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Keywords:
Allen–Cahn equation; anisotropic diffusion; finite volume method; MR–DTI; MR tractography; medical visualization
Allen–Cahn equation; anisotropic diffusion; finite volume method; MR–DTI; MR tractography; medical visualization
Summary:
Magnetic Resonance Diffusion Tensor Imaging (MR–DTI) is a noninvasive in vivo method capable of examining the structure of human brain, providing information about the position and orientation of the neural tracts. After a short introduction to the principles of MR–DTI, this paper describes the steps of the proposed neural tract visualization technique based on the DTI data. The cornerstone of the algorithm is a texture diffusion procedure modeled mathematically by the problem for the Allen–Cahn equation with diffusion anisotropy controlled by a tensor field. Focus is put on the issues of the numerical solution of the given problem, using the finite volume method for spatial domain discretization. Several numerical schemes are compared with the aim of reducing the artificial (numerical) isotropic diffusion. The remaining steps of the algorithm are commented on as well, including the acquisition of the tensor field before the actual computation begins and the postprocessing used to obtain the final images. Finally, the visualization results are presented.
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