This INRIA ARC project 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 INRIA 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 white matter 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.In this project we will help to better understand the anatomical organization and role of the basal ganglia as a prerequisite to the study of their dysfunction in dystonia. 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.

Scientific objectives of the associate team Diffusion MRI is a technique introduced in the mid-1980s (Le Bihan & al., 1985; Merboldt & al, 1985; Taylor & al, 1985) from which has stemmed a number of variations, such as Diffusion Tensor Imaging (DTI), which was invented by Dr. Basser, a partner in this team, in the mid-1990s (P.J. Basser & al, 1994). High Angular Resolution Diffusion Imaging (HARDI) techniques such as Q-Ball Imaging (QBI) or Diffusion Spectrum Imaging (DSI) pioneered by Tuch & al. (Tuch; 2002) are more recent examples of DMRI. These powerful techniques have helped efficiently tackle and solve a number of important and challenging problems. They have also opened up a landscape of extremely exciting discoveries for medicine and neuroscience. The development of novel mathematical analysis tools for DTI or HARDI such as Q-Ball Imaging (QBI) will result in fundamental advancements for research on stroke, multiple sclerosis, amyotrophic lateral sclerosis, Alzheimer's and Parkinson's diseases, HIV/AIDS, neurosurgery, tumor growth modeling or neuropsychiatric disorders like schizophrenia. Moreover, our understanding of the development of the human brain, the effect of aging or the organization of anatomo-functional networks has already started to greatly benefit from this unprecedented insight into brain microstructure. Our main objectives within this research proposal are:

• To develop rigorous mathematical and computational tools for the analysis of Diffusion MRI data
• To improve acquisition techniques and push forward the state-of-the-art in Computational Diffusion MRI achieved through:
  • Joint publications in international conferences and journals dedicated to promoting advances in computational methods for Diffusion MRI analysis and/or use of Diffusion MRI in clinical and neuroscience applications.
  • Development of software packages that will be used at INRIA, NIH and the University of Minnesota's Center for Magnetic Resonance Research in a first stage and then made available to our other partners.
• To help address pressing and challenging clinical and neuroscience questions.

EEG++ is an INRIA Color project (collaborations locales) to trigger the collaboration between Odyssée and ``La Timone'' hospital in Marseille on the subject of conductivity estimation for electro-encephalography.

Ce projet de collaboration est consacré à l'étude des tenseurs d'ordre supérieur à deux et à son application au développement de méthodes robustes et rigoureuses pour l'estimation et la régularisation d'un champ de tenseurs d'ordre 4 à partir de données d'IRM de Diffusion. Cette technique d'acquisition d'images IRM de Diffusion qui ne date que du début des années 80 est l'unique moyen disponible à ce jour pour mesurer la propagation des molécules d'eau dans un tissu biologique et pour explorer in-vivo et de façon non-invasive la micro-structure de tissus biologiques comme les faisceaux de fibres de la matière blanche cérébrale.Ces informations sont d'une très grande aide dans la résolution d'un certain nombre de problèmes fondamentaux en neurosciences et en imagerie cérébrale comme celui de la réalisation d'une cartographie aussi précise que possible des trajectoires des grands faisceaux d'association à travers le cerveau humain (un des jalons du prochain Plan Stratégique de l'INRIA) et oeuvrer ainsi à une meilleure compréhension du fonctionnement du cerveau au travers de son observation in-vivo.Par ailleurs, l'IRM de Diffusion impacte déjà dans le domaine de la santé avec certaines applications cliniques de l'IRM du Tenseur (d'ordre deux seulement à ce jour...) de Diffusion, comme par exemple l'accident ischémique cérébral et possède aussi de très fortes potentialités à avancer de façon significative l'étude de certaines pathologies neurodégénératives importantes comme la maladie de Parkinson qui impliquent clairement des désordres de certains noyaux gris centraux, pour lesquels une étude de la caractérisation cytoarchitectonique pourrait apporter de nouveaux éléments quant aux modifications de leur structure microscopique.