A Fast Fiber k-Nearest-Neighbor Algorithm with Application to Group-Wise White Matter Topography Analysis

Abstract

Finding the fiber k-nearest-neighbors (k-NN) is often essential to brain white matter analysis yet it is computationally prohibitive, and no efficient approximation to it is known to the best of our knowledge. We observe a strong relationship between the point-wise distances and tract-wise distances. Based on this observation, we propose a fast algorithm for approximating the k-NN distances of large fiber bundles with point-wise K-NN algorithm, and we call it the fast fiber k-NN algorithm. Furthermore, we apply our fast fiber k-NN algorithm to white matter topography analysis, which is an emerging problem in brain connectomics reasearch. For the latter task, we first propose to quantify the white matter topography by metric embedding, which gives rise to the first anatomically meaningful fiber-wise measure of white matter topography to the best of our knowledge. In addition, we extend the individual white matter topography analysis to group-wise analysis using the k-NN fiber distances computed with our fast algorithm. In our experiments, (a) we find that our fast fiber k-NN algorithm reasonably approximates the ground-truth distance at 1–2 percent of its computational cost, (b) we also verify the anatomical validity of our proposed topographic measure, and (c) we find that our fast fiber k-NN algorithm performs identically well compared with the exhaustive fiber distance computation, for the group-wise white matter topography analysis for 792 subjects from the Human Connectome Project.