Author(s)

Hongyun Wang¹, Wesley A. Burgei², Hong Zhou^3*

¹Department of Applied Mathematics, University of California, Santa Cruz, CA, USA.
²U.S. Department of Defense, Joint Intermediate Force Capabilities Office, Quantico, VA, USA.
³Department of Applied Mathematics, Naval Postgraduate School, Monterey, CA, USA.

Previously we introduced a concise dose-response model for the heat-induced withdrawal reflex caused by millimeter wave radiation. The model predicts the occurrence of withdrawal reflex from the given spatial temperature profile. It was formulated on the assumption that the density of nociceptors in skin is uniform, independent of the depth. The model has only two parameters: the activation temperature of heat-sensitive nociceptors and the critical threshold on the activated volume for triggering withdrawal reflex. In this study, we consider the case of depth-dependent nociceptor density in skin. We use a general parametric form with a scaling parameter in the depth direction to represent the nociceptor density. We analyze system behaviors for four density types of this form. Based on the theoretical results, we develop a methodology for 1) identifying from test data the density form of nociceptors distribution, 2) finding from test data the scaling parameter in the density form, and 3) determining from test data the activation temperature of nociceptors.

High-Energy Millimeter Wave Radiation, Heat-Induced Pain, Depth-Dependent Nociceptor Density In Skin

Wang, H. , Burgei, W. and Zhou, H. (2020) Effect of Depth-Dependent Nociceptor Density on the Heat-Induced Withdrawal Reflex. Applied Mathematics, 11, 788-824. doi: 10.4236/am.2020.118053.