Section: Scientific Foundations
Because the relationship between brain structure and brain function is fundamental to neuroscience, developing techniques that allow to recover the anatomical connectivity in the in vivo brain is of utmost importance and a major goal to achieve if one wants to understand how the brain works and acquire a better understanding of its mechanisms.
Diffusion Magnetic Resonance Imaging (DMRI) not only gives scientists access to data relating to local white matter architecture but is also the unique non invasive method currently available to explore the microstructure of biological tisssues like those of the white matter in the human brain. This is why our research deals with the development of new processing tools for DMRI. Because of the complexity of the data, this imaging modality raises a large amount of mathematical and computational challenges. We have therefore started by developing new algorithms relying on Riemannian geometry, differential geometry, partial differential equations and front propagation techniques to correctly and efficiently estimate, regularize, segment and process Diffusion Tensor MRI (DT-MRI). (see  , 
Diffusion Tensor Magnetic Resonance Imaging is an MRI technique that allows to measure in-vivo and in a non-invasise way the restricted diffusion of water molecule in a biological tissue. A tensor describes the 3D shape of diffusion
However, due to the limited current resolution of diffusion-weighted (DW) MRI, one third to two thirds of imaging voxels in the human brain white matter contain fiber crossing bundles. Therefore, it's also of utmost importance to tackle the problem of recovering fiber crossing and develop techniques that go beyond the limitations of diffusion tensor imaging (DTI). We are contributing towards these objectives and or recent work deals with the development of local reconstruction methods, segmentation and tractography algorithms able to infer multiple fiber crossing from diffusion data. To do so, high angular resolution diffusion imaging (HARDI) is used to measure diffusion images along several directions. Q-ball imaging (QBI) is a recent such HARDI technique that reconstructs the diffusion orientation distribution function (ODF), a spherical function that has its maxima aligned with the underlying fiber directions at every voxel. QBI and the diffusion ODF play a central role in our work focused on the development of a robust and linear spherical harmonic estimation of the HARDI signal and our development of a regularized, fast and robust analytical QBI solution that outperform the state-of-the-art ODF numerical technique available. Those contributions are fundamentals and have already started to impact on the Diffusion MRI, HARDI and Q-Ball Imaging community. These contributions are the basis of our probabilistic and deterministic tractography algorithms exploiting the full distribution of the fiber ODF (see  , 
Q-Ball Imaging is a HARDI method that measures apparent diffusion coefficients along many directions distributed almost isotropically on the surface of a sphere
High Angular Resolution Diffusion Imaging allows apparent diffusion coefficients to be measured along a large number of directions, poses no assumptions on the underlying diffusion process and is capable of detecting the presence of multiple diffusion directions within an individual voxel
The Orientation Distribution Function describes the probability distribution for a water molecule to displace in a given direction
Overall, we are now able to show local reconstruction, segmentation and tracking results on complex fiber regions with known fiber crossing on simulated HARDI data, on a biological phantom and on multiple human brain datasets. Most current DTI based methods neglect these complex fibers, which might lead to wrong interpretations of the brain anatomy and functioning.
In order to acquire a better understanding of the brain mechanisms and to improve the diagnosis of neurological disorders, we are also interested by the application of our tools to important neuroscience problems: the analysis of the connections between the cerebral cortex and the basal ganglia, implicated in motor tasks, the study of the anatomo-functional network of the human visual cortex and the reconstruction of the transcallosal fibers intersecting with the corona radiata and superior longitudinal fasciculus, regions usually neglected by most DTI-based methods and recovered thanks to the ODF-based probabilistic. Our work is done in collaboration with the Center for Magnetic Resonance Research of the University of Minnesota (Minneapolis), the centre IRMf of the hospital la Timone (Marseille), the Centre for Neuro Imaging Research (CENIR - Pitié-Salpêtrière - Paris), the Max Planck Institute for Human Cognitive and Brain Sciences (Leipzig,Germany) and the Montreal Neurological Institute (McGill - Montréal).