The Department of Applied Mathematics weekly seminar is given by scholars and researchers working in applied mathematics, broadly interpreted.
Title: High Fidelity MRI by Time Optimal Control
Abstract: Magnetic Resonance Imaging and Spectroscopy provide detailed images and information on the chemical composition of the human body combining a strong, static magnetic field B0, and a radio frequency (RF) field B1. Together, they act on the net magnetization vector through the Bloch equations, which constitute a system of partial differential equations.
Imperfect B0 and B1 fields impact the temporal evolution of the magnetization vector, influencing the entire MR measurement. Dedicated RF pulses can alleviate the effects of these imperfect fields. One example is the class of adiabatic RF pulses, but they come with limitations, including high RF amplitude, pulse duration, and adaptability.
To overcome these limitations, RF pulse design through optimal control has shown excellent results in terms of flexibility. In this approach, robustness to field inhomogeneities is the primary objective within the cost functional, with the Bloch equations serving as constraints that describe the underlying physics. This method results in an excellent efficiency of magnetization performance.
Using two examples, namely magnetization inversion for in vivo MRI, and robust excitation for 31P MRS, the outstanding characteristics of RF pulse design by optimal control are demonstrated.