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Transit and lifespan in neutrophil production: implications for drug intervention

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Abstract

A comparison of the transit compartment ordinary differential equation modelling approach to distributed and discrete delay differential equation models is studied by focusing on Quartino’s extension to the Friberg transit compartment model of myelosuppression, widely relied upon in the pharmaceutical sciences to predict the neutrophil response after chemotherapy, and on a QSP delay differential equation model of granulopoiesis. An extension to the Quartino model is provided by considering a general number of transit compartments and introducing an extra parameter that allows for the decoupling of the maturation time from the production rate of cells. An overview of the well established linear chain technique, used to reformulate transit compartment models with constant transit rates as distributed delay differential equations (DDEs), is then given. A state-dependent time rescaling of the Quartino model is performed to apply the linear chain technique and rewrite the Quartino model as a distributed DDE, yielding a discrete DDE model in a certain parameter limit. Next, stability and bifurcation analyses are undertaken in an effort to situate such studies in a mathematical pharmacology context. We show that both the original Friberg and the Quartino extension models incorrectly define the mean maturation time, essentially treating the proliferative pool as an additional maturation compartment. This misspecification can have far reaching consequences on the development of future models of myelosuppression in PK/PD.

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Fig. 1

Figure reproduced from: Craig [12] with the permission of Wiley (Color figure online)

Fig. 2

Figure reproduced from: Quartino et al. [38, p. 3396] with the permission of Springer

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Acknowledgements

DCS was supported by National Council for Scientific and Technological Development of Brazil (CNPq) postdoctoral fellowship 201105/2014-4. MC was supported by an Natural Sciences and Engineering Research Council of Canada (NSERC) postdoctoral fellowship and Grant DP5OD019851 from the Office of the Director at the National Institutes of Health to her PI. TC was supported by the Alberta government via the Sir James Lougheed Award of Distinction as well as the Centre de recherches mathématiques, Montréal. FN and JL are funded by FN’s NSERC Industrial Chair in Pharmacometrics, supported by Novartis, Pfizer, and inVentiv Health Clinics, and an FrQNT projet d’équipe. JB and ARH are grateful to NSERC, Canada for funding through the Discovery Grant program. We are appreciative for our many very useful discussions with Michael C. Mackey.

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Author notes

  1. Daniel Câmara De Souza and Morgan Craig are the co-first authors.

Authors and Affiliations

  1. Department of Mathematics & Statistics, McGill University, Montreal, QC, H3A 0B9, Canada

    Daniel Câmara De Souza & Tyler Cassidy

  2. Program for Evolutionary Dynamics, Harvard University, Cambridge, MA, 02138, USA

    Morgan Craig

  3. Faculté de Pharmacie, Université de Montréal, Montreal, QC, H3C 3J7, Canada

    Jun Li & Fahima Nekka

  4. Département de mathématiques et de statistique, Université de Montréal, Montreal, QC, H3C 3J7, Canada

    Jacques Bélair

  5. Departments of Mathematics & Statistics, and Physiology, McGill University, Montreal, QC, H3A 0B9, Canada

    Antony R. Humphries

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  1. Daniel Câmara De Souza
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Correspondence to Morgan Craig.

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Câmara De Souza, D., Craig, M., Cassidy, T. et al. Transit and lifespan in neutrophil production: implications for drug intervention. J Pharmacokinet Pharmacodyn 45, 59–77 (2018). https://doi.org/10.1007/s10928-017-9560-y

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