MATHEMATICAL MODELS OF THERMAL REGULATION

The thermal characteristics of animal and human tissues determine in important ways the absolute temperature of such tissues and organ systems in response to varying ambient conditions and different levels of metabolic activity. The presence of the circulatory system adds convective heat transport to the other thermal characteristics governing heat transfer such as conduction and heat capacitance. Most tissues exhibit a high degree of anisotropy in their structure and in addition may have a variable rate of heat production and blood flow. Many organs, in addition, are involved in the system that regulates the body temperature of homoiotherms, and this can result in such tissues changing important thermal characteristics in response to neural commands originating in other parts of the body. All animals, including man, live in a constantly changing thermal environment, with a widely varying internal heat production. As a result, the thermal gains and losses are constantly varying, with different factors participating at different times. Although responses to a given set of environmental conditions can be measured in a test exposure, the universe of possible conditions is so great that it is not feasible to test all such conditions. Mathematical simulation models have been constructed by a number of investigators. These models incorporate insights from anatomy, physiology, and mechanical engineering and provide a simplified system that reacts to internal and external thermal stimuli in essentially the same manner as the real system does. One of many such systems was developed at the John B. Pierce Foundation Laboratory, New Haven, Connecticut. An early version was formulated for implementation on an analog computer.' Since then, advanced versions have been described by this Laboratory" as well as by a number of authors who have adapted or expanded this later version for special applications. Gagge et al.' developed a very simplified version for assessment of complex thermal environments. Montgomery' adapted the advanced model for the simulation of heat transfer in divers wearing diving suits. Azer and Hsu6 adapted various models to the prediction of thermal sensation. The National Aeronautics and Space Administration used simulations of various physiological control systems including the thermoregulatory system quoted above.