Area-Averaged Transmitted Power Density at Skin Surface as Metric to Estimate Surface Temperature Elevation

In the international guidelines/standards for human protection, the specific absorption rate (SAR) is used as a metric to prevent excessive surface temperature elevation at frequencies up to 3 or 10 GHz. Above that transition frequency, including the frequency region assigned to 5th generation wireless communication systems, an area-averaged incident power density on human body surface is used as the physical quantity to specify the restrictions on human exposure to electromagnetic fields. However, the incident power density is an external physical quantity, resulting in frequency-dependent temperature elevation, which is attributable to frequency-dependent variations in the reflection coefficient at the skin surface and energy penetration depth into tissue. In this paper, we discuss analytically and computationally the effectiveness of the transmitted power density (TPD) at the skin as a new metric to estimate the steady-state skin temperature elevation above the transition frequency. We also consider simplified models for uniform and Gaussian beam patterns and the analytical solutions to the bioheat equation for an one-dimensional model, which are in good agreement with numerical solutions. These show that the TPD provides an excellent estimate of skin temperature elevation through the millimetre-wave band (30-300 GHz) and a reasonable and conservative estimate down to 10 GHz, whereas the SAR is a good metric below 3 GHz. Computational results for the dipole and patch antenna arrays demonstrated that the one-dimensional analysis is conservative metric as compared with the TPD averaged over the area of 4 cm2 (2-cm square). Considering extreme cases, averaging area smaller than 4 cm2 is needed above 30 GHz for beam exposure with small diameters. Finally, we consider the choice of averaging area as related to peak temperature increases for small beams. For extremely small exposure areas, limits on peak power density may be needed.