Bloch simulations with intra-voxel spin dephasing

A common problem in simulations of MRI-experiments based on the numerical solution of the Bloch equations is the finite number of isochromats used in the calculations. This usually results in false or spurious signals and is a source of various differences between calculated and experimentally obtained data. In this paper, we are proposing a technique representing each sample voxel by a central and three additional isochromats, slightly shifted in orthogonal directions from center, thus providing a linear approximation of intra-voxel dephasing. This approach allows for further improvement and precision of the calculated NMR signal and virtually avoids the problem related to an finite set of isochromats. Here we provide details of the algorithm together with examples of simulations which prove the efficiency of this approach.