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.