# American Institute of Mathematical Sciences

September  2012, 11(5): 2157-2177. doi: 10.3934/cpaa.2012.11.2157

## Neuronal Fiber--tracking via optimal mass transportation

 1 Signal Processing Laboratory (LTS5), Ecole Polytechnique Federale de Lausanne (EPFL), ELD 232 - CH-1015 Lausanne, Swaziland 2 Department of Computer Sciences, University of Verona, Strada Le Grazie, 15 - I-37134 Verona, Italy, Italy, Italy

Received  April 2011 Revised  September 2011 Published  March 2012

Diffusion Magnetic Resonance Imaging (MRI) is used to (non-invasively) study neuronal fibers in the brain white matter. Reconstructing fiber paths from such data (tractography problem) is relevant in particular to study the connectivity between two given cerebral regions. Fiber-tracking models rely on how water molecules diffusion is represented in each MRI voxel. The Diffusion Spectrum Imaging (DSI) technique represents the diffusion as a probability density function (DDF) defined on a set of predefined directions inside each voxel. DSI is able to describe complex tissue configurations (compared e.g. with Diffusion Tensor Imaging), but ignores the actual density of fibers forming bundle trajectories among adjacent voxels, preventing any evaluation of the real physical dimension of these fiber bundles.
By considering the fiber paths between two given areas as geodesics of a suitable well-posed optimal control problem (related to optimal mass transportation) which takes into account the whole information given by the DDF, we are able to provide a quantitative criterion to estimate the connectivity between two given cerebral regions, and to recover the actual distribution of neuronal fibers between them.
Citation: A. Daducci, A. Marigonda, G. Orlandi, R. Posenato. Neuronal Fiber--tracking via optimal mass transportation. Communications on Pure & Applied Analysis, 2012, 11 (5) : 2157-2177. doi: 10.3934/cpaa.2012.11.2157
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