In physiological research, inductive reasoning has traditionally been the rule, rather than the exception. This is because mathematical formulations of human body function inevitably lead to indeterminate situations where there are more unknown quantities than there are equations to describe them. Thus, variational and optimization methods may be employed to generate additional equations of motion which render the problem determinate in a deductive sense.
Several examples illustrate the successful use of variational methods in biodynamic modelling.
The maintenance of life requires a steady-state internal environment that must be held relatively constant within carefully prescribed limits. Feedback control mechanisms that provide this type of restraint work through homeostatic regulators that transmit information through a corresponding syntax that is uniquely their own. The analysis of homeostasis within the context of feedback control theory reduces seemingly complex, unrelated sequences of physiologic processes into more readily identifiable sets of common denominators that illucidate some basic principles of biologic function. Appropriate interpretation of these biologic principles may help us move closer to success in our efforts to improve the health, comfort and understanding of man. Values of and are tabulated for various scenarios typical of transport processes occurring in physiologic systems.