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This study examines thermal responses of skin to pulsed millimeter wave (mm-wave) and radiofrequency (RF) radiation. We review limits for pulse fluence in the IEEE Std. C95.1-2019 and the 2020 guideline of the International Commission on Nonionizing Radiation Protection (ICNIRP), as well as the recently re-affirmed guidelines of the U.S. Federal Communications Commission (FCC). The focus of the study is on millimeter-wave frequencies (30-300 GHz) where energy is absorbed close to the body surface and intense pulses could potentially cause high temperature gradients at the skin, but the model is extended to lower frequencies as well. The study employs a simple one-dimensional baseline thermal model for skin and Pennes' bioheat equation (BHTE), together with a baseline model for thermal damage to skin based on a standard model. The predicted temperature increases produced by 3-sec pulses at 94 GHz are consistent with previous experimental results with no adjustable parameters in the model. The few reported data on thermal damage to the skin from pulsed 94 GHz energy are insufficient to enable a conventional analysis of damage thresholds and the data may be affected by errors in dosimetry. The baseline model suggests that the implicit limits on pulse fluence in the present FCC guidelines might allow, in extreme (but in practice unrealistic) cases, transient increases in skin temperature that approach thresholds for thermal pain but which remain well below levels anticipated to cause thermal damage. Limits on pulse fluence in the current IEEE and ICNIRP exposure guidelines would preclude such effects. Such extreme pulses are far above those that are emitted by wireless and other technologies but may be emitted by some nonlethal weapons systems. FCC's proposed “device-based time averaging” rules will restrict thermal transients in skin from mm-wave transmitters to levels that are roughly an order of magnitude below the slower temperature increases produced by the low-frequency components of the modulation waveform and appear to be excessively conservative. An appendix discusses the applicability of two approximations to the analytical solutions to the bioheat equation that can be used to estimate temperature increases in skin from exposure to mm-waves.

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.

In this paper, mechanisms of RF energy absorption by body tissue in close proximity to wireless equipment, are studied using numerical simulations at frequencies above 24 GHz. It is shown that at millimeter-wave (mmW) frequencies, of relevance for 5G mobile communications, and for realistic source to body separation distances, the contribution from the reactive near-field to the energy deposition in the tissue is small. Furthermore, the interaction between the source and the exposed body is modest. The results suggest that the effects of the near-field body interactions are small when evaluating electromagnetic field compliance at mmW frequencies.

Biological experiments that expose living cells or tissues to RF energy must have an aqueous medium to provide essential water, ions, nutrients, and growth factors. However, as we show here, the medium inherently functions as a receiving antenna that conveys RF energy to the biological entity in a manner entirely determined by exposure vessel geometry, orientation to the incident RF flux, frequency, and dielectric properties of the medium. We show for two common experimental arrangements that basic antenna theory can predict electromagnetic energy patterns that agree well with those otherwise obtained by computationally intensive methods that require specialized resources.

This paper considers the specific absorption rate (SAR) in tissue of radiofrequency (RF) energy and temperature increases produced by RF currents on short conductors (0.03–0.1λ). We consider a cylindrical model in which a center-feeds, insulated antenna is embedded in tissue. We introduce a new method for the analytic evaluation of the fields in the cylindrical phantom taking advantage of the axial symmetry of the antenna and the tissue. Results of the analytical model are compared to results of numerical (finite difference time domain) simulations; in addition, the thermal response of the exposed material is calculated by finite element solution of the heat conduction equation. For model antennas of 1 to 3 cm total length with a feedpoint current of 10mA RMS at 900MHz, the maximum SAR (in tissue next to the antenna) is less than ∼2.5W/kg. SAR decays rapidly with radial distance from the antenna (∼r−4 for the 1cm antenna) and creates a steady-state temperature rise less than 0.05K at the location of SARmax. Heat conduction causes the temperature to decline steeply with radius (depth into tissue).