Fast Electromagnetic and RF Circuit Co-Simulation for Passive Resonator Field Calculation and Optimization in MRI

Passive resonators have been widely used in MRI to manipulate RF field distributions. However, optimizing these structures using full-wave electromagnetic simulations is computationally prohibitive, particularly for large passive resonator arrays with many degrees of freedom. This work presents a co-simulation framework tailored specifically for the analysis and optimization of passive resonators. The framework performs a single full-wave electromagnetic simulation in which the resonator's lumped components are replaced by ports, followed by circuit-level computations to evaluate arbitrary capacitor and inductor configurations. This allows integration with a genetic algorithm to rapidly optimize resonator parameters and enhance the B1 field in a targeted region of interest (ROI). We validated the method in three scenarios: (1) a single-loop passive resonator on a spherical phantom, (2) a two-loop array on a cylindrical phantom, and (3) a two-loop array on a human head model. In all cases, the co-simulation results showed excellent agreement with full-wave simulations, with relative errors below 1%. The genetic-algorithm-driven optimization, involving tens of thousands of capacitor combinations, completed in under 5 minutes, whereas equivalent full-wave EM sweeps would require an impractically long computation time. This work extends co-simulation methodology to passive resonator design for first time, enabling the fast, accurate, and scalable optimization. The approach significantly reduces computational burden while preserving full-wave accuracy, making it a powerful tool for passive RF structure development in MRI.