Design of Distributed Spiral Resonators for the Decoupling of MRI Double-Tuned RF Coils

Abstract

A systematic analytical approach to design Spiral Resonators (SRs), acting as distributed magnetic traps (DMTs), for the decoupling of Double-Tuned (DT) RF coils suitable for Ultra-High Field (7 T) MRI is presented. Methods: The design is based on small planar SRs placed in between the two RF loops (used for signal detection of the two nuclei of interest). We developed a general framework based on a fully analytical approach to estimate the mutual coupling between the RF coils and to provide design guidelines for the geometry and number of SRs to be employed. Starting from the full-analytical estimations of the SRs geometry, electromagnetic simulations for improving and validating the performance can be carried out. Results and Conclusion:We applied the method to a test case of a DT RF coil consisting of two concentric and coplanar loops used for 7 T MRI, tuned at the Larmor frequencies of the proton ( 1 H, 298 MHz) and sodium ( 23 Na, 79 MHz) nuclei, respectively. We performed numerical simulations and experimental measurements on fabricated prototypes, which both demonstrated the effectiveness of the proposed design procedure. Significance: The decoupling is achieved by printing the SRs on the same dielectric substrate of the RF coils thus allowing a drastic simplification of the fabrication procedure. It is worth noting that there are no physical connections between the decoupling SRs and the 1 H/ 23 Na RF coils, thus providing a mechanically robust experimental set-up, and improving the transceiver design with respect to other traditional decoupling techniques.

An Accurate Equivalent Circuit Model of Metasurface-Based Wireless Power Transfer Systems

“…It may be worth noticing that the slab presence drastically changes the behavior of the mutual coupling between driver and receiver. Indeed, the Z21 parameter for a conventional configuration without the metasurface would be a classical inductive term: its insertion modifies this term, making it resonant with the appearance of an additional real component [36].…”

“…This can be achieved not only by Lx maximization, but also through the mutual coefficients Zij between unit-cells. For a typical planar configuration where unit-cells lay adjacent, the mutual coefficients Zij are purely reactive and negative [36].…”

Analytical Approach for MRI RF Array Coils Decoupling by Using Counter-Coupled Passive Resonators

“…As already described in [34], under magneto-static hypothesis, we can apply the Biot-Savart formulation to estimate the mutual coupling between two generic RF coils [35], [36]. Indeed, the main contribution to mutual coupling at the MRI frequencies is the inductive one [37].…”

“…Thus, from a circuital point of view, we can consider globally only a filtering element between two adjacent RF coils (respectively, numbered 4 and 5 in Fig. 2); obviously, the relative terms in the circuital equations have to be multiplied by the number of independent unit-cells N present between two adjacent RF coils [34]. Therefore, the entire system equations can be written as: In particular, we have condensed the two equations corresponding to the filter unit-cells 4 and 5 into a single condition (from now on, numbered 4), thanks to the previously observed symmetries.…”

“…In this paper, we introduce a novel analytical framework to analyze the complex interactions between all the elements of an MRI array and to design an opportune filter for their decoupling using passive counter-coupled resonators as unitcells. A related approach was first presented in [32]- [34] for the simple case of two concentric RF loops in a Dual Tuned configuration ( 1 H/ 23 Na). Here, we generalize such approach, modeling and also considering the coupling between nextnearest neighbors coils pairs, as required for typical phased arrays.…”