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General Coupling Matrix Synthesis for Decoupling MRI RF Arrays

Multi-channel radio-frequency (RF) arrays, composed of multiple resonant coils, provide significant benefits for MRI during both signal reception (receive) and excitation (transmit). Demonstration of increased signal-to-noise ratio (SNR) and acceleration factors during parallel acquisitions has lead to the development of receive arrays. Conversely, transmit arrays have demonstrated considerable potential for mitigating excitation inhomogeneity arising at ultra-high magnetic field strengths ( ≥ 7 T), present due to wave-like interactions inside the sample. Due to geometric constraints, the design of both receive and transmit arrays requires the resonating coils to be closely spaced. Significant overlap in the near-field distributions from each coil results in coupling. Without an adequate decoupling strategy applied between individual elements in an RF array, the MRI performance of the array can be significantly degraded. This work presents a method to design decoupling networks for arbitrarily large RF arrays based on direct synthesis of a coupling matrix. Reflection coefficients are fitted to transfer polynomials with transmission coefficients simultaneously minimized through a nonlinear optimization. The method demonstrates the design of nth-order distributed filters and lumped element networks that compensate for all first-order and cross-coupling terms arising in an RF array suitable for MRI. The synthesis results are computed for 4-, 8-, and 32-channel RF arrays. Monte Carlo analyses and experimental results for two RF array constructions demonstrate the robustness of this approach.