Probabilistic Tractography for Topographically Organized Connectomes

Abstract

While tractography is widely used in brain imaging research, its quantitative validation is highly difficult. Many fiber systems, however, have well-known topographic organization which can even be quantitatively mapped such as the retinotopy of visual pathway. Motivated by this previously untapped anatomical knowledge, we develop a novel tractography method that preserves both topographic and geometric regularity of fiber systems. For topographic preservation, we propose a novel likelihood function that tests the match between parallel curves and fiber orientation distributions. For geometric regularity, we use Gaussian distributions of Frenet-Serret frames. Taken together, we develop a Bayesian framework for generating highly organized tracks that accurately follow neuroanatomy. Using multi-shell diffusion images of 56 subjects from Human Connectome Project, we compare our method with algorithms from MRtrix. By applying regression analysis between retinotopic eccentricity and tracks, we quantitatively demonstrate that our method achieves superior performance in preserving the retinotopic organization of optic radiation.

Keywords: Bayesian inference; probabilistic tractography; visual path-way.

Fig. 1

(a) At t = 0, without prior information, we select a random curve among the red candidate curves based on their likelihood. The thicker the curve, the higher posterior probability it has. (b) By solving the Frenet-Serret ODE, we propagate by Δs. (c) At t = 1, we calculate the prior probability for candidate curves for a smooth transition from the previous curve ${\mathbf{c}}_{p^1}^1$ shown in green. (d) Propagate to p².

Fig. 2

(a) To estimate the likelihood of a curve, we randomly pick a number of points within the integration radius, r. (b) Parallel curves passing through the random points. (c) We compute the tangents of parallel curves for each point and obtain the average FOD. (d)(e) Estimated likelihoods are shown in proportion to the thickness of curves.

Fig. 3

Qualitative comparison of our method with MRTrix algorithms on the reconstruction of a left optic radiation of an HCP subject.

Fig. 4

Quantitative comparison of the bundles show in Fig.3. Top row shows the labels for three sub-bundles of the optic radiation. Bottom row shows the eccentricity values and the quality of quadratic fit using MSE and R². The low MSE and high R²values obtained by the proposed technique corroborate the qualitative observation.