A mathematical model of physiological processes and its application to the study of aging
The behavior of a physiological system which, after displacement, returns by homeostatic mechanisms to its original condition can be described by a simple differential equation in which the "recovery time" is a parameter. Two such systems, which influence one another, can be linked mathematically by the use of "coupling" or "feedback" coefficients. These concepts are the basis for many mathematical models of physiological behavior, and we describe the general nature of such models. Next, we introduce the concept of a "fatal limit" for the displacement of a physiological system, and show how measures of such limits can be included in mathematical models. We show how the numerical values of such limits depend on the values of other system parameters, i.e., recovery times and coupling coefficients, and suggest ways of measuring all these parameters experimentally, for example by monitoring changes induced by X-irradiation. Next, we discuss age-related changes in these parameters, and show how the parameters of mortality statistics, such as the famous Gompertz parameters, can be derived from experimentally measurable changes. Concepts of onset-of-aging, critical or fatal limits, equilibrium value (homeostasis), recovery times and coupling constants are involved. Illustrations are given using published data from mouse and rat populations. We believe that this method of deriving survival patterns from model that is experimentally testable is unique.