The MRI signal (diffusion weighted) is the sum of the magnetization in a volume of cell tissue (a voxel). The magnetization at the scale of the cell microstructure can be modeled by a partial differential equation called the Bloch-Torrey equation. What makes the numerical solution of this equation difficult is the presence of complex interfaces (i.e., cell membranes) over which the solution is discontinuous. I will discuss the numerical solution of the direct problem of the Bloch-Torrey equation, and briefly mention some ideas for the inverse problem.