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Statistical Modeling of Brain Imaging Data: An Overview, Challenges, and Future Directions. SAMSI Analysis of Object Data (AOOD) September 14, 2010 DuBois Bowman, Ph.D . Department of Biostatistics and Bioinformatics Center for Biomedical Imaging Statistics Emory University. - PowerPoint PPT Presentation
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Statistical Modeling of Brain Imaging Data:
An Overview, Challenges, and Future Directions
SAMSI Analysis of Object Data (AOOD)September 14, 2010
DuBois Bowman, Ph.D.
Department of Biostatistics and BioinformaticsCenter for Biomedical Imaging Statistics
Emory University
The Human Brain
• Controls all body activities– Heart rate, breathing, sexual
function– Motor activities and senses– Learning, memory, language– Emotion, mood, behavior
• Daunting task for an organ that is– 3 pounds of fatty tissue– The size of 4 sheets of paper
(cortex)
Research Triangle Park, NCSAMSI - AOOD 2010 2
Colin, Montreal Neurological Institute.
The Human Brain
• What enables this amazing functionality?– Signaling via a network of an
estimated 100 billion neurons– Highly sophisticated organization– Each neuron has (on average)
7,000 synaptic connections, giving up to 700 trillion connections.[1 quadrillion at age 3]
3SAMSI - AOOD 2010 Research Triangle Park, NC
Acquisition• Popular functional
neuroimaging methods measure correlates of blood flow and metabolism as a proxy for brain activity– Functional magnetic resonance
imaging (fMRI)– Positron emission tomography
(PET)
Research Triangle Park, NCSAMSI - AOOD 2010 4
RF pulse (excitation)
MeasurementM
R si
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State NormalState
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TT22* Effect in * Effect in fMRIfMRI
RF pulse (excitation)
MeasurementM
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The Human Brain
• Brain imaging research:– Link behavior to brain function– Link alterations in “normal”
brain function to addiction, psychiatric disorders, and neurologic disorders.
– How treatments work• Mechanisms of action• Optimizing treatment
selectionsResearch Triangle Park, NCSAMSI - AOOD 2010 5
Data: Scanning
• Serial 3-D scans for each subject
– Scans acquired under different experimental stimuli (tasks)
– Hundreds of thousands of voxels– fMRI: S usually in the hundreds (PET: T<20)
Research Triangle Park, NCSAMSI - AOOD 2010 6
T
• Block Designs: stimuli of the same condition grouped together in blocks.– Increased SNR, power, and robustness
• Event-related Designs: arbitrary (random) presentation of stimuli– Avoids confounds due to habituation,
anticipation, or strategy.
Data:Study Designs
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Data Characteristics
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11 T
1
V
V x T(#voxels) x (#meas. times)
Data Applications
Research Triangle Park, NCSAMSI - AOOD 2010 9
• Motor tasks• Face processing (memory)• Language processing• Pain processing• Psychiatric disorders
(Depression, Schizophrenia, OCD, Social anxiety, etc.)
• Psychopathy
Data Example
fMRI from Working Memory Task:
• n=28 subjects– 15 schizophrenia patients– 13 healthy controls
• 177 scans per session acquired during a working memory task (TR=2 sec)
• Two sessions: – 24 hours - 3 weeks later
101010SAMSI - AOOD 2010 Research Triangle Park, NC
Challenges
• Massive amounts of data• Complex correlation structures
– Temporal (scans/epochs/sessions)– Spatial
• Multiplicity issues for inference• Number of voxel-pairs prohibits full
voxel-level covariance modeling and network analyses
1111SAMSI - AOOD 2010 Research Triangle Park, NC
Challenges
• Massive amounts of data– ≈ 319.5 million data points per subject!– ≈ 8.9 billion data points for all subjects!!
• Complex correlation structures
1212SAMSI - AOOD 2010 Research Triangle Park, NC
Bowman (2007), JASA
Challenges
• Multiplicity issues for inference– 902,629 voxels– Statistical dependence between voxels
• Number of voxel-pairs prohibits full voxel-level covariance modeling and network analyses– ≈ 45,263,000,000 voxel pairs
1313SAMSI - AOOD 2010 Research Triangle Park, NC
Pre-Processing
Steps:
• Slice timing correction
• Motion correction
• Coregistration of functional and anatomical data
• Spatial normalization
• Spatial smoothing
• Temporal filtering
• Convolving the stimulus function and the HRF
1414
T2* EPI image (low resolution)
T1 structural MR image (high resolution)
SAMSI - AOOD 2010 Research Triangle Park, NC
Analysis Methods• Activation Analysis:
– Changes between tasks, sessions, subgroups, etc.– Scale of localization
Voxel-level analyses Region-level analyses
• Network Analysis: – Partitioning methods– Functional connectivity (correlations)
• Prediction:– Prediction for neural activity
Research Triangle Park, NCSAMSI - AOOD 2010 15
Statistical MethodsActivation Analysis:
Identifying localized alterations in brain activity
Methods: Activation
• Two-Stage Linear Model: Stage I
• Pre-coloring/temporal smoothing [Worsley and Friston, 1995]• Pre-whitening [Bullmore et al, 1996; Purdon and Weisskoff, 1998]• Alternative structures available for PET [Bowman and Kilts, 2003]
Research Triangle Park, NCSAMSI - AOOD 2010 17
filtering pass-high e.g. ,covariatesother containsmean izedindividual ssubject' about error random1
effects izedindividual containingvector parameter 1) all (common to st variableindependen containingmatrix design
)cluster (within BOLD) (e.g.location at activity brain serial1
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Methods: Activation
Stage II General Linear Model
• Voxel-level test statistic maps• Threshold
– Mutiple testing adjustment: FDR, RFT, Bonferonni, etc.
18
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18SAMSI - AOOD 2010 Research Triangle Park, NC
Methods: Activation
Stage II General Linear Model • Voxel-by-voxel analyses
• Model assumes independence between brain activity measures at different brain locations
1919SAMSI - AOOD 2010 Research Triangle Park, NC
Methods: Activation
Spatial Models•Regional parcellation•Correlations
– Within regions– Between regions
•Inferences– Voxel level– Regional
20
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ρ13 ρ23
ρ12
20SAMSI - AOOD 2010 Research Triangle Park, NC
Methods: Activation
Stage II: Spatial Bayesian Hierarchical Model (SBHM)
21
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21SAMSI - AOOD 2010 Research Triangle Park, NC
Bowman et al., 2008, NeuroImage
Research Triangle Park, NCSAMSI - AOOD 2010 22
Methods: Activation
Stage II Spatial BHM• Voxel and region-level posterior
probability maps
Research Triangle Park, NCSAMSI - AOOD 2010 23
Methods: Activation
Stage II Spatial BHM• (Spatial) Correlations between distinct brain locations
(functional connectivity)
Methods: Activation
Alternative Approaches• Non-parametric methods
– Permutation tests [Nichols and Holmes, 2002]
– Wavelet-based resampling methods [Bullmore et al., 2004, among others]
• Extended simultaneous autoregressive models [Derado et al., 2010]
24
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24SAMSI - AOOD 2010 Research Triangle Park, NC
Statistical MethodsNetwork Analysis:
Identifying Associations in Brain Function
Methods: Brain NetworksICA
Goal: Decompose observed fMRI data as a linear combination of spatio-temporal processes of underlying source signals.
Component 1
×≈ ×+
• • •
1
T
+ • • •
Component 2
Figure: MELODIC at http://www.fmrib.ox.ac.uk/analysis/research/melodic/
Temporal responses
Spatial map
Observed fMRI data
SAMSI - AOOD 2010 26Research Triangle Park, NC
… Y
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27
Methods: Brain NetworksICA
27SAMSI - AOOD 2010 Research Triangle Park, NC
observed fMRI measurements
Mixing matrix; each colum is a latent time series associated with a specific source signal
Rows are statistically independent spatial source signals
Noise not explained by IC’s
Spatial activation maps and time series of 3 selected ICs
pall =0.054
pon =0.298
poff <0.001
pall =0.005pon =0.044poff <0.001
pall<.001pon<.001 poff<.001
28
Methods: Brain NetworksGroup ICA
28SAMSI - AOOD 2010 Research Triangle Park, NC
Clustering: New application of an old statistical method
• Objective: Partition the brain into groups of voxels exhibiting similar function (temporal/spectral) within.
• Based on distances between temporal profiles, e.g.
[Bowman et al., 2004; Bowman and Patel, 2004]29
Methods: Brain Networks
29
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SAMSI - AOOD 2010 Research Triangle Park, NC
Methods: FC
Clustering Illustration
3030SAMSI - AOOD 2010 Research Triangle Park, NC
Research Triangle Park, NCSAMSI - AOOD 2010
Whole-brain networks
3131
Methods: Brain Networks
Courtesy of Indiana University
Statistical MethodsPrediction
Methods: Prediction
Objective:
• Predict neural activity based on functional brain images and other relevant subject information.
Research Triangle Park, NCSAMSI - AOOD 2010 33
Develop the prediction algorithm
Training subjects
Characteristics (treatment group; …)
… …
Pre-treatment
Post-treatment
…
1
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);;(ˆtrt-pre_trt-post_ θXYY iii f
Prediction AlgorithmModel Building
Apply the prediction algorithm
Prediction Algorithm);;(ˆ
trt-pre_trt-post_ θXYY iii fNew
subjects …
Pre-treatment
1
m
1
m
…
Predicted Post-treatment Maps
input output
…
Characteristics
1
m
Methods: Predicting neural activity Neural activity
34
Source: Guo et al. 2008, Human Brain Mapping.
34SAMSI - AOOD 2010 Research Triangle Park, NC
• Goal: predict the post-treatment rCBF or mean BOLD response.
• Use conditional dist. of post-trt. given pre-trt. where
with
))(),((~)](),(),(),(|)([ )2()1(12 vvNvvvvv ii 2.12.1 ΣμλλβYY
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Methods: Predicting neural activity
3535SAMSI - AOOD 2010 Research Triangle Park, NC
Results: Cocaine dependence data
Methods: Predicting neural activity
+12 +20 +32 +48
(a) Ratio of prediction mean square error (PMSE) to average brain activity
(b) Coverage probabilities of prediction intervals +12 +20 +32 +48
36
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36SAMSI - AOOD 2010 Research Triangle Park, NC
Future Directions• Multimodality imaging:
integrate various types of imaging data with different– Temporal/frequency properties– Spatial properties– Inherent meanings
(structure/function)– Examples
• fMRI/EEG• fMRI/DTI• PET/MR
Research Triangle Park, NCSAMSI - AOOD 2010 37
Future Directions• Curve modeling (FDA)
– Anesthesia/pain studies• Prediction: use 4-D data object (plus
other patient information) to predict clinical response to treatment.
• Unified spatio-temporal modeling• Causal relationships in neural activity• Drug intervention studies
Research Triangle Park, NCSAMSI - AOOD 2010 38
Software
Software Resources• Statistical Parametric Mapping (SPM)
– http://www.fil.ion.ucl.ac.uk/spm/
• FMRIB Software Library (FSL)– http://www.fmrib.ox.ac.uk/fsl/
• Analysis of Functional NeuroImages (AFNI)– http://afni.nimh.nih.gov/afni
• BrainVoyager– http://www.brainvoyager.com/
• Group ICA of fMRI Toolbox (GIFT)– http://icatb.sourceforge.net
• Free-surfer– http://surfer.nmr.mgh.harvard.edu/
• MRIcro/MRIcron– http://www.sph.sc.edu/comd/rorden/mricro.html
• Center for Biomedical Imaging Statistics (CBIS)– http://www.sph.emory.edu/bios/CBIS/
404040SAMSI - AOOD 2010 Research Triangle Park, NC
Research Triangle Park, NCSAMSI - AOOD 2010
Website: http://www.sph.emory.edu/bios/CBIS1. Amaro, E., Barker, G.J. (2006). Study design in MRI: Basic principles. Brain and
Cognition 60:220-232.2. Beckmann, C.F., Smith, S.M., (2005). Tensorial extensions of independent
component analysis for multisubject FMRI analysis. Neuroimage 25:294-311.3. Bowman, F. D., Caffo, B. A, Bassett, S., and Kilts, C. (2008). Bayesian
Hierarchical Framework for Spatial Modeling of fMRI Data. NeuroImage 39:146-156.
4. Bowman, F. D. (2007). Spatio-Temporal Models for Region of Interest Analyses of Functional Neuroimaging Data, Journal of the American Statistical Association 102(478): 442-453.
5. Bowman, F. D. and Patel, R. (2004) Identifying spatial relationships in neural processing using a multiple classification approach. NeuroImage 23: 260-268.
6. Bullmore, Fadili, Breakspear, Salvador, Suckling and Brammer (2003). Wavelets and statistical analysis of functional magnetic resonance images of the human brain. Statistical Methods in Medical Research 12(5):375-399.
7. Calhoun, V.D., Adali, T., Pearlson, G.D., Pekar, J.J. (2001). A method for making group inferences from functional MRI data using independent component analysis. Human Brain Mapping 14:140-151.
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References
41
9. Chen, S., Derado, G., Guo, Y., Bowman, F.D. (2009). Classification methods for identifying the neural characterics of antidepressant treatment. Abstract. 15th Annual Meeting of the Organization for Human Brain Mapping, San Francisco, CA.
10.Dale, A.M. (1999). Optimal experimental design for event-related fMRI. Human Brain Mapping 8:109-114.
11.Friston, K.J., Harrison, L. and Penny, W. (2003). Dynamic causal modelling. Neuroimage 19(4):1273-302.
12.Friston, K J; Frith, C D; Liddle, P F; Frackowiak, R S J. (1993). J Cereb Blood Flow Metab 13:5-14.
13.Grafton, S.T., Sutton, J. Couldwell, W., et al. (1994). Network analysis of motor system connectivity in Parkinson’s disease: modulation of thalamocortical interactions after pallidotomy. Human Brain Mapping 2:45-55.
14.Granger, C.W.J. (1969). Investigating causal relations by econometric methods and cross-spectral Methods. Econometrica 34:424-438.
15.Guo, Y., Bowman, F.D., Kilts, C. (2008). Predicting the brain response to treatment using a Bayesian Hierarchical model. Human Brain Mapping 29(9): 1092-1109.
16.Guo, Y. and Pagnoni, G. (2008). A unified framework for group independent component analysis for multi-subject fMRI data. NeuroImage 42: 1078-1093.
42
References
4242SAMSI - AOOD 2010 Research Triangle Park, NC
18.Henson, R.N. (2006). Efficient experimental design for fMRI. (2006). In K. Friston, J. Ashburner, S. Kiebel, T. Nichols, and W. Penny (Eds), Statistical Parametric Mapping: The analysis of functional brain images. Elsevier, London, pp. 193-210.
19.Nichols and Holmes (2002). Nonparametric permutation tests for functional neuroimaging: A primer with examples. Human Brain Mapping 15(1): 1-25.
20.Patel, R., Bowman, F.D., Rilling, J.K. (2006). A bayesian approach to determining connectivity of the human brain. Human Brain Mapping 27:267-276.
21.Roebroeck, A., Formisano, E., Goebel, R. (2005). Mapping directed influence over the brain using Granger causality and fMRI.
22.Tzourio-Mazoyer, N., Landeau, B., Papathanassiou, D., Crivello, F., Etard, O., Delcroix, N., Mazoyer, B., M, J., (2002). Automated anatomical labeling of activations in SPM using a macroscopic anatomical parcellation of the MNI MRI single-subject brain. NeuroImage 15: 273-289.
23.Wager, T.D., Nichols, T.E. (2003). Optimization of experimental design in fMRI: a general framework using a genetic algorithm. NeuroImage 18:293-309.
43
References
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