Neuronal Fiber--tracking via optimal mass transportation
Diffusion Magnetic Resonance Imaging (MRI) is a powerful non-invasively method pro- ducing images of biological tissues exploiting the water molecules diffusion into the living tissues under a magnetic field. In the last decade, diffusion MRI data have been widely applied to the study of fiber bundle trajectories into the brain white matter and many methods have been proposed in order to reconstruct the fiber bundle trajectories from such data. The quality of data that fiber-tracking (tractography) methods can exploit depends on the choice of the model describing the water molecules diffusion into an MRI voxel. The Diffusion Spectrum Imaging (DSI) model describes the diffusion inside each voxel as a probability density function defined on a set of predefined directions inside the voxel. DSI is able to successfully describe more complex tissue configurations than other models as, for example, Diffusion Tensor Imaging (DTI), but lacks to consider the density of fibers going to make up a bundle trajectory among adjacent voxels, preventing any evaluation of the real physical dimension of neuronal fiber bundles. In this paper we propose a new approach, based on ideas from mass transportation the- ory, that takes into account the whole information given by DSI in order to reconstruct the whole underlying diffusion process, and recover the actual density of neuronal fibers.