george chen, evelina fedorenko , nancy kanwisher , polina golland
DESCRIPTION
Deformation-Invariant Sparse Coding for Modeling Spatial Variability of Functional Patterns in the Brain. George Chen, Evelina Fedorenko , Nancy Kanwisher , Polina Golland. Talk Outline. Finding correspondences between functional regions in the brain A new generative model - PowerPoint PPT PresentationTRANSCRIPT
Deformation-Invariant Sparse Coding for Modeling Spatial Variability of Functional Patterns in the Brain
George Chen, Evelina Fedorenko, Nancy Kanwisher, Polina Golland
12/16/2011 NIPS MLINI Workshop 2011 1
Talk Outline
1. Finding correspondences between functional regions in the brain
2. A new generative model
3. Results for language fMRI study
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Functional Region Correspondences
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• Given stimulus, get functional activation regions
Subject 1
Subject 2
Align to common anatomical space
Functional variability!
Goal: Find correspondences between “parcels”
contiguous region in brain
group-level parcels
Parcel: contiguous region in brainBiology:brain compartmentalized into functional modules parcels represent these modules
Functional Variability• Standard approach: just average in common
anatomical space
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Functional variability less pronounced activation in group average
spaceSubject 1
Subject 2space
Averagespace
Alignedspace
Previous Work• Thirion et al. 2007: treat parcels as discrete
objects and find parcel correspondences across subjects by matching
• Xu et al. 2009: generative, hierarchical model representing activation regions as Gaussian mixtures
• Sabuncu et al. 2010: groupwise functional registration
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Previous Work• Thirion et al. 2007: treat parcels as discrete
objects and find parcel correspondences across subjects by matching
• Xu et al. 2009: generative, hierarchical model representing activation regions as Gaussian mixtures
• Sabuncu et al. 2010: groupwise functional registration
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Our Generative Model
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To generate image for a subject:1. Choose weights for each
group-level parcel2. Form weighted sum of
group-level parcels
3. Deform pre-image and add noise
Pre-image
e.g. (0.2, 1)
𝐷1
𝐷2
𝑦 𝑛
𝑤𝑛
Deformation:
𝑛=1 ,…,𝑁
Group-level parcels
1:
2:
0.2× +1× ¿
…𝐷𝐾
𝑦 𝑛=(∑𝑘=1
𝐾
𝑤𝑛𝑘𝐷𝑘)∘Φ𝑛−1+noise
sparse, no deformations sparse coding
i.i.d. entriesi.i.d. prior
Goal: Estimate group-level parcels and deformations
Estimating Group-level Parcels and Deformations
• Priors on group-level parcels and deformations–
from image registration– Want to be parcel, have sparse support, and smooth
• Want MAP estimate:
• Use generalized EM algorithm for MAP estimation12/16/2011 NIPS MLINI Workshop 2011 8
𝑝 (𝐷𝑘 )∝ exp (−𝜉‖𝐷𝑘‖1−𝜂 𝐷𝑘𝑇𝐋 𝐷𝑘 ) 𝕝 {𝐷𝑘is unimodal∧‖𝐷𝑘‖2≤1}
argmax𝐷 , Φ
𝑝 (𝐷 ,Φ|𝑦 )=argmax𝐷 ,Φ
𝑝 ( 𝑦 ,𝐷 ,Φ )
Don’t get to observe ’s!
sparsity smoothness parcel identifiability
¿ argmax𝐷 , Φ
𝑝 (𝐷 )𝑝 (Φ)∑𝑤𝑝 (𝑦 ,𝑤|𝐷 ,Φ )
Language fMRI Study• Data
– Substantial functional variability!– 33 subjects– Contrast: reading sentences vs. pronounceable
nonwords– are t-statistic images from standard fMRI preprocessing– All images initially brought into common anatomical
space• What we’ll show
– Estimated group-level parcels correspond to language processing regions
– Estimated deformations improve fMRI group analysis
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• Left frontal lobe• Left temporal lobe
Estimated Group-level Parcels• Correspond to known language processing
regions
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Spatial support of group-level parcels
• Right temporal lobe • Right cerebellum
Example group-level parcels
• Apply estimated deformation to fMRI data for each subject and redo standard fMRI group analysis on separate data
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Modeling functional variability increases statistical significance in each group-level parcel
Group-level Parcel Index
Negative log p-value
Improving fMRI Group Analysis with Estimated Deformations
Improving fMRI Group Analysis with Estimated Deformations
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spaceSubject 1
Subject 2
Average
Alignedspace
space
space
Why is the variance so high for statistical significance values for our model?
Improving fMRI Group Analysis with Estimated Deformations
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Averagespace
Why is the variance so high for statistical significance values for our model?
Group-level parcel support
Variation using anatomical
alignment only
Variation using our model
• Apply estimated deformation to fMRI data for each subject and redo standard fMRI group analysis
12/16/2011 NIPS MLINI Workshop 2011 14
Modeling functional variability increases statistical significance in each group-level parcel
Group-level Parcel Index
Negative log p-value
Improving fMRI Group Analysis with Estimated Deformations
Contributions• Generative model for finding group-level parcels
– Represent discrete set of parcels as images– Model implicitly represents correspondences
Just look at where -th group-level parcel shows up in each subject!
– Get deformations out of model, not just parcel correspondences! Improves fMRI group analysis
• Future directions– Use estimated parcels in other fMRI studies as markers
for language processing (and other stimuli!)
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