Abstract
Geodesic tractography is an elegant, though typically time consuming method for finding connections or ‘tracks’ between given endpoints from diffusion-weighted MRI images, which can be representative of brain white matter fibers. In this work we consider the problem of constructing bundles of tracks between seed and target regions in the most efficient way. In contrast to streamline based methods, a naive region-to-region geodesic approach for finding the true bundle requires connecting all pairs of voxels in seed and target regions and then selecting the appropriate tracks. The running time of this approach is quadratic in the number of voxels, which is prohibitively long for clinical use. Moreover, matching full seed and target regions may include voxels that are not part of the target bundle, e.g. due to segmentation inaccuracies. In order to bring geodesic tractography closer to clinical applicability, we present a novel, efficient algorithm for region-to-region geodesic tractography which extends existing point-to-point algorithms and incorporates anatomical knowledge by assuming a topographic organization of fibers. The proposed method connects only seed and target voxels that belong to the target bundle, based on iterative refinement of a Delaunay tessellation of sample points. In addition, it can be used in combination with any point-to-point tractography algorithm. A theoretical analysis shows that, under reasonable assumptions, our algorithm is significantly more efficient than the quadratic-time solution. This is also confirmed by the experiments, which reveal a reduction in computation time of up to three orders of magnitude.
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Notes
- 1.
For simplicity we present the algorithm for two sets of equal size n, but this can be replaced by sets of different sizes \(n_1\) and \(n_2\) by minor adjustments.
- 2.
To regularize the tessellation near the domain boundary, we add a band of ‘dummy’ sample points around the sampling domains to avoid ‘overstretching’ tetrahedra. These samples are not used to construct any tracks and are always labeled ‘−’, and are solely used for the construction of the Delaunay tessellation.
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Acknowledgements
This work is part of the research programme Diffusion MRI Tractography with Uncertainty Propagation for the Neurosurgical Workflow with project number 16338, which is (partly) financed by the Netherlands Organisation for Scientific Research (NWO). The work of A. Fuster is part of the research program of the Foundation for Fundamental Research on Matter (FOM), which is financially supported by the Netherlands Organisation for Scientific Research (NWO). We would like to thank the department of Neurosurgery at the Elisabeth TweeSteden Hospital (ETZ) in Tilburg, The Netherlands, for acquiring the clinical data set used in our experiments. Use of patient data was approved by the local ethics committee (METC Brabant).
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Smolders, L., Sengers, R., Fuster, A., de Berg, M., Florack, L. (2021). A Novel Algorithm for Region-to-Region Tractography in Diffusion Tensor Imaging. In: Cetin-Karayumak, S., et al. Computational Diffusion MRI. CDMRI 2021. Lecture Notes in Computer Science(), vol 13006. Springer, Cham. https://doi.org/10.1007/978-3-030-87615-9_7
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