Unsupervised white matter fiber clustering and tract probability map generation: Applications of a Gaussian process framework for white matter fibers

doi:10.1016/j.neuroimage.2010.01.004

NeuroImage

Volume 51, Issue 1, 15 May 2010, Pages 228-241

https://doi.org/10.1016/j.neuroimage.2010.01.004 Get rights and content

Abstract

With the increasing importance of fiber tracking in diffusion tensor images for clinical needs, there has been a growing demand for an objective mathematical framework to perform quantitative analysis of white matter fiber bundles incorporating their underlying physical significance.

This article presents such a novel mathematical framework that facilitates mathematical operations between tracts using an inner product between fibres. Such inner product operation, based on Gaussian processes, spans a metric space. This metric facilitates combination of fiber tracts, rendering operations like tract membership to a bundle or bundle similarity simple. Based on this framework, we have designed an automated unsupervised atlas-based clustering method that does not require manual initialization nor an a priori knowledge of the number of clusters. Quantitative analysis can now be performed on the clustered tract volumes across subjects, thereby avoiding the need for point parameterization of these fibers, or the use of medial or envelope representations as in previous work. Experiments on synthetic data demonstrate the mathematical operations. Subsequently, the applicability of the unsupervised clustering framework has been demonstrated on a 21-subject dataset.

Introduction

Diffusion MRI non-invasively recovers the in vivo effective diffusion of water molecules in biological tissues. This information characterizes tissue micro-structure and its architectural organization (Basser and Pierpaoli, 1996) by modeling the local anisotropy of the diffusion process of water molecules, providing unique biologically and clinically relevant information not available from other imaging modalities. Once the diffusion information has been recovered within each voxel, it can be synthesized in the form of a diffusion tensor (Basser et al., 1994). Brain connectivity can then be assessed by assembling the tensors into tracts using tractography methods (Mori et al., 1999, Koch et al., 2002, Descoteaux et al., 2009). Among these methods, streamline tractography (Mori et al., 1999) recovers white matter fiber tracts from a seed voxel by following the principal direction of the diffusion tensor. Using this technique, white matter fiber tracts are represented as points sampled from a three-dimensional curve. Finally, these fibers can then be grouped into fiber bundles based on anatomic knowledge (O'Donnell and Westin, 2007, Maddah et al., 2008a). The cortico-spinal tract (CST) or the corpus callosum (CC) are prominent examples of the latter.

In this article, we address the important problem of developing a mathematical framework for the quantitative analysis of fiber bundles, which has become a very active research area, with the aim of facilitating subsequent clustering and group-based statistical analysis on the bundles. The effects of pathology on tracts are evident, as in the case of brain tumors that grossly displace tracts, or can be subtle, as in the case of neuropsychiatric disorders, such as schizophrenia, which can manifest as changes in the tracts (Kubicki et al., 2007, Ciccarelli et al., 2008). We propose a framework for tract analysis based on a novel metric between bundles that serves as a probabilistic measure of inclusion of a fiber tract into a bundle. This framework is then used to develop a method for automated clustering of bundles, which are now quantifiable on the basis of membership and ready for statistics based on the distances between bundles. Once obtained, the clusters can be mapped to tract probability maps (Hua et al., 2008) enabling tract-based statistics on the cerebral white matter.

Section snippets

Prior work

The clustering of different fiber tracts into an anatomically coherent bundle, like the CC or the CST, is a challenging task for several reasons. In the first place, as seen in Fig. 1, axons composing a bundle can diverge from it connecting cortical and subcortical areas. This renders approaches that quantify similarity among white matter fibers using the whole fiber instead of analyzing partial overlaps like shape statistics or rigid transformations (Veltkamp, 2001) unsuited for the clustering

Results

We applied the clustering and tract-querying procedure to a 21-subject database. In order to provide qualitative assessment, we show the results of our clustering and tract-querying algorithms for 2 different selected subjects in Fig. 9. In this figure, we note that tracts obtained by means of our clustering-querying procedures are consistent with manually obtained tracts by experts in diffusion MRI images (Wakana et al., 2004, Figs. 3, 4, and 5) and macroscopical preparations (Lawes et al.,

Discussion

Results showed that our clustering and tract-querying method automatically differentiates white matter fiber bundles consistently across subjects. Furthermore, results demonstrate that we are able to identify white matter structures that agree with several works which manually perform white matter fiber bundle identification. Firstly, results of individual subjects are consistent with manually obtained tracts by experts (Wakana et al., 2004) and macroscopical preparations (Lawes et al., 2008).

Conclusion

We presented a mathematical framework to perform statistical operations on white matter fibers obtained from diffusion tensor MRI tractography. In doing so, we showed that this framework constitutes an inner product space that is appropriate for performing statistical operations among white matter bundles. We used this framework to build a clustering algorithm and a tract-querying algorithm, which allow automatic fiber bundle identification with the white matter queries as a sole parameter.

Acknowledgments

This work was partly supported by the INRIA ARC Diffusion MRI Program, the CORDI-S INRIA program, and the Odyssée-EADS Grant 2118. Ragini Verma and Luke Bloy acknowledge support from the NIH grants R01MH079938 and T32-EB000814, respectively. The data were acquired as part of the NIH grant R01MH060722. Demian Wassermann wants to acknowledge Rebecca Wolpin for English language editing and Romain Veltz for helpful discussions.

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Unsupervised white matter fiber clustering and tract probability map generation: Applications of a Gaussian process framework for white matter fibers

Abstract

Introduction

Section snippets

Prior work

Results

Discussion

Conclusion

Acknowledgments

J. Magn. Res. B

Biophys. J.

NeuroImage

Lancet Neurol.

MIA

NeuroImage

NeuroImage

NeuroImage

J. Psych. Res.

NeuroImage

NeuroImage

MIA

NeuroImage

Magn. Reson. Imaging

NeuroImage

NeuroImage

NeuroImage

In vivo fiber tractography using DT-MRI data

Magn. Reson. Med.

Quantification of the shape of fiber tracts

MRM

Optimal Statistical Decisions

Regularized, fast and robust analytical q-ball imaging

MRM

Deterministic and probabilistic tractography based on complex fiber orientation distributions

Trans. Med. Imag.