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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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Validation scenarios.Reticulocytes (A) and HB (B) after multiple injections of EPO Beta (data were extracted from [32]): dots represent patient means, grey dotted lines mean  standard deviation. (C) HB under eight cycles of CHOP-14 therapy (we have access to the raw data, the study is described in [18]): dots represent patient medians, grey lines represent interquartile range of patient data. Reticulocytes (%) (D) and EPO serum concentrations (E,F) after multiple EPO Alfa injections at different subcutaneous sites [31], [33]: dots represent patient means. Solid black curve represents model predictions throughout.
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pone-0065630-g010: Validation scenarios.Reticulocytes (A) and HB (B) after multiple injections of EPO Beta (data were extracted from [32]): dots represent patient means, grey dotted lines mean standard deviation. (C) HB under eight cycles of CHOP-14 therapy (we have access to the raw data, the study is described in [18]): dots represent patient medians, grey lines represent interquartile range of patient data. Reticulocytes (%) (D) and EPO serum concentrations (E,F) after multiple EPO Alfa injections at different subcutaneous sites [31], [33]: dots represent patient means. Solid black curve represents model predictions throughout.

Mentions: A few data sets were not utilised for parameter fitting, but were used for model validation. Data sets can be used for validation if no additional parameters must be fitted, i.e. the chemotherapy toxicities and the injection model parameters are known from a different data set. These data comprise the following scenarios: EPO serum concentration from athletes receiving a single dose of 50 IU/kg or multiple application of a high dose of 200 IU/kg EPO Alfa on day 0, 2, 4, 7, and 10 into the upper arm [31], data of HCT, HB and reticulocyte time courses after multiple injections of 5000 IU EPO Beta over a long time period of 15 weeks [32], as well as one scenario from Cheung et al. with weekly injections of 600 IU EPO Alfa into the thigh [33]. Predictions of all scenarios fitted well to the observed clinical data (see figure 10). For validation of our model of chemotherapy, we used time series data of HB under eight cycles of CHOP-14 therapy retrieved from the RICOVER trial [18]. Results of model simulation fit well for the cycles 1–6. But HB values of the last two cycles were slightly underestimated.


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

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

Validation scenarios.Reticulocytes (A) and HB (B) after multiple injections of EPO Beta (data were extracted from [32]): dots represent patient means, grey dotted lines mean  standard deviation. (C) HB under eight cycles of CHOP-14 therapy (we have access to the raw data, the study is described in [18]): dots represent patient medians, grey lines represent interquartile range of patient data. Reticulocytes (%) (D) and EPO serum concentrations (E,F) after multiple EPO Alfa injections at different subcutaneous sites [31], [33]: dots represent patient means. Solid black curve represents model predictions throughout.
© Copyright Policy
Related In: Results  -  Collection

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

pone-0065630-g010: Validation scenarios.Reticulocytes (A) and HB (B) after multiple injections of EPO Beta (data were extracted from [32]): dots represent patient means, grey dotted lines mean standard deviation. (C) HB under eight cycles of CHOP-14 therapy (we have access to the raw data, the study is described in [18]): dots represent patient medians, grey lines represent interquartile range of patient data. Reticulocytes (%) (D) and EPO serum concentrations (E,F) after multiple EPO Alfa injections at different subcutaneous sites [31], [33]: dots represent patient means. Solid black curve represents model predictions throughout.
Mentions: A few data sets were not utilised for parameter fitting, but were used for model validation. Data sets can be used for validation if no additional parameters must be fitted, i.e. the chemotherapy toxicities and the injection model parameters are known from a different data set. These data comprise the following scenarios: EPO serum concentration from athletes receiving a single dose of 50 IU/kg or multiple application of a high dose of 200 IU/kg EPO Alfa on day 0, 2, 4, 7, and 10 into the upper arm [31], data of HCT, HB and reticulocyte time courses after multiple injections of 5000 IU EPO Beta over a long time period of 15 weeks [32], as well as one scenario from Cheung et al. with weekly injections of 600 IU EPO Alfa into the thigh [33]. Predictions of all scenarios fitted well to the observed clinical data (see figure 10). For validation of our model of chemotherapy, we used time series data of HB under eight cycles of CHOP-14 therapy retrieved from the RICOVER trial [18]. Results of model simulation fit well for the cycles 1–6. But HB values of the last two cycles were slightly underestimated.

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