Abstract

The phase-contrast magnetic resonance imaging (PC-MRI) is a diagnostic tool capable of providing valuable insight into physiological and pathophysiological flows, but due to its multimodal acquisition process and large range of parameters, the sources of the intrinsic artifacts are challenging to distinguish. Furthermore, the physical principle of the PC-MRI (magnetization precession and relaxation), as described by the Bloch Equation, does not possess analytical solution in flow fields due to non-zero convective terms. This issue is often bypassed by the use of a Lagrangian approach, capable of solving for individual particles along the flow, but limited due to the high computational cost and reduced resolution. Thus, this study aims to develop a Eulerian approach to solve the Bloch equation in flow fields. The Bloch equation was discretized by the Discontinuous Galerkin Method (DGM) and solved in a step-by-step manner. Numerical examples of 1-dimensional magnetization motion in a constant velocity showed that the L2 relative errors of the numerical solution was below 1.5% when compared to a single particle trajectory, and below 1.9% when compared to a grid throughout the domain with low undershooting and overshooting observed at discontinuities.