Alignment of Tractograms As Graph Matching

Emanuele Olivetti,Nusrat Sharmin,Paolo Avesani

doi:10.3389/fnins.2016.00554

Emanuele Olivetti, Nusrat Sharmin + Show 1 more

Open Access

https://doi.org/10.3389/fnins.2016.00554

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Abstract

The white matter pathways of the brain can be reconstructed as 3D polylines, called streamlines, through the analysis of diffusion magnetic resonance imaging (dMRI) data. The whole set of streamlines is called tractogram and represents the structural connectome of the brain. In multiple applications, like group-analysis, segmentation, or atlasing, tractograms of different subjects need to be aligned. Typically, this is done with registration methods, that transform the tractograms in order to increase their similarity. In contrast with transformation-based registration methods, in this work we propose the concept of tractogram correspondence, whose aim is to find which streamline of one tractogram corresponds to which streamline in another tractogram, i.e., a map from one tractogram to another. As a further contribution, we propose to use the relational information of each streamline, i.e., its distances from the other streamlines in its own tractogram, as the building block to define the optimal correspondence. We provide an operational procedure to find the optimal correspondence through a combinatorial optimization problem and we discuss its similarity to the graph matching problem. In this work, we propose to represent tractograms as graphs and we adopt a recent inexact sub-graph matching algorithm to approximate the solution of the tractogram correspondence problem. On tractograms generated from the Human Connectome Project dataset, we report experimental evidence that tractogram correspondence, implemented as graph matching, provides much better alignment than affine registration and comparable if not better results than non-linear registration of volumes.

Highlights

Diffusion magnetic resonance imaging data (Basser et al, 1994), provide quantitative information about the white matter of the brain, in terms of local main direction(s) of the neuronal axons
In order to obtain the correspondence between tractograms, we introduced a further approximation with a simple three-steps procedure, similar to the one proposed for the streamline linear registration (SLR) algorithm in Garyfallidis et al (2015): 1. We clustered each tractogram into a given number of clusters (k = 1000) and defined the median streamline as the representative for each cluster
FNIRT deformation fields were already available within the Human Connectome Project (HCP) dataset, anyway they usually require a few minutes of computation

Summary

Introduction

Diffusion magnetic resonance imaging (dMRI) data (Basser et al, 1994), provide quantitative information about the white matter of the brain, in terms of local main direction(s) of the neuronal axons Such information allows to approximate the main paths of large sets of axons with polylines, called streamlines. Alignment of Tractograms as Graph Matching of the tractograms1 In the literature, both linear and non-linear methods have been proposed to register volumetric data, see Christiaens et al (2014). In Durrleman et al (2011), the use of the framework of currents is proposed to warp the streamlines of bundles, for registration, atlasing, and variability analysis This literature addresses non-linear bundle alignment but not whole tractogram alignment, for the high computational cost of the algorithms. This approach is mentioned in Christiaens et al (2012), but without a quantitative evaluation of its effect

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