multi-group functional mri analysis using statistical activation priors deepti bathula, larry staib,...
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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!