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Structural and Probabilistic Approaches in Group Analysis of fMRI Data

Brain and ICT workshop

Bertrand Thirion1, Alan Tucholka2, Philippe Pinel3, Jean-Baptiste Poline2

1: INRIA Futurs, 2: CEA, Neurospin, 3:INSERM U562, Neurospin

october 21st, 2007

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Neurospin

INRIA@NS

IRM 7T

IRM 11.7T

Neurospin

LNAO LRMN LBIOM LCOGN

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Group Analysis in functional neuroimaging

RFX statistic

thresholding

Activity maps of the subjects: β(s,v) for subject s, voxel v

Under H0, assuming normal signal distribution RFX follows a student law with (S-1) degrees of freedom

Thresholding is performed to control the rate of false detections. significance level α: threshold θ so that P(RFX> θ | H0)<α

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Inter-subject variability

Inter-subject variability is a prominent effect in neuroimaging

Anatomically… …functionally

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Problems with standard inference

- Statistical: Small sample size, non-normal distribution- Localization: Normalization does not provide perfect correspondences

- Model: voxel-based inference is not really adapted

Partial solution: Consider the individual data and model the activation patterns

T100

7

3.3

Example: Localizer experiment :computation -sentence listening

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The where ? question

See Brett et al., Nature Neuroscience, 2002

Which referential for the brain ?

Talairach system

MNI average brain

Cytoarchitectonic maps(Zilles et al.)

Approximated Brodmann(Mazoyer et al.)

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Structural approaches in functional neuroimaging

Our aim: Account for the common activated regions across subjects as well as for inter-subject differences, in spite of small-scale variability

-Which structures should be extracted from the data ?

- scale-space blobs [Poline:94, Coulon:00]

- sparse GMM [Penny:03]

- Activity peaks [Thirion:05]

- Watershed, [Thirion:06, Davatzikos:O7]

- Parcels [Flandin:04,Thirion05]

How to discriminate truly activated regions and false positives ?

- tests on signal/size [Poline:94]

- pseudo-posterior [Coulon:00]- test on the spatial

distribution [Thirion:06/07] How to associate structures across subjects ?- Global MRFs [Coulon:00]- Pairwise comparison and groupwise-clustering [Thirion:06/07]

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input:individual activationmaps

Subject s

Blob extraction Mixture modelling

Other subjects

ROIs + significance ROIs + significance

Spatial Dirichlet Process Mixture Model

ROIs +posterior probabilities

pairwise correspondences between ROIs

Group-level correspondences between ROIs

Selected ROIs

+ Group-level positions

nested ROIs

Pipeline

Output:

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structural modelm

n

l

φs

l m

Simplified structural model

l m

n

Structural model: the blob

activity mapφs(v) in subject s

Merge the small regions (e.g.<5voxels) into their father region

Notations:The regions

will be denoted aj

s

k

k

j

j

j

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Assessment of the intra-subject cluster significance

Gamma-Gaussian Mixture Model:

Provide an estimate of

P(Hi | φj

s ),i=0,1[woolrich:05]

Problem : All the regions do not have the same likelihood of being truely active regions.

Discriminate the significance level of the regions based on the average signalφj

s = mean φ(v) v∈aj

s

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Significance of the regions: Bayesian approach

Probability of being an activated region given the signal

Probability of the position of the region given its class

Posterior Probability of being an activated region given the signal and the position

Next point: Define the likelihood under both hypotheses

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DPMMGroup-level

spatial model of activated

regions p(t|H1)And validated individual ROIs

Individual data

Inference procedure

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Searching for correspondences

Bayesian Network Model

Initilization:

Probabilistic Evidence

Subject s1

Subject s2

k

j

l

f(j)

Inference: Belief propagation

f(j)

j

l

k

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Extracting maximal cliques from the correspondence graph

Replicator dynamics Equations (Pelillo:95, Lohmann:02)

Initialize x(0) randomly or uniformly then update

Input : Belief matrix B = probabilistic correspondence graph

The coordinates of x that do not vanish correspond to a maximal clique

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Effect on the sensitivity of the analysis

The proposed method

10 subjects, what the voxels/regions with significant activity for the computation-understanding contrast ?

Cluster-level Mixed Effects

(p<0.05)

Cluster-level RFX (p<0.05)

RFX (p<0.001) uncorrected

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Effect on the reliability of the analysis

The definition of the confidence

regions for activated areas is

more reliable than other activation

detection methods.Puerly voxel-based methods have low

performance

Method : see Thirion et al., NeuroImage, 2007

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Results: subject-based patterns

Group template

Individual data

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Comparing subjects : unsupervised classification

Larger cohort of 102 subjects:55 regions found

Computation of the average ROI-based signal and inter-subject comparison

A relatively homogeneous population

A few outliers

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Comparing subjects : supervised methods

Correlation of the signal with the ability to perform a

mental rotation task

Correlation of the signal with the sex

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Conclusion

In the Future:- A more integrated and fully Bayesian framework (generative model) ?- Towards anatomo-functional atlases ?

Introduction of a new structural approach for fMRI group inference Enable to discover correspondences across subjects Novel way to perform group inference/ group comparison More sensitivity, higher reliability Bayesian control of the sensitivity/specificity

Implemented in nipy, available soon in Brainvisa software

Many tanks to Alan Tucholka, Cécilia Damon, Merlin Keller, Philippe Pinel, Philippe Ciuciu, Alexis Roche, J.-F. Mangin and J.-B. Poline