With recent advancements of image reconstruction techniques, magnetic resonance imaging (MRI) can produce real-time images at a temporal resolution of 10 to 40 ms to observe complex physiological processes and also serves as a powerful tool for quantitative studies. However, a comprehensive quantitative understanding of the mechanisms that lead to MRI signal alterations when imaging flowing spins or other dynamic processes is still lacking. This thesis aims at the quantitative analysis of dynamic signal changes using modeling and numerical simulation of Bloch equations for MRI with a special focus on flow. To this end, a numerical simulator was developed for spatially stationary objects and was extended further for flowing objects. Operator splitting approaches were used extensively for the development of the simulator. Parallelizing with graphical processing unit (GPU) computations resulted in a significant reduction in the simulation time. Simulation methods were tested against in vitro experiments with static phantom and fluid flow. The simulated results support the experimental evidence of remarkable sensitivity of signal magnitude to slow flow. Also, the results hint at the possibility of computer-aided estimation of experimental parameters like flow velocity or relaxation time constants, which can cater for the growing demand in MRI for estimation of clinically relevant quantitative informations.
