Jing Rebecca Li1, Donna Calhoun2, Chun-Hung Yeh3, Cyril Poupon4, Denis Le Bihan4
1INRIA-Saclay, Palaiseau Cedex , France; 2CEA, Saclay, France; 3National Yang-Ming University, Taiwan; 4CEA Neurospin, Saclay, France
We propose a numerical method for solving the Bloch-Torrey partial differential equation to compute the bulk magnetization of a sample under the influence of a diffusion gradient. We couple a mass-conserving finite element 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 rapidly and accurately, making it a reasonable candidate as the forward solver in the inner iterative loop of an inverse problem solver going from signals to biological parameters.