = 0.01). This required an ensemble of only 32 epochs to extract a fully featured

ABR with latency variations associated with the latency-intensity curve. However, use

of the computationally redundant stationary wavelet transform yielded significantly bet-

ter results (p < 0.01) compared to the discrete wavelet transform with a MSE of 0.11

(SD = 0.01). The resultant 32 epochs is a significant improvement compared to con-

ventional moving time averaging which uses approximately 1024 epochs to extract the

ABR.

The systematic analysis of rapid extraction of the ABR concluded that CSTD wavelet

method produced the optimum result with only an ensemble of 32 epochs to produce

an ABR with characteristic features and their time-scale variations out performing ARX

modelling methods. Future developments of this work could include recording the ABR

in an ambulatory mode to document and understand the normal population, and such

developments could also find subsequent clinical applications.

Acknowledgement

Over the four years since I started this research, many people have supported encouraged

and given me valuable advice.

Foremost, I acknowledge my supervisors Dr. Mark Schier and A/Prof. David Liley who

kept me focused and guided me towards the light through the intricacies of the research

path. Apart from the research, the support given by way of understanding the life in a

foreign country is much appreciated.

I acknowledge the support given by Nicolas Sinclair from Brain Science Institute (now

with BionicVision Australia) with the collaborative work carried out in evoked response

modelling.

Also I acknowledge the financial support given by the Sensory Neuroscience Laboratory

and Ian Black of the Swinburne TAFE for providing me an employment opportunity to

financially support my living which helped me to concentrate on work related to this thesis

with a peaceful mind.

I acknowledge the valuable advice given by Prof. Peter Cadusch of the Faculty of

Engineering and Industrial Sciences and Martin Dubaj from the Sensory Neuroscience

Laboratory regarding wavelets and Prof. Andrew Wood and David Simpson from the

Faculty of Life and Social Sciences regarding hardware setup for data collection. Also I

acknowledge Chris Anthony from the Faculty of Life and Social Sciences and Jim Barbour

of Media and Communications Group for helping me in the laboratory and expertise given

in the area of acoustics.

I would like to extend special thanks to Dr. Dario Toncich who is the initiator of this

research through which I gained invaluable exposure.

My gratitude is extended to all the friends who were with me every step of the way

sharing hard times, embracing good times and encouraging me to reach this level, especially

by filling the gaps of home touch.

My heartfelt appreciation goes to my mother, father and the sister who gave me con-

stant and unconditional support throughout. You are the invisible force behind the journey

of life. Also my special thanks is extended to my uncles Prof. Nihal Kodikara and Prof.

Saman Gunathilake for valuable advice.

Finally I acknowledge the patience and understanding of my dear wife Pabarasi, to

whom I have to prove a lot from the outcome of this thesis.

Sincerely,

Anjula De Silva.

Abbreviations

AABR Automated Auditory Brainstem Evoked ResponseAAI A-Line ARX indexABR Auditory Brainstem ResponseAEP Auditory Evoked PotentialsALR Auditory Late ResponseAMLR Auditory Middle Latency ResponseAR AutoregressiveARX Autoregressive model with an exogenous inputASSR Auditory Steady State ResponseBCI Brain Computer InterfaceCI Confidence IntervalCNS Central Nervous SystemCSTD Cyclic Shift Tree DenoisingCTMC Constant Threshold with Matching Coefficientsdof degree of freedomDWT Discrete Wavelet TransformECG ElectrocardiogramECochG ElectrocochleogramEEG ElectroencephalogramEMG ElectromyogramEOG ElectrooculogramEP Evoked PotentialERP Event Related PotentialFIR Finite Impulse ResponseFPE Final Prediction ErrorFsp F statistics at a single pointIIR Infinite Impulse ResponseL-I Latency-IntensityMA Moving AverageMLAEP Middle Latency Auditory Evoked PotentialMSE Mean Square ErrorMTA Moving Time AveragenHL Normal Hearing LevelOAE Otoacoustic EmissionPSWC Periodic Sharp Wave ComplexesREPE Robust Evoked Potential EstimatorSAET Stimulus Artifact End TimeSEP Somatosensory Evoked PotentialsSNR Signal to Noise RatioSWT Stationary Wavelet TransformTWMC Temporal Windowing with Matching CoefficientsUNHS Universal Neonatal Hearing ScreeningVEP Visual Evoked PotentialWT Wavelet TransformZ Integers

Contents

1 Introduction 1

1.1 Evoked potentials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.2 Rapid extraction of EPs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

1.2.1 Parametric modelling . . . . . . . . . . . . . . . . . . . . . . . . . . 7

1.2.2 Wavelet denoising . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

1.3 Thesis objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

1.4 Perceived contributions of the research . . . . . . . . . . . . . . . . . . . . . 11

1.5 Organization of the thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

2 A review of the ABR and its extraction 14

2.1 Review of evoked potentials and the auditory brainstem response . . . . . . 15

2.1.1 Evoked potentials . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

2.1.2 Auditory evoked potentials . . . . . . . . . . . . . . . . . . . . . . . 16

2.1.3 Origin of the auditory brainstem response . . . . . . . . . . . . . . . 17

2.1.4 Factors influencing the ABR . . . . . . . . . . . . . . . . . . . . . . 22

2.1.5 EPs in brain computer interfacing . . . . . . . . . . . . . . . . . . . 28

2.1.6 ABRs for rapid extraction . . . . . . . . . . . . . . . . . . . . . . . . 29

2.2 Review of ARX modelling based extraction methods . . . . . . . . . . . . . 30

2.2.1 Moving time averaging to parametric modelling . . . . . . . . . . . . 30

i

2.2.2 The ARX(p, q, d) model . . . . . . . . . . . . . . . . . . . . . . . . . 32

2.2.3 Applications of ARX modelling . . . . . . . . . . . . . . . . . . . . . 35

2.2.4 Robust evoked potential estimator (REPE) . . . . . . . . . . . . . . 38

2.2.5 Simulation studies and drawbacks . . . . . . . . . . . . . . . . . . . 39

2.2.6 Scope of the current study . . . . . . . . . . . . . . . . . . . . . . . . 41

2.3 Review of wavelet based extraction methods . . . . . . . . . . . . . . . . . . 42

2.3.1 Wavelets in the extraction of ABRs and in general EPs . . . . . . . 43

2.3.2 Concept of wavelets . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

2.3.3 Basis wavelets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

2.3.4 DWT with Biorthogonal wavelets . . . . . . . . . . . . . . . . . . . . 51

2.3.5 Shift variance of DWT . . . . . . . . . . . . . . . . . . . . . . . . . . 52

2.3.6 Stationary wavelet transform . . . . . . . . . . . . . . . . . . . . . . 54

2.4 Summation of the ABR extraction methodologies . . . . . . . . . . . . . . . 54

2.4.1 Hypotheses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

2.5 ABR data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

2.5.1 Types of ABR data . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

2.5.2 Simulated ABR data . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

2.5.3 Real ABR data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

3 Recording and constructing synthetic ABR data 63

3.1 Recording of ABR data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

3.1.1 Equipment and parameters . . . . . . . . . . . . . . . . . . . . . . . 64

3.1.2 Participant details . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

3.1.3 MTA and statistically significant SNR . . . . . . . . . . . . . . . . . 67

3.1.4 Data organisation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

3.1.5 The template . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

CONTENTS ii

3.2 Latency-intensity and amplitude-intensity curves . . . . . . . . . . . . . . . 71

3.2.1 Compatibility of the L-I curve model . . . . . . . . . . . . . . . . . . 73

3.3 Synthetic ABR model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

3.3.1 Construction of the ABR model . . . . . . . . . . . . . . . . . . . . 74

3.3.2 Construction of synthetic datasets . . . . . . . . . . . . . . . . . . . 75

3.3.3 Adding noise to simulated datasets . . . . . . . . . . . . . . . . . . . 78

4 ARX modelling in rapid extraction of the ABR 80

4.1 Introduction to the simulation study . . . . . . . . . . . . . . . . . . . . . . 81

4.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81

4.2.1 Simulation study domain and extrapolation . . . . . . . . . . . . . . 81

4.2.2 Simulated reference ABR and datasets . . . . . . . . . . . . . . . . . 82

4.2.3 Acquisition of real ABR data . . . . . . . . . . . . . . . . . . . . . . 83

4.2.4 Predetermined models . . . . . . . . . . . . . . . . . . . . . . . . . . 83

4.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88

4.3.1 The efficacy of identifying the predefined models . . . . . . . . . . . 88

4.3.2 Estimation of model orders . . . . . . . . . . . . . . . . . . . . . . . 89

4.3.3 Comparison of model performance . . . . . . . . . . . . . . . . . . . 93

4.3.4 Estimated single sweep of an ABR . . . . . . . . . . . . . . . . . . . 96

4.3.5 Tracking variations of a single sweep . . . . . . . . . . . . . . . . . . 98

4.3.6 Confirmation of simulated results with actual ABRs . . . . . . . . . 106

4.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111

4.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113

5 Wavelets in rapid extraction of the ABR 116

5.1 Wavelet extracting methods . . . . . . . . . . . . . . . . . . . . . . . . . . . 118

5.1.1 Synthetic and real ABR template . . . . . . . . . . . . . . . . . . . . 118

CONTENTS iii

5.1.2 Wavelet decomposition levels . . . . . . . . . . . . . . . . . . . . . . 118

5.1.3 Constant thresholds with matching coefficients (CTMC) . . . . . . . 119

5.1.4 Time windowing with matching coefficients (TWMC) . . . . . . . . 121

5.1.5 Cyclic shift tree denoising (CSTD) . . . . . . . . . . . . . . . . . . . 122

5.1.6 Use of SWT algorithm in CTMC, TWMC and CSTD . . . . . . . . 127

5.2 Choice of the basis wavelet . . . . . . . . . . . . . . . . . . . . . . . . . . . 128

5.3 Simulation study on wavelet methods . . . . . . . . . . . . . . . . . . . . . 129

5.3.1 Denoising . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129

5.3.2 Latency tracking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131

5.4 Evaluation of wavelet methods on real ABR Data . . . . . . . . . . . . . . . 132

5.4.1 Denoising ability of wavelet methods . . . . . . . . . . . . . . . . . . 134

5.4.2 Latency tracking ability of wavelet methods . . . . . . . . . . . . . . 134

5.5 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135

5.5.1 Determination of a common basis wavelet for analysis . . . . . . . . 135

5.5.2 Determination of CSTD level threshold function . . . . . . . . . . . 136

5.5.3 Noise reduction of wavelet methods with DWT . . . . . . . . . . . . 136

5.5.4 Fsp threshold in quantifying the effectiveness of wavelet filtered ABRs140

5.5.5 Comparison of noise reduction between DWT and SWT . . . . . . . 146

5.5.6 Latency tracking results of wavelet methods with DWT . . . . . . . 149

5.5.7 Latency tracking results of wavelet methods with SWT . . . . . . . 155

5.6 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158

5.6.1 Evaluation of de-noising capacity of wavelet methods using DWT . . 158

5.6.2 Performance comparison of DWT and SWT decomposition algorithms159

5.6.3 Evaluation of latency tracking with DWT and SWT . . . . . . . . . 160

5.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163

CONTENTS iv

6 Overall conclusions and further work 165

6.1 The approach towards the extraction of ABR . . . . . . . . . . . . . . . . . 166

6.2 Rapid extraction with ARX and REPE . . . . . . . . . . . . . . . . . . . . 166

6.3 Rapid extraction with wavelets . . . . . . . . . . . . . . . . . . . . . . . . . 168

6.4 Limitations of the current study and future work . . . . . . . . . . . . . . . 170

A Appendix A I

B Appendix B IV

C Appendix C XXI

D Appendix D XL

E Appendix E LIX

F Appendix F LXIII

CONTENTS v

List of Figures

2.1 The AEPs include early, middle and late potentials . . . . . . . . . . . . . . 17

2.2 A fully featured ABR recorded from a participant . . . . . . . . . . . . . . 19

2.3 Auditory pathway from inner ear to the primary auditory cortex . . . . . . 20

2.4 Presumed generators of the ABR waves I-V . . . . . . . . . . . . . . . . . . 22

2.5 Latency-intensity curves of wave I, wave III and wave V . . . . . . . . . . . 26

2.6 The process of the ARX model . . . . . . . . . . . . . . . . . . . . . . . . . 34

2.7 The process of the REPE . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

2.8 SNR improvement of ARXE (same as ARX) and REPE . . . . . . . . . . . 41

2.9 Mallat’s cascaded filter multiresolution analysis . . . . . . . . . . . . . . . . 53

2.10 Decomposition and the synthesis tree of the SWT . . . . . . . . . . . . . . 55

2.11 Types of auditory stimulus and their frequency spectrums . . . . . . . . . . 59

2.12 Possible electrode montages for ABR recordings . . . . . . . . . . . . . . . . 61

3.1 ABR recording with a stimulus artifact . . . . . . . . . . . . . . . . . . . . 67

3.2 Typical recording setup on a participant . . . . . . . . . . . . . . . . . . . . 68

3.3 Fsp plot for a worst-case scenario. . . . . . . . . . . . . . . . . . . . . . . . 70

3.4 Synthetic and the Real ABR templates . . . . . . . . . . . . . . . . . . . . . 71

3.5 Latency and amplitude intensity curves derived from recorded data . . . . . 72

3.6 The theoretical and the derived L-I curve of wave V . . . . . . . . . . . . . 73

vi


3.8 Comparison spectra of the ABR model and the real ABR . . . . . . . . . . 76

3.9 Types of datasets used in the simulation study . . . . . . . . . . . . . . . . 77

3.10 Spectra of associated noise compared to Gaussian white noise . . . . . . . . 78

4.1 Characteristics of the transfer function of the ARX model . . . . . . . . . . 85

4.2 Characteristics of the transfer function of the REPE . . . . . . . . . . . . . 87

4.3 Estimated Pole (x) and Zero (o) plots of the ARX model . . . . . . . . . . 89

4.4 Estimated Pole (x) and Zero (o) plots of the REPE . . . . . . . . . . . . . 90

4.5 Results of the fixed model order determination of the ARX model . . . . . 92

4.6 Results of the fixed model order determination of the REPE . . . . . . . . . 94

4.7 The SNR improvement of the estimated ABR . . . . . . . . . . . . . . . . . 95

4.8 Detection of wave V with empirical and theoretical model orders . . . . . . 96

4.9 Single sweep estimated with ARX model and REPE . . . . . . . . . . . . . 97

4.10 Wave V latency (1 ms) tracking using ARX(6,7,0) . . . . . . . . . . . . . . 100

4.11 Wave V latency (2 ms) tracking using ARX(6,7,0) . . . . . . . . . . . . . . 101

4.12 Comparison of the latency tracking of the ARX estimation and the MTA . 102

4.13 Wave V latency (1ms) tracking using REPE(6,7,8,0) . . . . . . . . . . . . . 104

4.14 Wave V latency (2 ms) tracking using REPE(6,7,8,0) . . . . . . . . . . . . . 105

4.15 Comparison of the latency tracking of the REPE estimation and the MTA . 106

4.16 Histograms of model order combinations for real ABR . . . . . . . . . . . . 108

4.17 L-I curves derived with a single epoch, MTA of 32, 128 and 256 . . . . . . . 110

4.18 Unstable model estimates . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111


5.2 Flowchart of the CTMC algorithm . . . . . . . . . . . . . . . . . . . . . . . 120

5.3 Flowchart of the TWMC algorithm . . . . . . . . . . . . . . . . . . . . . . . 122

LIST OF FIGURES vii

5.4 Temporal windows defined for the TWMC . . . . . . . . . . . . . . . . . . . 123

5.5 The flowchart of the CSTD algorithm . . . . . . . . . . . . . . . . . . . . . 124

5.6 Averaging sequence of the CSTD algorithm . . . . . . . . . . . . . . . . . . 126

5.7 Defined temporal windows for TWMC with SWT algorithm . . . . . . . . . 129

5.8 The constructed array with SWT coefficients to suit CSTD . . . . . . . . . 130

5.9 Improvement in the SNR with wavelet filtering methods . . . . . . . . . . . 131

5.10 Latency tracking results with simulated ABR datasets . . . . . . . . . . . . 133

5.11 Effect of Biorthogonal basis wavelets on denoising methods . . . . . . . . . 135

5.12 Effect of level threshold functions in CSTD . . . . . . . . . . . . . . . . . . 137

5.13 Denoising effect of Wavelet methods . . . . . . . . . . . . . . . . . . . . . . 138

5.14 Surface plots of CTMC filtered ABRs . . . . . . . . . . . . . . . . . . . . . 141

5.15 Surface plots of TWMC filtered ABRs . . . . . . . . . . . . . . . . . . . . . 142

5.16 Surface plots of CSTD filtered ABRs . . . . . . . . . . . . . . . . . . . . . . 143

5.17 Mean correlation coefficients between the template and CTMC filtered ABRs144

5.18 Denoised ABRs at a block size of 32 . . . . . . . . . . . . . . . . . . . . . . 145

5.19 Effect of dof of F statistics on the threshold criteria . . . . . . . . . . . . . 146

5.20 Comparison of Denoising of SWT and DWT . . . . . . . . . . . . . . . . . . 148

5.21 The plot of the effect of denoising of SWT and DWT on Random ABRs . . 150

5.22 Latency tracking with wavelet methods using DWT . . . . . . . . . . . . . 153

5.23 L-I curves derived from estimated models with DWT . . . . . . . . . . . . . 154

5.24 Latency tracking with wavelet methods using SWT . . . . . . . . . . . . . . 156

5.25 L-I curves derived from estimated models with SWT . . . . . . . . . . . . . 157

5.26 The difference of the MSE of the L-I curves derived using DWT and SWT . 163

LIST OF FIGURES viii

List of Tables

2.1 A brief summary of the types of EPs, their generators and features . . . . . 16

2.2 Normative Latencies and Amplitudes for ABR wave features . . . . . . . . 19

2.3 Specifications of key algorithms for rapid extraction . . . . . . . . . . . . . 47

2.4 Settings for a typical ABR recording . . . . . . . . . . . . . . . . . . . . . . 58

3.1 Finalised parameters for the data collection for the main study . . . . . . . 65

4.1 Unstable estimated epochs percentage (%) . . . . . . . . . . . . . . . . . . . 109

5.1 Frequency Content of wavelet subspaces . . . . . . . . . . . . . . . . . . . . 119

5.2 Coefficients of SWT and DWT . . . . . . . . . . . . . . . . . . . . . . . . . 127

5.3 ANOVA results comparing MSEs produced by CSTD, TWMC and CTMC 138

5.4 Tukey post-hoc comparison of CSTD against TWMC and CTMC . . . . . . 139

5.5 Results of paired t-test between the MSEs of DWT and SWT denoised ABRs149

5.6 Coefficients of the estimated models of the L-I curves derived with DWT . . 154

5.7 Results of the t-test for DWT derived curves . . . . . . . . . . . . . . . . . 154

5.8 Coefficients of the estimated models of the L-I curves derived with SWT . . 157

5.9 Results of the t-test for SWT derived curves . . . . . . . . . . . . . . . . . . 157

ix

Chapter 1

Introduction

Bioelectric signals are key tools used by physicians for diagnosis, research, therapy and

prognosis of the health of patients and recently for brain-computer interfacing (BCI). These

signals are obtained through electrodes which sense the variations in electrical potentials

generated by physiological systems. Bioelectric signals originate as a result of groups of

neural or muscular cells producing an electric field which propagates through tissues in

the body (Adelman & Smith 1999). A few of these include electroencephalogram (EEG),

electrooculogram (EOG), electrocardiogram (ECG) and electromyogram (EMG).

Evoked potentials (EPs) are a sub-group of EEG that directly measure the electrical

response of the cortex to sensory, stimuli or affective and cognitive processes. In gen-

eral EPs are relatively small in amplitude (less than 30 µV) compared to the ongoing

EEG (20-50 µV), especially early components such as the auditory brainstem response

(ABR) in the range of one tenth of a microvolt. Therefore biomedical signal processing

techniques are extensively used to extract these EPs to enhance features for accurate di-

agnosis and prognosis. Currently signal processing related to extraction of EPs is a major

area of research which looks into rapid and accurate variation tracking for intraoperative

neurophysiological monitoring and patient comfort related applications.

1

1.1 Evoked potentials

Evoked potentials are bioelectric signals recorded from the scalp in response to a variety

of controlled internal and external stimuli. The time locked stimuli activate a series of

neuronal populations along the path from the receptor to the brain. It should be noted

that event related potentials (ERPs) are another sub-group of EEG that directly result

from a thought or perception such as P300, N400 and P600. They are usually confused

with EPs e.g. the ABR is a measured brain response to sound that is not directly the

result of a thought or perception.

Both EPs and ERPs produced by the activation of neuronal populations can be

recorded via scalp electrodes. In general, an EP lasts for a few hundreds of millisec-

onds, with its various features categorised into early, middle and late components. In this

thesis, we investigate the auditory brainstem response (ABR) which is one of the early

components of auditory EPs, arising within 0-10 ms reflecting compound action potentials

along auditory pathway from the distal vestibulocochlear nerve (VIII cranial nerve) to the

inferior colliculus in the brainstem (Hall 2007).

Features of EPs that are of clinical and physiological relevance include amplitude and

latency variations of specific, well defined peaks. These provide important information

regarding cortical activity and therefore are measures of the functional state of the cortex.

The latency and amplitude effects on EPs have been observed and are affected by;

neurophysiological disorders, subject factors, stimulus and acquisition factors and drug

and muscular artefacts.

Neurological disorders have an effect on a range of EPs, especially on the ABR with

multiple sclerosis, Parkinson’s disease, Tumors and Strokes (Chiappa & Ropper 1982, Ko-

dama, Ieda, Hirayama, Koike, Ito & Sobue 1999, Misra & Kakita 1999). Also, the ABR is

used as an important tool in intraoperative monitoring of the acoustic nerve during acous-

tic neuroma and brainstem tumor resections (Lee, Song, Kim, Lee & Kang 2009, Morawski,

Niemczyk, Sokolowski & Telischi 2010, Matthies 2008) along with ECochG (Gouveris

Introduction 2

& Mann 2009) and direct cochlear nerve action potential (CNAP) (Aihara, Murakami,

Watanabe, Takahashi, Inagaki, Tanikawa & Yamada 2009, Yamakami, Yoshinori, Saeki,

Wada & Oka 2009). Further, variations of the peak amplitude of middle latency auditory

evoked potentials (MLAEPs) have been recorded in response to anaesthetic agents such as

propofol and analgesics; alfentanil, fentanyl and morphine (Davies, Mantzaridis, Kenny &

Fisher 1996, Schwender, Rimkus, Haessler, Klasing, Poppel & Peter 1993, Thornton 1991).

The correlation between the amplitude of the MLAEP and depth of anaesthesia was pos-

itively identified from the results of an artificial neural network fed with selective com-

ponents extracted from applying discrete wavelet transform on the MLAEP (Nayak &

Roy 1998). Further, MLAEP has been commercially used as an automated monitoring

tool by means of A-liner index (Jensen, Nygaard & Henneberg 1998). The emerging field

of brain computer interfacing (BCI) is heavily dependent upon visual and auditory P300

response which is related to the perception and auditory steady state response (ASSR)

(Furdea, Halder, Krusienski, Bross, Nijboer, Birbaumer & Kbler 2009, Lee, Hsieh, Wu,

Shyu & Wu 2008, Lopez, Pomares, Pelayo, Urquiza & Perez 2009, Nijboer, Furdea, Gunst,

Mellinger, McFarland, Birbaumer & Kbler 2008, Pham, Hinterberger, Neumann, Kbler,

Hofmayer, Grether, Wilhelm, Vatine & Birbaumer 2005).

While changes in the morphology of EP peaks are slow (hours, days) for neuro-

logical disorders, changes due to surgical procedures, drug administration and stimu-

lus parameters can, in contrast, be very rapid (seconds, minutes) (Jensen, Lindholm &

Henneberg 1996). The detection rate of ERPs generated for BCI applications similarly

needs to be close to real-time for the external system to be able to meaningfully react to

the brain state. But the delay associated with the time point of emitting the EP/ERP

and the interpretation of it, is a common issue in BCI systems (Lopez et al. 2009) and in

intraoperative monitoring (Yamakami et al. 2009) when using conventional moving time

average method of detecting EP/ERP changes, therefore highlighting the need of a rapid

extraction method.

Introduction 3

1.2 Rapid extraction of EPs

The far field recordings of EPs challenge extraction due to distortion by the comparatively

larger amplitudes of spontaneous EEG. Typically, early and middle components of an EP

have a signal to noise ratio (SNR) in the range of -20 to -30 dB (or 0.1 to 0.03:1 ratio

of amplitudes). Conventionally, moving time average of a large ensemble of time locked

responses is used to extract the deterministic EP and to suppress random spontaneous

EEG assumed to be uncorrelated to the EP. This is true for early components but less so for

late and middle components due to the wide range of neuronal populations involved in the

generation. In conventional ABR extraction, a moving time average of approximately 1000

sweeps is considered to suppress the noise and arrive at the ABR i.e. a SNR improvement

of ' 30 dB (Rushaidin, Salleh, Swee, Najeb & Arooj 2009, Strauss, Delb, Plinkert &

Schmidt 2004, Shangkai & Loew 1986, Wilson 2004, Stuart, Yang & Botea 1996).

The use of a conventional moving time average in these applications however results in

poor time resolution and therefore cannot be used to detect the fast variations in latency

and amplitude of EPs. In practice, an initial ABR study (as the first step) investigating

the response of the auditory system to different stimulus intensities takes approximately 30

minutes using conventional moving time averaging (i.e. both ears are tested using only one

stimulus frequency, five stimulus intensities and two repeat traces per intensity) (Moller,

Jho, Yokota & Jannetta 1995). A more detailed ABR study investigating how the auditory

system responds to different stimulus frequencies and intensities takes approximately 60

minutes using current technology (i.e. both ears are tested using four stimulus frequencies,

three stimulus intensities and two repeat traces per intensity) (Wilson, Mills, Bradley,

Petoe, Smith & Dzulkarnain 2011, Vannier & Nat-Ali 2004).

In addition, the underlying assumptions of time invariance of the EP and the inde-

pendence of background spontaneous EEG with the EP makes conventional moving time

average unsuitable to extract a series of EPs with time varying features. The irrationality

of these assumptions could be further explained as follows (Sun & Chen 2008):

Introduction 4

• The active and adaptive ability of the cerebrum and the nervous system, the evoked

response is not necessarily a definite process itself, but of stochastic nature.

• Multiple excitations during traditional ABR tests will cause the nervous system to

react repeatedly and fatigue chronically, which will affect the waveform of the final

induced responses to some extent.

• The relation between the signal and noise cannot be described by simple additive

model, i.e., the signal and noise may not be kept wholly irrelevant. It is found that

the sound stimulation may have phase control effect on the self-induced brain stem

potential (Hanrahan 1990).

Further drawbacks are reported on the current technology for extraction of ABRs in

international heath schemes. According to Universal Neonatal Hearing Screening pro-

gram (UNHS), Automated Auditory Brainstem Evoked Response (AABR) technology is

the most preferred screening tool due to the low false positive rate of 4% (Tann, Wil-

son, Bradley & Wanless 2009). However, this is a multi-stage process where Otoacoustic

Emission (OAE) test is performed prior to the referral of AABR. This multi-stage process

is prone to inaccuracies, unnecessary time delays and additional costs involved to equip

test centres with OAE devices which account for approximately 60% of installed devices

globally (Moller et al. 1995).

In eliminating these drawbacks, two significant limitations that impede AABR as the

sole clinical neonatal hearing screening device are:

• Lengthy ABR acquisition times limit the diagnosis to only be able to assess at

near-threshold stimulus intensity (typically 35 dB nHL). Although a more thorough

and accurate ABR test could be performed if both the results above and below the

hearing threshold are included.

• The acquisition of the ABR is subject to high levels of noise interference from

both external noise sources and the neonate being tested. Therefore, data acqui-

sition times for the near-threshold ABR waveforms required for UNHS are typically

Introduction 5

around 5 minutes and in less favourable acquisition conditions, extend to 20 min-

utes (Corona-Strauss, Delb, Schick & Strauss 2010a), after which testing is typically

aborted until another time which cause parental anxiety.

• An automated and objective audiological method which is able to quantify the hear-

ing threshold within a short measurement time (less than 2 or 3 minutes) without

sedation or general anaesthesia could drastically reduce the number of audiological

examinations that need to be performed under anaesthesia (Strauss et al. 2004).

The identification of these constraints led to further analysis and improved rapid ex-

traction methods. Recent literature has reported considerable work on the reduction of the

number of epochs required to obtain EPs in general and ABRs in particular. Early noise

reduction methods such as matched filters (Delgado & Ozdamar 1994), use of templates

(Vannier, Adam, Karasinski, Ohresser & Motsch 2001) and Wiener filtering (Doyle 1975)

make the assumption that the signal is stationary.

However, ABR signals are transient (non-stationary) in nature and present with vari-

able peak morphology, both within a single ABR and between different ABRs (De Weerd

1981). In other words, the frequency content of bioelectric waveforms such as ABRs vary

over their time courses and are localised in time, as such they are non-stationary in time

viz. transient (Samar, Bopardikar, Rao & Swartz 1999).

Woody (1967) introduced an iterative method for EP/ERP latency estimation based

on common averages. He determined the time instant of the best correlation between a

template (EP/ERP average) and single trials by shifting the latter in time. A similar

method has been adopted by Vannier et al. (2001) and Delgado & Ozdamar (1994) by

shifting a template for each peak of the ABR. While these methods correct possible latency

variability of EPs/ERPs, the performance was highly dependent on the choice of templates.

Eliminating these drawbacks, the Wiener filter (Doyle 1975), uses spectral estimation

to reduce uncorrelated noise. This technique, however, is less accurate for EPs/ERPs,

because the time course of transient signals is lost in the Fourier domain (Effern, Lehnertz,

Fernndez, Grunwald, David & Elger 2000). The disadvantages of Fourier analysis arise

Introduction 6

due to the decomposition of the signal of interest into linear combinations of sine and

cosine waves, which are highly localized in frequency, but strictly not localized in time

(Raz, Dickerson & Turetsky 1999, Quian Quiroga 2000).

1.2.1 Parametric modelling

One common approach to rapidly extract EPs that avoid the above mentioned drawbacks

is to parametrically model the EP using an autoregressive model with an exogenous in-

put (ARX). Here a single sweep is modelled with a reference signal (exogenous input)

and white noise. ARX modelling has been widely adopted by researchers to rapidly ex-

tract MLAEP, visual evoked potentials (VEP) and somatosensory evoked potentials (SEP)

(Cerutti, Baselli, Liberati & Pavesi 1987, Jensen et al. 1996, Rossi, Bianchi, Merzagora,

Gaggiani, Cerutti & Bracchi 2007). This method of rapid extraction has been used to

quantify changes in MLAEP during anaesthesia (Jensen et al. 1996, Mainardi, Kupila,

Nieminen, Korhonen, Bianchi, Pattini, Takala, Karhu & Cerutti 2000, Urhonen, Jensen

& Lund 2000), changes in auditory N100, as a means of monitoring sedation in cardiac

surgery patients (Mainardi et al. 2000) and changes in SEPs to investigate a combined

spinal cord intraoperative neuromonitoring technique. The ARX method has also been

extended to make the single sweep estimation process resistant to noise using the robust

evoked potential estimator (REPE) (Lange & Inbar 1996).

To date, ARX and REPE methods of rapid extraction have been evaluated on the basis

of their ability to detect assumed variations in actual EP data. Since the actual EP is

unknown in real data, simulated data is required so that (in order to provide a deterministic

EP) ARX methods for rapid extraction can be meaningfully evaluated. Therefore, a set

of synthetic data with predefined, but physiologically plausible, variations in latency and

amplitude provide a better basis to compare the model estimation rather than using real

EPs which inherit large variances due to physiological and recording conditions. While a

range of attempts have been made to conduct simulation studies (Cerutti et al. 1987, Lange

& Inbar 1996, Rossi et al. 2007), these suffer from:

Introduction 7

• Use of grand average of real EP data as the reference signal.

– “An actual average over 99 sweeps of a visual evoked potential is taken as the

reference signal u” (Cerutti et al. 1987)

– “An averaged 200-trial ensemble of a finger tapping experiment was used as the

signal s(n)” (Lange & Inbar 1996)

Such experimental ERPs are not reproducible due to obvious reasons such as; par-

ticipant conditions, experimental setup and noise associated in the recording envi-

ronment. Therefore a comparison or a performance evaluation with previous work

is impossible.

• Ambiguity of the selection criteria for model parameters with qualitative statements,

such as:

– “The transfer function B(z)/A(z) is designed in such a way as to perform only

a temporal delay on the reference signal u” (Cerutti et al. 1987).

– “Then, single-trial realizations with . . . varying gains were synthesized from

the simulated signal and ongoing activity at different SNRs, . . . ” (Lange &

Inbar 1996)

Such qualitative statements make the validation of the model performance with

previous work impossible.

• The range of latency variations tested in the simulated ERP is limited, e.g.

– “. . . single-trial realizations with a constant latency shift of three sample points

. . . ” (Lange & Inbar 1996)

Maximum latency shift of a typical ABR recording is 80 sample points (explained

further in chapter 4), thus such studies do not encompass the expected range of

physiological variation of the ABR.

Therefore, one of the aims of this thesis is to systematically address these shortcomings

and provide a solid evaluation criterion for denoising signals with parametric modelling.

Introduction 8

1.2.2 Wavelet denoising

Recently wavelet domain filtering has been widely studied in conjunction with EPs for its

ability to analyse time-variant signals. The wavelet transform (WT) considers the signal

to be non-stationary and provides the additional advantage of having a time-frequency

representation with resolution control in both time and frequency domains. Analysis and

synthesis of the WT with a range of wavelet base functions has an advantage over other

conventional transformations with only a cosine base function. Use of closely matched

wavelet base functions to the morphology of the EP improves the spectral feature which

leads to better feature localization (Samar et al. 1999). Also wavelets are localized in both

time and frequency domains with the ‘compact support’ feature and the band limited

spectrum of the wavelet suits features of EPs as oppose to infinite length in time and

single frequency of the cosine base signal.

The main analysis technique, discrete wavelet transform (DWT) decomposes the EP

into number of temporal scales based on the frequency distribution. Then various thresh-

olding methods are applied to retain only the relevant coefficients to the EP such as; fixed

thresholding (Maglione, Pincilotti, Acevedo, Bonell & Gentiletti 2003, McCullagh, Wang,

Zheng, Lightbody & McAllister 2007, Wilson, Winter, Kerr & Aghdasi 1998, Zhang, McAl-

lister, Scotney, McClean & Houston 2006), soft thresholding (Causevic, Morley, Wicker-

hauser & Jacquin 2005, Donoho 1995) and thresholding based on temporal distribution

of coefficients (Quian Quiroga 2005). In addition to DWT, there are other wavelet trans-

formation methods such as continuous wavelet transform for an analogue transformation

from which DWT got inspired, stationary wavelet transform without decimation which

reduces the shift invariance of DWT (Nason & Silverman 1995), wavelet packet decom-

position to achieve a fully decomposed tree (Coifman & Wickerhauser 1992), dual tree

complex wavelet transform to achieve shift invariance of signals (Kingsbury 2001).

The wavelet studies reported in the literature are predominantly related to middle

and late components of EPs and to a lesser extent to the ABR. However these studies

concentrate more on the denoising aspect and the classification of the ABR according to

Introduction 9

the presence of wave V (Corona-Strauss, Delb, Schick & Strauss 2010b, Zhang et al. 2006).

In contrast, the research conducted for this thesis, in addition to denoising, concentrates

on extracting a fully featured ABR using a minimum ensemble of epochs and accurate

tracking of time-scale variations of ABR features. The approach for the evaluation consists

of estimating systematic variation of ABR peaks using the below mentioned WT denoising

approaches based on (Zhang et al. 2006, Quian Quiroga 2005, Causevic et al. 2005) with

simulated data followed by real ABRs recorded from a group of human participants:

• Constant thresholds with matching coefficients (CTMC)

• Temporal windowing with matching coefficients (TWMC)

• Cyclic shift tree denoising (CSTD)

1.3 Thesis objectives

The principal objective of this thesis is to evaluate the two identified methods of ARX

modelling and wavelets and their variations, for the potential rapid extraction of the ABR.

To our knowledge a systematic study has not been performed with these methods on the

ABR. Such a detailed study could be used as an analysis tool for a better choice of EPs

which could use parametric modelling and wavelet denoising to calculate a fine grained

measure of the brain state, thereby providing a better understanding of brain structures

relevant to the generation of EPs.

In particular, short lasting alterations which may provide relevant information about

cognitive functions are probably smoothed or even masked by the averaging process.

Therefore, investigators are interested in single trial analysis, that allows extraction of

reliable signal characteristics out of single EP/ERP sequences (Effern, Lehnertz, Fern-

ndez, Grunwald, David & Elger 2000, Wada 1986).

To suit this new application domain of ABRs, the following improvements were made

to the tested algorithms.

Introduction 10

• ARX and REPE models

– Model order selection criterion

– Derive new model orders relevant to the ABR

– Defining a reference signal

• Wavelets

– Selection of optimum basis wavelet

– Defining threshold functions and temporal windows for wavelet subbands to

optimise the characteristics of the filtered ABR

Specific details are given in chapter 4 and 5.

With these improvements, the thesis aims to:

• To conduct a well defined, reproducible simulation study to determine the robust-

ness of ARX and REPE rapid extraction methods (in terms of noise removal) to

variations in the SNR of the simulated EPs and the evaluation of the ability of these

rapid extraction methods to accurately track time-scale variations in the latency of

simulated EP components;

• To analyse and optimise the wavelet denoising methods CTMC, TWMC and CSTD

using a common set of real ABR data for the purpose of rapid extraction. The

evaluation covers the denoising and time-scale variation tracking ability of these

methods;

• To explicitly identify the limitations and implications of using ARX modelling and

specific wavelet denoising methods.

1.4 Perceived contributions of the research

This research provides original contributions for rapid extraction of ABR applications

using ARX modelling and specific wavelet denoising algorithms. The major contributions

of the research can be summarised as follows:

• Determination of limitations of temporal variation tracking ability of ARX mod-

elling using physiologically plausible variations related to ABRs. The contradictory

Introduction 11

outcome generated with REPE is discussed in this thesis and several shortcomings

in the original study are pointed out.

• Optimization of CTMC, TWMC and CSTD wavelet denoising methods to suit ex-

traction of ABRs. This included the determination of a compatible mother wavelet,

threshold functions and temporal windows to suit the new domain of application.

• Identification of the suitability and limitations of CTMC, TWMC and CSTD wavelet

denoising methods to apply as a rapid extraction method of ABRs by reproducing

known time-scale variations (in response to intensity of the stimulation).

1.5 Organization of the thesis

This thesis elaborates the research carried out in the chapters that follow. In summary,

the content of these chapters are:

Chapter 2 - ABR and its extraction is a study of the literature including the

ABR, in general EPs and their extraction methods. This chapter initially reviews the

physiological origin of the ABR and its clinical importance. The applications related in

general to EPs and the ABR are then discussed. Finally a comprehensive literature review

of ARX modelling and wavelet methods is presented in conjunction with the extraction of

EPs and specifically of the ABR.

Chapter 3 - Recording and constructing synthetic ABR data presents the

stimulation and acquisition parameters used for ABR data recording and discuss the suit-

ability of these data to use in evaluating denoising methods. A mathematical model for

the ABR is also introduced in this chapter, from which multiple datasets are constructed

in order to evaluate denoising methods representing ideal conditions in later chapters.

Chapter 4 - Effectiveness of ARX modelling in rapid extraction of the

ABR analyses ARX modelling and its extension REPE systematically using synthetic

ABRs. The findings of this chapter refine the ambiguity of previous research findings and

establish clear boundaries for the use of ARX methods in rapid extraction applications.

The simulated results are confirmed with the use of real ABR recordings.

Chapter 5 - Effectiveness of wavelet techniques in the rapid extraction of

Introduction 12

the ABR investigates the ability to rapidly track ABR variations using CTMC, TWMC

and CSTD wavelet denoising methods. This analysis is carried out in two steps, one which

determines the denoising capacity of wavelet methods and the other for assess ability of

tracking temporal variations. Similar datasets were used to that of Chapter 3, including

simulated and real ABR recordings for direct comparison to establish thorough conclusions.

Chapter 6 - Overall conclusions and future work highlights the overall effec-

tiveness of ARX modelling and wavelet methods in the rapid extraction of ABRs. Several

issues that have not been addressed and possible solutions that could guide future work

are also discussed here.

Introduction 13

Chapter 2

A review of the ABR and its

extraction

This chapter presents information collected from relevant literature to provide the basis

for rapid extraction of ABRs and include:

• The origin and the importance of ABR and EPs

• Recording of ABR data

• Review of ARX modelling for rapid extraction of EPs

• Review of wavelets as a method of rapid extraction of EPs

The importance of a fast extraction method of the ABR highlights due to the proximity of

its generators to critical physiological structures of the brain. These important applications

provide the basis to formulate a methodology to evaluate rapid extraction algorithms

discussed throughout the thesis, using systematic variations of ABR features. Recording

an accurate ABR depends on effective stimulation, acquisition and signal processing of

EEG. Therefore, initially the setup used for stimulation and acquisition of the ABR will

be discussed. Then, the two identified approaches for processing the ABR; ARX and

wavelets are discussed in relation to rapid extraction. Specific drawbacks of the existing

implementation and modifications with novel features that can be added to enhance the

rapid extraction process will also be discussed.

14

2.1 Review of evoked potentials and the auditory

brainstem response

2.1.1 Evoked potentials

As information is processed within the neural networks of the human brain, the electrical

activity arising from millions of participating neurons is summed to form field potentials

that can be recorded through the intact scalp. The brain’s field potentials include the

rhythmic voltage oscillation of the ongoing electroencephalogram (EEG) and the short

evoked potentials (EPs) that arise in association with specific sensory, motor and cognitive

events. While the spontaneous EEG rhythms are sensitive monitors of general states of

arousal, consciousness and the sleep-waking cycle, the EPs are believed to represent more

discrete patterns of neural activity that reflect specific perceptual and cognitive processes.

EPs are categorised into auditory, visual, somatosensory and motor evoked potentials

depending on the modality of stimulation eliciting the respective evoked potential. A brief

summary of most notable features of these EPs are summarized in table 2.1. The reader

should note that there are more features of these EPs which could be relevant on the basis

of application and are direct to Chiappa et al. (1997) for further information. Visual

evoked potentials (VEPs) are caused by sensory stimulation of a subject’s visual field with

flashing lights or checkerboards on a video screen that flicker between black and white. The

commonly used feature of a VEP is P100 with amplitude in the range of 10-12 µV (Misra

& Kakita 1999). Somatosensory evoked potentials (SEPs) are generated mainly by the

large diameter sensory fibres in the peripheral and central portion of the nervous system,

typically in response to an electrical stimulus. SEPs are mainly relevant to the monitoring

and diagnosis of lesions in relatively long sensory pathways from peripheral nerve to spinal

cord and cerebral cortex. The clinically significant features; N9, P13 and N20 are in

the range of 3-5 µV in amplitude (Chiappa 1990). Motor evoked potentials (MEPs)

are recorded from the muscles following stimulation of the motor cortex or spinal cord,

through magnetic or electrical stimulation. While magnetic stimulation can penetrate

tissues regardless of electrical resistance, electrical stimulation achieving better depth of

penetration allowing direct spinal cord stimulation, but with a trade-off of local discomfort

A review of the ABR and its extraction 15

EP Generators Importantfeatures

Amplituderange

AEP Auditory stimulation of the auditory pathwayfrom the in-ear to the auditory cortex throughthe brainstem

Wave V,Pa, P300

0.1-5 µV

VEP Stimulation of the visual field (rods and conecells in the retina)

P100 10-12 µV

SEP Electrical stimulation of sensory fibres in theperipheral and central portion of the nervoussystem

N9, P13,N20

3-5 µV

MEP Electrical or magnetic stimulation of motorcortex and the spinal cord

D-waves,I-waves

hundreds ofmV

Table 2.1: A brief summary of the types of EPs, their generators and features. Note: for further informationregarding other features related to these EPs refer (Chiappa 1997)

to the patient. In contrast to other EPs, the MEPs possess larger amplitudes in the range

of milli-volts, and therefore do not require special signal processing methods for extraction.

In contrast, the early component of the auditory evoked potential, the auditory brain-

stem response which is the signal of interest for the current thesis has comparatively

smaller amplitude (of the order of one tenth of a micro-volt), and therefore requires spe-

cial extraction methods. The following section presents a description of these auditory

evoked potentials.

2.1.2 Auditory evoked potentials

Auditory evoked potentials (AEPs) are scalp recordable electrical potentials generated by

the central nervous system in response to an auditory stimulus. This evoked electrical

response lasts for approximately 600 ms and consists of a number of well defined features

that can be divided into early, middle and late components. Figure 2.1 illustrates a window

of approximately 300 ms from the stimulus onset. Early components typically occur within

10 ms after initiating the stimulus and are generated in the distal portion of the cochlea

nerve through to the brainstem and are called the auditory brainstem response (ABR)

(Roeser, Valente & Hosford-Dunn 2000). Middle latency components (middle latency

auditory evoked response, (MLAEP)) are those occurring within 10 to 50 ms and are

generally believed to be generated by the serial activation of the brainstem, thalamus and


Figure 2.1: The log time scale distribution of AEP includes early, middle and late potentials. Extractedand modified from (Adelman & Smith 1999). The polarity of the features is inverted here due to theelectrode placement on the scalp while recording.

cortex (Hall 2007). In contrast, the late components (auditory late response, (ALR)) arise

between 50 to 300 ms post stimulus are thought to arise exclusively from the activation

of cerebral cortex and in particular the auditory cortex resident in the temporal lobe

(Adelman & Smith 1999).

Typically, AEPs cannot be distinguished from the ongoing EEG activity by the naked

human eye. Given that most AEP components have an amplitude of the order of 0.2-

0.5 µV and the background EEG is of the order of 10-100 µV RMS, amount to a signal to

noise ratio of approximately -30 dB (Aurlien, Gjerde, Aarseth, Elden, Karlsen, Skeidsvoll

& Gilhus 2004). Therefore in order to reliably extract the amplitude and latency of the

various AEP components, special signal processing methods are mandatory.

2.1.3 Origin of the auditory brainstem response

Auditory brainstem responses (ABRs) are the early latency evoked potentials within 10

ms post stimulus generated by the serial activation of the auditory pathways beginning

at the distal portion of the eighth cranial nerve and terminating at the medial geniculate


nucleus of the thalamus. Since the first thorough study by Jewett & Williston (1971), the

human ABR has been correlated with a range of physiological functions, and has therefore

been used as an important tool for diagnosing and monitoring purposes.

A fully featured ABR consists of seven distinct peaks labelled with Roman numerals

I to VII, out of which waves I, III and V are of clinical significance. Such a fully featured

ABR is illustrated in figure 2.2, which is the moving time average of 1024 epochs extracted

from a healthy 24 year old female participant, stimulated at 55 dB nHL. Parameters of

the ABR that are of clinical and physiological relevance are the amplitude and latency

variations of these peaks. The amplitude of a peak is measured relative to the preceding

or the following trough, which reflects the activity level of a specific neurogenerator. The

absolute latency of a peak (commonly known as, latency) is measured as the time interval

between the onset of a stimulus and its peak. The latency is thought to largely reflect

the actual conduction time along the neural pathway. It is often useful to define inter-

peak latencies, which are relative time intervals, measured between two different waves,

typically I-III, I-V and III-V. Such latency differences represent the axonal conduction

time along neuron pathways and/or synaptic delays between the respective populations of

neurons responsible for the generation of a particular evoked component (Ponton, Moore

& Eggermont 1996). Normative values for such absolute and inter-wave latencies and peak

amplitudes for the main features of the ABR are shown in table 2.2. These values are

obtained with 786 healthy human participants at stimulus intensity level of 80 dB nHL.

The morphology of the ABR is the overall shape of the waveform and is usually de-

scribed with reference to a standard template. Even though wave component latencies

and amplitudes are within the standard range, the morphology should be similar to the

template for it to be considered as a proper ABR.

Knowledge of the brain structures that generate the features of the ABR are important

in interpreting the abnormalities of the ABR and thereby diagnose pathological disorders.

Figure 2.3 illustrates the auditory pathways along which the ABR is generated. The

sound wave carrying the auditory stimulus transmits through the external and middle ear

to the fluid compartment of the inner ear containing the cochlea. Vibration of the basilar

membrane of the cochlea, due to sound induced movement of fluid in the cochlea, results


Wave componentLatency range (ms) Amplitude

range(µV)Mean SD

Wave I 1.65 0.14 0.40Wave II 2.67 0.13Wave III 3.80 0.18Wave IV similar to wave VWave V 5.64 0.23 0.50-0.75Inter-wave I-III 2.15 0.14Inter-wave III-V 1.84 0.14Inter-wave I-V 3.99 0.20

Table 2.2: Normative Latencies and Amplitudes for ABR wave features. Number of participants included:786. Adopted from (Joseph et al. 1987).

in the stimulation of hair cells in the organ of Corti. The activity of these hair cells induces

activity in the cochlear branch of the eighth cranial nerve. The stimulation amplitude of

the hair cells is directly proportional to the intensity of the auditory stimulus. Once a

neural response to a sound is generated in the inner ear, the signal is transferred to a series

of nuclei in the brainstem. Output from these nuclei is sent to a relay in the thalamus, the

medial geniculate nucleus. Finally, the medial geniculate nucleus projects to the primary

! " ! #

Figure 2.2: A fully featured ABR recorded from a 24-year-old healthy female participant. The derivationof this ABR included a moving time average of 1024 epochs.


auditory cortex located in the temporal lobe.

The exact brain structures contributing to the human ABR are subjected to much

debate. Despite the confident claim by Jewett & Williston (1971) of the origin of wave I

to be the cochlea nerve (eighth cranial nerve) the remaining waves II, III, IV, V, VI and

VII repeatedly appeared as over simplistic anatomically matched diagrams presenting in-

accurate schematics (Hall 2007). Mostly, these schematics were inferred from small animal

studies (rat, cat, guinea pig) in which brainstem structures were significantly smaller than

corresponding structures in humans (Moore 1987, Moller et al. 1995).

Hall J. W. (2007) points out two factors, which inhibit the understanding of the ex-

act anatomical structures of the ABR peaks. 1) Technical limitations related to placing

Figure 2.3: Auditory pathway from inner ear to the primary auditory cortex. Adopted from (Kiernan 2007).


the electrode to achieve a true reference. 2) The complications associated with far-field

recordings that do not lead to pin point the origin. However, it could be concluded from

the evidence at hand that multiple anatomic sites may contribute to a single ABR wave

and conversely a single anatomic site may generate multiple ABR waves.

There is evidence that wave II is generated by the eighth cranial nerve from the in-

tracranial recordings of Moller (Moller 1987, Moller et al. 1995) and clinical evidence

suggest that it originates from eighth cranial nerve at the root entry zone, as it enters the

brainstem and thus the proximal portion of the eighth cranial nerve (Hall III, Mackey-

Hargadine & Kim 1985).

Wave III was traditionally believed to originate from the contralateral superior olivary

complex based on the lesion studies in small animals (Buchwald & Huang 1975). However,

a contradictory conclusion was derived by Achor and Starr (1980) stating the origin to be

the ipsilateral superior olivary complex. In contrast, human studies have found the origin

of wave III to be the cochlear nucleus (Moller 1987, Moller et al. 1995) even though Scherg

and Von Cramon (1985) were unable to derive the pinpoint location as their conclusion

which was beyond the eighth cranial nerve and the trapezoid body.

Wave IV is less observed in clinical practice as it is not consistently recorded and often

appears as the leading shoulder on wave V. Determination of the precise generators of wave

IV is complicated by the likelihood of multiple crossings of the midline for auditory fibres

beyond the cochlear nucleus. As Moller et al. (1995) suggest, generation of wave IV is

mainly associated with the third order neurons located in the superior olivary complex but

evidence of contribution from second and third order neurons is also reported by Scherg

et al. (1985). Moore (1987) also suggests that the contribution of the lateral lemniscus to

wave IV in human ABR is probably minor.

Wave V is the most frequently analysed ABR feature due to its prominent large ampli-

tude, which is affected by neurophysiological disorders. It is therefore critical to identify

its anatomic origin. Traditionally the origin of wave V was considered to be the inferior

colliculus (Buchwald & Huang 1975) but depth electrode and spatio-temporal dipole model

findings in humans have suggested that wave V is generated at the termination of lateral

lemniscus fibres as they enter the inferior colliculus (Moller et al. 1995). The resulting


dendritic potentials within the inferior colliculus are thought to be responsible for the

large, broad negative voltage trough following wave V. These conclusions are supported

by anatomical findings to the effect that pathways to the inferior colliculus have varying

lengths and varying numbers of synapses, which would result in a large but relatively

broad ABR wave because of the less synchronized activation of the nucleus. Second-order

neuron activity may also contribute in some way to wave V (Hall 2007).

While the less significant wave VI and VII suggest to originate in the thalamic region

(Stockard & Rossiter 1977), some studies have narrowed the site of origin down to the

continuous firing of neurons in inferior colliculus (Moller et al. 1995).

As evident, the the origin of ABR wave features are uncertain and require further

investigations with improved methods, which may could benefit by the conclusions of this

thesis. However, an illustration of presumed anatomic correlation of major peaks of the

ABR is shown in Figure 2.4, which is extracted from (Hall 2007).

2.1.4 Factors influencing the ABR

The features of the ABR in terms of latency and amplitude are affected by various patho-

logic and non-pathologic factors. Evaluation of methods of rapid identification of these

Figure 2.4: Presumed generators of the ABR waves I-V. Note that one anatomic structure may give riseto more than one ABR wave and conversely more than one anatomic structure may contribute to a singleABR wave. Adopted from (Hall 2007).


variations is the main objective of the thesis. This section presents significant factors,

which cause variations in ABR features.

Pathologic factors Hearing impairment - ABR is widely used in the screening of

hearing of neonates and uncooperative adult patients where a behavioural feedback is dif-

ficult to achieve (Hall 2007). In these cases, the presence of wave V at low sound intensities

is observed to assess the hearing ability. The sound intensity of the stimuli is varied from

70 dB to 30 dB to detect the hearing threshold (Intracoustics 2011, Incorporated 2011,

Otometrics 2011).

Multiple sclerosis - Multiple sclerosis is a chronic, often disabling disease which

randomly attacks the central nervous system. ABR abnormalities caused by this disease

include, prolonged inter-peak latencies I-III, III-V, I-V, decreased amplitude of wave V,

poor morphology, occasional total absence of wave I and V (Antonelli, Bonfioli, Cappiello,

Peretti, Zanetti & Capra 1988, Papathanasiou, Pantzaris, Myrianthopoulou, Kkolou &

Papacostas 2010, Soustiel, Hafner, Chistyakov, Barzilai & Feinsod 1995).

Parkinson’s disease - Parkinson’s disease is a consequence of the depletion of dopamine

in the CNS due to damage of the substantia nigra pars compacta. Symptomatically it is

characterised by bradykinesia, rigidity and tremor. Interestingly, changes in the ABR

have been reported due to Parkinson’s disease. Some research suggests that there is an

abnormality in wave III with prolongation of the latency and reduction in the amplitude

(Yousefi 2004) whereas a separate study observed significantly increased latencies in wave

V and I-V inter-peak latencies (Ylmaz, Karal, Tokmak, Gl, Koer & ztrk 2009). While

a number of these results are conflicting, ABR changes may prove to be of relevance for

the early sub-clinical diagnosis of Parkinson’s disease. As an example, a study conducted

to find a diagnostic tool to differentiate Multiple System Atrophy and Parkinson’s dis-

ease suggest that there is no effect of Parkinson’s disease on the ABR features (Kodama

et al. 1999).

Alzheimer’s disease and dementia - There are reports of pathologic involvement

of the inferior colliculus, medial geniculate body and both primary and secondary au-

ditory cortex in Alzheimer’s disease and dementia (O’Mahony, Rowan, Feely, Walsh &


Coakley 1994). An analysis of ABR data of demented patients showed increased wave

I-V inter-peak latency values (Harkins 1981, O’Mahony et al. 1994). It is of interest that

abnormalities of the late components of the AEP have also been reported in Alzheimer’s

disease (Egerhzi, Glaub, Balla, Berecz & Degrell 2008, Graf, Marterer & Sluga 1992).

Acoustic neuroma - This is the most common cerebellopontine angle tumor ac-

counting for 80% of the lesions in this area (Misra & Kakita 1999). Acoustic neuromas

are almost invariably associated with an increase in inter-peak latencies I-III and I-V and

absence of peaks beyond wave I (Parker, Chiappa & Brooks 1980).

Coma and Brain Death - A considerable amount of literature exists regarding the

role of ABR as a diagnostic tool for coma and brain death as spontaneous EEG and

CT scan are inadequate in the assessment of the physiological integrity of the brainstem.

Absence of waves I, II, III and V were associated with death and vegetative states of these

disorders (Goldie, Chiappa, Young & Brooks 1981).

Stroke - ABR has been used for evaluation and prognosis of acute brainstem stroke.

Mainly, the wave peak ratio of IV/V increased in patients with strokes while less significant

abnormalities include prolonged inter-peak latency I-III and ABRs with only wave I or no

waves (Ferbert, Buchner, Bruckmann, Zeumer & Hacke 1988).

Diabetes mellitus and hypothyroidism - Degenerative diseases such as diabetes

mellitus and hypothyroidism were found to have an effect on the ABR with prolongation

of absolute and inter-peak latencies of main waves I, III and V (Fedele, Martini & Cardone

1984, Khedr, Toony, Tarkhan & Abdella 2000).

The use of rapid (single/limited trial) extraction methods in the detection and diagnosis

of such pathological abnormalities would have the following advantages:

(i) Reduction of clinical test times

(ii) Enhancement of patient comfort at stimulus delivery by reducing the number of

stimuli, especially for long term monitoring systems such as in a potential wearable

device

(iii) Detection of short term variability of the ABR such as in intraoperative monitoring

applications


Stimulus and subject factors In addition to aberrations in evoked auditory activity

caused by pathological states, a range of stimulus and subject related factors are well

known to systematically change one or more early, middle or late components. Stimulus

dependent parameters include the frequency, duration, intensity and polarity of the stimu-

lus, whereas subject dependent factors mainly include age, gender and body temperature.

The latency of the ABR waves changes considerably up to one year of age (Kaga &

Tanaka 1980). The latency reduces by 1 to 1.5 ms as the child reaches one year and then

stabilises. After the age of 25 up to at least 55, there is prolongation of approximately

0.2 ms of the latency which however remains constant beyond that age (Hecox & Galambos

1974). The effect of gender on the ABR is observed with shorter latencies and larger

amplitudes in females than in males. Such gender based latency difference range from

0.1 to 0.2 ms (Rosenhall, Bjrkman, Pedersen & Kall 1985, Chu 1985). Since age and

gender is a constant for a given participant in a diagnosis scenario and do not have an

advantage of using a rapid extraction system. In contrast, tracking the effects of core

body temperature on the ABR latencies (Markand, Lee, Warren, Stoelting, King, Brown

& Mahomed 1987) could be greatly benefitted by a rapid extraction system. It is found

that inter-wave latencies were prolonged by 0.2 ms per 0C in cases of hypothermia, and

reduced by 0.15 ms per 0C in cases of hyperthermia (Kohshi & Konda 1990).

The properties of the auditory stimulus greatly affect ABR component latencies and

amplitudes. In general, these changes vary systematically with changes in the frequency

and intensity of the auditory stimulus. As the stimulus intensity is increased, the ab-

solute latency of ABR peaks reduces while their amplitude increases (Collet, Delorme,

Chanal, Dubreuil, Morgon & Salle 1987, Babkoff, Pratt & Kempinski 1984, Pratt &

Sohmer 1977). This reduction in peak latency at higher stimulus intensities is caused

by the rapid approach of summed postsynaptic excitation potentials to the neuronal firing

threshold (Hall 2007). In general, the latency of the ABR components is found to smoothly

decrease with an increasing stimulus intensity. This pattern is shown in figure 2.5 with typ-

ical latency-intensity curves for wave I, II, III, V and VI (Delgado & Ozdamar 1994). Due

to the infrequent appearance of wave IV, variation of its latency with stimulus intensity

has not been systematically determined.


The most common clinical convention of presenting the stimulus intensity is in decibel

(dB) relative to the normal behavioural hearing threshold level for a stimulus (Hall 2007).

This is usually denoted as ‘dB nHL’. The hearing threshold level for the stimulus is deter-

mined by stimulating a group of normal subjects and taking the average of the intensity

at which the click is just audible. This intensity is defined as 0 dB nHL and used as the

reference level to indicate subsequent intensity levels.

The amplitude variations of ABR features affected by the sound intensity are charac-

teristically more variable than changes in the latency (Jewett & Williston 1971, Lasky, Ru-

pert & Waller 1987). Therefore, clinicians use consistent latency variations for diagnosing

conductive and sensory hearing loss of patients (Steinhoff, Bhnke & Janssen 1988, Suter

& Brewer 1983). Based on similar reasons, verification methods of this thesis are also

based on latency-intensity curves produced by controlled stimulus intensity delivered to

participants.

Effect of anaesthetic agents on the ABR The effects of anaesthetic agents are

prominent on the ABR and especially on the MLAEP. Such effects are essential in neuro-

Figure 2.5: Latency-intensity curves of wave I, II, III, V and VI. Dotted lines represent peaks labelled by thehuman experts and solid lines represent an automated system. Adopted from (Delgado & Ozdamar 1994)


monitoring during surgery. It has been reported that administration of propofol induce an

increase in absolute and inter-peak latencies of the ABR by 0.15 to 0.5 ms depending on the

dosage up to 8 µg/ml (Chassard, Joubaud, Colson, Guiraud, Dubreuil & Banssillon 1989).

Halothane and isoflurane cause statistically significant prolongation of latency by 0.2 ms

in ABR peaks (Cohen & Britt 1982) where as enflurane cause linear prolongation of inter-

peak I-III and I-V latencies with the dosage (Thornton, Heneghan, James & Jones 1984).

An average variation of 0.23 ms in inter-peak latencies were observed due to the effect

of sevoflurane (Kitahara, Fukatsu & Koizumi 1995). In contrast to methohexial sodium

which induced a prolongation of 0.4 ms in the wave V latency. A similar effect was ob-

served in wave V absolute and inter-peak latencies with prolongations of 6.16 to 6.87 ms

with thiopental (Drummond, Todd & Hoi Sang 1985).

However, the amplitude of MLAEP is usually considered to measure the depth of anaes-

thesia even though there is an effect of latency of MLAEP components (Garcia-Larrera,

Fischer & Artru 1993). Considering the consistent and prominent amplitude variation

as a result of anaesthetic agents has lead to the production of commercial products for

monitoring depth of anaesthesia.

Typical detection times for depth of anaesthesia with MLAEP are in the order of

few seconds. Therefore it is reasonable to assume that measuring depth of anaesthesia

using the ABR extracted by conventional moving time average is not feasible as almost one

minute of recording is required to extract only a single ABR. This duration is considered for

a typical extraction scenario in an operating room/intensive care unit/neonatal intensive

care unit with electromagnetic interference up to 220 µT (Sokolov, Kurtz, Steinman, Long

& Sokolova 2005) where in average 1024 stimulation is presented at a rate of 21.1 Hz.

However, an exact number of stimuli required could be estimated by statistical methods

such as Fsp based on the signal to noise ratio (Elberling & Don 1984). With the presence

of a rapid extraction methods, short-term variations in the ABR could be revealed and

these may potentially be used to detect monitor depth of anaesthesia.


2.1.5 EPs in brain computer interfacing

A brain computer interface (BCI) is a way of communication between human/animals and

computers that does not use any muscular movement such as talking, writing or mimic,

rather it uses brain signals. EPs are the basis for BCI applications due to the event driven

nature. At present, even though ABRs are not directly involved in BCI applications, fast

extraction algorithms evaluated in this thesis could lead to a innovative paradigm shift and

improve the performance of existing applications. The commonly used P300 signal in BCI

is a non-stationary signal similar to the ABR, and therefore compatible with algorithms

developed to ABR compatible. Further, the adaptation of the algorithms developed for

ABRs will be more effective in relation to P300 as the characteristic SNR is high compared

to the ABR.

The late event related potential P300, is elicited when users attend to a random series

of stimulus events that contain an infrequently presented set of items which, forms an odd-

ball paradigm. Patients suffering with communication disabilities caused by amyotrophic

lateral scleroses, severe cerebral palsy, head trauma, multiple sclerosis and muscular dys-

trophies are helped with a speller driven by visual P300 to improve their communication

ability (Lee et al. 2008). In addition, patients having difficulties in voluntary control of

gaze have been assisted with auditory BCI driven by auditory P300 (Furdea et al. 2009),

ASSR (Lopez et al. 2009), self-regulation of slow cortical potentials (Pham et al. 2005)

and sensorimotor rhythm (Nijboer et al. 2008). Also, the PC based gaming industry is

increasingly using BCI peripherals produced by companies such as Emotiv (EPOC) and

Ocz Technology (NIA game controller).

Such applications suggest that real time EP extraction algorithms are essential in

BCI where reaction time between the emission of the EP and the interpretation of the

action is critical. BCI applications help subjects with severe motor impairment with

no other way of communication but to capture subjects’ intent directly from the brain.

But poor information transmission rate from the time point of emitting the EP and the

interpretation of it is a common issue in BCI systems when using conventional MTA in

detecting EP changes (Lopez et al. 2009).


2.1.6 ABRs for rapid extraction

From the foregoing discussion, it is evident that the early components of the EPs provide

important information regarding the functional state and integrity of a variety of sensory

pathways. The conventional method for extracting EPs is to calculate a time locked

average of the EP to multiple sequential presentations of an identical stimulus. For the

ABR, such a time average more often requires (considering the noise associated) the order

of no less than one thousand sweeps, spread over approximately 60 seconds, in order to

sufficiently resolve its components for diagnostic and quantitative analysis purposes. The

following issues arise with the time span associated with such an extraction system.

(i) Inability to observe short-time variations with the delayed output of the ABR.

(ii) Patient discomfort due to prolonged auditory stimulation associated with a long

term monitoring system (potentially a wearable device).

(iii) Generation of muscle artifacts at infant hearing screening with prolonged test times.

Similar effects could be observed with adult patients due to fatigue when testing is

conducted with a series of sound intensities for a long period of time.

Close to real-time applications of EPs exist such as depth of anaesthesia monitoring

and BCI related applications as they use variety of rapid extraction methods. In contrast

ABRs are excluded from such ‘close-to real time’ applications due to the substantial times

required to extract using present moving time averaging. The resultant low time resolution

leads to loss of short-time information, which limits the understanding of the internal brain

structures that cause variations in ABR peaks. With improved extraction methods, there

is a potential to identify the exact origin of the ABR peaks, and such methods can thereby

be used as a potential non-invasive technique to localize lesions along the auditory pathway.

Therefore the necessity of rapid extraction methods for ABRs and in general EPs is

essential. This thesis evaluates two such methods ARX modelling and wavelet filtering,

both identified as having significant potential to removing noise and tracking time scale

variations associated with ABR features.


2.2 Review of ARX modelling based extraction methods

2.2.1 Moving time averaging to parametric modelling

Based on the relation to the simple additive signal + noise model and for the ease of

calculations, moving time average (MTA) is typically used in clinical applications related

to EPs. MTA is calculated by averaging a large number of time locked responses to

suppress random spontaneous EEG assumed to be uncorrelated to the deterministic ABR

and thereby retaining the ABR. Such a synchronous summation of responses improves

the signal component while reducing noise. This is true for early EP components but

less so for late and middle components due to the fact that the evoked component almost

certainly depends on the seemingly random prestimulus activity (Makeig, Westerfield,

Jung, Enghoff, Townsend, Courchesne & Sejnowski 2002). A single sweep of a recorded

ABR yi(k), is typically described with the conventional additive model:

yi(k) = s(k) + ni(k) (2.1)

where s(k) is the deterministic ABR component and is the Gaussian white noise compo-

nent, i.e. the spontaneous EEG at the i th sweep and k is the discrete time point. s(k) is

extracted by taking a MTA of a large number of sweeps, assuming the random nature of

the underlying EEG noise will progressively decrease the noise component with an increas-

ing number of averages. This improves the SNR of the ABR by: 10 log10(N) dB, where N

is the number of sweeps averaged in the MTA. In conventional ABR extraction, a MTA

of approximately 1000 sweeps is considered enough to suppress the noise and arrive at the

ABR i.e. a SNR improvement of 30 dB (Don & Elberling 1996).

The use of a conventional MTA in these applications however results in poor time

resolution and thus cannot be used to detect the rapid variations of latency and amplitude

of EPs which are expected to attend cognition. Also the underlying assumption of the

time invariant ABR makes conventional MTA not suitable to extract a series of ABRs

with time varying features (Ozdamar & Kalayci 1999).

The identification of these drawbacks has lead to concerted efforts to develop im-

proved extraction methods such as weighted averaging techniques (John, Dimitrijevic


& Picton 2001), Wiener filtering (Doyle 1975, Boston 1983), adaptive filtering (Vaz &

Thakor 1989), median averaging (Ozdamar & Kalayci 1999), independent component

analysis (Scott, Anthony, Tzyy-ping & Terrence 1996, Hu, Zhang, Hung, Luk, Iannetti

& Hu 2011), principal component analysis (Lins, Picton, Berg & Scherg 1993), Spatial

weighted averaging (Ivannikov, Karkkainen, Ristaniemi & Lyytinen 2010), parametric

modelling and denoising with wavelet filter banks.

Weighted averaging is a modification to the conventional MTA with the same number of

epochs involved, and thus not leading to rapid extraction. The process of Wiener filtering

s(k) = g(k)∗ [s(k)+n(k)] assumes spectral properties of the signal s(k) and noise n(k) and

then attempts to estimate the signal s(k) with a minimum error compared to the actual

signal by adjusting the Wiener filter g(k). The major disadvantage of Wiener filtering is

the underlying assumption that the signal to be analysed being stationary. However in

adaptive filtering, even though the non-stationary nature of an EP is considered, it tends

to be vulnerable to highly coloured noise. Independent component analysis and principal

component analysis is a means of removing artifacts generated from different sources such

as eye blinks and movements, muscle noise, cardiac signals and line noise. Independent

component analysis performs superior to principal component analysis with the ability to

separate EEG and its artifacts within the same analysis (Jung, Humphries, Lee, Makeig,

McKeown, Iragui & Sejnowski 1998). Also independent component analysis preserves and

recovers more brain activity than principal component analysis in decomposing EEG data

(Jung et al. 1998). The Spatial weighted averaging is an improved version of independent

component analysis from which direct separation of subspaces is achieved in raw data

among EP and noise sources and thus leads to rapid extraction and possible single sweep

analysis (Ivannikov et al. 2010). In contrast, separation of EPs from raw data seems less

effective at very low SNRs with independent component analysis, due to its tendency to

concentrate only on large components.

A more widely used approach to the rapid extraction of EPs is to parametrically model

EPs using an autoregressive model with an exogenous input (ARX). Here a single sweep

of an EP is modelled with a reference signal (exogenous input) and white noise, which

is compatible with the conventional additive model. ARX modelling has been widely


adopted by researchers to rapidly extract MLAEP, VEP and SEP. Cerutti etal. (1987)

introduced the ARX model to extract single sweeps by fitting it to a reference signal

defined by a MTA of an ensemble of sweeps. The validity of this method further can

be said to underpin its use in the calculation of the A-LineTMIndex (Jensen et al. 1998)

in the depth of anaesthesia monitoring device ‘AEP Monitor/2’ produced by Danmeter

aps (DanmeterAps 2010). Given the successful application of the ARX based methods

to the rapid extraction of middle and late latency EP components, it logically follows to

systematically investigate the application of this method to the rapid extraction of ABRs.

The following section describes the general principles of the ARX modelling method.

2.2.2 The ARX(p, q, d) model

The adaptation of the auto-regressive model with an exogenous model (ARX) black-box

model to a signal generation mechanism Cerutti et al. (1987) allowed representation of

a single sweep as the sum of an autoregressive pseudo-random term and the output of a

proper filter with a deterministic input. According to the convention, it is assumed that

a single EP sweep consists of true signal ep plus additive noise n i.e.

yi(k) = epi(k) + n(k) ⇐⇒ Yi(z) = EPi(z) +N(z) (2.2)

where k is the corresponding sample for the ith sweep. The right-hand-side shows the

z-transform of the corresponding time domain additive model.

Now consider the general form of an ARX model for a single sweep in equation (2.3):

yi(k) = −p

∑

j=1

ajyi(k − j) +

q+d−1∑

l=d

blu(k − l) + ei(k) (2.3)

Here, the single sweep yi(k) is modelled with the reference input u(k) and Gaussian white

noise ei(k). u(k) is the exogenous input to the ARX model which in theory, represents the

true nature of the EP. In practice, with the absence of the true response, u(k) is assigned

with a MTA of appropriate number of sweeps with a close representation. p and q are the

orders of the autoregressive (AR) and moving average (MA) parts respectively, aj ’s and

bj ’s are the model coefficients. The number of poles of the estimated filter is therefore p


whereas the number of zeros is (q− 1). The delay d is the temporal lag between the input

and the output to the model. This time domain model can be re-written in the z-domain

as the following

Y (z) =B(z)

A(z)U(z) +

1

A(z)E(z) (2.4)

where Y (z), U(z), E(z) are the z-transform of yi(k), u(k), ei(k) respectively and A(z) =

1 +∑p

j=1 ajz−j , B(z) =

∑q+d−1l=d blz

−l) . By comparing equations (2.2) and (2.4), a noise

free single sweep EP estimate is derived as; EPi(z) =B(z)A(z)U(z).

Therefore, by filtering the template signal U(z) with the filter defined by the ARX

model, in principle, a noise reduced single sweep EP is derived. The fact that the noise

and the evoked response both depend on the same autoregressive component A(z) however

does imply a partial loss of generality as the estimated evoked response and noise are not

independent of each other. Despite this restriction the ARX model is typically preferred

due to the computational simplicity. Removing this restriction would result in the additive

noise model being described by the following ARMAX process

Y (z) = B(z)A(z)U(z) + 1

C(z)E(z)

⇒ Y (z)D(z) = U(z)F (z) +A(z)E(z)

where D(z) = C(z)A(z) and F (z) = B(z)C(z). Thus a noise free single sweep estimate

would be given by U(z)F (z)/D(z). However, difficulties in the robust estimation of AR-

MAX models has resulted in frequent use of the ARX model in single sweep estimations

(Makeig et al. 2002).

If the two series yi(k) and u(k) are known for each sweep (i), it is possible to calculate

aj and bj for each n, m and d using a batch least-square-method which minimises the

prediction error (Broersen 2006),

Ji =1

N

N∑

k=1

e2i (k)

Where N is the number of samples in a sweep and ei(k) = yi(k)− yi(k) where yi(k) is the

measured sweep and its model estimation yi(k).

For a given single sweep, optimum model orders p and q are determined by the mini-


mum value of the final prediction error (FPE) (Ljung 1987),

FPEi =N + s

N − sJi (2.5)

where s = p+ q. FPE gives a measurement of model estimation error combined with the

model orders as a penalty factor in order to determine the optimum estimation error with

a minimum number of model orders.

According to the schematic diagram of the ARX model implementation shown in fig-

ure 2.6, s(k) is the signal of interest that needs to be extracted from background noise n(k).

The deterministic ABR s(k) is derived by filtering the reference u(k), i.e. S(z) = B(z)A(z)U(z).

The transfer function B(z)A(z) merely represents a mechanism to incorporate deterministic sin-

gle sweep EP variations into the reference signal rather than a physiologically meaningful

process. The ongoing EEG n(k) is derived by filtering Gaussian white noise e(k) with an

all pole filter (AR model) i.e. N(z) = 1A(z)E(z). Finally, the single sweep y(k) corresponds

to the additive model in equation (2.4). Then a template u(k) is derived from MTA of an

ensemble of y(k) which is then used as the exogenous input to the derived ARX A(z) and

B(z). The output to the model is a single sweep of y(k) and model orders are determined

using minimum FPE. The estimated ABR s(k) is then derived as:

S(z) =B(z)

A(z)U(z) (2.6)

Figure 2.6: The process of the ARX model


2.2.3 Applications of ARX modelling

Cerutti et al. (1987) used the ARX model to extract single sweep estimates of VEPs

with a MTA of 99 sweeps as the reference input u(k) to the model. Model orders were

determined by minimizing the Final Prediction Error (FPE) function (Akaike 1970) and

were set to p = 6, q = 7. The FPE is a measure of model goodness of fit and represents

a compromise between model complexity (i.e. the number of parameters (p+ q − 1) and

model prediction error. These model orders were the minimum required to accurately

represent the relationship between the single sweep, exogenous reference signal and the

Gaussian white noise. The estimated single sweeps had four types of characteristics; 70%

of the single sweeps had a close morphology to that of the reference input providing a

statistically consistent value of the mean pattern of all responses. 12% of the estimated

sweeps did not represent a VEP due to the small amplitudes. 5% of the estimated sweeps

resembled the VEP only during the first half of the sweep whereas 13% of it had completely

different morphology to that of the reference. The reason for negative results in this study,

is limited to an assumption of the absence of VEP due to loss of attention in the subject,

which leads to bad focusing of the stimulus on the retina (Cerutti et al. 1987). However

the lack of actual EP when using empirical data, poses a major disadvantage to determine

whether corrupt results are due to the noise present in the data or due to shortcomings of

the ARX methodology.

The lack of standard procedure to assess the effectiveness of the ARX method may

have led to misinterpreted results. A simulation study with reproducible EPs at each single

sweep could avoid such uncertainties and provide an unbiased opinion on the aberrations

of the estimated single sweep.

Based on the development of single sweep extraction, ARX modelling was initially used

to rapidly quantify the effects that anaesthetics on MLAEP in order to quantify the depth

of anaesthesia (Jensen et al. 1996). It is well known that anaesthetics systematically and

reversibly affect the amplitude and latencies of the major middle latency components Na,

Pa, Nb and Pb (Church & Gritzke 1987, Church & Gritzke 1988). Jensen et al. compared

the behaviour of Na-Pa amplitude extracted using ARXmodelling, with conventional MTA

during combined propofol and alfentanil anaesthetic agents. ARX model parameters were


fixed in such a way that, a MTA of 256 epochs of MLAEP assigned to the reference input

u(k) to suppress the noise by 24 dB, a single epoch was assigned to yi(k) (therefore single

sweep estimation) and model orders were fixed to p = q = 5 on the basis of FPE. Results

of the ARX model output indicated that onset of unconsciousness occurs in the order

of 1.5 minutes earlier than conventional MTA. Also the change in the amplitudes was

larger in ARX extracted results, providing a clearer distinguishable characteristic between

unconscious and the awake state.

This application of ARX model leads to the development of the A-Line ARX index

(AAI) to quantify the depth of anaesthesia (Jensen et al. 1998) and was eventually used

commercially in AEP Monitor/2 (DanmeterAps 2010). The parameters of the ARX model

to calculate the AAI is slightly different. It uses a MTA of 15 epochs for the output of the

model yi(k) instead of a single sweep, whilst maintaining the other parameters to be the

same as those mentioned earlier. The modified yi(k) improves the efficiency of the esti-

mation process by reducing noise associated with it. In a separate study, which compares

conventional MTA and ARX in AAI, states that A-Line index detects the transition from

awake to unconscious in 6 seconds whereas MTA of 256 sweeps detect it after 28.4 seconds

(Litvan, Jensen, Galan, Lund, Rodriguez, Henneberg, Caminal & Villar Landeira 2002).

Similar promising results were achieved with patients who had anaesthesia induced with

thiopentone and were subsequently maintained with isoflurane and alfentanil when con-

ducting tracheal intubation (Urhonen et al. 2000). Also AAI was tested for the effects

of sevoflurane with a rapid response compared to MTA and recorded encouraging results

(Alpiger, Helbo-Hansen & Jensen 2002).

Further evidence for the successful use of ARX modelling based on rapid extraction is

reported with the findings of monitoring sedation in cardiac surgery patients (Mainardi

et al. 2000). Amplitude differences between P50 and N100 features of ALRs were moni-

tored in patients undergoing anaesthesia with propofol-alfentanil or midazolam-fentanyl.

Here, single sweeps were extracted using a reference signal u(k) with a MTA of 40 sweeps.

The low number of sweeps for the reference signal is due to the high SNR of ALRs com-

pared to MLAEPs.

Apart from monitoring anaesthetic effects, ARX modelling is used to extract SEPs


and H-reflex responses induced by stimulating the spinal cord (Rossi et al. 2007). Such

applications are essential for recommended intraoperative neuromonitoring during surgery

where the spinal cord functional integrity is at risk. In this application, a modification has

been made to the way the reference signal is calculated by taking an average of 50 trials

with exponential weights attribute to minimise the effect of past trials. The model orders

were set to p = 2, q = 4. Results suggest an improved temporal resolution of 1 second

and therefore this method is deemed suitable for an online rapid extraction system. Also

a DSP based hardware system has been successfully built to incorporate this algorithm

(Bracchi, Perale, Rossi, Gaggiani & Bianchi 2003).

ARX modelling was also used to analyse the shape and the time course of periodic

sharp wave complexes (PSWCs) of flash VEPs, which assisted in clinically diagnosing

Creutzfeldt-Jacob disease (Visani, Agazzi, Scaioli, Giaccone, Binelli, Canafoglia, Panzica,

Tagliavini, Bugiani, Avanzini & Franceschetti 2005). The chosen model orders for the

analysis were p = q = 4. However this study did not report the number of sweeps averaged

for the reference input (one could assume it to be a single sweep). The single sweep results

extracted, contributed to clarifying the much-debated problem of the occurrence of giant

flash VEPs in Creutzfeldt-Jacob disease and their relationships with the spontaneous

periodic EEG patterns.

In summary, the review suggests major contributions in which ARX modelling has

been successfully used to extract EPs. According to the noise present in the interested

physiological signal, some have estimated a single sweep while others have estimated the

resultant of an ensemble of sweeps. However, it was found that ARX modelling has not

been used to extract the ABR during the conduct of this literature survey. Therefore

the use of ARX on ABR may be considered a worthwhile endevour, with many potential

applications.

With regards to anaesthesia monitoring, the tracking of time scale variations of phys-

iological signals has not been studied due to the emphasis being given to anaesthesia

monitoring applications that predominantly depend upon amplitude variations. A study

of the latency tracking ability of the ARX modelling will open a new paradigm of appli-

cations where time scale varying features are of importance.


In addition the validity of the extracted signals so far has been assessed using recorded

EP data. Due to the high inconsistency of real EPs, it is worthwhile to carry out an initial

simulation study with synthetic data to verify the model performance.

2.2.4 Robust evoked potential estimator - REPE(p, q, r, d)

Because of much lower SNR of the ABR compared to the other EPs, of the order of -

30 to -20 dB compared to the MLAEP of about 0 dB, it is reasonable to assume that

the rapid extraction of ABR using ARX methodologies will require modification. Lange

& Inbar (1996) have proposed a method claimed to resist such noise conditions by pre-

whitening the template u(k) before applying the ARX model calculations. The resulting

implementation, referred to as the Robust Evoked Potential Estimator (REPE), is based

on the fact that a successful estimation of a system is achieved by exciting the input of the

model with a wide band of frequencies (Box & Jenkins 1976). Otherwise, where when the

input is driven by a narrow-band signal, it might not excite the system to its full modality,

resulting only in a partial identification of the examined signal. Therefore in REPE, the

exogenous input to the ARX model is pre-whitened via an AR process to broaden the

frequency distribution. This can be expressed as u(k) = −∑r

j=1 cju(k − j) + ξ(k), where

cj ’s are model coefficients and r is the order of the AR process. As shown in figure 2.7,

the process after z-transform could be formulated as:

A(z)Y (z) = B(z)C(z)U(z) + E(z) (2.7)

where C(z) =∑r

j=1 cjz−j . AR model order r and model coefficients cj ’s are calculated

using FPE and a batch-least-square method respectively. Here, the exogenous input to

the conventional ARX model is W (z) = C(z)U(z). The estimated EP s(k) is then derived

as:

S(z) =B(z)C(z)

A(z)U(z) (2.8)

In verifying the REPE, Lange & Inbar (1996) used EPs obtained from a finger tapping

experiment with a MTA of 200 sweeps as the reference signal. Initially, the pre-whitening

model order was determined to be r = 8 followed by the calculation of other model or-


Figure 2.7: The process of the REPE

ders to be p = 8, q = 6 (i.e. REPE(8,6,8,0)) by minimising the prediction error as per

the FPE (2.5). A comparison with conventional ARX(8,7,0) model in general suggested

that REPE(8,6,8,0) estimated single sweeps maintain a close resemblance to the average

response both in shape and amplitude where as ARX estimations often display high ampli-

tudes which ‘may be’ noise related and sometimes fail to describe the general wave shape

(Lange & Inbar 1996)

2.2.5 Simulation studies and drawbacks

To date, these ARX methods of rapid extraction have been evaluated by their ability to

detect assumed variations in recorded EP data. Since the deterministic EP is unknown in

the actual data, simulated data are essential in order to provide a deterministic EP so that

ARX modelling methods for rapid extraction can be meaningfully evaluated. According to

information gathered through this literature review, none of the research has conducted a

complete study with simulated data. Therefore, a set of synthetic EP data with predefined

but physiologically plausible variations of those EP features could provide a less biased

basis to investigate the model estimations compared to those studies which use actual

single sweep EPs, whose characteristics are highly variable.

Few attempts have been made to verify the effectiveness of tracking varying features

using semi-simulated data where an actual EP template is subjected to predefined mod-

ifications. The lack of precise definition of the EP template has made reproduction of

the results impossible and comparisons inaccurate. Cerutti et al. (Cerutti et al. 1987)

has made an attempt to verify the amplitude variation tracking ability of the ARX model


by inducing variations to the single sweeps by changing the gain in the signal generating

model. However, the gain values were not quantified here thus making it impossible to

determine the limitations of extracting amplitude variations with the ARX model.

Also, Rossi et al. (2007) have attempted to perform a simulation study to extract the

amplitude variations of SEPs, which are used for a spinal cord intraoperative neuromoni-

toring technique using conventional ARX modelling. Here, the evaluation is limited only

to the tracking of amplitude variations with a concluding remark stating, ‘the early de-

tection of changes in the EP could be better achieved by ARX than MTA’ which is the

apparent result. The narrow variation of amplitude (limited to the specific application

domain) tested, absence of latency variations and the fixed initial SNR (typically -5 dB of

SEPs which is higher than ABRs of -30 dB (assuming following amplitudes: SEP=15 µV

ABR=1 µV, EEG=30 µV)) are the significant shortcomings of this simulation study.

With regards to REPE, Lange & Inbar (1996) have attempted to verify the performance

in two stages; 1) The denoising ability 2) The variation tracking ability. They quantified

the denoising ability by calculating the improvement in the SNR, SNRimprovement, defined

as;

SNRimprovement = 10. log10

(

SNRfinal

SNRinitial

)

(2.9)

where SNRfinal =E[s2(k)]

s(k)−s(k))2and SNRinitial =

E[s2(k)]E[n2(k)]

. A comparison of ARX estimator

and REPE methods for single sweep extraction suggested the SNRimprovement achieved by

the REPE is substantially higher than the ARX for low SNRs, reaching a 20 dB advantage

at an initial SNR of -35 dB (shown in figure 2.8). The REPE exhibits a linearly increasing

SNRimprovement with respect to higher initial SNR and saturate below -15 dB initial SNR,

while the ARX presents an almost constant improvement in SNR of approximately 6 dB

irrespective of the initial SNR.

However, even though there is a significant improvement in the SNR around an initial

SNR of -30 dB, Lange & Inbar have not assessed the morphology of the extracted EP for

the presence of its features. Given the importance of estimating variations in the latency

of various AEP components, it is essential to systematically investigated the effects of the

REPE method on morphological characteristics at such low initial SNRs.


Figure 2.8: SNR improvement of ARXE (same as ARX) and REPE. The difference in the curves suggeststhat there is a considerable improvement in SNR when REPE is used (Lange & Inbar 1996).

2.2.6 Scope of the current study

The single trial extraction methods of ARX and REPE have been applied with much

apparent success to a range of evoked responses (Cerutti et al. 1987, Lange & Inbar 1996,

Rossi et al. 2007) (specific details were discussed in section 2.2.3). However, attempts

to systematically verify the validity of these methods using simulated data suffer from

following drawbacks;

(i) Use of grand average of real EP data as the reference/template signal. Such EPs

are not reproducible thus a comparison or a performance evaluation with previous

work is impossible.

(ii) Ambiguity of the selection criteria for model parameters makes the validation of

model performance with previous work impossible.

(iii) The range of latency variations tested in the simulated EP is limited and does not

encompass the expected range of physiological variation.

Because of the promising results produced in extracting single sweeps of AEP compo-

nents, it is important to systematically evaluate the performance using synthetic data in


order to clearly define the scope for the use of ARX and REPE methods. On this basis,

this thesis presents an original, well defined, reproducible simulation study to determine

the effectiveness of ARX and REPE rapid extraction methods to variations in the SNR of a

simulated ABR and the ability of these methods to accurately track time-scale variations

(latency) of simulated ABR components. This study follows from a similar simulation

study but in a different paradigm, in which three algorithms; correlation based, adaptive

least mean square based and p-norm based were compared with respect to their ability to

track EP latency variations (Kong & Oiu 2001).

Chapter 4 and 5 present systematic simulation studies performed on a mathemati-

cally modelled ABR which is reproducible and added typical EEG noise to determine the

limitations of single sweep extraction. A range of physiologically plausible latency varia-

tions were induced to this model to assess the range over which accurate tracking can be

achieved. This study will lead to a better choice of applications which could use paramet-

ric modelling to calculate a fine-grained measure of the brain state, thereby providing a

better understanding of relevant brain structures which generate EPs. The methodology

and the results of this study are described in sections 4.2 andsec:ARXRes respectively. To

confirm these results, real ABR recorded from human participants were then subjected to

ARX and REPE methods and results were discussed in section 4.3.6 with respect to the

practical implementation of these methods.

2.3 Review of wavelet based extraction methods

Wavelet analysis was recently used with much success on the EPs and ERPs including the

ABR. In general, EPs are recorded from multiple electrode arrays with variable frequency

content over time and across spatial location on the scalp, therefore are characterised as

non-stationary in both time and space. Also the features and variations of these EPs

which interest neuroscientists and clinicians are transient (localized in time), prominent

over certain scalp regions (localized in space), and restricted to certain ranges of temporal

and spatial frequencies (localized in scale).

One of the major advantages of using wavelets on such signals is that, it permits ac-

curate decomposition of EPs into a set of sub-waveforms which can isolate all frequencies


from the largest to the smallest pattern of variation in time and space which is a character-

istic of non-stationary EPs. Consequently, wavelet analysis provides flexible control over

the resolution which enables components of the EP and their variations to be localized in

time, frequency and space. This control over resolution translates directly into increased

power in statistical waveform analyses and improved digital processing techniques to de-

tect and analyse anatomical structures and pathological effects which contribute to such

variations.

In contrast to parametric modelling (ARX and REPE) which is based on characteristics

of noise (ongoing EEG), wavelet analysis depends upon the morphological characteristics

the signal of interest. The choice of basis wavelet is critical in a wavelet analysis to

produce accurate estimates (Wilson & Aghdasi 1999, Wilson et al. 1998). Therefore this

thesis presents a comparable analysis of the ABR through wavelets as a new paradigm

and compares this with parametric modelling results to arrive at a conclusion.

2.3.1 Wavelets in the extraction of ABRs and in general EPs

Considering the advantages, researchers have implemented several wavelet techniques to

extract EPs, predominantly for auditory middle and late components and in some cases

for the early ABR.

Due to relatively high SNR of middle and late EPs, single sweep extraction was widely

examined for rapid extraction using wavelets (Demiralp, Yordanova, Kolev, Ademoglu,

Devrim & Samar 1999, Quian Quiroga 2005). Quian Quiroga (2005) reported a wavelet

denoising method; Time Windowing with Matching Coefficients (TWMC) using discrete

wavelet transform (DWT) to extract single sweeps of MLAEPs and VEPs. These EPs

are of the same order of SNR, but high compared to a typical ABR. TWMC resulted

in superior denoising compared to Wiener filtering when applied to a simulated signal

having a SNR of 0 dB. However, Woody averaging performed to enhance the EPs prior

to applications of TWMC (Woody 1967) is prone to errors with large amplitudes of noise

associated with the ABR. Such preprocessing could lead to false peak identification, thus

rendering it unsuitable to apply on ABRs. Therefore, it is worthwhile to investigate the

applicability of TWMC to unmodified ABRs for rapid extraction purposes.


Demiralp et al. (1999) reported analysis of alpha (8-16 Hz), theta (4-8 Hz) and delta

(0.5-4 Hz) bands of single sweep of middle EPs and P300 by decomposing with DWT.

This study investigates the temporal locations of EP components in relation to specific

cognitive processes. However, the wavelets are used for the separation of frequency bands

with decomposed wavelet sub-spaces which reflect conventional band-pass filtering. In

contrast, overlap of the ABR bandwidth with noise spectrum (as a result of fast ABR

components) such simple methods cannot be applied to extract the ABR. Similar studies

are reported by Acir et al. (2006), Bradley & Wilson (2005) and McCullagh et al. (2007)

involving DWT but does not aim at rapid extraction. Instead, these studies use an ABR

derived from a grand average of more than 1000 epochs and then band-limit using DWT

to analyse the ABR.

Further use of wavelets in EP studies is reported by Effern et al. (2000) who introduced

a method for single trial analysis of P300 that combines non-linear state-space time series

analysis with the wavelet transform. However, results indicate optimum filter characteris-

tics were not be achieved producing misleading interpretations in the absence of necessary

arrangement of the single trial ensemble, and thus were not used for further analysis.

In contrast, Causevic et al. (2005), Maglione et al. (2003) and Zhang et al. (2006) have

made attempts to reduce the number of epochs involved in the analysis using different

thresholding criteria.

A constant threshold with matching coefficients (CTMC) with a template was im-

plemented by Zhang et al. (2006) to detect the presence of an ABR using a Bayesian

network. This is an improved version of the basic thresholding method (Donoho 1995)

suitable for signals with low SNRs. Here, the presence of an ABR is based on the detection

of only wave V (the only wave present at low stimulus intensities). This study reports

the extraction of wave V using an MTA of 64 and 128 epochs leading to rapid extraction

with an accuracy of 78.8% and 84.2% respectively. In contrast, the study presents in this

thesis aims to extract a fully featured ABR including the three main waves I, III and V.

Also, time scale variation tracking has not been investigated in previous studies which are

critical for the context of this thesis. The need for such an investigation is highlighted in

that the use of a template in CTMC could possibly limit the range of time scale variation


tracking capability.

However, based on the encouraging results reported for the rapid nature of the extrac-

tion, this method was considered, to further explore and analyse the possibility of using

as an algorithm to rapidly extract an ABR.

In a separate study, Strauss et al. (2004) reported a signal classifier using vectors

generated by wavelets as the input and achieved 100% sensitivity and 90% specificity in

classifying the presence of the wave V at a stimulus intensity of 30 dB. This study presents

significant motivation for the use of wavelets in rapid extraction of the ABR. However, the

study described in this thesis pursues a morphologically correct ABR showing wave I, III

and V for potential identification of aberrations due to neurological disorders in addition

to hearing screening. In this regard, the following differences were identified in the series

of work reported by Strauss et al. compared to the aim of this thesis.

• In Strauss et al. (2004), even though the feature extraction is of a single sweep,

the novelty detection scheme which identifies the presence and absence of the ABR

features consist of an average of 10 feature vectors to reduce the accidental changes

in the measurement setup.

• The method reported in Corona-Strauss, Delb, Bloching and Strauss (2007) and

Corona-Strauss, Delb, Hecker and Strauss Citeyear,Corona-Strauss2007b suffers from

generalisation for all patient conditions (i.e. patient specific) as a result of inter-

individual variations of the synchronization stabilities. This impedes the application

of such a method in clinical situations as it is not possible to establish an absolute

threshold. On the contrary, the denoising method recommended in this thesis should

be independent of the patient condition, thus making it better suited for adaptation

for all patient conditions.

• In addition, a systematic simulation study or a time scale feature tracking study was

not performed in any of Strauss et al.s‘ work. This contrasts to the investigations

conducted in this thesis with the use of reliable latency-intensity curves.

Another promising fast estimation method based on thresholding was introduced by


Causevic et al. (2005) called cyclic shift tree denoising (CSTD). This method consists of a

circular averaging technique with an additional thresholding criterion. Circular averaging

creates additional averages (which is the most reliable and conventional method) leading

to better noise suppression. Non-linearity of the averaging process makes it an improved

version of conventional moving time averaging. MLAEPs and ABRs were used to assess

the performance of the CSTD and have yielded promising results. But the rapid nature of

extraction is not highlighted in this study where they have presented denoised waveforms of

a moving time average of 512 ABR epochs and 256 MLAEP epochs. Even though Causevic

et al. (2005) have mentioned the improvement in SNR in general, specific features of filtered

ABRs involving smaller number of epochs have not been analysed. Another shortcoming

in this study is the absence of an evaluation of the method under time scale variations of

the ABR which is a common drawback of previously mentioned studies.

According to the literature available at the time of this research, the exact nature of

a fully featured ABR extraction including critical time-scale variations were not analysed

(even though several promising rapid extraction algorithms were formulated). Table 2.3

summarises the specifications of the following three most probable algorithms for rapid

extraction:

• Constant thresholds with matching coefficients (CTMC)

• Temporal windowing with matching coefficients (TWMC)

• Cyclic shift tree denoising (CSTD)

In summarising the research literature, CTMC was used to test the ABR but concen-

trated only on peak V. TWMC was used to investigate P300 but not ABR. CSTD was

used to test MLAEP and ABR but was not used to quantify the morphology of the ABR.

All these techniques have contributed to rapid extraction in their own right. However,

this thesis investigates the performance of denoising of these three wavelet methods using

a common set of ABR data.

In addition, the thesis presents an investigation of these methods under time varying

conditions, close to what would be seen in clinical practice using latency-intensity curves.


Features of thealgorithm

Zhang (2006)CTMC

QuianQuiroga (2005)TWMC

Causevic (2005)CSTD

Wavelet algorithm DWT DWT DWTbasis wavelet Biorthogonal 5.5 Biorthogonal 4.4 Biorthogonal 4.4Use of a template Yes Yes NoAnalysed EP ABR ALR MLAEP and

ABRMinimum number ofepochs involved

64 Single sweep MLAEP - 256ABR - 512

EP features analysed Wave V P100, N200, P300 ALMR - Na, Nb,Pa, Pb

ABR - overallmorphology

Table 2.3: Specifications of key algorithms for rapid extraction.

It has been reported that shift variance plays a key role in filtering time-shifted data with

DWT (Bradley & Wilson 2004, Kingsbury 2001). Therefore, CTMC, TWMC and CSTD

were implemented with DWT and reformulated to stationary wavelet transform (SWT)

to identify such temporal distortions described in section 5.1.6.

To achieve comparable results for these wavelet-denoising methods, a common basis

wavelet is essential. As shown in table 2.3, the order of the Biorthogonal wavelets used for

each method is different as a result of adopting recommendations of other similar studies.

Therefore thIS thesis presents a study to choose the optimum, common Biorthogonal

wavelet for all three denoising methods; CTMC, TWMC and CSTD. The methodology

for this study is described in section 5.2.

The following sections describe the theoretical background of wavelets in detail and

the way in which contribute as a powerful tool to analyse the ABR.

2.3.2 Concept of wavelets

A wavelet is a time domain function which inherits specific properties of the energy content,

frequency content and the length in time. The wavelet function defined over the real axis

(−∞,∞) must satisfy two basic properties; 1) zero mean 2) unity energy. These can be


mathematically expressed as in (2.10) and (2.11).

∞∫

−∞

ψ(t)dt = 0 (2.10)

∞∫

−∞

ψ2(t)dt = 1 (2.11)

The notion of ‘small wave’ or ‘wavelet’ is related to the limited interval associated in

time scale (Haar 1910). If we assume that there exist δ, very close to zero, there must be

an interval of finite length of which the energy of the wavelet is;

T∫

−T

ψ2(t)dt < 1− δ (2.12)

Because, the deviation of ψ(t) outside the interval [T,−T ] will be insignificant, the

activity of the wavelet is limited within the interval [T,−T ] and negligible outside. Since

the total waveform energy is concentrated strictly within this time window (i.e. zero

amplitude out of the window) or if the majority of the waveform energy is within the

window (i.e. low amplitudes out of the window), those wavelets are defined as “compact

support”. In contrast, even though the cosine base signal in Fourier transform fulfils the

criterion for the mean in (2.10), the energy would be diverging to infinity and cannot

be normalised to unity, and therefore is not considered as a wavelet. Also, distinct from

the Fourier base function, the band limited frequency content in the wavelet sub-bands

enhances the dynamic nature when used to analyse transient signals.

Scaling and translating are the two main principles of wavelet analysis. A wavelet can

be scaled in time by stretching or shrinking the wavelet and can be translated by shifting

to different time positions without changing its basic wavelet shape. An orthonormal,

compactly supported wavelet basis is formed by the scales j and translations k of a single

real valued function ψ(j,k)(t) =1jψ

(

t−kj

)

defined as the wavelet and its scaling function

ϕ(j,k)(t). The result will be a set of coefficients for each scale and translation representing

the extent to which the wavelet has been matched with the signal of interest. This implies

that larger coefficients are related to the actual signal and noise is mostly represented by


smaller coefficients (the the choice of morphologically similar wavelet basis function for

such analysis is critical). Therefore the systematic removal of less significant coefficients

leads to refining the signal of interest. These coefficients could then be used to reconstruct

the denoised signal of interest by an inverse calculation.

2.3.3 Basis wavelets

A basis wavelet (also known as a mother wavelet) is defined as a basic waveform shape.

Haar, Daubechies, Symlet, Morlet and Biorthogonal are few examples of different wave-

form shapes. Different orders of each basis wavelet forms a wavelet family in which the

higher orders make the wavelet smoother. Each wavelet family possesses unique properties

that make them more appropriate for a certain range of applications including extraction

of the ABR. Some of these essential properties are explained below.

• Symmetry - The phase response of a filter, and therefore a wavelet, is defined by

its symmetry properties. If a basis wavelet possesses either even or odd symmetry,

then the corresponding phase response is linear (Parameswariah & Cox 2006). A

linear filtered preserves the in-phase frequency components filtered in contrast to an

asymmetric filter with a non-linear phase response which produces phase distortions

(Oppenheim & Schafer 1999). With the exception of the orthogonal Haar wavelet (a

B-spline of degree zero), only Biorthogonal basis wavelets can be designed to have

linear phase responses.

One of the main foci of the context of this thesis is to study the ability of wavelet

methods to track time-scale variations of specific ABR features. Therefore the preser-

vation of the locations of these features is critical, thus signifying the necessity of

symmetric filters.

In addition, the symmetry of the basis wavelet reduces the number of multiplications

in the convolution integral by half. This is achieved by adding signal samples prior

to multiplication by the filter coefficient (Bradley & Wilson 2004).

• Smoothness - There are several factors which affect the smoothness of the basis

wavelet. Smoothness defines the differentiability of the wavelet. Since the EPs such


as the ABR is a smooth continuous signal, the smoothness of the basis wavelet

improves the morphology of the reconstructed waveform (Burrus, Gopinath & Guo

1998).

The order (also called vanishing moments) directly affects the smoothness or the

regularity of the basis wavelet. In theory, higher orders allow more complex signals

to be accurately represented by the scaling functions of the wavelet. As the order

represents the accuracy (Strang & Nguyen 1997), wavelets with a higher order, in

general, approximate signals with fewer non-zero coefficients, thus providing a sparse

representation suitable for data compression and fast calculations (Mallat 1998).

The choice of a basis wavelet for filtering varies depending on the EPs. Some choices of

reported literature appear vague with no justification for the choice of the basis wavelet.

For example, Huang & Nayak (1999) have used 20th order Daubechies wavelet to mea-

sure the depth of anaesthesia with MLAEP and Kochs et al. (2001) uses the 3rd order

Daubechies wavelet. Similarly, Effern et al. (Effern, Lehnertz, Fernndez, Grunwald, David

& Elger 2000, Effern, Lehnertz, Schreiber, Grunwald, David & Elger 2000) has introduced

and examined an ALR analysis method using a single sweep with wavelets but has failed

to reveal the basis wavelet used in the study. However, some of the literature has justi-

fied the choice of basis wavelet, on the basis of various properties of the chosen family of

wavelets. Wilson et al. (1998) has investigated the use of three basis wavelets; Biorthogo-

nal 3.5, Daubechies 5 and Symlet 4 for their ability to analyse ABRs and concluded that

a so-called best basis wavelet is less distinct. Therefore, they suggest choosing the best

basis wavelet for each wavelet decomposition sub-band. Hoppe et al. (2001) in their study

of automatic sequential recognition of ALR has identified that Mallat’s wavelet produced

best results compared to Daubechies and Biorthogonal.

Wilson et al. (1998) on the other hand, have provided reasons for his choice of 5th

order Daubechies wavelet for analysing ABRs including: exact reconstruction, similarity

in morphology, arbitrary regularity and asymmetry (suitable for the irregularly shaped

ABR waveform), compact support and orthogonality. But according to the suitability

criteria mentioned above with symmetry and smoothness, several arguments of Wilson et


al. (1998) have failed. Exact reconstruction can only be achieved if all the coefficients

are involved in the reconstruction process (inverse wavelet transform). But in contrast,

denoising applications always nullify irrelevant coefficients therefore prohibit exact recon-

struction. Also the choice of asymmetric basis wavelets in Wilson et al. (1998) affects the

orthogonality (except Haar wavelet) leading to a non-linear phase distortions during the

filtering process.

However, the literature review presented here revealed that wavelets in the Biorthogo-

nal family are used frequently with justification. Causevic et al. (2005) and Quian Quiroga

(2005) have used Biorthogonal 4.4, Bradley & Wilson (2004) and Zhang et al. (2006) have

used Biorthogonal 5.5. Also Basar et al. (2001) have used Biorthogonal wavelets but have

not mentioned the order. In addition to EP related applications, Biorthogonal wavelets

contribute to compression of 2D data by retaining relevant coefficients related to the en-

ergy distribution as it is used in JPEG2000 image compression (ISO/IEC 2004) and in

the fingerprint information storage system in FBI uses wavelet/scalar quantization (WSQ)

image coding standard (Bradley & Brislawn 1994). The symmetry of the filter is critical

when choosing the family of wavelets with stable linear-phase FIR filter which does not

distort the filtered waveform (Parameswariah & Cox 2006) and the reduction of the shift

variance effect (Singh & Tiwari 2006). In addition, further reasons stated for the choice

of Biorthogonal basis wavelets are; the order of the wavelet for better match for the ABR,

compact support nature to reduce the computational complexity and visual similarity to

individual ABR peaks.

2.3.4 DWT with Biorthogonal wavelets

Wavelet analysis and its efficient computer implementation of DWT is extensively de-

scribed in (Mallat 1998) and specific applications related to the ABR are explained in

(Samar et al. 1999, Raz et al. 1999). The wavelet transform in its pure form calculates all

the wavelet coefficients at all the scales and translations, which are both computationally

redundant and a time consuming process. Therefore a subset of scales and translations of

dyadic nature (based on power of two) is used for more efficient analysis. Mallat (1989)

has introduced a filter bank consisting high-pass and low-pass filters to calculate wavelet


coefficients of a given sequence of a discrete time series.

The algorithm of the DWT of a signal x(t) of length N consists of performing several

elementary decomposition steps. Starting with the signal x(t), the first step produces

two vectors of coefficients: approximation coefficients a1 and detail coefficients d1. These

vectors are obtained by a convolution of the signal x(t) with the low-pass filter h for

the approximation and with the high-pass filter g for the detail, followed in both cases

by a dyadic decimation. They are approximately N/2 in length. The convolution of the

signal x(t) by a filter h is defined by [x ∗ h]n =∑

k

xn−khk. The dyadic decimation of

the signals defined by yn = x2n.

This operation leads to higher order decomposition levels by breaking up the approx-

imation coefficients into two, replacing a1 by a2 and d2. The algorithm follows the same

pattern of decomposing up to level l as shown in figure 2.9, decomposition half. System-

atic nullification of these coefficients leads to efficient removal of noise. Such three similar

methods are implemented in this study to extract features of the ABR and are explained

in section 5.1.

In the case of using Biorthogonal basis wavelets, there are two separate filters for

decomposition and synthesis. Such Biorthogonal compliments of decomposition filters for

synthesis are defined as h representing low-pass filter and g representing high-pass

filter .

The inverse DWT performs a reconstruction of the original signal by up-sampling

coefficients by a factor of 2 and then convolving with the synthesis low-pass filter h and

high-pass filter g. The perfect reconstruction of the original signal is shown in synthesis

section of the figure 2.9.

2.3.5 Shift variance of DWT

It is well known that, DWT suffers from shift variance in the time domain i.e. even in the

case of periodic extension of a signal x(t), the DWT of a translated version of x(t) is not,

in general, the translated version of the DWT of x(t).

In other words, time shifts in the signal are not properly represented by the decomposed

approximation and detailed functions of the DWT. Therefore, reconstructed signals using


( )x t

g

h

2 ↓

2 ↓

d1

d2

dl

al

Level 1 Level 2 Level l

+

2 ↑

2 ↑

Decomposition Synthesis Approximation

and detail

coefficients

g

h

g g

g

g

h h

h

h

( )x t2 ↓

2 ↓

2 ↓

2 ↓

2 ↑

2 ↑

2 ↑

2 ↑

+

Figure 2.9: Mallat’s cascaded filter multiresolution analysis. x(t) is decomposed by analysis filter coeffi-cients h and g. Resultant approximation and detail coefficients are then inverse filtered by synthesisfilter coefficients h and g to arrive at the reconstructed x(t).

the thresholded coefficients of the DWT are prone to latency distortions (Bradley &Wilson

2004, Coifman & Donoho 1995, Kingsbury 2000). This is as a result of down-sampling

the decomposed coefficients by a factor of two at each decomposition level in the DWT.

That is, when the wavelet transform sub-bands (which nominally have half the bandwidth

of the original signal) are sub-sampled by a factor of two results in violating the Nyquist

criterion and frequency components above (or below) the cut-off frequency of the filter are

aliased into the wrong sub-band.

Several decomposition methods have been suggested to suppress shift variance with

continuous wavelet transform, dual tree complex wavelet transform (Kingsbury 2001), sta-

tionary wavelet transform (SWT) (Misiti, Misiti & Oppenheim 2006) and over complete

discrete wavelet transform (Bradley & Wilson 2004). Continuous wavelet transform is a

highly redundant method whereas dual tree complex wavelet transform needs special basis

wavelets to implement, thus both were not suitable for implementation of denoising meth-

ods evaluated in this thesis. Over complete discrete wavelet transform is a combination of

conventional DWT and SWT in which critically sampled DWT is applied to the first M

levels of an L level wavelet decomposition and then the fully sampled SWT is applied to

the remaining (L −M) levels (Bradley & Wilson 2004). This however produces a slight

shift variance even though it is computationally efficient.

In this thesis, to evaluate denoising methods in an unbiased manner, the perfect shift


invariant SWT was used in addition to the conventional DWT. This way, latencies of

filtered ABRs are guaranteed to be preserved, thereby expecting to generate an accurate

result.

2.3.6 Stationary wavelet transform

Stationary wavelet transform (SWT) follows a similar decomposition tree to that of DWT.

The only difference is the elimination of dyadic down sampling at each decomposition

levels preserving all of the information of the signal at decomposition levels thus avoiding

aliasing.

The algorithm used for the calculation of the SWT possesses similar features to that of

the DWT. Level 1 decomposition of a given signal can be obtained by convolving it with

appropriate filters, as in the case of the DWT but without decimating. In this case the

approximation and detail coefficients at level 1, a1 and d1 both have a length N , which is

the length of the original signal.

In general, the approximation coefficients at the level l are convolved with an up-

sampled version of the two usual filters to produce the approximation al+1 and detail

dl+1 coefficients at the j + 1 level. The algorithm can be visualised as per the schematic

diagram presented in figure 2.10.

2.4 Summation of the ABR extraction methodologies

According to the information revealed in this chapter, the ABR is associated with key

pathologic conditions in the auditory central nervous system as well as non-pathologic

conditions such as drug administration and stimulation parameters. While hearing screen-

ing related applications of the ABR are well established, correlation with other pathologic

and non-pathologic conditions is a grey area thus imposing a barrier to use in practice.

The main drawback of the conventional ABR extraction method is the prolonged dura-

tion which results in the inability to observe the short-term variations which could provide

critical information about internal brain structures. Therefore the need arises for a rapid

system which can accurately estimate the features of the ABR. Such systems could also


( )x t

g

h

d1

d2

dl

al

Level 1 Level 2 Level l

+

Decomposition Synthesis Approximation

and detail

coefficients

g

h

g g

g

g

h h

h

h

( )x t+

+

lh ↑2 1+lh

lg ↑2 1+lg

1ˆ

+lh lh

1ˆ

+lg

lg

↑2

↑2

Figure 2.10: Decomposition and the synthesis tree of the SWT with a Biorthogonal basis wavelet. Dyadicdown-sampling is eliminated here. To implement this, filter coefficients have up-sampled (h and g)for the decomposition and down-sampled (h and g) for the synthesis of x(t).

potentially be able to be use in intraoperative monitoring systems and in long term patient

monitoring systems to record continuous readings with enhanced comfort to the patient.

The signal processing algorithm is the key features of such a system. Therefore this

thesis mainly aims to:

• Investigate the denoising capacity of ARX and REPE with a well defined, repro-

ducible simulation study under variable SNRs and to evaluate the ability to track

time scale variations in the latency of simulated EP components followed by applying

these methods to real ABRs.

• Compare the performance with a simulation study with CTMC, TWMC and CSTD

wavelet methods for comparison purposes followed by optimising these wavelet meth-

ods on real ABRs to evaluate the performance of noise removal and time-scale vari-

ation tracking.

• Determine limitations and implications of using ARX modelling and specific wavelet

denoising methods in extracting the ABR.


2.4.1 Hypotheses

The large coefficients that are derived from wavelet transformation (with a closely com-

patible basis wavelet) of a noisy ABR in general are related to the underlying signal and

comparatively smaller coefficients are related to the noise. Imposing a threshold on these

coefficients retains the larger coefficients and neglects the lesser coefficients. Therefore

the general hypothesis of wavelet denoising is that the coefficients that are neglected by

thresholds are related to spontaneous EEG noise, where as the retained coefficients are

relevant to the ABR.The specific hypotheses related to denoising methods are as follows.

• It is hypothesised that the use of a template in CTMC algorithm improves the

conventional thresholding by retaining wavelet coefficients of the noisy signal related

to the temporal locations of the template.

• In TWMC, it is hypothesised that specific ABR features occur at predetermined

time windows along the time frame of the response.

• In both CTMC and TWMC it is hypothesised that a fixed template accommodates

detection of time scale variations of the ABR.

• It is hypothesised that the template independent CSTD method will allow tracking

latency variations without constrains.

It is hypothesised that shift invariant SWT yields better denoising results (in terms

of mean square error) and latency approximations compared to the use of DWT as the

decomposition algorithm.

2.5 ABR data

2.5.1 Types of ABR data

According to the drawbacks identified in section 2.2 and 2.3 the extraction methods eval-

uated in this thesis were initially subjected to simulated data and then those results were

justified and practical implications were studies through ABR data recorded from human

participants.


2.5.2 Simulated ABR data

As identified in section 2.2.5 a systematic evaluation has not been performed on either ARX

or wavelet methods. One of the major drawbacks of existing simulations studies in ARX

modelling is the derivation of the template with an ensemble average of real EP data (Lange

& Inbar 1996, Cerutti, Chiarenza, Liberati, Mascellani & Pavesi 1988). Simulation of

noise has been the major focus in wavelet studies where some studies use a cosine wave for

performance comparison (Causevic et al. 2005). As identified, contrasting characteristics of

the non-stationary ABR to that of stationary cosine wave warrant establishing a systematic

simulation basis for performance comparison. The ABR model introduced in the thesis

intends to include following characteristics.

• Similarity in morphology including clinically important wave I, III and V.

• Obtain systematic variations in the amplitude and latency of individual waves.

• Comparable spectral characteristics to that of a real ABR.

An ABR model including these characteristics is presented in section 3.3 and both ARX

modelling and wavelet methods will be subjected to this model and its variations for an

initial feasibility study before subjecting them to real ABRs.

2.5.3 Real ABR data

The recording task of ABRs is non-trivial due to the small amplitude which is highly

susceptible to background noise including ongoing EEG, noise of the recording setup and

ambient electromagnetic noise. The short time span (10 ms) of the ABR activity includes

high frequency components which could overlap such a noise bandwidth. To avoid con-

tamination, a general set of parameters has been established for ABR data recording and

is listed in table 2.4 (Hall 1992, Van Campen, Sammeth, Hall 3rd & Peek 1992). The

importance of these parameters is heightened due to:

• optimised ability to detect the ABR suppressing substantial noise interference

• providing a standard recording environment.


Parameter Settings

Stimulus parameters

Type ClickPulse width 0.1 msPolarity a square pulse with a negative polarityFrequency > 20 HzIntensity Variable in dB nHLNo. of epochs Variable to obtain an ABR with adequate SNRMode MonauralMasking Only if the ABR is abnormalAcquisition parameters

Electrode montageNon-inverting Cz or FzInverting A or M (ipsilateral)Ground FpzFilteringHigh-pass 30 HzLow-pass 3 kHzAmplification 100000Sampling rate 40 kHzAnalysis time 15 msPre-stimulus interval 10% of the analysis time

Table 2.4: Settings for a typical ABR recording (Hall 1992, Van Campen et al. 1992).

Also, myogenic artefacts can induce voltage fluctuations in the order of 100 µV which

result in saturation of the bio amplifier. Epochs containing such artefacts are removed with

artefact rejection methods before further processing with wavelets or any other extraction

method.

The most common stimulus types used in ABR recordings are the ‘click’ and the tone

burst (refer figure 2.11a). A ‘click’ stimulus is preferred in ABR recordings over tone

bursts due to the inherent broad frequency spectrum as shown in figure 2.11b. The high

frequencies affect the basal end of the cochlea and the low frequencies affect the apical

end of the cochlea. Thus ‘click’ stimuli are able to produce all features in the ABR and

help clinicians to assess the functionality of the auditory pathway of a patient (Misra &

Kakita 1999).

Stimulus frequency is typically set above 20 Hz to shorten the recording time and

usually set to an odd number with fractions to create an asynchronous alignment of 50


(a) Waveforms of a click stimulus and a tone burst. (b) Spectrum of the click stimulus and the tone burst.

Figure 2.11: Types of auditory stimulus and their frequency spectrums. It is evident that the click stimulushas a broader frequency spectrum than the tone burst.

Hz line frequency components so that they will nullify during the moving time averaging

process. The number of epochs recorded per trial varies according to the noise condition

of the recording setup and the signal processing method.

The number of sweeps required to arrive at an ABR depends upon the electrical and

physiological noise contributing to the final SNR of the MTA. Given perfect conditions

viz. quiet environment, clam and normal hearing participant subjected to high stimulus

intensities, few number of sweeps such as 100-200 is sufficient where as 2000 or more sweeps

are required for a restless participant (e.g. infants) with hearing impairment at low sound

intensities (Hall 2007). This measurement in clinical practice is mostly determined by

calculating the Fsp value and the averaging is terminated when Fsp reaches 3.1 (Elberling

& Don 1984). That is, when Fsp ≥ 3.1 the probability of arriving at a noise signal is 1%

(false positive). However, given imperfect recording conditions, the number of sweeps in

the MTA contributing to the ABR often reaches the order of thousands (Strauss et al. 2004,

Wilson 2004, Wilson et al. 1998, Bradley & Wilson 2004, Shangkai & Loew 1986, Stuart

et al. 1996).

In a typical diagnostic ABR assessment, both ears are tested (one after the other) so

that interaural comparisons can be made. The non-test ear (contralateral) will be masked,


in the case of stimulus intensity in the test ear (ipsilateral) being high enough to cross

over via bone conduction to stimulate the cochlea of the non-test ear. The masking noise

is typically white which masks the entire cochlea in the non-test ear.

Two standard electrode montages, based on the international 10-20 system, are used

for data acquisition purposes (refer figure 2.12). The position for the ground electrode is

at Fpz for both montages. The non-inverting electrode is placed either at Cz or at Fz

and the inverting electrode is placed either at the ipsilateral earlobe or mastoid. These

positions are chosen due to the close proximity of the ABR generators; eighth nerve is

close to earlobe and mastoid and the nucleus of lateral lemniscus or inferior colliculus is

close to Cz and Fz.

Electrode montages for ABR recording include various possibilities; vertical (Cz-Nape

of neck), ipsilateral (Cz-Mi), contralateral (Cz-Mc), and horizontal (Mc-Mi) with the

ground electrode at Fz or Cz (these positions are based on the international 10-20 system).

Following are the implications of using these montages.

• Vertical: prominent wave V low wave I and III (Stuart et al. 1996)

• Horizontal: absent of wave I (Stuart et al. 1996)

• Contralateral: prominent wave II (Kato, Kimura, Shiraishi, Eura, Morizono & Soda

1995)

• Ipsilateral: prominent wave I, III and V (Stuart et al. 1996)

It is widely acknowledged that the ipsilateral electrode montage is entirely adequate

for most ABR applications in adults (Hall 2007) and in infants (Stuart et al. 1996). But in

cases where there is insufficient room to place the active electrode on Fz and the ground

electrode on Fpz, the ground electrode is often placed on the nape/shoulder.

Inter-electrode impedance is a critical parameter in recording an ABR to reduce the

noise and improve the quality of the ABR. Therefore the electrode site at the scalp should

be thoroughly prepared to achieve an impedance of less than 5 kΩ (Chiappa, Gladstone

& Young 1979).


Figure 2.12: Possible electrode montages for ABR recordings. F-Frontal P-Parietal C-Central z-zero(midline)

Other acquisition parameters (according to the table 2.4) can be set at the amplifier

or in the recording software. The standard time window for an ABR is 15 ms with 10%

of it as the pre-stimulus interval (Hall 2007). The window of 10 ms after the onset of the

stimulus includes the important wave V approximately at the 6 ms time point and the

comparatively less significant wave VII approximately at 9 ms.

Electromagnetic interference in the recording environment should be minimised. Elec-

tronic and electrical recording equipment should be kept at a distance from the participant

(Moller 1987). To avoid extraneous auditory stimulation other than the click stimulus, the

recording should be carried out in an anechoic chamber (at minimum in a quiet room).

Also it is advised to rest the head of the participant on a support (or lay on a supine

position (Wilson et al. 1998)) and to close the participants‘ eyes while recording to avoid

myogenic artefacts (Sokolov et al. 2005).

The stimulus artifact The major source of external noise at the point of stimulation is

from the audio transducer which will result in a ‘stimulus artefact’. The stimulus artefact

is generated when the electromagnetic field produced by the audio transducer interacts

with the electrodes placed on the scalp (Coats, Jenkins & Monroe 1984, Elberling &

Salomon 1973, Sokolov et al. 2005). The electrode and the instrumentation, which are fine

tuned to pickup small ABRs could easily record this noise and suppress early components

of the ABR. However, the issue of stimulus artefact is not uncommon. Usual methods


used to minimise this effect are (Hall 2007):

(i) Use of µ-metal shielded headphones to absorb the magnetic field.

(ii) Use of audio couplers to create a distance between the headphone and the scalp

electrodes.

(iii) Use of insert earphones (Etymotic ER-3A) to minimise the effect of the magnetic

field on the electrode by confining to the ear canal.

Insert earphones are associated with additional costs ($498 (Inc 2011)) and the use of

audio couplers and µ-metal shielded headphones increases the complexity of the recording

setup (Cooper & Parker 1981), introducing a delay to the ABR while the sound travels from

the headphone through the audio coupler to the tympanic membrane. An alternative is

to make use of cost effective and less complicated audio transducers that produce artifacts

with little or no impact on early components of the ABR, especially wave I.

Equipment, stimulation and acquisition parameters and participants involved for data

collection are presented in section 3.1. These data were collected so that the effect of the

above mentioned drawbacks are minimised according to the resources and time permitted

to conduct this research.

A separate study conducted on the periphers to the main aim of the thesis comparing

results from various types of audio transducers is included in Appendix C. This formulates

a methodology to compare results from these transducers with different orientations and

strengths of magnetic fields, to determine their suitability for use in an ABR study as

substitutes for the more expensive and complicated transducer setups.


Chapter 3

Recording and constructing

synthetic ABR data

To obtain reliable results from an analysis of the extraction methods, fidelity and com-

patibility of ABR data is critical. In analysing the identified parametric modelling and

wavelet methods; simulated data were initially used and then applied on real recorded

ABR data to arrive at conclusions.

Recording of ABRs in practice is non-trivial. It needs careful preparation of the record-

ing setup and the participant. Such methods are discussed in detail in this chapter. Exact

recording parameters of ABR data used in evaluating parametric modelling and wavelets

are also presented.

Use of simulated data avoids the uncertainty of generating the ABR in practical record-

ings and eliminates the influence of physiological and non-physiological artifacts. In addi-

tion simulated data generated with a defined mathematical model will enables comparisons

with future research. This chapter describes the ABR mathematical model and its varia-

tions in generating datasets to evaluate ABR extraction methods.

63

3.1 Recording of ABR data

The recording setup of ABRs should be be done with great care as the small magnitudes

of the ABR could easily be contaminated with potentially larger noise sources within the

subject and in the recording environment. Such sources include; ongoing EEG, myogenic

artifacts, stimulus artifacts, noise of the recording setup and ambient electromagnetic

noise. Of these high frequency noise could contaminate the ABR due to the short time

span ('10 ms). Therefore recording parameters and subject/participant factors were

optimised for maximum suppression of such noise sources. With the help of published

parameters listed in table 2.4 and information gathered from New Handbook of Auditory

Evoked Responses (Hall 2007) the following setup was utilised.

3.1.1 Equipment and parameters

The specific stimulus and acquisition parameters used to record ABR data for the en-

tirety of this thesis is listed in table 3.1. The auditory stimulus was a negative polarity

square pulse with a pulse width of 0.1 ms at a frequency of 21.1 Hz and delivered via a

TelephonicTMTDH-49 headphone. Three electrodes were utilised, located at the Interna-

tional 10-20 sites of Cz, Fpz, and A1. Disposable, self-adhesive electrodes (3MTM) were

used at Fpz and A1 (where clear access to the scalp was available). At Cz, a domed

electrode was used with viscous electrode paste to provide attachment and electrical con-

ductivity. All the electrodes were silver/silver chloride to achieve comparable surface

impedances. The scalp was prepared so that the inter-electrode impedances were below

5 kΩ.

The specific stimulus and acquisition parameters used to record ABR data for the

entirety of this thesis is listed in table 3.1. The auditory stimulus was a negative polarity

square pulse with a pulse width of 0.1 ms at a frequency of 21.1 Hz and delivered via a

TelephonicTMTDH-49 headphone. A conducting gel-injected disk electrode was used at

Cz and 3MTMdisposable electrodes were used at A1 and Fpz locations. All the electrodes

had silver chloride surfaces to achieve comparable surface impedances. The scalp was

prepared to keep the inter-electrode impedances below 5 kΩ.

Recording and constructing synthetic ABR data 64

The Recording setup consisted of Dual Bio Amp/Stimulator, PowerLab amplifiers

and Chart-5 software produced by ADInstruments (Sydney, Australia). The Dual Bio

Amp/Simulator was used as the main amplifier which is accurate to ±1% of the gain of

100k in an amplification range of ±5 µV. The specified RMS noise is 1.3 µV within the

bandwidth of 0.1 Hz to 5 kHz. This value was reconfirmed in the recording environment

to be 1.6 µV from the amplifier noise recorded with the leads short-circuited (refer Fig-

ure 3.10). Such a noise profile is characteristic to any amplifier affected by thermal and

Johnson noise. The PowerLab amplifier was used as the ADC with a resolution of 16

bits. Any unrelated equipment was turned off (to avoid unwanted electrical or magnetic

fields) and the subject was kept at a distance to the recording equipment to reduce any

Parameter Setting

Stimulus parameters

Transducer TDH-49pType Click (square wave)Pulse width 0.1 msPolarity NegativeFrequency 21.1 HzIntensity 10-75 dB nHLRepetitions 1024Mode MonauralMasking nonAcquisition parameters

Electrode montageNon-inverting CzInverting A1Ground FpzElectrode material AgClInter-electrode impedance <5 kΩFilteringHigh-pass 100 HzLow-pass 3 kHzAmplification 100000Sampling rate 40 kHzAnalysis time 10 msPre-stimulus interval 1 ms

Table 3.1: Finalised parameters for the data collection for the main study.


interfering field.

The data were sampled at a frequency of 40 kHz and an artifact rejection process was

performed within the window of interest, so that amplitudes that exceeded a threshold

of 25 µV were excluded from further analysis. The retained epochs were then band-

pass filtered between 100-3000 Hz with a 3rd order Butterworth filter using a zero-phase

shifting method (Oppenheim & Schafer 1999). A low cut-off frequency of 100 Hz as

opposed to 30 Hz (seen in table 2.4) was chosen in order to minimize the effect of noise

from ongoing EEG and myogenic artifacts (Corona-Strauss et al. 2010b, Rushaidin et al.

2009, Petoe, Bradley & Wilson 2010). The zero-phase shifting filter was specifically used

here to preserve the latencies of the ABR waves. The ABR is convolved in both the

forward and backward directions to regain the phase shift created when filtered only in one

direction. This operation doubles the filter order, leading to additional computation but

with an added advantage of retaining phase characteristics. Participants were stimulated

with sound intensities ranging from 10-75 dB nHL at intervals of 5 dB. Such a range of

stimulation enabled construction of the L-I curve of ABR waves to performance evaluate

latency tracking of extraction methods.

Custom written scripts were used for offline analysis using MATLABTMproduced by

MathWorks (MATLAB 2008). These scripts are attached in Appendix D.

Stimulus artifact

As a result of the magnetic field generated in the audio transducer at the time of stim-

ulus delivery, an artifact is present when using with TDH-49 headphones. The observed

stimulus artifact at the onset of the auditory stimulation (t = 0 ms) is shown in figure 3.1.

The critical observation is the time duration of the stimulus artifact, which appears to ter-

minate well before the wave I suggesting minimum or no effect from the stimulus artifact

on ABR wave features. Therefore, to avoid such stimulus artifacts, we truncated the ABR

time window to 1-10 ms. Such time window avoided false positives in the artifact rejection

process explained in section 3.1.1. The reader is referred to a more detailed study on the

stimulus artifact attached in Appendix C if further information is required. In summary,

it states that the average stimulus artifact end time is 0.54 ms and the average latency of


Figure 3.1: An ABR with a stimulus artifact at t=0 ms (De Silva & Schier 2009). It is evident that thereis no effect on wave I due to the stimulus artifact.

wave I is 1.62 ms (SD=0.12).

3.1.2 Participant details

ABRs were recorded from 8 normal hearing participants (4 males and 4 females) in an

age range from 24 to 34 years (mean=26.7, SD=2.6). Participants were rested between

the stimulation of each intensity and were asked if they were feeling comfortable to avoid

variation in the ABR due to auditory fatigue. The Swinburne University Human Ex-

perimentation Ethics Committee approved the data collection, and each participant gave

written informed consent in accordance with these requirements. The official ethics ap-

proval details are attached in Appendix A. A visualization of the recording setup is shown

in figure 3.2. The photograph was included with the full consent the participant.

3.1.3 MTA and statistically significant SNR

The ensemble of epochs required to arrive at an ABR depends upon the underlying noise

contributed by electrical and physiological activity. Given perfect conditions viz. quiet

environment, calm and normal-hearing participant and high stimulus intensity, only a

small number of sweeps (as few as 100-200) are sufficient. This contrasts with imperfect

conditions in practice such as restless participant (e.g. infants) with a hearing impairment,

or low stimulus intensities which require of the order of thousands of sweeps (Strauss


Figure 3.2: Recording setup with electrodes placed on the scalp and TDH-49 headphones are worn by theparticipant. The photograph was included with the full consent the participant.

et al. 2004, Shangkai & Loew 1986, Wilson 2004, Bradley &Wilson 2004, Stuart et al. 1996,

Hall 2007). The size of such ensembles, in clinical practice are determined by calculating

the single point F ratio (Fsp). The MTA process is terminated when the value of Fsp

reaches 3.1 (Elberling & Don 1984). That is, when the value of Fsp ≥ 3.1 the probability

of arriving at a signal contaminated with noise is 1% (false positive).

Definition of Fsp

The Fsp is defined as the ratio between the variance of the averaged ABR and the average

variance of a single point across the ensemble of ABRs. The mathematical interpretation

is as follows:

Fsp =V AR(ABRi)

V AR(ABRk)(3.1)

Here, the variance of the averaged ABR is defined as V AR(ABRi) =

400∑

k=1

ABRi

2(k)

400 , where

k is the number of sample points in the ABR derived by averaging i number of epochs

(ABRi). The average variance of the single point is defined as V AR(ABRk) =

N∑

i=1

ABRi2(240)

N

such that the variance of the single point ABRk is determined by k= 240th a single point

(which corresponds to wave V).

To avoid the outliers of Fsp values due to highly variable physiological noise (Ozdamar

& Delgado 1996), the property of linearity of Fsp against the number of averaged epochs


was used to approximate a linear trend with a robust linear regression method using

iteratively re-weighted least-squares (also known as the Welsch approximation) (Holland

& Welsch 1977). In other words, a statistically significant ABR was deemed to have

achieved when the Welsch approximated curve reached the threshold of Fsp = 3.1.

Application of Fsp method to the artifact rejected ensemble of epochs from all the

participants involved in this study revealed that the number of epochs required in average

to be 968 (SD = 36). The closest power of 2 led to setting the ensemble of epochs to 1024

given the limitations of the block size of CSTD since it is possible to have only combinations

of 2x where x ∈ Z+. However, more justification is provided below for the validity of this

choice in all conditions pertaining to this study. An example of an ABR where the Fsp

value is not sufficient for a statistical significant ABR is in figure 3.3. An extrapolation of

Welsch approximation suggests the threshold is reached at i = 1238th epoch. However, a

large variation of the averaged ABR cannot be expected between ensembles of 1024 and

1238 as the correlation coefficient of progressive averages compared to the MTA of 1024 in

figure 3.3 suggests saturation after a MTA of approximately 500. This therefore justifies

an ABR at a MTA of 1024 epochs specific to the experimental setup of this thesis, and is

closely related to clinically acceptable standards. Therefore, all the grand averaged ABRs

in this thesis are derived from a MTA of 1024.

3.1.4 Data organisation

A fully featured grand averaged ABR template was generated using a MTA of 1024 epochs

recorded at 55 dB nHL. Out of 1024 epochs collected at each sound intensity level, ‘block

sizes’ of 256, 128, 64, 32, 16 and 8 epochs were tested for rapid extraction. A total of 769

ABRs were extracted for each block size at a single sound intensity level with a sliding

window of length corresponding to the block size. These blocks were processed with ARX

and wavelet methods to arrive at a rapid extraction system.

3.1.5 The template

A fully featured reference ABR template is mandatory to;


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. / 0 / 1 2 3 / 4 5 6 7 8 9 5 2 : ; <= >?@A BCCDE FGH BIJBDKKH JH DIG Fsp of the ABR

Welsch approx

Correlation coefficient

Fsp threshold

Figure 3.3: A worst-case scenario of the Fsp curve derived fromMTA of a series of ABR epochs. TheWelschapproximated robust linear trend suggests 1238 epochs are required to reach a statistically significant SNR.However, the correlation coefficient suggests minimal variations occur between a MTA of 1024 and 1238.Therefore, all the grand averaged ABRs in this thesis are derived from a MTA of 1024.

1. Provide a morphologically accurate template for ARX, REPE, CTMC and TWMC

methods.

2. Compare filtered/estimated ABRs from ARX and wavelet methods.

A moving time average of 1024 sweeps of ABR recorded at 55 dB nHL (shown in figure 3.4)

was used as the template throughout this thesis as the important features wave I, III and

V are easily identified in this ABR. In addition, less significant wave II and wave VI can

also be identified. The absence of wave IV, which normally appears before wave V could

be due to the associated noise or a characteristic of the participant (Kjaer 1980). A sound

intensity level of 55 dB nHL is used here because;

1. It is greater than threshold to eliminate non-responses due to threshold variation.

2. It is in the mid range of the L-I curve, which provides a balance when evaluating

tracking latency.

3. Stimulating at this sound intensity level were more comfortable for the participants

compared to stimulating at higher levels.


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; 7 M 2 N M 6 OP Q?EHG RS DT RUV W X Y Z [

W X Y Z \W X Y Z [ [ [W X Y Z [ [ W X Y Z \ [Figure 3.4: The reference ABR template used in wavelet denoising methods. Generated with MTA of 1024sweeps at 55 dB nHL showing main wave features I, III and V and additional features wave II and VI.

3.2 Latency-intensity and amplitude-intensity curves

Inducing systematic variations of ABR features are critical for the outcome of this thesis.

Such variations could be artificially induced by varying the stimulus intensity, thereby

producing latency-intensity and amplitude-intensity curves (Vannier et al. 2001). Varia-

tions produced in these controlled environments are ideal for the validation of algorithms

due to the predictable nature of the outcome.

The curves plotted in figure 3.5 represent the average of 8 participants with each ABR

at a given intensity derived by a MTA of 1024 epochs. Then the peaks, wave I, III and V

were manually determined by an independent observer, with around 25 years of experience

with evaluation of EEG and EP signals. The method was to visually inspect the waveforms

for evidence of peaks at the approximate latency, from which amplitude and latency were

calculated.

The curves clearly indicate the characteristic reduction in latency and increase in

amplitude with the increase in stimulus intensity. The critical observation however, is

the consistency and the reduced variability of the latency-intensity (L-I) curve compared

to the amplitude-intensity curve, which supports the use of the L-I curve to verify the


!

(a) Latency intensity curves

!" #$

(b) Amplitude intensity curves

Figure 3.5: Latency and amplitude intensity curves derived from recorded data. These curves were derivedusing ABRs generated from 8 participants with the parameters given in table 3.1. Error bars representstandard error among participants.


variation tracking ability of the algorithms developed in Chapters 4 and 5.

3.2.1 Compatibility of the L-I curve model

The validity of the L-I curves were tested by comparing the L-I curve of the most prminent

wave V, with the theoretical model in (3.2) reported by Picton et al. (1981) (where L is

the wave V latency in ms and I is the stimulus intensity in dB). The deviation of this

curve is usually about 0.2 ms at 70 dB and 0.3 ms at 30 dB.

log10(L) = −0.0025I + 0.924 (3.2)

Figure 3.6 illustrates the comparative plots of experimental and theoretical wave V L-I

curves. It is apparent that the derived curve closely follows the theoretical model, and

is well within one standard deviation confidence limits. This it therefore validates the

experimental data recorded in this study. This L-I curve of wave V was then considered

to be the benchmark for later comparisons of the ARX and wavelet estimated L-I curves

was considered acceptable.

] ^ _ ^ ` ^ a ^ b ^ c ^ d ^]_ à bcdef] ^

g h i j k l j m n j o l m p q k r j s t uv wx yz| ~ n h n m l n l n k h j k n n

Figure 3.6: The theoretical and the derived L-I curve of wave V. The curve derived by the grand averageof experimental data follows the theoretical curve and well within the theoretical range.


3.3 Synthetic ABR model

The absence of a mathematical model for the ABR and systematic simulation studies

(refer sections 2.2.5, 2.5.2) in the literature gave an impetus to construct an ABR model

and conduct simulation studies. As opposed to using recorded ABR, the presence of the

exact deterministic ABR in simulated data improves the reliability of derived results. The

study conducted for this thesis was intended to achieve the following:

• A well-defined simulation study that is reproducible.

• A comparison of the performance of ARX model based and wavelet based extraction

methods.

In general, such a model of the ABR will enable researchers to validate and compare novel

extraction methods based on a universal benchmark.

3.3.1 Construction of the ABR model

The introduced simulated ABR model has three prominent features with similar mor-

phological characteristics to the ABR waves I, III and V: having approximately similar

latencies and amplitudes. These features of the ABR are the most dominant and are

clinically significance compared to other waves (II, IV, VI and VII). The synthetic ABR

u(k) expressed in (3.3).

u(k) =

aIsinc[0.13π(4k − 8 + lI)] +

aIIIsinc[0.13π(4k − 16 + lIII)]+

aV sinc[0.13π(4k − 24 + lV )]

(3.3)

Here, 0 ≤ k ≤ 10 ms with 400 data points to represent a typical ABR recorded at a

sampling frequency of 40 kHz. The three sinc functions represent ABR waves I, III and

V. The terms lI , lIII , lV define the latency of wave I, III and V respectively and are set

to 2, 4 and 6 ms at lI = lIII = lV = 0. The terms aI , aIII , aV define the amplitudes

of wave I, III and V respectively and are set to aI = 0.25, aIII = 0.5, aV = 1 to mimic

morphological characteristics. The synthetic ABR model with an unperturbed latency

(lI = lIII = lV = 0) is shown in figure 3.7a and the comparable recorded real ABR (at 55


dB nHL) is shown in figure 3.7b.

The ABR model formulated in (3.3) possess following favourable characteristics.

• Morphological similarities with regards to wave I, III and V.

• Ability to derive systematic variations of amplitude and latency of individual waves.

• Comparable spectral characteristics to that of a real ABR (as detailed in figure 3.8).

Both the ARX modelling and wavelet methods will be subjected to datasets derived from

this model for an initial feasibility study before applying them to real ABRs.

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± ² ³ ´ µ ¶ · ¸ ¹ ± º» º ¼ ²ºº ¼ ²º ¼ ´º ¼ ¶º ¼ ¸½ ¾ ¿ À Á ¿ Â ÃÄ ÅÆÇÈÉ ÊË ÌÍ µ

ÎÏ Ð Ñ Ò Ó Ô Ð Ñ Ò Ó ÕÐ Ñ Ò Ó Ô Ô Ô(b) Actual ABR recorded at 55 dB nHL

Figure 3.7: Synthetic and the Real ABR templates. These possess comparable features in terms of latencyand amplitude for ABR waves I, III and V.

3.3.2 Construction of synthetic datasets

To assess the full functionality of the ARX and wavelet methods, appropriate datasets were

created using the ABR defined in (3.3). Two types of datasets were created from u(k) to

specifically analyse: 1) Denoising performance and 2) Variation tracking performance.

(i) With no latency variations to evaluate denoising capacity. This dataset was

created with l = 0 using (3.3) to assess the improvement in SNR for ARX and

wavelet methods. The simulated dataset is shown in figure 3.9a as a surface plot. It

consist 60 s of recording assuming a stimulus frequency of 20 Hz.


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Figure 3.8: Comparison spectra of the ABR model and the real ABR template derived from MTA of 1024epochs. The characteristic frequencies at 100, 500 and 900 Hz are evident in the ABR model spectrumsuggesting spectrum compatibility.

(ii) With periodic (modulated) latency variations to evaluate latency tracking. 12

datasets representing 60 s of a recording were created with a combination of aL= 1,

1.5, 2 ms and fL = 0.025, 0.05, 0.1, 1 Hz. A visualisation of 3 datasets are shown in

figure 3.9b, 3.9c and 3.9d with [aL, fL] = [1, 1], [1.5, 0.05] and [2, 0.025] respectively.


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toassesstheden

oisingcapability(b)Datasetwitha

maxim

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latency

variationof1msatafrequen

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variationof1.5msatafrequen

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withamaxim

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variationof2msatafrequen

cyof0.025Hz.


3.3.3 Adding noise to simulated datasets

In the conventional scalp recorded EP model (refer (2.2)), noise n(k) is assumed to rep-

resent Gaussian white noise within the bandwidth of interest (100-3000 Hz). Therefore,

repeated averaging of a large number of sweeps removes such random noise and retains

the deterministic ABR. However, it is important to characterise actual noise in the ABR

recording and add noise of similar characteristics to the synthetic datasets.

In reality, the spectrum of n(k) is dominated by ongoing EEG. While, in conditions

other than awake, EEG spectrum is skewed (Hauri, Orr & Company 1982), within the

framework of this thesis and in clinical studies pertaining to the ABR, EEG is predom-

inantly recorded while the participant is awake. Therefore it is reasonable to assume

the spectrum of ongoing EEG is less contaminated with large amplitude, low frequency

components, thereby reducing the skewness.

The EEG spectral power while awake, lies below 100 Hz (gamma 25-100 Hz), therefore

is extraneous to the ABR bandwidth (100-3000 Hz). The equipment noise (mainly from

the recording equipment used for the data collection for the thesis) was measured to be

white as shown in figure 3.10 confirming the conventional assumption. Also the explicit

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Figure 3.10: Spectra of EEG, EEG+ABR and equipment noise compared to Gaussian white noise suggestthat Equipment noise could be approximated by Gaussian white noise.


band-pass filtering between 100-3000 Hz of scalp recorded EEG+ABR used in this thesis

eliminates the contamination from low frequency artifacts from delta to gamma or any

myogenic or ocular artefacts (Hall 2007, Cerutti et al. 1988). As is evident, the EEG

spectrum is smooth and contains no identifiable spectral peaks. Any deviation from this

could be due to the filter rather than characteristics of the signal. Simulated data in

the study assumes a flat spectrum revealing the upper bound effects of ARX modelling.

Deviations from such a flat spectrum would yield worse results.

Based on these arguments, the synthetic ABR datasets had Gaussian white noise added

with the necessary power for the simulation studies involving ARX and wavelet studies.

Adding coloured noise could be conducted as a separate study to suit patient conditions

other than awake or with other artefacts, such as myogenic and ocular potentials.


Chapter 4

Effectiveness of ARX modelling in

rapid extraction of the ABR

Performance evaluation of two parametric modelling methods; autoregressive model with

an exogenous input (ARX) and its extension for robust evoked potential estimator (REPE)

is presented in this chapter in relation to rapid extraction of ABRs. According to the

review in section 2.2, ARX modelling is a frequently used single sweep extraction method

of middle and late EP components. As an extension, this chapter looks into the feasibility

of using ARX modelling to extract early ABR. Initially, a simulation study was performed

for better evaluation of the ARX methodology applied to the new signal domain. Recorded

real ABRs were then used to verify the result of the simulation study.

It was found that ARX and REPE methods of rapid extraction were not suitable to

denoise the ABR due to the comparatively low SNR to that of middle and late EPs.

Performance of variation tracking revealed the limited scope of ARX based extraction

methods in ABRs.

80

4.1 Introduction to the simulation study

Analysing the performance of the ARX and REPE methods in extracting single sweeps

of simulated EPs is of critical importance before these methods are used in a new domain

of physiological signals. Also, the following shortcomings identified in previous studies

prompted systematic adaptation of ARX algorithms (these points are discussed in detail

in section 2.2.5).

• Reproducibility of the reference signal (grand average)

• Ambiguity of the selection criteria of model parameters

• Limited variations induced in the EP

ARX model in z-domain is represented as S(z) = [B(z)/A(z)]U(z) + [1/A(z)]E(z),

where S(z) is the single/limited averaged sweep, U(z) is the reference/template signal,

E(z) is ongoing EEG noise assumed to be white and A(z) and B(z) are the trans-

formed AR and MA filter coefficients. After generating the filter coefficients with a batch

least square method, the estimated single/limited averaged sweep is derived with S(z) =

[B(z)/A(z)]U(z). Based on the fact that, excitation of the model using a signal with a

wide bandwidth improves its estimation, REPE pre-whiten the input to the basic ARX

model. REPE is defined in the z-domain as S(z) = [B(z)C(z)/A(z)]U(z) + [1/A(z)]E(z),

where C(z) is the converted coefficients of the pre-whitening filter. The REPE estimated

single/limited averaged sweep is derived with S(z) = [B(z)C(z)/A(z)]U(z). The reader is

referred to section 2.2.2 and 2.2.4 for further information on the derivation of ARX and

REPE methods.

4.2 Methods

4.2.1 Simulation study domain and extrapolation

The absence of well defined simulation study in literature gave an impetus to conduct such

a study. In summary, ARX modelling based extraction methods were used to extract a

synthesised ABR embedded in noise. This systematic simulation study described in this

thesis aims to achieve the following:

ARX modelling in rapid extraction of the ABR 81

• A well defined simulation study which is reproducible

• A comparison of the performance of the conventional ARX model and its extension

REPE adjusting few parameters of their original studies to prevent ambiguity

• An investigation of the noise reduction ability of the two modelling methods

• An investigation of the time-scale variation tracking ability of the two modelling

methods

The study presented in this chapter is limited to extract a single sweep si(k) using

a template si(k) derived from a MTA of 100 sweeps of simulated ABRs. A range of

SNRs have been used to evaluate the resistance of these methods to noise. In this way,

it is possible to determine the feasibility of single sweep extraction of an ABR. However,

modifying this method to extract an averaged ensemble of sweeps instead of a single sweep

is trivial, and could be performed as a further study if required.

With constant epoch ensembles for the template/reference u(k) and output y(k) with

predefined SNRs, this study expected to determine the range of amplitude (aL) and the

frequency (fL) of latency variations that can be tracked using ARX and REPE methods.

The use of known variations in simulated data makes the adaptation of these methods to

real ABR applications straight forward. The reader is referred to section 3.3 for detailed

information on these datasets.

4.2.2 Simulated reference ABR and datasets

The mathematically modeled reference ABR used in this study (refer (3.3)) consisted of

three clinically significant features with similar morphological characteristics to the real

ABR waves I, III and V having approximately the same latencies and amplitudes (shown

in figure 3.7a).

The datasets derived from this ABR aims at: 1) Performance evaluation of denoising

2) Performance evaluation of time-scale (latency) variation tracking. In summary, one

dataset was created with a constant latency (l = 0) to evaluate the improvement in SNR

for ARX and REPE methods and another 12 datasets were created with a systematic

latency shift combination of aL= 1, 1.5, 2 ms and fL = 0.025, 0.05, 0.1, 1 Hz to evaluate


the latency tracking of ARX and REPE methods. They consist of 60 s of recordings

assuming a stimulus frequency of 20 Hz.

The reader is referred to section 3.3.2 for a detailed description of these datasets.

4.2.3 Acquisition of real ABR data

Expanding the analysis and to confirm the outcome of the simulation study, a similar

methodology was applied to real ABR data from a participant. Stimulus and acquisition

parameters in table 3.1 were used on a healthy female participant of age 24 for ABR

data acquisition. In order to construct the L-I curve, the participant was stimulated with

intensities ranging from 10-75 dB nHL at intervals of 5 dB. The reader is referred to

section 3.1 for a comprehensive description of these stimulus and acquisition parameters.

Output to the model y(k) was tested with a single sweep, MTA of block sizes 32, 128

and 256. To reduce the complexity of the analysis, the exogenous input to the model u(k)

was fixed to a fully featured ABR template generated using MTA of 1024 epochs recorded

at 55 dB nHL (refer section 3.1.5 for more details).

4.2.4 Predetermined models

To produce a realistic set of simulated EEG data y(k) (which includes the ABRs and

the noise associated with ongoing EEG), predetermined filter models with physiologically

plausible responses were constructed. These models are described in the following two

sections.

ARX(p, q, d) model

Arbitrary model orders were sufficient for the simulation study provided that the ABR

u(k) retains its features after the filtering process. Since an ARX model has not been

constructed for the ABR before, similar applications related to middle and late evoked

potentials prompted us to use model parameters derived in Cerutti et al. (1987). Ac-

cordingly, the predefined model orders chosen for this simulation study were p = 6 and

q = 7 ARX(6,7,0) while the delay d was made to zero because the application of input

and output data was performed at the same time. The coefficients of this predefined ARX


model were set to form a low pass filter which preserved the morphology of the reference

signal u(k) ensuring the additive noise is meaningfully incorporated into the model for the

purposes of extraction. The transfer function satisfying these conditions is expressed in

(4.1). Figure 4.1a, 4.1b and 4.1c shows the pole-zero plot, the magnitude response and the

impulse response respectively depicting the stability of the transfer function. The ABR

s(k) derived by filtering synthetic reference signal u(k) with the transfer function in (4.1)

is shown in figure 4.1d illustrating major peaks present in s(k) similar to u(k). The power

s(k) was maintained at the same level as u(k) to normalise any gains associated with the

predefined transfer function. The amount of filtered noise n(k) was maintained such that

the initial SNR is at -10 dB in between s(k) and n(k) 1.

B(z)

A(z)=z−1 − 3.3z−2 + 4.4z−3 − 2.2z−4 + 2.7z−5 − 2.5z−7 + z−8

1− 2.9z−1 + 3.5z−2 − 2.4z−3 + z−4 − 0.3z−5 + 0.1z−6(4.1)

REPE(p, q, r, d)

To improve the resistance to noise of the ARX model, the improved REPE is used to

estimate the ABR. Model orders were set to p = 6, q = 7, r = 8 and d = 0 REPE(6,7,8,0)

considering the previous ARX(6,7,0) model and the work of Lange & Inbar (1996). The

choice of these model orders are justified for the similar reason as in the ARX model

suggesting that, even though arbitrary model orders are sufficient for the simulation study,

the use of orders derived from a physiological signal improves the validity. A pre-whitened

template was derived by adding noise to the template with an appropriate inverse filter

C(z) before subjecting to the ARX process. The underlying reason for the pre-whitening

process is to improve the excitation of the model which is then able to generate a more

accurate set of coefficients. The pre-whitening was performed using an autoregressive

model of order AR(8) (Lange & Inbar 1996) with the transfer function expressed in (2.8)

which was then used as the exogenous input to the ARX model of orders ARX(6,7,0). The

1This section of the thesis concentrate on the degree of accuracy of the ARX model in identifyingpredefined model parameters, therefore the expected outcome is a set of poles and zeros in the vicinity ofpredefined. Use of a low SNR e.g. -30 dB would produce dispersed poles and zeros and will not be able tojudge the model performance. Based on this fact, use of -30 dB will not yield useful information whereas-10 dB of noise could differentiate the performance. The accuracy of the models at -30 dB is indirectlymeasured in figure 4.7.


÷ ø ÷ ù ú û ù ù ú û ø÷ ø÷ ù ú ûùù ú ûø üý þ ÿ

(a) (b)

(c)

(d)

Figure 4.1: Characteristics of the transfer function of the ARX model. (a) Pole-zero plot of the transferfunction (b) Magnitude plot (c) Impulse response of the transfer function (d) Filtered s(k) and referenceu(k) showing preserved features in s(k).


transfer function B(z)/A(z) in REPE was set according to (4.2) to obtain comparable

results or both REPE and ARX.

C(z) = 1− 0.5z−1 − 0.4z−2 − 0.2z−3 − 0.1z−4 − 0.2z−5 + 0.1z−6 + 0.2z−7 + 0.2z−8 (4.2)

Figure 4.2a, 4.2b and 4.2c shows the pole-zero plot, the magnitude response and the

impulse response respectively depicting the properties of the AR(8) model. The effect of

pre-whitening process is evident in figure 4.2d with power spectral density estimations of

the template u(k) and its pre-whitened version w(k). The power of w(k) was maintained

at the same level of u(k) to normalise any gains associated with the predefined transfer

function. The flat band for w(k) results in an even distribution of frequency components,

providing a better excitation at ARX model (Lange & Inbar 1996).


! ! ! ! " # $ % &

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(c) (d)

Figure 4.2: Characteristics of the transfer function of the REPE (a) Pole-zero plot (b) Magnitude plot (c)Impulse response of the transfer function 1/C(z) (d) Effect of pre-whitening the template u(k) resultingin flat spectrum for w(k)


4.3 Results

4.3.1 The efficacy of identifying the predefined models

Quantifying the performance of ARX and REPE methods in extracting single sweeps of

simulated EPs with controlled noise addition is of critical importance before these methods

are applied in real world applications where access to noise free EPs is not possible. On

this basis, we compared the poles and zeros of the estimated model with the predefined

counterparts. With the assumption of similarity between the predefined and the estimated

models, predefined model orders were set to ARX(6,7,0) and REPE(6,7,8,0). The dataset

with a constant latency was then used for this test as illustrated in figure 3.9a.

ARX model

Figure 4.3 shows the plots of poles and zeros of the predefined and estimated models.

These models were obtained by a dataset with an initial SNR of -10 dB subject to

(2.4). Coefficients of the model were derived using a Batch Least Squares algorithm which

minimises the quadratic error function between the estimated and empirical ABR (Cerutti

et al. 1987). For each sweep in the dataset (1200 sweeps), an ARX model was created

and the resulting poles and zeros are shown as clouds. It suggests that the identification

of poles (figure 4.3a) in the estimated model have approached to that of predefined but

locations of estimated zeros (figure 4.3b) have a noticeable offset.

REPE model The estimated model parameters for the pre-whitening process shown in

figure 4.4b suggest an accurate estimation of the predefined AR(8) process. The estimated

ARX process in REPE does produce similar characteristics to that of the pure ARX model.

Figure 4.4b suggests an accurate estimation of poles in contrast, figure 4.4c suggests zeros

have been estimated with a systematic offset. While poles have converged to certain

positions (compared to the positioning of the zeros of the ARX model) these do not

necessarily correspond to the predefined values.

1This section concentrates on the degree of accuracy of the ARX model in identifying predefined modelparameters. The expected outcome is a set of estimated poles and zeros in the vicinity of relevant predefinedpoles and zeros. Use of a low SNR i.e. -30 dB, would produce dispersed poles and zeros and will not be ableto assess the model performance. Given this fact, use of such low SNRs will not yield useful information,where as a SNR of -10 dB could enable assessing the model performance.


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3 45 67(a)

) * + , ) * ) - + , - - + , * * + ,) * + ,) *) - + ,-- + ,** + ,. / 0 1 2

3 45 67(b)

Figure 4.3: Estimated Pole (x) and Zero (o) plots of the ARX model. (a) Pole plot of predefined andestimated models (b) Zero plot of predefined and estimated models. Estimated poles have converged topredefined values but not zeros.

4.3.2 Estimation of model orders

A range of model orders from 1 to 10 for p, q and r with a zero delay for d were tested on

each sweep of the test dataset (with a constant latency refer figure 3.9a) using the final

prediction error (FPE) (2.5) to find the optimum model order. The consistent asymptotic

behaviour of FPE at each model led us to set a criterion to automatically extract the

optimum model order as the first local minimum. Even though there are local minima at

higher model orders, the difference of FPE is negligible compared to lower model orders.

This is further clarified in following sections, separately for ARX and REPE models.

ARX(p, q, d) model

The FPE values for all model order combinations applied on a typical single sweep are

shown in figure 4.5a. The general observation is a sharp drop in FPE at low AR(p) orders

and asymptotic at higher orders which is a typical scenario seen in system identification

based on ARX modelling. In contrast, FPE values of MA(q) orders have a small variation.

A closer observation of the extracted FPE curves in figure 4.5b of AR(p) at MA(4) confirms

prior observation but the zoomed in version of the same curve indicates a local minimum

at AR(4). A similar local minimum could be observed at MA(4) with the extracted FPE

curve in figure 4.5c of MA(q) at AR(4). This trend could be seen in other model order


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3 45 67(a)

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3 45 67(b)

) * + , ) * ) - + , - - + , * * + ,) * + ,) *) - + ,-- + ,** + ,. / 0 1 2

3 45 67(c)

Figure 4.4: Estimated Pole (x) and Zero (o) plots of the REPE. (a) Pole plot of the predefined andestimated AR(8) pre-whitening model. (b) Pole plot of the predefined and estimated ARX(6,7,0) modelin the REPE. (c) Zero plot of the predefined and estimated ARX(6,7,0) model in the REPE.


combinations and sweeps, thus was used to automatically extract the optimum model

order.

Based on the above mentioned observation, the following algorithm was developed to

detect the optimum order:

For a given single sweep with a MA(q) order, the optimum AR(p) order was detected

by locating the first local minimum in AR(p) curve. Likewise, the mode of 10 optimum

AR(p) for a single sweep was considered to be the optimum orders for that sweep. The

same procedure was followed to detect the optimum MA(q) order for that sweep.

These criteria were applied to all the sweeps in the dataset and the resulting histogram

of optimum model pairs is shown in figure 4.5d. This suggests the most frequently identi-

fied model pairs are AR(4) and MA(4). Therefore for subsequent evaluation of ARX rapid

extraction, the empirical model was fixed to ARX(4,4,0).

Similar criterion of FPE was then used to determine the optimum, empirical model

orders of the REPE method. These details are reported in the following section.

REPE(p, q, r, d)

The FPE values for the pre-whitening AR(r) model is shown in figure 4.6a. Even though

it seems to be asymptotic at higher model orders, a zoomed in version of the same curve

indicates a minimum at AR(8) and is consistent with the optimum model order detection

criteria mentioned earlier. Repeated measures concluded a model order of AR(8) was

optimum for the pre-whitening model.

For a single sweep, FPE results for the estimation of ARX(p, q, d) in the REPE is

shown in figure 4.6b suggesting a similar behaviour to that of previous ARX model. A

closer observation of an individual FPE curve of all AR(p) at MA(3) shown in figure 4.6c

suggests an asymptotic nature of FPE after AR(4). But a zoomed in version of the same

curve suggests that there exist a local minimum at AR(4). This is consistent with the

optimum model order detection criteria. A closer look at individual MA(p, q, d) curve

at AR(4) in figure 4.6d suggests a gradual reduction in FPE with several local minima.

Therefore the optimum MA(p, q, d) order was detected by locating the first local minimum

in MA(p, q, d) curve in accordance with the optimum model order detection criteria. The


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?@A < . 0 2 (c)

* , * - *,* --* - - -< . 0 > 2; < 0 = 2

(d)

Figure 4.5: Results of the fixed model order determination of the ARX model. (a) Surface plot of FPEvalues for model order combinations of p and q between 1 and 10 applied on a typical single sweep. (b)Extracted FPE curves from (a) at MA(4) showing saturation at MA(4) and the zoomed in version of itshows the first local minimum at AR(4). (c) Extracted FPE curves from (a) at AR(4) showing the firstlocal minimum at MA(4). (d) Histogram of the optimum model order pairs derived from all the sweeps inthe dataset suggests the optimum estimated model to be ARX(4,4,0).


resultant histogram of the optimum model pairs obtained by applying this criterion to all

sweeps in the dataset shown in figure 4.6e suggests an optimum model orders of AR(4)

and MA(3). Therefore for subsequent evaluation of REPE rapid extraction, the empirical

model was fixed to REPE(4,3,8,0).

4.3.3 Comparison of model performance

Performance of the two models is evaluated using two methods. One of these is the pre-

viously reported improvement in SNR (dB) = 10log10(E[n2(k)]/E[(s(k)− s(k))2]) which

indicates ratio of initial noise n(k) to the final residual noise between the estimated signal

s(k) and the original signal s(k) (Lange & Inbar 1996). The other method is by comparing

latency and amplitude of the estimated wave V with the simulated wave V which is of

clinical importance.

Improvement in the SNR

The performance of two algorithms were analysed within a range of 10 to -30 dB ini-

tial noise in accordance with (2.9). The figure 4.7 shows the SNR improvement of the

estimated ABR using theoretical ARX(6,7,0), REPE (6,7,8,0) and empirical ARX(4,4,0),

REPE(4,3,8,0) models across 100 responses. It is evident that the REPE shows a superior

performance at low initial SNRs, and ARX has a fairly constant but lower improvement

throughout. These SNR improvement values are comparable with the results reported in

Lange et al. (1996) for MLAEPs (refer figure 2.8). When considering the performance of

the empirical and theoretical models in figure 4.7, a superior performance is evident with

the empirical model over theoretical producing higher SNR improvement values. However,

this measurement considers the overall signal but not a specific feature of it, therefore it

is not able to conclude that the result generated from this method has a clinical signifi-

cance. Therefore the latency and the amplitude of wave V were compared to evaluate the

performance of the empirical and theoretical models.

Latency and amplitude of wave V

Figure 4.8a compares the latency detection of two models with theoretical and empirical


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Figure 4.6: Results of the fixed model order determination of the REPE. (a) FPE curve for AR(r) modelorders and the zoomed in version of it shows the first local minimum at AR(8). (b) Surface plot of FPEvalues for model order combinations of p and p, q, d between 1 and10 applied on a typical single sweep.(c) FPE curve for all AR(p) orders at MA(3) and the zoomed in version of it shows a local minima atAR(4). (d) FPE curve for all MA(p, q, d) orders at AR(4) indicating the local minimum at MA(3). (e)Histogram of the optimum model order pairs derived from all the sweeps in the dataset suggests, theoptimum estimated model to be REPE(4,3,8,0).


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í î ï ð ï ñ ò ó ô õ ö ÷ ø ùúûüý þÿþ

Figure 4.7: The SNR improvement of the estimated ABR. Using theoretical ARX(6,7,0), REPE(6,7,8,0)and empirical ARX(4,4,0), REPE(4,3,8,0) models. Error bars represent standard deviation across 100responses.

model orders. In general ARX estimated sweeps produce a close match to the actual value

with an overall MSE of 0.002 compared to REPE producing a MSE of 0.013. But there

is a considerable deviation with a MSE of 0.006 in REPE from 0 to -15 dB initial SNR

which cannot be seen in ARX estimated latency curve with a MSE of 0.001. Within them,

theoretical model orders ARX(6,7,0) and REPE(6,7,8,0) have close latency values, with a

MSE of 0.002 compared to empirical model orders ARX(4,4,0) and REPE(4,3,8,0) with a

MSE of 0.004. The amplitude variations shown in figure 4.8b indicate a similar behaviour

showing more accurate amplitudes in ARX with a MSE of 0.288 than in REPE with a

MSE of 0.697 even though there is a 0.012 improvement in MSE for REPE at low initial

SNRs. Therefore in general, the variations of amplitude suggest that theoretical model

orders perform superior to the empirical.

On the other hand, when estimating model orders of an unknown signal, the similarity

in the results generated from theoretical and empirical (as shown in figure 4.8) is an

advantage given the fact that the only plausible method of estimation model orders in this


case is by analysing FPE values.

Within the context of this thesis and considering the clinical importance of extracting

EPs, the theoretical model orders of ARX(6,7,0) and REPE(6,7,8,0) were used for further

analysis.

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Figure 4.8: Detection of wave V with empirical and theoretical model orders. (a) and (b) are latency andamplitude of wave V. Standard deviation has an expected increase at low SNRs. It is evident that thecurves derived from theoretical model orders have a closer match to the actual in all the plots. Howeverthe difference of the empirical model orders is not significant.

4.3.4 Estimated single sweep of an ABR

Figures 4.9a and 4.9b show estimated single sweep s(k) using theoretical model orders

in (2.6) for the ARX and (2.8) for the REPE respectively. A simple visual comparison

suggests better morphology (i.e. similar to u) in ARX estimation than in REPE, confirming

the results shown in figure 4.8. In contrast this proves that improvement in SNR at -10 dB

initial SNR shown in figure 4.7 does not depict the actual amplitudes and latencies of ABR

features.


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ss

(b)

Figure 4.9: Single sweep estimated with ARX model and REPE. (a) A single sweep estimated using anARX(6,7,0) model at initial SNR of -10 dB. (b) A single sweep estimated using an REPE(6,7,8,0) modelat initial SNR of -10 dB. u(k) - derived reference ABR, S - deterministic ABR, s(k) - estimated ABR.Having a close u(k) to S with the ARX model provides the best result compared to REPE.


4.3.5 Tracking variations of a single sweep

It is critical to accurately track variations of the EP (in terms of latency and amplitude)

when monitoring or diagnosing the physiological status of a patient. The importance of

the accurate variation tracking highlights with the inclusion of a template in the ARX

based modelling methods. To examine possible limitations, latency variations of single

sweeps were estimated using ARX(6,7,0) model and REPE(6,7,8,0) and compared to that

of the MTA. The most prominent wave V was tracked in datasets.

Single sweep variations estimated using ARX modelling

The latency tracking capability of ARX estimated ABR is shown for a minimal variation

of 1 ms in figure 4.10 and maximum variation of 2 ms in figure 4.11 at different SNRs from

0 dB to -20 dB. The maximum variation was limited to 2 ms considering the variation of

the L-I curve. Also, the extracted wave V latency of the conventional MTA is also plotted

for comparison purposes. Figure 4.10 suggests that latency tracking is achievable in 0 dB

and -5 dB. They show a clear phase difference in MTA latency at fL = 0.05 Hz and 0.1 Hz

and a flat line in 1 Hz. But the ARX estimated latency is closely following the actual

latency variation of the ABR. However, at lower SNRs of -10 dB and -20 dB, latency of

the estimated ABR is not consistent suggesting vulnerability of ARX estimations at low

SNRs. In contrast, figure 4.11 with a latency variation of 2 ms, in general results in poor

tracking. A closer look at the 0 dB plot suggests that latency tracking is reasonable up to

fL = 0.05 Hz but not at either higher frequencies or below SNR of 0 dB.

This visual observation was quantified by calculating the MSE of s(k) and u(k) com-

pared to s(k). With an additional peak-to-peak latency variation of 1.5 ms, the MSE

values are represented in figure 4.12 at different SNRs. Figure 4.12a and 4.12b suggest

peak-to-peak latency variation of up to 1.5 ms produce lower MSEs by the ARX esti-

mation compared to the MTA at all frequencies, and therefore indicates superior latency

tracking performance. However, tracking of peak-to-peak variation of 2 ms from both

ARX estimated and MTA perform similarly with a high MSE, suggesting tracking such

large variations are not possible. Figure 4.12c and 4.12d with lower SNRs, indicates a

deterioration of the latency tracking performance of peak-to-peak variations of 1 ms and


1.5 ms. ARX estimated ABRs have an equal performance to the MTA at a SNR of -10 dB

and worse at -20 dB. Therefore the range of latency variation that could be tracked by

the ARX model are at a higher initial SNR of -5 dB with a maximum latency variation

of 2 ms peak-to-peak at 1 Hz.


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Single sweep variations estimated using REPE

Following similar methodology to that of ARX estimates, figure 4.13 and figure 4.14 illus-

trate the latency tracking capability of REPE(6,7,8,0) at a peak-to-peak latency variation

of 1 ms and 2 ms. Similar to ARX latency tracking, REPE show poor performance to

large variations in latency as can be seen in figure 4.14. A close observation of plots in

figure 4.13 suggests the REPE(6,7,8,0) estimated latency follows the latencies derived by

MTA producing poor tracking performance compared to ARX(6,7,0).


MSE plots in figure 4.15 confirm the poor latency tracking of REPE estimations com-

pared to MTA and also compared to ARX estimations in figure 4.12. Even at 0 dB

(figure 4.15a) estimated latency shows a similar or higher MSE compared to the MTA

derived latency.










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Figure 4.15: MSE values comparing the latency tracking of the REPE estimation and the MTA. At latencyvariations of 1 ms, 1.5 ms, 2 ms. (a), (b), (c) and (d) represent initial SNRs of 0 dB, -5 dB, -10 dB and-20 dB.

4.3.6 Confirmation of simulated results with actual ABRs

Model order determination

Since empirical results derived from REPE were not promising, real ABR data were

applied only to the ARX model.

Complying with the norm when estimating EPs with an ARX model (Jensen et al.

1998, Litvan et al. 2002), a unique fixed model order was determined with respect to

the recorded ABR to generate the L-I curve of wave V. Estimating with a fixed model

order as opposed to estimating model orders for individual epochs is acceptable due to


the minimal variation of orders among epochs and to save the estimation time associated

with calculating those model orders.

Histograms of the optimum model order pairs for each model output block size are

shown figure 4.16. They suggest that the optimum model order combination to be

ARX(3,2,0) with the only exception at a block size of 128 epochs with ARX(3,3,0). The

model order of ARX(3,2,0) was considered to estimate ABRs to derive the L-I curve for

the following reasons:

i difference of one model order has minimal effect at the output

ii the accuracy of model orders are critical at smaller block sizes for a rapid extraction

system

.

Estimation of L-I curves

Plots in figure 4.17 present latency of the wave V of 100 random ABR epochs from each

sound intensity from 10 to 75 B nHL. Randomly selected estimated individual ABRs used

to construct these L-I curves are shown in Appendix E. It is clearly evident that the block

size of the output y(k) has a major effect on the ARX model estimate. As expected,

a converging pattern of the estimated L-I curve could be seen as the number of epochs

included in the average increases. ARX estimated curves approach closer to the grand

average derived curves at a block size of 128 and 256. Another observation is the high

variability at low sound intensity levels even at these block sizes. This is an effect of small

wave V amplitudes at low sound intensities which results in low SNRs in epochs compared

to high sound intensities. The ARX estimated L I curve closely follows from a sound

intensity of 40 dB nHL at a block size of 128 and improves it up to 30 dB nHL at a block

size of 256 (with a small deviation at 35 dB nHL). These results indicate that ARX is not

suitable to extract ABRs at low stimulus intensity levels.

ARX model stability

Another critical aspect of the ARX modelling is the stability of the generated model


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(a) y(k)= 1 epoch

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(d) y(k)= MTA of 256 epoch

Figure 4.16: Histograms of model order combinations resulted in when using a single epoch, MTA of 32,128 and 256 as the output to the ARX model with an exogenous input of a grand averaged real ABR.


for each epoch. The location of poles of the estimated model in the unit circle of the

z-plane determines a realistic ABR estimation. Instability of the automatically generated

model results in distorted estimations of the ABR. While generating ARX models for

the ABRs used to derive L-I curves, the models which contained poles outside the unit

circle were counted and discarded. Examples of such two unstable models are shown in

figure 4.18 with a pole outside the unit circle ([1.011,0] and [1.004,0]) in the z-plane and

correspondingly out of shape estimates. The percentage of these unstable models (while

generating 100 stable models) are tabulated in table 4.1. This suggests the unstable

models are unavoidable and expected to be at an average of 25% more than the stable

models generated. This results in prolongation of analysis time which is an additional

disadvantage for a rapid extraction system.

Blocksize

Sound Intensity (dB nHL)10 15 20 25 30 35 40 45 50 55 60 65 70 75 Average

1 21 15 21 17 11 18 19 16 19 11 12 22 19 18 17%32 16 16 39 12 1 26 38 3 54 8 27 14 17 19 21%128 70 40 1 50 1 41 1 1 35 1 7 9 40 24 23%256 65 26 12 26 1 72 6 1 1 1 12 49 80 11 26%

Table 4.1: Unstable estimated epochs percentage (%) at each sound intensity level associated with differentblock sizes to the output to the ARX model


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Figure 4.17: L-I curves derived with a single epoch, MTA of 32, 128 and 256 as the output to the ARXmodel. 100 random estimated epochs at each sound intensity was picked to plot these curves. A highvariance is observed at small block sizes with improved L-I curves which are closer to the benchmark couldbe observed at a MTA of 256 epochs (only above 30 dB nHL) with MSEs of single epoch-0.18, 32-0.14,128-0.05, 256-0.02


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Os(k)

u(k)

Figure 4.18: Two unstable model estimates derived by the ARX model with a pole outside of the unitcircle [1.011,0] and [1.004,0] (top and bottom plot respectively) resulted in morphologically uncharacteristicABRs

4.4 Discussion

Systematic evaluation of two parametric modelling methods (ARX, REPE) were presented

here, for rapid extraction of EPs based on the filtering of a canonical template to determine

both the ability to remove noise from a ABR single sweep and to track latency variations

of the respective components. This systematic study included a simulation followed by a

confirmation of those results by physiological ABR recordings. The ability of the ARX

and REPE methods to remove noise was comparable to that of previous studies producing

similar improvements in the SNR. In contrast the ability to meaningfully track simulated

changes in the latency of dominant ABR components was possible only with ARX mod-

elling as opposed to the REPE. The application of these parametric models to real ABR

data revealed that, while the ARX modelling is effective at high SNRs producing a close

L-I curve to that of the standard (MSEs corresponding to block sizes; 1-0.18, 32-0.14,

128-0.05, 256-0.02), it is compromised with low initial SNRs and single sweeps (or small

block sizes), therefore unable contribute to a rapid extraction system.


By producing similar improvements in SNR, the section 4.3.3 confirms that this sim-

ulation study is comparable with the previous studies by Cerutti (1988) and Lange &

Inbar (1996). Further investigations were carried out to evaluate the performance using

simulated data with deterministic EPs. Performance of tracking latency variation by using

wave V of the ABR introduced in this study provide to be of clinical significance.

The latency tracking results provide new insight into the performance and limitations

of using ARX and REPE as a rapid feature extraction method. The scope of this study

is limited to a template with a MTA of 100 sweeps and estimation of a single sweep.

The unique study conducted here with known and physiologically plausible latency vari-

ations of the ABR (e.g. 1 ms, 1.5 ms, 2 ms) revealed that results which previous research

approximated as ‘uncertainties due to physiological phenomena’ are in fact caused by inac-

curacies of the methodology itself. As an example, this study concludes that even though

REPE produces superior performance in improving the SNR compared to ARX, it under

performed in tracking latency variations, producing similar results to conventional MTA.

The reasons for the underperformance of the REPE could be due to the formulation of

noise n(k) as defined by Lange & Inbar (1996) using a finite impulse response MA process

rather an infinite impulse response AR process, which contradicts (2.4) in section 2.2.4.

Further, simulations reported in (Lange & Inbar 1996), low-pass filtered the test dataset

before applying the REPE in which case the effective transfer function of the system is

changed from the original.

Further, the study in this thesis on REPE revealed that normalization of the amplitude

after the pre-whitening stage is essential as the signal power is attenuated producing a

signal which is unable to excite the ARX model for optimum performance. Another

shortcoming of the original article (Lange & Inbar 1996) considering the application of the

ABR, is the amount of induced latency variation on the template. Lange & Inbar (1996)

varied the latency by 3 time points. In contrast the current study induces a minimum

variation of 40 time points which coincides with physiological latency variation of 1 ms

of the ABR at a sampling frequency of 40 kHz. The original study which introduced

the ARX modelling for variation tracking by Cerutti (1988), induced latency variations

through the model transfer function but neither specification nor any analysis has been


performed on them.

Results of the simulation study further suggests that, extraction of latency variations

with the ARX model is superior (producing low MSEs) with a capacity to extract latency

variations of up to 1 ms at 1 Hz at an initial SNR of -5 dB and up to 2 ms variations

at 0.05 Hz at an initial SNR of 0 dB. A recorded actual ABR (and also most of EPs)

possesses SNRs lower than -5 dB. Therefore, for ARX to be effectively used, a MTA

of more than 100 to the exogenous input u(k) to and 1 to the output y(k) should be

considered. However, the higher MSEs (viz. poor performance) of REPE in variation

tracking suggests inapplicability of extracting ABR variations.

To confirm these simulated results, ARX modelling was then applied to real ABR

data. According to the L-I curves derived (as a measurement tool to evaluate time-scale

variation tracking), the optimum result was generated with the output of a MTA of 256.

The derived L-I curve coincided with the benchmark L-I curve within the range of 30-75

dB nHL with a MSE of 0.02. Smaller block sizes of 128, 32 and the single epoch produced

worse L-I curves higher MSEs 0.05, 0.14, 0.18 respectively with a high variability. The

inability to derive the L-I curve at low intensities is due to the low amplitudes of the

ABR which results in lower SNRs compared to the larger amplitudes found at higher

sound intensities of 30-75 dB nHL. This implies that, to generate a complete L-I curve,

an ensemble of more than 256 epochs should be included in the MTA to generate the

reference to the ARX model.

4.5 Conclusion

Within the framework of the simulation study, we can conclude that the parametric

method of autoregressive modelling with an exogenous input (ARX) model is capable

of extracting time-scale varying features of a signal within the range of real physiological

signals. Even though the robust evoked potential estimator (REPE) is superior in the

SNR improvement, it is unable to track time-scale variations of the signal.

Results generated with the L-I curve impede the use of ARX modelling in rapid extrac-

tion of the ABR. The conclusions derived from the simulation study are strengthened by

these results with recorded ABRs. Even with a fully featured template generated with a


MTA of 1024 (grand average), an excess of 256 epochs are required to derive a complete L-I

curve. Therefore, compared to the conventional MTA, ARX modelling does not provide

an improvement for the rapid extraction. Rather the ARX modelling requires additional

processing time by estimating unstable models during the filtering process. Therefore we

conclude that rapid extraction of ABR using ARX modelling methods is not a feasible as

it is highly susceptible to the magnitude of noise associated with the ABR.

As it is evident, even though the use of templates enables noise to be removed from

a morphologically similar EP, it imposes a limitation for tracking substantial offsets

(>2 ms/80 time points) from the template. Therefore it is worthwhile to evaluate the

performance of feature extraction methods which are not based on parametric mod-

elling. Wavelet based methods have shown promising results in removing noise from

non-stationary EPs. The robust decomposition methods combined with efficient wavelet

coefficient selection algorithms were emerging at the time of this research. The following

chapter describes a detailed study and the resulting conclusions for a rapid extraction

system of the ABR based on wavelet theories.


%————————————————————————-


Chapter 5

Effectiveness of wavelet techniques

in the rapid extraction of the ABR

Extraction of the ABR with wavelets mainly investigate three denoising methods: con-

stant thresholds with matching coefficients (CTMC), temporal windowing with match-

ing coefficients (TWMC) and cyclic shift tree denoising (CSTD). This chapter presents

the methodology of modifying these methods and evaluating them as a rapid extraction

method of the ABR. In addition, two wavelet decomposition algorithms; DWT and SWT

were involved to investigate the accuracy of results produced. Using an approach similar

that in Chapter 4, a simulation study was followed by applying these methods to real ABR

data. Both these approaches included evaluation of denoising capacity and the ability to

track time-scale variations. The specific aims of this chapter are:

• To optimise of CTMC, TWMC and CSTD algorithms for the ABR signal domain.

• To conduct a comparable simulation study to that of ARX modelling methods.

• To determine the minimum number of epochs required to extract a fully featured

ABR.

• To investigate the effect of the template on time-scale variation tracking ability using

L-I curves.

• Novel implementation of wavelet denoising methods with SWT and analyse the effect

of shift-invariance.

116

The Journal article published (De Silva & Schier 2011) in association with this chapter is

attached in Appendix B.

Wavelets in rapid extraction of the ABR 117

5.1 Wavelet extracting methods

Prerequisites for defining wavelet denoising methods used in this chapter are explained in

the following two sections 5.1.1 and 5.1.2 viz. the synthetic and real ABR templates and

necessary wavelet decomposition sub-bands.

5.1.1 Synthetic and real ABR template

The essential fully featured reference ABR templates were adopted from sections 3.3.1

and 3.1.5. These templates were used in CTMC, TWMC and to determine the common

optimum basis wavelet derived with MTA of 1024 sweeps of ABR recorded at 55 dB nHL.

The synthetic template was based on (3.3) featuring the important ABR waves I, III and

V. Both these synthetic and real templates are shown in figure 5.1(These are identical to

the template shown in section3.3.1).

_ ` a b c d e f g _ hi h j chh j c _

k l m n o m p qr stuvw xy z µ

| ~ ~ ~ (a) Synthetic reference signal with no latency variation(l=0)

Ø µ

Ü ¡ ¢ £ ¤ ¥ ¡ ¢ £ ¤ ¦¡ ¢ £ ¤ ¥ ¥ ¥(b) Actual ABR recorded at 55 dB nHL

Figure 5.1: The reference ABR template used in wavelet denoising methods. Generated with MTA of 1024sweeps at 55 dB nHL showing main features wave I, wave III and wave V and additional features wave IIand wave VI. These are identical to the templates shown in 3.7

.

5.1.2 Wavelet decomposition levels

The number of wavelet decomposition levels calculated was based on the frequency content

of the ABR. The spectrum of the significant features of the ABR is dominated by frequen-

cies; 200, 500 and 900 Hz (Boston 1981, Delgado & Ozdamar 1994). Therefore a 6-level


wavelet decomposition tree was considered to include these three dominant frequencies in

separate levels to allow better noise reduction. As shown in table 5.1 the ABR recording

sampled at 40 kHz is divided into dyadic scales with frequency ranges becoming half of

the previous level. Levels A6, D6 and D5 contain the dominant frequencies of the ABR.

Also D4 (1.25-2.5 kHz) was included in the analysis to comply with the substantial signal

power of the ABR included within 100-3000 Hz as per Hall J. W. (2007) Further evidence

related to wavelets is presented in figure 5.4b with substantial amplitudes in reconstructed

waveform in D4 subband.

DWT level D1 D2 D5 D3 D4 D6 A6

Frequencycontent(Hz)

20k-10k 10k-5k 5k-2.5k 2.5k-1.25k 1.25k-625 625-312.5 312.5-0

Table 5.1: Frequency Content of wavelet subspaces. 6-level DWT decomposition levels at a samplingfrequency of 40 kHz

5.1.3 Constant thresholds with matching coefficients (CTMC)

The CTMC is based on an idealised template of the signal to be extracted. It is assumed

that an increase in noise reduction is achieved by matching coefficients of the noisy signal

with the template.

Applying a threshold alone will not be able to arrive at a clean ABR due to the

small amplitudes of the ABR compared to the background spontaneous EEG. Therefore

in addition to the fundamental thresholding of wavelet coefficients, to make the denoising

robust, a matching process is implemented for the threshold coefficients of the noisy ABR

with the template.

According to the flowchart shown in figure 5.2, first the block with the reduced number

of averages was decomposed using DWT into six levels. Then the thresholds were applied

to each level as follows:

• Level A6 - all the coefficients were retained

• Levels D6 to D4 - 20% of the most prominent coefficients were retained

• Levels D3 to D1 - all the coefficients were nullified


Generate the template

Decompose using DWT

Apply the threshold on

coefficients

Calculate the average of

the block

Decompose using DWT

Apply the threshold on

coefficients

Retain the matching

coefficients compared

with threshold coefficients

of the template

Reconstruct the denoised

block using IDWT

CTMC

Figure 5.2: Flowchart of the CTMC algorithm The flow above the dotted line represents the use oftemplate defining temporal windows based on the template and below the dotted line represents applyingthose temporal windows to a noisy ABR.

Since the coefficients at level A6 provide the base of the ABR, all of its coefficients

were retained. A threshold was applied to retain 20% of the highest coefficients in levels

D6 to D4. The threshold level of 20% was chosen as a compromise between

i a lower threshold which neglects important coefficients at higher scales and in con-

trast allows to reduce high frequency noise at lower scales and,

ii a higher threshold which includes important low frequency components at higher

scales at the expense of adding noise at lower scales.

All coefficients were nullified at levels D3 to D1 to remove high frequency noise generated

from spontaneous EEG in between 2.5 and 20 kHz.

The fully featured reference template defined in section 5.1.1 was used as the template

for this method to match thresholded coefficients.


The coefficient matching process started with applying the threshold scheme to the de-

composed template using DWT. Then the temporal locations of these retained coefficients

were matched with threshold coefficients of the noisy ABR. The common coefficients were

then used to reconstruct the refined ABR using inverse DWT.

5.1.4 Time windowing with matching coefficients (TWMC)

Using the time domain representation of wavelet transform, TWMC method identifies and

suppresses noise components distributed along wavelet subspaces and extracts the ABR.

TWMC is based on the assumption that specific ABR features occur at predetermined time

windows within the response. Such time windows are assumed to reduce distortions from

latency variations caused by the stimulus or pathological conditions of the participants. At

the same time, these time windows should minimise uncorrelated wavelet coefficients form

being involved in the reconstruction process and thereby removing noise. To incorporate

these features, time windows should be heuristically determined so that time locations of

ABR template features coincide. As a result, TWMC is template dependent and as such

the effect of using the template is presented in section 5.6.3

According to the flowchart in figure 5.3, the standard template (section 5.1.1) was

decomposed into 6 levels using DWT. Under the assumption of the noise free template,

the ABR is generated only with wavelet coefficients with large magnitudes. Figure 5.4a

illustrates the template and its decomposed wavelet coefficients on the same time scale with

prominent coefficients aligned along with features of the ABR template. Since frequency

ranges of decomposition levels D1, D2 and D3 are out of the ABR spectrum, no windows

were defined for them. In all the other decomposition levels, time windows were defined

such that prominent coefficients related to wave I, III and V were included. The process

of defining these windows was experimental (thus heuristic) allowing sufficient width to

accommodate any latency variations when applying to recorded ABRs. The effect of these

temporal windows at each decomposition level is illustrated in figure 5.4b. The algebraic

sum of these individual signals can be used to arrive at the refined template as seen in

figure 5.4 uppermost plots. Here, the reconstructed template contains all the important

features and was expected to preserve similar features in noisy ABRS.


Generate the template

Decompose using DWT

Define windows on each

decomposition level

Verify the reconstructed

template using IDWT

Calculate the average of the

block

Decompose using DWT

Apply windows defined on

the template


block using IDWT

TWMC

Figure 5.3: The flowchart of the algorithm of TWMC The flow above the dotted line represents definingtemporal windows based on the template and below the dotted line represents applying those temporalwindows to a noisy ABR.

According to TWMC algorithm in figure 5.3, the next step after verifying the temporal

windows with the template, is to apply those to a noisy ABR which has been derived from

MTA of reduced number of epochs. Similar to the template, this noisy ABR is decomposed

into 6 levels and then predefined temporal windows were applied to them to arrive at the

noise reduced ABR.

5.1.5 Cyclic shift tree denoising (CSTD)

CSTD uses linear averaging of epochs and thresholding of wavelet coefficients in a system-

atic iteration to achieve a greater reduction in noise.

When using the basic and the most reliable method of extracting ABRs; the MTA,

CSTD hypothesised that increasing the number of averages within the same number of

epochs will yield improved noise reduction, and thereby suppressing random ongoing EEG


(a)

_ ` a b c d e f g _ hk l m n o m p q§ zstu ¨w z©ª©«©¬©©®©©°(b)

Figure 5.4: Temporal windows defined for the TWMC. (a) Temporal windows defined according to thesignificant coefficients correlated to ABR features are indicated in grey shades. (b) Reconstructed signalat each decomposition level using only the windowed coefficients. The direct summation of these D1-D6and A6 reconstructed signals gives the final refined template.


Create the array of epochs

( N) in the block

Decompose each epoch

using DWT

Average as per CSTD

Apply scale thresholds

Calculate the linear ave r age

of the last CSTD level


block using IDWT

Apply CSTD level

thres h olds

Iter ate

ln(N)

times

CSTD

Figure 5.5: The flowchart of the CSTD algorithm. This is an iterative process which does not depend ona template compared to CTMC and TWMC.

noise. In the implementation, CSTD utilises MTAs in a cyclic manner to create additional

averages on a block of epochs. Also CSTD hypothesises that the application of additional

thresholds thus improving the SNR. Therefore two types of thresholds are applied to

wavelet coefficients that are derived from cyclic averaging.

The unique feature of the CSTD algorithm compared to CTMC and TWMC is that, it

does not depend on a template. This has the potential benefits of extracting the wide range

of temporal variations in the ABR as a result of stimulation and pathological conditions of

the participant. The effectiveness of the use of a template will be assessed in sections 5.5.7

and 5.5.7 in detail.

Figure 5.5 shows the iterative process of the CSTD algorithm in contrast to CTMC

and TWMC which is based on a template. First a block of N epochs are created where

N = 2i, i = 2, 3, 4, 5, 6, 7. Then these individual epochs are decomposed into six levels


using DWT. The coefficients derived from the decomposition are then subjected to a

thresholding process (described in section 5.1.5). The thresholded coefficients are then

subjected to dyadic averaging with cyclic shifts to create the next level of CSTD algorithm

(described in section 5.1.5). These coefficients are then processed with the second level

of thresholding called CSTD ‘level thresholding’ (described in section 5.1.5). There are

L = ln(N) number of iterations i.e. ‘CSTD levels’, given N number of epochs included

in a block. After CSTD has reached the last level, a single set of wavelet coefficients is

calculated representing only one epoch and then reconstructed the denoised ABR using

inverse DWT.

Cyclic shift dyadic averaging

At each CSTD level l (1 ≤ l ≤ L), two adjacent epochs at level l − 1 (dyads) are

averaged and denoised to create the new CSTD level. The dyadic averages consider not

only adjacent epochs, but also dyadic averages of a cyclical shift by one epoch at that

level. This process is illustrated in figure 5.6 for N = 8 scenario. As an example, the

cyclic shift nature of this algorithm is evident in the CSTD level l = 2 at the last dyadic

average showing E81. According to CSTD algorithm, the last CSTD level l = 4 indicates

that each epoch at the last CSTD level is identical to linear average of epochs at the initial

level and that they are included only once in that process. Therefore the last N epochs

are the linear average of initial N epochs but derived through different paths of the tree

structure. But the application of thresholds at each wavelet and CSTD levels makes the

CSTD algorithm a nonlinear process. As a results the last N epochs derived with cyclic

shift dyadic averages after applying the threshold vary from each other. The following

sections 5.1.5 and 5.1.5 will describe the application of thresholds.

Wavelet level thresholds

Distinct to the constant threshold used in CTMC, CSTD uses a threshold function which

depends upon the wavelet decomposition level δl. A decreasing function δw+1 = 2−w/2δw

from D1 to D6 and A6 (where w = 1, 2, 3, 4, 5, 6) was chosen for this study with the initial

value δ1 = 1 (Causevic et al. 2005, Donoho 1995). Such a decreasing function removes most


E1 E2 E3 E4 E5 E6 E7 E8

E12 E34 E56 E78 E23 E45 E67 E81

L=1

The block of initial N=8 epochs

N

L=2

Arrive at L=2 by cyclic shift dyadic averaging and applying CSTD level threshold

N/2 N/2

1δ

δ

E1234 E5678 E3456 E7812 E2345 E6781 E4567 E8123

E12345678 E56781234 E34567812 E78123456 E23456781 E67812345 E45678123 E81234567

N/8 N/8 N/8 N/8 N/8 N/8 N/8 N/8

L=4


The linear average of these final 8 epochs is the refined signal

L=3


N/4 N/4 N/4 N/4

1δ

2δ

3δ

Figure 5.6: Averaging sequence of the CSTD algorithm. Cyclic shift dyadic averaging and application ofCSTD level threshold algorithm for a case of N = 8 epochs.

of the coefficients generated by high frequency noisy data at initial wavelet decomposition

levels with a high threshold and retains relevant coefficients at lower wavelet decomposition

levels.

CSTD level thresholds

The CSTD level threshold is unique to CSTD and an additional thresholding process

when compared with the conventional wavelet denoising. This threshold is applied to

epochs in all the CSTD levels. A unique function δl and an initial value for CSTD level

threshold were required to be determined for the purpose of this study. The deviation

from the original study (Causevic et al. 2005) is due to the difference in the basis wavelet.

A set of increasing, constant and decreasing functions as shown in (5.1) with a range of

initial values were tested using the recorded data to determine the CSTD level threshold


function δl and the results are presented in section 5.5.2.

δl+1 = 0.05l + δl

δl+1 = δl

δl+1 =1

2l2δl

δl+1 =1

exp(l)δl

δl+1 =1l δl

δl+1 =1l2δl

(5.1)

5.1.6 Use of SWT algorithm in CTMC, TWMC and CSTD

To eliminate the drawback of shift-variance in DWT which causes time scale distortions

of the reconstructed signal, we tested the above mentioned denoising methods with the

SWT. As suggested in section 2.3.6 and 2.3.5 the absence of sub sampling makes SWT

shift-invariant, however with a trade-off of increasing computational complexity.

The major difference between the DWT and the SWT algorithms is the dyadic decima-

tion at each decomposition level. As shown in table 5.2, the number of wavelet coefficients

of a 6 level decomposed SWT contain the same number of coefficients to that of the anal-

ysed signal at all decomposition levels where as in DWT, the number of coefficients is

reduced in dyadic scales.

Decomposition levels D1 D2 D3 D4 D5 D6 D6

SWT N N N N N N NDWT N/2 N/4 N/8 N/16 N/32 N/64 N/64

Table 5.2: Coefficients of SWT and DWT. Number of wavelet coefficients at each decomposition level ofDWT and SWT of a signal length of N .

Given a constant number of decomposition levels, the only difference between DWT

and SWT is the number of wavelet coefficients at each decomposition level. Taking this

point in to consideration, the adaptation of CTMC, TWMC and CSTD to the SWT

algorithm is described as follows.

CTMC applies a 20% threshold at each detailed decomposition level of both the tem-

plate and the noisy ABR in order to retain the common coefficients based on the temporal


locations prior to reconstructing the denoised ABR. This method can be directly imple-

mented using SWT derived wavelet coefficients instead of DWT with the only difference

of having N number of coefficients in each decomposition level. The 20% threshold can

be applied to these coefficients in methods identical to those described in section 5.1.2.

In modifying TWMC to suit the SWT algorithm, a new set of windows was determined

to suit new temporal locations of the coefficients. Figure 5.7 illustrates the windows defined

to be compatible with the coefficients derived from SWT decomposition algorithm. These

windows are different from the DWT windows defined in figure 5.4. These newly defined

windows were then imposed on noisy ABRs to filter noise in a similar method to those

shown in figure 5.3.

The CSTD in contrast has two independent processes; application of thresholds and

circular averaging. Application of thresholds is similar to that of CTMC and thus adap-

tation from DWT to SWT is similar. But, it was necessary to rearrange the wavelet

coefficients derived from SWT to suit the circular averaging due to the resultant lengths

of the arrays from MATLABTMfunctions. The resulting coefficients after SWT from each

decomposition level were arranged in an array as shown in figure 5.8 for the convenience

of circular averaging. This represents only one decomposed epochs (Ei) in figure 5.6. Such

arrays were then used with the CSTD algorithm according to the flow chart in figure 5.5.

5.2 Choice of the basis wavelet

The fully featured template shown in figure 3.4 with added Gaussian white noise was used

to determine the suitable basis wavelet. Synthesised noise was used here to achieve a

consistent noise profile, thereby avoiding any spurious effects that might occur in recorded

ongoing EEG. The SNR of the tested ABR was kept at -15 dB which is equivalent to a

theoretical MTA of 32 sweeps having an initial SNR of -30 dB.

Biorthogonal basis wavelets of orders 3.3, 3.5, 3.7, 3.9, 4.4, 5.5 and 6.8 were tested with

denoising methods CTMC, TWMC and CSTD using their default parameters related to

the ABR application. The results are presented in section 5.5.1 in the form of MSEs.


± ² ³ ´ µ ¶ · ¸ ¹ ± º» º ¼ µºº ¼ µ ±± ² ³ ´ µ ¶ · ¸ ¹ ± º» º ¼ ²» º ¼ ±ºº ¼ ±º ¼ ²½¾± ² ³ ´ µ ¶ · ¸ ¹ ± º» º ¼ µºº ¼ µ ±½¿± ² ³ ´ µ ¶ · ¸ ¹ ± º» ²» ±º ±²½À± ² ³ ´ µ ¶ · ¸ ¹ ± º» ²» ±º ±² Á Â Ã Ä Å Ã Æ ÇÈÀ

Figure 5.7: Defined temporal windows for TWMC with SWT algorithm. Blue - coefficients of the originaltemplate. Red - windowed coefficients.

5.3 Simulation study on wavelet methods

Similar to the one shown in Chapter 4, a simulation study was conducted with chosen

wavelet denoising methods to assess the noise removal and latency tracking ability of

CTMC, TWMC and CSTD. Such a study enables a direct comparison to parametric

modelling methods and an unbiased estimation of the performance before applying them

to real ABRs. The simulation study is twofold; 1) Evaluation of denoising. 2) Evaluation

of latency tracking of ABR wave V.

5.3.1 Denoising

The reference signal for the simulation study is the synthetic ABR model defined in (3.3)

and illustrated in figure 5.1a characterised with similar morphology. The dataset including


Figure 5.8: The constructed array with SWT coefficients to suit circular averaging of CSTD. Each decom-position level consists of N number of coefficients.

1200 ABRs (duration of 60 seconds of recording at a stimulus frequency of 20 Hz) with

no latency variations as shown in figure 3.9a was filtered with each wavelet method at

different SNRs. The noise addition was based on a SNR of -30 dB for a single sweep (also

known as the initial SNR). Accordingly, to represent block sizes of 8, 16, 32, 64, 128 and

256, Gaussian white noise was added with noise powers of -22 dB, -18 dB, 15 dB, -12 dB,

-9 dB and -6 dB respectively based on theoretical SNR = 10log10

(√N)

.

Parameters of the wavelet methods for the simulation study and results

CTMC used a threshold which retained the highest 20% of coefficients of wavelet sub-

bands A6, D6, D5 and D4. For TWMC, windows were defined for each wavelet subband

to suit the synthetic template similar to figure 5.4 such that minimum number of coef-

ficients was used to reconstruct a morphologically comparable template. According to

the original study (Causevic et al. 2005), the CSTD level threshold function was set to

δl+1c = 1/exp(l)δl with an initial value of δ1 = 0.8 and the wavelet threshold function was

set to δw+1 = 2−w/2δw with an initial value of δ1 = 1. New functions that would explicitly

suit the ABR were not investigated here. However, these were investigated in depth with

the application of real ABRs.

The effect of wavelet filtered ABRs quantified in terms of improvement in SNR is shown

in figure 5.9 which is directly comparable with the performance of the parametric modelling

in figure 4.7 (improvement in SNR is calculated according to (2.9)). In general, it suggests

that the wavelet methods are superior to conventional MTA and prominent at low SNRs

(even though the improvement reduces as the initial SNR reduce). In comparison to the

parametric modelling; initial SNRs above -25 dB indicate superior improvement and about

par below that. As a result, the decision to use wavelet methods is justified given the fact

that wavelet methods yield superior improvement in SNR. These results therefore justify


É Ê Ë É Ë Ì É Ë Í É Ë Ê É Î É ÏË ÏË ÌÊ ÐÊ ÊÊ ÑÊ ÏÊ ÌÒ ÐÒ ÊÒ Ñ

Ó Ô Õ Ö Õ × Ø Ù Ú Û Ü Ý Þ ß Ü à á â â ã ä å á Ô Ý Õ Ô æ ç Ø á à è ä Õ é ã ßê ëìíîïðëðñòó ñôõö÷øùúû ü ý þ ü û þ ü ÿ û þ þ ü Ê Í Ï Ï Ñ Ë Ê Ì Ì Ë Ï Ò Ê

Figure 5.9: Improvement in the SNR with wavelet filtering methods suggest superior performance to thatof parametric modelling.

the use of real ABR data for a comprehensive analysis.

5.3.2 Latency tracking

As pointed out in Chapter 2, tracking time-scale variations are critical in identifying

pathological conditions of a patient. Therefore, we used periodic latency variations (mod-

ulated) with several datasets representing 60 s of a recording as shown in figure 3.9.

The range of amplitude variations included aL = 1, 2 ms and latency variations included

fL = 0.025, 0.05, 0.1, 1 Hz creating a total of 8 datasets. These combinations were then

used to assess the latency variation tracking capability of the three wavelet denoising

methods. It should be noted that these datasets are identical to those used in the ARX

simulation study in section 4.3.5.

To clarify such limitations and to assess the property of time-scale (latency) variation

tracking, the synthetic ABR with aL = 0 was used as the template in CTMC and TWMC

to extract variations. Similar to the analysis in Chapter 4 simulation study, variations of

wave V were extracted in MTA and wavelet filtered ABR datasets for comparison.

Results shown in figure 5.10 suggest a comparatively low MSE was produced by CSTD

implying superior latency tracking. However, contradicting the obvious implication of


producing low MSEs by wavelet filtered ABRs, CTMC and TWMC indicate comparatively

high MSE. The underlying reason could be that the limitations imposed by the template

in these methods limits the tracking of latency variations. However, the use of a template

in CTMC and TWMC could potentially limit the feature extraction with the induced

latency variations. It can be observed that this difference is prominent when aL = 2 ms

compared to aL = 1 ms. A one-way ANOVA of aL = 2 ms at each fL suggests a significant

difference of the mean of CSTD compared to other methods (e.g. at a block size of 32;

F (2, 2997) = 134.64, p < 0.01). However, such a difference was not recorded at aL = 1 ms

(e.g. at a block size of 32; F(2,2997)=1.736 , p = 0.1764).

This study provides the basis to conduct a similar analysis with real ABRs. Due to

the difficulty of obtaining sinusoidal variations in the latency, we used the L-I curve of

wave V by controlling the intensity of auditory stimuli.

5.4 Evaluation of wavelet methods on real ABR Data

Motivated by the promising results of the simulation study, CTMC, TWMC, CSTD

wavelet filtering methods were applied on recorded ABR data to confirm and finalise

an effective method for the rapid extraction of a fully featured ABR from a minimum

block size). During the performance evaluation of these wavelet methods, the following

critical factors were considered:

i Denoising and the ability to produce a fully featured ABR.

ii The ability to track latency variations induced in ABR features.

Initial analysis was performed with DWT as the decomposition algorithm (similar to

original studies of the three wavelet denoising methods). The Choice of basis wavelets and

threshold functions were determined according to DWT implementation. The performance

of denoising and latency tracking was then compared with the results generated from the

SWT decomposition algorithm. The comparison led to a conclusion with regards to the

possible use of these methods in a system for rapid extraction of ABRs.


Figure 5.10: [Latency tracking results with simulated ABR dataset suggests difference is prominent whenaL = 2 ms compared to aL = 1 ms. However, such a difference was not recorded at aL = 1 ms.


5.4.1 Denoising ability of wavelet methods

The performance evaluation of denoising included quantitative measurements such as MSE

and correlation coefficient and qualitative peak detection by an expert. Given the reason

that MSE and correlation coefficient compares two signals as a whole rather than their

individual features, we carried out a visual inspection to arrive at a thorough conclusion

of the minimum block size that gives optimum ABR features.

For evaluation purposes it was important to have a fully featured reference template

when calculating MSE. Therefore the fully featured template derived at 55 dB nHL, men-

tioned in section 5.1.1 was used for this purpose. MSE was calculated for each of the three

wavelet methods at all block sizes. To establish a baseline comparison for the wavelet

methods, a conventional band-pass filtering of 100-3000 Hz was also performed.

Initially, analysis was carried out using conventional DWT and its performance in

terms of the minimum block size which leads to rapid extraction. Then these results were

compared with SWT derived results to arrive at a final conclusion of the performance.

5.4.2 Latency tracking ability of wavelet methods

As discussed in section 2.1.4, due to the effect on the latency as a result of various patholog-

ical conditions and the usefulness to patients of these wavelet methods in practice depends

upon the range of latency variations that could be accurately tracked. For the purpose of

this study, latency variations were induced by controlled variation of the stimulus intensity.

Then the latency tracking ability of wavelet methods was evaluated by comparing the L-I

curve of wave V derived using the grand average at each sound intensity level with that of

the wavelet filtered. The block size used to generate the L-I curve was determined as per

the denoising performance presented in section 5.5.3. Both DWT and SWT decomposition

algorithms were used with the three denoising methods to arrive at a conclusion as to the

optimum latency tracking method.


5.5 Results

5.5.1 Determination of a common basis wavelet for analysis

The MSE values shown in figure 5.11 result from using different orders of Biorthogonal

basis wavelet in CTMC, TWMC and CSTD. In general, these MSE values have a common

trend of reduction as the order increases, caused by the accurate representation of the

detail and approximation functions to the ABR waveform morphology. A close observa-

tion suggests that there is an optimum MSE value for CSTD and TWMC methods at

Biorthogonal 5.5, where as CTMC shows almost equal MSE values with Biorthogonal 5.5

and 6.8. Since low filter orders reduce computational complexity, processing speed and

memory requirements leading to rapid extraction, the Biorthogonal 5.5 basis wavelet was

considered to be the optimum choice, and will be used throughout this chapter. A similar

conclusion is supported by the work of Bradley & Wilson (2004).

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Z [ \ ] \ ^ [ _ ` a ` bc d e c d f e c c g d hFigure 5.11: Effect of Biorthogonal basis wavelets on denoising methods. The performance of denoisingmethods CTMC, TWMC and CSTD in terms of MSE when used different orders of the Biorthogonal basiswavelet (error bars represent SD). This suggests that Biorthogonal 5.5 is optimum for all three denoisingmethods.


5.5.2 Determination of CSTD level threshold function

The CSTD level threshold function had to be uniquely determined for this study due to

the use of a different basis wavelet to that of the original study (Causevic et al. 2005). The

test dataset used for this evaluation is a block of 32 ABRs recorded at 55 dB nHL and the

template (refer figure 5.1 for comparison i.e. to calculate MSE. Six threshold functions in

(5.1) were tested with a range of initial values. The resultant MSE values are plotted in

figure 5.12.

The results confirmed our assumptions. The natural behaviour of the CSTD produced

fewer noise components at low CSTD levels, and the use of constant and increasing func-

tions produced high MSEs removing relevant wavelet coefficients to the ABR at lower

levels. In contrast decreasing functions resulted in an optimum initial value for a given

function within the range of initial values. Out of the three decreasing functions tested,

δl+1c = 1/exp(l) δl produces the lowest MSE at an initial value of δ1 = 0.8. Therefore

these settings are used for the CSTD level threshold function from here onwards.

Note that the sudden termination of curves is due to the thresholds of above 100%

being applied to wavelet coefficients which resulted in no coefficients to reconstruct an

ABR.

5.5.3 Noise reduction of wavelet methods with DWT

The noise reduction of the wavelet methods was evaluated using MSE and a visual com-

parison followed by a statistical significance test of correlation coefficients, to arrive at the

lower bound limit of the block size (number of epochs required in the MTA) that produce

a fully featured ABR. The data used for this analysis were recorded at a sound intensity

of 55 dB nHL for all the 8 participants as per the section 3.1. 769 ABRs were extracted

at a single block size by sweeping through the total number of 1024 epochs from single

participants. Each extracted ABR was filtered with CTMC, TWMC and CSTD using

DWT and conventional Butterworth band pass filtering with cut-off frequencies at 100 Hz

and 3000 Hz for comparison purposes. The MSE was calculated for each filtered ABR

with reference to the grand average at 55 dB nHL of the respective participant.

The average of MSE values across all the participants at each block size for the different


i i j k l l j k m m j k ni j l oi j mi j m mi j m pi j m qi j m oi j ni j n mi j n pi j n qi j n o

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|~δl+1 = 1

exp(l)δl

δl+1 = 1

2l/2δl

δl+1 = 1lδl

δl+1 = 1l2δl

δl+1 = δl

δl+1 = 0.05l+ δl

Figure 5.12: Effect of level threshold functions in CSTD showing MSE of the filtered signal according tothe level threshold function and the initial value used. The function 1/exp(k) at an initial value of 0.8has the minimum MSE.

filtering methods are plotted in figure 5.13. As expected these values show an exponential

reduction in MSE as the block size increases. Also, it is evident that all wavelet methods

have a superior performance compared to conventional band-pass filtering (i.e. MTA) at

all block sizes, with a greater effect at small block sizes, thus suggesting that wavelets are

most effective at low SNRs. Among the wavelet filtering methods, in general at all block

sizes, CSTD produce a superior performance according to the MSE compared to CTMC

and TWMC. The observation is statistically justified with one-way ANOVA (p < 0.01)

results shown in table 5.3 and specific Tukey post-hoc comparison results between CSTD-

TWMC and CSTD-CTMC in table 5.4. Therefore the early indication is that CSTD is a

potential method to rapidly extract the ABR.

However, in determining the smallest block size for rapid extraction, while MSE values

indicate the noise reduction aspect, they do not represent the quality of the actual filtered

signal. Also, the MSE value does not indicate the extent to which the filtered ABR in a

particular block size is close to the grand averaged template. Therefore a visual comparison

was carried out to check which block size produces a detectable ABR.

Figures 5.14, 5.15 and 5.16 show the surface plots of the same ABR dataset filtered


Figure 5.13: Denoising effect of Wavelet methods. Average MSE of 8 participants for each wavelet methodand band-pass filtering for all block sizes at a sound intensity level of 55 dB nHL. Wavelet methods arebetter than conventional band-pass filtering and CSTD produces the lowest MSE among wavelet methodsat any given block size.

Table 5.3: One-way ANOVA results comparing MSEs produced by ABRs filtered from CSTD, TWMC andCTMC suggest that there is a significant difference between the group MSE means. The specific differencesare identified with a Tukey post-hoc comparisons study from which the results are tabulated in table 5.4

Block size df F p

256 (2,18453) 222.9 <0.01128 (2,18453) 175.8 <0.0164 (2,18453) 138.4 <0.0132 (2,18453) 181.8 <0.0116 (2,18453) 245.2 <0.018 (2,18453) 84.7 <0.01


Table 5.4: Tukey post-hoc comparison of CSTD against TWMC and CTMC suggest there exist a siginifi-cant difference in mean MSE at all block sizes (as CI does not include zero) confirming superior performanceof CSTD

Block size Comparisonagainst

Meandifference

CI

256 TWMC -0.0050 -0.0058 :-0.0043CTMC -0.0042 -0.0049 :-0.0034

128TWMC -0.0086 -0.0103 :-0.0069CTMC -0.0103 -0.0120 :-0.0086

64TWMC -0.0200 -0.0160 :-0.0120CTMC -0.0261 -0.0221 :-0.0181

32TWMC -0.0431 -0.0341 :-0.0250CTMC -0.0678 -0.0588 :-0.0498

16TWMC -0.0905 -0.1128 :-0.0683CTMC -0.1687 -0.1910 :-0.1465

8 TWMC -0.1768 -0.2243 :-0.1292CTMC -0.1905 -0.2380 :-0.1429

with the three wavelet methods. Six plots in each figure represent block sizes from 256 to

8 with 769 epochs across the y-axis. The wave V at a latency of 6 ms is clearly visible as

a vertical red strip at a block size of 256 in all the wavelet methods. This strip gradually

becomes overshadowed by noise towards smaller bock sizes. Due to this prominence, wave

V was considered as a good indicator of determining the effect of denoising. It could be

observed that below a block size of 32, wave V cannot be distinguished from noise in all

the wavelet methods.

To confirm this visual observation, a statistical analysis was carried out using corre-

lation coefficients derived from the template and denoised ABRs with CTMC including

data of all the participants. The choice of CTMC is based on the worst case scenario

according to MSE values. A one-way ANOVA calculation suggests that there exists a sig-

nificant difference of means between block sizes, F (5, 4608) = 287.77, p < 0.01 suggesting

the presence of a block size that is not contaminated with noise. The comparison of these

mean correlation coefficients is illustrated in figure 5.17. Tukey post-hoc comparisons of

the block sizes revealed that the difference of correlation coefficients generated between a

block size of 8 (M = 0.355, 95%CI[0.334, 0.377]) and 16 (M = 0.393, 95%CI[0.3710.415])

was not significant (p = 0.51) suggesting similar interference from noise. However, con-


firming the visual observation, block size of 32 revealed a significant difference compared

to the noise corrupted block size of 16 (M = 0.453, 95%CI[0.432, 0.474]) with p < 0.01.

With all these results we concluded that, ABR extraction could be performed at a

rapid rate using an ensemble of only 32 epochs compared to the conventional 1024 epochs.

The argument is further strengthened when examining a randomly selected block of

size 32 filtered with three wavelet methods shown in figure 5.18 illustrating the ability

to extract ABR features of the template. CTMC extracted wave III and V but failed to

extract wave I and II. Also we could see a spurious peak after wave V which was not in

the template. TWMC shows only wave V with a distorted combination of wave II and

III while wave I appears to be absent. It is possible that this effect causes due to the

predetermined windows in TWMC. In contrast CSTD is able to extract waves I, II, III

and V. An important observation here is that wave IV which is difficult to observe is also

visible immediately before wave V (similar to the ideal ABR shown in figure 2.2). One of

the important aspects of rapid extraction is demonstrated with this example where reduced

number of averages provide more information and variations than a grand averaged ABR.

One could argue that false peaks to the right of wave V are noise, but a clinician would

know that these are out of the range of peaks of interest, therefore the chances of being

misled are minimal. In contrast, the band-pass filtered ABR contains a large amount

of noise from spontaneous EEG. A trained eye could identify wave III and V but with

minimal accuracy of their latencies.

5.5.4 Fsp threshold in quantifying the effectiveness of wavelet filtered

ABRs

It is arguable that statistical methods such as Fsp could be used to quantify the noise

associated with wavelet filtered ABRs. However, such a claim should be systematically

investigated as there could be a contradiction of the underlying assumptions. The main

assumption in the Fsp calculation is that the noise associated with a MTA of a signal is

F distributed with degrees of freedom fixed on v1 = 5 and v2 = 250. It is apparent that

MTA is not the only filter imposed in wavelet filtering (or in ARX modelling). Therefore,

the degrees of freedom of the F distribution could be different. The potential effect on


Time (ms)

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Figure 5.14: normalised surface plots of 769 filtered ABRs with CTMC of a participant at block sizes from256 down to 8. The highlighted vertical strip around 6 ms shows the wave V. It gradually becomes obscuredby noise when block size is reduced. The smallest block size where the wave V was readily identifiable was32.


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Figure 5.15: normalised surface plots of 769 filtered ABRs with TWMC of a participant at block sizesfrom 256 down to 8. The highlighted vertical strip around 6 ms shows the wave V. It gradually becomesobscured by noise when block size is reduced. The smallest block size where the wave V was readilyidentifiable was 32.


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Figure 5.16: normalised surface plots of 769 filtered ABRs with CSTD of a participant at block sizes from256 down to 8. The highlighted vertical strip around 6 ms shows the wave V. It gradually becomes obscuredby noise when block size is reduced. The smallest block size where the wave V was readily identifiable was32.


Figure 5.17: Mean correlation coefficients between the template and CTMC filtered ABRs at differentblock sizes suggesting a significant difference between the block size of 32 and noise corrupted block sizeof 16. Error bars represent 95% confidence interval

the threshold in such a difference is explained below.

In the original study, it was estimated that MTA of 250 epochs of EEG noise has a

degree of freedom v1 = 5, v2 = 250 (F (v1, v2) statistics, where v1 and v2 are degrees

of freedom of numerator and denominator) (Elberling & Don 1984). According to the

current study assuming v1 = 5 F (5, v2) values derived for v2 = 1 to 1024 is shown in

the figure 5.19. It is reasonable to state that the deviation from established threshold of

F (5, 250) = 3.1 is minimal at v2 = 1024 considering the natural variation of Fsp.

However, a slight variation in the v1 could have an impact on the standard threshold

as is evident in figure 5.19 with F (10, 250) = 2.392. As per (Elberling & Don 1984) v1

depends on the filter imposed on white noise e.g. for white noise v1 =number of data

points in the epoch (160) where as for pink noise v1 = 15.

Considering the nonlinearity of wavelet filtering imposed on the ABR, it is not correct

to use v1 = 5 viz. the threshold of Fsp = 3.1. Determination of new Fsp threshold for

wavelet filtering is out of the scope of this thesis. Therefore Fsp values were not used

either for objective quantification of wavelet filtered ABRs in this thesis nor for ARX

model derived ABRs.


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Figure 5.19: Effect of dof of F (v1, v2) statistics on the threshold criteria. The threshold curve where v1 = 5has contrasting effect to the threshold curve compared to v1 = 10. Here, v2 = 1− 1024. v1 depends uponthe filter imposed therefore direct application of Fsp = 3.1 is not suitable.

5.5.5 Comparison of noise reduction between DWT and SWT

To compare denoising of DWT and SWT decomposition algorithms, the same real ABR

dataset and identical settings were used as in section 5.5.3. The results are shown in

figure 5.20 for comparison with 5.20a and 5.20b) showing results of SWT and DWT re-

spectively.

It could be observed that the trend of MSEs produced by both SWT and DWT remains

the same across denoising methods so that CSTD produces the minimum MSE is followed

by TWMC and CTMC. A closer visual inspection suggests an improvement in mean MSE

of SWT compared to DWT in TWMC and CSTD as opposed to minimal improvement

in CTMC. A paired t-test was performed to statistically justify the results across the 8

participants (df = 7 and at 5% significance). The summary of the t-test tabulated in

table 5.5 confirms the visual inspection and suggests similar mean values of MSEs with

CTMC being the only exception of a block size of 8. On the contrary, with TWMC and

CSTD, mean MSEs are significantly different with the only exception in CSTD at a block


size of 256.

The reason for the improvement could be due to the advantage of shift invariance in

SWT. Even at a constant sound intensity level, there could be temporal variations in the

ABR due to imperfections in the recording setup and the physiological condition of the

participant. As SWT preserves the shift invariance without affecting such time jitters, a

close approximation to the template could be achieved compared to that of the DWT.


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Table 5.5: Results of paired t-test (df = 7 and at 5% significance) between the MSEs of DWT and SWTdenoised ABRs.

Block size CTMC TWMC CSTDt p CI t p CI t p CI

256 0.381 0.714 -0.001 0.001 4.426 0.003 0.005 0.015 1.609 0.152 -0.001 0.006128 1.08 0.316 -0.001 0.004 4.335 0.003 0.008 0.027 5.183 0.001 0.007 0.01864 1.831 0.11 -0.001 0.01 4.326 0.003 0.015 0.05 5.977 0.001 0.019 0.04532 2.134 0.07 -0.001 0.02 4.234 0.004 0.028 0.099 5.936 0.001 0.046 0.10716 1.504 0.176 -0.009 0.042 4.518 0.003 0.065 0.208 5.697 0.001 0.103 0.2498 4.344 0.003 0.035 0.119 3.921 0.006 0.131 0.527 4.615 0.002 0.206 0.638

The statistical results are further confirmed by individual ABRs extracted from SWT

and DWT processes. Figure 5.21 presents such randomly selected ABRs (corresponding

to each other) at a block size of 32, filtered by the three wavelet methods (CTMC, TWMC

and CSTD) with the conventional band-pass filter (MTA). A block size of 32 was selected

for comparison with the results from section 5.5.3. It is clearly visible in figure 5.21a and

5.21c that CTMC and CSTD filtered ABRs with SWT produce closer amplitudes to the

template for wave V than with DWT. In general, SWT filtered ABRs tended to produce

closer amplitudes to that of the template compared to DWT. However the lack of waves

I, II and III in CTMC filtered ABRs resulted in a high MSEs, and therefore it was not

ideal for feature extraction. In figure 5.21b and 5.21d, a comparison of SWT and DWT

reiterates the reason for having low MSEs with SWT. In this randomly selected epoch, the

large noise component at the start of the ABR was remarkably removed by TWMC and

CSTD with SWT but residue with DWT. CTMC does not suppress that paticular noise

component thus revealing one of its disadvantages: in the presence of noise components

at a similar magnitude CTMC incorrectly detects these noise components as a related

ABR wave component. In conclusion, out of TWMC and CSTD implemented with both

SWT and DWT decomposition algorithms, the CSTD with SWT yields arguably the best

estimates of the ABR.

5.5.6 Latency tracking results of wavelet methods with DWT

The ability to track latency variations using wavelet methods, is evaluated using the L-I

curve of wave V. The validity of the grand averaged (MTA of 1024) L-I curve with recorded

ABRs are well within the standard model (3.2) as per the section 3.2.1. Therefore this


1 2 3 4 5 6 7 8 9 10-1

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Figure 5.21: The plot of the effect of denoising of SWT and DWT on Random ABRs. At a block size of32 filtered with different filter methods using SWT and DWT.


curve was considered as the benchmark and the best match L-I curve derived by wavelet

filtered ABRs.

All the data from 8 participants were then independently filtered with the three wavelet

methods using DWT, and the wave V latencies were extracted using settings similar to

that of the grand average (refer section 3.2). The resultant curves and the overall average

across all the participants are shown in figure 5.22. It should be noted that the template

ABR used for CTMC and TWMC was derived from the grand average at 55 dB nHL for

each participant and was kept constant while denoising ABRs at all sound intensities for

each participant. This enables us to arrive at a conclusion of the range of latency variations

that could be tracked using a constant template with CTMC and TWMC. In addition,

such a constant template enables the representation of a practical situation where the

actual ABR of a patient is a priori unknown.

The overall results in figure 5.22 indicate that the L-I curve derived from CSTD follows

the reference curve better than the CTMC and TWMC derived curves. This difference is

prominent at low sound intensities. According to the behaviour of the L-I curves derived

by CTMC and TWMC, we could see that the variation tracking is limited compared

to that of CSTD. The individual L-I curves follow a similar trend except in the case of

Female(31) and Female(27) where all the wavelet methods follow the reference curve at

all sound intensities. The limitations of latency tracking based on these results will be

discussed with more detail in section 5.6.3.

To confirm this visual observation, a statistical analysis was performed by approxi-

mating similar polynomial models (as in (5.1)) for the derived L-I curves. The coefficients

calculated for each wavelet method and the grand average (1024) derived from 800 epochs

across 8 participants including 14 sound intensity levels are tabulated in table 5.6 in the

form of log10(L) = a1I + a2. The comparative plot of these estimated models are shown

in figure 5.23. A one sample t-test was carried out to statistically quantify the significance

of these estimations. It was hypothesised that a1 and a2 of filtered curves are similar to

those of the theoretical curve.

According to the t-test results in table 5.7, the grand averaged L-I curve does not have

a significant difference in the mean compared to the theoretical curve, with a p value of


both a1 and a2 greater than 0.01. Therefore in general, the data collected for this study

is valid and the results acquired from further processing of this data should also produce

valid results. Among the three curves derived with wavelet methods, only CSTD produced

a curve (t(799) = -1.4018, p = 0.1615, 95% CI for the mean (-0.0026, -0.0025)) with no

significant difference to that of the slope (a1) of the theoretical curve. The difference in the

intercept (a2) could be due to the systematic differences in the experimental setup which

affect the overall recording voltage. The curves derived from both CTMC and TWMC

indicates significant differences in the slope (a1), thus less effective than CSTD.


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Figure 5.22: Latency tracking with wavelet methods using DWT. Derived L-I curves from the three waveletmethods with DWT and the grand average for individual participants and the overall effect. Overall L-Icurves suggest CSTD is close to the benchmark curve. To identify inter-subject variability, L-I curves ofindividual participants are plotted with 4 male and 4 female participants with theirs age shown in brackets.


K L M L N L O L P L Q L R L S LPP T PQQ T PRR T PSS T P

U V W X Y Z X [ \ X ] ^ [ _ ` Y a X b c de fg hijkl mno p q \ V r \ [ ^ s t uK L M Ov p w vp x w vv U p y

Figure 5.23: L-I curves derived from estimated models according to log10(L) = a1I + a2 with DWT.

These curves represent each filtering method using ABR data from all participants. The estimated modelcoefficients are shown in table 5.6.

Method a1 a2

Theoretical -0.0025 0.9241024 -0.0026 0.9306CTMC -0.002 0.9044TWMC -0.0019 0.8978CSTD -0.0026 0.9203

Table 5.6: Coefficients of the estimated models of the L-I curves according to log10(L) = a1I + a2 derived

using DWT.

Methoda1 a2

t p CI t p CI

1024 -0.8677 0.4143 -0.0028 : -0.0023 0.7451 0.4805 0.9097 : 0.9514CTMC 15.4439 < 0.01 -0.0021 : -0.0020 -11.5464 < 0.01 0.9011 : 0.9077TWMC 22.031 < 0.01 -0.0019 : -0.0018 -12.9731 < 0.01 0.8939 : 0.9018CSTD -1.4018 0.1615 -0.0026 : -0.0025 -3.203 0.0014 0.9180 : 0.9226

Table 5.7: Results of the t-test to determine the significant difference between the derived curves and thetheoretical using DWT as the decomposition algorithm. Null hypothesis: equal means to the theoreticalcurve (P < 0.01), df = 799


5.5.7 Latency tracking results of wavelet methods with SWT

The same datasets were used as in the previous section 5.5.6 and were processed inde-

pendently with the three wavelet denoising methods using SWT as the decomposition

algorithm instead of DWT. The resultant average curve across all participants and indi-

vidual curves are shown in figure 5.24. It should be noted that the ABR template used

for CTMC and TWMC was derived from the grand average of data at 55 dB nHL for

each participant and was kept constant while denoising ABRs at all sound intensities for

each participant. These results closely resemble the curves derived from DWT. The effect

of using the template is visible in CTMC and TWMC with deviated curves at low sound

intensity levels.

A similar statistical analysis to that of previous section for DWT was carried out to

confirm the visual observation when used SWT as the decomposition algorithm. The

coefficients calculated for each wavelet method and the grand average (1024) derived from

800 epochs across 8 participants including 14 sound intensity levels, are tabulated in

table 5.8 in the form of log10(L) = a1I + a2. The plot of these models in figure 5.25

with the theoretical curve, suggests that the grand averaged and the CSTD derived curves

are a visually closer approximation to the theoretical curve compared to the CTMC and

TWMC derived curves. A one sample t-test was carried out to statistically quantify the

significance of these estimations. It was hypothesised that a1 and a2 of filtered curves are

similar to that of the theoretical curve.

According to the t-test results in table 5.9, among the three curves derived with wavelet

methods, only CSTD produced a curve (t(799) = -0.9062, p = 0.3950, 95% CI for the mean

(-0.0030, -0.0023)) with no significant difference to that of the slope (a1) of the theoretical

curve. The curves derived from both CTMC and TWMC indicate significant differences in

the slope (a1), thus these methods are less effective in latency tracking compared to CSTD.

In addition SWT derived p values are higher than those derived with DWT, suggesting the

positive effect of shift-invariance in SWT. Supporting this argument, the intercept (a2)

of the CSTD derived L-I curve show no significant difference compared to the theoretical

curve.


z z | | ~ ~ | | | | | | |

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£ ¤ ¥ ¡ ¢ ¢ ¤ ¡ ¥ ¡ ¡ ¢ ~ ¡ ¢ ~ z ¡ ¢ ¦ § ¨ ¡ ¢ ~ z § ¨ ¡ ¢ § ¨ ¡ ¢ | § ¨ ¡ ¢ |

Figure 5.24: Latency tracking with wavelet methods using SWT. Derived L-I curves from the three waveletmethods with SWT and the grand average for individual participants and the overall effect. Overall L-Icurves suggest CSTD is close to the benchmark curve. To identify inter-subject variability, L-I curves ofindividual participants are plotted with 4 male and 4 female participants with theirs age shown in brackets.These results closely resemble the L-I curves derived using DWT.


© ª « ª ¬ ª ª ® ª ¯ ª ° ª ± ª®® ² ®¯ ² ®°° ² ®±± ² ®

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Figure 5.25: L-I curves derived from estimated models according to log10(L) = a1I + a2 with SWT.

These curves represent each filtering method using ABR data from all participants. The estimated modelcoefficients are shown in table 5.8

Method a1 a2

Theoretical -0.0025 0.924Grand average -0.0026 0.9306CTMC -0.0023 0.906TWMC -0.0019 0.8813CSTD -0.0026 0.9265

Table 5.8: Coefficients of the estimated models of the L-I curves according to log10(L) = a1I + a2 derived

using SWT.

Methoda1 a2

t p CI t p CI

Grand average -0.8677 0.4143 -0.0028 : -0.0023 0.7451 0.4805 0.9097 : 0.9514CTMC 2.3677 0.0498 -0.0025 : -0.0021 -5.6873 < 0.01 0.8985 : 0.9135TWMC 6.9367 < 0.01 -0.0021 : -0.0016 -16.822 < 0.01 0.8753 : 0.8873CSTD -0.9062 0.395 -0.0030 : -0.0023 0.5682 0.5877 0.9161 : 0.9368

Table 5.9: Results of the t-test to determine the significant difference of the derived curves compared tothe theoretical. Null hypothesis is equal mean to the theoretical curve (P < 0.01), df = 799. SWT is usedas the decomposition algorithm.


5.6 Discussion

5.6.1 Evaluation of de-noising capacity of wavelet methods using DWT

The wavelet methods evaluated in this study are based on the common hypothesis that the

nullified wavelet coefficients by applying thresholds are related to spontaneous EEG noise

and retains the coefficients generated as a result of the ABR. The contribution of these

wavelet methods towards this hypothesis appeared to be different with the results obtained

in sections 5.5.3 and 5.5.5. The purpose of this discussion is to critically determine the

advantages and disadvantages of these methods and arrive at a efficient and a reliable

wavelet method for rapid extraction of the ABR. Therefore the discussion is initiated with

a summary of the performance of each wavelet method CTMC, TWMC and CSTD.

The use of a constant threshold of 20% at all the wavelet decomposition levels in CTMC

is improved by matching them with the thresholded coefficients of the template. Here,

similar thresholds are applied to high frequency noise and low frequency ABR coefficients.

Therefore high frequency components that are relevant to ABR features were removed

thus producing ABRs with distorted morphology (absence of wave I and III) as evident

in figure 5.18 and 5.21. The inability to extract such features leads to a high MSEs as

evident in figure 5.13. On the contrary, the ability to extract only wave V without the

other wave components could be beneficial in applications such as in screening of hearing,

where the presence of wave V indicates that the sound has been heard by the patient.

The use of temporal windows in TWMC appears to produce less MSE than CTMC

according to figure 5.13. The unique implementation of temporal windows, exactly tar-

get the relevant coefficients of the ABR and extract them. The effect of nullification of

irrelevant coefficients towards the end of the ABR epoch (7 ms to 10 ms) is clearly visible

in figure 5.15. However, some spurious effects could be observed in TWMC filtered ABR

in figure 5.18 in the range of 1 ms to 5 ms. This could be due to the close proximity of

the wave I and III which leads the to temporal windows being defined too close to each

other in that range. Originally TWMC was implemented to extract features of VEPs and

MLAEPs where their features are located well apart from each other on the time-scale

(Quian Quiroga 2005, Quian Quiroga 2000). But it should be noted that distortion of wave


I and III is not always the case for this method, with the evidence attached in Appendix F.

In contrast, the performance of the CSTD algorithm is superior to that of CTMC

and TWMC in terms of MSE and the extraction of features from the ABR. This unique

enhancement is due to the systematic nullification of coefficients and additional averages

to remove uncorrelated ongoing EEG. Compared to CTMC, this algorithm uses a variable

threshold on each decomposition level so that more coefficients will get nullified at higher

levels which include high frequency noise and retain more coefficients at lower levels which

are related to low frequency ABR components. In addition, the CSTD level threshold

removes more noise components resulting in a closer match to the template. The most

impressive outcome of this method is the presence of small wave components such as wave

I and III and potentially even wave II and IV with an ensemble of just 32 epochs.

In summary, when considering the rapid denoising aspect of the CTMC, TWMC and

CSTD wavelet algorithms, CSTD performs better with the DWT decomposition algorithm.

Another unique feature in CSTD is the independence of a template. The importance of this

feature, related to tracking variations of the ABR latency, is explained in the section 5.6.3.

5.6.2 Performance comparison of DWT and SWT decomposition

algorithms

It is a well known fact that the shift-variance in DWT as mentioned in section 5.1.6

distort signals with a temporal shift and SWT is one of the alternatives to prevent

such aberrations. The earlier studies published on CTMC (Zhang et al. 2006), TWMC

(Quian Quiroga 2000, Quian Quiroga 2005) and CSTD (Causevic et al. 2005) use DWT

wavelet decomposition algorithms. This study extends these methods by applying the

SWT decomposition algorithm thus replacing the DWT to avoid shift-variances. Apart

from computational complexities and redundancies in SWT, the hypothesis was that the

SWT would yield better results compared to DWT.

Complying with the hypothesis, the MSE of the SWT filtered signals yielded a lower

value compared to DWT filtered signals as evidenced in figure 5.20, supported by two

typical ABRs shown in figure 5.21. This clearly illustrates that distortions are minimised

when SWT is used in comparison with DWT; and CSTD still maintains a low MSE with


the SWT implementation.

All this evidence suggests that the combination of CSTD with SWT produces the best

method of denoising the ABR with minimum distortions in its amplitude and latency of

features (quantified by MSE). However it is important to consider the processing time of

the SWT given that the application of these methods is for a rapid extraction system.

Doubling of coefficients at each decomposition level creates a time delay. On the contrary,

given the improved accuracy of the result, a high speed processor could be easily used for

such devices to reduce the processing time with reasonable cost effectiveness.

5.6.3 Evaluation of latency tracking of wavelet methods with DWT

and SWT

The ability to track time scale variations is a key feature that should be integrated in

an algorithm used to extract ABRs. The importance of this feature becomes critical if

required for monitoring a patient with varying conditions, such as intraoperative monitor-

ing, whether the patient is undergoing a drug administration or in cases where a patient

may be suffering a neurological disorder. This thesis reports an analysis of the ability to

track such temporal variations (in terms of latency) of three wavelet algorithms. The fol-

lowing discussion will look into assessing the optimum wavelet denoising method and the

decomposition algorithm to track latency variations as well as determine the limitations

of using a template.

The overall performance of tracking latency variations using the DWT decomposition

algorithm in figure 5.22 indicates that CSTD performs better than CTMC and TWMC.

This observation is statistically confirmed by results presented in table 5.7. Additionally,

a closer observation suggests contrasting behaviour at high sound intensity levels and low

sound intensities.

At higher intensity levels, all wavelet methods follow the L-I curve of the template. For

CTMC and TWMC, this is due to the effect of the fixed reference template at 55 dB nHL.

In contrast, at low sound intensity levels, the overall L-I curve derived by CTMC sug-

gests that deviation from the benchmark curve that starts at the sound intensity level of

25 dB nHL. This is likely to be a result of using a fixed reference template. Therefore


the variation that can be tracked with CTMC is limited to ±1 ms with respect to the

latency of the reference template. The individual ABRs observed in figure 5.18 indicate

that CTMC neglects the smaller peaks, wave I and II, which may be critical in clinical

examinations. Therefore CTMC has two disadvantages according to the context of this

study.

i Inability to track latency variation greater than ±1 ms (in the case of constructing

the L-I curve in audiometry).

ii Inability to produce a fully featured ABR.

However, modifying the method to use a continuously updating the template with

CTMC would be a worthwhile endevour for a future study.

TWMC produces an overall L-I curve close to the benchmark curve at sound intensities

greater than 35 dB nHL with a mean difference of 0.2 ms (SD=0.03) but shows a larger

deviation from the standard below 35c with a mean difference of 1.56 ms (SD=0.04)

than CTMC 1.03 ms (SD=0.02). Since this method has used temporal windows defined

at 55 dB nHL, the latency variation tracking has been impossible beyond 35 dB nHL.

According to figure 5.22, the L-I curve from TWMC suggests that the maximum variation

that it can track is ±0.5 ms with respect to the latency of the reference template. This

verifies Quian Quiroga’s statement in regards to this method being resistant for latency

jitter (Quian Quiroga 2005). In addition the current study has quantified the limitation

of maximum latency jitter that can be detected to be ±0.5 ms relative to the reference

template.

In contrast, the overall L-I curve of CSTD follows the benchmark L-I curve along

the full range of sound intensities with a mean difference of 0.94 ms (SD=0.11). This

behaviour could be explained by the reference template independency of CSTD and the

superior denoising capability.

Inter-participant variability is briefly addressed, as there is a known relationship of

differences in ABRs among age and gender, for example ABR wave V latency is shorter

in females and younger adults than in males and older adults (Wilson & Aghdasi 1999).

Figure 5.22 illustrates the individual L-I curves for 4 male and 4 female participants. A


mean wave V latency prolongation of 0.3 ms (SD=0.07) can be seen in the benchmark curve

of males compared to females. This difference is closely preserved by the L-I curve derived

by CSTD with a difference of 0.12 ms (SD=0.04). In contrast, it is impossible to compare

L-I curves for CTMC and TWMC where they do not represent an accurate variation at

low sound intensities. The variation due to age appears negligible in these plots due to

the narrow age range of the participants 24 to 34 years (mean=26.7, SD=2.6). However,

a visual inspection suggests the superior performance of CSTD following the benchmark

curve at all ages.

According to the statistical analysis of the use of DWT and SWT as the decomposition

algorithm for latency tracking, it can be concluded that even with SWT as the decompo-

sition algorithm, CSTD performs superior (p = 0.395) to other wavelet filtering methods

(p < 0.01) thus revealing the limitation of using a template when tracking time-scale

variations.

A similar result is achieved by using the SWT algorithm in figure 5.24 with CSTD

performing better than CTMC and TWMC. Similar effects of the template could be seen

here with diverging L-I curves towards low sound intensity levels derived from CTMC and

TWMC.

Quantification of the MSEs of overall L-I curves in figure 5.26 reflects the similarity in

the performance of DWT and SWT algorithms. A large variation is present at low sound

intensities. However, this variation converges to very low MSE values from 30 dB nHL

onwards. This result does not entirely satisfy the hypothesis of shift-invariance property

which is, to produce an improved approximation of latency with SWT compared to the

shift-variant DWT.

However, it should be noted that the L-I curves constructed here are derived using

discrete datasets recorded at each intensity level. The drawback of shift-variance in DWT

is less observed for this type of data due to the minimal variation in ABRs produced at

constant stimulus intensity. In contrast, a dataset recorded with continuously varying

sound intensity levels as in most practical situations will have a considerable time-scale

variations in ABR latency. Even though it would be interesting to see the performance of

shift-variant DWT and the shift-invariant SWT on such a dataset, due to the limitation


Figure 5.26: The difference of the MSE of the L-I curves derived using DWT and SWT for each denoisingmethod with reference to the L-I curve derived from the MTA. i.e. (MSEDWT - MSESWT) suggestingthat MSE>0 indicates better performance of SWT and MSE<0 indicates better performance of DWT.

of time and data for this thesis, this analysis was not performed.

5.7 Conclusion

Considering the frequent use of wavelets in denoising applications, three different wavelet

denoising methods were analysed for rapid extraction of ABRs with minimum number

of epochs. CTMC and TWMC methods were based on a template while the CSTD

method was independent of a template. Two wavelet decomposition algorithms were also

considered in this analysis to assess the distortion produced by shift-variance in DWT

compared to shift-invariant SWT.

Use of constant templates in CTMC and TWMC supports the hypothesis of tracking

time-scale variations (section 2.4.1). CTMC detects latencies of ±1 ms with reference

to the template and TWMC allow latencies of ±0.5 ms. Supporting the hypothesis that

the shift invariance of the SWT decomposition algorithm produces better denoised ABRs,

MSE values were low compared to that of DWT. In contrast, contradictory results were

observed in tracking latency changes of the ABR. However, it is worthwhile to examine


the performance of the CSTD using SWT decomposition algorithm with an ABR dataset

having continuously varying latencies.

The denoising results suggested that CSTD denoising method with SWT decomposi-

tion algorithm produced a fully featured ABR. Only 32 epochs were required for the ABR

extraction which is a considerable improvement in the rapid extraction of ABRs, com-

pared to the conventional MTA of 1024 epochs. Latency tracking results suggested that

template independent CSTD is superior to the template depended methods. According

to the results of this study, CSTD with DWT decomposition algorithm is suitable for an

ABR rapid extraction system. With only 32 epochs, CSTD with DWT decomposition was

able to arrive at a fully featured ABR.

The Journal article published (De Silva & Schier 2011) including these conclusions is

attached in Appendix B.


Chapter 6

Overall conclusions and further

work

A summary of the independent studies carried out towards the common objective of eval-

uating a rapid method to extract ABRs is presented in this chapter. In the exploration of

a rapid extraction algorithm of the ABR, ARX modelling and wavelet denoising revealed

contrasting results with different levels of susceptibility to noise and time-scale variations.

It was determined for parametric model-based extraction algorithms that the conven-

tional ARX modelling outperformed REPE for MSE. However, superior performance was

observed in the CSTD wavelet denoising algorithm, which produced a fully featured ABR.

This chapter presents the conclusions drawn, application domain, limitations and pos-

sible future expansions, based upon the investigated methods.

165

6.1 The approach towards the extraction of ABR

Lengthy acquisition times required to extract the ABR impose significant restrictions

on its use in diagnostic and monitoring applications. Typically it takes of the order of

minutes to acquire a sufficiently noise free ABR, using conventional MTA methods, so that

the amplitude and latency of its major components can be identified. Further, lengthy

acquisition times increase the likelihood that a range of externally generated artifacts,

particularly patient movements, will compromise the fidelity of the acquisition.

In order to overcome such limitations, studies were constituted to investigate the effi-

cacy of algorithms to rapidly acquire the ABR using a minimal number of epochs. Based

on an extensive review of the literature concerning the rapid extraction of evoked re-

sponses, the ARX modelling and wavelet based denoising methods were considered the

most promising for ABR rapid extraction.

6.2 Rapid extraction with ARX and REPE

Because ARX modelling has not been used previously to extract short latency ABRs,

this study systematically establishes the suitability of the ARX approach along with the

variant REPE, for single/limited sweep extraction in a high noise environment. The use of

real ABR data for the evaluation imposes an often-unacknowledged drawback of assuming

the availability of an actual noise-free EP/ABR for each epoch recorded. To address

this limitation and uncertainty; the ability to extract the ABR was tested with a well-

defined and reproducible simulation study involving a synthetic ABR model with additive

noise. On this basis, the following specific features were evaluated for the ARX and REPE

methods:

• The accurate identification of the actual model parameters with ARX and REPE

algorithms.

• Quantification of noise reduction/denoising achieved by the ARX and REPE algo-

rithms.

Overall conclusions and further work 166

• Quantification of the range of wave V latency variations tracked with ARX and

REPE algorithms.

• The application and confirmation of these findings with real ABRs.

The systematic evaluation these features of the ARX and REPE methods revealed the

following:

• Estimation of predefined model parameters performed for both ARX and the REPE

methods revealed that the poles approached the predetermined values, but with an

offset for the zeros. This suggests that the estimated ABR does not possess the exact

spectral characteristics of the original. The scattered zeros could be as a result of

the noise imposed on the ABR.

• REPE produced a superior SNR improvement of 23 dB at -30 dB initial SNR com-

pared to the ARX. In contrast, inspection of individual ABR epochs, suggested that

ARX produced a closer match to the reference ABR with a mean correlation coeffi-

cient of 0.84 (SD = 0.02) compared to the REPE with a mean correlation coefficient

of 0.63 (SD = 0.06), suggesting the introduction of pre-whitening in the REPE has

a detrimental effect on the estimated ABR.

• ARX modelling performed superior in tracking latency variations compared to the

REPE. This was evident with the ARX able to estimate latency offsets of 2 ms at

a frequency of 1 Hz with an initial SNR of -5 dB. In contrast, REPE was unable to

estimate latency variations (even at a SNR of 0 dB).

• Since the SNR of a physiological ABR is approximately -30 dB, the ARX model

required an ensemble of epochs rather than a single sweep to provide an output of

the model. Application of the ARX modelling to real ABRs confirmed that even

with an ideal reference input template u(k), the output of the model y(k) would

require an ensemble average of more than 256 sweeps. According to these results,

rapid extraction cannot be achieved with ARX modelling. Therefore ARX modelling

is unsuitable for the extraction of signals with low SNR such as ABRs.


The contributions to the field by the study carried out for this thesis are largely to

clarify the applicability of the ARX model in extracting the ABR features and their

time-scale variations as well as to clarify shortcomings of previous, related studies. In

previous research, aberrations of estimated signals from the ARX model were suspected

to arrive from the inconsistency of the generation of the EP (Cerutti et al. 1987, Rossi

et al. 2007). But with the simulation study in this thesis (with synthetic ABRs and known

presence of the EP), the effect of SNR and the latency variability were highlighted as

contributors to the aberration of the estimated EP. Thereby, boundaries were determined

for the successful estimation of single sweep ABRs with ARX modelling. It was confirmed

both in previous research and in the current study that the REPE produced approximately

10 dB SNR improvement compared to the conventional ARX modelling. However, the

latency variation tracking ability of the REPE was poor (following the MTA estimate)

and hence was deemed not suitable for ABR extraction.

6.3 Rapid extraction with wavelets

There also exists the possibility of rapidly extracting ABRs using a different paradigm.

Considering the success of wavelet based denoising methods in EP applications, three

wavelet denoising methods, CTMC, TWMC and CSTD were adopted to the ABR. CTMC

and TWMC are based on a template of the ABR whereas CSTD is executed without such

a template. Denoising of CTMC imposes only thresholds, whereas CSTD also employed

a cyclic averaging technique. In contrast, TWMC used a denoising technique based on

temporal windowing of wavelet coefficients. The following were examined in order to

determine the suitability of these methods to use in a rapid extraction method of the

ABR.

• Identification of optimum threshold functions and time windows compatible with

the ABR.

• Evaluation of the most effective denoising method at low SNR i.e. with reduced

number of epochs.


• Identification of the most effective time-scale variation tracking wavelet denoising

method.

• Analysis of the effect of DWT and SWT decomposition algorithms on chosen three

denoising methods.

The following conclusions were drawn from the results generated by subjecting real ABRs

to the specific wavelet methods.

• Performance of CSTD is superior in denoising ABRs compared to CTMC and

TWMC with a significant difference in MSEs (p < 0.01). The two optimum threshold

functions and the circular averaging contribute to this effective noise reduction.

• Performance of noise reduction in CSTD compared to CTMC and TWMC is con-

sistent for both DWT and SWT decomposition algorithms. However, an improved

noise reduction resulted when using SWT as the decomposition algorithm, thus re-

vealing the advantage of the shift-invariance (p < 0.01).

• An ensemble of 32 epochs is sufficient to extract a fully featured ABR denoised with

CSTD as a result of a significant difference in correlation coefficients (p < 0.01).

• Latency variations are closely tracked by the CSTD with similar slopes (a1 in the L-I

curve model) (p = 0.1615). Independence of a template (reference signal) appears

to assist the CSTD to track latency variations without any limitations.

• With a constant template, CTMC is able to track latency variations of ±1 ms ref-

erence to the template, while TWMC is able to track latency variations of ±0.5 ms.

These limitations impose a barrier for their use in clinical practice.

• As a method of extracting ABRs from underlying EEG with the association of

reduced number of sweeps, cyclic shift tree denoising (CSTD) algorithm is the opti-

mum among the wavelet algorithms compared. Therefore, the systematic evaluation

confirms that the CSTD wavelet method can be used for rapid extraction of ABRs.


6.4 Limitations of the current study and future work

The promising results generated during this study provide scope for further refinements

and developments. Considering the clinical importance of the amplitude variations of the

ABR (especially in hearing screening), it would be worthwhile to evaluate these variations

using both ARX and wavelet methods in addition to the latency examined here.

A specific limitation of this study exists in the discrete datasets recorded at each sound

intensity level. The L-I curves constructed with this data created discontinuities along the

curve. It would be worthwhile for the future examination of the performance of the CSTD

using SWT decomposition algorithm with an ABR dataset derived from a continuous

variation of sound intensity levels (which leads to a continuous variation in ABR latency).

This would give a profound indication of the performance comparison of the DWT and

SWT decomposition algorithms. In addition, for the special case of identifying only wave

V, modifying the CTMC method to use a continuously updating template would be a

worthwhile investigation.

As conventional statistical threshold methods (Fsp) do not fulfil the underlying as-

sumptions, estimating the distribution of the residual noise could be beneficial thereby

determining a new threshold compatible to non MTA methods.

Finally, the evaluation of the CSTD method, with optimised parameters using a large

pool of ABR recordings would lead to a fully functional device for the rapid extraction

of ABRs. It would also be important to include participants with pathological disorders

which are known to affect ABR features.


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Appendix A

Ethics approval

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

Appendix B

Journal Publications

PLEASE NOTE

Appendix B is unable to be reproduced online.

Please consult print copy held in the Swinburne Library or click on the links below.

De Silva, AC, Schier, MA (2011) Evaluation of wavelet techniques in

rapid extraction of ABR variations from underlying EEG. Physiological Measurement 32 (11) 1747-1761

DOI: 10.1088/0967-3334/32/11/s03

De Silva, AC, Sinclair, NC, Liley, DT (2012) Limitations in the rapid extraction of evoked potentials using parametric modelling.

IEEE Transactions in Biomedical Engineering 59(5) 1462-1471 DOI: 10.1109/TBME.2012.2188527

http://dx.doi.org/10.1088/0967-3334/32/11/s03

http://dx.doi.org/10.1109/TBME.2012.2188527

Appendix C

Stimulation and acquisition of the

ABR

i Introduction

The study about the ABR recording setup is peripheral to the main aim of this thesis,

thus presented as an appendix. During the recordings aberrations were observed and an

exploration of the parameters affecting the quality of the ABR recording was warranted.

This study aims to achieve the following:

• Explore parameters affecting the stimulus artifact

– Type of transducer used for auditory stimulation

– Electrode montage used to record scalp voltages

• Assess the quality of ABRs produced by a range of audio transducers

• Minimise the effect of the stimulus artifact

In summary the results suggest that, even though all the transducers generated a

stimulus artifact with considerably large amplitudes, its duration did not affect the early

components of the ABR. Temporal delays of ABR components were observed with some

transducers which required calibration before their use in diagnosis tests.

Appendix C I

ii Methodology

ii.i Pilot study

The initial recording was conducted with a one participant stimulated at an intensity

of 60 dB nHL at 21.1 Hz. Electrodes were placed at Cz, Fpz and at the mastoid. The

remainder of the parameters were set according to table 1. The resultant ABR with a MTA

of 1024 epochs (deemed to be sufficient with an Fsp = 3.51) is shown in figure 1. Here,

the prominent observation is a stimulus artifact at the onset of the auditory stimulation

(t = 0 ms) generated by the magnetic field induced by the audio transducer. The critical

observation is the time duration of the stimulus artifact which appears to reach towards

1 ms posing a threat to distort wave I. However, the general morphology of the ABR is

visible with the maximum peak at 5.8 ms corresponding to the wave V.

As a result, we formulated a method to investigate the suitability of a variety of audio

transducers in stimulating the ABR. The experimental setup and the results obtained

from this study are reported in following sections.

V W X Y Z [ V\ ]\ W\ [V [W]X

^ _ ` a b ` c de fghi j kl mn µ

op q r _ ` s t s c u v r _ w u x r

Figure 1: ABR recording with a stimulus artifact at t=0 (De Silva & Schier 2009)

Appendix C II

Parameter Settings

Stimulus parameters

Type ClickPulse width 0.1 msPolarity a square pulse with a negative polarityFrequency > 20 HzIntensity Variable in dB nHLNo. of epochs Variable to obtain an ABR with adequate SNRMode MonauralMasking Only if the ABR is abnormalAcquisition parameters

Electrode montageNon-inverting Cz or FzInverting A or M (ipsilateral)Ground FpzFilteringHigh-pass 30 HzLow-pass 3 kHzAmplification 100000Sampling rate 40 kHzAnalysis time 15 msPre-stimulus interval 10% of the analysis time

Table 1: Settings for a typical ABR recording (Hall 2007, Van Campen et al. 1992).

ii.ii Selection of audio transducers

Eight audio transducers based on moving-coil technology were tested and are summarised

in table 2. These transducers included supra-aural and circum-aural headphones (with

different padding at the ear piece) and outer-ear and in-ear earphones with different posi-

tioning at the ear. The TDH-49 and TDH-39 headphones were considered as the ‘gold stan-

dard ’ for comparison purposes (Hall 2007). QantasTM, PanasonicTMand NokiaTMouter-ear

earphones were selected considering the common availability. The 1.2M earphone provided

in-ear positioning which could stimulate the tympanic membrane with less distortion due

to the close proximity and analogues to clinically used Etymotic ER-3A insert earphones

(Hall 2007, Wilson 2004, Wilson & Aghdasi 1999). Superior sound quality prompted

AltronicsTMand PhilipsTMcircum-aural headphones to be tested to deliver stimuli. All

the audio transducers will be referred with the specific letter label, ‘A’ to ‘H’ in table 2

Appendix C III

Label Model Type Description

A TDH-49p Supra-aural Headphones Telephonics (Audiometer)B TDH-39 Supra-aural Headphones Telephonics Voyager 522C Qantas Outer-ear Earphones Comfort kit (Entertainment)D Panasonic Outer-ear Earphones RQ-E27V (Entertainment)E Nokia Outer-ear Earphones 5200 (Communication)F 1.2M (in-ear) In-ear Earphones Capdase (Entertainment)G Altronics Circum-aural Headset C 9073 (Professional pilot)H Philips Circum-aural Headphone SB347 (Entertainment)

Table 2: Description of the audio transducers used in this study.

from here onwards.

ii.iii Selection of electrode montages

A potential implication of using non-standard audio transducers is the possibility of in-

ducing a stimulus artifact by the interaction of scalp electrodes and the stray magnetic

field generated by the trasducer. To study an such effect, out of the standard electrode

montages mentioned in table 1, inverting electrode at the earlobe and the mastoid posi-

tions were assessed due to the closest proximity to the audio transducer. Non-inverting

and the ground electrodes were kept at Cz and Fpz respectively. The choice of Cz for

the non-inverting electrode instead of Fz was to obtain a larger wave V (Kavanagh &

Clark 1989). These two electrode montages evaluated are summarised in table 3.

Earlobe montage Mastoid montage

Non-inverting Cz CzInverting Earlobe MastoidGround Fpz Fpz

Table 3: Two electrode montages tested in this study. The position of the inverting electrode differed intwo montages from earlobe to the mastoid to assess the interaction with the EM field of the transducer.

ii.iv Measurement approaches

As evident in figure 1, it is difficult to determine the end time point of the stimulus artifact

due to the overlap of ongoing EEG. Therefore a phantom head with a realistic shape and

Appendix C IV

(a) Human participant

(b) Phantom

Figure 2: Recording setup with electrode placement and headphones TDH-49p headphones are worn herewith the electrodes connected in earlobe montage. Picture was taken with the permission of the participant.

similar electrical properties to that of an average human head was used to examine the

stimulus artifact produced without the interference of any physiological potential. Then

the same audio transducers were tested on human participants to analyse the combined

effect with ABRs. Both electrode montages in table 3 were tested on the phantom head

and on human participants.

Data were collected from four healthy human participants (2 male and 2 female) with

an age range of 24 to 26 years. The Swinburne University Human Experimentation Ethics

Committee approved this study, and each participant gave written informed consent in

accordance with these requirements. The official ethics clearance details are attached

in Appendix A. All the headphones listed in table 2 were used on each participant. A

visualization of this recording setup is shown in figure 2a. The polystyrene phantom head

is shown in figure 2b with dimensions similar to an average human head to study the

stimulus artifact in isolation.

Simulating inter-electrode impedance is the critical electrical parameter which affects

voltage measurements from the scalp. Therefore a series combination of resistors and

capacitors was used on the phantom scalp in between ground-inverting and ground-non-

inverting electrode combinations (Wood, Hamblin & Croft 2003). The inter-electrode

impedances used at the phantom scalp was based on the average impedances of the human

Appendix C V

Resistance (kΩ) Capacitance (µF) No. of measurements

Human scalp 3.0 ± 1.4 2.3 ± 0.9 32Phantom 3.1 3 16

Table 4: Average inter-electrode impedance measurements between ground-inverting and ground-non-inverting at 100 Hz. Variation values indicate standard deviation.

participants. The values obtained from the 32 independent readings of human participants

and the comparable values used for the phantom is tabulated in table 4 indicating the

validity of the phantom model. All the impedances were measured at 100 Hz using GW

Digital LCR meter produced by GW InstekTM(New Taipei City, Taiwan).

ii.v Equipment and parameters

A conducting gel-injected disk electrode was used at Cz and 3MTMdisposable electrodes

at earlobe, mastoid and Fpz locations. All the electrodes had silver chloride surfaces to

achieve comparable surface impedances. Recording setup consisted of PowerLabTMamplifier

with a gain of 100k and Chart-5 software produced by ADInstrumentsTM(Sydney, Aus-

tralia) as the interface to collect data. The auditory stimulus was a negative polarity

square pulse with a width of 0.1 ms at a frequency of 21.1 Hz and was dilivered via a

TelephonicTMTDH-49 headphone. The data were sampled at a frequency of 40 kHz and

band-pass filtered between 100-3000 Hz with a 3rd order Butterworth filter using a zero-

phase shifting method (Oppenheim & Schafer 1999). Choice of the low cut-off frequency

of 100 Hz as oppose to 30 Hz in table 1 is to minimize the effect of noise from on going

EEG and myogenic artifacts (Corona-Strauss, Delb, Schick & Strauss 2010, Rushaidin,

Salleh, Swee, Najeb & Arooj 2009, Petoe, Bradley & Wilson 2010). The zero-phase shift-

ing filter was specifically used here to preserve the latencies of the ABR waves. The ABR

is convolved in both the forward and backward directions to regain the phase shift created

when filtered only in one direction. This operation doubles the filter order, leading to

additional computation but with an added advantage of retaining phase characteristics.

A sound intensity of 60 dB nHL was maintained at each audio transducer output. Custom

written scripts were used for offline analysis using MATLABTM(MATLAB 2008) produced

Appendix C VI

by MathWorks (Natick, Massachusetts, USA).

ii.vi Analysis criteria

To achieve the objective of determining the best setup for recording ABR data, following

criteria were analysed with each audio transducer.

(i) Determine the minimum impact of the stimulus artifact among earlobe and mastoid

electrode montages using phantom recordings

(ii) Analyse the separation between the stimulus artifact and the wave I

(iii) Analyse the ABR latencies produced in comparison to normative data

ii.vii Stimulus artifact end time (SAET)

As identified, the amplitude of the stimulus artifact is less important in its effect on the

early components of the ABR than the width of the artifact. Therefore a new measurement

y z z | ~y y y ~y ||~

Figure 3: Measurement of stimulus artifact end time (SAET). Standard deviation is calculated for thepre-stimulus interval from -1 to 0 ms. Here the decaying stimulus artifact reaches within the standarddeviation just after 0.5 ms. Therefore according to the criterion SAET = 0.65 ms.

Appendix C VII

defined as the stimulus artifact end time (SAET) was used to analyse the duration of the

stimulus artifact. SAET is the time period from the onset of the stimulus to the time point

of the decaying stimulus artifact reach within 1 standard deviation of the pre-stimulus

baseline. A visualisation of SAET is shown in figure 3.

ii.viii Normative latency data

The introduction of new transducers should be assessed by the quality of the ABRs pro-

duced by them. Two measurement approaches were consider here by examining the pres-

ence of wave I, II, III and V and the latencies of them. The latencies of ABR features were

benchmarked with normative data to strengthen the conclusion. Table 5 shows published

literature values for ABR wave latencies with similar experimental conditions. Stimulus

intensity is the critical stimulus parameter which affects the ABR latency. However, these

data have been extracted from ABRs generated with sound intensities in the range of

75-85 dB nHL. As evident in the figure 3.5(a), latency variations at high intensities are

negligible, thus latencies in table 5 are comparable with each other within the relevant

variance. These were used as normative data for comparison purposes with the range of

audio transducers and montages.

Appendix C VIII

iii Results

iii.i Effect of the stimulus artifact on electrode montages with the

phantom

To observe the effect of the magnetic field on inverting electrode placed at the earlobe

and mastoid, results were generated by conducting recordings on the phantom with all

the transducers. A visualization of the stimulus artifact at the earlobe is shown in figure 4

and that of the mastoid is shown in figure 5. The labels on the vertical axis are referred to

the audio transducers listed in the table 2. The SAETs calculated from these recordings

are tabulated in table 6 for both electrode montages.

iii.ii Results for the separation between the stimulus artifact and wave

I

Figure 6 and figure 7 show the ABR recordings of a single participant using the two elec-

trode montages. Each figure shows 8 ABRs which were obtained using audio transducers

AudioTransducer

Wave I Wave II Wave III Wave V Source

x σ x σ x σ x σ

TDH-49 1.62 0.12 N/A 3.76 0.14 5.74 0.2 (Van Campenet al. 1992)

TDH-39 1.61 0.13 N/A 3.78 0.17 5.76 0.21 (Van Campenet al. 1992)

TDH-39 1.54 0.08 2.67 0.13 3.73 0.1 5.52 0.15 (Antonelli,Bellotto &Grandori1987)

TDH-39 1.87 0.18 2.88 0.2 3.83 0.2 5.82 0.25 (Rowe III1978)

ER-3A 1.54 0.1 N/A 3.7 0.15 5.6 0.19 (Schwartz,Pratt Jr &Schwartz1989)

Table 5: Published data for ABR waves in literature. These will be considered as normative data and thegold standard for this study.

Appendix C IX

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Figure 4: Phantom recordings with inverting electrode at earlobe

¾ ¿ À Á Â Ã ¾ÄÅ ÆÇÈÉ ÊË

Ì Í Î Ï Ð Î Ñ ÒÓ ÔÕÖ×Ø ÙÚÛÔ×

Figure 5: Phantom recordings with inverting electrode at mastoid

Appendix C X

Transducer label SAETEarlobe (ms) Mastoid (ms)

A 0.5 0.58B 0.6 0.5C 0.65 0.68D 0.65 0.68E 0.65 0.48F 0.63 0.63G 0.65 0.65H 0.65 0.65x 0.62 0.61σ 0.05 0.08

Table 6: SAETs for all the transducers. The inverting electrode at the earlobe and mastoid. Refer table 2for transducer descriptions

listed in table 2. Physiologically important waves I, II, III and V are shown on top of each

ABR with vertical markers from left to right. The latency of the wave I was calculated

with these data to determine the distortion by the stimulus artifact.

Figure 8 shows the separation time between the wave I and the SAET for all the

participants. Here, SAETs were the values derived from phantom data in table 6. It is

evident that there exists an effect of the audio transducer on the separation time and a

variation between electrode montages.

Appendix C XI

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® ¯ ° ± ² ° ³ ´µ ¶·¹º »¼½¶

Figure 6: ABRs produced with inverting electrode at earlobe. These ABRs contain average of 1024 epochsfor each transducer A-H. Vertical markers on ABR show wave I, II, III and V from left to right.

¾ ¿ À Á Â Ã ¾ÄÅ ÆÇÈÉ ÊË

Ì Í Î Ï Ð Î Ñ ÒÓ ÔÕÖ×Ø ÙÚÛÔ×

Figure 7: ABRs produced with inverting electrode at mastoid. These ABRs contain average of 1024 epochsfor each transducer A-H. Vertical markers on ABR show wave I, II, III and V from left to right.

Appendix C XII

Figure 8: The average separation between the SAET and the ABR wave I. Across all participants for eachtransducer. SAETs are taken from phantom measurements.

iii.iii Effect of transducer type on the latency

Figure 9a and 9b show the latencies of waves I, II, III and V for the earlobe and mastoid

electrode montages respectively. These values are an average across all participants. The

standard deviation among them is shown in horizontal error bars. Vertical grey bars

represent the probable range for each wave latency according published normative data

in table 5. This allows a direct comparison of the results obtained from this study with

standard data published.

Appendix C XIII

(a) Average latency of wave I, II, III and V from all participants with invertingelectrode at earlobe.

(b) Average latency of wave I, II, III and V from all participants with invertingelectrode at mastoid.

Figure 9: Latency of ABR waves with inverting electrode at earlobe and mastoid. The horizontal axisrepresents transducers from A-H on the vertical axis. Standard deviation is in horizontal error bars.Vertical grey bars represent the average range of published data for ABR waves.

Appendix C XIV

iv Discussion

iv.i Stimulus artifact and electrode montage

A visual inspection of figure 4 and 5 suggests that the end of the stimulus artifact is

aligned closely within each electrode montage. A paired two tailed t-test of SAETs in

table 6 confirms that the difference of SAET in between the earlobe and the mastoid

electrode montages are not significant (t(7) = 0.57, p = 0.58, 95%). Therefore, we can

conclude that there is no effect on the length of the stimulus artifact from either the

transducer or the electrode montage.

It is also evident from these figures that there exists a variation in amplitudes of the

stimulus artifacts. But this measure has no adverse effect on ABR features.

A comparison of stimulus artifact amplitudes with the gold standard transducers A

and B suggest, transducer F in earlobe (figure 4) and C, D, E and F in mastoid (figure 5)

electrode montages have comparable values. Therefore they have the potential to be used

in ABR recordings. The variable amplitudes of the same transducer in two electrode

montages confirm the assumption that the electrode montages have a considerable effect

on the stimulus artifact.

In terms of substitutions for an audio transducer for stimulation, all the transducers

tested here provided promising results for the SAET. Therefore they all were tested and

analysed further on human participants for:

1. separation between the stimulus artifact and the wave I

2. quality of the ABR produced

in order to arrive at a comprehensive conclusion in sections (iv.ii) and section (iv.iii).

Appendix C XV

iv.ii Analysis of the separation of SAET and wave I

A visual observation of figure 6 and 7 indicates a clear separation in time between stimulus

artifact and the wave I for all the transducers in both electrode montages. With regard

to amplitudes, a similar visual comparison reveals, the introduced transducers D, F and

G with reference to the earlobe and C, G and H with reference to the mastoid have

comparatively larger amplitudes to gold standard transducers A and B.

Precise values for the average separation among all participants shown in figure 8

suggest all the introduced transducers produce an average separation time of 1 ms which

is comparable with 1.06 ms of separation produced by the gold standard transducers A

and B.

An ANOVA was performed on separation values presented in figure 8 to investigate

the effect of the magnetic field on electrode montages for each transducer. Results suggest

that there is no significant effect on separation time among the two electrode montages

for all the transducers tested (F (1, 63) = 0.11, p = 0.74, 95%). Therefore, despite all these

minor variations, the separation between the stimulus artifact and the wave I produced by

the introduced transducers (C, D, E, F, G and H) are comparable with the gold standard

transducers.

As observed, the stimulus artifact is unavoidable when the transducer is located close

to the head. Therefore, it is important to exclude this artifact at the signal processing stage

of the ABR because some processing methods might pickup the artifact as an important

feature and neglect actual ABR waves.

iv.iii Quality of the ABRs

It can be observed that wave I, II, III and V are present in all ABRs evoked all the

transducers in figures 6 and 7. This is an encouraging result when assessing the quality of

transducers for the purpose of generating ABRs.

Appendix C XVI

The absolute latencies of ABR waves are constant for a given participant at a specific

sound intensity level (Misra & Kakita 1999). Therefore the reliability of the ABR produced

by each audio transducer could be determined by comparing latencies of wave I, II, III

and V with published normative data (Table 5).

According to figure 9, resultant mean latencies of all waves produced by the gold stan-

dard transducers A and B fall well within the normative ranges and produce a substantially

overlapped variation. Since there is no assumption of a significant difference in wave V

latency above 60 dB nHL, it is confirmed that the experimental conditions are comparable

with the conditions of the previous research.

Referring to figure 9, a noticeable lag for the transducer G and a lead for the transducer

F exists for all ABR features. This is as a result of the proximity of the transducer to the

eardrum. The bulky Altronics headphone (G) has its transducer positioned away from

the outer ear creating a lag and the in-ear earphone (F) has it inside the ear canal close to

the eardrum creating a lead. However there is not enough variation to warrant a latency

correction for these two transducers in both electrode montages.

The reader should note that there are other measurements which can improve the

comparison study such as, the spectral characteristics of the audio output which would

have a considerable effect on the stimulation of hair cells. Also calibration of the output

of all earphones to a common reference would have greatly benefited when interpreting

variations in figures 6, 7 and 9. Including these as a future study could be of great benefit

to increase its coherence.

The ABR features produced by all the transducers in figure 9 suggest that both earlobe

and mastoid electrode montages produce consistent results for all the introduced audio

transducers.

Appendix C XVII

v Summary

According to the analysis criteria stated in section (ii.vi), the results of this study are

summarised as shown below.

(i) The type of the transducer and the electrode montage did not affect the SAET.

Even though the amplitudes of the stimulus artifact from introduced transducers

were larger than those of the gold standard, it had no impact on the ABR features.

(ii) The time separation between the SAET and the wave I for introduced transducers

did not produce significant differences to that of gold standard transducers A and

B.

(iii) ABR features were produced by all the transducers and mean latencies of them were

within the normative ranges. A small latency shift of approximately 0.2 ms was

observed in the ABR depending on the proximity of the transducer relative to the

tympanic membrane.

The conclusion, considering the above statements suggest the feasibility to use most com-

mercially available audio transducers in ABR studies. The latency shifts incorporated

with the ABR due to transducers could be adjusted to achieve a more accurate result.

Truncating the ABR with time window of 1-10 ms will suppress the inevitable stimulus

artifact and prevent any false peaks.

The comparable morphology of the ABRs and its variations to that of previously

published reports gave an impetus to evaluate noise reduction methods for rapid extraction

with confidence. As literature suggested, commercially used (at the time of the research)

MLAEP extraction method based on ARX was comprehensively evaluated in the next

chapter for its adaptation to the early components i.e. ABR.

Appendix C XVIII

Appendix D

MATLAB scripts

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å æ ç è é ê ë ì é ì í î ï î æ ð í ð ñ ò ó ô ò õ ï ö ì ë ì î ï ë ÷ ð ø æ î ù é õ æ î ù ú û ó% Processing data of a single sound intensity level with CTMC using DWT The template is derived with the grand average at 55 dB nHL clear all WT = 'bior5.5'; % mother wavelet level = 6; % decomposition levels threshold = 0.8; % retain (1-threshold) bkl = [256 128 64 32 16 8]; % analysed block lengths %% Template calculation using 55 dB nHL load('sw_epochs_55_-11-10.mat'); [b,a] = butter(3,[100/20000,3000/20000]); % generate band pass filter coefficients epochs = filtfilt(b,a,epochs); % zero phase filtering tmpl = mean(epochs(401:840,1:1024),2); % calculating the grand average tmpl((1:80),1) = 0; % remove stimulus artifact; tapering - zeros till 1ms %% Loading dataset to be denoised epochs = []; load('sw_epochs_75_-11-10.mat') epochs = filtfilt(b,a,epochs); [C(:,1),Ltmpl] = wavedec(tmpl,level,WT); % wavelet decomposition of the template for n = 1:length(bkl) %loop for different block lengths for k = 1:1024-256+1 %loop for continuous sweeping through the dataset %% Signal calculations sig(:,k) = mean(epochs(401:840,256-bkl(n)+k:256+k-1),2); % generate the noisy ABR with reduced number epochs sig((1:80),k) = 0; [C(:,2),Lsig] = wavedec(sig(:,k),level,WT); % wavelet decomposition of the noisy ABR %normalizing the simple average to plot signorm(:,k) = sig(:,k) - min(sig(:,k)); signorm(:,k) = signorm(:,k)/max(signorm(:,k)); %normaling the block signorm((1:80),k) = 0; %tapering - zeros till 1ms %% Extraction of thresholded coefficients of the template and the noisy ABR Ct(:,1) = zeros(length(C),1); % initialise coefficients of the thresholded template Ct(:,2) = zeros(length(C),1); % initialise coefficients of the thresholded signal for j = 1:2 %thresholding of template and signal coefficients % A6 - retaining all the coefficients A6 = C(1:Lsig(1,1),j); for i = 1:Lsig(1,1) Ct(i,j) = A6(i,1); end %D6 D6 = C(Lsig(1,1)+1:sum(Lsig(1:2)),j); top20 = find(abs(D6)>max(abs(D6))*threshold); % applying the threshold for i = 1:length(top20) Ct(Lsig(1,1)+top20(i,1),j) = C(Lsig(1,1)+top20(i,1),j); end %D5 D5 = C(sum(Lsig(1:2))+1:sum(Lsig(1:3)),j);

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top20 = find(abs(D5)>max(abs(D5))*threshold); % applying the threshold for i = 1:length(top20) Ct(sum(Lsig(1:2))+top20(i,1),j) = C(sum(Lsig(1:2))+top20(i,1),j); end % D4 D4 = C(sum(Lsig(1:3))+1:sum(Lsig(1:4)),j); top20 = find(abs(D4)>max(abs(D4))*threshold); % applying the threshold for i = 1:length(top20) Ct(sum(Lsig(1:3))+top20(i,1),j) = C(sum(Lsig(1:3))+top20(i,1),j); end % D3 D3 = C(sum(Lsig(1:4))+1:sum(Lsig(1:5)),j); top20 = find(abs(D3)>max(abs(D3))*threshold); for i = 1:length(top20) Ct(sum(Lsig(1:4))+top20(i,1),j) = 0; % set all coefficients to zero; out of the bandwith of the ABR end % D2 D2 = C(sum(Lsig(1:5))+1:sum(Lsig(1:6)),j); top20 = find(abs(D2)>max(abs(D2))*threshold); for i = 1:length(top20) Ct(sum(Lsig(1:5))+top20(i,1),j) = 0; % set all coefficients to zero; out of the bandwith of the ABR end % D1 D1 = C(sum(Lsig(1:6))+1:sum(Lsig(1:7)),j); top20 = find(abs(D1)>max(abs(D1))*threshold); for i = 1:length(top20) Ct(sum(Lsig(1:6))+top20(i,1),j) = 0; % set all coefficients to zero; out of the bandwith of the ABR end end %% Matching thresholded template coefficients and thresholded noisy ABR coefficients for further refining match = find(abs(Ct(:,1))>0); % find significant coefficients of the template Ct(:,3) = zeros(length(C),1); % intialise coefficients of the matched signal with the thresholded template for i = 1:length(match) Ct(match(i,1),3) = Ct(match(i,1),2); end %% Reconstructing and plotting the denoised ABR recon(:,k) = waverec(Ct(:,3),Lsig,WT); % reconstruction of the denoised ABR %normalizing the filtered average to plot reconnorm(:,k) = recon(:,k) - min(recon(:,k)); reconnorm(:,k) = reconnorm(:,k)/max(reconnorm(:,k)); %normalising reconnorm((1:80),k) = 0; %tapering - zeros till 1ms %% MSE calculation (amount of noise compared to the template) mse_at(k,n) = mean((tmpl-sig(81:440,k)).^2); % between conventional average and template mse_wt(k,n) = mean((tmpl-recon(81:440,k)).^2); % between wavelet filtering and template end %% Plots figure

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contourf((41:400)/40,256:k+256-1,flipdim(reconnorm(81:440,:)',1),'LineStyle','none') title(['CTMC - Filtered average of ',num2str(bkl(n)),' blocks - ',WT]) xlabel('Time (ms)'),ylabel('Epochs') end è é ê ë ì é ì í î ï î æ ð í ð ñ ó û ô ò õ ï ö ì ë ì î ï ë ÷ ð ø æ î ù é õ æ î ù ú û ó% Processing data of a single sound intensity level with TWMC % The template is derived with the grand average at 55 dB nHL clear all WT = 'bior5.5'; % mother wavelet level = 6; % decomposition levels bkl = [256 128 64 32 16 8]; % analysed block lengths %% Template calculation using 55 dB nHL load('sw_epochs_55_-11-10.mat'); [b,a] = butter(3,[100/20000,3000/20000]); % generate band pass filter coefficients epochs = filtfilt(b,a,epochs); % zero phase filtering tmpl = mean(epochs(401:840,1:1024),2); % calculating the grand average tmpl((1:80),1) = 0; % remove stimulus artifact; tapering - zeros till 1ms %% Loading signal to be denoised epochs = []; load(['sw_epochs_75_-11-10.mat']); epochs = filtfilt(b,a,epochs); for j = 1:length(bkl) %loop for different block lengths for k = 1:1024-256+1 %loop for continuous blocks %% Signal calculations sig(:,k) = mean(epochs(401:840,256-bkl(j)+k:256+k-1),2); % generate the noisy ABR with reduced number epochs sig((1:80),k) = 0; %normalizing the simple average to plot (1-10ms) signorm(:,k) = sig(:,k) - min(sig(:,k)); %normalizing the block signorm(:,k) = signorm(:,k)/max(signorm(:,k)); %normalizing the block [Csig,Lsig] = wavedec(sig(:,k),level,WT); % wavelet decomposition of the noisy ABR for i = 1:level % reconstruction of the signal at each decomposition level sigcoeff(:,i) = wrcoef('d',Csig,Lsig,WT,i); if i ==level sigcoeff(:,i+1) = wrcoef('a',Csig,Lsig,WT,i); end end coeff = []; coeff_A6 = Csig(1:Lsig(1,1),1); coeff_D6 = Csig(Lsig(1,1)+1:sum(Lsig(1:2)),1); coeff_D5 = Csig(sum(Lsig(1:2))+1:sum(Lsig(1:3)),1); coeff_D4 = Csig(sum(Lsig(1:3))+1:sum(Lsig(1:4)),1); coeff_D3 = Csig(sum(Lsig(1:4))+1:sum(Lsig(1:5)),1); coeff_D2 = Csig(sum(Lsig(1:5))+1:sum(Lsig(1:6)),1); coeff_D1 = Csig(sum(Lsig(1:6))+1:sum(Lsig(1:7)),1); %% Choosing A6 coefficients

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Csig_filt = Csig; % creating a new variable to assign filtered coefficients filt_coeff_A6 = zeros(Lsig(1),1); % filtered A6 A6 = [7 9 10 11]; % retaining coefficients for i = 1:length(A6) filt_coeff_A6(A6(i),1) = coeff_A6(A6(i),1); end Csig_filt(1:Lsig(1,1),1) = filt_coeff_A6; %% Choosing D6 coefficients filt_coeff_D6 = zeros(Lsig(2),1); %filtered D6 D6 = [7 8 9 10]; %retaining coefficients for i = 1:length(D6) filt_coeff_D6(D6(i),1) = coeff_D6(D6(i),1); end Csig_filt(Lsig(1,1)+1:sum(Lsig(1:2)),1) = filt_coeff_D6; %% Choosing D5 coefficients filt_coeff_D5 = zeros(Lsig(3),1); %filtered D5 D5 = [9 12 13 14]; %retaining coefficients for i = 1:length(D5) filt_coeff_D5(D5(i),1) = coeff_D5(D5(i),1); end Csig_filt(sum(Lsig(1:2))+1:sum(Lsig(1:3)),1) = filt_coeff_D5; %% Choosing D4 coefficients filt_coeff_D4 = zeros(Lsig(4),1); %filtered D4 D4 = [9 10 11 13 20]; %retaining coefficients for i = 1:length(D4) filt_coeff_D4(D4(i),1) = coeff_D4(D4(i),1); end Csig_filt(sum(Lsig(1:3))+1:sum(Lsig(1:4)),1) = filt_coeff_D4; %% Choosing D3 coefficients filt_coeff_D3 = zeros(Lsig(5),1); %filtered D3 no coefficients are retained Csig_filt(sum(Lsig(1:4))+1:sum(Lsig(1:5)),1) = filt_coeff_D3; %% Choosing D2 coefficients filt_coeff_D2 = zeros(Lsig(6),1); %filtered D2 no coefficients are retained Csig_filt(sum(Lsig(1:5))+1:sum(Lsig(1:6)),1) = filt_coeff_D2; %% Choosing D1 coefficients filt_coeff_D1 = zeros(Lsig(7),1); %filtered D1 no coefficients are retained Csig_filt(sum(Lsig(1:6))+1:sum(Lsig(1:7)),1) = filt_coeff_D1; %% Reconstruction of the filtered decomposition levels for i = 1:level sigcoeff_recon(:,i) = wrcoef('d',Csig_filt,Lsig,WT,i); if i ==level sigcoeff_recon(:,i+1) = wrcoef('a',Csig_filt,Lsig,WT,i); end end %% Reconstruction of the filtered template recon(:,k) = sum(sigcoeff_recon,2); reconnorm(:,k) = recon(:,k) - min(recon(:,k)); % normalizing each block between 0 and 1 reconnorm(:,k) = reconnorm(:,k)/max(reconnorm(:,k)) ; % normalizing each block between 0 and 1 %% MSE calculation (amount of noise compared to the template) mse_at(k,j) = mean((tmpl(:,1)-sig(81:440,k)).^2); % between conventional average and template

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mse_wt(k,j) = mean((tmpl(:,1)-recon(81:440,k)).^2); % between wavelet filtering and template end %% Plots figure contourf((41:400)/40,256:k+256-1,flipdim(reconnorm(81:440,:)',1),'LineStyle','none') title(['TWMC - Filtered average of ',num2str(bkl(n)),' blocks - ',WT]) xlabel('Time (ms)'),ylabel('Epochs') end è é ê ë ì é ì í î ï î æ ð í ð ñ ò ó ú õ ï ö ì ë ì î ï ë ÷ ð ø æ î ù é õ æ î ù ú û ó % Processing data of a single sound intensity level with CSTD clear all WT = 'bior5.5'; % mother wavelet level = 6; % decomposition levels bkl = [256 128 64 32 16 8]; % analysed block lengths t = (41:400)/40; % 1ms - 10ms d = [1 1 1 0.2500 0.1768 0.1250]; % scale thresholds dk = d1/(2)^(k/2), d1=1, d1 is applied to initial set of frames h = [0.7358 0.2707 0.0996 0.0366 0.0135 0.0050 0.0018 0.0007]; % CSTD level thresholds dl = d1/exp(l); d1=0.8 %% Reference ABR epochs=[]; load 'sw_epochs_55_1-10.mat' [b,a] = butter(3,[100/20000,3000/20000]); % generate band pass filter coefficients epochs = filtfilt(b,a,epochs); % zero phase filtering tmpl = mean(epochs(:,:),2); % calculating the grand average %% One block of each average for i = 1:6 f = epochs(:,1:2^(i+1)); sig = f; switch i case 1 % calling the fucntion to denoise a block of 8 epochs for j = 1:1024-256+1 f = epochs(:,256-2^(i+1)+j:256+j-1); sig = f; [onerecon,frecon8(:,j),mse_at(j,i),mse_wt(j,i),max_ncr_at(j,i),max_ncr_wt(j,i)] = CSTD_8_fun_2(f,WT,lvl,d,h,tmpl,sig); end mse_wt_avg(1,i) = mean(mse_wt(1:1024/2^(i+1),i)); case 2 % calling the fucntion to denoise a block of 16 epochs for j = 1:1024-256+1 f = epochs(:,256-2^(i+1)+j:256+j-1); sig = f; [frecon16(:,j),mse_at(j,i),mse_wt(j,i),max_ncr_at(j,i),max_ncr_wt(j,i)] = CSTD_16_fun_2(f,WT,lvl,d,h,tmpl,sig); end mse_wt_avg(1,i) = mean(mse_wt(1:1024/2^(i+1),i)); case 3 % calling the fucntion to denoise a block of 32 epochs for j = 1:1024-256+1 f = epochs(:,256-2^(i+1)+j:256+j-1); sig = f;

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[frecon32(:,j),mse_at(j,i),mse_wt(j,i),max_ncr_at(j,i),max_ncr_wt(j,i)] = CSTD_32_fun_2(f,WT,lvl,d,h,tmpl,sig); end mse_wt_avg(1,i) = mean(mse_wt(1:1024/2^(i+1),i)); case 4 % calling the fucntion to denoise a block of 64 epochs for j = 1:1024-256+1 f = epochs(:,256-2^(i+1)+j:256+j-1); sig = f; [frecon64(:,j),mse_at(j,i),mse_wt(j,i),max_ncr_at(j,i),max_ncr_wt(j,i)] = CSTD_64_fun_2(f,WT,lvl,d,h,tmpl,sig); end mse_wt_avg(1,i) = mean(mse_wt(1:1024/2^(i+1),i)); case 5 % calling the fucntion to denoise a block of 128 epochs for j = 1:1024-256+1 f = epochs(:,256-2^(i+1)+j:256+j-1); sig = f; [frecon128(:,j),mse_at(j,i),mse_wt(j,i),max_ncr_at(j,i),max_ncr_wt(j,i)] = CSTD_128_fun_2(f,WT,lvl,d,h,tmpl,sig); end mse_wt_avg(1,i) = mean(mse_wt(1:1024/2^(i+1),i)); case 6 % calling the fucntion to denoise a block of 256 epochs for j = 1:1024-256+1 f = epochs(:,256-2^(i+1)+j:256+j-1); sig = f; [frecon256(:,j),mse_at(j,i),mse_wt(j,i),max_ncr_at(j,i),max_ncr_wt(j,i)] = CSTD_256_fun_2(f,WT,lvl,d,h,tmpl,sig); end mse_wt_avg(1,i) = mean(mse_wt(1:1024/2^(i+1),i)); end end function [frecon,mse_at,mse_wt,max_ncr_at,max_ncr_wt] = CSTD_32_fun_2 (f,WT,lvl,d,h,tmpl,sig) % Implementation of CSTD for a block size of 32 epochs %% Wavelet transform for i = 1:size(f,2) [C(:,i),L] = wavedec(f(:,i),lvl,WT); end f = C; %% CSTD level 1 for i = 1:size(f,2)/2 f1(:,i) = mean(f(:,2*i-1:2*i),2); end for i = size(f,2)/2+1:size(f,2) if 2*i-(size(f,2)-1)>size(f,2) f1(:,i) = (f(:,2*i-size(f,2))+f(:,1))/2; else f1(:,i) = mean(f(:,2*i-size(f,2):2*i-(size(f,2)-1)),2); end end %% Scale Thresholding ff1 = f1; f1 = zeros(size(f1)); for k = 1:size(f,2) %loop for number of epochs/frames %approximation coefficients


th = []; th = find(abs(ff1(1:L(1,1),k))>max(abs(ff1(1:L(1,1),k)))*d(1,lvl)); for i = 1:length(th) f1(th(i,1),k) = ff1(th(i,1),k); end for n = 1:lvl % loop for number of decomposition levels %detail coefficients th = []; th = find(abs(ff1(sum(L(1:n,1))+1:sum(L(1:n+1,1)),k))>max(abs(ff1(sum(L(1:n,1))+1:sum(L(1:n+1,1)),k))*d(1,lvl-n+1))); for i = 1:length(th) f1(th(i,1)+sum(L(1:n,1)),k) = ff1(th(i,1)+sum(L(1:n,1)),k); end end end %% Level Thresholding ff1 = f1; f1 = zeros(size(f1)); for k = 1:size(f,2) %loop for number of epochs/frames %approximation coefficients th = []; th = find(abs(ff1(1:L(1,1),k))>max(abs(ff1(1:L(1,1),k)))*h(1,1)); for i = 1:length(th) f1(th(i,1),k) = ff1(th(i,1),k); end for n = 1:lvl % loop for number of decomposition levels %detail coefficients th = []; th = find(abs(ff1(sum(L(1:n,1))+1:sum(L(1:n+1,1)),k))>max(abs(ff1(sum(L(1:n,1))+1:sum(L(1:n+1,1)),k))*h(1,1))); for i = 1:length(th) f1(th(i,1)+sum(L(1:n,1)),k) = ff1(th(i,1)+sum(L(1:n,1)),k); end end end %% CSTD level 2 for i = 1:size(f,2)/4 f2(:,i) = mean(f1(:,2*i-1:2*i),2); end for i = size(f,2)/4+1:size(f,2)/2 if 2*i-15>size(f,2)/2 f2(:,i) = (f1(:,2*i-16)+f1(:,1))/2; else f2(:,i) = mean(f1(:,2*i-16:2*i-15),2); end end for i = size(f,2)/2+1:size(f,2)/4*3 f2(:,i) = mean(f1(:,2*i-17:2*i-16),2); end for i = size(f,2)/4*3+1:size(f,2) if 2*i-31>size(f,2) f2(:,i) = (f1(:,2*i-32)+f1(:,size(f,2)/2+1))/2; else f2(:,i) = mean(f1(:,2*i-32:2*i-31),2); end end %% Scale Thresholding ff2 = f2; f2 = zeros(size(f2)); for k = 1:size(f,2) %loop for number of epochs/frames


%approximation coefficients th = []; th = find(abs(ff2(1:L(1,1),k))>max(abs(ff2(1:L(1,1),k)))*d(1,lvl)); for i = 1:length(th) f2(th(i,1),k) = ff2(th(i,1),k); end for n = 1:lvl % loop for number of decomposition levels %detail coefficients th = []; th = find(abs(ff2(sum(L(1:n,1))+1:sum(L(1:n+1,1)),k))>max(abs(ff2(sum(L(1:n,1))+1:sum(L(1:n+1,1)),k))*d(1,lvl-n+1))); for i = 1:length(th) f2(th(i,1)+sum(L(1:n,1)),k) = ff2(th(i,1)+sum(L(1:n,1)),k); end end end %% Level Thresholding ff2 = f2; f2 = zeros(size(f2)); for k = 1:size(f,2) %loop for number of epochs/frames %approximation coefficients th = []; th = find(abs(ff2(1:L(1,1),k))>max(abs(ff2(1:L(1,1),k)))*h(1,2)); for i = 1:length(th) f2(th(i,1),k) = ff2(th(i,1),k); end for n = 1:lvl % loop for number of decomposition levels %detail coefficients th = []; th = find(abs(ff2(sum(L(1:n,1))+1:sum(L(1:n+1,1)),k))>max(abs(ff2(sum(L(1:n,1))+1:sum(L(1:n+1,1)),k))*h(1,2))); for i = 1:length(th) f2(th(i,1)+sum(L(1:n,1)),k) = ff2(th(i,1)+sum(L(1:n,1)),k); end end end %% CSTD level 3 for i = 1:size(f,2)/8 f3(:,i) = mean(f2(:,2*i-1:2*i),2); end for i = size(f,2)/8+1:size(f,2)/8*2 if 2*i-7>size(f,2)/8*2 f3(:,i) = (f2(:,2*i-8)+f2(:,1))/2; else f3(:,i) = mean(f2(:,2*i-8:2*i-7),2); end end for k = 1:3 for i = size(f,2)/8*2*k+1:size(f,2)/8*(2*k+1) f3(:,i) = mean(f2(:,2*i-(8*k+1):2*i-8*k),2); end for i = size(f,2)/8*(2*k+1)+1:size(f,2)/8*(2*k+2) if 2*i-(8*(k+1)-1)>size(f,2)/8*(2*k+2) f3(:,i) = (f2(:,2*i-8*(k+1))+f2(:,size(f,2)/8*2*k+1))/2; else f3(:,i) = mean(f2(:,2*i-8*(k+1):2*i-(8*(k+1)-1)),2); end end end

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%% Scale Thresholding ff3 = f3; f3 = zeros(size(f3)); for k = 1:size(f,2) %loop for number of epochs/frames %approximation coefficients th = []; th = find(abs(ff3(1:L(1,1),k))>max(abs(ff3(1:L(1,1),k)))*d(1,lvl)); for i = 1:length(th) f3(th(i,1),k) = ff3(th(i,1),k); end for n = 1:lvl % loop for number of decomposition levels %detail coefficients th = []; th = find(abs(ff3(sum(L(1:n,1))+1:sum(L(1:n+1,1)),k))>max(abs(ff3(sum(L(1:n,1))+1:sum(L(1:n+1,1)),k))*d(1,lvl-n+1))); for i = 1:length(th) f3(th(i,1)+sum(L(1:n,1)),k) = ff3(th(i,1)+sum(L(1:n,1)),k); end end end %% Level Thresholding ff3 = f3; f3 = zeros(size(f3)); for k = 1:size(f,2) %loop for number of epochs/frames %approximation coefficients th = []; th = find(abs(ff3(1:L(1,1),k))>max(abs(ff3(1:L(1,1),k)))*h(1,3)); for i = 1:length(th) f3(th(i,1),k) = ff3(th(i,1),k); end for n = 1:lvl % loop for number of decomposition levels %detail coefficients th = []; th = find(abs(ff3(sum(L(1:n,1))+1:sum(L(1:n+1,1)),k))>max(abs(ff3(sum(L(1:n,1))+1:sum(L(1:n+1,1)),k))*h(1,3))); for i = 1:length(th) f3(th(i,1)+sum(L(1:n,1)),k) = ff3(th(i,1)+sum(L(1:n,1)),k); end end end %% CSTD level 4 for i = 1:size(f,2)/16 f4(:,i) = mean(f3(:,2*i-1:2*i),2); end for i = size(f,2)/16+1:size(f,2)/16*2 if 2*i-3>size(f,2)/16*2 f4(:,i) = (f3(:,2*i-4)+f3(:,1))/2; else f4(:,i) = mean(f3(:,2*i-4:2*i-3),2); end end for k = 1:7 for i = size(f,2)/16*2*k+1:size(f,2)/16*(2*k+1) f4(:,i) = mean(f3(:,2*i-(4*k+1):2*i-4*k),2); end for i = size(f,2)/16*(2*k+1)+1:size(f,2)/16*(2*k+2) if 2*i-(4*(k+1)-1)>size(f,2)/16*(2*k+2) f4(:,i) = (f3(:,2*i-4*(k+1))+f3(:,size(f,2)/16*2*k+1))/2;

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else f4(:,i) = mean(f3(:,2*i-4*(k+1):2*i-(4*(k+1)-1)),2); end end end %% Scale Thresholding ff4 = f4; f4 = zeros(size(f4)); for k = 1:size(f,2) %loop for number of epochs/frames %approximation coefficients th = []; th = find(abs(ff4(1:L(1,1),k))>max(abs(ff4(1:L(1,1),k)))*d(1,lvl)); for i = 1:length(th) f4(th(i,1),k) = ff4(th(i,1),k); end for n = 1:lvl % loop for number of decomposition levels %detail coefficients th = []; th = find(abs(ff4(sum(L(1:n,1))+1:sum(L(1:n+1,1)),k))>max(abs(ff4(sum(L(1:n,1))+1:sum(L(1:n+1,1)),k))*d(1,lvl-n+1))); for i = 1:length(th) f4(th(i,1)+sum(L(1:n,1)),k) = ff4(th(i,1)+sum(L(1:n,1)),k); end end end %% Level Thresholding ff4 = f4; f4 = zeros(size(f4)); for k = 1:size(f,2) %loop for number of epochs/frames %approximation coefficients th = []; th = find(abs(ff4(1:L(1,1),k))>max(abs(ff4(1:L(1,1),k)))*h(1,4)); for i = 1:length(th) f4(th(i,1),k) = ff4(th(i,1),k); end for n = 1:lvl % loop for number of decomposition levels %detail coefficients th = []; th = find(abs(ff4(sum(L(1:n,1))+1:sum(L(1:n+1,1)),k))>max(abs(ff4(sum(L(1:n,1))+1:sum(L(1:n+1,1)),k))*h(1,4))); for i = 1:length(th) f4(th(i,1)+sum(L(1:n,1)),k) = ff4(th(i,1)+sum(L(1:n,1)),k); end end end %% CSTD level 5 for i = 1:size(f,2) if mod(i,2)==1 %check odd i f5(:,i) =mean(f4(:,i:i+1),2); else f5(:,i) =mean(f4(:,i-1:i),2); end end %% Scale Thresholding ff5 = f5; f5 = zeros(size(f5)); for k = 1:size(f,2) %loop for number of epochs/frames %approximation coefficients th = [];

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th = find(abs(ff5(1:L(1,1),k))>max(abs(ff5(1:L(1,1),k)))*d(1,lvl)); for i = 1:length(th) f5(th(i,1),k) = ff5(th(i,1),k); end for n = 1:lvl % loop for number of decomposition levels %detail coefficients th = []; th = find(abs(ff5(sum(L(1:n,1))+1:sum(L(1:n+1,1)),k))>max(abs(ff5(sum(L(1:n,1))+1:sum(L(1:n+1,1)),k))*d(1,lvl-n+1))); for i = 1:length(th) f5(th(i,1)+sum(L(1:n,1)),k) = ff5(th(i,1)+sum(L(1:n,1)),k); end end end %% Level Thresholding ff5 = f5; f5 = zeros(size(f5)); for k = 1:size(f,2) %loop for number of epochs/frames %approximation coefficients th = []; th = find(abs(ff5(1:L(1,1),k))>max(abs(ff5(1:L(1,1),k)))*h(1,5)); for i = 1:length(th) f5(th(i,1),k) = ff5(th(i,1),k); end for n = 1:lvl % loop for number of decomposition levels %detail coefficients th = []; th = find(abs(ff5(sum(L(1:n,1))+1:sum(L(1:n+1,1)),k))>max(abs(ff5(sum(L(1:n,1))+1:sum(L(1:n+1,1)),k))*h(1,5))); for i = 1:length(th) f5(th(i,1)+sum(L(1:n,1)),k) = ff5(th(i,1)+sum(L(1:n,1)),k); end end end %% Final Average favg = mean(f5,2); %% Inverse wavelet tranform frecon = waverec(favg,L,WT); %% MSE calculation (amount of noise compared to the template) mse_at = mean((tmpl-mean(sig,2)).^2); % between conventional average and template mse_wt = mean((tmpl-frecon).^2); % between wavelet filtering and template


è é ê ë ì é ì í î ï î æ ð í ð ñ ò ó ô ò õ ï ö ì ë ì î ï ë ÷ ð ø æ î ù é õ æ î ù û ó% Processing data of a single sound intensity level with CTMC using SWT % The template is derived with the grand average at 55 dB nHL %% Template calculation using 55 dB load('sw_epochs_55_-11-10.mat'); tmpl_nonext = mean(epochs(481:840,1:1024),2); % signal from 1ms to 10ms tmpl = wextend('1','sym',tmpl_nonext,76); % extended template for swt % Decomposing the template with SWT [swat,swdt] = swt(tmpl,level,WT); % Application of thresholds to the tempate as per CTMC %% Noisy ABR filtering for n = 1:length(bkl) %loop for different block lengths for k = 1:1024-256+1 %loop for continuous blocks % Noisy ABR calculations sig_nonext(:,k) = mean(epochs(481:840,256-bkl(n)+k:256+k-1),2); sig(:,k) = wextend('1','sym',sig_nonext(:,k),76); %extended noisy ABR for swt % Decomposing with SWT [swas,swds] = swt(sig(:,k),level,WT); % Application of thresholds to the noisy ABR as per CTMC % Reconstructing the denoised ABR recon(k,:) = iswt(swas_th,swds_mat,WT); end end è é ê ë ì é ì í î ï î æ ð í ð ñ ó û ô ò õ ï ö ì ë ì î ï ë ÷ ð ø æ î ù é õ æ î ù û ó% Processing data of a single sound intensity level with TWMC using SWT % The template is derived with the grand average at 55 dB nHL %% Template calculation using 55 dB load('sw_epochs_55_-11-10.mat'); tmpl_nonext = mean(epochs(481:840,1:1024),2); % signal from 1ms to 10ms tmpl = wextend('1','sym',tmpl_nonext,76); % extended template for swt %% Loading signal to be denoised epochs = []; load('sw_epochs_75_-11-10.mat'); epochs = filtfilt(b,a,epochs); for n = 1:length(bkl) % loop for different block lengths for k = 1:1024-256+1 % loop for continuous blocks sig_nonext(:,k) = mean(epochs(481:840,256-bkl(n)+k:256+k-1),2); % mean for the block sig(:,k) = wextend('1','sym',sig_nonext(:,k),76); % extended noisy ABR for swt % Decomposing with SWT [swas,swds] = swt(sig(:,k),level,WT); % Application of thresholds to the noisy ABR as per TWMC recon(:,k) = iswt(swas_win,swds_win,WT); end


end è é ê ë ì é ì í î ï î æ ð í ð ñ ò ó ú õ ï ö ì ë ì î ï ë ÷ ð ø æ î ù é õ æ î ù û ó ! " ! " ! # $ % & ! ' ( ) & * & $ ' * # $ + , $ " $ % & $ # ! % " $ ' & ! * % - . function [frecon,mse_at,mse_wt] = CSTD_32(f,WT,lvl,d,h,tmpl,sig) % Implementation of CSTD for a block size of 32 epochs with SWT %% Wavelet transform for i = 1:size(f,2) [swa,swd] = swt(f(:,i),lvl,WT); C(1:512,i) = swa(6,:); for k = 1:6 C(512*k+1:512*(k+1),i) = swd(6-k+1,:); end L = [512,512,512,512,512,512,512,512]'; end f = C; % Application of scale and level thresholds to the noisy ABR as per CSTD % Inverse wavelet transform frecon = iswt(swa_rec,swd_rec,WT); / ì í ì ø ï î æ ð í ð ñ î ù ì 0 1 í î ù ì î æ 2 3 4 5 6 ï î ï 0 ì î ñ ð ø 3 5 7 é ð 6 ì ë æ í ÷% Generating datasets with the synthetic ABR with its amplitude and latency variation. clear all;clc x = linspace(-4*pi,4*pi,400); t = linspace(0,2*pi,1200); % number of repetition blocks y = 1.3*sin(20*t)/4; % main shape sin(t) yn = ones(1,length(y)); % length function max_rep = 1; % maximum repetitions m = 1; for i = 1:length(y) n = 1; sig0 = sin(2*(x+(12-(y(1,i)*12-1))*pi/5))./(2*(x+(12-(y(1,i)*12-1))*pi/5)); % sinc function 1 sig1 = 0.25*sig0; sig = sin(2*(x+(4-(y(1,i)*12-1))*pi/5))./(2*(x+(4-(y(1,i)*12-1))*pi/5)); % sinc function 2 sig2 = 0.5*sig; sig = sin(2*(x+(-4-(y(1,i)*12-1))*pi/5))./(2*(x+(-4-(y(1,i)*12-1))*pi/5)); % sinc function 3 sig3 = sig; sig = sig1+sig2+sig3; sig = sig/max(sig); % normalising sig = sig-mean(sig); % base shifting to mean zero n = n+1; for j = 1:max_rep*yn(1,i) syn (m,:) = sig;

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m = m+1; end end syn = syn'; %% Plot figure,contourf(syn,'LineStyle','none') ô ð 6 ì ë ð ø 6 ì ø 6 ì î ì ø é æ í ï î æ ð í ñ ð ø î ù ì 3 5 7 é ð 6 ì ë% Ditermination of model orders using FPE with a dataset of constant latency clear all;clc % Arbirary poles and zeros (using unfiltered real data fitted to an ARMA model) a = [1.0000 -2.8664 3.4718 -2.3611 0.9599 -0.2721 0.0686]; %AR(6) b = [0 1.0000 -3.3171 4.4271 -2.1791 -1.1732 2.7485 -2.5161 0.9903]; %MA(7) N = 10; % range of model orders for AR part M = 10+1; % range of model orders for MA part noise_seed = 4; load('u.mat') % load the synthetic ABR l = 100; % number of sweeps u = repmat(synthetic',1,l); e = wgn(400,l,-2,1,noise_seed); s = filter(b,a,u); pu = mean(u.^2); ps = mean(s.^2); s=s./repmat(sqrt(ps),400,1).*repmat(sqrt(pu),400,1); % normalize power of the whitened template to the s(k) n = filter(1,a,e); pe = mean(e.^2); pn = mean(n.^2); n=n./repmat(sqrt(pn),400,1).*repmat(sqrt(pe),400,1); % normalize power of the whitened template to the n(k) y = s + n; y = y - repmat(mean(y),400,1); % making mean zero for i = 1:100 snr(1,i) = 10*log10(mean((s(:,i).^2)/mean(n(:,i).^2))); end snr_initial = round(mean(snr,2)) %% ARX model calculation u_hat = mean(y,2); % derived template u_hat = u_hat - mean(u_hat); % making mean zero for k = 1:100 %sweep through each sweep fpe=[];dat=[];m=[];df=[];ind=[]; for i = 1:N % run through all the sweeps dat = iddata(y(:,k),u_hat,1/40000); for j = 2:M m = arx(dat,[i j 0]); %na is the number of poles, nb is the number of zeros plus 1, nk is the number of samples before the input affects the system output fpe(i,j-1) = m.es.FPE; end end %% Find the optimum order at the fist local minima for AR(p)

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df=[]; for i = 1:N df = diff(fpe,1,1);cnt1=0; for j = 1:N-2 if df(j,i)<0 && df(j+1,i)>0 cnt1=1; ind(i,1)=j+1; break end end if cnt1 == 0 %if not found a local minima (gradual decrease) then get the 5% of the minimum FPE df1 = fpe(:,i) - repmat(min(fpe(:,i))*1.05,10,1); % 5% ind(i,1) = find(abs(df1) == min(abs(df1))); end end %% Find the optimum order at the fist local minima for MA(q) df=[]; for i = 1:N df = diff(fpe,1,2);cnt1=0; for j = 1:N-2 if df(i,j)<0 && df(i,j+1)>0 cnt1=1; ind(i,2)=j+1; break end end if cnt1 == 0 %if not found a local minima (gradual decrease) then get the 5% of the minimum FPE df1 = fpe(i,:) - repmat(min(fpe(i,:))*1.05,1,10); % 5% ind(i,2) = find(abs(df1) == min(abs(df1))); end end orders(k,:) = mode(ind); end %% Histogram of ARMA(p,q) orders H=zeros(N,M-1); for nn=1:N; for mm=1:M-1 for r=1:100 if ((orders(r,1)==nn) && (orders(r,2)==mm)) H(nn,mm)=H(nn,mm)+1; end end end end figure surf(H) xlabel('MA(q)'),ylabel('AR(p)'),zlabel('Frequency') 3 4 5 ì 0 î æ é ï î æ ð í ï í 6 ë ï î ì í 2 1 î ø ï 2 8 æ í ÷ õ æ î ù î ù ì 3 5 7 é ð 6 ì ë% Latency tracking with ARX model with predeitermined model orders (6,7,0) clear all;clc % Arbirary poles and zeros (using unfiltered real data fitted to an ARMA model) a = [1.0000 -2.8664 3.4718 -2.3611 0.9599 -0.2721 0.0686]; %AR(6)

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b = [0 1.0000 -3.3171 4.4271 -2.1791 -1.1732 2.7485 -2.5161 0.9903]; %MA(7) N = 6; % fixed model order for the AR part M = 7+1; % fixed model order for the MA part noise_seed = 4; file = 'ampl_2ms_freq_1.0_1min.mat'; % load the dataset with the latency variations load(file) l = 1200; %number of sweeps e = wgn(400,l,-7,1,noise_seed); s = filter(b,a,u); pu = mean(u.^2); ps = mean(s.^2); s=s./repmat(sqrt(ps),400,1).*repmat(sqrt(pu),400,1); %normalize power of the whitened template to the s(k) n = filter(1,a,e); pe = mean(e.^2); pn = mean(n.^2); n=n./repmat(sqrt(pn),400,1).*repmat(sqrt(pe),400,1); %normalize power of the whitened template to the n(k) y = s + n; y = y - repmat(mean(y),400,1); %making mean zero % Intial SNR for i = 1:l snr(1,i) = 10*log10(mean((s(:,i).^2)/mean(n(:,i).^2))); end snr_initial = round(mean(snr,2)) %% ARX model calculation tmpll = 100; for i = 1:l-tmpll+1 u_hat(:,i+tmpll-1) = mean(y(:,i:i+tmpll-1),2); % derived template u_hat(:,i+tmpll-1) = u_hat(:,i+tmpll-1) - mean(u_hat(:,i+tmpll-1)); % making mean zero dat = iddata(y(:,i+tmpll-1),u_hat(:,i+tmpll-1),1/40000); % creating the data object for the model calculation m = arx(dat,[N M 0]); % determination of the model s_hat(:,i+tmpll-1) = filter(m.b,m.a,u_hat(:,i+tmpll-1)); % derivation of the estimated ABR end %% Peak detection Lamp=182:260; % wave V latency for i = 1:l [rc_s(i,1),rc_s(i,2)] = find(s(:,i)==max(s(Lamp,i))); end np=0;rc_s_hat=zeros(l,1); for i = 1:l-tmpll+1 epo= i+tmpll-1; df = diff(s_hat(Lamp,epo)); cnt = 0;rrr=0; for j = 1:length(df)-1 if df(j)>0 && df(j+1)<0; cnt = cnt+1; [rrr(cnt),ccc] = find(s_hat(:,epo)==s_hat(j+1,epo)); end end if cnt ~= 0


[rc_s_hat_temp(1,1),rc_s_hat_temp(1,2)] = find(s_hat(:,epo) == max(s_hat(rrr+Lamp(1)-1,epo))); [rc_s_hat_max(1,1),rc_s_hat_max(1,2)] = find(s_hat(:,epo)==max(s_hat(Lamp,epo))); if rc_s_hat_temp(1,1)>=rc_s_hat_max(1,1) rc_s_hat(epo,1) = rc_s_hat_temp(1,1); else np=np+1; no_peak_s_hat(1,np)=epo; end else np=np+1; no_peak_s_hat(1,np)=epo; end end np=0;rc_u_hat=zeros(l,1); for i = 1:l-tmpll+1 epo= i+tmpll-1; df = diff(u_hat(Lamp,epo)); cnt = 0;rrr=0; for j = 1:length(df)-1 if df(j)>0 && df(j+1)<0; cnt = cnt+1; [rrr(cnt),ccc] = find(u_hat(:,epo)==u_hat(j+1,epo)); end end if cnt ~= 0 [rc_u_hat_temp(1,1),rc_u_hat_temp(1,2)] = find(u_hat(:,epo)==max(u_hat(rrr+Lamp(1)-1,epo))); [rc_u_hat_max(1,1),rc_u_hat_max(1,2)] = find(u_hat(:,epo)==max(u_hat(Lamp,epo))); if rc_u_hat_temp(1,1)>=rc_u_hat_max(1,1) rc_u_hat(epo,1) = rc_u_hat_temp(1,1); else np=np+1; no_peak_u_hat(1,np)=epo; end else np=np+1; no_peak_u_hat(1,np)=epo; end end %MSE calculation (after ignoring very high MSEs in s_hat) mse_s_shat = mean((rc_s(find(rc_s_hat),1)/40-rc_s_hat(find(rc_s_hat),1)/40).^2) mse_s_uhat = mean((rc_s(find(rc_u_hat),1)/40-rc_u_hat(find(rc_u_hat),1)/40).^2) l-100+1-length(no_peak_s_hat) length(no_peak_u_hat) è é ê ë ì é ì í î ï î æ ð í ð ñ î ù ì 5 9 : 9% Predefined model parameters a = [1.0000 -2.8664 3.4718 -2.3611 0.9599 -0.2721 0.0686]; %AR(6) b = [0 1.0000 -3.3171 4.4271 -2.1791 -1.1732 2.7485 -2.5161 0.9903]; %MA(7) c = [1.0000 -0.5473 -0.3750 -0.2088 -0.0579 -0.1965 0.1101 0.1557 0.1582];% AR(8) for pre-whitening % Data generation (only the pre-whitening coding is presented here)


w = filter(c,1,u); %whitening the template pu = mean(u.^2); pw = mean(w.^2); w=w./repmat(sqrt(pw),400,1).*repmat(sqrt(pu),400,1); %normalize power of the whitened template to the u(k) w = w - repmat(mean(w),400,1); %making mean zero s = filter(b,a,w); ps = mean(s.^2); s=s./repmat(sqrt(ps),400,1).*repmat(sqrt(pu),400,1); %normalize power of the whitened template to the s(k) %% REPE implementation tmpll = 100; for i = 1:l-tmpll+1 u_hat(:,i+tmpll-1) = mean(y(:,i:i+tmpll-1),2); % derived template u_hat(:,i+tmpll-1) = u_hat(:,i+tmpll-1) - u_hat(1,i+tmpll-1); %shift to make the starting sample to zero datw = iddata(u_hat(:,i+tmpll-1),[],1/40000); % creating the data object for the model calculation mw = ar(datw,8); w_hat(:,i+tmpll-1) = filter(mw.a,1,u_hat(:,i+tmpll-1)); %pre-whitening the template pu_hat = mean(u_hat(:,i+tmpll-1).^2); pw_hat = mean(w_hat(:,i+tmpll-1).^2); w_hat(:,i+tmpll-1)=w_hat(:,i+tmpll-1)/sqrt(pw_hat)*sqrt(pu_hat); %normalize power of the whitened template to the u(k) w_hat(:,i+tmpll-1) = w_hat(:,i+tmpll-1) - mean(w_hat(:,i+tmpll-1)); %making mean zero dat = iddata(y(:,i+tmpll-1),w_hat(:,i+tmpll-1),1/40000); m = arx(dat,[N M 0]); %na is the number of poles, nb is the number of zeros plus 1, nk is the number of samples before the input affects the system output s_hat(:,i+tmpll-1) = filter(m.b,m.a,w_hat(:,i+tmpll-1)); end

Appendix E

ARX estimated ABRs

ü ý ý þ ÿ ; ä< = > ? @ A B C @ D E F B F G H A = G B ? = G B = D E F @ I > ? H > G B > F H G J K L @ A M N O P Q ? R > S T U H G E = > @ I G C I G V W @ D X F H Y B @ K Z Q [ G @G E B \ < A @ ? B W ] ä > B = D E C W @ G ^ G E B B F G H A = G B ? \ R < H F D @ A C = L B ? U H G E G E B _ L = > ? = ` B L = _ B ? G B A C W = G B = > ? G E BD @ L L B F C @ > ? H > _ \ R < V B K @ L B G E B B F G H A = G H @ > ] a E B _ B > B L = W @ V F B L ` = G H @ > H F G E B B F G H A = G B ? \ R < F = G E H _ E B LH > G B > F H G H B F F E @ U L B W B ` = > G K B = G I L B V I G > @ G = G W @ U F @ I > ? H > G B > F H G H B F ]

b c d e f gh fgf i g j k l m nb c d e f gh fgf i i j k l m n b c d e f gh fgf d g j k l m nb c d e f gh fgf d i j k l m n b c d e f gh fgf o g j k l m nb c d e f gh fgf o i j k l m n

b c d e f gh fgf f g j k l m n b c d e f gh fgf f i j k l m nb c d e f gh fgf b g j k l m n b c d e f gh fgf b i j k l m nb c d e f gh fgf p g j k l m n b c d e f gh fgf p i j k l m nb c d e f gh b gb c g j k l m n b c d e f gh fgf c i j k l m n

ü ý ý þ ÿ ; ä ä

< = > ? @ A B C @ D E F B F G H A = G B ? = G B = D E F @ I > ? H > G B > F H G J K L @ A q N O P Q ? R > S T U H G E = > @ I G C I G V W @ D X F H Y B @ K q Z G @G E B \ < A @ ? B W ] ä > B = D E C W @ G ^ G E B B F G H A = G B ? \ R < H F D @ A C = L B ? U H G E G E B _ L = > ? = ` B L = _ B ? G B A C W = G B = > ? G E BD @ L L B F C @ > ? H > _ \ R < V B K @ L B G E B B F G H A = G H @ > ] a E B _ B > B L = W @ V F B L ` = G H @ > H F G E B B F G H A = G B ? \ R < F E = ` B = U = ` B W = G B > D J @ K K F B G B ` B > = G E H _ E B L H > G B > F H G H B F U H G E > @ \ R < C L B F B > G = G W @ U F @ I > ? H > G B > F H G H B F ]

r s t u v wx vwv v w y z | r s t u v wx rwr v ~ y z | r s t u v wx rwr r w y z | r s t u v wx rwr r ~ y z | r s t u v wx rwr w y z | r s t u v wx vwv ~ y z | r s t u v wx rwr s w y z |

ü ý ý þ ÿ ; ä ä ä

< = > ? @ A B C @ D E F B F G H A = G B ? = G B = D E F @ I > ? H > G B > F H G J K L @ A q N O P Q ? R > S T U H G E = > @ I G C I G F H > _ W B B C @ D E G @ G E B\ < A @ ? B W ] ä > B = D E C W @ G ^ G E B B F G H A = G B ? \ R < H F D @ A C = L B ? U H G E G E B _ L = > ? = ` B L = _ B ? G B A C W = G B = > ? G E BD @ L L B F C @ > ? H > _ \ R < V B K @ L B G E B B F G H A = G H @ > ] T = L _ B = A C W H G I ? B F D @ I W ? V B @ V F B L ` B ? H > G E B B F G H A = G B ? \ R <L B F B A V W H > _ G E B F H > _ W B B C @ D E V B K @ L B G E B B F G H A = G H @ > V I G > @ G G E B G B A C W = G B ]

Appendix F

Wavelet estimated ABRs

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Evaluation of methods for the rapid extraction of the ......trial extraction techniques are better suited to study rapid extraction of the auditory brainstem response (ABR) compared