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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.
Aging human circadian rhythms: conventional wisdom may not always be right
This review discusses the ways in which the circadian rhythms of older people are different from those of younger adults. After a brief discussion of clinical issues, the review describes the conventional wisdom regarding age-related changes in circadian rhythms. These can be summarized as four assertions regarding what happens to people as they get older: 1) the amplitude of their circadian rhythms reduces, 2) the phase of their circadian rhythms becomes earlier, 3) their natural free-running period (tau) shortens, and 4) their ability to tolerate abrupt phase shifts (e.g., from jet travel or night work) worsens. The review then discusses the empirical evidence for and against these assertions and discusses some alternative explanations. The conclusions are that although older people undoubtedly have earlier circadian phases than younger adults, and have more trouble coping with shift work and jet lag, evidence for the assertions about rhythm amplitude and tau are, at best, mixed.