Modeling of Pharmacokinetics and Pharmacodynamics with Application to Cancer and Arthritis

Abstract

Mathematical modeling of pharmacokinetics / pharmacodynamics (PKPD) is an important and growing field in drug development. In this work we develop preclinical PKPD models based on fundamental biological and pharmacological principles.Equipped with a PKPD model, different dosing schedules could be simulated and therefore, a valuable contribution to first in human dose selection could be achieved. We consider different mathematical model figures and discuss the properties and biological basis. Such tools serve as modules for a final PKPD model. We apply ordinary and delay differential equations and especially focus on modeling of delays and lifespans in populations. We show a fundamental relationship between transit compartments and lifespan models. Moreover, we investigate the weighted least squares estimator and derive statistical characteristics of model parameter.We present a PKPD model to describe tumor growth and anticancer effects for mono- and combination therapy. Further, we construct a PKPD model for arthritis development and antibody effects.Summarizing, we develop (semi)-mechanistic mathematical PKPD models based on pharmacological assumptions and apply our models to measured data from preclinical phase.