"This research concentrates on two major engineering areas associated with biomedical instrumentation that have recently gained significant academic and industrial interest: the gradient coil design for Magnetic Resonance Imaging (MRI) and the high frequency full-wave field simulations with the Method of Moments (MoM). A new computational approach to the design of gradient coils for magnetic resonance imaging is introduced. The theoretical formulation involves a constrained cost function between the desired field in a particular region of interest in space and the current-carrying coil plane. Based on Biot-Savart’s integral equation, an appropriate weight function is introduced in conjunction with linear approximation functions. This permits the transformation of the problem formulation into a linear matrix equation whose solution yields discrete current elements in terms of magnitude and direction within a specified coil plane. These current elements can be synthesized into practical wire configuration by suitably combining the individual wire loops. Numerical predictions and measurements underscore the success of this approach in terms of achieving a highly linear field while maintaining low parasitic fields, low inductance and a sufficient degree of shielding. Experimental results confirm the field predictions of the computational approach. Extending the numerical modeling efforts to dynamic phenomena, a novel MoM formulation permits the computation of electromagnetic fields in conductive surfaces and in three-dimensional biological bodies. The excitation can be provided with current loops, voltage sources, or an incident electromagnetic wave. This method enables us to solve a broad spectrum of problems arising in MRI: full-wave RF coil simulations, eddy currents predictions in the magnet bore, and induced currents in the biological body. Surfaces are represented as triangles and the three-dimensional bodies are subdivided into tetrahedra. This numerical discretization methodology makes the approach very flexible to handle a wide range of practical coil geometries. Specifically, in this thesis the MoM is employed to study the effect of switching gradient coils in the presence of a biological load. "

In vivo pressure estimations for therapeutic ultrasound has the potential of rendering treatments using non-invasive ultrasound targeting safer and more reliable. By quantifying pressures and their respective spatial locations, better acoustic predictions and models can be made. In this thesis, we aim to measure a pressure field from a piezo-electric transducer through a ballistic gel medium by using an external gradient coil to encode the pressure field in a way that can be read and quantified using an MRI scanner. We describe the methods and the results pertaining to visualizing a pressure field. The setup was able to capture pressure field images and quantify low pressures, as compared to a hydrophone measurement, with maximum peaks of 100 kPa. We found that the confidence interval of the MRI estimated pressure to have a 95% confidence interval of 46 kPa as compared to the hydrophone measurement. We also showed that the MRI measurement setup had an accuracy of 5 kPa within 2 cm from the front of the transducer. The results showed that pressure fields could eventually be reconstructed with precision and accuracies close to that of a hydrophone equivalent acquisition. However, there are still many changes to the methodology that would need to be done.