Multi-Group Functional MRI Analysis

Using Statistical Activation Priors

Deepti Bathula, Larry Staib, Hemant Tagare, Xenios Papademetris, Bob Schultz, Jim Duncan

Image Processing & Analysis Group

Yale University

MICCAI 2009 fMRI Workshop

Introduction

• Functional MRI Experiments– Relationships between brain structure and function

across subjects

– Infer differences between populations

– Success relies on accurate assessment of individual brain activity

• Functional MRI Analysis– fMRI data has poor signal-to-noise ratio

– Leads to false detection of task-related activity

– Requires signal processing techniques

Literature Review• Salli, et al.,“Contextual clustering for analysis of fMRI

data” (IEEE TMI, 2001)

• Solo, et al.,“A signal estimation approach to Functional MRI” (IEEE TMI, 2001)

• Descombes, et al., “Spatio-temporal fMRI analysis using Markov Random Fields” (IEEE TMI, 1998)

• Goutte, et al., “On Clustering Time Series”, (NeuroImage, 1999)

• Ou & Golland, “From spatial regularization to anatomical priors in fMRI analysis” (IPMI, 2005)

• Kiebel, et al., “Anatomically informed basis functions” (NeuroImage, 2000)

• Flandin & Penny, “Bayesian fMRI data analysis with sparse spatial basis function priors” (NeuroImage, 2007)

Statistical Activation Priors

• Inspired by statistical shape priors in image segmentation

• Learn brain activation patterns (strength, shape and location) from training data

• Define functionally informed priors for improved analysis of new subjects

• Compensate for low SNR by inducing sensitivity to task-related regions of the brain

• Demonstrated to be more robust than spatio-temporal regularization priors (Bathula, MICCAI08)

Multi-Group fMRI Analysis

• Issues related to training-based priors

– Studies with known group classification• Priors from individual groups or mixed pool?

– Studies where existence of sub-groups is unknown• How does a prior from mixed population perform?

• Current work investigates

• Application of statistical activation priors

• Evaluation of statistical learning techniques• Principal & Independent Component Analysis

• Performance compared with GLM based methods

Time-Series (Y)

Design Matrix (X)

Test Image

EstimationEstimationFunctionally InformedFunctionally Informed

GLMGLMY = X Y = X ββ + E + E

Prior (Prior (ββ))

Temporal Model

Spatial

Model • Low Dimensional

Subspace (S)

β-mapsTraining Images

GLM

PCA/ICA

Schematic – Statistical Activation Priors(Align in Tailarach coordinates)

Bayesian Formulation

• Maximum A Posteriori Estimate (MAP)

£̂ map = argmax£

p(£ jY )

= argmax£

p(Y j£ ) p(£ )

= argmax£

[ lnp(Y j£ ) + ®lnp(£ ) ]

time series data agreement prior termprior weight

• Maximum Likelihood Estimate (ML)– No prior information

– General Linear Model (GLM)

£ = fB;¸g ) p(£ jY ) / p(Y j£ ) p(£ )

B̂ml = B̂ glm = argmax¯

p(Y jB)

Ө = { B, Other hyper-parameters}

• Temporal Modeling– Linear combination of explanatory variables and noise

We desire to have (next slides):– Spatial coherency modeled into activation parameters

– Focus on modeling spatial correlations• Can be extended to incorporate temporal correlations

Likelihood Model

p(Y jB ;¸) =VY

v=1

p(yvj¯v;¸v)

=VY

v=1

N (yv;X ¯v;¸ ¡ 1v I T )

y – fMRI time series signalβ – Regression coefficient vectorX – Design matrixε – Decomposition residualsλ – Noise precision

yv = X ¯v + ²v; ²v » N (0;¸ ¡ 1v I T )

Prior Models – p(B)

• Prior probability densities of activation patterns– Estimated from low dimensional feature spaces

• Principal Component Analysis (PCA) (Yang et al., MICCAI 2004)

– Prior density estimation using eigenspace decomposition

– Assumes Gaussian distribution of patterns (unimodal)

– Tends to bias posterior estimate towards mean pattern

• Independent Component Analysis (ICA) (Bathula et al., MICCAI 2008)

– Source patterns are maximally, statistically independent

– Does not impose any normality assumptions

– Accounts for inter-subject variability in functional anatomy

PCA finds directions of maximum variance

ICA finds directions which maximize independence

Group Test Statistics

Student’s t-Test• Standard parametric test

• Assumes normal distribution

• Not robust to outliers

• Lack of sensitivity

t =

pn(n ¡ 1) ¹̄

q P ni=1 (¯ i ¡ ¹̄)2

Wilcoxon’s Test• Nonparametric alternative

• No normality assumption

• Better sensitivity/robustness tradeoff

tw =nX

i=1

rank(j¯ i j) £ sign(¯ i )

Young Male Adult(Typical)

Young Male Adult(Autism)

Attention Modulation Experiment (Faces Vs Houses)

Source: Robert T. Schultz, Int. J. Developmental Neuroscience 23 (2005) 125–141

• Red/Yellow – Fusiform Face Area (FFA) (circled)

• Blue/Purple – Parahippocampal Place Area (PPA)

Experiment (all done in Talairach Space)

• ScannerSiemens Trio 3T

• Subjects– 11 Healthy Adults– 10 Normal Kids– 18 Autism Subjects

– N1 = 21 Control– N2 = 18 Autism

• Resolution3.5mm3

• Repeats5 Runs with 140 time samples per run

Ground Truth(GLM-5 Run)

Group ICA(2-Run)

(K = 8, α = 0.8)

GLM (2 Run)

Smoothed-GLM(2-Run)

(FWHM = 6mm)

Group PCA(2-Run)

(K = 8, α = 0.8)

Mixed ICA(2-Run)

(K = 13, α = 0.7)

Structural Scan(FFA, PPA, STS, IPS, SLG)

Mixed PCA(2-Run)

(K = 13, α = 0.7)

(p < 0.01, uncorrected)

Group Activation Maps – Controls(Group prior =normals only; mixed= both normals and Autism)

Student’s t-Test (leave-one-out analysis)

GLM (2 Run)

Ground Truth(GLM-5 Run)

Smoothed-GLM(2-Run)

(FWHM = 6mm)

Group ICA(2-Run)

(K = 8, α = 0.8)

Mixed ICA(2-Run)

(K = 13, α = 0.7)

Group PCA(2-Run)

(K = 8, α = 0.8)

Mixed PCA(2-Run)

(K = 13, α = 0.7)

Structural Scan(FFA, PPA, STS, IPS, SLG)

Group Activation Maps - ControlsWilcoxon’s Signed Rank Test

(p < 0.01, uncorrected)

Ground Truth(GLM-5 Run)

GLM (2 Run)

Group ICA(2-Run)

(K = 8, α = 0.8)

Group PCA(2-Run)

(K = 8, α = 0.8)

Smoothed-GLM(2-Run)

(FWHM = 6mm)

Mixed ICA(2-Run)

(K = 13, α = 0.7)

Structural Scan(FFA, PPA, STS, IPS, SLG)

Mixed PCA(2-Run)

(K = 13, α = 0.7)

Group Activation Maps - Autism(Group prior=Autism only; mixed= both normals and Autism)

Student’s t-Test (p < 0.01, uncorrected)

Group Activation Maps - AutismWilcoxon’s Signed Rank Test

Ground Truth(GLM-5 Run)

GLM (2 Run) Smoothed-GLM(2-Run)

(FWHM = 6mm)

Group ICA(2-Run)

(K = 8, α = 0.8)

Mixed ICA(2-Run)

(K = 13, α = 0.7)

Group PCA(2-Run)

(K = 8, α = 0.8)

Mixed PCA(2-Run)

(K = 13, α = 0.7)

Structural Scan(FFA, PPA, STS, IPS, SLG)

(p < 0.01, uncorrected)

Multi-Group Experiment(compare 5-run beta maps to 2-run estimates across all 21 normal + 18

Autism subjects)

Quantitative Analysis

Sum-of-Squares Error

(SSE)Correlation Coefficient

(ρ)

GLM 52.95 ± 14.91 0.68 ± 0.18

Smoothed-GLM 41.94 ± 13.00 0.65 ± 0.20

Group-PCA 28.30 ± 17.63 0.77 ± 0.16

Group-ICA 27.06 ± 15.36 0.79 ± 0.13

Mixed-ICA 24.49 ± 15.97 0.76 ± 0.15

Mixed-PCA 35.30 ± 18.41 0.72 ± 0.13

Conclusions• Training based prior models

– Significant improvement in estimation

– Compensate for low SNR by inducing sensitivity to task-related regions of the brain

– Potential for reducing acquisition time in test subjects

• Multi-Group fMRI Analysis– Group-wise priors more effective than mixed priors

– PCA regresses to mean activation pattern

– ICA accounts for inter-subject variability

– ICA more suitable for studies with unknown sub-groups

Future Work

• Integrating temporal correlations into the Bayesian framework

• More effective method for exploiting anatomical information

• Nonlinear methods for more plausible modeling of fMRI data

• Functional connectivity analysis using statistical prior information

Thank You!