Resolving complex fibre configurations using two-tensor random-walk stochastic algorithms

Fibre tractography using diffusion tensor imaging allows the study of anatomical connectivity of the brain, and is an important diagnostic tool for a range of neurological diseases. Deterministic tractography algorithms assume that the fibre direction coincides with the principal eigenvector of a diffusion tensor. This is, however, not the case for regions with crossing fibres. In addition noise introduces uncertainty and makes the computation of fibre directions difficult. Stochastic tractography algorithms have been developed to overcome the uncertainties of deterministic algorithms. However, generally, both parametric and non-parametric stochastic algorithms require longer computational time and large amounts of memory. Multi-tensor fibre tracking methods can alleviate the problems when crossing fibres are encountered. In this study simple and computationally efficient random-walk algorithms are described for estimating anatomical connectivity in white matter. These algorithms are then applied to a two-tensor model to compute the probabilities of connections between regions with complex fibre configurations. We analyze the random-walk models quantitatively using simulated data and estimate the optimal parameter values of the models. The performance of the tracking algorithms is verified using a physical phantom and an in vivo dataset with a wide variety of seed points. The results confirm the effectiveness of the proposed approach, which gives comparable results to other stochastic methods. Our approach is however significantly faster and requires less memory. The results of two-tensor random-walk algorithms demonstrate that our algorithms can accurately identify fibre bundles in complex fibre regions.