Numerical Solution of the Bloch-Torrey Equation Applied to the DMRI of Biological Tissue
Donna Calhoun, Jing-Rebecca Li
SIAM Conference on Computational Science and Engineering, Society for Industrial and Applied Mathematics, Boston, MA (Mini-symposium speaker) Feb 25 - Mar 01, 2013
We propose a numerical method to solve the Bloch-Torrey partial differential equation in multiple diffusion compartments to simulate the bulk magnetization of a sample under the influence of a diffusion gradient. We couple a mass-conserving finite volume discretization in space with a stable time discretization using an explicit Runge-Kutta-Chebyshev method. We are able to solve the Bloch-Torrey PDE in multiple compartments for an arbitrary diffusion sequence with reasonable accuracy for moderately complicated geometries in computational time that is on the order of tens of minutes per bvalue on a laptop computer. We show simulation results for nearly isotropic as well as anistropic diffusion, for the PGSE as well cosine OGSE sequences.