title: Distributed transit compartments for arbitrary lifespan distributions in aging populations.
abstract: Transit compartment models (TCM) are often used to describe aging populations where every individual has its own lifespan. However, in the TCM approach these lifespans are gamma-distributed which is a serious limitation because often the Weibull or more complex distributions are realistic. Therefore, we extend the TCM concept to approximately describe any lifespan distribution and call this generalized concept distributed transit compartment models (DTCMs). The validity of DTCMs is obtained by convergence investigations. From the mechanistic perspective the transit rates are directly controlled by the lifespan distribution. Further, DTCMs could be used to approximate the convolution of a signal with a probability density function. As example a stimulatory effect of a drug in an aging population with a Weibull-distributed lifespan is presented where distribution and model parameters are estimated based on simulated data.
authors.affiliation: Department of Pharmaceutical Sciences, State University of New York at Buffalo, 403 Kapoor Hall, Buffalo, NY 14214, USA; Pediatric Pharmacology and Pharmacometrics Research Center, University of Basel, Children׳s Hospital (UKBB), Spitalstrasse 33, 4056 Basel, Switzerland. Electronic address: gilbert.koch@web.de.
authors.forename: Gilbert
authors.initials: G
authors.lastname: Koch
authors.affiliation: Department of Mathematics and Statistics, University of Konstanz, PO Box 195, 78457 Konstanz, Germany.
authors.forename: Johannes
authors.initials: J
authors.lastname: Schropp
mesh_terms: D000375:Aging / Q000502:physiology*; D006801:Humans; D008017:Life Expectancy
keywords: Cell maturation; Convolution; Gompertz–Makeham; Survival function; Weibull