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. By considering the fiber paths between two given areas as geodesies of a suitable well-posed optimal control problem (related to optimal mass transportation), 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.
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