The computational simulation of brain connectivity using diffusion tensor MRI

Qiang Yu, Fa Wang Liu, Ian Turner, Viktor Vegh

Abstract


Water molecule diffusion in the brain is measured using a magnetic resonance imaging method. The anisotropy of the diffusion tensor is of particular interest in brain images, as it relates to white matter fibre tracts. Depending on the interrelation of eigenvalues, diffusion can be divided into the three cases of linear diffusion, planar diffusion and spherical diffusion. We present additional information from the (brain image) diffusion tensor magnetic resonance imaging of a patient with Parkinson's disease. This information includes maps of diffusion tensor components, fractional anisotropy and an fractional anisotropy weighted colour coded orientation. We also investigate linear diffusion, time fractional diffusion, and space fractional diffusion, as well as proposing computational simulations of connectivity in the brain using numerical methods for the analysis of diffusion tensor magnetic resonance imaging.

References
  • P. G. Batchelor, D. L. G. Hill, F. Calamante and D. Atkinson, Study of connectivity in the brain using the full diffusion tensor from DT-MRI. Proceedings of Information Processing in Medical Imaging IPMI, 2082: 121--133, 2001.
  • E. R. Melhem, S. Mori, G. Mukundan, M. A. Kraut, M. G. Pomper and P. C. M. van Zijl, Diffusion Tensor MR Imaging of the Brain and White Matter Tractography, American Journal of Roentgenology, 178: 3--16, 2002. http://www.ajronline.org/cgi/content/full/178/1/3.
  • A. Leemans, Modeling and processing of diffusion tensor magnetic resonance images for improved analysis of brain connectivity. PhD thesis, University of Antwerp, Belgium, 2006.
  • S. Mori, Introduction to Diffusion Tensor Imaging. Elsevier B.V., 2007.
  • M. Sarntinoranont, X. Chen, J. Zhao and T. H. Mareci, Computational model of interstitial transport in the spinal cord using diffusion tensor imaging. Annals of Biomedical Engineering, 34(8): 1304--1321, 2006.
  • F. Liu, V. Anh, I. Turner Numerical solution of the space fractional Fokker-Planck equation. Journal of Computational and Applied Mathematics, 166: 209--219, 2004. doi:10.1016/j.cam.2003.09.028
  • R. Magin, X. Feng, D. Baleanu, Solving the fractional order Bloch equation, Concepts in Magnetic Resonance Part A, 34A(1): 16--23, 2009.
  • P. Zhuang, F. Liu, V. Anh and I. Turner, New solution and analytical techniques of the implicit numerical methods for the anomalous sub-diffusion equation. SIAM J. on Numerical Analysis, 46(2): 1079--1095, 2008. doi:10.1137/060673114
  • Z. Zhao, Z. G. Yu, V. V. Anh, Topological properties and fractal dimension of the Sierpinske and generalized Sierpinski networks. Commun. Frac. Calc., 1: 15--26, 2010.
  • M. P. Velasco, J. Trujillo, D. A. Reiter, R. G. Spencer, W. Li, and R. L. Magin, Anomalous Fractional Order Models of NMR Relaxation. Proceedings of Fractional Differentiation and its Applications FDA'10, FDA10-058, 2010.
  • R. Metzler and J. Klafter, The random walk°Øs guide to anomalous diffusion: A fractional dynamics approach, Phys. Rep., 339: 1--77, 2000. doi:10.1016/S0370-1573(00)00070-3
  • M. Ledoux, The Geometry of Markov Diffusion Generators, Annales de la Facult°‰e des Sciences de Toulouse, 6(9): 305--366, 2000.

Keywords


fractional calculus; numerical method; diffusion tensor; MRI; fractional anisotropy

Full Text:

PDF BibTeX


DOI: http://dx.doi.org/10.21914/anziamj.v52i0.3931



Remember, for most actions you have to record/upload into this online system
and then inform the editor/author via clicking on an email icon or Completion button.
ANZIAM Journal, ISSN 1446-8735, copyright Australian Mathematical Society.