Probabilistic tractography, Path Integrals and the Fokker Planck equation

Abstract

Probabilistic tractography based on diffusion weighted MRI has become a powerful approach for quantifying structural brain connectivities. In several works the similarity of probabilistic tractography and path integrals was already pointed out. This work investigates this connection more closely. For the so called Wiener process, a Gaussian random walker, the equivalence is worked out. We identify the source of the asymmetry of usual random walkers approaches and show that there is a proper symmetrization, which leads to a new symmetric connectivity measure. To compute this measure we will use the Fokker-Planck equation, which is an equivalent representation of a Wiener process in terms of a partial differential equation. In experiments we show that the proposed approach leads a symmetric and robust connectivity measure.