Diffusion MRI is a Magnetic Resonance Imaging (MRI) modality able to quantify non-invasively and in vivo the diffusion of water molecules in biological tissues. This relatively new imaging modality, pioneered twenty years ago by Le Bihan (LeBihan and Breton, 1985), acquires at each voxel, image intensities, referred to as diffusion, related to the relative mobility of endogenous tissue water molecules and reflecting the structure of the underlying biological tissues at a microscopic scale, well beyond the usual image resolution. As of today, Diffusion MRI is the only non-invasive method that opens the possibility of recovering a detailed geometric description of the anatomical connectivity between brain areas and distinguishes the anatomical structures of the cerebral white matter.

Diffusion MRI is therefore an excellent research domain for scientists and medical doctors in order to study fiber connections in biological tissues. This ARC proposal involves three partners : The INRIA Odyssée project team, the INSERM Imparabl team of the Laboratoire d’Imagerie Fonctionnelle LIF/U678 Faculté de Médecine Pierre et Marie Curie - Hopital Pitié-Salpêtrière and the CENIR : Center for NeuroImaging Research of the Hopital Pitié-Salpêtrière.

In this ARC project, our broad goal is to develop and validate algorithms that will help us to have a better knowledge and better understand the structural organization of the whitematter fiber bundles in the human brain and help to identify the neural connectivity patterns with the help of Diffusion Magnetic Resonance Imaging (MRI). Our algorithms will be based on formulations using tensor calculus, partial differential equations, variational methods and differential geometry and will ultimately be useful for clinicians as well as researchers. For example, damage to the basal ganglia leads to movement disorders such dystonia, as well as more cognitive deficits in human. We will help in this project to better understand the anatomical organization and role of the basal ganglia as a prerequisite to the study of their dysfunction in dystonia. In this project we will adress the following aims :

• Aim #1: Conventional fiber tract reconstruction methods have several limitations that could be overcomed if fiber tracktography takes benefit from new mathematical methods and also from new high resolution acquisition techniques. In this project, we will focus on both aspects and propose to develop an innovative research program to develop new fibers tracking methods as well as explore the high resolution diffusion MRI data on developing new tools to study basal ganglia pathology.
• Aim #2: We will develop a three dimensional atlas of striatal territories based on cortico - striatal connections and of cortico - striatal fibers by using the new fiber tracking methods. The atlas will serve to locate precisely basal ganglia lesions within basal ganglia territories, and to specifically study diffusion variables within each territory in basal ganglia pathologies.
• Aim #3: New statistical methods will be explored to quantify diffusion values and orientation properties within each cortico -striatal fiber tract and each basal ganglia territory. This will provide new biomarkers to study basal ganglia pathology.

Overall, it is expected that the new mathematical methods that will be explored within both DTI (Diffusion Tensor Imaging) and HARDI (High Angular Resolution Diffusion Imaging) schemes could be extremely useful to a wide range of clinical applications related for example to brain ischemia detection stroke, Alzheimer disease, or schizophrenia where Diffusion MRI has already been shown to be particularly relevant.