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

• Published in: NMR in biomedicine Vol. 30; no. 10
• Main Authors: Avdievich, N. I., Pfrommer, A., Giapitzakis, I. A., Henning, A.
• Format: Journal Article
• Language: English
• Published: England Wiley Subscription Services, Inc 01-10-2017
• Subjects: analytical model; array optimization; Biological products; Circuits; Decoupling; Dependence; Electricity; Evaluation; Green's functions; Humans; Impedance matrix; Inductance; Magnetic Fields; Magnetic Resonance Imaging; Mathematical analysis; Mathematical models; Modelling; Models, Theoretical; Mutual coupling; Phantoms, Imaging; Phased arrays; Quadratures; Reproducibility of Results; Signal to noise ratio; Solvers; transceiver arrays; ultrahigh‐field MRI; impedance matrix; ultrahigh-field MRI; transceiver arrays; analytical model; array optimization; decoupling
• ISSN: 0952-3480; 1099-1492
• DOI: 10.1002/nbm.3759

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.
For the evaluation of coupling between elements of transmit arrays at ultrahigh fields (≥7 T), an analytical model based on dyadic Green's functions was developed and validated. It describes the impedance matrix for two rectangular loops placed on a cylindrical surface. Based on the modeling, a two‐loop transceiver array was optimized at 400 MHz, such that, by simply overlapping the loops, both the mutual inductance and the mutual resistance were compensated. By providing quick coupling assessment, the modeling can significantly accelerate array optimization.