Jing-Rebecca Li: Towards relating diffusion MRI signal to tissue properties

We model the bulk magnetization of a tissue sample under the influence of a diffusion magnetic gradient field by the Bloch-Torrey partial differential equation posed on a domain with two (intra and extra-cellular) compartments connected by infinitely thin permeable membranes. We solve the PDE by coupling a mass-conserving finite volume discretization in space with a stable time discretization using an explicit Runge-Kutta-Chebyshev method.

We are able to obtain reasonably accurate numerical solutions in short computational time, making this method a good candidate as the forward solver in the inner iterative loop of an inverse problem solver going from signals to biological parameters. If time permits, I will briefly touch on the inverse problem.