Elsevier

NeuroImage

Volume 49, Issue 1, 1 January 2010, Pages 249-256
NeuroImage

Crossing fibres in tract-based spatial statistics

https://doi.org/10.1016/j.neuroimage.2009.08.039Get rights and content

Abstract

Voxelwise analysis of white matter properties typically relies on scalar measurements derived, for example, from a tensor model fit to diffusion MRI data. These are spatially matched across subjects prior to statistical modelling. In this paper, we show why and how this can be improved through the use of directionally dependent measurements. In the case where different orientations relate to different fibre populations (e.g., in the presence of crossing fibres), distinguishing and matching those populations of fibres across subjects are important prior to any statistical modelling. It allows one to compare measurements that are related to the same fibres across subjects. We show how this framework applies to the parameters of a crossing fibre model and discuss its implications for voxelwise analysis of the white matter.

Introduction

Diffusion MRI is widely used to probe white matter variations across individuals. The tensor model (Basser et al., 1994) is still very popular for in vivo human studies, as it provides semi-quantitative scalar measures such as fractional anisotropy (FA) and mean apparent diffusivity (MD) that have been related to white matter micro-structural “integrity” (e.g., Song et al., 2003).

Voxelwise analysis of diffusion MRI aims at modelling or quantifying changes in white matter across individuals. This relies on the precise matching of anatomical locations across subjects, which is necessary in order for the experimenter to be confident that any result from the analysis is due to genuine changes in white matter microstructure rather than variations in brain structures' shape, size or position. For example, tract-based spatial statistics (TBSS; Smith et al., 2006) attempts to achieve this by restricting the statistical comparisons to the centres of white matter tracts after non-linear registration of different subjects into a common space. TBSS uses FA measurements to realign subjects and extract the centres of white matter tracts.

The tensor model is based on the assumption that water self-diffusion has a Gaussian diffusion profile. It does not assume any particular arrangement of the tissue microstructure, nor does it explicitly relate micro-structural features to the diffusion profile. This means that changes (e.g., across space or across subjects) in tensor-derived scalar quantities such as FA and MD cannot always be related to micro-architecture in a straightforward, unambiguous and quantitative manner (Beaulieu, 2002). One claim that one can make from a tensor model, with relative confidence, is that the principal diffusion direction is aligned with the main orientation of axonal fibres, at least when all the axons within a voxel have the same orientation.

More complex models of the diffusion MR signal go beyond the Gaussian assumption of the tensor model, and some attempt to relate the signal to aspects of the underlying white matter micro-architecture. For example, one may consider the distinction between intra-cellular and extra-cellular diffusion and assume the former to be restricted by regular geometries such as cylinders (axons) and the latter hindered as a result of axonal packing (Assaf and Basser, 2005). Another extension of the tensor model may simply consist of considering the presence of distinct populations of fibre bundles with distinct orientations within a single imaging voxel. Using such crossing fibre models, one can infer on the orientations from the diffusion measurements (Tournier et al., 2004, Hosey et al., 2005, Parker and Alexander, 2005, Behrens et al., 2007). One may also consider that the contribution of each fibre population to the diffusion MR signal is related to the amount of space that is occupied by each fibre population. In the context of voxelwise white matter analysis, these partial volume fractions (PVFs) may be more interpretable than FA in locations where white matter bundles supporting distinct brain functions contribute to the signal within one voxel.

We argue that voxelwise studies of the white matter could benefit from the use of such models. Including information about the relative amounts of specialised fibres within a voxel could enhance the interpretability of a finding. One would hope to be able to associate a local change in white matter with a particular fibre population. Our interpretation of any local change in white matter would therefore become more tract specific. In fact, interpreting FA changes in locations where functionally distinct fibre bundles are present is sometimes more challenging than simply knowing which fibres are inducing the observed changes. The directionality of the changes, i.e., whether, for example, FA correlates positively or negatively with a variable of interest can also be ambiguous. In one of the first studies that reported a strong and tract-specific correlation between FA and a behavioural measure, Tuch et al. (2005) have noticed that FA along the optic radiations was negatively correlated with individual skills in a visuo-motor task. The effect was strong, but the sign of the correlations was counter-intuitive. The authors acknowledged the fact that this may be due to crossing fibres (for an illustration of this issue, see Fig. 1). This crossing fibre issue was also noted by Pierpaoli et al. (2001) and more recently by Wheeler-Kingshott and Cercignani (2009), where it was suggested that changes in tensor-derived scalar measurements (such as FA and diffusivity) should only be interpreted as being related to axonal integrity in locations where fibre bundles are aligned coherently.

In this paper, we will focus on an extension of the TBSS framework to accounting for crossing fibre models. We will use as an example the crossing fibre model outlined in (Behrens et al., 2007). Extending TBSS to crossing fibre models requires some careful considerations with regard to the data, which we present in detail in the Methods section. The methodology is extremely straightforward and integrates naturally within the TBSS framework. Although we primarily discuss the extension of TBSS to crossing fibre models, the same methodology could potentially be applied within other frameworks for white matter analysis (Yushkevich et al., 2008, Eckstein et al., 2009, Goodlett et al., 2009, O'Donnell et al., 2009).

Section snippets

Methods

Throughout this paper, we will use the crossing fibre model described by Behrens et al. (2007). In this context, the diffusion signal is modelled as a weighted sum of signals accounting for the contribution of various compartments in each voxel: an infinitely anisotropic component for each fibre orientation and a single isotropic component. The weights of the signals from the anisotropic compartments will be denoted f1, f2, etc. The method described below may be generalized to any other

Interpretation of the partial volume fractions

In this paper, we illustrate the use of crossing fibres in TBSS using the partial volume model presented by Hosey et al. (2005) and Behrens et al. (2007). The diffusion signal is modelled as a weighted sum of signals accounting for the contribution of various compartments in each voxel: an infinitely anisotropic component for each fibre orientation and a single isotropic component. The weights, or partial volume fractions, are inferred from the data and represent the contribution of each

Acknowledgments

This work was supported by the Medical Research Council. The authors would like to thank the many researchers in the FMRIB Centre who have contributed to the diffusion database that has been used in this article.

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