Signal-to-noise ratio (SNR) can be improved by placing high permittivity materials (HPM) (εr>80) between a radio-frequency (RF) coil and the object^1,2. However, the beneficial effect of HPMs on the relative balance between coil signal and noise sensitivity has not been elucidated. To gain physical insight, our work analyzes the effects of HPMs on ideal current patterns³, corresponding to the ultimate intrinsic SNR (UISNR) at a voxel of interest. Ideal current patterns cover a larger region in the presence of HPMs⁴, but it is unclear whether this is primarily due to signal propagation effects through the HPM layer, or a consequence of reduced sample noise ($$$\int_{}^{} \sigma E\cdot E^{\star}dv$$$). Our objective is to interpret these findings by studying ideal current patterns, the corresponding optimal electric (E) fields, and a signal-only propagation model.

1) Ideal current patterns: An in-house simulation framework based on dyadic Green’s functions (DGF) was used to calculate the ideal current patterns³ corresponding to the UISNR at a voxel 3.4cm from the center of a sphere at 7T (Fig. 1). A mode expansion order of 60 was used to ensure convergence. Calculations were repeated in the presence and absence of a HPM layer surrounding the object with εr = 1000.

2) Signal-only propagation model: A circularly polarized local magnetic field source at the operating frequency (Fig. 1) was modeled to simulate a precessing spin at the voxel of interest using numerical simulation software (CST, 2015). The corresponding tangential E field, which may be associated with a putative detector current pattern well matched to the precessing spin’s field, and hence well suited for efficient signal reception, was calculated on a curved spherical surface (Fig. 1) to investigate the effects of signal propagation through HPMs. Approximately one million mesh cells were used. An accuracy of -50 dB was used to ensure convergence.

3) Optimal E fields: The optimal net E field generated by the ideal current patterns was calculated (Fig.5) and its spatial distribution was investigated to test the hypothesis that reduced E field penetration, and consequently reduced sample noise is associated with larger ideal current patterns.

Size and phase of the ideal current patterns changed depending on the thickness of the HPM layer (Fig. 2). This suggests that the SNR-optimal diameter of a surface coil changes in the presence of HPMs. The tangential E field in the signal model exhibited a different phase delay depending on the HPM thickness (Fig. 3), but there was no appreciable change in size (Fig 4), suggesting that signal-propagation delay in the HPMs affects the phase, but not the size, of the ideal current patterns. Other factors must contribute to the phase changes in the ideal current patterns, since they could not be predicted exactly by the HPM thickness. For example, the patterns in Fig 2B (λ/4 HPM thickness) should be delayed by 90^o (figure-eight shape) from those in Fig. 2A, but they are delayed by 180^o (loop with inverted current direction). This could be due to the fact that the ideal current patterns cover a larger area, adding to the effective distance. While the ideal current patterns alternate between a localized loop and figure-eight³, the tangential E fields appear as distributed loops that sweep across the surface. This difference is because the ideal current patterns are optimized to maximize signal at the voxel of interest while minimizing received noise, whereas the tangential E field is simply the field produced by precessing spins at the voxel. The optimal E fields associated with the ideal current patterns showed that particular thicknesses of the HPM layer limited the propagation of the E field, consequently reducing sample noise (Fig. 5). Reduced E fields within the sample (Fig. 5B,E) correspond to larger loops in the ideal current patterns (Fig. 2B,E), indicating that larger loops can maximize the received signal when E field attenuation reduces sample noise penalty. The patterns of concentric loops with mutually opposite directions (Fig 2D) could be an effect of SNR optimization⁵, or due to a standing wave or resonance-like behavior⁶ observed in the optimal E fields (Fig 5D), but further investigation is needed. Our results demonstrate that the phase changes observed in the ideal current patterns are likely due to signal propagation effects within the HPM, while the increase in size of the ideal current patterns is a consequence of reduced E field penetration into the sample for different HPM thicknesses. Our results provide an intuitive understanding of the signal and noise sensitivity changes and the optimal radius for coils in the presence of HPMs.