Nonlinear Alignment of Whole Tractograms with the Linear Assignment Problem

Abstract

After registration of the imaging data of two brains, homologous anatomical structures are expected to overlap better than before registration. Diffusion magnetic resonance imaging (dMRI) techniques and tractography techniques provide a representation of the anatomical connections in the white matter, as hundreds of thousands of streamlines, forming the tractogram. The literature on methods for aligning tractograms is in active development and provides methods that operate either from voxel information, e.g. fractional anisotropy, orientation distribution function, T1-weighted MRI, or directly from streamline information. In this work, we align streamlines using the linear assignment problem (LAP) and propose a method to reduce the high computational cost of aligning whole brain tractograms. As further contribution, we present a comparison among some of the freely-available linear and nonlinear tractogram alignment methods, where we show that our LAP-based method outperforms all others. In discussing the results, we show that a main limitation of all streamline-based nonlinear registration methods is the computational cost and that addressing such problem may lead to further improvement in the quality of registration.

BundleWarp, streamline-based nonlinear registration of white matter tracts

“…However, static and moving bundles often do not have the same number of streamlines, and one-to-one mapping would not suffice in that case. Therefore, we design a many-to-one pairwise streamline correspondence approach based on the rectangular Linear Assignment Problem (rLAP) (Olivetti et al, 2020; Kuhn, 1955) for bundles with a varying number of streamlines that we call iterLAP.…”

“…In this paper, building on our previous work on the direct alignment of tractograms/tracts in streamline-space(Garyfallidis et al, 2015; Olivetti et al, 2020; Chandio and Garyfallidis, 2020), we introduce a new method, BundleWarp. BundleWarp is a method for streamline-based nonlinear registration of white matter tracts.…”

“…All of these approaches do not take into consideration the streamline topological connectivity in the registration process. However, recently, a nonlinear streamline matching method was proposed (Olivetti et al, 2020) that aims to find nonrigid correspondence between streamlines of two whole-brain tractograms. Although it does not apply a transformation or generate a warp map, it does pave the way for direct streamline-based nonlinear registration of tracts.…”

How Does White Matter Registration Affect Tractography Alignment?

“…The problem of tractogram alignment has been recently reformulated as finding the correspondence among streamlines. According to this perspective, different solutions have been proposed based on graph matching [12], linear assignment problem (LAP) [13], and optimal transport [14]. The output of these methods is no more a transformation, either linear or non-linear, but a pairwise relation that defines the correspondence between the streamlines of two tractograms of two distinct individuals.…”

“…Affine and diffeomorphic transformation for DTI and FOD data were performed using DTIREG and mrregister respectively. For tractography based method, we computed the affine transformation with SLR while for correspondence methods we referred to LAP [13] because the implementation based on optimal transport does not scale up to 10 7 streamlines.…”