Thermal Analysis of Averaging Times in Radio-Frequency Exposure Limits Above 1 GHz

Abstract

This paper considers the problem of choosing an appropriate “averaging time” in radiofrequency (RF) exposure limits to protect against thermal hazards, focusing on the RF frequency range above 3–10 GHz. Analysis is based on examination of the dynamic properties of thermal models for tissue using Pennes’ bioheat equation. Three models are considered: a baseline model consisting of a uniform half space with dielectric and thermal properties similar to those of human skin with adiabatic boundary conditions; a layered 1D model with dielectric and thermal properties similar to those of skin, fat, and underlying muscle, with convective boundary conditions appropriate for room environments; and exposures to the head of an anatomically detailed image-based model (“Taro”). RF exposure consisted of plane wave radiation incident on the two planar models, and radiation from resonant dipoles located 1.5 cm from the head model, at frequencies ranging from 1 to 300 GHz. The dynamic properties of the models were explored by analytic solution of the baseline model, and from numerical solutions of the thermal responses of the layered and head models. From the step responses of the models (increases in surface temperature to a suddenly imposed exposure), the impulse and frequency responses of the models were obtained. In the frequency domain, the thermal models exhibit extreme lowpass characteristics with cutoff (−3 dB response) frequencies below 1 mHz. The impulse response to millimeter wave radiation (30–300 GHz) shows a sharp peak at zero time, due to short term accumulation of heat near the surface, which dissipates quickly as heat is conducted into deeper layers of tissue. Simple analytical results of a further simplified model assuming purely surface heating agree well with results of a more detailed assessment for millimeter waves. Response of the model to pulse trains and to single maximum fluence “big bang” pulses in which all allowable energy over a 6-min averaging time is delivered in one short pulse raises the possibility of excessive transient temperature increases at the tissue surface from exposure to short high-fluence pulses at mm-wave frequencies. Such exposures are not produced by current technologies apart from certain military weapons systems but may occur from future high-power mm-wave technology. By contrast, simulations of exposure from a communications waveform at 1.9 GHz show extremely tiny transient temperature fluctuations. The results generally confirm the present choice of 6 min for an averaging time in the current generation of RF exposure limits but suggest the need for additional limits on fluence for brief high-fluence pulses at mm-wave frequencies. This paper addresses thermal hazards only, and a larger range of evidence would need to be evaluated as well in revising exposure limits.