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 semi-discretization 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.

Mean and standard deviation velocities and Re based on the mean velocity for diferent operating voltages of the Ćow pump at temperature 16 • C (kinematic viscosity ν = 1.1092 × 10 −2 cm 2 /s [137]). . . . . . . . . and magnetic gradient Ąelds. Altering this pattern, which is commonly known as a MRI pulse sequence, it is possible to exploit a wide range of contrast mechanisms including access to physiological functions such as difusion, Ćow, blood oxygenation, cellular metabolism and tissue temperature. Therefore, MRI is not restricted to a qualitative description of anatomy, but also serves as a powerful tool for interventional, functional, metabolic and quantitative studies, which have a huge signiĄcance in diagnostic imaging.