Elsevier

Medical Image Analysis

Volume 15, Issue 4, August 2011, Pages 414-425
Medical Image Analysis

A Hough transform global probabilistic approach to multiple-subject diffusion MRI tractography

https://doi.org/10.1016/j.media.2011.01.003Get rights and content

Abstract

A global probabilistic fiber tracking approach based on the voting process provided by the Hough transform is introduced in this work. The proposed framework tests candidate 3D curves in the volume, assigning to each one a score computed from the diffusion images, and then selects the curves with the highest scores as the potential anatomical connections. The algorithm avoids local minima by performing an exhaustive search at the desired resolution. The technique is easily extended to multiple subjects, considering a single representative volume where the registered high-angular resolution diffusion images (HARDI) from all the subjects are non-linearly combined, thereby obtaining population-representative tracts. The tractography algorithm is run only once for the multiple subjects, and no tract alignment is necessary. We present experimental results on HARDI volumes, ranging from simulated and 1.5T physical phantoms to 7T and 4T human brain and 7T monkey brain datasets.

Graphical abstract

(Left) Different possible curves are tested. (Middle) The highest-score curve is selected. (Right) The process is repeated for all the seed points.

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Research highlights

► Global probabilistic tractography based on the Hough transform is introduced. ► Local minima are avoided by an exhaustive search at the desired resolution. ► The technique is easily extended to multiple subjects. ► Results are presented on simulated and real 1.5T, 4T, and 7T HARDI datasets.

Introduction

Understanding the connectivity between different areas of the brain is essential in studying brain function and development. Diffusion-weighted magnetic resonance imaging (DWI) provides, through tractography, a unique in vivo quantitative measurement of the brain’s anatomical connectivity. In addition to its benefits in neurosurgical planning, DWI tractography has considerable clinical importance by noninvasively quantifying changes in the white matter connectivity at different stages of diseases or development. Moreover, it can be used to segment fiber bundles of the central nervous system, or in tract-based statistical analysis of scalars such as the fractional anisotropy (FA). Performing tractography in multiple subjects is invaluable for population studies and creating fiber bundle atlases.

DWI provides local information about the fiber orientation by measuring the diffusion of the tissue water, in vivo, assuming a high correlation between the fiber and diffusion orientations. However, there is no unique solution as to how to integrate these voxel-scale local orientations to infer global connectivity. Early fiber tractography algorithms, known as streamline methods, are based on following the principal diffusion orientation (Basser et al., 2000, Conturo et al., 1999, Jones et al., 1999, Lazar et al., 2003, Mori et al., 1999). Despite their simplicity, these methods are prone to cumulative errors caused by noise, partial volume effects, and discrete integration, and have difficulty in distinguishing fiber crossing and kissing mostly due to the fact that the entire diffusion information is not globally used and integrated. This led to the development of other successful approaches, including probabilistic techniques (Behrens et al., 2007, Björnemo et al., 2002, Descoteaux et al., 2009, Friman et al., 2006, Jones, 2008, Lazar and Alexander, 2005, Parker et al., 2003), global techniques based on front propagation (Campbell et al., 2005, Jackowski et al., 2005, Parker et al., 2002, Pichon et al., 2005, Prados et al., 2006, Tournier et al., 2003), simulation of the diffusion process or fluid flow (Batchelor et al., 2001, Hageman et al., 2009, Hagmann et al., 2003, Kang et al., 2005, O’Donnell et al., 2002, Yörük et al., 2005), DWI geodesic computations (Jbabdi et al., 2008, Lenglet et al., 2009a, Melonakos et al., 2007, Pechaud et al., 2009), graph theoretical techniques (Iturria-Medina et al., 2007, Sotiropoulos et al., 2010, Zalesky, 2008), spin glass models (Fillard et al., 2009, Mangin et al., 2002), and Gibbs tracking (Kreher et al., 2008). Generally speaking, for virtually every tractography method, a particular putative subset of all possible curves is implicitly considered from which the resulting tracts are chosen according to some criteria, which are different depending on the particular selection strategy. The closer the subset is to the universal set of curves, the more accurate we expect the results to be. For a recent thorough discussion on different tractography techniques, see (Behrens and Jbabdi, 2009).

Prior approaches for multi-subject tractography are typically based on the post-processing of tractography results from individual subjects (El Kouby et al., 2005, Jbabdi et al., 2009, Leemans et al., 2006, Maddah et al., 2006, O’Donnell and Westin, 2007, Voineskos et al., 2009, Wakana et al., 2004). These methods generally require aligning the tracts and mapping them into a common fiber coordinate system, which is challenging due to the large number of high-dimensional fiber trajectories per subject and the lack of clearly defined criteria for aligning curves and particularly tracts.

In this work, we present a global probabilistic approach inspired by the voting procedure provided by the popular Hough transform (Duda and Hart, 1972, Gonzalez and Woods, 2008). Our proposed tractography algorithm essentially tests candidate 3D curves in the volume, assigning a score to each of them, and then returning the curves with the highest scores as the potential anatomical connections. The score is accordingly derived from the DWI data. Being an exhaustive search, this proposed algorithm avoids entrapment in local minima within the discretization resolution of the parameter space.1 Furthermore, the specific definition of the candidate tract score has the desired effect of attenuating the noise through the integration of the real-valued local votes derived from the diffusion data. We also introduce a simultaneous multi-subject tractography technique which takes as input a single representative volume – where the HARDI data from all the (registered) subjects are non-linearly integrated – and generates population-representative tracts. The multi-subject tractography algorithm is run only once, and no tract alignment is necessary. We present experimental results on HARDI volumes such as a simulated phantom, a biological phantom dataset acquired at 1.5T, a monkey brain dataset acquired at 7T, and a number of human brain datasets acquired at 4T and 7T.2

In Section 2 we present the proposed algorithm in detail. Experimental results are presented in Section 3, and Section 4 concludes with a review of the contributions. Additional implementation details are provided in the Appendix.

Section snippets

Methods

We first randomly generate a sufficiently high number of initial seed points inside a brain mask or a region of interest. From each initial point, we consider as many passing curves as desired, based on the expected resolution and available computational resources (Fig. 1, left). A score is computed for each curve, and the one(s) with the maximum score is (are) then chosen as the best curve(s) representing the fiber bundle passing through that seed point (Fig. 1, middle & right).

Results for single subjects

We tested our method on various HARDI datasets, also using each of them to explain a different aspect of the proposed algorithm. The FA and the CSA-ODFs of each dataset were computed as explained in Section 2.2. The initial seed points were chosen randomly with a spatial probability distribution proportional to the FA, except for the simulated and the monkey brain datasets where the distribution was uniform.

To validate our approach, we first show results on artificial data and compare our

Conclusions

We have introduced a global approach for single- and multi-subject probabilistic tractography, based on the voting process provided by the Hough transform. We presented experimental results on a physical phantom and brain HARDI datasets, and showed that using this approach, data from multiple subjects can be non-linearly combined and exploited to obtain population statistics and more accurate tractography results. The incorporation of spatial coherence and continuity in curve score computation,

Acknowledgments

This work was partly supported by NIH (P41 RR008079, P30 NS057091, R01 HD050735, R01 EB007813, R01 MH060662, R01 EB008432, R01 EB008645, CON000000004051–3014, CON000000015793–3014, NLM T15 LM07356), NSF, ONR, NGA, ARO, DARPA, and the University of Minnesota Institute for Translational Neuroscience. Computing resources were provided by the University of Minnesota Supercomputing Institute, and the Laboratory of Neuro Imaging (UCLA). We would like to thank Jennifer Campbell of McGill University,

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