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A biomathematical model of human erythropoiesis under erythropoietin and chemotherapy administration.

Schirm S, Engel C, Loeffler M, Scholz M - PLoS ONE (2013)

Bottom Line: We added a model of EPO absorption after injection at different sites and a pharmacokinetic model of EPO derivatives to account for the effects of external EPO applications.Parameter fittings resulted in a good agreement of model and data.Prospective clinical studies are needed to validate model predictions and to explore the feasibility and effectiveness of the proposed schedules.

View Article: PubMed Central - PubMed

Affiliation: Institute for Medical Informatics, Statistics and Epidemiology, University of Leipzig, Leipzig, Germany. sibylle.schirm@imise.uni-leipzig.de

ABSTRACT
Anaemia is a common haematologic side effect of dose-dense multi-cycle cytotoxic polychemotherapy requiring erythrocyte transfusions or erythropoietin (EPO) administration. To simulate the effectiveness of different EPO application schedules, we performed both modelling of erythropoiesis under chemotherapy and pharmacokinetic and dynamic modelling of EPO applications in the framework of a single comprehensive biomathematical model. For this purpose, a cell kinetic model of bone marrow erythropoiesis was developed that is based on a set of differential compartment equations describing proliferation and maturation of erythropoietic cell stages. The system is regulated by several feedback loops comprising those mediated by EPO. We added a model of EPO absorption after injection at different sites and a pharmacokinetic model of EPO derivatives to account for the effects of external EPO applications. Chemotherapy is modelled by a transient depletion of bone marrow cell stages. Unknown model parameters were determined by fitting the predictions of the model to data sets of circulating erythrocytes, haemoglobin, haematocrit, percentage of reticulocytes or EPO serum concentrations derived from the literature or cooperating clinical study groups. Parameter fittings resulted in a good agreement of model and data. Depending on site of injection and derivative (Alfa, Beta, Delta, Darbepoetin), nine groups of EPO applications were distinguished differing in either absorption kinetics or pharmacokinetics. Finally, eight different chemotherapy protocols were modelled. The model was validated on the basis of scenarios not used for parameter fitting. Simulations were performed to analyze the impact of EPO applications on the risk of anaemia during chemotherapy. We conclude that we established a model of erythropoiesis under chemotherapy that explains a large set of time series data under EPO and chemotherapy applications. It allows predictions regarding yet untested EPO schedules. Prospective clinical studies are needed to validate model predictions and to explore the feasibility and effectiveness of the proposed schedules.

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Pharmacokinetic model of EPO.Boxes represent compartments. Arrows represent actions or flows. The pharmacokinetic model of erythropoietin was adapted from [13].
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pone-0065630-g002: Pharmacokinetic model of EPO.Boxes represent compartments. Arrows represent actions or flows. The pharmacokinetic model of erythropoietin was adapted from [13].

Mentions: All three assumptions are natural extensions of the model. A schematic illustration is shown in figure 2. The first assumption translates in the following (adapted) equation of the central compartment:(3)where is a function of external EPO applications specified later. The function of endogenous EPO production is defined as follows:(4)where equals one in steady state, so that equation 3 equals zero. depends on the oxygen partial pressure and the number of circulating red blood cells (details see section A.2 in the file S1 or [7]–[9]).


A biomathematical model of human erythropoiesis under erythropoietin and chemotherapy administration.

Schirm S, Engel C, Loeffler M, Scholz M - PLoS ONE (2013)

Pharmacokinetic model of EPO.Boxes represent compartments. Arrows represent actions or flows. The pharmacokinetic model of erythropoietin was adapted from [13].
© Copyright Policy
Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC3675041&req=5

pone-0065630-g002: Pharmacokinetic model of EPO.Boxes represent compartments. Arrows represent actions or flows. The pharmacokinetic model of erythropoietin was adapted from [13].
Mentions: All three assumptions are natural extensions of the model. A schematic illustration is shown in figure 2. The first assumption translates in the following (adapted) equation of the central compartment:(3)where is a function of external EPO applications specified later. The function of endogenous EPO production is defined as follows:(4)where equals one in steady state, so that equation 3 equals zero. depends on the oxygen partial pressure and the number of circulating red blood cells (details see section A.2 in the file S1 or [7]–[9]).

Bottom Line: We added a model of EPO absorption after injection at different sites and a pharmacokinetic model of EPO derivatives to account for the effects of external EPO applications.Parameter fittings resulted in a good agreement of model and data.Prospective clinical studies are needed to validate model predictions and to explore the feasibility and effectiveness of the proposed schedules.

View Article: PubMed Central - PubMed

Affiliation: Institute for Medical Informatics, Statistics and Epidemiology, University of Leipzig, Leipzig, Germany. sibylle.schirm@imise.uni-leipzig.de

ABSTRACT
Anaemia is a common haematologic side effect of dose-dense multi-cycle cytotoxic polychemotherapy requiring erythrocyte transfusions or erythropoietin (EPO) administration. To simulate the effectiveness of different EPO application schedules, we performed both modelling of erythropoiesis under chemotherapy and pharmacokinetic and dynamic modelling of EPO applications in the framework of a single comprehensive biomathematical model. For this purpose, a cell kinetic model of bone marrow erythropoiesis was developed that is based on a set of differential compartment equations describing proliferation and maturation of erythropoietic cell stages. The system is regulated by several feedback loops comprising those mediated by EPO. We added a model of EPO absorption after injection at different sites and a pharmacokinetic model of EPO derivatives to account for the effects of external EPO applications. Chemotherapy is modelled by a transient depletion of bone marrow cell stages. Unknown model parameters were determined by fitting the predictions of the model to data sets of circulating erythrocytes, haemoglobin, haematocrit, percentage of reticulocytes or EPO serum concentrations derived from the literature or cooperating clinical study groups. Parameter fittings resulted in a good agreement of model and data. Depending on site of injection and derivative (Alfa, Beta, Delta, Darbepoetin), nine groups of EPO applications were distinguished differing in either absorption kinetics or pharmacokinetics. Finally, eight different chemotherapy protocols were modelled. The model was validated on the basis of scenarios not used for parameter fitting. Simulations were performed to analyze the impact of EPO applications on the risk of anaemia during chemotherapy. We conclude that we established a model of erythropoiesis under chemotherapy that explains a large set of time series data under EPO and chemotherapy applications. It allows predictions regarding yet untested EPO schedules. Prospective clinical studies are needed to validate model predictions and to explore the feasibility and effectiveness of the proposed schedules.

Show MeSH
Related in: MedlinePlus