Implementation of the MR tractography visualization kit based on the anisotropic Allen-Cahn equation

Pavel Strachota

Kybernetika (2009)

  • Volume: 45, Issue: 4, page 657-669
  • ISSN: 0023-5954

Abstract

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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.

How to cite

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Strachota, Pavel. "Implementation of the MR tractography visualization kit based on the anisotropic Allen-Cahn equation." Kybernetika 45.4 (2009): 657-669. <http://eudml.org/doc/37726>.

@article{Strachota2009,
abstract = {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.},
author = {Strachota, Pavel},
journal = {Kybernetika},
keywords = {Allen–Cahn equation; anisotropic diffusion; finite volume method; MR–DTI; MR tractography; medical visualization; finite volume method; Allen-Cahn equation; anisotropic diffusion; MR-DTI; MR tractography; medical visualization},
language = {eng},
number = {4},
pages = {657-669},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Implementation of the MR tractography visualization kit based on the anisotropic Allen-Cahn equation},
url = {http://eudml.org/doc/37726},
volume = {45},
year = {2009},
}

TY - JOUR
AU - Strachota, Pavel
TI - Implementation of the MR tractography visualization kit based on the anisotropic Allen-Cahn equation
JO - Kybernetika
PY - 2009
PB - Institute of Information Theory and Automation AS CR
VL - 45
IS - 4
SP - 657
EP - 669
AB - 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.
LA - eng
KW - Allen–Cahn equation; anisotropic diffusion; finite volume method; MR–DTI; MR tractography; medical visualization; finite volume method; Allen-Cahn equation; anisotropic diffusion; MR-DTI; MR tractography; medical visualization
UR - http://eudml.org/doc/37726
ER -

References

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