Radiofrequency pulse design through optimal control and model order reduction of the Bloch equation

Abstract

Magnetic resonance imaging (MRI) is a tool used mostly in the medical world for creating images of the human body for diagnosis. An advantage of MRI over other medical imaging modalities is that it does not require the use of ionizing radiation. Images are based on magnetization dynamics of hydrogen protons in the body. The dynamics indicate the type of biological tissue the protons are a part of. Radiofrequency (RF) pulses bring the magnetization into an excited state, where it generates a signal. The response of the magnetization to an RF pulse is described by the Bloch equation. Radiofrequency pulse design deals with the inverse problem of finding an RF pulse that transfers the magnetization to a desired state. Most pulse design methods invert the Bloch equation under some strict assumptions. The optimal control method allows for more freedom in pulse design, at the cost of requiring the repeated calculation of the magnetization dynamic. Calculating the magnetization dynamic is computationally costly, and so is the optimal control method as a consequence. Finding a method for model order reduction of the Bloch equation can greatly reduce the simulation time. Leading to a more efficient optimal control method.