title: A return to time, cells, systems, and aging: III. Gompertzian models of biological aging and some possible roles for critical elements.
abstract: In this paper, I continue my investigation into the modeling of senescence in biological hierarchies. Making use of my previous discussion on non-reestablishable biological components, I derive a mathematical model which has Gompertzian-like dynamics. I show how this model may be approximated, in certain instances, by a Gompertzian equation. I then demonstrate how our approach yields a biological interpretation for the parameters in the Gompertzian equation. I then demonstrate how changes in the parameter values may be interpreted in light of the biology. Subsequently, I review the literature on the allometry of aging, and I demonstrate how my reliability model may be used to obtain--in a qualitative manner--some of the lifespan curves found in the literature. I close my discussion by constructing a more complex reliability model which incorporates the deterministic failure of biological components with stochastic aspects of senescence.
mesh_terms: D000375:Aging; D000818:Animals; D001921:Brain / Q000254:growth & development; D006801:Humans; D008017:Life Expectancy; D008136:Longevity; D008433:Mathematics; D008954:Models, Biological