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 (EM) simulations is computationally prohibitive, particularly for massive-element passive resonator arrays with many degrees of freedom.

While EM and RF circuit co-simulation methods have previously been applied to RF coil design, this work presents a co-simulation framework specifically tailored 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 B₁ fields in a targeted region of interest.

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.

To the best of our knowledge, this work represents the first systematic extension of the co-simulation methodology to passive resonator design, 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.