Combinatorial fiber-tracking of the human brain

Abstract

This paper presents a novel fiber-tracking algorithm, termed combinatorial tracking, which uses stochastic process modeling and global optimization algorithm for tractography. Combinatorial tracking is a probabilistic tracking algorithm that transforms the brain's white matter into a grid in which each voxel has 26 weighted connections with adjacent voxels. We model the random walk on this graph using a Markov Chain model and suggest two approaches for fiber reconstruction. In the first approach, we find the most probable paths between two voxels with prior connectivity knowledge using a shortest path algorithm. In the second approach, the all-pairs mean first passage time (MFPT) matrix M (or hitting time as referred to in the Spectral Graph theory literature) is calculated analytically. We suggest that M can be interpreted as a global connectivity matrix and use it for fiber reconstruction. We also introduce a simulation framework that can be used to calculate specific elements of the matrix M, and show how it can be employed to select the target of a fiber in a high resolution diffusion tensor imaging (DTI) dataset. Because any source and any target voxel can be connected, combinatorial tracking permits true connectivity analysis, overcoming the limitations of conventional tracking, especially stopping criteria (e.g. low FA). We applied combinatorial tracking to a standard DTI dataset and demonstrated the reconstruction of the cortico-thalamic pathway, the pyramidal decussation, and the medial cerebellar peduncle fibers. While the DTI ellipsoid served as input for the algorithms, any diffusion imaging based orientation density function (ODF) can be used. This framework can potentially turn diffusion imaging tractography into a true connectivity measure.