Structural and Probabilistic Approaches in Group Analysis of fMRI Data
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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