Active control of the spatial MRI phase distribution with optimal control theory

This paper investigates the use of Optimal Control (OC) theory to design Radio-Frequency (RF) pulses that actively control the spatial distribution of the MRI magnetization phase. The RF pulses are generated through the application of the Pontryagin Maximum Principle and optimized so that the resulting transverse magnetization reproduces various non-trivial and spatial phase patterns. Two different phase patterns are defined and the resulting optimal pulses are tested both numerically with the ODIN MRI simulator and experimentally with an agar gel phantom on a 4.7 T small-animal MR scanner. Phase images obtained in simulations and experiments are both consistent with the defined phase patterns. A practical application of phase control with OC-designed pulses is also presented, with the generation of RF pulses adapted for a Magnetic Resonance Elastography experiment. This study demonstrates the possibility to use OC-designed RF pulses to encode information in the magnetization phase and could have applications in MRI sequences using phase images.