1/35 Structural and Probabilistic Approaches in Group Analysis of fMRI Data Brain and ICT workshop Bertrand Thirion 1, Alan Tucholka 2, Philippe Pinel 3, Jean-Baptiste Poline 2 1: INRIA Futurs, 2: CEA, Neurospin, 3:INSERM U562, Neurospin october 21st, 2007

2/35 Neurospin IRM 7T IRM 11.7T Neurospin LNAO LRMNLBIOMLCOGN

3/35 Group Analysis in functional neuroimaging RFX statistic thresholding Activity maps of the subjects: β(s,v) for subject s, voxel v Under H 0, 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 | H 0 )<α

4/35 Inter-subject variability Inter-subject variability is a prominent effect in neuroimaging Anatomically……functionally

5/35 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 T Example: Localizer experiment :computation -sentence listening

6/35 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.)

7/35 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] Brain Functional Landmarks (Thirion: MICCAI’05) represent isolated regions with specific activity. It is however a very conservative approach 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]

8/35 input: individual activation maps Subject s Blob extraction Mixture modelling Other subjects 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:

9/35 0  =2.2 5 structural model m n l φsφs l m Simplified structural model l m n Structural model: the blob activity map φ s (v) in subject s Merge the small regions (e.g.<5voxels) into their father region Notations: The regions will be denoted a j s k k j j j

10/35 Assessment of the intra-subject cluster significance Gamma-Gaussian Mixture Model: Provide an estimate of P(H i | φ j 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 signal φ j s = mean φ(v) v∈ajsv∈ajs

11/35 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

12/35 DPMM Group-level spatial model of activated regions p(t|H 1 ) And validated individual ROIs Individual data Inference procedure

13/35 Searching for correspondences Bayesian Network Model Initilization: Probabilistic Evidence Subject s 1 Subject s 2 k j l f(j) Inference: Belief propagation f(j) j l k

14/35 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

15/35 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

16/35 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

17/35 Results: subject-based patterns Group template Individual data

18/35 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

19/35 Comparing subjects : supervised methods Correlation of the signal with the ability to perform a mental rotation task Correlation of the signal with the sex

20/35 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