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J Magn Reson. 2012 Sep;222:59-67. doi: 10.1016/j.jmr.2012.06.005. Epub 2012 Jun 19.

Elimination of mutual inductance in NMR phased arrays: the paddle design revisited.

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Department of Mechanical and Manufacturing Engineering, School of Engineering, University of Cyprus, Cyprus.


This study proposes a method to empirically minimize mutual inductance, using passive end-ring circular paddles, with neighboring coil loops placed in a non-overlapped configuration. The proposed concepts are validated through B(1)-field simulations for resonant coils at f(o)=300.5 MHz, having various sizes (3-10 cm), and for paddles with sizes ranging from 16 to 30 mm, and bench tests on constructed 4×4cm(2) two- (1×2) and four-coil loop (2×2) planar arrays. Simulation results yield total mean percentage B(1)-field differences of only 7.03% between the two non-overlapping coil array configurations (paddles vs. no-paddles). Pair-wise comparisons of elicited mean B(1)-field differences from the use of different circular and rectangular paddle sizes, yield values <5.3%. Theoretical calculation of the normalized mutual coupling coefficient in the non-overlapped coil configuration reduces to almost zero with optimally sized-paddles having a radius of approximately 28% the coil's largest dimension. In the absence of paddles, differences in the split of resonance peaks of 9.9 MHz were observed for the two coils in the 1×2 array, which vanished with paddle placement. Single coil responses (unloaded/loaded) without paddles, and responses from array coils with use of optimally-sized paddles yielded quality factor ratios that ranged between 1.1-1.86 and 1.0-1.5, respectively. Phantom and mouse loaded reflection coefficients S(11)/S(22) were -16.7/-16.2dB and -28.2/-16.1 dB, for the two array loops, respectively. Under unloaded conditions and in the absence of paddles, split resonances were observed for the 1×2 array, yielding transmission coefficients of -5.5 to -8.1 dB, reversing to single resonance responses upon paddle placements, with transmission coefficients of -14.4 to -15.6 dB.


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