Modified geodesic ray-tracing for diffusion tensor imaging

In this paper we develop a modified ray-tracing algorithm for geodesic tractography in the context of brain Diffusion Tensor Imaging (DTI). Our technique is based on computing multi-valued geodesics connecting two given points and tracking the evolution of adjacent geodesics. In order to do so we introduce a new Riemannian metric given by the adjugate sharpened diffusion tensor, combined with a constraint on the tracts outcome based on the geodesic deviation. We present tractography results, and compare our method with the existing ray-tracing approach and deterministic streamlining. Our preliminary results show an improved performance of modified ray-tracing regarding false positive fibers. We also show experiments on subcortical short association U-fibers, whose reconstruction is well-known to be hard in a DTI setting

An innovative geodesic based multi-valued fiber-tracking algorithm for diffusion tensor imaging

We propose a new geodesic based algorithm for fiber tracking in diffusion tensor imaging data. Our algorithm computes the multi-valued solutions from the Euler-Lagrange form of the geodesic equations. Compared to other geodesic based approaches, multi-valued solutions at each grid point are computed rather than just computing the viscosity solution. This allows us to compute fibers in a region with sharp orientation, or when the correct physical solution is not the fiber computed from the first arrival time. Compared to the classical stream-line approach, our method is less sensitive to noise, since the complete tensor is used. We also compare our algorithm with the Hamilton-Jacobi equation (HJ) based approach. We show that in the cases where U-shaped bundles appear, our algorithm can capture the underlying fiber structure while other approaches may fail. The results for synthetic and real data are shown for both methods

Riemann-Finsler multi-valued geodesic tractography for HARDI

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

Riemann-Finsler multi-valued geodesic tractography for HARDI

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