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

Data-based modeling of breast cancer and optimal therapy

Excessive accumulation of β-catenin proteins is a vital driver in the development of breast cancer. Many clinical assessments incorporating immunotherapy with targeted mRNA of β-catenin are costly endeavor. This paper develops novel mathematical models for different treatments by invoking available clinical data to calibrate models, along with the selection and evaluation of therapy strategies in a faster manner with lower cost. Firstly, in order to explore the interactions between cancer cells and the immune system within the tumor microenvironment, we construct different types of breast cancer treatment models based on RNA interference technique and immune checkpoint inhibitors, which have been proved to be an effective combined therapy in pre-clinical trials associated with the inhibition of β-catenin proteins to enhance intrinsic anti-tumor immune response. Secondly, various techniques including MCMC are adopted to estimate multiple parameters and thus simulations in agreement with experimental results sustain the validity of our models. Furthermore, the gradient descent method and particle swarm algorithm are designed to optimize therapy schemes to inhibit the growth of tumor and lower the treatment cost. Considering the mechanisms of drug resistance in vivo, simulations exhibit that therapies are ineffective resulting in cancer relapse in the prolonged time. For this reason, parametric sensitivity analysis sheds light on the choice of new treatments which indicate that, in addition to inhibiting β-catenin proteins and improving self-immunity, the injection of dendritic cells promoting immunity may provide a novel vision for the future of cancer treatment. Overall, our study provides witness of principle from a mathematical perspective to guide clinical trials and the selection of treatment regimens.

Effects of Prophylactic Administration of Granulocyte Colony-Stimulating Factor on Peripheral Leukocyte and Neutrophil Counts Levels After Chemotherapy in Patients With Early-Stage Breast Cancer: A Retrospective Cohort Study

Background

Both chemotherapy-induced neutropenia (CIN) and febrile neutropenia (FN) frequently occur and can lead to dose-limiting toxicity and even fatal chemotherapy side effects. The prophylactic use of recombinant human granulocyte colony-stimulating factor (rhG-CSF), including pegylated rhG-CSF (PEG-rhG-CSF), significantly reduces the risks of CIN and FN during chemotherapy in early-stage breast cancer (ESBC) patients. However, whether the prophylactic use of granulocyte colony-stimulating factor (G-CSF), especially PEG-rhG-CSF, can influence white blood cell (WBC) counts and absolute neutrophil counts (ANCs) after finishing the chemotherapy remains unknown. Therefore, exploring the development and recovery tendency of WBC counts and ANCs during and after chemotherapy is crucial.

Objective

We aimed to investigate the variation tendency and recovery of WBC counts and ANCs during and after chemotherapy and evaluate the independent factors influencing leukopenia and neutropenia lasting longer after chemotherapy. We also aimed to provide individualized prophylactically leukocyte elevation therapy for breast cancer patients.

Methods

This single-center retrospective cohort study evaluated 515 ESBC patients who received rhG-CSF or PEG-G-CSF for prophylaxis after adjuvant or neoadjuvant chemotherapy. Blood test reports were analyzed during chemotherapy, and on a 12-month follow-up period after finishing the chemotherapy. The WBC counts and ANCs were measured to assess their variation tendency characteristics and to identify independent factors that influenced the occurrence of leukopenia and neutropenia lasting longer than 12 months after chemotherapy.

Results

Prophylaxis with rhG-CSF or PEG-rhG-CSF kept the mean values of WBC counts and ANCs within the normal range during chemotherapy, but a significant difference in WBC levels was detected before the end of the last chemotherapy compared to the prechemotherapy period (baseline) (p < 0.001). During the 12-month follow-up after the end of the last chemotherapy, WBC counts and ANCs gradually recovered, but the group that used only PEG-rhG-CSF (long-acting group, p _WBC = 0.012) or rhG-CSF (short-acting group, p _WBC = 0.0005) had better leukocyte elevation effects than the mixed treatment group (PEG-rhG-CSF mixed rhG-CSF). Besides, the short-acting group had a better neutrophil elevation effect than the longer-acting (p _ANC = 0.019) and mixed (p _ANC = 0.002) groups. Leukopenia was still present in 92 (17.9%) patients and neutropenia in 63 (12.2%) 12 months after the end of the last chemotherapy. The duration of leukopenia over 12 months was closely associated with the baseline WBC level (p < 0.001), G-CSF types (p = 0.027), and surgical method (p = 0.041). Moreover, the duration of neutropenia over 12 months was closely related to the baseline ANC (p < 0.001), G-CSF types (p = 0.043), and molecular typing (p = 0.025).

Conclusion

The prophylactic application of G-CSF effectively stabilized the WBC counts and ANCs during chemotherapy in ESBC patients. Nevertheless, the recovery of WBC counts and ANCs after chemotherapy varied between different G-CSF treatment groups. The risk of leukopenia and neutropenia persisting for more than 12 months after chemotherapy was associated with G-CSF types, the baseline level of WBC count/ANCs, surgical method, and molecular typing.

Translational approaches to treating dynamical diseases through in silico clinical trials

The primary goal of drug developers is to establish efficient and effective therapeutic protocols. Multifactorial pathologies, including dynamical diseases and complex disorders, can be difficult to treat, given the high degree of inter- and intra-patient variability and nonlinear physiological relationships. Quantitative approaches combining mechanistic disease modeling and computational strategies are increasingly leveraged to rationalize pre-clinical and clinical studies and to establish effective treatment strategies. The development of clinical trials has led to new computational methods that allow for large clinical data sets to be combined with pharmacokinetic and pharmacodynamic models of diseases. Here, we discuss recent progress using in silico clinical trials to explore treatments for a variety of complex diseases, ultimately demonstrating the immense utility of quantitative methods in drug development and medicine.

Characterizing Chemotherapy-Induced Neutropenia and Monocytopenia Through Mathematical Modelling

In spite of the recent focus on the development of novel targeted drugs to treat cancer, cytotoxic chemotherapy remains the standard treatment for the vast majority of patients. Unfortunately, chemotherapy is associated with high hematopoietic toxicity that may limit its efficacy. We have previously established potential strategies to mitigate chemotherapy-induced neutropenia (a lack of circulating neutrophils) using a mechanistic model of granulopoiesis to predict the interactions defining the neutrophil response to chemotherapy and to define optimal strategies for concurrent chemotherapy/prophylactic granulocyte colony-stimulating factor (G-CSF). Here, we extend our analyses to include monocyte production by constructing and parameterizing a model of monocytopoiesis. Using data for neutrophil and monocyte concentrations during chemotherapy in a large cohort of childhood acute lymphoblastic leukemia patients, we leveraged our model to determine the relationship between the monocyte and neutrophil nadirs during cyclic chemotherapy. We show that monocytopenia precedes neutropenia by 3 days, and rationalize the use of G-CSF during chemotherapy by establishing that the onset of monocytopenia can be used as a clinical marker for G-CSF dosing post-chemotherapy. This work therefore has important clinical applications as a comprehensive approach to understanding the relationship between monocyte and neutrophils after cyclic chemotherapy with or without G-CSF support.

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.

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.

A Mathematical Model of Granulopoiesis Incorporating the Negative Feedback Dynamics and Kinetics of G-CSF/Neutrophil Binding and Internalization

We develop a physiological model of granulopoiesis which includes explicit modelling of the kinetics of the cytokine granulocyte colony-stimulating factor (G-CSF) incorporating both the freely circulating concentration and the concentration of the cytokine bound to mature neutrophils. G-CSF concentrations are used to directly regulate neutrophil production, with the rate of differentiation of stem cells to neutrophil precursors, the effective proliferation rate in mitosis, the maturation time, and the release rate from the mature marrow reservoir into circulation all dependent on the level of G-CSF in the system. The dependence of the maturation time on the cytokine concentration introduces a state-dependent delay into our differential equation model, and we show how this is derived from an age-structured partial differential equation model of the mitosis and maturation and also detail the derivation of the rest of our model. The model and its estimated parameters are shown to successfully predict the neutrophil and G-CSF responses to a variety of treatment scenarios, including the combined administration of chemotherapy and exogenous G-CSF. This concomitant treatment was reproduced without any additional fitting to characterize drug-drug interactions.

Prognostic Value of Neutrophil-Related Factors in Locally Advanced Cervical Squamous Cell Carcinoma Patients Treated with Cisplatin-Based Concurrent Chemoradiotherapy

The aim of this study was to explore the relationship between neutrophil-related factors, including neutrophil-lymphocyte ratio (NLR) and the responses of neutrophil to granulocyte colony-stimulating factors (RNG), and the prognosis of patients with locally advanced cervical squamous cell carcinoma (LACSCC) undergoing cisplatin-based concurrent chemoradiotherapy (CCCRT). A total of sixty LACSCC patients were enrolled in this study. We analyzed the association of NLR or RNG with clinicopathologic characteristics of these patients. The prognostic factors were evaluated by univariate and multivariate survival analysis. The optimal cut-off value of the NLR was determined to be 2.0 for the overall survival (OS). A higher level of the NLR was associated with younger age (P = 0.017) and higher baseline platelet count (P = 0.040). NLR was identified to be the only independent prognostic factor for OS by multivariate analysis (P = 0.037). The median RNG was 3.01, with a range of 1.19-16.84. RNG level was significantly associated with lymph node metastasis of these patients (P = 0.023). And higher RNG was identified as being a closely independent poor prognostic factor for OS (P = 0.055). This study showed that NLR and RNG may be used as potential biomarkers for survival prediction in patients with LACSCC receiving CCCRT.

Mouse Resistin (mRetn): cloning, expression and purification in Escherichia coli and the potential regulative effects on murine bone marrow hematopoiesis

Background

Resistin (Retn) is a cytokine which has a controversial physiological role regarding its involvement with obesity and type II diabetes mellitus. Recently, murine Retn was found to be a possibly potential regulator of hematopoiesis in mice shown in the screening results of a set of gene chips which mapped the expression level of murine genes during regeneration of impaired bone marrow (BM) by 5-fluorouracil.

Results

Recombinant mice Retn was expressed in Escherichia coli and purified using ion exchange chromatography. Totally 11.4 mg rmRetn was obtained from 500 ml culture with endotoxin level less than 1.0 EU/ug. The purity of recombinant murine Resistin reached to at least 97.6 % via SDS-PAGE analysis and HPLC. The protein possessed chemotaxis effects in the mouse aortic endothelial cells in vitro in transwell analysis. In vitro, rmRetn could up regulate the CFU number of mice BM and after rmRetn was administered, the cell number of murine bone marrow was significantly increased in vivo after chemotherapy. Finally, rmRetn was found able to protect mice from the chemotoxicity of 5-fluorouracil.

Conclusions

The discovery demonstrated a new function of murine Retn and suggested that it could potentially accelerate bone marrow regeneration post chemotherapy.

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.

Dynamical disease: Challenges for nonlinear dynamics and medicine

Dynamical disease refers to illnesses that are associated with striking changes in the dynamics of some bodily function. There is a large literature in mathematics and physics which proposes mathematical models for the physiological systems and carries out analyses of the properties of these models using nonlinear dynamics concepts involving analyses of the stability and bifurcations of attractors. This paper discusses how these concepts can be applied to medicine.

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.