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Models of Systems Failure in Aging

Leonid A. Gavrilov and Natalia S. Gavrilova

Mathematical models of systems failure are critically important for understanding the mechanisms of aging because aging of organisms is associated with increased risk of failure of its physiological systems.

Theoretical analysis of systems failure in aging leads naturally to apply the existing general theory of systems failure, which is also known as the reliability theory. Reliability-theory approach to biological aging is useful for three reasons. (1) It provides a useful scientific language (definitions and cross-cutting principles) helping to create a general theoretical framework for organizing numerous and diverse observation on aging into a coherent picture. This is very important for researchers, because it helps them to understand each other despite a disruptive specialization of aging studies. (2) It allows researchers to develop a scientific intuition and understanding of the main principles of the aging process by considering simplified mathematical models of systems failure, having some general features of real aging organisms. (3) It helps to generate and test specific predictions on age-related dynamics of systems failure, and to get deeper insights in the mechanisms of aging by more creative analysis of already collected data.

This chapter reviews the existing theoretical reliability models and approaches, which help us to understand the mechanisms and age-dynamics of systems failure. Empirical observations on systems failure in aging are also reviewed (the Gompertz and Weibull failure laws, the compensation law of systems failure, and the late-life failure rate leveling-off), and are theoretically explained through the observed decline in system's redundancy with age. The causes offailure rate increase with age are discussed and explained using five simple mathematical models of systems failure in aging as an illustration.

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