Section: Software

BlochTorreyPDESolver

Participants : Jing-Rebecca Li [correspondant] , Dang Van Nguyen.

We developed numerical codes to solve the multiple compartment Bloch Torrey partial differential equation in 2D and 3D to simulate the bulk magnetization of a sample under the influence of a diffusion-encoding gradient magnetic field. We coupled a mass-conserving spatial discretization with a stable time discretization using an explicit Runge-Kutta-Chebyshev method and 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.

This code has been implemented in Fortran90, C++, as well as Matlab. A Matlab Toolbox with graphical user interface for the simulation of DMRI signals in 2D and 3D cellular geometries using this numerical method is being developed.

The version of the code using Finite Volume discretization on a Cartesian grid is complete (written by Jing-Rebecca Li). The version of the code using linear Finite Elements discretization is in the final testing phase (written by Dang Van Nguyen)

See the web page http://www.cmap.polytechnique.fr/~jingrebeccali/ for more details.