Probabilistic Shortest Path Tractography in DTI Using Gaussian Process ODE Solvers

Abstract

Abstract. Tractography in diffusion tensor imaging estimates connectivity in the brain through observations of local diffusivity. These observations are noisy and of low resolution and, as a consequence, connections cannot be found with high precision. We use probabilistic numerics to estimate connectivity between regions of interest and contribute a Gaussian Process tractography algorithm which allows for both quantification and visualization of its posterior uncertainty. We use the uncertainty both in visualization of individual tracts as well as in heat maps of tract locations. Finally, we provide a quantitative evaluation of different metrics and algorithms showing that the adjoint metric [8] combined with our algorithm produces paths which agree most often with experts.

Adjugate Diffusion Tensors for Geodesic Tractography in White Matter

“…We therefore conclude that the adjugate framework leads to better results, also in the case of sharpening. The positive performance of our adjugate approach on real diffusion data agrees with the recent literature [36].…”

“…In recent work, both the inverse diffusion tensor and our metric have been extensively evaluated (using 40 subjects from the Human Connectome Project database) in combination with probabilistic shortest path tractography [36]. It has been shown that our metric produces paths which agree most often with experts.…”

A Random Riemannian Metric for Probabilistic Shortest-Path Tractography

“…The geodesic uncertainty appears related to data noise. This is not attained with other GP ODE solvers [19] as they model constant observation noise.…”

“…This is a smooth curve c(t) : [0, 1] → R 3 , which must be estimated numerically. We use probabilistic numerics that solves the ODE using Gaussian process (GP) regression [12,18,20] We extend previous work [19] to handle uncertainty in the ODE due to a noisy metric.…”

“…This is statistical regression. This view gives rise to probabilistic ODE solvers [5,12,[18][19][20] implemented using GP regression. In these solvers, uncertainty represents the approximation of not evaluating the ODE at the true solution, but at the current approximation.…”