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. 2013 Nov 1;7:117.
doi: 10.1186/1752-0509-7-117.

Merging Concepts - Coupling an Agent-Based Model of Hematopoietic Stem Cells With an ODE Model of Granulopoiesis

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Free PMC article

Merging Concepts - Coupling an Agent-Based Model of Hematopoietic Stem Cells With an ODE Model of Granulopoiesis

Axel Krinner et al. BMC Syst Biol. .
Free PMC article

Abstract

Background: Hematopoiesis is a complex process involving different cell types and feedback mechanisms mediated by cytokines. This complexity stimulated various models with different scopes and applications. A combination of complementary models promises to provide their mutual confirmation and to explain a broader range of scenarios. Here we propose a combination of an ordinary differential equation (ODE) model of human granulopoiesis and an agent-based model (ABM) of hematopoietic stem cell (HSC) organization. The first describes the dynamics of bone marrow cell stages and circulating cells under various perturbations such as G-CSF treatment or chemotherapy. In contrast to the ODE model describing cell numbers, our ABM focuses on the organization of individual cells in the stem population.

Results: We combined the two models by replacing the HSC compartment of the ODE model by a difference equation formulation of the ABM. In this hybrid model, regulatory mechanisms and parameters of the original models were kept unchanged except for a few specific improvements: (i) Effect of chemotherapy was restricted to proliferating HSC and (ii) HSC regulation in the ODE model was replaced by the intrinsic regulation of the ABM. Model simulations of bleeding, chronic irradiation and stem cell transplantation revealed that the dynamics of hybrid and ODE model differ markedly in scenarios with stem cell damage. Despite these differences in response to stem cell damage, both models explain clinical data of leukocyte dynamics under four chemotherapy regimens.

Conclusions: ABM and ODE model proved to be compatible and were combined without altering the structure of both models. The new hybrid model introduces model improvements by considering the proliferative state of stem cells and enabling a cell cycle-dependent effect of chemotherapy. We demonstrated that it is able to explain and predict granulopoietic dynamics for a large variety of scenarios such as irradiation, bone marrow transplantation, chemotherapy and growth factor applications. Therefore, it promises to serve as a valuable tool for studies in a broader range of clinical applications, in particular where stem cell activation and proliferation are involved.

Figures

Figure 1
Figure 1
Schematic representation of the ODE model. Compartments representing cell types and growth factors are depicted as boxes (s. Table 1). Compartment MGB is substructured into G4-6 to model maturation with Γ-distributed transit times. Cell fluxes between compartments are shown as black arrows, the effect of chemotherapy as gray arrows with associated kill rate kX indicated by a label and feedbacks as colored arrows: intrinsic stem cell feedback (red), feedback from bone-marrow cells to stem cells (green) and feedback between later stages of granulopoiesis mediated by explicitly modeled growth-factors (blue). The colored arrows indicate the input for the feedback functions (s. Appendix A2.1) that dynamically control compartment parameters mentioned by the labels.
Figure 2
Figure 2
Scheme of the agent-based stem cell model and its coupling in the hybrid model. Each cell is characterized by its affiliation to one GE, niche affinity a < amax and cell cycle position c. The two GEs represent functionally different environments: in GE Α affinity a increases with time and is limited by amax. In GE Ω it decreases and cells proliferate. When a drops below the threshold a = amin, the cells lose the ability to switch to Α and leave the stem cell compartment. In the hybrid model they enter the progenitor compartment CG. The effect of chemotherapy CX was modeled as cell loss in GE Ω without affecting GE A.
Figure 3
Figure 3
Responses of ODE and hybrid model after depletion of compartments MGB and GRA. In both models the depleted compartments are repopulated within 3d. a) In the ODE model, the feedback to the SCC causes a transient decrease in stem cell number and damped oscillations. b) The hybrid model does not activate the SCC and the perturbation has vanished in all compartments after ~23 days without oscillations.
Figure 4
Figure 4
Simulations of bone marrow transplantation with G-CSF support after myeloablative conditioning. All bone marrow compartments were initialized with 1%, only GRA with 50% of its equilibrium value. We present relative cell numbers throughout. a) In the ODE model, S repopulates 50% after 18d and 100% after 60d. GRA repopulates 50% after 6d and 100% after 7d. b) Both GEs in the SCC of the hybrid model are reduced. Repopulation is slow and not completed after 100d. c) Stem cell reduction is limited to the proliferative GE Ω. S repopulates 98% in 5 days, PGB and GRA 100% after 9.5d. The other compartments repopulate within the next 40 days.
Figure 5
Figure 5
Simulations of chronic irradiation. Constant kill rates are applied to S, CG and PGB (with kCG = kPGB = 0.66 kS). Cell numbers in S, CG, PGB and GRA are recorded after 100 days. a) In the ODE model reductions in S and CG are similar. PGB and GRA almost maintain cell numbers at low doses. At higher doses cell numbers in PGB and GRA decrease rapidly. b,c) In the hybrid model damage in S is smaller than in all other compartments. b) If both GEs Α and Ω are damaged, the system is sensitive to kill rates that are an order of magnitude smaller than for the ODE model. c) If damage is restricted to GE Ω, the SCC is more robust at kill rates comparable to those of the ODE model. All other compartments are more sensitive in comparison to stem cells.
Figure 6
Figure 6
Comparison of the predictions of the hybrid model with clinical data on leukocyte dynamics in peripheral blood during chemotherapy without G-CSF. Clinical data of a) CHOP-21 and b) CHOEP-21 administration (Blue: median of patients, black: 25 and 75 percentiles) are compared with corresponding simulation results of the hybrid model (red). Simulation results fit well to clinical data in the sense that they lie in the interquartile range of data for almost all time points. Cell numbers are normalized with respect to the average WBC/leukocyte count value of healthy individuals (7000 cells/μl).
Figure 7
Figure 7
Comparison of the predictions of the hybrid model with clinical data on leukocyte dynamics in peripheral blood during chemotherapy with G-CSF support. Clinical data of a) CHOP-14 and b) CHOEP-14 administration (Blue: median of patients, black: 25 and 75 percentiles) are compared with corresponding simulation results of the hybrid model (red). The effect of growth factor support is reflected by the peak approximately one day after starting the G-CSF treatment at day 4 in each cycle. As for the regimens without G-CSF, simulation results fit well to clinical data. Cell numbers are normalized with respect to the average WBC/leukocyte count value of healthy individuals (7000 cells/μl).
Figure 8
Figure 8
Comparison of stem cell dynamics in ODE and hybrid model. a) Stem cell number in the ODE model (green) is heavily reduced and does not recover within one cycle. In the hybrid model, total stem cell number (red) is only reduced to ~80%. Depletion of proliferative stem cells (blue) is similar to the ODE model, but regeneration is fast. b) Effluxes from the ODE SCC (green) and the hybrid model (red) almost vanish after drug administration, but increase simultaneously around day 7.
Figure 9
Figure 9
Preliminary simulation of myeloablative bone marrow transplant with modified transition characteristics. While keeping the equilibrium values of the transition characteristics nearly unchanged, for smaller cell numbers NΑ and NΩ the transition characteristics increase much stronger than for the established human parameter set. The more dynamic switching behavior results effectively in stem cell activation and much faster recovery. Stem cells repopulate completely after 31 days and GRA recovers 25% of its equilibrium value after 36 days. Again G-CSF application was continued until the recovery of GRA.

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