Johannes Schropp (1) and Gilbert Koch (2)-(3)
(1) Department of Mathematics and Statistics, University of Konstanz, Konstanz, Germany (2) Department of Pharmaceutical Sciences, State University of New York at Buffalo, Buffalo NY, USA (3) Pediatric Pharmacology and Pharmacometrics Research Center, University Children’s Hospital of Basel (UKBB), Basel, Switzerland
Objectives: In an aging population every individual has its own and unique lifespan, and after expiration the individual has to leave the population. Transit compartment models (TCM) are often used to characterize aging populations [1], e.g. to describe stimulation effects of erythropoietin on cell maturation [2]. However, a serious limitation is the gamma-distributed lifespan in TCMs. In general, lifespans follow e.g. the Weibull or more complex distributions [3]. Therefore, we extend the TCM concept to approximately describe any distribution and call this generalized method distributed transit compartment models (DTCM).
Methods: In general, in the compartment approach every state defines a subpopulation with a certain age range, and the sum of all states describes the total aging population. In DTCMs the transit rate between the compartments is now controlled by the survival function of the lifespan distribution, and the number of compartments controls the quality of approximation. The DTCM can be equivalently reformulated with the same underlying ordinary differential equations as TCMs and only summation of the states differs.
Results: Convergence investigations of the approximated lifespan distribution towards the original distribution are visualized. An acceptable amount of compartments is sufficient for a convenient approximation quality. A pharmacokinetics / pharmacodynamics (PK/PD) example is presented and data with Weibull-distributed lifespans is fitted.
Conclusion: DTCMs are an extension of TCMs to approximately describe any lifespan distribution. DTCMs are implemented equally as TCMs and only summation of the states differs. Therefore, DTCMs could be applied in any PK/PD software like NONMEM, WINNOLIN or MONOLIX
References:
[1] Harker LA, Roskos LK, Marzec UM, Carter RA, Cherry JK, Sundell B, Cheung EN, Terry D, Sheridan W (2000) Effects of megakaryocyte growth and development factor on platelet production, platelet life span, and platelet function in healthy human volunteers. Blood 95(8): 2514-2522
[2] Perez-Ruixo JJ, Krzyzanski W, Hing J (2008) Pharmacodynamic Analysis of Recombinant Human Erythropoietin Effect on Reticulocyte Production Rate and Age Distribution in Healthy Subjects. Clin Pharmacokinet 47(6):399-415
[3] Korell J, Coulter CV, Duffull SB (2011) Evaluation of red blood cell labelling methods based on a statistical model for red blood cell survival. J Theor Biol 291:88-98
Reference: PAGE 24 (2015) Abstr 3404 [www.page-meeting.org/?abstract=3404]
Poster: Methodology - New Modelling Approaches