On the Extension of MARIE Coil Simulation to Low Frequencies and Arbitrarily Fine Meshes

Motivation: Accurate and precise simulation of low field MR, as well as simulation of high field MR with arbitrary granularity. Goal(s): To assess and address the limitations in the Magnetic Resonance Integral Equation (MARIE) suite that prevent successful low field simulation. Approach: We achieved these goals using a number of numerical analysis techniques, such as Taylor series approximations and Kahan summation. Results: We successfully identified and addressed the limitations of MARIE, which we attributed to catastrophic loss of numerical precision. In doing so, we enabled low frequency and fine mesh simulation. Impact: Low field and detailed simulation of coils would enable many applications, such as coil optimization, synthetic generation of MR data for machine learning algorithms, computational pulse sequence optimization, accurate safety assessments in simulation, among many other applications.