Calculus of Variations and Geometric Measure Theory

A. Daducci - A. Marigonda - G. Orlandi - R. Posenato

Neuronal fiber-tracking via optimal mass transportation

created by orlandi on 04 Mar 2012
modified on 26 Jul 2012


Published Paper

Inserted: 4 mar 2012
Last Updated: 26 jul 2012

Journal: Comm. Pure Appl. Analysis
Volume: 11
Number: 5
Pages: 2157-2177
Year: 2012


Di ffusion Magnetic Resonance Imaging (MRI) is used to (noninvasively)study neuronal fi bers in the brain white matter. Reconstructing fi ber 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 diff usion is represented in each MRI voxel. The Di ffusion Spectrum Imaging (DSI) technique represents the diff usion as a probability density function (DDF) defi ned on a set of predefi ned directions inside each voxel. DSI is able to describe complex tissue con figurations (compared e.g. with Di ffusion Tensor Imaging), but ignores the actual density of fi bers forming bundle trajectories among adjacent voxels, preventing any evaluation of the real physical dimension of these fi ber bundles. By considering the fi ber 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 in principle the actual distribution of neuronal fibers between them.

Keywords: Variational methods, imaging, tractography, optimal mass transportation