Riemann-Finsler multi-valued geodesic tractography for HARDI

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We introduce a geodesic based tractography method for High Angular Resolution Diffusion Imaging (HARDI). The concepts used are similar to the ones in geodesic based tractography for Diffusion Tensor Imaging (DTI). In DTI, the inverse of the second-order diffusion tensor is used to define the manifold where the geodesics are traced. HARDI models have been developed to resolve complex fiber populations within a voxel, and higher order tensors (HOT) are possible representations for HARDI data. In our framework, we apply Finsler geometry, which extends Riemannian geometry to a directionally dependent metric. A Finsler metric is defined in terms of HARDI higher order tensors. Furthermore, the Euler-Lagrange geodesic equations are derived based on the Finsler geometry. In contrast to other geodesic based tractography algorithms, the multi-valued numerical solution of the geodesic equations can be obtained. This gives the possibility to capture all geodesics arriving at a single voxel instead of only computing the shortest one. Results are analyzed to show the potential and characteristics of our algorithm.
Original languageEnglish
Title of host publicationVisualization and Processing of Tensors and Higher Order Descriptors for Multi-Valued Data
EditorsC.F. Westin, A. Vilanova, B. Burgeth
Place of PublicationBerlin
Number of pages17
ISBN (Electronic)978-3-642-54301-2
ISBN (Print)978-3-642-54300-5
Publication statusPublished - 2014

Publication series

NameMathematics and Visualization
ISSN (Print)1612-3786


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