Jan-Gerd Tenberge1 and Patrick Schiffler1
1University of Münster, Münster, Germany
Synopsis
We present a GPU-accelerated method to compute a structural connectome of the human brain with voxel-level resolution from diffusion weighted images.Introduction
The analysis of white matter properties has been increasingly important in multiple sclerosis research. White matter integrity is most often analysed on a per-voxel or per-region basis of diffusion parameters. It is known that patients suffering from MS also have a decreased network efficiency [3], which was also shown by graph analysis on the ROI-level.
Recent advancements in network analysis and computer science now allow us to study graph efficiency and whole-brain structural connectivity with voxel-level resolution. We present an approach to generate voxel-by-voxel connectivity maps from diffusion weighted images using a GPU implementation of the Bellman–Ford algorithm and a voxel-to-voxel connectivity score based on diffusion tensor estimates.
Methods
Diffusion weighted images were aquired on a Siemens MAGNETOM Prisma with a resolution of 1.8 x 1.8 x 1.92 mm and diffusion tensor estimation was performed with dtifit, part of the FSL toolbox. A binary brain mask is applied and thresholding based on the fractional anisotropy is performed. The remaining voxel's tensor data is copied to the GPU where we run the Bellman–Ford using each image voxel as a seed point, creating a whole-brain connectivity map. The path-finding algorithm is implemented in OpenCL and be run on either the CPU or GPU.
For the path finding algorithm we define the connectivity of two neighbouring voxels at positions v_i, v_j with diffusion tensors $$$D_i, D_j$$$ to be $$c_{ij} = c_{ji} = a_{ij}\, \text{norm}(D_i + D_j)\,a_{ji}$$ where $$$a_{ij} = v_i - v_j$$$ and $$$\text{norm}(D)$$$ is the normalisation of the tensor given by $$$D/\text{trace}(D)$$$. This is an adaption of the method presented in [2].
The connectivity matrix is written to disk in a format compatible with Stijn van Dongen's mcl clustering toolkit [1]. Clustering of the voxels is performed through mcl and the matrix is re-ordered to display voxels of the same cluster in adjacent rows and columns. The order of rows and columns is identical.
Results
Areas of densely interconnected voxels can easily be seen near the diagonal of the matrix, whereas pathways connecting these areas are visible as clusters of high connectivity further off the diagonal. The pairwise occurence of similar sized clusters hints at similar structures in both hemispheres of the brain.
Discussion
The presented approach opens up new possibilities in the analysis of network integrity in the brain. The size of the output matrices, which are $$$O(n^2)$$$, n being the number of voxels in the input image, makes them difficult to work with but we expect to overcome this limitation by employing GPU-accelerated graph analysis frameworks in the future. Even without further processing we will investigate changes in the size and intra-cluster connectivity scores and their association with progressing multiple sclerosis.
Acknowledgements
No acknowledgement found.References
[1] Stijn van Dongen, Graph Clustering by Flow Simulation. PhD thesis, University of Utrecht, May 2000
[2] Everts, Maarten H., Henk Bekker, and Jos BTM Roerdink. "Visualizing white matter structure of the brain using Dijkstra's algorithm." Image and Signal Processing and Analysis, 2009. ISPA 2009. Proceedings of 6th International Symposium on. IEEE, 2009.
[3] Shu, Ni, et al. "Diffusion tensor tractography reveals disrupted topological efficiency in white matter structural networks in multiple sclerosis." Cerebral Cortex 21.11 (2011): 2565-2577.