Efficient simulation of magnetic resonance imaging with Bloch-Torrey equations using intra-voxel magnetization gradients

The process of image formation in magnetic resonance imaging (MRI) can be simulated by means of an iterative solution of Bloch-Torrey equations. This is a useful accessory to analyze the influence of sample properties, sequence parameters and hardware specifications on the MRI signal. In this paper, a computer algorithm is presented which is based on calculating partial derivatives of the magnetization vector. This technique allows more efficient simulation than summation of isochromats (the latter being commonly employed for this purpose) and, as a result, the effect of diffusion on the MRI signal can be calculated iteratively. A detailed description of the algorithm is given, and its feasibility for different applications is studied. It is shown that the algorithm is most applicable to simulating the effect of field perturbations, i.e. intra-voxel dephasing, but is also useful for other typical imaging experiments and the simulation of diffusion weighting.