SELF-MIXING INTERFEROMETRY AND ITS APPLICATIONS IN NONINVASIVE PULSE DETECTION

JUKKAHAST

Department of Electrical andInformation Engineering,

University of Oulu

OULU 2003

JUKKA HAST

SELF-MIXING INTERFEROMETRY AND ITS APPLICATIONS IN NONINVASIVE PULSE DETECTION

Academic Dissertation to be presented with the assent ofthe Faculty of Technology, University of Oulu, for publicdiscussion in Raahensali (Auditorium L10), Linnanmaa, onApril 25th, 2003, at 12 noon.

OULUN YLIOPISTO, OULU 2003

Copyright © 2003University of Oulu, 2003

Supervised byProfessor Risto Myllylä

Reviewed byProfessor Kalju MeigasDocent Raimo Silvennoinen

ISBN 951-42-6973-X (URL: http://herkules.oulu.fi/isbn951426973X/)

ALSO AVAILABLE IN PRINTED FORMATActa Univ. Oul. C 182, 2003ISBN 951-42-6972-1ISSN 0355-3213 (URL: http://herkules.oulu.fi/issn03553213/)

OULU UNIVERSITY PRESSOULU 2003

Hast, Jukka, Self-mixing interferometry and its applications in noninvasive pulsedetection Department of Electrical and Information Engineering, University of Oulu, P.O.Box 4500, FIN-90014 University of Oulu, Finland Oulu, Finland2003

Abstract

This thesis describes the laser Doppler technique based on a self-mixing effect in a diode laser tononinvasive cardiovascular pulse detection in a human wrist above the radial artery. The mainapplications of self-mixing interferometry described in this thesis in addition to pulse detection arearterial pulse shape and autonomic regulation measurements. The elastic properties of the arterialwall are evaluated and compared to pulse wave velocity variation at different pressure conditionsinside the radial artery.

The main advantages of self-mixing interferometry compared to conventional interferometers arethat the measurement set up is simple, because basically only one optical component, the laser diode,is needed. The use of fewer components decreases the price of the device, thus making it inexpensiveto use. Moreover, an interferometer can be implemented in a small size and it is easy to controlbecause only one optical axis has to be adjusted. In addition, an accuracy, which corresponds to halfof the wavelength of the light source, can be achieved. These benefits make this technique interestingfor application to the measurement of different parameters of the cardiovascular pulse.

In this thesis, measurement of three different parameters from cardiovascular pulsation in the wristis studied. The first study considers arterial pulse shape measurement. It was found that an arterialpulse shape reconstructed from the Doppler signal correlates well to the pulse shape of a bloodpressure pulse measured with a commercial photoplethysmograph. The second study considersmeasurement of autonomic regulation using the Doppler technique. It was found that the baroreflexpart of autonomic regulation can be measured from the displacement of the arterial wall, which isaffected by blood pressure variation inside the artery. In the third study, self-mixing interferometry issuperimposed to evaluate the elastic properties of the arterial wall. It was found that the elasticmodulus of the arterial wall increases as blood pressure increases. Correlations betweenmeasurements and theoretical values were found but deviation in measured values was large. It wasnoticed that the elastic modulus of the arterial wall and pulse wave velocity behave similarly as afunction of blood pressure. When the arterial pressure increases, both the elastic modulus and pulsewave velocity reach higher values than in lower pressure.

Keywords: arterial elasticity, arterial pulse, autonomic regulation, blood pressure, laserDoppler, pulse wave velocity, self-mixing effect

Acknowledgements

The work reported in this thesis was carried out at the Optoelectronics and Measurement Techniques Laboratory, Department of Electrical and Information Engineering, Faculty of Technology, University of Oulu, during years 1999-2002. I wish to express my deepest gratitude to Professor Risto Myllylä for supervising this work. I also want to thank TkL Hannu Sorvoja for his supervision and assistance during the project.

This research has been done partly in collaboration with Polar Electro Oy, and I wish to thank Dr. Seppo Nissilä and DI Jari Miettinen for their support and for the fruitful discussions in the many meetings we had.

I wish to thank Professor Kalju Meigas and Dr. Raimo Silvennoinen for reviewing this thesis. Also to be thanked is Mr. Timo Mäntyvaara for revising the English of the manuscript. Mr. Rauno Varonen is gratefully thanked for revising the English of the original papers I, III-VI. Professor Alexander Priezzhev is thanked for revising and reviewing the original paper II.

I also wish to thank the Graduate School in Electronics, Telecommunications and Automation (GETA) for their financial support and travelling grants. Financial support from the Tauno Tönning Foundation, Oulun yliopiston tukisäätiö, Tekniikan edistämissäätiö and Seppo Säynäjäkankaan tiedesäätiö is gratefully acknowledged.

I thank all my fellow workers at the Optoelectronics and Measurement Techniques Laboratory and in the Workshop of the Department, especially Mr. Vesa Kaltio and Mr. Anssi Rimpiläinen for mechanical work, DI Erkki Alarousu for great discussions, DI Mikko Heikkinen at VTT Electronics for providing me with an introduction to interferometry at the early stage of this work. Mr. Ville Kampman is thanked for his assistance with the reference measurements for the original paper I.

Finally, I would like to thank my mother and father, as well as my brother and his family, for their enormous support, and last but not least Johanna for all her patience and understanding during the late nights and weekends I have spent on the project. Oulu, February 2003 Jukka Hast

List of terms, symbols and abbreviations

3D Three-dimensional AD Analog to digital CO2 Carbon dioxide DAQ Data acquisition ECG Electrocardiogram EMFi Electromechanical film ESC European Society of Cardiology FFT Fast Fourier transform HF High frequency HeNe Helium neon laser IEEE Institute of Electrical and Electronics Engineers, Inc. I/O Input/output LASER Light amplification by simulated emission of radiation LDF Laser Doppler flowmetry LED Light-emitting diode LF Low frequency MAP Mean arterial pressure MMG Mechanomyogram MRI Magnetic resonance image NASPE North American Society of Pacing and Electrophysiology PC Personal computer PD Photo detector PPG Photo-plethysmography PSD Power spectral density PTT Pulse transit time PVDF Polyvinylidene fluoride PWV Pulse wave velocity QW Quantum well RR Time difference between R-peaks at ECG-signal RSA Respiratory sinus arrhythmia

SLD Super luminescent diode SNR Signal-to-noise ratio SPIE Society of Photo-Optical Instrumentation Engineers VLF Very low frequency WHO World Health Organization a Lower integration limit A Area A’ Unit area b Higher integration limit c Speed of light, 300 000 km/s c0 Wave velocity of pressure wave C Compliance Cfb Feedback parameter in the self-mixing effect Cα First order compliance factor Cβ Second order compliance factor E Elastic modulus F Force Fs Sampling frequency gc Threshold gain for compound cavity in external feedback gth Threshold gain without external feedback g12 Phase term of reference and measurement wave fronts hv Thickness of the vessel wall I Current Ith Threshold current for laser diode I1 Intensity of the reference arm I2 Intensity of the measurement arm L Length of laser cavity Lext Length of external cavity m Integer M1 Laser mirror located at the backside of laser cavity M2 Laser mirror located at light output Mext External target ns Refractive index of skin na Refractive index of air N Length of data sequence P Pressure Ptm Transmural pressure r Radial co-ordinate rvi Radius of the vessel lumen in diastole rv Radius of the vessel lumen as function of pressure r2 Amplitude reflection coefficient of effective mirror r2s Amplitude reflection coefficient of laser mirror M2 r2ext Amplitude reflection coefficient of external target Rt Target reflectivity

Re Real part of complex number std Standard deviation t Time Ts Period of the sampling signal u Radial velocity component of the fluid U Superposition of electromagnetic fields U0 Electromagnetic wave that is emitted from the source U1 Part of electromagnetic wave that travels along the first route U2 Part of electromagnetic wave that travels along the second route v Velocity vv Radial velocity of arterial wall V Volume w Longitudinal velocity component of the fluid x Longitudinal co-ordinate Xcorr Cross correlation coefficient z Optical axis α Laser parameter related to amount of stimulated emission αs Laser cavity loss coefficient β Phase constant of the optical wave ε Strain ∆φL Round trip phase change compared to 2πm φr Phase term of the external cavity η Viscosity ηeff Coupling efficiency of the backscattered light into the laser diode ϕ Angle between laser beam and velocity vector κext Coupling coefficient λ Wavelength µe Effective refractive index of laser cavity µeg Effective group refractive index ν Optical frequency, frequency of light νD Doppler frequency ρ Density ρb Density of blood ρv Density of the vessel wall σ Stress τL Round trip delay back and forth through the laser cavity τext Round trip delay back and forth through the external cavity ω Angular frequency ξ Radial dilation of the vessel wall as complex form ψ Visibility function NOTE: Some terms, symbols or abbreviations might have a different meaning in the original papers.

List of original papers

This thesis is a summary of the work published in the following six papers: I Hast J., Myllylä R., Sorvoja H., Miettinen J. (2001) A noninvasive laser Doppler

system to study cardiovascular pulsation and its properties, Asian Journal of Physics, 10(4): 15 pages

II Hast J., Myllylä R., Sorvoja H., Miettinen J. (2002) Arterial pulse shape

measurement using self-mixing effect in a diode laser, Quantum Electronics, 32: 975-980

III Hast J., Myllylä R., Sorvoja H., Miettinen J. (2001) Self-mixing interferometry

in noninvasive pulse wave velocity measurement, Molecular and Quantum Acoustics, 22: 95-106

IV Hast J., Myllylä R., Sorvoja H., Nissilä S. (2001) Baroreflex regulation

measurement using a noninvasive laser Doppler method, Proceedings of SPIE, Coherence domain optical methods in biomedical science and clinical applications V, 23-24 January 2001, San Jose, USA, 4251: 232-241.

V Hast J., Myllylä R., Sorvoja H., Miettinen J. (2002) Comparison between the

elasticity of the arterial wall and pulse wave velocity using the laser Doppler method, Proceedings of SPIE, Coherence domain optical methods in biomedical science and clinical applications VI, 21-23 January 2002, San Jose, USA, 4619: 259-268.

VI Hast J., Myllylä R., Sorvoja H., Nissilä S. (2000) Arterial compliance

measurement using a non-invasive laser Doppler measurement system, Proceedings of SPIE, Optical techniques and instrumentation for the measurement of blood composition, structure and dynamics, 7-8 July 2000, Amsterdam, Netherlands, 4163: 24-32.

The main aspect in all of these papers is the study of self-mixing interferometry for cardiovascular pulse measurements. Paper I discusses the theory of self-mixing interferometry and the accuracy of the self-mixing interferometer is studied. In addition, the relationship between blood pressure, the radial velocity of the arterial wall and the elastic modulus of the arterial wall is derived. Paper II focuses on arterial pulse shape measurement using the self-mixing technique. Paper III discusses pulse wave velocity measurement using self-mixing interferometry. Paper IV presents the results of autonomic regulation measurements. Papers V and VI present the results from an evaluation of the elasticity of the arterial wall.

Contents

Abstract Acknowledgements List of terms, symbols and abbreviations List of original papers Contents 1 Introduction ...................................................................................................................15

1.1 Motivation to this work ..........................................................................................15 1.2 Laser Doppler technique in biomedical optics........................................................17 1.3 Contents of this work..............................................................................................18

2 Self-mixing interferometry ............................................................................................20 2.1 Short introduction to interferometry .......................................................................20 2.2 The self-mixing effect and its historical phases ......................................................21 2.3 Theory of self-mixing interferometry .....................................................................22 2.4 Experimental measurements based on the self-mixing effect .................................26

2.4.1 Velocity measurement......................................................................................26 2.4.2 Displacement measurement .............................................................................28

3 Cardiovascular pulsation ...............................................................................................31 3.1 Noninvasive cardiovascular pulse measurement from the wrist .............................31 3.2 Structure and radial dilation of the arterial wall......................................................33

3.2.1 Structure of the arterial wall ............................................................................33 3.2.2 Radial dilation of the arterial wall ...................................................................34

3.2.2.1 Approach using the Navier-Stokes equation .............................................35 3.2.2.2 Approach using Bernoulli’s law................................................................36

3.3 Pulse wave velocity and autonomic regulation.......................................................38 3.3.1 Pulse wave velocity .........................................................................................38 3.3.2 Autonomic regulation ......................................................................................39

4 Measurement system .....................................................................................................42 4.1 Measurement probe ................................................................................................42 4.2 PC interface card.....................................................................................................43 4.3 Data acquisition and signal processing ...................................................................43

4.4 Composition of Doppler signal from radial artery..................................................44

5 Self-mixing interferometry in cardiovascular pulse measurements...............................47 5.1 Pulse detection ........................................................................................................47

5.1.1 Normal blood pressure pulse ...........................................................................47 5.1.2 Abnormal blood pressure pulse........................................................................49

5.2 Pulse shape measurements......................................................................................50 5.3 An example of signal degradation...........................................................................52 5.4 Autonomic regulation measurement .......................................................................53 5.5 Evaluation of elasticity and pulse wave velocity ....................................................56

6 Discussion......................................................................................................................60 6.1 Measurements .........................................................................................................61 6.2 Future research........................................................................................................62

7 Summary........................................................................................................................64 References ........................................................................................................................66

1 INTRODUCTION

1.1 Motivation to this work

Cardiovascular diseases are the leading cause of death in the world. According to the World Health Organization (WHO), in 2001 they caused one third of all deaths in the world (WHO 2002). On the other hand, age distribution develops in such a way that the number of older people in the total population increases. For example, in Finland the percentual share of people over 65 years of age has grown 10% during 1990-2000 compared to the beginning of 1900s (Tilastokeskus 2002). To save health care costs home care is used more often. These facts alone serve to illustrate the importance of focusing research on the development of new methods and devices for everyday practical use and patient monitoring.

One of the traditional indicators of the condition of the human body is cardiovascular pulsation. Different cardiovascular diseases can be diagnosed depending on the shape, amplitude and rhythm of this pulsation. Some of the possible diseases which can be diagnosed from different types of cardiovascular pulsation are listed in Table 1 (Bates 1995). A more detailed description of pulse shapes and the causes for abnormal pulse shapes are also listed (O’Rourke et al. 1992). Factors that affect cardiovascular pulsation are the stroke volume of the heart, the compliance of the cardiovascular network and the character of the systolic heart ejection (Bates 1995). Different types of abnormal cardiovascular pulses are shown in Fig. 1. From this point of view, a sensor that can detect the pulse, measure the pulse shape accurately and, furthermore, can evaluate the elastic properties of the arterial wall has great potential in the medical field.

Optical sensors are popular in biomedical diagnostics. They have several advantages compared to other types of sensors. One of the advantages of optical measurement methods is that many vital functions can be measured noninvasively, i.e. there is no need to injure the skin during measurements. Moreover, the optical methods are safe to use, as there is not direct electrical contact between the measurement device and the measured person, as the information is transmitted in an electromagnetic field. The diagnostic devices based on optics use low emitted power, which is typically less than several mW. In addition, the rapid development of information technology allows implementation of

16

multichannel and real-time monitoring devices, which are capable of analysing many different parameters in real time.

Table 1. Possible diseases which can be diagnosed based on the different types of cardiovascular pulse shapes (Bates 1995).

Pulse type Physiological cause Possible disease

small & weak decreased stroke volume

increased peripheral resistance heart failure, hypovolemia, severe aortic

stenosis

large & bounding increased stroke volume

decreased peripheral resistance decreased compliance

fever, anaemia, hyperthyroidism, aortic regurgitation, bradycardia, heart block,

atherosclerosis

bisferiens increased arterial pulse with double systolic

peak

aortic regurgitation, aortic stenosis and regurgitation, hypertropic

cardiomyopathy

pulsus alternans pulse amplitude varies from peak to peak,

rhythm basically regular left ventricular failure

Fig. 1. Different types of cardiovascular pulse shapes (Bates 1995). One very widely used optical technique for biomedical diagnostics is the laser Doppler technique. In this technique, the information is carried in the electromagnetic field, which is a superposition of two wave fronts which have travelled along different routes. One of these wave fronts has undergone a frequency shift due to interaction with a moving target or particles. This frequency shift is called the Doppler shift. After coherent mixing of these two waves at a photo detector, information about the velocity of the target can be obtained from the frequency of the superposition signal. When visible or near infrared wavelengths (600-1500nm) are used, it is possible to achieve a resolution of 300-750 nm

Normal pulses

Small and weak pulses

Large & bounding pulses

Bisferiens pulses

Pulsus alternans

17

if only one detector is used and the difference of constructive and destructive interference is considered. The Doppler technique is typically used for vibration or velocity measurements. Therefore it is a competitive technique for cardiovascular pulse measurements, where both blood flow velocity and vessel wall changes are variable during the cardiac cycle.

1.2 Laser Doppler technique in biomedical optics

The triumphal march of laser in biomedical optics started soon after the first ruby laser was invented in 1960 (Maiman 1960). The properties of laser light are well suited to the needs of the biomedical field. Properties like high intensity, low divergence, monochromaticity and coherence are remarkable features from a measurement point of view. Four years later it was proposed how the velocity of particles in a solution might be measured by interpretation of Doppler shifted light (Cummins et al. 1964). Laser Doppler velocimetry, which uses the Doppler shift of laser light as the information carrier, was first introduced to the flow measurement of red blood cells in a glass tube (Riva et al. 1972) and then some years later it was used for blood perfusion measurement in microcirculation (Stern 1975). Since then a number of clinical and experimental applications of laser Doppler flowmetry (LDF) have been implemented (Watkins & Holloway 1978, Nilsson et al. 1980, Bonner & Nossal 1981, Shepherd & Riedel 1982, Nilsson 1990,). The technique and measurement applications of LDF are summarized in two books (Belcaro et al. 1994) and (Shepherd et al. 1990). In addition, the laser Doppler technique has been applied to laser Doppler microscopy (Mishina et al. 1975, Priezzhev et al. 1997) and perfusion imaging (Wårdell et al. 1993).

In biomedical optics the Doppler technique has mainly been applied to the previously discussed blood flow measurements. Cardiovascular pulse measurements have been in the background. The first reports concerning cardiovascular pulse wave registration were published at the beginning of the 1990s (Tuchin et al. 1991). In this work, a laser speckle interferometer for biovibration measurements was presented. Later this technique was also reported to have been used in cardiodiagnostics and examples of cardiovascular pulse detection were shown (Ul’yanov et al. 1994, Kutzmin et al. 1996).

At the same time, another group had been working on no touch pulse measurements by optical interferometry (Hong & Fox 1994, Hong & Fox 1997). In their system, the laser Doppler system was used to detect pulsation profiles from major arteries. It was shown that the pulse profile can be measured from several different arteries below the skin’s surface. They introduced an excellent approach to the problem of measuring the cardiovascular pulsation from different parts of the human body (Hong 1994).

The advantage of the laser Doppler technique is that a very high accuracy can be achieved for skin displacement measurement. This is extremely important, since skin displacement due to the cardiovascular pulse can very easily merge with muscular tonus or absorb into surrounding soft tissue. Basically, an accuracy of λ/2 can be achieved with a Michelson interferometer, which is the difference between the constructive and destructive interferences of the wave front. With a HeNe light source this means an

18

accuracy of 316 nm. In addition, it is important to avoid any extra loading factors towards the skin surface because these can cause distortions to the pulsation signal. With the noninvasive Doppler technique these can be avoided.

In previous works on cardiovascular pulse measurements with a laser speckle and the Doppler technique, the laser Doppler apparatus was based on the Michelson interferometer, where a HeNe-laser was used as light source. The interferometer was constructed using a free space structure, in which optical fibers were used to guide the light into the measurement arm. From a practical point of view this configuration was large in size and expensive, because a large number of different optical components were used. Because of this, these devices can only be used in laboratory conditions.

A simple way to construct an interferometer is to use the so-called self-mixing effect that occurs in the laser cavity, when external light is coupled back to the laser cavity. This technique enables simple, compact size and cheap interferometer devices to be implemented, because basically the only required component is the laser itself. Later in this thesis many examples of different measurement applications using this technique are presented. This technique is also applied to cardiovascular pulse registration measurements (Meigas et al. 1998).

1.3 Contents of this work

In this thesis, the laser Doppler apparatus used in the cardiovascular pulse measurements is based on a self-mixing effect in a single-mode diode laser. The self-mixing technique is explained more briefly in chapter 2, where first an introduction to interferometry and typical constructions of traditional interferometer configurations are shortly discussed. Then the historical background of the self-mixing effect, measurement applications and theory of the self-mixing effect in a laser diode are given. Two measurement experiments for velocity and displacement measurements of a scattering surface using this technique are also presented. These experiments serve as a basis for understanding the phenomenon before the final measurement system was constructed.

Chapter 3 focuses on discussing cardiovascular pulse measurement in the wrist above the radial artery. The basics of the physiology of cardiovascular pulsation and the reasons why the radial artery was chosen as the measurement object are presented. In addition, other sensor types for pulse measurements in the wrist are shortly discussed. After this, the structure of a small muscular artery is presented and two approaches to describing the radial dilation of the arterial wall are derived. Finally, two other parameters, autonomic regulation and pulse wave velocity (PWV), are discussed, since they are also considered in this thesis.

General information about the measurement device used in this study and signal processing is presented in chapter 4. Chapter 5 summarizes the results of the experimental measurements. Firstly, noninvasive pulse detection from a normal blood pressure pulse and an experimentally manipulated blood pressure pulse are shown. Then the results of the arterial pulse shape and baroreflex regulation measurements are presented. The last part of the chapter presents the results of the evaluation of the

19

elasticity of the arterial wall, which are also compared to the changes in PWV. More details of the measurements can be found in the original papers I-VI at the end of this thesis.

The results of the work and possible future research are discussed in chapter 6 and the summary of the work is given in chapter 7.

2 SELF-MIXING INTERFEROMETRY

2.1 Short introduction to interferometry

An interferometer is an optical instrument which measures the superposition of the waves which have propagated through different paths. The interferometer splits an electromagnetic wave, U0, into two different parts, U1 and U2, using a beamsplitter. Then the two beams are delayed by unequal distances, redirected and recombined and finally the superposition of the intensity of the waves, U, is detected. Traditional interferometer configurations are the previously mentioned Michelson, Mach-Zehnder and Sagnac interferometers, Fig. 2 (Saleh & Teich 1991). The principle in all of these is the same. In the Sagnac interferometer the two waves propagate through the same path in opposite directions.

Fig. 2. Michelson a), Mach-Zehnder b) and Sagnac c) interferometer configurations. When these types of interferometers are used, several external components must be used. The beamsplitter, which was already mentioned earlier, divides the electromagnetic field into two parts. In addition, depending on the measurement applications, different lenses are needed to control the spatial distribution of the light wave. In free space solutions, the optical axis must be controlled with careful positioning of the different optical components. In fiber optic structures, single-mode fibers must be used to avoid modal

a) b) c)

U=U1+U2

U0

U1

U2

U1

U2 U=U1+U2U0

U=U1+U2

U1

U2

U0

21

dispersion, which might cause serious problems in multimode fibers. Consequently, these facts increase the price of the interferometer and make the configurations typically quite large in size.

2.2 The self-mixing effect and its historical phases

A self-mixing effect in a laser occurs when some part of the emitted laser light enters back into the laser cavity, where it interacts with the original laser light, causing fluctuations to the laser power. These power fluctuations can be detected using a photodetector placed on the opposite side of the laser cavity than the primary light output. If the external light is frequency-shifted and it is mixed coherently to the original laser light, interference occurs and this can be superimposed to many different measurement applications. For clarity some definitions concerning self-mixing techniques are given. A self-mixing interferometer is a measurement device, which is based on the self-mixing effect explained above. Self-mixing interferometry is a measurement technique, where the self-mixing interferometer is used to measure some physical phenomenon.

Generally, the self-mixing interferometer measures the superposition of internal and external electric fields. This configuration, shown in Fig. 3, significantly reduces the size of the interferometer compared to traditional configurations. In addition, the reduced number of optical components decreases the price of the device. Moreover, this technique is accurate and in a certain range a λ/2 accuracy can be achieved. Finally, it is simple to use because there is only one optical axis to control.

History of the self-mixing effect goes back to 1960 when the laser was invented. It was noticed that external feedback into the laser cavity induces intensity modulation in the output of a gas laser (King & Steward 1963). A few years later, the first laser Doppler velocimeter, in which the laser cavity was used as an optical mixer was presented (Rudd 1968). It was also noticed that the fringe shift caused by an external reflector corresponds to the optical displacement of λ/2, where λ is the operating wavelength of the laser. In addition, the intensity modulation was noticed to be comparable to conventional interferometers. Based on these two features, the phenomenon was given the name self-mixing effect. Sometimes the names ‘autodyne effect’ or ‘self-modulation’ are also used in the literature.

In the beginning the intensity modulation of the self-mixing effect was modelled as variable losses in a laser cavity and it was used for refractive index monitoring (Gerardo et al. 1963, Hooper et al. 1966, Wheeler et al. 1972). The self-mixing effect has also been explained as backscatter modulation in a CO2 laser (Churnside 1984). In semiconductor lasers, intensity modulation has been explained in terms of the conventional interference between the original laser light and an external light coupled back to the cavity (Jentik et al. 1988). Nowadays, a three-mirror Fabry-Perot cavity is the most common way of explaining the signal generation in self-mixing interferometry (de Groot et al. 1988). Here intensity modulation is explained by the change of the carrier density inside the laser cavity.

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Spectral effects in the self-mixing effect have a twofold influence on the operation of a laser diode. The spectral line width may be narrowed extremely in optical feedback. Even 1 Hz spectral linewidths have been reported with Rayleigh backscattering reflection from the end of a long fiber (Mark et al. 1985). In addition, in weak feedback line width reduction and frequency tuning has been done (Patzak et al. 1983, Agrawal 1984, Chuang et al. 1990). On the other hand, the original spectral linewidth of the laser may broaden. This is termed coherence collapse, where the feedback field changes from coherent to incoherent (Miles et al. 1980, Lenstra et al. 1985).

Self-mixing interferometry has been exploited by many research teams to develop different measurement applications for velocimetry (Shinohara et al. 1986, Shibata et al. 1999, Özdemir et al. 1999), displacement, distance and vibration measurements (Donati et al. 1995, Gharbi et al. 1997, Gouaux et al. 1998, Mourat et al. 2000, Rodrigo et al. 2001), ranging (Beheim et al. 1986, de Groot et al. 1988) and 3D-imaging (Gagnon et al. 1999). It has also been used widely in biomedical optics for LDF (de Mul et al. 1992, Özdemir et al. 2000), blood pressure pulse registration (Meigas et al. 1999), continuous blood pressure registration (Meigas et al. 2001) and measurement of skin vibration due to MMG (Courteville et al. 1998).

The self-mixing effect also occurs in low coherence light sources like super luminescent diodes (SLD) and the effect has been demonstrated in applications of low-coherent interferometry (Rovati et al. 1998).

Recently, the self-mixing technique has also been introduced to everyday practical applications. It is reported to have been used in optical touch sensitive interfaces (Hewett 2002), where two self-mixing interferometers measure the movement of the fingertip. The movement of the finger is used to control the optical scroll device. In addition, the same phenomenon is modelled for use in compact disk readers for direct readout (Aikio et al. 2001).

2.3 Theory of self-mixing interferometry

The following theory of the self-mixing effect is considered in a weak optical feedback for a single mode semiconductor laser and the presentation is also available in the original paper I. The self-mixing effect can be modelled as a three-mirror Fabry-Perot structure. The schematic arrangement of the self-mixing effect in a semiconductor laser is presented in Fig. 3. Mirrors M1 and M2 form the laser cavity, the length of which is L and which has an effective refractive index of µe. The external target, Mext, is located on the optical axis z, at distance Lext. PD is a monitor diode located in the laser package behind the laser cavity to measure power fluctuations within it.

23

),2cos(L

gg extext

thc πντκ−=−

Fig. 3. Three-mirror model and compound cavity model for self-mixing effect in a single mode semiconductor laser.

According to the theory, mirror M2 is replaced with an effective mirror, which combines the laser cavity and the external cavity to form a compound cavity. The amplitude reflection coefficient of the effective mirror r2 is (Petermann 1991)

(1)

where r2s and r2ext are the amplitude reflection coefficients of laser mirror M2 and external target Mext, respectively. The optical frequency is ν and τext corresponds to the round trip delay back and forth through the external cavity, τext=2Lext/c, which is assumed to be air in this case. The speed of light is c.

To archive successful operation of the laser, both the phase and amplitude conditions must be fulfilled. The phase condition states that the round trip phase of the compound cavity must be an integer multiple of 2π

(2)

where β is the phase constant of the optical wave (β=2πνµe/c), m is an integer and φr is the phase term of the external cavity. The amplitude condition states that the gain of the compound cavity must exceed the cavity losses to produce leasing

(3)

where gc is the threshold gain for the compound cavity and αs is the cavity loss factor (Petermann 1991).

For weak feedback, the following equation for gain variation due to external feedback can be derived

(4)

( ) ,exprr1r)(r ext2jext2

2s2s22

πντ−⋅⋅−+=ν

,m2L2 r π=φ+β

,1exprr L)g(21

sc =α−

M1 M2 Mext

µe

PDr1 r2s

r2ext

zL Lext

24

)),arctan(2sin(1)(2 ext2

extthLL α+πντα+κ+ν−νπτ=φ∆

where gth is the threshold gain without optical feedback. κext is the coupling coefficient which varies between zero and one, defined as κext=(1-|r2s|2)r2ext/r2s. The gain in the diode laser is produced by driving a high current density into the active area. Because external optical feedback causes gain variation, the self-mixing phenomenon can also be measured from the pump current of the diode laser (Meigas et al. 1998).

In the same feedback conditions, the following equation for the laser frequency variations can be derived

(5)

where ∆φL is the round trip phase change compared to 2πm. τL is the round trip delay in the laser cavity (τL=2Lµeg/c), where µeg is the effective group refractive index. α is related to the amount of stimulated emission and it is the ratio of the real to imaginary parts of the variation in the complex refractive index. The possible emission frequencies can be numerically solved from equation (5) and after calculation of ν, the gain gc can be solved from equation (4) (Petermann 1991, Koelink et al. 1992).

The strength of external feedback is an important consideration in self-mixing interferometry. The feedback parameter of the self-mixing effect is defined as

(6)

If the parameter Cfb << 1, power fluctuations at the laser output are sinusoidal. When Cfb increases, the fluctuations become more saw-tooth-like. When Cfb > 1, the operation of the laser is no longer stable, leading to increased noise and mode hopping (Acket et al. 1984, Koelink et al. 1992). On the other hand, the saw-tooth signal can be used to detect the direction of a moving target, because the self-mixing signal changes its inclination in respect to the phase of the external target (Wang et al. 1993).

The effect of external feedback strength to the shape of the interference signal with two different values of Cfb is shown in Fig. 4 (Wang et al. 1994). The solid line shows the interference signal for Cfb=0.7 and the dotted line shows the same signal for Cfb=0.2. The dashed line shows the driver signal of the vibration of the external reflector. The saw-tooth effect is clearly visible, when the value of Cfb is changed from 0.2 to 0.7. In addition, in the case of stronger feedback the inclination change can be also detected, when the direction of the movement of the external target is changed.

.1C 2ext

L

extfb α+κ

ττ=

25

,c/)vtL(2 extext +=τ

).c/L4c/vt4cos(L

ggP extext

thc νπ+πντκ−=−≈∆

),cos(v2D ϕ

λ=ν

Fig. 4. Effect of feedback strength on the shape of the interference signal (Wang et al. 1994). Until now, the self-mixing effect has been considered only in the case where the target remains at constant distance Lext from the front facet of the laser diode. If the external target moves with a uniform velocity v in the positive direction along the z-axis, then τext varies as

(7)

where Lext is now the distance between target and laser at zero time and t denotes time. Substituting equation (7) into equation (4), power fluctuations become (Koelink et al. 1992)

(8)

When the target moves, the reflected or scattered light contains a frequency shift, which is proportional to the velocity of the moving target. According to the Doppler theorem, the Doppler frequency, νD, is

(9)

where v is the velocity of the moving target, λ is the operating wavelength of the diode laser and ϕ is the angle between the moving target and the laser beam. If the measurement is perpendicular to the target, equation (9) is reduced to νD=2v/λ and further, solving the velocity, v=νDλ/2. Substituting this to equation (8) it can be seen that the power fluctuations of the laser diode are related to the Doppler frequency. Thus, it is possible to determine the velocity of the target measuring these power fluctuations.

26

2.4 Experimental measurements based on the self-mixing effect

Two experimental studies of self-mixing interferometry were performed before the biomedical measurements. These two experiments are velocity (Hast et al. 1999) and displacement (Paper I) measurements. In both cases, the measurement target is a paper-covered disk. Paper was chosen because it is as highly scattering as the human skin. The final application is to measure the skin displacement induced by a cardiovascular pulse, and in this regard it is important to understand the behavior of the self-mixing interferometer on scattering surface measurements.

2.4.1 Velocity measurement

In the velocity measurement of a rotating disk, a fiber-coupled single-mode laser diode (Hewlett Packard, LST0605-FC-A, λ=1300 µm) was used as the light source. Emitted light was delivered to the surface of the paper-covered disk using a multimode fiber with a core diameter of 62.5 µm. A microlens (Selfoc ) was used to focus the emitted light onto the surface of the disk, which was positioned 40 mm from the centre of the disk. The Doppler probe was tilted 10° from its normal position towards the disk. The Doppler shifted light from the disk was guided back to the laser cavity using the same fiber, and a monitor diode was used to detect the Doppler frequency. A spectrum analyzer was used to measure the Doppler spectrum, and the velocity of the disk was calculated using equation (9) after the maximum Doppler frequency component was detected. Each Doppler spectrum is an average of 100 measurements. For reference, the rotation frequency of the disk was determined using a LED-PD couple. When the location of the Doppler probe and the rotation frequency of the disk are known, the reference velocity of the disk can be calculated. The measurement setup is shown in Fig. 5.

Fig. 5. Velocity measurement setup. Fig. 6 (a) shows the linearity between the measured velocities as a function of calculated velocity. The line using a linear mean square approximation was fitted to the data points. The difference between the measured and calculated velocities was less than 5%, when

Rotating disk

LED-PD couple

Multimode fiber

Self-mixinginterferometer

Microlens

Spectrumanalyzer

Oscilloscope

vDC-motor

27

efftth

th R1I/I

I/IP η

−

≈∆

the velocity was less than 0.9 m/s. In higher velocities the difference increases to approximately 10%. The percentual difference between the measured and calculated velocities is shown in Fig. 6 (b). The reason for this increased error at higher velocities is that the disk as it rotates has a small jitter towards the laser beam. Thus the focus point on the disk surface has another velocity component. At higher velocities this effect causes variation in the Doppler frequency and also leads to variation in the measured velocity.

Fig. 6. Measured velocity as function of calculated velocity (a) and percentual difference of measured velocity and calculated velocity (b). The intensity modulation of the self-mixing effect has an interesting behaviour as a function of the operation current of the diode laser. The power fluctuations can also be written as

(10)

(a)

0

0.5

1

1.5

2

0 0.5 1 1.5 2

Calculated velocity [m/s]

Mea

sure

d ve

loci

ty [m

/s]

(b)

02468

10

0.08 0.10 0.15 0.19 0.29 0.43 0.58 0.77 0.90 1.12 1.48

Measured velocity [m/s]

Perc

entu

al d

iffer

ence

[%

]

28

where I is the operating current of a diode laser and Ith corresponds to the threshold current. Rt is the reflectivity of the target and ηeff is the coupling efficiency of the backscattered light into the laser diode (de Groot et al. 1989).

Fig. 7 presents the optical power of the diode laser and the corresponding maximum amplitude of the Doppler spectrum as a function of the laser’s operating current. The velocity of the disk was held constant at 0.5 m/s. Below the threshold current, there is no visible Doppler signal, but immediately after the operating current of the laser reaches the threshold region the Doppler spectrum has maximum amplitude. When the operating current increases, the amplitude starts to decrease following equation (10). Above an operating current of 15.8 mA, the amplitude of the Doppler spectrum settles to the level of 20 mVrms. Thus, optimal operation of the self-mixing interferometer can be obtained just above the threshold.

Fig. 7. Optical power and amplitude of the Doppler spectrum as function of operating current.

2.4.2 Displacement measurement

In the displacement measurement, the self-mixing interferometer was constructed in a single mode laser diode (Sharp LT016MD, λ=810 nm). For reference, displacement was also measured with a conventional Michelson interferometer. The emitted light was collimated and then focused onto the paper-covered membrane of the loudspeaker using a plano convex lens, with a 10 mm diameter and a focal length of 100 mm. The spot size of the beam on the membrane was 10 µm and the depth of the focus of the beam was approximately 200 µm. The loudspeaker was driven with a sinusoidal signal at a frequency of 1 Hz. The peak-to-peak control voltage of the signal was tuned between 1-12 V. Data acquisition and processing was done with a PC. The measurement setup is shown in Fig. 8 and the results shown here have been obtained with new optics after the publication of the original paper I.

0

100

200

300

400

12.9 13.3 13.8 14.3 14.8 15.4 16.1 16.7

Operating current [mA]

Opt

ical

pow

er [µ

W]

0

20

40

60

80

Am

plitu

de [m

Vrm

s]

PowerAmplitude

29

Fig. 8. Measurement setup of displacement measurement. The calculated displacements for the self-mixing and Michelson interferometers are shown in Fig. 9. The line using a linear mean square approximation was fitted to the data points measured with the Michelson interferometer. The deviation between the results of the self-mixing and Michelson interferometers was less than 0.5 µm when the displacement was shorter than 200 µm. All data points are mean values of 10 measurements. Standard deviation in all cases is around 500 nm.

Fig. 9. Measured displacements as function of control voltage. When the displacement is longer than the Rayleigh area of the focusing lens, the speckle effect on the paper surface causes fluctuations to the self-mixing signal, and this reduces the accuracy of the self-mixing interferometer. When the displacement is 300 µm, the difference between results is approximately 1% (2 µm).

The speckle effect in a self-mixing signal is demonstrated in Fig. 10. Two interference signals from 100 and 300 µm displacement sweeps are shown. In the shorter sweep the interference signal is sinusoidal through the whole sweep distance. The amplitude decreases when the distance to the external target increases. In Fig. 10 (b), the

050

100150200250300350

0 2 4 6 8 10 12 14

Control voltage [Vpp]

Dis

plac

emen

t [µm

]

Self-mixingMichelsson

Self-mixinginterferometer

Signal generatorFocus lens

Loud

spea

ker Collimator

30

interference signal is strongly distorted due to the deformation of the speckle pattern on the surface of the rough external target. The resulting optical wave is a superposition of several coherent waves coming from several points of the speckle pattern on the surface of the external target. The size of the speckle grain on the surface of the paper with the optic used is 9.8 µm. When the sweep distance of the loudspeaker increases over the focus range of the lens and the illuminated area on the paper increases, several other speckle grains start to interfere with each other causing fluctuations to the interference signal. The same effect has also been observed in velocity measurements performed on a rough surface (Plantier et al. 2001, Bosch et al. 2001).

The self-mixing interferometer is also tested in displacement measurement without any optics between the laser diode and the target. The setup is the same as in Fig. 8, except that the optics are removed and the external cavity length is fixed to 15 mm. In this case, the speckle effect starts to influence accuracy at lower displacements. However, an accuracy of ±1 µm can be achieved, when the displacement is lower than 140 µm as shown in the original paper I.

Fig. 10. Interference signals from 100 µm sweep (a) and 300 µm sweep (b). The speckle effect is visible in 300 µm sweep as amplitude fluctuations in the interference signal.

(a)

(b)

3 CARDIOVASCULAR PULSATION

3.1 Noninvasive cardiovascular pulse measurement from the wrist

The term cardiovascular is related to the heart, cardio, and the network of arteries and veins, vascular. The cardiovascular system can be divided into two parts. The first is the central circulation system, which includes the pulmonary circulation and the heart. The second part is the systemic circulation system, which is the circulation to and from the heart. The heart acts as a pump which transfers the blood from the lower pressure veins to the arteries, where higher pressure is prevailed (Green 1984).

The cardiovascular pulse is generated in the heart, when the chambers contract and blood bursts into the aorta from the left chamber. The blood travels through the arterial network and returns back to the heart through the vein network (Carola et al. 1990). However, the velocity of blood and the pressure pulse are different. The velocity of blood at the aorta is several meters per second and it slows down to several mm/s in the peripheral network. The pressure pulse travels much faster than blood in the cardiovascular network. There are many different factors, for example arterial elasticity, which affect the velocity of the pressure pulse. Typical values range from 5 m/s, with young people in central arteries, to 15 m/s, in peripheral and old arteries (O’Rourke & Mancia 1999). The velocity of the pressure pulse, i.e. PWV, is considered more closely in subsection 3.6.1.

In this thesis the study of cardiovascular pulsation focuses on the radial artery in the wrist, and in this sense the term arterial pulse could be also used. The wrist in the human hand offers a fascinating location for a noninvasive measurement device. There are both physiological and practical reasons which make the wrist so interesting for measurement purposes. The physiological reasons can easily be seen in the magnetic resonance image (MRI) in Fig. 11. The main arteries in the wrist, especially the radial artery, are close to the skin surface and consequently pulsation can be easily detected. In addition, the wrist bone under the radial artery offers good mechanical support for the measurement device. From a practical point of view, the measurement location is very handy, since the pulsation is easily detected and the measurement device is easy to put on. Therefore you don’t need any special skills to use the device.

32

Fig. 11. MRI from cross section of wrist.

Easy access to cardiovascular pulsation at the radial artery has made it possible to study heart rate and blood pressure in the wrist. Many different sensor types for pulse detection in the wrist have been developed. Pulse detection in heart rate and blood pressure measurements has been implemented by means of piezoelectric sensors, where the mechanical stimulus generated by the pressure pulse in converted to an electrical signal for further signal processing (Im et al. 1995, Tamura et al. 1995). A strain gauge differential pressure sensor was used in a measurement system where a low-pressure cuff was wrapped around the wrist and then the pressure modulation in the cuff caused by the pressure pulse was measured with strain gauges (Dupuis & Eugẻne 2000). New electrostatic materials like electromechanical film (EMFi) and polyvinylidene fluoride (PVDF) have been used in sensors for pulse detection in the radial artery (Sorvoja 1998, Ruha et al. 1996). Fiber optic sensors have also been used (Gagnadre et al. 1998). Here a multimode optical fiber is placed between two aluminium plates. The force generated by the pressure pulse causes variation in the modal distribution in the fiber and the pulse is detected using a photodetector.

Optical sensors in cardiovascular pulse detection typically measure the optical power variation which is due to absorption or scattering when the amount of blood in the measurement volume varies. This kind of measurement is called photo-plethysmography (PPG) and it was invented in the 1930s (Hertzman 1937). PPG is mainly used for measuring the pulsation in the capillary network, but it is also applied to measurements above the radial artery (Hast 1999, Aritomo et al. 1999). The shape of the pulse can be easily obtained from the tissue, but it cannot be used to study absolute values, when the amplitude of the signal is considered. It is important to point out that there are many variables which affect the PPG signal. For example, in the capillary system the amount of blood vessels is different between people, and for this reason the signal amplitude varies because the measurement volume contains a different amount of blood. However, it has to be noted that measurement of time intervals between cardiovascular pulses using the

Radial artery Ulnaris artery

Elbow bone Radial bone

33

PPG technique can be used to diagnose many different cardiovascular diseases. In pulse oximetry, two different wavelengths are used and from the ratio of the two signals, the percent of blood haemoglobin saturation with oxygen can be calculated (Northrop 2002).

The advantage of optical interferometry in cardiovascular pulse detection is that the velocity profile of the movement of the arterial wall caused by the pressure pulse can be measured accurately. The displacement of the arterial wall can be calculated by integrating the velocity profile in time and the changes in the arterial lumen during the cardiac cycle can be determined. The time domain information can also be determined from the changes in the velocity profile. Thus, optical interferometry gives both the amplitude information and time domain information of the cardiovascular pulse.

3.2 Structure and radial dilation of the arterial wall

3.2.1 Structure of the arterial wall

The arteries of the human body are divided into four different groups. These are elastic arteries, medium muscular arteries, small arteries and arterioles. The radial artery belongs in the group of medium muscular arteries. The structure of a muscular artery wall consists of three different layers. The innermost layer is the tunica intima. The middle layer is the tunica media and the outermost layer is the tunica adventitia. The structure of a small muscular artery is shown in Fig. 12 (Kangasniemi & Opas 1997).

The structure of the arterial wall is anisotropic, multi-storey and nonlinearly elastic, which makes its material properties highly nonlinear (Langewouters et al. 1984). The tunica intima consists of three layers. The innermost is the layer of endothelian cells. In the middle, the tunica intima contains a connective tissue, which is a thin subendothelian layer of fine areolar tissue. Outermost is a thin membrane of connective tissue. The tunica media is the thickest layer and it is composed mainly of connective tissue, smooth muscle cells and elastic tissue. The structure of the tunica media also depends on the type of artery. In larger arteries it consists of connective tissues, elastic tissue and elastic fibers. In smaller arteries, like the arteries in the arm, smooth muscle cells replace the elastic fiber layer. The tunica media predominantly determines the mechanical properties of the arterial wall. The tunica adventitia consists of collagen fibers and elastic tissue (Carola et al. 1990).

In general, the overall mechanical properties of the arterial wall are determined by how different compositions of collagen, elastin and protein are linked. The general rule is that when the elastin ratio is higher than the collagen ratio, the elastic modulus decreases and distensibility increases and vice versa (Doublin et al. 1969).

34

Fig. 12. Structure of a medium-size muscular artery (Kangasniemi & Opas 1997).

3.2.2 Radial dilation of the arterial wall

The self-mixing interferometer is used to measure the radial displacement of the radial artery. Thus, it is important to know which are the physical parameters that influence the amount of the displacement of the arterial wall. It has to be remembered that the Doppler signal is proportional to the velocity of the radial displacement, and this is why the radial velocity of the arterial wall is considered. The displacement can be determined from the velocity profile integrating the profile as a function of time. The equation for the radial velocity of the arterial wall can be derived in two ways and it can be found in the literature. The first way is to solve the Navier Stokes equations (Milnor 1982) and the second way is to use Bernoulli’s law (Sepponen 1979). Here both approaches are shortly presented and a more detailed consideration can be found in the references.

In both cases some assumptions have to be made. The wall is assumed to be homogenous and circular. During blood injection to the vessel segment, the arterial wall expands regularly into all directions in the same plane as the cross section of the artery. The longitudinal expansion of the arterial wall is neglected. The blood flow is assumed to be Newtonian and axially symmetric (Milnor 1982).

Tunica intima Endothelian cells Connective tissue Elastic tissue

Tunica media Tunica adventitia

35

3.2.2.1 Approach using the Navier-Stokes equation

The Navier-Stokes equations can be used for mathematical analysis of blood pressure in a cardiovascular network. They describe the pressure gradients in cylinder co-ordinates along the longitudinal x- and radial r-axis as follows

(11)

(12)

and

(13)

In these equations, P is pressure, w is the longitudinal velocity of the fluid in the x direction and u is the radial velocity of the fluid in the r direction. In equations (11) and (12), the first three terms on the right-hand side are multiplied by density, ρ, representing inertial forces, while the last three terms are multiplied by viscosity, η, representing viscous forces. Thus, the equations state that a pressure drop per unit length equals the inertial forces minus the viscous losses. Equation (13) is a continuity equation stating that the net rate of mass influx into any segment of the tube equals the mass storage rate of the segment (Milnor 1989).

Although no general solution has been presented to Navier-Stokes equations, some analytic solutions have been calculated for certain special cases, including longitudinal flow velocity and longitudinal volume flow in an elastic tube (Milnor 1989). These solutions are based on linearized Navier-Stokes equations with so-called Womersley parameters (Womersley 1955& 1957). These complex solutions allow the possibility of taking into account amplitude and phase information concerning the pressure wave that travels inside the tube, the radial dilation of the wall of the tube and the fluid in question. The pressure wave is assumed to vary sinusoidally, P(t)=P0ejωt, which causes the complex term to these equations.

The following equation, which presents the radial dilation of the vessel wall as complex form, ξ, can be derived (Milnor 1989, Hong 1994) as:

(14)

where ρv is the density of the vessel wall, rvi is the radius of the vessel lumen in diastole and c0 is the wave velocity of the pressure wave defined as

,dx

wddrdw

r1

drwd

dxdww

drdwu

dtdw

dxdP

2

2

2

2

++η−

++ρ=−

−++η−

++ρ=− 22

2

2

2

ru

dxud

drdu

r1

drud

dxduw

drduu

dtdu

drdP

.0dxdw

ru

drdu =++

,c

ePr83)t( 2

0v

tj0

vi ρ=ξ

ω

36

(15)

In the equation of c0, E is the elastic modulus of the vessel wall and hv the thickness of the vessel wall. The velocity profile of the radial dilation of the vessel wall, vv, can be derived from the Navier-Stokes equations (Milnor 1989, Hong 1994)

(16)

where ρb is the density of blood. Re presents the real part of complex number. This equation bears a strong resemblance to the empirically derived equation (Hong 1994)

(17)

where rv is the radius of the vessel lumen as function of pressure, Ptm is the transmural pressure and Cα and Cβ are the first and second order compliance factors, respectively. The radial velocity can be derived differentiating equation (17) as function of time. Thus, we get the radial velocity

(18)

The compliance factor Cβ is much smaller than Cα for all types of vessels. Now, equation (18) can be estimated as (Hong 1994)

(19)

Cα, describing the elastic properties of the arterial wall, can be calculated from equation (19) when blood pressure and the radial velocity of the arterial wall are known.

3.2.2.2 Approach using Bernoulli’s law

In the second approach Bernoulli’s law is used (Sepponen 1973) and a more detailed consideration can be found in the original paper I. When blood flows in a vessel, pressure losses are generated in the direction of the flow. These pressure losses cause a force F, the

,dtdP

Ehr2

83Rev

v

2vi

v

bv

ρρ=

.dt

dPCPr2dt

dPCrdtdrv tm

tmvitm

viv

v βα −==

.dt

dPCrv tmviv α≈

[ ],PCPC1rr 2tmtmviv βα −+=

.r2Ehc

vvi

2v

0 ρ=

37

.EhPrr

v

2vi

v =

direction of which is perpendicular to the cross section of the vessel. The amount of this force is

(20)

where ρb is the density of blood and P blood pressure. Again x is the longitudal coordinate and w is the longitudinal velocity. A’ is the unit area of the arterial lumen. According to equation (20), the pressure gradient towards x is

(21)

The change of stress, ∆σ, to the vessel wall generated by a pressure impulse ∆P is

(22)

where hv is the thickness of the vessel wall, and rvi is the radius of the arterial lumen. The strain, ∆ε, caused by this stress in the vessel wall can be expressed using the radial displacement rv of the vessel wall

(23)

Now, the stress of the vessel wall can be expressed using the strain. According to Hooke’s law

(24)

where E is the elastic modulus of the vessel wall. Using equations (21), (23) and (24), the equation for the radial displacement is

(25)

The radial velocity of the vessel wall is received by differentiating equation (25) with respect to time

(26)

In medium sized blood vessels such as the radial artery, hv is typically of approximately the same size as rvi (Bates 1995), and we get

,dx'Adtdwdx

dxdP'AF bρ=−=

.dtdw

dxdP

bρ−=

,hrP

v

vi∆=σ∆

.rr

vi

v=ε∆

,E ε∆=σ∆

.dtdP

Ehr

dtdr

v

2viv =

38

(27)

As can be seen, equations (19) and (27) are otherwise the same, but (19) is the compliance term and (27) is the elastic modulus. Here also the transmural pressure is equal to the blood pressure. Both equations combine blood pressure and radial velocity. We may solve the elastic modulus or compliance factor, which can be solved when the other parameters are known. E describes the stiffening of the vessel wall when pressure increases and Cα describes the decrease of elasticity of the vessel wall when pressure increases.

Now, when the radial displacement of the arterial wall is measured and if the blood pressure is known, it is possible to evaluate E or Cα from equations (19) and (27). However, the internal radius must also be known. In the literature the average value for the radial artery of adults is rvi=1.74 mm (O’Rourke et al. 1992), and this value is also used in computer simulations (Hong 1994).

3.3 Pulse wave velocity and autonomic regulation

Other considered medical parameters in this study are PWV and autonomic regulation, which are shortly discussed in following two chapters. Both are very important diagnostic tools for different cardiovascular diseases.

3.3.1 Pulse wave velocity

The pressure pulse travels much faster than the blood itself, as was mentioned in chapter 3.1. PWV describes how quickly a blood pressure pulse travels from one point to another in the human body. The time difference between these two locations is known as the pulse transit time (PTT). PWV is typically measured between the carotid and the femoral artery. Atherosclerosis causes the arterial wall to become thicker and harder and narrows the arterial lumen (Ross 1999). The increased inflexibility of the arterial wall serves to increase PWV, because the energy of the blood pressure pulse cannot be stored in an inflexible wall. PWV can be used as an index of arterial distensibility (Asmar et al. 1995). In recent years, a number of papers have been published on the diagnosis of cardiovascular diseases and mortality risk prediction (Blacher et al. 1999, Laurent et al. 2001, van Popele et al. 2001, Safar et al. 1998). In terms of medical diagnosis, PWV is a highly interesting subject, because it provides an estimate of the condition of the cardiovascular system based on a large area of the human body.

Self-mixing interferometry has several advantages in PWV measurements. Firstly, it can also be used for pulse detection from underlying tissue. Secondly, the radial

.vdtdP

Er

dtdr

vviv =≈

39

,AAP1PWV

b

⋅∆∆

ρ=

,r2

EhPWVvib

v

ρ=

distensibility of the examined artery can be measured and thus it can be used to evaluate the arterial compliance according to the Bramwell-Hill equation.

Arterial elasticity (compliance) is determined as the ratio of change in volume to change in pressure, C=∆V/∆P. Alternatively volume can be replaced by the cross sectional area, ∆A (Pythoud et al. 1994). The elastic and geometric properties of the arterial tree also determine how fast a pressure pulse travels through the cardiovascular system. PWV can be expressed by the Bramwell-Hill equation (McDonald 1974)

(28)

where ρb is the density of blood and A is the cross-sectional area of the arterial lumen in diastole. This relation enables the study of compliance by measuring the PWV. In addition, PWV can be formalised by the Moens-Korteweg equation (McDonald 1974)

(29)

where E is the elastic modulus, hv is the thickness of the arterial wall and rvi is the internal radius of the artery.

3.3.2 Autonomic regulation

The human body is controlled by a host of regulation mechanisms, which, in turn, serve as major indicators of its condition. The actions of the mechanisms, particularly that of the autonomic nervous system, are reflected in rhythmical variations in the blood pressure shown in Fig. 13. The autonomic nervous system is closely connected with other regulatory systems, including the neuroendocrine and energy balance systems (Laitinen 2000). Malfunctions in autonomic cardiovascular regulation may result in cardiovascular diseases, including orthostatic intolerance, hypertension, coronary heart disease, cardiac dysrhythmia and heart failure (Bannister et al. 1992). Especially older people and diabetics show an increased mortality rate caused by these diseases (Tsuji et al. 1994, Ewing et al. 1980). The risk of sudden arrhythmic death is clearly increased in people with diminished vagal heart rate control after acute myocardial infarction (Hartikainen et al. 1996). The complex behaviour of the baroreflex system poses a problem owing to its strongly nonlinear components. So, to improve their understanding of the cardiovascular system, researchers use various mathematical models to describe it (Madwed et al. 1989, Ursino et al. 1994, Ursino 1999).

40

Fig. 13. Rhythmical variations in blood pressure.

The cardiovascular regulation system comprises baroreflex regulation, whose main function is to maintain normal arterial pressure despite large alterations in physical stress. The central autonomic network controls baroreflex regulation via baroreceptors, which are mainly located in the aortic arch and the carotid sinus region. Baroreceptors measure the stretch caused by blood pressure against the arterial wall and pass their response to the centre of the autonomic network. As a result, the activity of the heart and blood vessels is either increased or decreased, depending on the response of the baroreceptors. Increased sympathetic outflow increases baroreflex regulation, whereas the exclusion of the sympathetic or parasympathetic outflow decreases it (Guyton & Hall 1998).

Other autonomic regulation mechanisms include thermoregulation and respiratory sinus arrhythmia (RSA), which, together with baroreflex regulation, affect heart rate variability. These three mechanisms can be detected from RR intervals. Thermoregulation (VLF component) operates at very low frequencies below 0.04 Hz, while baroreflex regulation is the low-frequency component (LF component), as it is located within the frequency range of 0.04 to 0.15 Hz. Finally, the frequency range between 0.15 and 0.4 Hz is known as the high-frequency component (HF-component). The effects of RSA can be found within this frequency band, depending on respiratory frequency. These spectral estimates are also recommendations of the Task Force of the European Society of Cardiology and the North American Society of Pacing and Electrophysiology

0

20

40

60

80

100

120

140

0 5 10 15 20 25 30Time [s]

Blo

od p

ress

ure

[mm

Hg]

41

(ESC/NASPE Task Force 1996). Table 2 summarises the spectral estimates of the different regulation mechanisms calculated from the RR interval.

Table 2. Frequency ranges for different autonomic regulation mechanisms and their frequency components (ESC/NASPE Task Force 1996).

Frequency range [Hz]

Frequency component

Regulation mechanism

≤ 0.04 VLF Thermoregulation 0.04-0.15 LF Baroreflex 0.15-0.40 HF RSA

Cardiovascular regulation mechanisms are normally studied by counting the RR intervals in the electrocardiogram (ECG). The rationale of the approach used in this thesis is that baroreflex-induced blood pressure changes in the artery affect the elastic properties of the arterial wall. The elastic properties of the wall, in turn, influence its movement. Thus, the effects of the baroreflex can be measured by measuring the movement of the arterial wall.

4 MEASUREMENT SYSTEM

The developed laser Doppler measurement system can be divided into three different blocks, shown in Fig. 14. These are the laser Doppler probe, where a self-mixing interferometer is implemented. The second block is a PC interface card, which contains the laser diode current source, analog signal condition unit and power supply. The third block is the data acquisition and processing block.

Fig. 14. Block diagram of the laser Doppler measurement system.

4.1 Measurement probe

The measurement probe comprises a single mode laser diode (Sharp LT016MD), whose monitoring diode is used to measure the interference signal. The current generated by the photo diode is amplified and converted to voltage in a DC-coupled transimpedance preamplifier. The whole probe is implemented in an aluminum chip 3 × 4 cm in size. The

PC interface card

LDMD

Transimpedancepreamplifier

Constant current source

Measurement probe

Variable gainvoltage amplifier

Software controlledfilter block

Data acquisition and processing

DAQ-card

PC

Power supply

43

height of the probe is 7 mm. The weight of the probe is approximately 34 g. The measurement probe and the PC interface card are connected by a 1.0 m long 12-pin flat cable, where 8 pins are used for grounding purposes. The flat cable is quite sensitive to electromagnetic interference because there is no shielding around the conductors. Nevertheless, a flat cable was used because it is much more flexible than a coaxial cable.

The measurement probe is attached to the volunteer’s hand using a plastic watchband. Special fabricated plastic supports are mounted using flexible tape underneath the measurement probe to provide good mechanical support for the wrist.

4.2 PC interface card

The PC interface card contains the main amplifier for the Doppler signal, which is a variable gain voltage amplifier. The gain of the amplifier can be set between 1-100. The software-controlled filter block contains four different high-pass filters to adapt the Doppler signal to the appropriate form for data acquisition. The filters were implemented using continuous time filter circuits. Selection of desired filter is done using an analog multiplexer, whose output line is selected using the digital I/O-lines of the measurement card. The upper cut-off frequencies of the filters are 1 kHz, 2 kHz, 4 kHz and 6 kHz. The lower cut-off frequency, 100 Hz, is same for all filters. The dynamic range of the output of the amplification unit is 9.4 V. Total noise at 1.5 mW optical power and 4 kHz bandwidth at the input of the AD-converter is around 10 mV. This gives a SNR of 59 dB for the system.

The constant current source is based on a power transistor, whose current is set by voltage reference. The current source drives the wanted operation current through the laser diode. It can be used to produce operation currents between 50-120 mA, which corresponds to an optical power of 0.2 mW to 16 mW. Voltage transients caused by the switching on of the device are eliminated by pass capacitors.

4.3 Data acquisition and signal processing

The data acquisition and signal processing are done with a PC. A DAQ card with a 12-bit AD-converter collects the measured data and also controls the filters at the interface card via digital I/O-lines. The measurement software has been made with LabView™ and final data analysis with Matlab™. More detailed information about the signal processing algorithms used in this thesis can be found in the original papers. However, the basic algorithms are presented in the following chapter.

The Doppler signal analysis is based on fast Fourier transform (FFT) calculation. This is done because in the time domain it is very difficult to calculate fringes due to the fluctuations shown in Fig. 10 (b). FFT is calculated using a 256 or 512 point sliding window over the Doppler data depending on the sampling frequency used (Fs). For Fs=10

44

kHz a 256 point window is used and for Fs=20 kHz 512 points is used. The formulas are presented in the following section.

As can be seen in equation (27), to be able to evaluate the elasticity, the blood pressure must be known. Comparative blood pressure measurements are performed with a Finapres Ohmeda 2300 finger blood pressure monitor operating on the basis of the so-called Penaz technique, according to which the externally applied pressure is kept equal to the arterial pressure during the whole cardiac cycle. The arterial walls are unloaded because of zero transmural pressure, the size of the arteries is not changed, and the blood volume remains constant. The blood volume is measured with a photopletysmograph and the analogue output of the device is scaled so that 1 V equals to 100 mmHg. Blood pressure is measured from the middle finger.

In the PWV measurements, an accurate starting point for PTT must also be known. For this purpose the ECG-signal is measured using an optoisolated ECG-amplifier. The ECG-signal is measured above the volunteer’s chest with a two-electrode heart rate belt. In addition, the ECG-signal is also used to determine the RR intervals in the baroreflex measurements.

The block diagram of the whole system is shown in Fig. 15. The ECG-amplifier, blood pressure monitor and Doppler device are connected to the data acquisition and processing block, which is implemented using a PC. The ECG is measured above the chest, blood pressure from the middle finger, and the laser Doppler probe is attached carefully to the wrist above the radial artery. The Doppler signal is also fed to a loudspeaker. This makes the positioning of the probe towards the artery easier.

Fig. 15. Block diagram of the whole laser Doppler measurement system.

4.4 Composition of Doppler signal from radial artery

During the cardiac cycle, the radial displacement of the arterial wall varies as presented in equations (19) and (27). The radial displacement of the arterial wall causes an elastic wave, which propagates through the soft tissue towards the skin surface. It is obvious that

Laser Dopplerprobe Blood pressure

probe

PC interface

Data acquisition and processing

Blood pressuremonitor

ECG ECG from chest

45

soft tissue absorbs some part of the energy of the wave, and in this sense the amount of skin displacement is not directly related to the displacement of the arterial wall. However, here the absorbing effect is assumed to be small and it is neglected because the radial artery in the wrist is very close to the skin surface as was presented in chapter 3.

When the laser beam illuminates the skin surface, approximately 5% of the light is reflected from the skin surface. This is due to the refractive index mismatch that occurs in the boundary of skin (ns=1.55) and air (na=1.00) (Tuchin 2000). The Fresnel reflection at the air-skin boundary is (ns-na)2/(ns+na)2≈0.05. The rest of the light penetrates into the tissue and undergoes a scattering process in non-homogeneous tissue. The laser cavity and the air-skin boundary form the three-mirror Fabry-Perot cavity as presented in chapter 2. If the laser beam is pointed towards the skin above the radial artery, the elastic waves move the skin surface and modulate the external cavity field. This causes intensity fluctuation to the laser power, and these fluctuations are detected with the photodiode on the backside of the laser cavity.

The Doppler relation states that the Doppler frequency is related to the velocity of the moving target. In this case, the frequency is proportional to the velocity of skin vibration. The skin vibration is related to the first derivative of the blood pressure pulse (dP/dt). If the Doppler spectrogram, which presents the Doppler frequency as a function of time, is reconstructed it should be comparable to dP/dt.

As was pointed out in the previous chapter, the best way to analyze the frequency information is to use FFT algorithms. Here the following discrete FFT algorithm is used (Ifeachor et al. 1993)

n = 0,1,…,N-1 (30)

where x(k) is the discrete time domain data sample and N is the length of this data vector, which is 256 or 512 points depending on Fs. This equation is used in the sliding FFT algorithm to reconstruct the Doppler spectrogram. An example of a time domain Doppler signal from a single cardiovascular pulse and the corresponding Doppler spectrogram is shown in the following chapter in Fig. 16.

The similarity between two different signals can be studied using a cross-correlation function. This is used in the pulse shape and baroreflex regulation analysis to find out the correlation degree of the measured parameters. The cross-correlation function between two signals with zero average is (Ifeachor et al. 1993)

(31)

where rxy(n) in an estimate of the cross-covariance defined as

,e)k(x)n(X1N

0k

N/kn2j∑−

=

π−=

,)0(r)0(r

)n(r)n(X 2/1

yyxx

xycorr =

46

and

[ ]∑−

=

=1N

0k

2yy )k(y

N1)0(r .

N is the length of two sequences x(k) and y(k).

The radial displacement of the arterial wall during a cardiac cycle can be calculated from the Doppler spectrogram integrating the velocity profile as a function of time. Here a trapezoidal integration method is used (Kreyzig 1999)

(32)

where a=x0 and b=xn are the integration limits, h=(b-a)/n and n=0…n is the index number of the data sample.

The derivative of the blood pressure pulse is calculated from the pressure signal using differential approximation and it is

i = 1…N-1 (33)

where P(ni) is the data sample of the pressure signal, Ts is the period of the sampling signal, which is equal to 1/Fs and N is the length of the blood pressure signal data vector.

−−=−

=+=

∑

∑−+

=

−−

=1nN

0k

1nN

0kxy

N,...,2,1,0n)k(y)nk(xN1

N,...,2,1,0n)nk(y)k(xN1

)n(r

,)b(f21)x(f...)x(f)x(f)a(f

21hdx)x(f

b

a1n21∫

+++++≈ −

,T

)n(P)n(PdtdP

s

i1i

1i

1i −= +

+

+

[ ]1

2

0

1(0) ( )N

xxk

r x kN

-

=

= Â

5 SELF-MIXING INTERFEROMETRY IN CARDIOVASCULAR PULSE MEASUREMENTS

This chapter presents the measurement results of self-mixing interferometry applied to cardiovascular pulse measurements. In section 5.1 the technique is used for pulse detection above the radial artery for normal blood pressure pulse and ‘abnormal’ blood pressure pulse, which is generated experimentally using the Valsalva manoeuvre. In section 5.2 it is shown that a strong correlation exists between the shapes of the first derivative of the blood pressure pulse and the Doppler spectrogram. Section 5.3 focuses on the measurement results of autonomic regulation. Finally, in section 5.4 the elasticity of the arterial wall is evaluated and its correlation to PWV is studied.

5.1 Pulse detection

5.1.1 Normal blood pressure pulse

A typical blood pressure pulse from the radial artery above the wrist is shown in Fig. 16 (a). When the chambers of the heart contract, the blood pressure in the artery increases and diastolic blood pressure changes to systolic blood pressure. The difference of these pressures is called pulse pressure. Normal blood pressure occurs when systolic pressure is less than 130 mmHg and diastolic blood pressure is less than 80 mmHg for adults (Bates 1995). Mean arterial pressure (MAP) is the mean pressure over one cardiac cycle.

Fig. 16 (b) presents the first derivative of the blood pressure pulse (dP/dt), which is calculated using equation (31). The derivative shows how fast the pressure changes. The pressure changes inside the artery force the arterial wall to move. The velocity of the radial movement of the arterial wall is relative to dP/dt.

48

Fig. 16. (a) Normal blood pressure pulse and (b) first derivative of the pulse, (c) Doppler signal of the blood pressure pulse and (d) spectrogram of the Doppler signal. Fig. 16 (c) presents the measured Doppler signal from the pressure pulse presented in Fig. 16 (a). Comparing the signals, it can be seen that the interference signal reacts to the changes in blood pressure. Hence, the interference patterns can be located to the rising and falling edges of the blood pressure pulse. In addition, small rises on the falling edge due to reflections of the blood pressure pulse can be registered.

The velocity information in the Doppler signal is related to its frequency. Applying a sliding FFT over the Doppler data using equation (30), a Doppler spectrogram, which presents the Doppler frequency as a function of time, can be obtained. This is shown in Fig. 16 (d).

The maximum Doppler frequency can be located to the rising edge of the blood pressure pulse, where diastolic blood pressure changes to systolic. In this pulse, the maximum frequency is 1.1 kHz, which corresponds to 445 µm/s radial velocity. In the work of Hong et al. (1997) a radial velocity of 350 µm/s was measured from the radial artery. The radial displacement of the radial artery for the pulse presented in Fig. 16 is 56 µm, calculated using the trapezoidal integration method (equation 32) from the Doppler spectrogram.

(c)

-1.5-1.0-0.50.00.51.01.5

0.0 0.2 0.4 0.6 0.8Time [s]

Dop

pler

sign

al [V

](d)

0200400600800

10001200

0 0.2 0.4 0.6 0.8Time [s]

Dop

pler

freq

. [H

z]

(a)

0

50

100

150

0 0.2 0.4 0.6 0.8

Time [s]

Pres

sure

[mm

Hg]

(b)

0123456

0 0.2 0.4 0.6 0.8

Time [s]

dP/d

t [a.

u.]

49

5.1.2 Abnormal blood pressure pulse

It is interesting to know whether the changes in the shape of the pressure profile can be registered if the pressure pulse changes. These results are presented in the original paper III. To achieve an abnormal pressure pulse, the blood pressure is manipulated by performing the so-called Valsalva manoeuvre. The Valsalva manoeuvre is used in medical research to study autonomic regulation (Sovijärvi et al. 1994). In the Valsalva manoeuvre the volunteer exhales against a pressure of 40 mmHg for 10 seconds. This blocks the vein returning to the heart. The resulting reduced blood flow decreases the blood pressure, which stimulates the heart to work more actively to maintain normal blood pressure. Fig. 17 presents the RR interval, MAP and PTT between heart and wrist during this manoeuvre.

Fig. 17. RR interval, MAP and PTT during Valsalva manoeuvre.

The exhalation phase is timed between 13-25 seconds. The MAP decreases due to the decreased vein return to the heart. The RR interval also decreases, reflecting the increased activity of the heart. The PTT between heart and wrist increases from 0.13 seconds at the beginning to 0.21 seconds at the end of the Valsalva manoeuvre. This can be explained by the elasticity changes in the arterial tree. When the MAP decreases the elasticity of the arterial tree increases. Thus, more of the energy of the pressure pulse can be stored in the arterial wall and this retards the velocity of the pressure pulse.

The blood pressure signal and the reconstructed Doppler spectrogram from the corresponding pulses during the exhalation phase of the Valsalva manoeuvre are shown in Fig. 18. The diastolic blood pressure decreases dramatically due to the reduced blood flow. In addition, the pulse pressure decreases to 20 mmHg and the shape of the pulsation is significantly altered from Fig. 16. However, the Doppler spectrogram follows the pressure variation exactly. The peaks in the Doppler spectrogram correspond to the maximums of the derivative of the blood pressure signal. The radial displacement is 25 µm on the rising edge of the blood pressure pulse.

00.20.40.60.8

11.2

1 5 9 13 17 21 25 29 33 37 41 45 49Time [s]

PTT,

RR

[s]

020406080100120

MA

P [m

mH

g]

PTT RR-interval MAP

Exhalation

Rest

50

Fig. 18. Blood pressure (black solid line) and Doppler spectrogram (gray solid line) during the exhalation phase of the Valsalva manoeuvre.

5.2 Pulse shape measurements

An important question in the pulse detection is how well the shapes of the dP/dt and the Doppler spectrogram match with each other. In other words what is the cross correlation between the pulse shapes shown in Fig. 16 (b) and (d). In the study, 10 healthy volunteers whose mean age was 26 years were measured. The length of each measurement was 60 seconds. A total of 738 pulses were obtained and then analysed.

Before calculation of the cross-correlation coefficient (Xcorr), each pulse in the dP/dt and the Doppler spectrogram are separated, normalized and zero-averaged. After this the Xcorr between the pulses is calculated using equation (31). More detailed information about the measurements, data analysis and results can be found in the original paper II. The summarized results of this study are presented in Table 3 and Fig. 19.

0

100

200

300

400

500

600

700

800

0.0 0.3 0.5 0.8 1.0 1.3 1.5 1.8 2.0

Time [s]

Dop

pler

freq

uenc

y [H

z]

010

203040

506070

8090

Blo

od p

ress

ure

[mm

Hg]

Doppler frequency [Hz] Blood pressure [mmHg]

51

Table 3. Results of pulse shape measurements. <Blood pressure> is the mean value of all systolic and diastolic pressures during the measurement sequence. Respectively, <Xcorr> is the mean value of all correlation coefficients, and std represents the standard deviation of <Xcorr> during each measurement sequence.

Vol.

Age

<Blood pressure> syst./diast. [mmHg]

Number of pulses

<Xcorr>

std 1 27 133/80 77 0.80 0.07 2 25 126/77 75 0.85 0.05 3 27 122/70 78 0.83 0.05 4 29 131/81 75 0.84 0.05 5 21 115/75 80 0.87 0.04 6 32 121/82 67 0.77 0.10 7 26 125/79 65 0.81 0.07 8 25 110/65 71 0.86 0.05 9 22 132/85 76 0.86 0.04 10 28 121/76 74 0.82 0.05

The Xcorr for all measured pulses is show in Fig. 19. The average Xcorr for the 738 measured pulses is 0.83, and standard deviation is 0.6. It can be seen from Fig. 19 that some of the pulses have a low Xcorr. An empirical constant, 0.7, is determined to set a limit for successfully measured pulses. If the pulses that have a lower Xcorr than 0.7 are neglected, the average Xcorr increases to 0.84 and deviation decreases to 0.05.

Fig. 19. Xcorr for all measured pulses. The average of Xcorr is shown as a solid line.

0

0.2

0.4

0.6

0.8

1

1 51 101 151 201 251 301 351 401 451 501 551 601 651 701

Pulse number

Xco

rr

52

5.3 An example of signal degradation

Effects that cause signal degradation are the variation of probe position above the radial artery and external artefacts which move the measurement probe. These might occur during measurements. Here an example of the variation of probe position is demonstrated.

In Table 3, the <Xcorr> of volunteer number six is 0.77. In addition, the standard deviation is 0.1 and it differs from the mean value by 50%. Fig. 20 shows Xcorr for volunteers 4 and 6 as a function of each measured pulse. In the case of volunteer number 4 the Xcorr has a constant mean value 0.84 throughout the measurement sequence. However, in the case of volunteer number 6, the Xcorr has a negative slope during the measurement sequence.

Fig. 20. Xcorr for volunteers 4 ( ) and 6 ( ).

The decrease in Xcorr in the case of volunteer number 6 can be explained by the poor attachment of the measurement probe above the radial artery. The probe moves slightly during the measurement and fails to detect the information from the skin displacement. The falsely detected pulse is shown in Fig. 21.

Fig. 21. dP/dt and Doppler spectrogram of pulse number 47 from volunteer number 6.

0

0.2

0.4

0.6

0.8

1

1 10 19 28 37 46 55 64 73

Pulse number

Xco

rr

(a)

00.20.40.60.8

11.2

0 0.25 0.5 0.75 1Time [s]

dP/d

t [a.

u.]

(b)

00.20.40.60.8

11.2

0 0.25 0.5 0.75 1Time [s]

Dop

pler

freq

. [a.

u.]

53

Fig. 21 (a) presents the normalized dP/dt signal of pulse number 47 from volunteer number 6. Respectively, Fig. 21 (b) presents the corresponding Doppler spectrogram for the same pulse. In the case of pulse number 47 from volunteer 6, the Xcorr is only 0.51. The largest differences between the signals can be seen at the falling edge of the blood pressure pulse, which can be located in these figures to 0.2 seconds. In the Doppler spectrogram, the frequency peak has significantly decreased compared to the dP/dt.

5.4 Autonomic regulation measurement

As was mentioned in section 3.4, the effect of autonomic regulation can be seen as sinusoidal variation in the blood pressure signal. Because of blood pressure variation, the stress inside the artery against the arterial wall varies, affecting the movement of the arterial wall. This is considered in the original paper IV.

Figures 22 (a) and (b) show 30 seconds of recorded blood pressure signal and the corresponding reconstructed Doppler spectrogram. Sinusoidal variation in the amplitude of the pressure signal is clearly visible. In the spectrogram, the same kind of variation in the Doppler frequency can be seen, but in this case it is in inverse phase when compared to the variation in the pressure signal.

The frequency variation in the Doppler signal can be explained by the variable stress against the arterial wall when blood pressure varies. During the measurement sequence the pulse pressure remains constant at approx. 40 mmHg. Thus, the impulse at the rising edge of the blood pressure pulse is approximately the same through the measurement cycle. In lower diastolic pressure the arterial wall is in a more flexible state than in higher diastolic pressure. For example, during sequence A, shown in Fig. 22 (a), the blood pressure is 130/90. At the same time, the Doppler frequency at the rising edge of the blood pressure pulse is around 900 Hz. During sequence B, the blood pressure decreases to 110/70, but now the Doppler frequency has increased to 1200 Hz. These differences between sequences A and B can be explained by the variable stress in the artery. It is obvious that the blood pressure variation has a clear effect on the radial movement of the arterial wall.

54

Fig. 22. (a) Blood pressure signal and (b) Doppler spectrogram from 30 second measurement.

The different autonomic regulation components in the ECG and Doppler signals are demonstrated in Fig. 23. Power spectral density (PSD) is calculated from the variation of the normalized RR interval and the Doppler frequency. When comparing the frequency peaks to the estimated ranges shown in Table 2, it can be seen that the baroreflex component is strongly visible in both signals at 0,1 Hz. In addition, thermoregulation is perceptible below 0.05 Hz. The effect of RSA is very low, but still detectable at 0.34 Hz.

(a)

40

60

80

100

120

140

0 5 10 15 20 25 30

Time [s]

Bloo

d pr

essu

re [m

mH

g]

(b)

0

300

600

900

1200

1500

0 5 10 15 20 25 30Time [s]

Dop

pler

freq

uenc

y [H

z]

A

B

55

Fig. 23. PSD of Doppler frequency variation and RR-interval variation.

Correlation between the variation in systolic, diastolic and pulse pressures to the Doppler frequency was studied in 10 volunteers who did not have any diagnosed diseases. Two 60 second measurements were done for each volunteer. More information can be found in the original paper IV.

The results of the experimental measurements are shown in Tables 4 and 5. The correlation between diastolic and systolic pressure variation to Doppler frequency variation is highly negative. Thus, correlation between these exists, but it is in inverse phase. This is true especially in the case of diastolic pressure. The correlation coefficient between pulse pressure and Doppler frequency is close to zero, because pulse pressure is almost constant throughout the measurement sequence and the effect of baroreflex regulation on it disappears.

Table 4. Results of the correlation study. XSYST, XDIAST and XPULSE are cross-correlation coefficients between systolic, diastolic and pulse pressure variation compared to Doppler frequency variation. The Baroreflex and RSA operation frequencies are determined from the Doppler frequency variation.

Baroreflex RSA Vol. XSYST XDIAST XPULSE [Hz] [Hz]

1. -0.47 -0.63 -0.04 0.09 0.35 2. -0.66 -0.78 -0.22 0.12 0.32 3. -0.48 -0.65 0.05 0.09 0.38 4. -0.44 -0.71 -0.12 0.11 0.25 5. -0.68 -0.79 -0.16 0.10 0.30 6. -0.43 -0.67 -0.11 0.08 0.40 7. -0.53 -0.65 -0.19 0.08 0.25 8. -0.63 -0.78 0.01 0.14 0.21 9. -0.44 -0.64 -0.07 0.11 0.41

10. -0.59 -0.77 -0.08 0.10 0.36

0

0.2

0.4

0.6

0.8

1

1.2

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7Frequency [Hz]

PSD

[a.u

.]RR-interval

DopplerBaroreflex

Thermoregulation

RSA

56

Table 5. Average and range in the correlation coefficients between volunteers.

XSYST XDIAST XPULSE Range -0.68 ↔ -0.43 -0.79 ↔ -0.63 -0.22 ↔ 0.05

Average -0.53 -0.71 -0.09

5.5 Evaluation of elasticity and pulse wave velocity

In the previous section it was determined that pressure variation inside the artery affects the movement of the arterial wall. When the pressure increases, the movement of the arterial wall decreases. By measuring the blood pressure and radial velocity of the arterial wall it is possible to evaluate the elastic modulus and estimate the elasticity of the arterial wall, as equation (27) predicts. However, the pressure variation is small, about 20 mmHg, if only the effect of the baroreflex is considered. To achieve a larger pressure range, the blood pressure must be manipulated in some way. The easiest way of accomplishing this is to move the limb. A three-step tilt-test was used during the measurement. In the first step, the volunteer pointed his hand downwards at an angle of 45 degrees from the horizontal plane. Then he lifted his hand to the horizontal plane for a new measurement and, finally, to complete the sequence, he raised the hand upwards to an angle of 45 degrees. As each step took 10 seconds, the duration of the entire sequence was 30 seconds. Fig. 24 presents a measurement sequence from a volunteer, and the different steps are shown in Fig. 24 (a).

In the first step, with the hand held down, both MAP and PWV are at a high level and the corresponding Doppler frequency at a low level. On raising the hand in step two, the MAP value starts to decrease and the flexibility of the vessel wall increases. The wall then absorbs an increased amount of the pulse's energy and the PWV decreases. In the last step, MAP reaches 65 mmHg, PWV decreases to 3.5 m/s and the Doppler frequency increases to 2.5 kHz.

The measurements were done on 16 healthy volunteers who didn’t have any diagnosed diseases. During the measurement sequence the ECG, blood pressure and Doppler signals were recorded for further data analysis. More information about the measurements can be found in original papers V and VI. The preliminary results are presented in paper VI and the corrected results based on more extensive measurements in paper V.

57

Fig. 24. MAP (a), PWV (b) and Doppler frequency (c) during the three-step tilt-test. Fig. 25 presents the PWV for all volunteers as a function of MAP. A trend line is fitted to the measured data, indicating that PWV increases when the MAP value increases. For the measurement range between 60-120 mmHg, the average PWV varies between 3.9-4.8 m/s. The relative change in PWV within the MAP range of 60-120 mmHg is 19%. In this range, the standard deviation is approximately 0.5 m/s.

(a)

5060708090

100110

0 5 10 15 20 25 30Time [s]

MA

P [m

mH

g]

(b)

2.002.50

3.003.50

4.004.50

0 5 10 15 20 25 30Time [s]

PWV

[m/s]

(c)

0.00

1.00

2.00

3.00

0 5 10 15 20 25 30Time [s]

Freq

. [kH

z]

1. 2.

3.

58

Fig. 25. Calculated elastic modulus as function of mean arterial pressure.

Fig. 26 presents the elastic modulus for all volunteers as a function of MAP. A trend line fitted to the data indicates that E increases when the MAP value increases. As the figure shows, E exhibits a large deviation. The relative change for E in the pressure range 60-120 mmHg is approximately 80 %.

Fig. 26. Pulse wave velocity as function of mean arterial pressure.

Because the deviation of E is large, the individual values of E were calculated in certain pressure ranges. Table 6 presents the calculated values for MAP, PWV and E for the pressures 40, 60, 80, 100, 120 and 140 mmHg, ± 5 mmHg. The standard deviations (std) for PWV and E are also presented. The last column presents the elastic modulus of a canine artery (Bergel 1961). The figures demonstrate that the mean values of E in this measurement are in same range as in the work of Bergel. For example, at 100 mmHg, we have E=636.8 ± 314 kPa, while Bergel reports E=690 ± 100 kPa at identical pressure.

0.0

1.0

2.0

3.0

4.0

5.0

6.0

0 20 40 60 80 100 120 140 160

MAP [mmHg]

PWV

[m/s

]

0

500

1000

1500

2000

2500

0 20 40 60 80 100 120 140 160

MAP [mmHg]

E [k

Pa]

59

The corresponding values at 40 mmHg are 111.1 ± 96 kPa and 120 ± 20 kPa (Bergel 1961), respectively.

Table 6. Mean values for MAP, PWV and E for the pressures 40, 60, 80, 100, 120 and 140 mmHg within ±5 mmHg range.

MAP ±5 [mmHg]

PWV [m/s]

std(PWV) [m/s]

E [kPa]

std(E) [kPa]

EBergel [kPa]

40.0 3.4 0.1 111.1 94.5 ≈100 60.0 3.9 0.4 198.7 172.5 ≈250 80.0 4.1 0.4 419.1 382.5 ≈350 100.0 4.5 0.5 636.8 315.7 ≈650 120.0 4.8 0.6 1056.7 486.3 ≈800 140.0 5.2 0.1 1010.1 164.0 ≈1000

6 DISCUSSION

The laser Doppler technique was chosen for use in this study because it makes it possible to measure skin vibrations accurately. If the vibrations are due to cardiovascular pulsation in the artery close to the skin surface, it is possible to measure the velocity profile of the movement of the arterial wall. Moreover, when the velocity profile is known, the displacement of the arterial wall can be calculated. Application of the laser Doppler technique for biomedicine, especially for blood flow measurements, has been widely studied. On the other hand, studies concerning cardiovascular pulse measurements are not widely reported, and thus in this sense some new information could be found.

The most important part in the laser Doppler device is the interferometer, which can be constructed in several ways, as was presented at the beginning of chapter 2. However, these configurations are quite large in size, use a lot of optics and are expensive. Self-mixing interferometry offers a simple, small-size and cheap way to implement the interferometer for measurement purposes. This is the reason why self-mixing interferometry was chosen for use in the Doppler device.

At the beginning of this work the aim was to measure the blood flow variation in the radial artery using the Doppler technique and use the variation of blood flow for pulse detection. Soon it was noted that the penetration depth at skin is too short to distinguish the Doppler shifted photons from moving blood cells. The penetration depth for Caucasian skin at 800 nm is approximately 1.2 mm (Anderson et al. 1981). In addition, the Doppler signal based on arterial wall movement had such a strong effect on the measurement signal that the signal is more likely to reflect variations in blood pressure than in blood flow. Moreover, when the preliminary measurements were done, it was noticed that the envelope of the Doppler spectrogram contains similar variations as the blood pressure signal, as is shown in chapter 5, in Fig. 22 and in the original paper IV. Also in the preliminary tilt tests, the calculated value of the elastic modulus was in the same range as for canines, as is shown in the original paper VI. These findings led to more detailed studies of these phenomena.

61

6.1 Measurements

The first studies focused on cardiovascular pulse detection in the wrist above the radial artery. The measurements were made from the normal blood pressure pulse, which can be obtained from the radial artery when the hand is positioned level with the heart, and it was noticed that the Doppler signal agrees with the first derivative of the blood pressure signal. However, the question remained whether this was still valid if the shape of the blood pressure pulse changes for some reason? To get an answer to this question, the Valsalva manoeuvre was used to manipulate the blood pressure experimentally and the results were reported in paper III. Some successful measurements were made and for the first time it was demonstrated that the Doppler signal follows the changes in blood pressure. The Valsalva manoeuvre offers an easy way to manipulate blood pressure or ECG without physical exertion. However, in these measurements the exhalation phase against the pressure causes strong body vibration and these interferes the Doppler signal.

To get an answer to the question how well the Doppler spectrogram and the first derivative of the blood pressure pulse correspond to each other, a large number of pulses were measured and the correlation between their shapes was analysed in the original paper II. In chapter 1, several studies on the measurement of the arterial pulse using the laser Doppler technique were mentioned, but studies which discuss the correlation between the pressure pulse and the Doppler signal have not been conducted. A high average correlation coefficient was obtained between the pulses in the Doppler spectrogram and the first derivative of the blood pressure pulse. These results show that self-mixing interferometry can be used to measure the shape of the cardiovascular pulsation above the radial artery.

In this thesis, baroreflex regulation was studied from the movement of the arterial wall. This study was done because it was noticed that the pressure variations affect the elastic properties of the arterial wall. Therefore, if the baroreflex is visible in the blood pressure it can also be measured using the Doppler technique. The best correlation was found between variation of diastolic blood pressure and Doppler frequency. For systolic pressure the correlation coefficient was somewhat lower. The correlation coefficient is decreased in both cases by the fact that the effect of the baroreflex is an individual event. For some people it can clearly be seen in the variation of blood pressure but for others it cannot be seen, except by counting the RR intervals. This is why it is typically studied by counting the RR intervals. However, the Doppler technique allows an alternative method for the study of the baroreflex.

The final and probably most interesting measurements were the ones in which the elasticity of the arterial wall was evaluated. The three-step tilt test was used to manipulate the blood pressure during the measurement sequence. The results were diverse. When the elastic modulus was analysed as a function of blood pressure, it was noticed that the standard deviation is very large. On the other hand, the mean values of the elastic modulus were close to the values found in the literature. The literature values used herein are old, but they are still used in many newer books which consider the elastic modulus of arteries. In addition, the reference values for elastic modulus are for the canine artery and differences to human values exist. The formula used for elastic modulus also contains many assumptions, and to achieve more accurate results, a more sophisticated approach

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based on Navier-Stokes equations should be used. In addition, the absorbing effect of soft tissue to elastic wave, which is generated by the movement of the arterial wall, should be taken into account.

6.2 Future research

In the Doppler device, a single-mode laser diode was used. The laser diode is based on double-heterostructure technology and has quite a high threshold current, approximately 80 mA. When a handheld monitoring device is considered this high a current consumes too much power for present-day battery technology. This means that a type of laser diode with a much lower threshold current should be used.

Semiconductor laser types which have very low operating currents are based on quantum well (QW) technology. In this technique, the thickness of the active region is reduced close to the deBroglie wavelength (Svelto 1998). Because of the reduced area of the active region, a lower current is needed for stimulated emission and thus laser operation. The threshold current for QW lasers is typically less than 10 mA.

The problem in cardiovascular pulse measurements are the external artefacts which cause disturbances to the Doppler signal. These artefacts are easily generated due to the high sensitivity of the interferometer. Unfortunately, the errors caused by the artefacts are typically on the same frequency band as the information signal from the displacement of the arterial wall.

One possible technique to reduce the effect of the artefacts on the Doppler signal is to use two self-mixing interferometers to measure the pulsation. The idea is to insert another self-mixing interferometer in the measurement probe. The first interferometer is positioned above the radial artery and it measures both the displacement of the arterial wall and possible errors caused by external artefacts. The second interferometer is positioned in such a way that it measures only the error signal. If both interferometer channels are identical, it could be possible to manipulate the signals so that effect of artefacts could be minimized. The idea of using a two-channel Michelson interferometer to decrease the effect of fibrillation on the Doppler signal has been proposed (Hong 1994).

From experience it is known that the Doppler signal from the pulsation of the radial artery in the wrist can only be found in a very small area. If the Doppler probe is moved for example 0.5 cm away from the radial artery, the Doppler signal will disappear. This has not been studied and in the future it would be interesting to study the propagation of elastic wave in the soft tissue around the artery. Because the wanted Doppler signal can only be found above the radial artery, the use of dual-beam self-mixing interferometry for pulse detection might improve its reliability.

An important consideration in interferometry is the visibility of the fringe pattern (ψ), which is the measure of the strength of interference. The ψ-function can be determined as (Saleh & Teich 1991)

63

(34)

where I1 is the intensity of reference arm, I2 the intensity of measurement arm and |g12| the phase term of reference and measurement wave fronts. The ψ-function depends only on the phase term, when I1=I2. This is why in the interferometer the intensities of the two arms should be equal, which can be achieved using appropriate optical filters. In the case of a self-mixing interferometer, the reference field is inside the laser cavity and thus the intensity cannot be controlled without changing the external field.

,gIIII2

1221

21

+=Ψ

7 SUMMARY

In this thesis, laser Doppler technique based on the self-mixing effect in the diode laser was used for cardiovascular pulse measurements above the radial artery in the wrist. The developed self-mixing interferometer was used to measure the skin displacement, which was induced by a cardiovascular pulse. The technique was first used to detect the pulse in normal pressure conditions. Then the pulse detection was carried out on an abnormal pulse, which was experimentally generated using the Valsalva manoeuvre. In both cases the reconstructed Doppler spectrogram was noticed to follow the first derivative of the corresponding blood pressure pulse.

In the second experiments, the correlation between the shapes of the Doppler spectrograms and the first derivative of the blood pressure pulse was studied. A total of 738 cardiovascular pulses obtained from 10 volunteers were analysed. It was found that as many as 94% of the pulses were detected successfully, when an empirical limit of 0.7 was used for misdetection. The correlation coefficient for all 10 measured volunteers was 0.95 with a standard deviation of 0.05.

In the third experiments, self-mixing interferometry was used to measure the baroreflex part of the autonomic regulation from the displacement of the arterial wall. It was noticed that pressure variation due to the baroreflex affects the elastic properties of the arterial wall. The best correlation, -0.71, was found between the variation of diastolic pressure and Doppler frequency. The correlation between systolic pressure and Doppler frequency was -0.53. For pulse pressure, the correlation was close to zero.

The final experiments focused on evaluating the elastic modulus of the arterial wall. An empirical formula for the radial velocity of the radial artery was derived from Navier-Stokes equations and Bernoulli’s law. Measuring the blood pressure and radial velocity of the arterial wall, and using an estimate for the internal radius, it is possible to evaluate the elastic modulus or compliance factor of the arterial wall. The measurements, in which 16 volunteers were measured, showed that there is very large deviation in elastic modulus against blood pressure. However, it was noticed that the mean values of elastic modulus are in the same class as the values found in the literature. In addition, when the behaviour of elastic modulus and PWV was compared as a function of pressure, similar effects were found. Both the elastic modulus and PWV increase when pressure increases. For elastic modulus this means that the arterial wall is under more strain when pressure increases.

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The increase of PWV is due to the same effect, where less of the energy of the pressure pulse can be stored in the inflexible arterial wall.

Self-mixing interferometry is a challenging method for these kind of measurements. It enables an accurate technique for skin vibration measurements. However, it suffers from the errors caused by external artefacts during the measurements, and for this reason it cannot be used for continuous monitoring of heart functions. Successful measurements can only be made in laboratory conditions on well-motivated test persons.

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