A combined model of human erythropoiesis and granulopoiesis under growth factor and chemotherapy treatment

Abstract

Background: Haematotoxicity of conventional chemotherapies often results in delays of treatment or reduction of chemotherapy dose. To ameliorate these side-effects, patients are routinely treated with blood transfusions or haematopoietic growth factors such as erythropoietin (EPO) or granulocyte colony-stimulating factor (G-CSF). For the latter ones, pharmaceutical derivatives are available, which differ in absorption kinetics, pharmacokinetic and -dynamic properties. Due to the complex interaction of cytotoxic effects of chemotherapy and the stimulating effects of different growth factor derivatives, optimal treatment is a non-trivial task. In the past, we developed mathematical models of thrombopoiesis, granulopoiesis and erythropoiesis under chemotherapy and growth-factor applications which can be used to perform clinically relevant predictions regarding the feasibility of chemotherapy schedules and cytopenia prophylaxis with haematopoietic growth factors. However, interactions of lineages and growth-factors were ignored so far.

Results: To close this gap, we constructed a hybrid model of human granulopoiesis and erythropoiesis under conventional chemotherapy, G-CSF and EPO applications. This was achieved by combining our single lineage models of human erythropoiesis and granulopoiesis with a common stem cell model. G-CSF effects on erythropoiesis were also implemented. Pharmacodynamic models are based on ordinary differential equations describing proliferation and maturation of haematopoietic cells. The system is regulated by feedback loops partly mediated by endogenous and exogenous EPO and G-CSF. Chemotherapy is modelled by depletion of cells. Unknown model parameters were determined by fitting the model predictions to time series data of blood counts and cytokine profiles. Data were extracted from literature or received from cooperating clinical study groups. Our model explains dynamics of mature blood cells and cytokines after growth-factor applications in healthy volunteers. Moreover, we modelled 15 different chemotherapeutic drugs by estimating their bone marrow toxicity. Taking into account different growth-factor schedules, this adds up to 33 different chemotherapy regimens explained by the model.

Conclusions: We conclude that we established a comprehensive biomathematical model to explain the dynamics of granulopoiesis and erythropoiesis under combined chemotherapy, G-CSF, and EPO applications. We demonstrate how it can be used to make predictions regarding haematotoxicity of yet untested chemotherapy and growth-factor schedules.

Figure 1

Structure of the model of erythropoiesis and granulopoiesis under chemotherapy, G-CSF and EPO application. 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, CG = granulopoietic progenitor cells (colony forming units of granulocytes and macrophages), PGB = proliferating granulopoietic precursor cells (myeloblasts, promyelocytes, myelocytes), MGB = maturing granulopoietic precursor cells (metamyelocytes, banded and segmented granulocytes)), GRA = granulocytes, LY = lymphocytes, CX = chemotherapy. Several regulatory feedback loops are displayed. The most important two are mediated by EPO and by G-CSF which are produced endogenously and could also be applied externally. Chemotherapy is modelled by a transient depletion of cells.

Figure 2

Regulatory functions in compartment CE. Regulatory functions describing the effect of Filgrastim, Pegfilgrastim, EPO and combinations of it on amplification rate and transition time in the compartment CE. While amplification is assumed to be unaffected by G-CSF, the transition time is delayed under G-CSF stimulation. A: Delay factor of transition time - dependence on endogenous G-CSF/Filgrastim concentration. We mark the values achieved at steady-state (green) and at maximum after a single s.c. application of 480 μg (black). B: Delay factor of transition time - dependence on Pegfilgrastim concentration. Values achieved at maximum after a single s.c. application of 6000 μg (black) and steady state (green) are marked. C: Amplification in CE - dependence on internalised EPO. No G-CSF effects are assumed here. D: Transition times in CE - dependence on internalised EPO and G-CSF concentration. We present the raw regulatory functions without considering G-CSF effects (dotted) and maximal deviations after either Filgrastim application of 480 μg (solid) or Pegfilgrastim application of 6000 μg (grey). Note that the regulatory functions presented in A and B are superimposed (Equation 16) under Pegfilgrastim or combined Pegfilgrastim/Filgrastim applications.

Figure 3

Model behaviour after single injection of EPO. We present cell counts normalised to steady state values after i.v. injection of 150 IU/kg EPO Alfa. After damped oscillations of compartment sizes the system converges to equilibrium state.

Figure 4

Model behaviour after single injection of G-CSF. Model behaviour after perturbation with respect to steady state values. We present cell counts normalised to steady state values after a single s.c. injection of 300 μg Filgrastim (left) or 300 μg Pegfilgrastim (right). A single Filgrastim injection results in damped oscillations of compartment sizes, which was not observed for Pegfilgrastim.

Figure 5

Model behaviour during continuous stimulation with EPO or G-CSF. Left: EPO, right: Filgrastim. New steady states are reached after a certain time.

Figure 6

Model behaviour after a single chemotherapy administration. We present cell counts normalised to steady state values after a single administration of CHOP chemotherapy. Except for erythrocytes, all lineages show damped oscillations over a longer time period.

Figure 7

Comparison of dynamics after CHOP chemotherapy. Comparison of the behaviour of the combined and the single lineage models after perturbation with CHOP chemotherapy. We present stem cell dynamics, CE, HB and WBC normalised to steady state values.

Figure 8

Model simulations of different CHOP chemotherapies with or without Filgrastim support. First row: Six cycles of CHOP with cycle duration of 21 days without Filgrastim, second row: Six cycles of CHOP with cycle duration of 14 days with Filgrastim at day 4–13 at each therapy cycle, third row: Eight cycles of CHOP with cycle duration of 14 days with Filgrastim at day 6–12 at each therapy cycle. We present time series of HB and WBC simulated with our combined model (black solid line) and compare it with corresponding simulation results of the single lineage models (grey solid line). We also compare model results with our clinical data (median: circles, first and third quartile: grey dashed line) taken from the trials published in [45,63].

Figure 9

Model simulations of six cycles of CHOP chemotherapy with cycle duration of 14 days and different Pegfilgrastim support. We present time series of HB and WBC simulated with our combined model (black solid line). We compare model results with our clinical data (median: circles, first and third quartile: grey dashed line) taken from clinical trials [5].

Figure 10

Hybrid model simulations after chemotherapy, Filgrastim or EPO. We present results of different breast cancer therapies. First row: four cycles of the drug combination epirubicine + cyclophosphamide followed by four cycles of paclitaxel with cycle duration of 21 days without G-CSF, second row: three single drug cycles of epirubicine, paclitaxel, cyclophosphamide applied consecutively with cycle duration of 14 days with Filgrastim on cycle days 3–10, third row: The same therapy as described in second row but with additional EPO Alfa. We show HB and WBC values of simulation (black line), medians (circle), 25th and 75th percentiles (grey dashed line) of patients data. While raw data are available for the first two scenarios, data of the third scenario are taken from [51].

Figure 11

Example validation scenario. Data of Lundby et al. [64] after multiple injections of EPO Beta. Time series of WBC, HB, Reticulocytes and HK are presented. Solid black curve represents simulation results. Circles and grey line represent means and standard deviations respectively [64].

Figure 12

Prediction scenarios. We present predictions regarding BEACOPP-escalated and CHOP 14 (elderly) supported by Filgrastim and weekly Darbepoetin starting on day 0. Simulation results of WBC and HB are shown as black curve. Grey curves show predictions of dynamics without additional Darbepoetin applications. Median of data is represented by circles, and grey hatched line describe first and third quartile of the data [49,63].