New unifying metric for NMR/MRI probe evaluation based on optimized solenoid coil geometry

A three-dimensional numerical simulation of the magnetic field distribution and Bloch equations for arbitrary radio frequency (RF) coils is developed and compared against nuclear magnetic resonance (NMR) experimental results to evaluate the NMR signal intensity. Because NMR is inherently insensitive and its signal intensity is dependent on RF coil geometry, the investigation of RF coil geometry to maximize signal intensity for a given sample volume is important for improving the signal-to-noise ratio (SNR) and shortening the accumulation time. The developed simulation can optimize the RF coil geometry, specifically a single-layer solenoid coil with a constant winding pitch, and the result of the solenoid coil simulation serves as a new unifying metric for evaluating NMR/MRI probes. It is found that the most efficient sample aspect ratio (ratio of sample length to sample diameter) and pitch to wire diameter ratio for the highest signal intensity are around 2.2 and 1.65, respectively. Some discrepancies from the solenoid coil geometry ratios for higher signal intensity in previous studies can be explained by the difference in the gap between the inner diameter of the solenoid coil and the sample diameter. These results are confirmed through NMR signal intensity expressed in voltages with three approaches: 3D simulation, experiment, and estimation based on probe parameters. The simulated signal intensity shows a maximum error of approximately 5 % and an average error of 1 % when compared to the experimental results. This result suggests that the developed methods hold the potential for application in quantitative NMR (qNMR) without relying on standard reference materials. Finally, this study introduces a standardized geometry for the optimized solenoid coil for higher signal intensity and uses it to establish an evaluation metric called the signal-to-optimized-solenoid-signal ratio (3SR). The 3SR addresses the volume-dependence problem in conventional metrics like SNR and SNR per sample volume. It provides a standardized approach for the unified evaluation of all RF coils and probe designs, regardless of sample volume and measurement frequency. Therefore, 3SR can be utilized as a useful metric in the search for optimal coil geometry, while metrics such as SNR or SNR per sample volume are currently used for such purpose. This metric is expected to be useful for NMR/magnetic resonance imaging (MRI) users and developers.