Deformation-Invariant Sparse Coding for Modeling Spatial Variability of Functional Patterns in the Brain George Chen, Evelina Fedorenko, Nancy Kanwisher,

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 brain

Biology: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

space

Subject 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 estimation

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𝑝 (𝐷𝑘 )∝ exp (−𝜉‖𝐷𝑘‖1−𝜂 𝐷𝑘𝑇𝐋𝐷𝑘 ) 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)∑𝑤

𝑝 (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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space

Subject 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

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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

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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