Neutrophil dynamics in response to chemotherapy and G-CSF

Efficacy of Neulasta or Neupogen on H-ARS and GI-ARS Mortality and Hematopoietic Recovery in Nonhuman Primates After 10-Gy Irradiation With 2.5% Bone Marrow Sparing

A nonhuman primate model of acute, partial-body, high-dose irradiation with minimal (2.5%) bone marrow sparing was used to assess endogenous gastrointestinal and hematopoietic recovery and the ability of Neulasta (pegylated granulocyte colony-stimulating factor) or Neupogen (granulocyte colony-stimulating factor) to enhance recovery from myelosuppression when administered at an increased interval between exposure and initiation of treatment. A secondary objective was to assess the effect of Neulasta or Neupogen on mortality and morbidity due to the hematopoietic acute radiation syndrome and concomitant gastrointestinal acute radiation syndrome. Nonhuman primates were exposed to 10.0 Gy, 6 MV, linear accelerator-derived photons delivered at 0.80 Gy min. All nonhuman primates received subject-based medical management. Nonhuman primates were dosed daily with control article (5% dextrose in water), initiated on day 1 postexposure; Neulasta (300 μg kg), administered on days 1, 8, and 15 or days 3, 10, and 17 postexposure; or Neupogen (10 μg kg), administered daily postexposure following its initiation on day 1 or day 3 until neutrophil recovery (absolute neutrophil count ≥1,000 cells μL for 3 consecutive days). Mortality in the irradiated cohorts suggested that administration of Neulasta or Neupogen on either schedule did not affect mortality due to gastrointestinal acute radiation syndrome or mitigate mortality due to hematopoietic acute radiation syndrome (plus gastrointestinal damage). Following 10.0 Gy partial-body irradiation with 2.5% bone marrow sparing, the mean duration of neutropenia (absolute neutrophil count <500 cells μL) was 22.4 d in the control cohort vs. 13.0 and 15.3 d in the Neulasta day 1, 8, 15 and day 3, 10, 17 cohorts, relative to 16.2 and 17.4 d in the Neupogen cohorts initiated on day 1 and day 3, respectively. The absolute neutrophil count nadirs were 48 cells μL in the controls; 117 cells μL and 40 cells μL in the Neulasta days 1, 8, and 15 or days 3, 10, and 17 cohorts, respectively; and 75 cells μL and 37 cells μL in the Neupogen day 1 and day 3 cohorts, respectively. Therefore, the earlier administration of Neulasta or Neupogen was more effective in this model of marginal 2.5% bone marrow sparing. The approximate 2.5% bone marrow sparing may approach the threshold for efficacy of the lineage-specific medical countermeasure. The partial-body irradiation with 2.5% bone marrow sparing model can be used to assess medical countermeasure efficacy in the context of the concomitant gastrointestinal and hematopoietic acute radiation syndrome sequelae.

Response of an oscillatory differential delay equation to a periodic stimulus

Periodic hematological diseases such as cyclical neutropenia or cyclical thrombocytopenia, with their characteristic oscillations of circulating neutrophils or platelets, may pose grave problems for patients. Likewise, periodically administered chemotherapy has the unintended side effect of establishing periodic fluctuations in circulating white cells, red cell precursors and/or platelets. These fluctuations, either spontaneous or induced, often have serious consequences for the patient (e.g. neutropenia, anemia, or thrombocytopenia respectively) which exogenously administered cytokines can partially correct. The question of when and how to administer these drugs is a difficult one for clinicians and not easily answered. In this paper we use a simple model consisting of a delay differential equation with a piecewise linear nonlinearity, that has a periodic solution, to model the effect of a periodic disease or periodic chemotherapy. We then examine the response of this toy model to both single and periodic perturbations, meant to mimic the drug administration, as a function of the drug dose and the duration and frequency of its administration to best determine how to avoid side effects.

Modeling large fluctuations of thousands of clones during hematopoiesis: The role of stem cell self-renewal and bursty progenitor dynamics in rhesus macaque

In a recent clone-tracking experiment, millions of uniquely tagged hematopoietic stem cells (HSCs) and progenitor cells were autologously transplanted into rhesus macaques and peripheral blood containing thousands of tags were sampled and sequenced over 14 years to quantify the abundance of hundreds to thousands of tags or “clones.” Two major puzzles of the data have been observed: consistent differences and massive temporal fluctuations of clone populations. The large sample-to-sample variability can lead clones to occasionally go “extinct” but “resurrect” themselves in subsequent samples. Although heterogeneity in HSC differentiation rates, potentially due to tagging, and random sampling of the animals’ blood and cellular demographic stochasticity might be invoked to explain these features, we show that random sampling cannot explain the magnitude of the temporal fluctuations. Moreover, we show through simpler neutral mechanistic and statistical models of hematopoiesis of tagged cells that a broad distribution in clone sizes can arise from stochastic HSC self-renewal instead of tag-induced heterogeneity. The very large clone population fluctuations that often lead to extinctions and resurrections can be naturally explained by a generation-limited proliferation constraint on the progenitor cells. This constraint leads to bursty cell population dynamics underlying the large temporal fluctuations. We analyzed experimental clone abundance data using a new statistic that counts clonal disappearances and provided least-squares estimates of two key model parameters in our model, the total HSC differentiation rate and the maximum number of progenitor-cell divisions.

Hematopoiesis of virally tagged cells in rhesus macaques is analyzed in the context of a mechanistic and statistical model. We find that the clone size distribution and the temporal variability in the abundance of each clone (viral tag) in peripheral blood are consistent with (i) stochastic HSC self-renewal during bone marrow repair, (ii) clonal aging that restricts the number of generations of progenitor cells, and (iii) infrequent and small-size samples. By fitting data, we infer two key parameters that control the level of fluctuations of clone sizes in our model: the total HSC differentiation rate and the maximum proliferation capacity of progenitor cells. Our analysis provides insight into the mechanisms of hematopoiesis and a framework to guide future multiclone barcoding/lineage tracking measurements.

Towards Quantitative Systems Pharmacology Models of Chemotherapy-Induced Neutropenia

Neutropenia is a serious toxic complication of chemotherapeutic treatment. For years, mathematical models have been developed to better predict hematological outcomes during chemotherapy in both the traditional pharmaceutical sciences and mathematical biology disciplines. An increasing number of quantitative systems pharmacology (QSP) models that combine systems approaches, physiology, and pharmacokinetics/pharmacodynamics have been successfully developed. Here, I detail the shift towards QSP efforts, emphasizing the importance of incorporating systems-level physiological considerations in pharmacometrics.

Optimized Treatment Schedules for Chronic Myeloid Leukemia

Over the past decade, several targeted therapies (e.g. imatinib, dasatinib, nilotinib) have been developed to treat Chronic Myeloid Leukemia (CML). Despite an initial response to therapy, drug resistance remains a problem for some CML patients. Recent studies have shown that resistance mutations that preexist treatment can be detected in a substantial number of patients, and that this may be associated with eventual treatment failure. One proposed method to extend treatment efficacy is to use a combination of multiple targeted therapies. However, the design of such combination therapies (timing, sequence, etc.) remains an open challenge. In this work we mathematically model the dynamics of CML response to combination therapy and analyze the impact of combination treatment schedules on treatment efficacy in patients with preexisting resistance. We then propose an optimization problem to find the best schedule of multiple therapies based on the evolution of CML according to our ordinary differential equation model. This resulting optimization problem is nontrivial due to the presence of ordinary different equation constraints and integer variables. Our model also incorporates drug toxicity constraints by tracking the dynamics of patient neutrophil counts in response to therapy. We determine optimal combination strategies that maximize time until treatment failure on hypothetical patients, using parameters estimated from clinical data in the literature.

Targeted therapy using imatinib, nilotinib or dasatinib has become standard treatment for chronicle myeloid leukemia. A minority of patients, however, fail to respond to treatment or relapse due to drug resistance. One primary driving factor of drug resistance are point mutations within the driving oncogene. Laboratory studies have shown that different leukemic mutants respond differently to different drugs, so a promising way to improve treatment efficacy is to combine multiple targeted therapies. We build a mathematical model to predict the dynamics of different leukemic mutants with imatinib, nilotinib and dasatinib, and employ optimization techniques to find the best treatment schedule of combining the three drugs sequentially. Our study shows that the optimally designed combination therapy is more effective at controlling the leukemic cell burden than any monotherapy under a wide range of scenarios. The structure of the optimal schedule depends heavily on the mutant types present, growth kinetics of leukemic cells and drug toxicity parameters. Our methodology is an important step towards the design of personalized optimal therapeutic schedules for chronicle myeloid leukemia.

The Effect of Radiation Dose and Variation in Neupogen® Initiation Schedule on the Mitigation of Myelosuppression during the Concomitant GI-ARS and H-ARS in a Nonhuman Primate Model of High-dose Exposure with Marrow Sparing

A nonhuman primate (NHP) model of acute high-dose, partial-body irradiation with 5% bone marrow (PBI/BM5) sparing was used to assess the effect of Neupogen® [granulocyte colony stimulating factor (G-CSF)] to mitigate the associated myelosuppression when administered at an increasing interval between exposure and initiation of treatment. A secondary objective was to assess the effect of Neupogen® on the mortality or morbidity of the hematopoietic (H)- acute radiation syndrome (ARS) and concurrent acute gastrointestinal radiation syndrome (GI-ARS). NHP were exposed to 10.0 or 11.0 Gy with 6 MV LINAC-derived photons at approximately 0.80 Gy min. All NHP received medical management. NHP were dosed daily with control article (5% dextrose in water) initiated on day 1 post-exposure or Neupogen® (10 μg kg) initiated on day 1, day 3, or day 5 until recovery [absolute neutrophil count (ANC) ≥ 1,000 cells μL for three consecutive days]. Mortality in both the 10.0 Gy and 11.0 Gy cohorts suggested that early administration of Neupogen® at day 1 post exposure may affect acute GI-ARS mortality, while Neupogen® appeared to mitigate mortality due to the H-ARS. However, the study was not powered to detect statistically significant differences in survival. The ability of Neupogen® to stimulate granulopoiesis was assessed by evaluating key parameters for ANC recovery: the depth of nadir, duration of neutropenia (ANC < 500 cells μL) and recovery time to ANC ≥ 1,000 cells μL. Following 10.0 Gy PBI/BM5, the mean duration of neutropenia was 11.6 d in the control cohort vs. 3.5 d and 4.6 d in the day 1 and day 3 Neupogen® cohorts, respectively. The respective ANC nadirs were 94 cells μL, 220 cells μL, and 243 cells μL for the control and day 1 and day 3 Neupogen® cohorts. Following 11.0 Gy PBI/BM5, the duration of neutropenia was 10.9 d in the control cohort vs. 2.8 d, 3.8 d, and 4.5 d in the day 1, day 3, and day 5 Neupogen® cohorts, respectively. The respective ANC nadirs for the control and day 1, day 3, and day 5 Neupogen® cohorts were 131 cells μL, 292 cells μL, 236 cells μL, and 217 cells μL, respectively. Therefore, the acceleration of granulopoiesis by Neupogen® in this model is independent of the time interval between radiation exposure and treatment initiation up to 5 d post-exposure. The PBI/BM5 model can be used to assess medical countermeasure efficacy in the context of the concurrent GI- and H-ARS.

Neutrophil dynamics during concurrent chemotherapy and G-CSF administration: Mathematical modelling guides dose optimisation to minimise neutropenia

The choice of chemotherapy regimens is often constrained by the patient's tolerance to the side effects of chemotherapeutic agents. This dose-limiting issue is a major concern in dose regimen design, which is typically focused on maximising drug benefits. Chemotherapy-induced neutropenia is one of the most prevalent toxic effects patients experience and frequently threatens the efficient use of chemotherapy. In response, granulocyte colony-stimulating factor (G-CSF) is co-administered during chemotherapy to stimulate neutrophil production, increase neutrophil counts, and hopefully avoid neutropenia. Its clinical use is, however, largely dictated by trial and error processes. Based on up-to-date knowledge and rational considerations, we develop a physiologically realistic model to mathematically characterise the neutrophil production in the bone marrow which we then integrate with pharmacokinetic and pharmacodynamic (PKPD) models of a chemotherapeutic agent and an exogenous form of G-CSF (recombinant human G-CSF, or rhG-CSF). In this work, model parameters represent the average values for a general patient and are extracted from the literature or estimated from available data. The dose effect predicted by the model is confirmed through previously published data. Using our model, we were able to determine clinically relevant dosing regimens that advantageously reduce the number of rhG-CSF administrations compared to original studies while significantly improving the neutropenia status. More particularly, we determine that it could be beneficial to delay the first administration of rhG-CSF to day seven post-chemotherapy and reduce the number of administrations from ten to three or four for a patient undergoing 14-day periodic chemotherapy.

Modelling chemotherapy effects on granulopoiesis

Background

Although the growth-factor G-CSF is widely used to prevent granulotoxic side effects of cytotoxic chemotherapies, its optimal use is still unknown since treatment outcome depends on many parameters such as dosing and timing of chemotherapies, pharmaceutical derivative of G-CSF used and individual risk factors. We showed in the past that a pharmacokinetic and –dynamic model of G-CSF and human granulopoiesis can be used to predict the performance of yet untested G-CSF schedules. However, only a single chemotherapy was considered so far.

In the present paper, we propose a comprehensive model of chemotherapy toxicity and combine it with our cell kinetic model of granulopoiesis. Major assumptions are: proportionality of cell numbers and cell loss, delayed action of chemotherapy, drug, drug-dose and cell stage specific toxicities, no interaction of drugs and higher toxicity of drugs at the first time of application. Correspondingly, chemotherapies can be characterized by a set of toxicity parameters which can be estimated by fitting the predictions of our model to clinical time series data of patients under therapy. Data were either extracted from the literature or were received from cooperating clinical study groups.

Results

Model assumptions proved to be feasible in explaining granulotoxicity of 10 different chemotherapeutic drugs or drug-combinations applied in 33 different schedules with and without G-CSF. Risk groups of granulotoxicity were traced back to differences in toxicity parameters.

Conclusion

We established a comprehensive model of combined G-CSF and chemotherapy action in humans which allows us to predict and compare the outcome of alternative G-CSF schedules. We aim to apply the model in different clinical contexts to optimize and individualize G-CSF treatment.

Electronic supplementary material

The online version of this article (doi:10.1186/s12918-014-0138-7) contains supplementary material, which is available to authorized users.

Understanding, treating and avoiding hematological disease: better medicine through mathematics?

This paper traces the experimental, clinical and mathematical modeling efforts to understand a periodic hematological disease-cyclical neutropenia. It is primarily a highly personal account by two scientists from quite different backgrounds of their interactions over almost 40 years and their attempts to understand this intriguing disease. It's also a story of their efforts to offer effective treatments for the patients who suffer from cyclic neutropenia and other conditions causing neutropenia and infections.

A pharmacodynamic model of Bcr-Abl signalling in chronic myeloid leukaemia

Chronic myeloid leukaemia (CML) is an unusual malignancy in which myeloid progenitor cells are transformed by a single chromosomal translocation where the Bcr domain of chromosome 22 is placed adjacent to the proto-oncogene c-Abl of chromosome 9, resulting in constitutive Abl tyrosine kinase activity. This has a twofold effect: it causes increased numbers of myeloid progenitor cells and circulating myeloid cells, and it causes leakage of reactive oxygen species from mitochondria. We describe a kinetic and pharmacodynamic (PD) model of Bcr-Abl signalling in myeloid cells that is used to simulate effects of four classes of drugs: Bcr-Abl signalling inhibitors, such as imatinib, cyclin-dependent kinase inhibitors, and pro- and anti-oxidants. The model also has the potential to describe the PD effects of agents acting on other sites in the Bcr-Abl signalling pathway. Having calibrated the model against dose-response curves of these drugs acting as single agents on Bcr-Abl-transformed cells in vitro, the model was used to predict effects of the agents in combination. Used in conjunction with pharmacokinetic models, our PD model enables an approach to protocol optimization: large numbers of doses and timings and (in the case of combination treatments) relative dose ratios can be simulated in silico. Predicted selectivity, as well as efficacy, can be extracted from the model. An understanding of the Bcr-Abl signalling pathway has implications for strategies to prevent acquired drug resistance, and for preventing or delaying CML progression to its blast phase.

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

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.

Merging concepts - coupling an agent-based model of hematopoietic stem cells with an ODE model of granulopoiesis

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.

Modelling c-Abl Signalling in Activated Neutrophils: the Anti-inflammatory Effect of Seliciclib

When mammalian tissues are infected by bacteria or fungi, inflammatory cytokines are released that cause circulating neutrophils to invade the infected tissue. The cytosolic tyrosine kinase, c-Abl, in these tissue neutrophils is activated by TNFα. c-Abl then phosphorylates STAT transcription factors, which results in production of the antiapoptotic protein Mcl-1. The normally short-lived tissue neutrophils are then unable to enter apoptosis. c-Abl also causes release of reactive oxygen species (ROS) from the mitochondria of the activated neutrophils. These ROS, and ROS generated by NADPH oxidase, are bactericidal agents of the innate immune system. In some inflammatory diseases, such as chronic obstructive pulmonary disease (COPD), the invading neutrophils become permanently activated, and the resulting ROS overproduction causes severe tissue damage. The cyclin-dependent kinase inhibitor, seliciclib, blocks transcription through inhibition of cdk9. This results in a relatively rapid decline of antiapoptotic Mcl-1 transcripts in activated neutrophils, an increase in neutrophil apoptosis, and less ROS leakage and oxidative damage. We present here a model of neutrophil kinetics that simulates the principal pathways of c-Abl signalling and use it to explore possible treatment options for inflammatory lung disease.

Neutropenia and G-CSF in lymphoproliferative diseases

BACKGROUND

Chemotherapy-induced neutropenia is a major cause of morbidity and mortality. It frequently causes dose reductions or treatment delay, which can be prevented or treated by the administration of granulocyte-colony-stimulating factor (G-CSF). However, a better knowledge of the incidence, day of onset after therapy, and duration of neutropenia is essential to optimize the use of G-CSF.

DESIGN AND METHODS

Six hundred and ninety-four patients from a single institution, affected by lympho-proliferative diseases, were retrospectively reviewed for the occurrence of grade 4 neutropenia and febrile neutropenia (FN). Duration of neutropenia and time of neutrophil nadir were also retrieved. The diagnoses included non-Hodgkin's lymphoma, Hodgkin's lymphoma, and multiple myeloma. Chemotherapy regimens were obviously different according to the diagnosis, disease stage, and first or subsequent lines of therapy.

RESULTS

No patient received G-CSF as primary prophylaxis. Median nadir did not significantly differ among patients treated with first or successive lines of therapy. The incidence of grade 4 neutropenia and FN ranged from 0 to 94%, depending on the chemotherapy regimen. Patients receiving a first-line chemotherapy regimen had a significantly lower incidence of febrile grade 4 neutropenia compared to patients treated with a second or subsequent line of therapy. The duration of grade 4 neutropenia was significantly longer in patients given second or subsequent lines.

CONCLUSION

The results of this study could be useful to define the nadir onset in the hematologic setting in order to correctly tailor timing and duration of G-CSF prophylaxis and to assess the lowest fully effective dose.

Neutrophil dynamics after chemotherapy and G-CSF: the role of pharmacokinetics in shaping the response

Chemotherapy has profound effects on the hematopoietic system, most notably leading to neutropenia. Granulocyte colony stimulating factor (G-CSF) is often used to deal with this neutropenia, but the response is highly variable. In this paper we examine the role of pharmacokinetics and delivery protocols in shaping the neutrophil responses to chemotherapy and G-CSF. Neutrophil responses to different protocols of chemotherapy administration with varying dosages, infusion times, and schedules are studied through a mathematical model. We find that a single dose of chemotherapy produces a damped oscillation in neutrophil levels, and short-term applications of chemotherapy can induce permanent oscillations in neutrophil level if there is a bistability in the system. In addition, we confirm previous findings [Zhuge et al., J. Theor. Biol., 293(2012), 111-120] that when periodic chemotherapy is given, there is a significant period of delivery that induces resonance in the system and exacerbates the corresponding neutropenia. The width of this resonant period peak increases with the recovery rate after a single chemotherapy, which is given by the real part of the dominant eigenvalue pair at the steady state, and both are determined by a single cooperativity coefficient in the feedback function for the neutrophils. Our numerical studies show that the neutropenia caused by chemotherapy can be overcome if G-CSF is given early after chemotherapy but can actually be worsened if G-CSF is given later, consistent with results reported in Zhuge et al. (2012). The nadir in neutrophil level is found to be more sensitive to the dosage of chemotherapy than that of the G-CSF. Furthermore, dependence of our results with changes in key pharmacokinetic parameters as well as initial functions are studied. Thus, this study illuminates the potential for destructive resonance leading to neutropenia in response to periodic chemotherapy, and explores and explains why the timing of G-CSF is so crucial for successful reversal of chemotherapy induced neutropenia.