Solution and implementation of distributed lifespan models

• Published in: Journal of pharmacokinetics and pharmacodynamics Vol. 40; no. 6; pp. 639 - 650
• Main Authors: Koch, Gilbert, Schropp, Johannes
• Format: Journal Article
• Language: English
• Published: Boston Springer US 01.12.2013; Springer Nature B.V
• Subjects: Algorithms; Biochemistry; Biomedical and Life Sciences; Biomedical Engineering and Bioengineering; Biomedicine; Cell Survival - drug effects; Erythrocytes - cytology; Erythrocytes - drug effects; Erythrocytes - metabolism; Erythropoietin - administration & dosage; Erythropoietin - pharmacokinetics; Erythropoietin - pharmacology; Erythropoietin - therapeutic use; Hemoglobins - analysis; Humans; Kidney Diseases - blood; Kidney Diseases - drug therapy; Models, Biological; Models, Statistical; Numerical Analysis, Computer-Assisted; Original Paper; Pharmacology/Toxicology; Pharmacy; Software; Statistical Distributions; Veterinary Medicine/Veterinary Science; Population; Convolution; Lifespan; Distribution
• ISSN: 1567-567X; 1573-8744
• DOI: 10.1007/s10928-013-9336-y

We consider a population where every individual has a unique lifespan. After expiring of its lifespan the individual has to leave the population. A realistic approach to describe these lifespans is by a continuous distribution. Such distributed lifespan models (DLSMs) were introduced earlier in the indirect response context and consist of the mathematical convolution operator to describe the rate of change. Therefore, DLSMs could not directly be implemented in standard PKPD software. In this work we present the solution representation of DLSMs with and without a precursor population and an implementation strategy for DLSMs in ADAPT , NONMEM and MATLAB . We fit hemoglobin measurements from literature and investigate computational properties.