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Section: New Results

Joint Morphometry of Fiber Tracts and Gray Matter structures using Double Diffeomorphisms

Participants : Pietro Gori [Correspondant] , Olivier Colliot, Linda Marrakchi-Kacem, Yulia Worbe, Alexandre Routier, Cyril Poupon, Andreas Hartmann, Nicholas Ayache, Stanley Durrleman.

This work proposes an atlas construction method to jointly analyse the relative position and shape of fiber tracts and gray matter structures. It is based on a double diffeomorphism which is a cascade of two diffeomorphisms. The first deformation acts only on the white matter keeping fixed the gray matter of the atlas. The resulting white matter, together with the gray matter, are then deformed by the second diffeomorphism which puts into correspondence the homologous anatomical structures across subjects. The first diffeomorphism makes the fiber bundles slide on the fixed gray matter revealing the variability in structural connectivity within the population, namely both the changes in the connected areas and in the geometry of the pathway of the tracts. Fiber bundles are approximated with weighted prototypes using the metric of weighted currents. The algorithm is based on a Bayesian framework which allows the automatic estimation of the covariance matrix of deformation parameters and of the noise variance of each structure. This approach is applied to patients with Tourette syndrome and controls showing a variability in the structural connectivity of the left cortico-putamen circuit.

More details in [26] .

Figure 2. Estimation of a virtual representation of brain structure from anatomical and diffusion images of 3 patients with Gilles de la Tourette syndrome and 2 control subjects. Deformation of the white matter fiber bundle along the first mode of variability is shown while the estimated grey matter frame is kept fixed. Colors refer to the magnitude of displacement during deformation.