Department of Mathematics & Statistics, McGill University, Montreal, QC, H3A 0B9, Canada.
Program for Evolutionary Dynamics, Harvard University, Cambridge, MA, 02138, USA.
J Pharmacokinet Pharmacodyn. 2018 Feb;45(1):59-77. doi: 10.1007/s10928-017-9560-y. Epub 2017 Dec 13.
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.
通过集中研究 Quartino 对 Friberg 骨髓抑制转运室模型的扩展，研究了转运室常微分方程建模方法与分布和离散时滞微分方程模型的比较，该模型广泛应用于药物科学领域，用于预测化疗后中性粒细胞的反应，以及粒细胞生成的 QSP 时滞微分方程模型。通过考虑一般数量的转运室并引入一个额外的参数，可以将成熟时间与细胞的产生率解耦，从而对 Quartino 模型进行扩展。然后，概述了一种成熟的线性链技术，用于将具有恒定转运率的转运室模型重新表述为分布时滞微分方程 (DDE)。对 Quartino 模型进行状态相关的时间重标度，以应用线性链技术并将 Quartino 模型重写为分布 DDE，在特定参数极限下得到离散 DDE 模型。接下来，进行稳定性和分支分析，努力将此类研究置于数学药理学背景下。我们表明，原始的 Friberg 和 Quartino 扩展模型都错误地定义了平均成熟时间，本质上将增殖池视为额外的成熟室。这种错误指定对 PK/PD 中骨髓抑制的未来模型的开发可能会产生深远的影响。
