White Matter Tract Segmentation as Multiple Linear Assignment Problems

Abstract

Diffusion magnetic resonance imaging (dMRI) allows to reconstruct the main pathways of axons within the white matter of the brain as a set of polylines, called streamlines. The set of streamlines of the whole brain is called the tractogram. Organizing tractograms into anatomically meaningful structures, called tracts, is known as the tract segmentation problem, with important applications to neurosurgical planning and tractometry. Automatic tract segmentation techniques can be unsupervised or supervised. A common criticism of unsupervised methods, like clustering, is that there is no guarantee to obtain anatomically meaningful tracts. In this work, we focus on supervised tract segmentation, which is driven by prior knowledge from anatomical atlases or from examples, i.e., segmented tracts from different subjects. We present a supervised tract segmentation method that segments a given tract of interest in the tractogram of a new subject using multiple examples as prior information. Our proposed tract segmentation method is based on the idea of streamline correspondence i.e., on finding corresponding streamlines across different tractograms. In the literature, streamline correspondence has been addressed with the nearest neighbor (NN) strategy. Differently, here we formulate the problem of streamline correspondence as a linear assignment problem (LAP), which is a cornerstone of combinatorial optimization. With respect to the NN, the LAP introduces a constraint of one-to-one correspondence between streamlines, that forces the correspondences to follow the local anatomical differences between the example and the target tract, neglected by the NN. In the proposed solution, we combined the Jonker-Volgenant algorithm (LAPJV) for solving the LAP together with an efficient way of computing the nearest neighbors of a streamline, which massively reduces the total amount of computations needed to segment a tract. Moreover, we propose a ranking strategy to merge correspondences coming from different examples. We validate the proposed method on tractograms generated from the human connectome project (HCP) dataset and compare the segmentations with the NN method and the ROI-based method. The results show that LAP-based segmentation is vastly more accurate than ROI-based segmentation and substantially more accurate than the NN strategy. We provide a Free/OpenSource implementation of the proposed method.

Classifyber, a robust streamline-based linear classifier for white matter bundle segmentation

“…We selected two methods based on the recent extensive comparison presented in Wasserthal et al (2018a), where TractSeg obtained the highest quality of bundle segmentation and Re-coBundles ranked as the second best method among those freely available. In our comparison we also included LAP, see Sharmin et al (2018), because it was not compared in Wasserthal et al (2018a) but proved to be superior to nearest neighbor methods, the category to which RecoBundles belongs. In some cases, we used variants of TractSeg and RecoBundles, referred to as TractSeg-retrained and RecoBundles-atlas.…”

“…Sharmin et al (2018) proposed a streamline-based segmentation method that takes as input multiple example bundles which are used to estimate the corresponding bundle in a target tractogram by means of finding corresponding streamlines through the solution of a Linear Assignment Problem (LAP) and a refinement step. We ran the algorithm following the original procedure and we set the parameter k, the only parameter of the method, corresponding to the number of nearest neighbors streamlines to compute the superset, equal to 2000 (default k = 500), since the total number of streamlines of the tractograms considered in our experiments are approximately 4 times higher than in the original study of Sharmin et al (2018). One limitation of LAP is that it is computationally too expensive for supersets larger than 100 thousands streamlines, both for memory and time requirements.…”

“…Both RecoBundles and LAP require a very small number of training subjects: 1 bundle/model for RecoBundles and around 5-10 for LAP, according to Sharmin et al (2018). On the contrary, TractSeg was trained on 84 subjects.…”

“…Unsupervised streamline-based methods, such as those in Brun et al (2004); Maddah et al (2005); O' Donnell and Westin (2007); Guevara et al (2012); Tunç et al (2014); Siless et al (2016); Zhang et al (2018), perform whole brain segmentation through clustering, without prior knowledge about the anatomy of the bundles and without leveraging examples of expert-made segmented bundles, limiting the quality of segmentation. In contrast, supervised streamline-based methods require one or more examples of the bundle to learn from, in order to segment such bundle in the target subject, such as those in Mayer et al (2011); Olivetti and Avesani (2011); Vercruysse et al (2014); Yoo et al (2015); Labra et al (2016); Garyfallidis et al (2018) and Sharmin et al (2018). It has been shown that streamline-based methods like those presented in Garyfallidis et al (2018), referred to as RecoBundles, and in Sharmin et al (2018), referred to as LAP, outperform connectivity based methods in terms of quality of segmented bundles.…”

“…In contrast, supervised streamline-based methods require one or more examples of the bundle to learn from, in order to segment such bundle in the target subject, such as those in Mayer et al (2011); Olivetti and Avesani (2011); Vercruysse et al (2014); Yoo et al (2015); Labra et al (2016); Garyfallidis et al (2018) and Sharmin et al (2018). It has been shown that streamline-based methods like those presented in Garyfallidis et al (2018), referred to as RecoBundles, and in Sharmin et al (2018), referred to as LAP, outperform connectivity based methods in terms of quality of segmented bundles.…”