Analytical modeling provides new insight into complex mutual coupling between surface loops at ultrahigh fields

Ultrahigh-field (UHF) (≥7 T) transmit (Tx) human head surface loop phased arrays improve both the Tx efficiency (B₁⁺ /√P) and homogeneity in comparison with single-channel quadrature Tx volume coils. For multi-channel arrays, decoupling becomes one of the major problems during the design process. Further insight into the coupling between array elements and its dependence on various factors can facilitate array development. The evaluation of the entire impedance matrix Z for an array loaded with a realistic voxel model or phantom is a time-consuming procedure when performed using electromagnetic (EM) solvers. This motivates the development of an analytical model, which could provide a quick assessment of the Z-matrix. In this work, an analytical model based on dyadic Green's functions was developed and validated using an EM solver and bench measurements. The model evaluates the complex coupling, including both the electric (mutual resistance) and magnetic (mutual inductance) coupling. Validation demonstrated that the model does well to describe the coupling at lower fields (≤3 T). At UHFs, the model also performs well for a practical case of low magnetic coupling. Based on the modeling, the geometry of a 400-MHz, two-loop transceiver array was optimized, such that, by simply overlapping the loops, both the mutual inductance and the mutual resistance were compensated at the same time. As a result, excellent decoupling (below -40 dB) was obtained without any additional decoupling circuits. An overlapped array prototype was compared (signal-to-noise ratio, Tx efficiency) favorably to a gapped array, a geometry which has been utilized previously in designs of UHF Tx arrays.