Multi-Group Functional MRI Analysis Using Statistical Activation Priors

1. 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.: AAAAAAAAAAA

2. 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

3. 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)

4. 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)

5. 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

6. β-maps Training Images GLM Design Matrix (X) Subspace (S) Time-Series (Y) GLM Y = X β + E Prior (β) PCA/ICA Temporal Model Test Image • Low Dimensional Spatial Model Estimation Functionally Informed Schematic – Statistical Activation Priors (Align in Tailarach coordinates)

7. time series data agreement prior weight prior term Bayesian Formulation • Maximum Likelihood Estimate (ML) • No prior information • General Linear Model (GLM) • Maximum A Posteriori Estimate (MAP) Ө = { B, Other hyper-parameters}

8. Likelihood Model y – fMRI time series signal β – Regression coefficient vector X – Design matrix ε – Decomposition residuals λ – Noise precision • 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

9. PCA finds directions of maximum variance ICA finds directions which maximize independence 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

10. 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 Group Test Statistics

11. Young Male Adult (Typical) Young Male Adult (Autism) Attention Modulation Experiment (Faces Vs Houses) • 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 • 3.5mm3 • Repeats • 5 Runs with 140 time samples per run • Red/Yellow – Fusiform Face Area (FFA) (circled) • Blue/Purple – Parahippocampal Place Area (PPA) Source: Robert T. Schultz, Int. J. Developmental Neuroscience 23 (2005) 125–141

12. Smoothed-GLM (2-Run) (FWHM = 6mm) Structural Scan (FFA, PPA, STS, IPS, SLG) Ground Truth (GLM-5 Run) GLM (2 Run) Mixed ICA (2-Run) (K = 13, α = 0.7) Group ICA (2-Run) (K = 8, α = 0.8) Mixed PCA (2-Run) (K = 13, α = 0.7) Group PCA (2-Run) (K = 8, α = 0.8) Group Activation Maps – Controls(Group prior =normals only; mixed= both normals and Autism) Student’s t-Test(leave-one-out analysis) (p < 0.01, uncorrected)

13. GLM (2 Run) Group ICA (2-Run) (K = 8, α = 0.8) Group PCA (2-Run) (K = 8, α = 0.8) Structural Scan (FFA, PPA, STS, IPS, SLG) Ground Truth (GLM-5 Run) Smoothed-GLM (2-Run) (FWHM = 6mm) Mixed PCA (2-Run) (K = 13, α = 0.7) Mixed ICA (2-Run) (K = 13, α = 0.7) Group Activation Maps - ControlsWilcoxon’s Signed Rank Test (p < 0.01, uncorrected)

14. GLM (2 Run) Group ICA (2-Run) (K = 8, α = 0.8) Group PCA (2-Run) (K = 8, α = 0.8) Structural Scan (FFA, PPA, STS, IPS, SLG) Ground Truth (GLM-5 Run) Smoothed-GLM (2-Run) (FWHM = 6mm) Mixed PCA (2-Run) (K = 13, α = 0.7) Mixed ICA (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)

15. Group ICA (2-Run) (K = 8, α = 0.8) Group PCA (2-Run) (K = 8, α = 0.8) GLM (2 Run) Structural Scan (FFA, PPA, STS, IPS, SLG) Ground Truth (GLM-5 Run) Smoothed-GLM (2-Run) (FWHM = 6mm) Mixed PCA (2-Run) (K = 13, α = 0.7) Mixed ICA (2-Run) (K = 13, α = 0.7) Group Activation Maps - AutismWilcoxon’s Signed Rank Test (p < 0.01, uncorrected)

16. Multi-Group Experiment(compare 5-run beta maps to 2-run estimates across all 21 normal + 18 Autism subjects)Quantitative Analysis

17. 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

18. 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

19. Thank You!