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 TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAA A A A A AA A

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 ImageEstimation Functionally Informed GLM Y = X β + E Prior (β) 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) time series data agreementprior termprior weight Maximum Likelihood Estimate (ML) –No prior information –General Linear Model (GLM) 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 y – fMRI time series signal β – Regression coefficient vector X – Design matrix ε – Decomposition residuals λ – Noise precision

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 Wilcoxon’s Test Nonparametric alternative No normality assumption Better sensitivity/robustness tradeoff

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) Scanner Siemens Trio 3T Subjects –11 Healthy Adults –10 Normal Kids –18 Autism Subjects –N1 = 21 Control –N2 = 18 Autism Resolution 3.5mm 3 Repeats 5 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 - Controls Wilcoxon’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 - Autism Wilcoxon’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) GLM52.95 ± ± 0.18 Smoothed-GLM41.94 ± ± 0.20 Group-PCA28.30 ± ± 0.16 Group-ICA27.06 ± ± 0.13 Mixed-ICA24.49 ± ± 0.15 Mixed-PCA35.30 ± ± 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!