Luc Florack ^* Rick Sengers

• Eindhoven University of Technology, Eindhoven, Netherlands

We propose a statistical physics based data assimilation model for the mobility of water-bound hydrogen nuclear spins in the brain in the context of diffusion weighted magnetic resonance imaging (DWI). Point of departure is a statistical hopping model that emulates molecular motion in the presence of static and stationary microscale obstacles, statistically reflected in the apparent inhomogeneous anisotropic DWI signal profiles. Subsequently we propose a Riemann-Finsler geometric interpretation in terms of a metric transform that simulates this molecular process as a free diffusion on a vacuous manifold with all diffusion obstacles absorbed in its geometry. The geometrization procedure supports the reconstruction of neural tracts (geodesic tractography) and their quantitative characterization (tractometry). The Riemann-DTI model for geodesic tractography based on diffusion tensor imaging (DTI) arises as a limiting case. The genuine Finslerian case is a geometric representation of high angular resolution DTI, i.e. a generalized rank-two DTI framework without the quadratic restriction implied by a simplifying Gaussianity assumption on local diffusion or a second order harmonic approximation of local orientation distributions.