On the discontinuous Galerkin solver for simulations of magnetization motion with flow transport

Flow magnetic resonance imaging (MRI) is a technique that allows the measurement of internal flow velocity fields with little interference, but its clinical application is still limited. Through computer simulations of the flow MRI based on the magnetization motion with flow transport, the MRI imaging artifacts can be analyzed, and post-processing techniques can be improved. In our previous study, we highlighted the advantages of Eulerian-based solvers using Cartesian grids for tracking magnetization transport. Therefore, in this paper, we extend the computational simulation solver to unstructured grids using the discontinuous Galerkin method (DGM), demonstrating its applicability through two-dimensional numerical examples. Computational domains containing static tissue and fluid regions with prescribed flow velocities were represented as a set of triangular elements. In it, the magnetization motion (excitation, precession, relaxation and flow transport) was spatially discretized by DGM and solved in a step-by-step manner under practical external magnetic field controls for flow velocity measurement, with the resulting magnetization distribution compared with analytical solutions. A numerical example of the Hagen-Poiseuille flow showed excellent agreement between the numerical and analytical solutions. In the backstep flow example, the numerical solution also exhibited excellent agreement to the analytical one, although the appearance of imaging artifacts varies depending on the scan parameters. These results demonstrate the applicability of the developed solver in simulating magnetization motion with flow transport in flow MRI.