Toward global tractography

doi:10.1016/j.neuroimage.2013.04.009

NeuroImage

Volume 80, 15 October 2013, Pages 290-296

https://doi.org/10.1016/j.neuroimage.2013.04.009 Get rights and content

Highlights

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Diffusion-based tractography is an ill-posed problem.
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Modeling tractography as a global inverse problem is a way to regularize the problem.
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Tractography in the neighborhood of ambiguous diffusion profiles helps to infer fiber directions.

Abstract

Diffusion-based tractography is an ill-posed problem, because the step-by-step reconstruction of a fibre bundle trajectory cannot afford any serious mistake in the evaluation of the local fibre orientations. Such evaluation is difficult, however, because the myriad fibres passing through a single voxel follow different directions. Modelling tractography as a global inverse problem is a simple framework which addresses the ill-posed nature of the problem. The key idea is that the results of tractography in the neighbourhood of an ambiguous local diffusion profile can help to infer the local fibre directions. This paper provides an overview of past achievements of global tractography and proposes guidelines for a future research programme in the hope that the potential of the technique will increase the interest of the community.

Graphical abstract

Section snippets

Introduction: the ill-posed nature of diffusion-based tractography

In the early days of MR diffusion-based tractography, the potential impact of the technique was so uplifting that the neuroscience community was comfortably blind to the ‘ill-posed’ nature of the problem: the step-by-step reconstruction of a fibre bundle trajectory cannot afford any serious mistake in the evaluation of the local fibre orientations. This major risk was difficult to deal with because it does not exist in the well-known invasive techniques used with animals: a marker injected in a

Global tractography

A recent paper by Jbabdi and Johansen-Berg (2011) provides a clear-cut overview of the current situation. Tractography can be a very useful technique for neuroscience provided that its limitations are clearly understood. Unfortunately, one of the current limitations is our inability to determine the precise transversal localization of connections in the cortex, which is largely related to the ill-posedness mentioned above. They suggest that spatial interactions between local modelling and

A concrete example: spin glass tractography

In order to provide a better understanding of the energy-based paradigm for global tractography, this section provides an overview of an upgrade of our framework presented a few years ago at the MICCAI conference (Fillard et al., 2009). Fibre fascicles are parameterized by small segments, called spins, which are optimised to minimise a twofold global energy: the first models fidelity to the diffusion data and the second models a low curvature prior. This new version called spin glass

Where do we go with global tractography?

The concept of global tractography can be developed in a lot of different directions. This section highlights some of them with a focus on the global inverse problem perspective. The future of MR imaging could provide additional features related to axon geometry like axon diameter (Assaf et al., 2008, Zhang et al., 2011). In the context of energy-based approaches, this could lead to new interaction potentials assuming slow variations of such features along the fascicles, which could help in

Conclusion

The goal of this paper was to attract more research fellows to the field of global tractography. In our opinion, the domain is at a stage where global modelling can provide qualitative improvements to tractograms. Furthermore, multiple analogies with the problem of contour completion, a fundamental process in computer vision, could provide a rich source of inspiration (MomayyezSiahkal and Siddiqi, 2013, Tupin et al., 1998). Note however that global modelling cannot overcome all the

Conflict of interest

None.

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