Statistical Modeling of Brain Imaging Data: An Overview, Challenges, and Future Directions

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)


RF pulse (excitation)

MeasurementM

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State NormalState

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TT22* Effect in * Effect in fMRIfMRI

RF pulse (excitation)

MeasurementM

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TT22* Effect in * Effect in fMRIfMRI

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

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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)


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


Data Characteristics


11 T

1

V

V x T(#voxels) x (#meas. times)

Data Applications


• 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


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


Challenges

• Massive amounts of data– ≈ 319.5 million data points per subject!– ≈ 8.9 billion data points for all subjects!!

• Complex correlation structures


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


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


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]


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.

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Methods: Activation

Stage II General Linear Model • Voxel-by-voxel analyses

• Model assumes independence between brain activity measures at different brain locations


Methods: Activation

Spatial Models•Regional parcellation•Correlations

– Within regions– Between regions

•Inferences– Voxel level– Regional

20

ρ2 ρ1

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Methods: Activation

Stage II: Spatial Bayesian Hierarchical Model (SBHM)

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Bowman et al., 2008, NeuroImage


Methods: Activation

Stage II Spatial BHM• Voxel and region-level posterior

probability maps


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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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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...1

Voxels

1 ………….. V

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Methods: Brain NetworksICA


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


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


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.


Develop the prediction algorithm

Training subjects

Characteristics (treatment group; …)

… …

Pre-treatment

Post-treatment

…

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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

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…

Predicted Post-treatment Maps

input output

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Characteristics

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Methods: Predicting neural activity Neural activity

34

Source: Guo et al. 2008, Human Brain Mapping.


• Goal: predict the post-treatment rCBF or mean BOLD response.

• Use conditional dist. of post-trt. given pre-trt. where

with

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Methods: Predicting neural activity


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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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


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


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/


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

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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.

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References


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.

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References


Statistical Modeling of Brain Imaging Data: An Overview, Challenges, and Future Directions

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