From Spatial Regularization to Anatomical Priors in fMRI Analysis

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From Spatial Regularization to Anatomical Priors
in fMRI Analysis
Fragmented Map
Regularized Map

• Wanmei Ou William Wells Polina Golland

Core 1 Meeting May 23rd, 2006
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Main Contributions

• Propose new spatial regularization method
  Incorporating Anatomical Information
• Empirically Compare proposed methods with
  traditional methods

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Road Map

• Background and Motivation
• Markov Random Field (MRF) and Anatomical Guided
  MRF Model
• Mean Field Approximation Solver
• Experimental Evaluation
• Conclusions

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Road Map

• Background and Motivation
• Markov Random Field (MRF) and Anatomical Guided
  MRF Model
• Mean Field Approximation Solver
• Experimental Evaluation
• Conclusions

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From fMRI Images to fMRI Analysis
Image Acquisition
fMRI
MRI
Task protocol Auditory, Vision, etc.
Spatial Regularization
Voxel-by-voxel detector
Threshold
Activation Map Scatter activation
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Road Map

• Background and Motivation
• Markov Random Field (MRF) and Anatomical Guided
  MRF Model
• Mean Field Approximation Solver
• Experimental Evaluation
• Conclusions

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Goal and Approaches
Goal Recover True Activation through Spatial
Regularization
Our Approach

• Incorporate MRF into General Linear Model (GLM)
  Statistic
• Include Anatomical Information into MRF

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Detailed Approaches
Our Approach

• 1. Incorporate MRF into GLM Statistic
• Capture spatial dependency
• Overcome over-smoothing effect

• 2. Include Anatomical Information into MRF
• Activation is more likely in gray matter
• Spatial dependency is strong within tissue type

Activation Maps
MRF
MRI
Synthetic Ground Truth
Segmentation Gray, White, Other
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General Linear Model (GLM)
Protocol-Independent Signal
Two Hypotheses
Not-active voxel
Active voxel
Protocol-Dependent Signal
GLM
ML Estimate
F or T statistic
P-value
Traditional Approach
General Log Likelihood Ratio (Cosman, 04)
Our Approach
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Markov Random Field
Spatial Priors
Likelihood
-- Hidden Activation State -- Noisy
Observation/Statistic
MAP Estimate
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Incorporating Anatomical Information
Combine activation state tissue type
MRI
Segmentation
-- Hidden Activation State -- Tissue Type
MAP Estimate
-- Segmentation Label -- Noise Statistic
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Markov Random Fields Solvers

• Binary MRF Min-Cut/Max-Flow (Min-Max) Binary
  MRF Only
• Gibbs Sampling Slow
• Simulated Annealing Slow
• Belief Propagation Fast, Approximation
• Mean Field Fast, Approximation

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Road Map

• Background and Motivation
• Markov Random Field (MRF) and Anatomical Guided
  MRF Model
• Mean Field Approximation Solver
• Experimental Evaluations
• Conclusion and Future work

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Mean Field

• Approximate by
  
• Iterative up-date rule

Belief Prob. Of voxel is active

• Approximated MAP

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Mean Field
Similar up-date rule while incorporating
anatomical information
Approximated MAP
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Alternative Anatomically Guided Filters

• No smoothing with Anatomical Information
• Suppress all activation in the non-gray matter.
• Anatomically Guided Gaussian Filter
• Adjust weights based on segmentation labels.

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Road Map

• Background and Motivation
• Markov Random Field (MRF) and Anatomical Guided
  MRF Model
• Mean Field Approximation Solver
• Experimental Evaluation
• Synthetic Data
• Real fMRI Data
• Conclusions

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Low SNR Fragmented Activation Maps
Experiments Synthetic Data Sets
Noise SNR -6.3dB
Noise SNR -9.3dB
Activation Maps
Threshold False positive 0.05
GLM Detector
Forward Model

Synthetic Ground Truth
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Experiments Synthetic Data Sets
Noise
GLM with different smoothing methods
Forward Model

Synthetic Ground Truth

• No Smoothing
• No Smoothing w/ Anatomical Info
• Gaussian Smoothing w/o Anatomical Info
• Gaussian Smoothing w/ Anatomical Info
• MRF w/o Anatomical Info
• MRF w/ Anatomical Info

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ROC Analysis
Without Anatomical Information Min-Max (Exact
Solver) vs. Mean Field (Approximation)
SNR -6dB
SNR -9dB
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ROC Analysis
Without Anatomical Information MRF (Mean Field)
vs. Gaussian Smoothing
SNR -6dB
SNR -9dB
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ROC Analysis
With Anatomical Information MRF (Mean Field) vs.
Gaussian Smoothing
SNR -6dB
SNR -9dB
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Road Map

• Background and Motivation
• Markov Random Field (MRF) and Anatomical Guided
  MRF Model
• Mean Field Approximation Solver
• Experimental Evaluation
• Synthetic Data
• Real fMRI Data
• Conclusions

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Evaluation on Real Data
Ground Truth
GLM
Majority Voting
GLM
8 task epochs
comparisons
GLM with various spatial regularizers
2 task epochs
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Activation Maps Comparison
Anat No Smoothing
Gaussian MRF
Ground Truth No SmoothingAnat
GaussianAnat MRFAnat
Three Epochs
sm007ep3
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Activation Maps Comparison
Anat No Smoothing
Gaussian MRF
Ground Truth No SmoothingAnat
GaussianAnat MRFAnat
Three Epochs
sm007ep3
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Activation Maps Comparison
Anat No Smoothing
Gaussian MRF
Ground Truth No SmoothingAnat
GaussianAnat MRFAnat
Three Epochs
sm007ep3
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Conclusions

• New Spatial Regularization method
• Anatomical Bias
• Empirical Evaluation
• ROC analysis
• Activation maps
• MRF Anatomical Information
• Increase detection accuracy with reduced-length
  signal