A Mathematical Model for Thermoregulation in Endotherms Including Heat Transport by Blood Flow and Thermal Feedback Control Mechanisms: Changes in Coat, Metabolic Rate, Blood Fluxes, Ventilation and Sweating Rates

Abstract

Thermoregulation in endotherms allows the maintenance of the body temperature independent of ambient temperature. Experimental data have revealed complex interactions between the physiological mechanisms of thermoregulation and environmental conditions. We derive a nonlinear partial integro-differential dynamical model based on physical first principles and fundamental physiological mechanisms to understand the role of some thermal control mechanisms in the thermoregulation process of endotherms. The model is composed of four layers representing different tissues and it incorporates six thermal feedback control mechanisms. These mechanisms are heat production due to metabolic rate and heat exchange within the body given its internal structure, and the model considers heat exchange due to conduction, heat transport by blood flow, heat exchange with the ambient through convection, radiation, and evaporation from the respiratory tract and superficial evaporation in both passive and active situations. Our model sheds new light on previous explanations about the classic metabolism-ambient temperature Ushaped curve.

A Kinetic Response Model for Standardized Regression Analyses of Inflammation-Triggered Hypothermic Body Temperature-Time Courses in Mice

“…The two free parameters, r and T n are kinetically interpretable: T n is the asymptotically stable normal body temperature and r quantifies the stabilizing force. This approach is in line with recent findings that the classical way of modeling thermal regulation in form of a linear dynamics appears to be oversimplified (Boldrini et al, 2018). In comparison to the linear dynamics, the logistic dynamics adds an inflection point in the hypothermic case, i.e., for a drop of temperature below T n .…”

“…Although this simpler regulation performs well in many cases, we opted for the nonlinear logistic regulation due to its flexibility. Moreover, it has been recently shown that the classical linear approach is over-simplified and a nonlinear form is needed (Boldrini et al, 2018). Close to the equilibrium, the simpler model corresponds to a Taylor approximation of the nonlinear model.…”

How hot are single cells?

“…The cause of this high resting-metabolic rate remains a source of controversy, but processes such as high ion permeability of plasma and mitochondrial membranes and high protein and membrane turnover have been proposed to underlie this phenomenon (Ruben, 1995). Importantly, the maintenance of homeothermic endothermy can be enhanced by dynamic "insulation" from the environment provided by feathers and fur, as well as more static structures such as subcutaneous fat and large body mass that greatly decreases the resting heat loss to the environment (Boldrinia et al, 2018). Oyama et al, in the current issue of Journal of General Physiology, present well-designed experiments measuring the surface temperature of different isolated cells during alterations in the energy metabolism to examine topology of heat production in single mammalian cells.…”