A Concise Model and Analysis for Heat-Induced Withdrawal Reflex Caused by Millimeter Wave Radiation

Abstract

In this study, we consider the heat-induced withdrawal reflex caused by exposure to an electromagnetic beam. We propose a concise dose-response relation for predicting the occurrence of withdrawal reflex from a given spatial temperature profile. Our model is distilled from sub-step components in the ADT CHEETEH-E model developed at the Institute for Defense Analyses. Our model has only two parameters: the activation temperature of nociceptors and the critical threshold on the activated volume. When the spatial temperature profile is measurable, the two parameters can be determined from test data. We connect this dose-response relation to a temperature evolution model for electromagnetic heating. The resulting composite model governs the process from the electromagnetic beam deposited on the skin to the binary outcome of subject's reflex response. We carry out non-dimensionalization in the time evolution model. The temperature solution of the non-dimensional system is the product of the applied power density and a parameter-free function. The effects of physical parameters are contained in non-dimensional time and depth. Scaling the physical temperature distribution into a parameter-free function greatly simplifies the analytical solution, and helps to pinpoint the effects of beam spot area and applied power density. With this formulation, we study the theoretical behaviors of the system, including the time of reflex, effect of heat conduction, biological latency in observed reflex, energy consumption by the time of reflex, and the strategy of selecting test conditions in experiments for the purpose of inferring model parameters from test data.

Inference of Median Subjective Threshold in Psychophysical Experiments

“…We model the subject response as solely determined by the stimulus (the exposure duration) and a subjective threshold that varies among test subjects and varies among different trial realizations for a given subject. The outside stimulus and the internal threshold are connected via the pain signal generated at the heat-sensitive nociceptors activated by the skin temperature increase [6]. The internal threshold on the nociceptors signal is manifested outside as the observable threshold on the exposure duration.…”

Thermal Effect of a Revolving Gaussian Beam on Activating Heat-Sensitive Nociceptors in Skin

“…We consider the situation where a skin area of the test subject is exposed to a moving beam [4] [5] [6]. We adopt a formulation similar to the one in our previous studies [3] [7]. Let ( ) , , T z t r denote the temperature of skin as a function of 3-D spatial coordinates ( ) , z r and time t. Here z is the depth from the skin surface and r is the 2-D coordinates on the skin surface.…”

Internal Temperature of Skin when Surface Temperature Is Controlled with an Electromagnetic Beam

“…We adopt a formulation similar to the one in our previous studies [5] [6] [7], Journal of Applied Mathematics and Physics briefly summarized below. Let ( ) , T z t denote the skin temperature along the beam center line as a function of depth z and time t. We assume 1) the electromagnetic beam is perpendicular to the skin surface (i.e., beam incident angle = 0); 2) before the exposure, the skin has a uniform initial temperature base T (the baseline temperature); and 3) heat conduction is included only in the depth direction [8] (which is justified given the small length scale of electromagnetic wave penetrating in the skin depth direction and the much larger length scale of beam cross-section, and which allows us to separate z from ( )…”