Integral Equation-Based Inverse Scattering and Coil Optimization in Magnetic Resonance Imaging

Abstract

One trend in Magnetic Resonance Imaging (MRI) over the years has been to steadily increase the static magnetic field strength and hence the frequency of operation, resulting in higher available signal-to-noise ratio that could be traded for shorter scan times and increased image quality. In the ultra-high field regime (≥7T), since the radiofrequency wavelength is comparable to the dimensions of body, quasi-static approaches cannot be used to simulate the interactions between electromagnetic field and biological tissue, which can result in unwanted energy deposition hot spots and in decreased image quality. The electrical properties of tissue (permittivity and conductivity) influence these interactions and the RF field distributions inside of the body. Although undesirable from the point of view of coil and pulse design, this dependence on EP opens the door to new imaging modalities using the same MR data. In this thesis, I detail how we applied highly accurate integral equation formulations to the tasks of 3D electrical properties estimation (inverse scattering) and parallel transmit (pTx) coil array optimization. I also present novel regularization strategies that are ideally suited for inverse problems. I also discuss how we validated these approaches with numerical examples, and the efforts that we undertook to estimate electrical properties of a phantom using data from an MR scanner.