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

Abstract

Ultrahigh-field (UHF) (≥7 T) transmit (Tx) human head surface loop phased arrays improve both the Tx efficiency (B /√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.

Decoupling of a tight‐fit transceiver phased array for human brain imaging at 9.4T: Loop overlapping rediscovered

“…Under the condition of weak coupling ( k m Q L , k e < < 1), S 12 can be evaluated as where Q L is a loaded Q‐factor. We also demonstrated previously that the mutual inductance M and thus the magnetic coupling k m is almost independent of changes in the frequency and loading, the latter is determined by the distance to the phantom. At the same time, k m strongly depends on the loop size .…”

“…We also demonstrated previously that the mutual inductance M and thus the magnetic coupling k m is almost independent of changes in the frequency and loading, the latter is determined by the distance to the phantom. At the same time, k m strongly depends on the loop size . Conversely, the electrical coupling revealed a very strong dependence on both the frequency and the distance.…”

“…Previously, to describe the magnetic, k m , and resistive (electric), k e , coupling between two rectangular wire loops, we used a full‐wave analytical model based on dyadic Green's functions . In this model, two rectangular wire loops were placed on the cylindrical surface (holder) and loaded with an infinitely long cylindrical phantom positioned symmetrically inside the holder.…”

“…In this work, we optimized the geometry and the relative positioning of the loops to simultaneously minimize both the resistive and the inductive coupling using analytical modeling of the impedance matrix of a pair of loops . Based on the optimization results, we constructed a single‐row tight‐fit eight‐element (1 × 8) human head transceiver array using overlapped loops at 9.4T (400 MHz).…”

The ultimate intrinsic signal‐to‐noise ratio of loop‐ and dipole‐like current patterns in a realistic human head model

“…The vector functions and are fundamental solutions to the Helmholtz equation in cylindrical coordinates and were already defined and discussed in Ref. . The boundary coefficients , and are specified in the supporting information in Equations S27‐S30.…”