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Mathematical Concepts in Pharmacokinetics and Pharmacodynamics with Application to Tumor Growth

Part of the Lecture Notes in Mathematics book series (LNMBIOS,volume 2102)

Abstract

Mathematical modeling plays an important and increasing role in drug development. The objective of this chapter is to present the concept of pharmacokinetic (PK) and pharmacodynamic (PD) modeling applied in the pharmaceutical industry. We will introduce typically PK and PD models and present the underlying pharmacological and biological interpretation. It turns out that any PKPD model is a nonautonomous dynamical system driven by the drug concentration. We state a theoretical result describing the general relationship between two widely used models, namely, transit compartments and lifespan models. Further, we develop a PKPD model for tumor growth and anticancer effects based on the present model figures and apply the model to measured data.

Keywords

  • Lifespan models
  • Mathematical modeling
  • Pharmacodynamics
  • Pharmacokinetics
  • Transit compartments
  • Tumor growth

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Fig. 7.1
Fig. 7.2

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Acknowledgements

The present project is supported by the National Research Fund, Luxembourg, and cofunded under the Marie Curie Actions of the European Commission (FP7-COFUND). The authors like to thank Dr. Antje Walz and Dr. Thomas Wagner for their valuable comments and remarks.

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Correspondence to Gilbert Koch .

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Koch, G., Schropp, J. (2013). Mathematical Concepts in Pharmacokinetics and Pharmacodynamics with Application to Tumor Growth. In: Kloeden, P., Pötzsche, C. (eds) Nonautonomous Dynamical Systems in the Life Sciences. Lecture Notes in Mathematics(), vol 2102. Springer, Cham. https://doi.org/10.1007/978-3-319-03080-7_7

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