Use of mathematical models of survivorship in the study of biomarkers of aging: the role of heterogeneity.

An ever increasing number of people have been engaging in aging research using various interventions aimed to modify aging processes, and/or life span, of experimental animals. Since this type of studies needs outcome parameters for assessing the efficacy of such interventions, research on biomarkers of aging (ABs) has received new stimuli. In the present paper, the problem of the occurrence of a vicious circle any time we study ABs and determinants of aging is addressed. In fact, while ABs would represent the standard reference to be used in the study of the main causes of processes of aging, these very determinants should already be known in order to get reliable ABs. A feasible way to overcome this impasse is proposed, using mathematical models of survivorship or mortality based on biological hypotheses and accounting for inter-individual heterogeneity, a necessary ingredient for a correct interpretation of survival results. Specific kinetics of experimental parameters that are candidates as ABs can be compared to the kinetics hypothesized for general biological functions entering the model. We have built a model of this type that can also be used to perform a reliable overall gross estimate of the rate of aging, R(a), in the population, a parameter useful when judging the success of interventions aimed to act on determinants of aging. The perspective that theory of complex systems can be of help in the search for ABs is also discussed.