Numerical Simulation of Bloch Equations for Dynamic Magnetic Resonance Imaging
For researchers in computational MRI, this provides a theoretical foundation and numerical method for simulating dynamic MRI with flow, but the results are preliminary and incremental.
The paper establishes well-posedness of the modified Bloch problem for flowing spins in MRI and analyzes its spatial semidiscretization using discontinuous Galerkin methods, demonstrating applicability on basic examples.
Magnetic Resonance Imaging (MRI) is a widely applied non-invasive imaging modality based on non-ionizing radiation which gives excellent images and soft tissue contrast of living tissues. We consider the modified Bloch problem as a model of MRI for flowing spins in an incompressible flow field. After establishing the well-posedness of the corresponding evolution problem, we analyze its spatial semidiscretization using discontinuous Galerkin methods. The high frequency time evolution requires a proper explicit and adaptive temporal discretization. The applicability of the approach is shown for basic examples.