Pharmacokinetic and -dynamic modelling of G-CSF derivatives in humans

Abstract

Background: The human granulocyte colony-stimulating factor (G-CSF) is routinely applied to support recovery of granulopoiesis during the course of cytotoxic chemotherapies. However, optimal use of the drug is largely unknown. We showed in the past that a biomathematical compartment model of human granulopoiesis can be used to make clinically relevant predictions regarding new, yet untested chemotherapy regimen. In the present paper, we aim to extend this model by a detailed pharmacokinetic and -dynamic modelling of two commonly used G-CSF derivatives Filgrastim and Pegfilgrastim.

Results: Model equations are based on our physiological understanding of the drugs which are delayed absorption of G-CSF when applied to the subcutaneous tissue, dose-dependent bioavailability, unspecific first order elimination, specific elimination in dependence on granulocyte counts and reversible protein binding. Pharmacokinetic differences between Filgrastim and Pegfilgrastim were modelled as different parameter sets. Our former cell-kinetic model of granulopoiesis was essentially preserved, except for a few additional assumptions and simplifications. We assumed a delayed action of G-CSF on the bone marrow, a delayed action of chemotherapy and differences between Filgrastim and Pegfilgrastim with respect to stimulation potency of the bone marrow. Additionally, we incorporated a model of combined action of Pegfilgrastim and Filgrastim or endogenous G-CSF which interact via concurrent receptor binding. Unknown pharmacokinetic or cell-kinetic parameters were determined by fitting the predictions of the model to available datasets of G-CSF applications, chemotherapy applications or combinations of it. Data were either extracted from the literature or were received from cooperating clinical study groups. Model predictions fitted well to both, datasets used for parameter estimation and validation scenarios as well. A unique set of parameters was identified which is valid for all scenarios considered. Differences in pharmacokinetic parameter estimates between Filgrastim and Pegfilgrastim were biologically plausible throughout.

Conclusion: We conclude that we established a comprehensive biomathematical model to explain the dynamics of granulopoiesis under chemotherapy and applications of two different G-CSF derivatives. We aim to apply the model to a large variety of chemotherapy regimen in the future in order to optimize corresponding G-CSF schedules or to individualize G-CSF treatment according to the granulotoxic risk of a patient.

Figure 1

(Basic structure of the cell-kinetic model of granulopoiesis). Major model compartments describing granulopoietic cell stages are S (pluripotent stem cells), CG (colony forming units of granulocytes and macrophages), PGB (proliferating granulopoietic blasts), MGB (maturing granulopoietic blasts - subdivided into metamyelocytes (G4),banded granulocytes (G5) and segmented granulocytes (G6)) and GRA (circulating granulocytes). The system is regulated by feedback loops. A major loop is mediated by G-CSF which is produced endogenously but can also be applied subcutaneously. Chemotherapy (CX) induces acute cell loss. The model is essentially the same as in [40].

Figure 2

(Model structure of the pharmacokinetic model of G-CSF). The major compartments, cytokine fluxes and regulations are presented (MM = Michaelis Menten kinetic). The subcutaneous compartment is divided into two subcompartments with first order transition.

Figure 3

(Estimated bioavailability of subcutaneously injected Filgrastim or Pegfilgrastim based on systematic model simulations): Bioavailability was estimated by calculating G-CSF amounts absorbed by the central compartment relative and the total amount of subcutaneously injected G-CSF (x-axis). Due to the modelled loss in the subcutaneous tissue, the bioavailability is dose-dependent. Circles indicate estimates for pharmaceutically available doses of 300μg and 480μg of Filgrastim or 6000 μg of Pegfilgrastim respectively [12,67].

Figure 4

(Comparison of model and data for G-CSF applications): Comparison of model and selected datasets of single Filgrastim injections (scenario A), multiple Filgrastim injections (scenario B) and single Pegfilgrastim injections of different doses (scenarios C and D). For each scenario, we present the time courses of ANC and G-CSF, respectively. A complete list of scenarios can be found in the Additional file 1.

Figure 5

(Regulation functions of Filgrastim and Pegfilgrastim): Comparison of Filgrastim and Pegfilgrastim with respect to the regulation function of the amplification in PGB. The circle marks the value under steady-state conditions.

Figure 6

(Effect of G-CSF delay): Effect of the delay parameter of G-CSF action on cell-counts of specific cell compartments.

Figure 7

(Effect of chemotherapy delay): Effect of the delay parameter of the chemotherapy studied for the CHOP regimen.

Figure 8

(Comparison of model and data for chemotherapy scenarios): Comparison of model and data for the CHOP-21 regimen and time intensified CHOP-14 regimen supported by various Filgrastim and Pegfilgrastim schedules. The solid line is the model prediction. Dots are patient medians at corresponding time points and the grey lines mark the interquartile range of the data. All scenarios are based on the same model parameters.

Figure 9

(Ratio of granulocytes and leukocytes): Based on model simulations, the ratio of granulocytes and leukocytes under CHOP-14 chemotherapy is predicted.

Figure 10

(Validation of model): Validation of the model on the basis of two datasets not used for model fitting. Solid line is the model prediction. Dots and dotted lines are the data and the interpolated data respectively.