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We introduce an analytical approach to design decoupling filters for MRI radiofrequency array elements, adopting counter-coupled passive resonators as unit-cells. Specifically, our method is based on a magneto-static hypothesis, thus a deep comprehension of the physical interactions between all the elements in the system and design guidelines can be achieved. In particular, the couplings between adjacent and next-nearest neighbors coils pairs are both modeled, hence addressing the requirements for MRI arrays. The analytically-obtained filter solution is subsequently refined resorting to targeted full-wave simulations, reducing the computational effort. To prove the validity of the proposed approach, we conceived a test-case consisting of three planar RF coils, tuned at the 7T proton Larmor frequency. We demonstrated through full-wave simulations that the analytical design method is accurate and effective. Moreover, we fabricated a prototype and we performed benchtop measurements, both in unloaded conditions and in the presence of a biological phantom, resulting in excellent agreement with simulations. The developed analytical framework can be useful to model and control the mutual interactions between the various elements of an RF MRI system. In addition, the possibility to print the decoupling elements and the RF coils on the same dielectric substrate leads to a mechanically robust prototype.

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