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Probabilistic tractography based on diffusion weighted MRI has become apowerful approach for quantifying structural brain connectivities. In severalworks the similarity of probabilistic tractography and path integrals wasalready pointed out. This work investigates this connection more closely. Forthe so called Wiener process, a Gaussian random walker, the equivalence isworked out. We identify the source of the asymmetry of usual random walkersapproaches and show that there is a proper symmetrization, which leads to a newsymmetric connectivity measure. To compute this measure we will use theFokker-Planck equation, which is an equivalent representation of a Wienerprocess in terms of a partial differential equation. In experiments we showthat the proposed approach leads a symmetric and robust connectivity measure.

Probabilistic tractography, Path Integrals and the Fokker Planck equation