Analytical simulation of motion in MRI using phase distribution graphs

Motivation: Motion is one of the most common sources of artifacts in MRI measurements. Phase distribution graphs (PDG) are the currently fastest method of simulating physically accurate signals. Support for motion brings it one step closer to reality. Goal(s): Derive an analytical solution for arbitrary phantom motion in PDG to accurately capture its influence on the measured signal. Approach: The spatially varying phase shift of the magnetization from the interplay of phantom movement and gradient trajectory of the MRI sequence was derived and integrated into the simulation. Results: Motion was simulated for different sequences and readouts, demonstrating their influence on the reconstructed image. Impact: PDG Bloch simulation is orders of magnitudes faster than isochromat solutions, produces physically correct signals and is fully differentiable. The introduction of motion brings the simulation even closer to reality and enables to include it in sequence development or optimization.