3D Stochastic Completion Fields for Fiber Tractography

The authors approach the problem of fiber tractography from the viewpoint that a computational theory should relate to the underlying quantity that is being measured - the diffusion of water molecules. The authors characterize the brownian motion of water by a 3D random walk described by a stochastic nonlinear differential equation. This paper shows that the maximum likelihood trajectories are 3D elastica, or curves of least energy. This paper illustrates the model with Monte-Carlo (Sequential) simulations and then develops a more efficient (Local, parallelizable) implementation, based on the Fokker-Planck equation.