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Bulletin of Mathematical Biology

, Volume 78, Issue 12, pp 2304–2357 | Cite as

A Mathematical Model of Granulopoiesis Incorporating the Negative Feedback Dynamics and Kinetics of G-CSF/Neutrophil Binding and Internalization

  • M. CraigEmail author
  • A. R. Humphries
  • M. C. Mackey
Original Article

Abstract

We develop a physiological model of granulopoiesis which includes explicit modelling of the kinetics of the cytokine granulocyte colony-stimulating factor (G-CSF) incorporating both the freely circulating concentration and the concentration of the cytokine bound to mature neutrophils. G-CSF concentrations are used to directly regulate neutrophil production, with the rate of differentiation of stem cells to neutrophil precursors, the effective proliferation rate in mitosis, the maturation time, and the release rate from the mature marrow reservoir into circulation all dependent on the level of G-CSF in the system. The dependence of the maturation time on the cytokine concentration introduces a state-dependent delay into our differential equation model, and we show how this is derived from an age-structured partial differential equation model of the mitosis and maturation and also detail the derivation of the rest of our model. The model and its estimated parameters are shown to successfully predict the neutrophil and G-CSF responses to a variety of treatment scenarios, including the combined administration of chemotherapy and exogenous G-CSF. This concomitant treatment was reproduced without any additional fitting to characterize drug–drug interactions.

Keywords

Granulopoiesis Mathematical modelling State-dependent delay differential equations Physiologically constructed pharmacokinetics G-CSF Bound and unbound drug concentrations 

Notes

Acknowledgments

A.R.H. and M.C.M. are grateful to the National Science and Engineering Research Council (NSERC), Canada, for funding through the Discovery Grant program. M.C. wishes to thank NSERC for funding from the PGS-D program. We are grateful to Fahima Nekka, Jun Li, Jacques Bélair, and David Dale for their insight and support. We would also like to thank both anonymous reviewers for their helpful and insightful comments.

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Copyright information

© Society for Mathematical Biology 2016

Authors and Affiliations

  1. 1.Faculté de PharmacieUniversité de MontréalMontréalCanada
  2. 2.Program for Evolutionary DynamicsHarvard UniversityCambridgeUSA
  3. 3.Department of Mathematics and StatisticsMcGill UniversityMontréalCanada
  4. 4.Departments of Mathematics, Physics and PhysiologyMcGill UniversityMontréalCanada

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