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. 2013 Jun 6;8(6):e65630.
doi: 10.1371/journal.pone.0065630. Print 2013.

A Biomathematical Model of Human Erythropoiesis Under Erythropoietin and Chemotherapy Administration

Free PMC article

A Biomathematical Model of Human Erythropoiesis Under Erythropoietin and Chemotherapy Administration

Sibylle Schirm et al. PLoS One. .
Free PMC article


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.

Conflict of interest statement

Competing Interests: The authors have declared that no competing interests exist.


Figure 1
Figure 1. Structure of the model of erythropoiesis under chemotherapy and EPO application.
We combined four independently developed models (cell kinetic, pharmacokinetic, injection, chemotherapy) into one comprehensive model. Model compartments are presented in boxes (S = stem cells, BE = burst forming units - erythroid, CE = colony forming units - erythroid, PEB = proliferating erythrocytic blasts, MEB = maturing erythrocytic blasts, RET = reticulocytes, ERY = erythrocytes, EPO = erythropoietin). Several regulatory feedback loops are implemented. The most important one is mediated by EPO which is produced endogenously and can also be applied externally. Chemotherapy is modelled by a transient depletion of cells.
Figure 2
Figure 2. Pharmacokinetic model of EPO.
Boxes represent compartments. Arrows represent actions or flows. The pharmacokinetic model of erythropoietin was adapted from .
Figure 3
Figure 3. Structure of the EPO injection model with two ways of EPO absorption.
The model is in analogy to . Boxes denote the compartments, arrows represent EPO fluxes between the compartments.
Figure 4
Figure 4. Model dynamics after single perturbations.
A) Continuous EPO stimulation. B) Effect of a single cycle of CHOP chemotherapy.
Figure 5
Figure 5. Comparison of model prediction and data of EPO serum concentration for different injection scenarios.
The data are taken from the following literature: , , , , –.
Figure 6
Figure 6. Estimated bioavailability of erythropoietin after different types of injection and in dependence on dose.
Here, bioavailability is defined as the ratio of the integrated influxes into the central compartment under subcutaneous and intravenous injection respectively.
Figure 7
Figure 7. Comparison of injection modes.
Comparison of erythrocytes, reticulocytes, HB values, and the sum of the bone marrow cell stages after intravenous (left) and different subcutaneous injection sites (right).
Figure 8
Figure 8. Comparison of model and data for a number of chemotherapy scenarios.
Dots represent patient medians (first four) or means (last two), grey solid lines the interquartile range of data, grey dotted lines mean formula image standard deviation. Black solid line is the model prediction.The following chemotherapies are displayed: CHOP, CHOEP, BEACOPP 21 escalated, BEACOPP 21, for which we have access to raw data (studies are described in [15], [16], [19], [20]), and Platinum plus Etoposide with or without Darbepoetin Alfa (data were extracted from the literature [59]).
Figure 9
Figure 9. Comparison of toxic effects between different chemotherapies.
We present the relations between stem cell toxicities and resulting AOC of reticulocytes and erythrocytes for a single therapy cycle.
Figure 10
Figure 10. 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 formula image 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 , : dots represent patient means. Solid black curve represents model predictions throughout.
Figure 11
Figure 11. Prediction.
Weekly administration of 150 IU/kg Darbepoetin Alfa has the potential to avoid anaemia in patients treated with 8 cycles of BEACOPP-21 escalated (left) or CHOP 14 (right).

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Grant support

S.S. was partially funded by a grant of the Federal Ministry of Education and Research of the Federal Republic of Germany (“Haematosys”, BMBF/PTJ0315452A) and by LIFE - Leipzig Research Center for Civilization Diseases, University of Leipzig. LIFE is funded by means of the European Union, by the European Regional Development Fund (ERDF) and by means of the Free State of Saxony within the framework of the excellence initiative. M.S. was also funded by LIFE. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.