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THE ROLE OF MODELS IN THEORETICAL BIOLOGY 197

results obtained from such models are really accurate, but they represent interesting conceptual models of the natural systems.

C.    Metabolic Control Models

Mathematical control models have been described for various aspects of metabolism. Ackerman et al. (1964) present a detailed analysis of factors controlling blood glucose levels following intake of a substantial dose of sugar, with representation of tissue metabolism, insulin action, liver glycogen storage, etc. A Computer was used to solve the necessary eąuations, and excellent correspondence was obtained between the mathematical model and data from over 750 human subjects given glucose-tolerance tests.

Analog-servomechanism theory has been used by Baker et al. (1964) to predict levels of nitrogen compounds in the gut, liver, blood, and urine following intake of meals with known amounts of nitrogenous materials. DeHaven and DeLand (1963) used a digital Computer to simulate homeostatic eąuilibration in the acid-base oxygen-carbon dioxide buffers of the blood, without inclusion of any neural mechanisms. A model of a generalized endocrine control, appropriate to thyroid, pituitary, or gonadal hormonal functions, and based on a set of simultaneous differ-ential eąuations, has been reported by Danziger and Elmergreen (1957). Many other reports pertaining to such models are available.

D.    Thermal Regulation

As a finał example of physiological control simulation, several papers shall be cited on thermal regulation. Studies of thermoregulation using analog Computer techniąues are available by A. C. Brown (1963), P. E. Smith (1962), Crosbie et al. (1961), and others. Thermo-regulation in mammals involves a variety of inputs and controlled variables. Among the inputs one may include: temperatures recorded in the skin, blood, and brain, existing ratę of metabolism, blood flow, sweating, and possibly electrolyte levels in the blood. Controlled output variables include ratę of metabolism, sweating, cardiac output, shivering, and other activity, and sometimes state of piloerection. A complete model must also in-corporate numerous physical mechanisms pertaining to generation of heat, its distribution in the circulation and tissues, heat losses at the skin and in the respiratory system, absorption of radiant energy at the skin, effects of wind, etc. Most of these factors have been included in several of the reports cited above and ąuite satisfactory model simula-tions obtained for the action of the entire system. It is elear however, that