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

Purpose: Passive resonators have been widely used in MRI to manipulate RF field distributions. However, optimizing these structures using full-wave electromagnetic (EM) simulations is computationally prohibitive, particularly for massive-element passive resonator arrays with many degrees of freedom.

Methods: While the EM and RF circuit co-simulation method has previously been applied to RF coil design, this work presents, for the first time, a co-simulation framework tailored specifically for the analysis and optimization of passive resonators. The framework performs a single full-wave EM simulation in which the resonator's lumped components are replaced by ports, followed by circuit-level computations to evaluate arbitrary capacitor/inductor configurations. This allows integration with a genetic algorithm to rapidly optimize the resonator parameters to enhance $B_1$ fields in a targeted region of interest (ROI).

Results: The proposed method was validated across three scenarios of increasing complexity: (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 EM 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.

Conclusion: This work extends co-simulation methodology to passive resonator design for the first time, enabling 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.