The complex effect of granulocyte colony-stimulating factor on human granulopoiesis analyzed by a new physiologically-based mathematical model

Neutrophil decline rate following autologous transplant for lymphoma is a predictor of patients' outcome

Neutropenia postchemotherapy is associated with favorable outcomes, which was attributed to optimal dosing. However, little is known about the neutrophil decline rate as a predictor of cancer outcomes, which may reflect a dynamic marker of chemosensitivity. We assessed the association between the neutrophil decline rate and disease outcomes in a known cohort of 212 lymphoma patients, treated with thiotepa, etoposide, cyclophosphamide, cytarabine, and melphalan (TECAM) conditioning followed by autologous transplant in our center between 2000 and 2013. Slower neutrophil decline rate was correlated with worse overall survival, mediated not by shorter time to progression (TTP), but rather by worse survival post-progression, possibly pointing to chemosensitivity at each line of therapy as the responsible mechanism. The effect was seen across histologies and was independent of stronger predictors of outcome like performance status (PS) and response before transplant. Prospective research is needed to confirm our results and expand their validity to other clinical scenarios.

A New Method for Optimizing Sepsis Therapy by Nivolumab and Meropenem Combination: Importance of Early Intervention and CTL Reinvigoration Rate as a Response Marker

Background: Recently, there has been a growing interest in applying immune checkpoint blockers (ICBs), so far used to treat cancer, to patients with bacterial sepsis. We aimed to develop a method for predicting the personal benefit of potential treatments for sepsis, and to apply it to therapy by meropenem, an antibiotic drug, and nivolumab, a programmed cell death-1 (PD-1) pathway inhibitor.

Methods: We defined an optimization problem as a concise framework of treatment aims and formulated a fitness function for grading sepsis treatments according to their success in accomplishing the pre-defined aims. We developed a mathematical model for the interactions between the pathogen, the cellular immune system and the drugs, whose simulations under diverse combined meropenem and nivolumab schedules, and calculation of the fitness function for each schedule served to plot the fitness landscapes for each set of treatments and personal patient parameters.

Results: Results show that treatment by meropenem and nivolumab has maximum benefit if the interval between the onset of the two drugs does not exceed a dose-dependent threshold, beyond which the benefit drops sharply. However, a second nivolumab application, within 7–10 days after the first, can extinguish a pathogen which the first nivolumab application failed to remove. The utility of increasing nivolumab total dose above 6 mg/kg is contingent on the patient's personal immune attributes, notably, the reinvigoration rate of exhausted CTLs and the overall suppression rates of functional CTLs. A baseline pathogen load, higher than 5,000 CFU/μL, precludes successful nivolumab and meropenem combination therapy, whereas when the initial load is lower than 3,000 CFU/μL, meropenem monotherapy suffices for removing the pathogen.

Discussion: Our study shows that early administration of nivolumab, 6 mg/kg, in combination with antibiotics, can alleviate bacterial sepsis in cases where antibiotics alone are insufficient and the initial pathogen load is not too high. The study pinpoints the role of precision medicine in sepsis, suggesting that personalized therapy by ICBs can improve pathogen elimination and dampen immunosuppression. Our results highlight the importance in using reliable markers for classifying patients according to their predicted response and provides a valuable tool in personalizing the drug regimens for patients with sepsis.

Alleviation of exhaustion-induced immunosuppression and sepsis by immune checkpoint blockers sequentially administered with antibiotics-analysis of a new mathematical model

Background

Sepsis-associated immune dysregulation, involving hyper-inflammation and immunosuppression, is common in intensive care patients, often leading to multiple organ dysfunction and death. The aim of this study was to identify the main driving force underlying immunosuppression in sepsis, and to suggest new therapeutic avenues for controlling this immune impairment and alleviating excessive pathogen load.

Methods

We developed two minimalistic (skeletal) mathematical models of pathogen-associated inflammation, which focus on the dynamics of myeloid, lymphocyte, and pathogen numbers in blood. Both models rely on the assumption that the presence of the pathogen causes a bias in hematopoietic stem cell differentiation toward the myeloid developmental line. Also in one of the models, we assumed that continuous exposure to pathogens induces lymphocyte exhaustion. In addition, we also created therapy models, both by antibiotics and by immunotherapy with PD-1/PD-L1 checkpoint inhibitors. Assuming realistic parameter ranges, we simulated the pathogen-associated inflammation models in silico with or without various antibiotic and immunotherapy schedules.

Results

Computer simulations of the two models show that the assumption of lymphocyte exhaustion is a prerequisite for attaining sepsis-associated immunosuppression, and that the ability of the innate and adaptive immune systems to control infections depends on the pathogen’s replication rate. Simulation results further show that combining antibiotics with immune checkpoint blockers can suffice for defeating even an aggressive pathogen within a relatively short period. This is so as long as the drugs are administered soon after diagnosis. In contrast, when applied as monotherapies, antibiotics or immune checkpoint blockers fall short of eliminating aggressive pathogens in reasonable time.

Conclusions

Our results suggest that lymphocyte exhaustion crucially drives immunosuppression in sepsis, and that one can efficiently resolve both immunosuppression and pathogenesis by timely coupling of antibiotics with an immune checkpoint blocker, but not by either one of these two treatment modalities alone. Following experimental validation, our model can be adapted to explore the potential of other therapeutic options in this field.

Electronic supplementary material

The online version of this article (10.1186/s40635-019-0260-3) contains supplementary material, which is available to authorized users.

CD38 Deficiency Promotes Inflammatory Response through Activating Sirt1/NF-κB-Mediated Inhibition of TLR2 Expression in Macrophages

CD38 was first identified as a lymphocyte-specific antigen and then has been found to be widely expressed in a variety of cell types. The functions of CD38 are involved in numerous biological processes including immune responses. Here, we showed the downregulations of both TLR2 mRNA and protein in macrophages from CD38^−/− mice and in CD38 knockdown RAW264.7 cells. Several NF-κB-binding motifs in the promoter region of the TLR2 gene were identified by the bioinformatics analysis and were confirmed by the luciferase activity assay with the different truncated TLR2 promoters. CD38 deficiency resulted in the reduction of NF-κB p65 and acetyl-NF-κB p65 (Ac-p65) levels as determined by Western blot. The expression of Sirt1 did not change, but an increased activity of Sirt1 was observed in CD38-deficient macrophages. Inhibition of the Sirt1/NF-κB signaling pathway resulted in downregulation of TLR2 expression in RAW264.7 cells. However, re-expression of CD38 in the knockdown clones reversed the effect on Sirt1/NF-κB/TLR2 signaling, which is NAD-dependent. Moreover, the inflammatory cytokines including G-CSF, IL-1alpha, IL-6, MCP-1, MIP-1alpha, and RANTES were increased in CD38 knockdown RAW264.7 cells. Taken together, our data demonstrated that CD38 deficiency enhances inflammatory response in macrophages, and the mechanism may be partly associated with increased Sirt1 activity, which promoted NF-κB deacetylation and then inhibited expression of the TLR2 gene. Obviously, our study may provide an insight into the molecular mechanisms in CD38-mediated inflammation.

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.

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.

Complex pattern of interleukin-11-induced inflammation revealed by mathematically modeling the dynamics of C-reactive protein

Inflammation underlies many diseases and is an undesired effect of several therapy modalities. Biomathematical modeling can help unravel the complex inflammatory processes and the mechanisms triggering their emergence. We developed a model for induction of C-reactive protein (CRP), a clinically reliable marker of inflammation, by interleukin (IL)-11, an approved cytokine for treatment of chemotherapy-induced thrombocytopenia. Due to paucity of information on the mechanisms underlying inflammation-induced CRP dynamics, our model was developed by systematically evaluating several models for their ability to retrieve variable CRP profiles observed in IL-11-treated breast cancer patients. The preliminary semi-mechanistic models were designed by non-linear mixed-effects modeling, and were evaluated by various performance criteria, which test goodness-of-fit, parsimony and uniqueness. The best-performing model, a robust population model with minimal inter-individual variability, uncovers new aspects of inflammation dynamics. It shows that CRP clearance is a nonlinear self-controlled process, indicating an adaptive anti-inflammatory reaction in humans. The model also reveals a dual IL-11 effect on CRP elevation, whereby the drug has not only a potent immediate influence on CRP incline, but also a long-term influence inducing elevated CRP levels for several months. Consistent with this, model simulations suggest that periodic IL-11 therapy may result in prolonged low-grade (chronic) inflammation post treatment. Future application of the model can therefore help design improved IL-11 regimens with minimized long-term CRP toxicity. Our study illuminates the dynamics of inflammation and its control, and provides a prototype for progressive modeling of complex biological processes in the medical realm and beyond.

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.

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.

Pharmacokinetic and -dynamic modelling of G-CSF derivatives in humans

Background

The human granulocyte colony-stimulating factor (G-CSF) is routinely applied to support recovery of granulopoiesis during the course of cytotoxic chemotherapies. However, optimal use of the drug is largely unknown. We showed in the past that a biomathematical compartment model of human granulopoiesis can be used to make clinically relevant predictions regarding new, yet untested chemotherapy regimen. In the present paper, we aim to extend this model by a detailed pharmacokinetic and -dynamic modelling of two commonly used G-CSF derivatives Filgrastim and Pegfilgrastim.

Results

Model equations are based on our physiological understanding of the drugs which are delayed absorption of G-CSF when applied to the subcutaneous tissue, dose-dependent bioavailability, unspecific first order elimination, specific elimination in dependence on granulocyte counts and reversible protein binding. Pharmacokinetic differences between Filgrastim and Pegfilgrastim were modelled as different parameter sets. Our former cell-kinetic model of granulopoiesis was essentially preserved, except for a few additional assumptions and simplifications. We assumed a delayed action of G-CSF on the bone marrow, a delayed action of chemotherapy and differences between Filgrastim and Pegfilgrastim with respect to stimulation potency of the bone marrow. Additionally, we incorporated a model of combined action of Pegfilgrastim and Filgrastim or endogenous G-CSF which interact via concurrent receptor binding. Unknown pharmacokinetic or cell-kinetic parameters were determined by fitting the predictions of the model to available datasets of G-CSF applications, chemotherapy applications or combinations of it. Data were either extracted from the literature or were received from cooperating clinical study groups. Model predictions fitted well to both, datasets used for parameter estimation and validation scenarios as well. A unique set of parameters was identified which is valid for all scenarios considered. Differences in pharmacokinetic parameter estimates between Filgrastim and Pegfilgrastim were biologically plausible throughout.

Conclusion

We conclude that we established a comprehensive biomathematical model to explain the dynamics of granulopoiesis under chemotherapy and applications of two different G-CSF derivatives. We aim to apply the model to a large variety of chemotherapy regimen in the future in order to optimize corresponding G-CSF schedules or to individualize G-CSF treatment according to the granulotoxic risk of a patient.

Personalising docetaxel and G-CSF schedules in cancer patients by a clinically validated computational model

Background:

This study was aimed to develop a new method for personalising chemotherapeutic and granulocyte colony-stimulating factor (G-CSF) combined schedules, and use it for suggesting efficacious chemotherapy with reduced neutropenia.

Methods:

Clinical data from 38 docetaxel (Doc)-treated metastatic breast cancer patients were employed for validating a new pharmacokinetic/pharmacodynamics model for Doc, combined with a mathematical model for granulopoiesis. An optimisation procedure was constructed and used for selecting improved treatment schedules.

Results:

The combined model accurately predicted observed nadir timing (r=0.99), grade 3 or 4 neutropenia (86% success) and neutrophil counts over time in individual patients (r=0.63), and showed robustness to CYP3A-induced variability in Doc clearance. For average patients, the predicted optimal support for the standard chemotherapy regimen, Doc 100 μg m⁻² tri-weekly, is G-CSF, 300 μg, Q1D × 3, starting day 7 post-Doc. This regimen largely moderates chemotherapy-induced neutrophil nadir and neutropenia duration. The more intensive Doc dose, 150 mg m⁻², is optimally supported by the slightly less cost-effective G-CSF 300 μg, Q1D × 4, 5 days post-Doc. The latter regimen is optimal for borderline patients (2000 neutrophils per μl) under Doc, 100–150 mg m⁻² tri-weekly.

Conclusions:

The new computational method can serve for tailoring efficacious cytotoxic and supportive treatments, minimising side effects to individual patients. Prospective clinical validation is warranted.

Comparison of different semi-mechanistic models for chemotherapy-related neutropenia: application to BI 2536 a Plk-1 inhibitor

PURPOSE

The aim of this investigation was to compare the performance of a commonly used semi-mechanistic model for drug-related neutropenia with other semi-mechanistic models published in the literature.

METHODS

After their implementation in NONMEM VI, five semi-mechanistic models were assessed using the pharmacokinetic and absolute neutrophil count data obtained from 95 patients with non-small cell lung cancer receiving either 200 mg on day 1 or 50 or 60 mg on days 1, 2 and 3 of a 21-day treatment course with the new Plk-1 inhibitor BI 2536. The model performance was compared by means of predictive (visual and numerical) checks, precision in the parameter estimates and objective function-based measures. Details of model parameterization, model stability and run times are also provided.

RESULTS

The time course of the drug plasma concentrations was described by a three compartment model with a first-order elimination rate. With respect to neutropenia, all models were successfully implemented in NONMEM and provided reasonable fits for the median (although not all models described all percentiles of the data well), and in general precise parameter estimates.

CONCLUSION

In the current evaluation performed in a single drug, none of the models showed superior performance compared to the most commonly used model first described by Friberg et al. (J Clin Oncol 20:4713-4721, 2002).

Mathematical study on kinetics of hematopoietic stem cells--theoretical conditions for successful transplantation

Numerous haematological diseases occur due to dysfunctions during homeostasis processes of blood cell production. Haematopoietic stem cell transplantation (HSCT) is a therapeutic option for the treatment of haematological malignancy and congenital immunodeficiency. Today, HSCT is widely applied as an alternative method to bone marrow transplantation; however, HSCT can be a risky procedure because of potential side effects and complications after transplantations. Although an optimal regimen to achieve successful HSCT while maintaining quality of life is to be developed, even theoretical considerations such as the evaluations of successful engraftments and proposals of clinical management strategies have not been fully discussed yet. In this paper, we construct and investigate mathematical models that describe the kinetics of hematopoietic stem cell self-renewal and granulopoiesis under the influence of growth factors. Moreover, we derive theoretical conditions for successful HSCT, primarily on the basis of the idea that the basic reproduction number R (0) represents a threshold condition for a population to successfully grow in a given steady-state environment. Successful engraftment of transplanted haematopoietic stem cells (HSCs) is subsequently ensured by employing a concept of dynamical systems theory known as 'persistence'. On the basis of the implications from the modelling study, we discuss how the conditions derived for a successful HSCT are used to link to experimental studies.

Population modeling of filgrastim PK-PD in healthy adults following intravenous and subcutaneous administrations

Filgrastim is a recombinant human granulocyte colony stimulating factor (G-CSF) that stimulates production of neutrophils. The objective of this analysis was to develop a pharmacokinetic (PK) and pharmacodynamic (PD) model to account for an increase in G-CSF clearance on multiple dosing because of an increase of the G-CSF receptor-mediated endocytosis. Data from 4 randomized studies involving healthy volunteers were used for analysis. Subjects received filgrastim (Neupogen) via subcutaneous (SC) and intravenous (IV) routes. Filgrastim was administered SC daily for 1 week at 2.5, 5, and 10 µg/kg doses and as single IV infusions (5 µg/kg over 0.5 hours) and SC (1 µg/kg) doses. PK data comprised serum concentration-time measurements and the blood absolute neutrophil count (ANC) was used for PD evaluations. Population nonlinear mixed-effect modeling was done using NONMEM VI (Version 6.1.0, Icon Development Solutions, Ellicott City, Maryland). The model depicted the decaying trend in C(max) values with repeated doses and an increase in ANC(max) values consistently with an increase in the G-CSF receptor pool. Simulated time courses of the total clearance exhibited an increasing pattern. The increase in filgrastim clearance on multiple dosing was attributed to the increased neutrophil count in the bone marrow and blood paralleled by an increase in the total G-CSF receptor density.

Prediction of neutropenia-related effects of a new combination therapy with the anticancer drugs BI 2536 (a Plk1 inhibitor) and pemetrexed

This study investigated the feasibility of predicting the neutropenia-related effects of a therapy that combines the investigational drug BI 2536 (inhibitor of Polo-like kinase 1) and pemetrexed, an approved anticancer drug. Predictions were arrived at using the pharmacokinetic/pharmacodynamic (PK/PD) parameters of each of the drugs obtained from monotherapy studies and assuming that the neutropenic effect is additive when the drugs are administered as a combination therapy. Subsequently, a PK/PD model was developed to determine whether this assumption of additive effect was reasonable in relation to these two drugs. All analyses and simulations were performed using the population approach in NONMEM, version VI.

From the evolution of toxin resistance to virtual clinical trials: the role of mathematical models in oncology

Sustainable delivery of quality healthcare at affordable cost is a major challenge, especially in oncology. Through interdisciplinary collaboration, researchers can provide new insights into familiar concepts and radically change the ways in which biopharmaceutical and medical studies are conducted and translated into clinical practice. One interdisciplinary approach is ‘Virtual R&D’, that is, biomedical research and development aided by mathematical models of the human body. This approach has facilitated the development of the ‘virtual patient’, a clinically validated modeling system that accurately predicts efficacy and toxicity of various oncology drug combinations in individuals and in populations. The use of virtual patients in clinical research will dramatically shorten the period of development of new drugs. Such models can also be used to personalize treatment regimens, substantially reducing the risk of clinical failure. This strategy can improve the quality of healthcare and reduce costs associated with clinical development.

Predictive ability of a semi-mechanistic model for neutropenia in the development of novel anti-cancer agents: two case studies

In cancer chemotherapy neutropenia is a common dose-limiting toxicity. An ability to predict the neutropenic effects of cytotoxic agents based on proposed trial designs and models conditioned on previous studies would be valuable. The aim of this study was to evaluate the ability of a semi-mechanistic pharmacokinetic/pharmacodynamic (PK/PD) model for myelosuppression to predict the neutropenia observed in Phase I clinical studies, based on parameter estimates obtained from prior trials. Pharmacokinetic and neutropenia data from 5 clinical trials for diflomotecan and from 4 clinical trials for indisulam were used. Data were analyzed and simulations were performed using the population approach with NONMEM VI. Parameter sets were estimated under the following scenarios: (a) data from each trial independently, (b) pooled data from all clinical trials and (c) pooled data from trials performed before the tested trial. Model performance in each of the scenarios was evaluated by means of predictive (visual and numerical) checks. The semi-mechanistic PK/PD model for neutropenia showed adequate predictive ability for both anti-cancer agents. For diflomotecan, similar predictions were obtained for the three scenarios. For indisulam predictions were better when based on data from the specific study, however when the model parameters were conditioned on data from trials performed prior to a specific study, similar predictions of the drug related-neutropenia profiles and descriptors were obtained as when all data were used. This work provides further indication that modeling and simulation tools can be applied in the early stages of drug development to optimize future trials.

Hematopoiesis and its disorders: a systems biology approach

Scientists have traditionally studied complex biologic systems by reducing them to simple building blocks. Genome sequencing, high-throughput screening, and proteomics have, however, generated large datasets, revealing a high level of complexity in components and interactions. Systems biology embraces this complexity with a combination of mathematical, engineering, and computational tools for constructing and validating models of biologic phenomena. The validity of mathematical modeling in hematopoiesis was established early by the pioneering work of Till and McCulloch. In reviewing more recent papers, we highlight deterministic, stochastic, statistical, and network-based models that have been used to better understand a range of topics in hematopoiesis, including blood cell production, the periodicity of cyclical neutropenia, stem cell production in response to cytokine administration, and the emergence of imatinib resistance in chronic myeloid leukemia. Future advances require technologic improvements in computing power, imaging, and proteomics as well as greater collaboration between experimentalists and modelers. Altogether, systems biology will improve our understanding of normal and abnormal hematopoiesis, better define stem cells and their daughter cells, and potentially lead to more effective therapies.

A pharmacokinetic model of filgrastim and pegfilgrastim application in normal mice and those with cyclophosphamide-induced granulocytopaenia

OBJECTIVES

Recombinant human granulocyte colony-stimulating factor (rhG-CSF) is widely used as treatment for granulocytopaenia during cytotoxic chemotherapy; however, optimal scheduling of this pharmaceutical is unknown. Biomathematical models can help to pre-select optimal application schedules but precise pharmacokinetic properties of the pharmaceuticals are required at first. In this study, we have aimed to construct a pharmacokinetic model of G-CSF derivatives filgrastim and pegfilgrastim in mice.

METHODS

Healthy CD-1 mice and those with cyclophosphamide-induced granulocytopaenia were studied after administration of filgrastim and pegfilgrastim in different dosing and timing schedules. Close meshed time series of granulocytes and G-CSF plasma concentrations were determined. An ordinary differential equations model of pharmacokinetics was constructed on the basis of known mechanisms of drug distribution and degradation.

RESULTS

Predictions of the model fit well with all experimental data for both filgrastim and pegfilgrastim. We obtained a unique parameter setting for all experimental scenarios. Differences in pharmacokinetics between filgrastim and pegfilgrastim can be explained by different estimates of model parameters rather than by different model mechanisms. Parameter estimates with respect to distribution and clearance of the drug derivatives are in agreement with qualitative experimental results.

CONCLUSION

Dynamics of filgrastim and pegfilgrastim plasma levels can be explained by the same pharmacokinetic model but different model parameters. Beause of a strong clearance mechanism mediated by granulocytes, granulocytotic and granulocytopaenic conditions must be studied simultaneously to construct a reliable model. The pharmacokinetic model will be extended to a murine model of granulopoiesis under chemotherapy and G-CSF application.

Efficacy of weekly docetaxel and bevacizumab in mesenchymal chondrosarcoma: a new theranostic method combining xenografted biopsies with a mathematical model

The paucity of clinical treatment data on rare tumors, such as mesenchymal chondrosarcoma (MCS), emphasizes the need in theranostic tools for these diseases. We put forward and validated a new theranostic method, combining tumor xenografts and mathematical models, and used it to suggest an improved treatment schedule for a particular MCS patient. Growth curves and gene expression analysis of xenografts, derived from a patient's lung metastasis, served for creating a mathematical model of MCS progression and adapting it to the xenograft setting. The pharmacokinetics and pharmacodynamics of six drugs were modeled, with model variables being adjusted by patient-specific chemosensitivity tests. The xenografted animals were treated by various monotherapy and combination schedules, and the MCS xenograft model was computer simulated under the same treatment scenario. The mathematical model for xenograft growth was then up-scaled to retrieve the MCS patient's tumor progression under different treatment schedules. An average accuracy of 87.1% was obtained when comparing model predictions with the observed tumor growth inhibition in the xenografted animals. Simulation results suggested that a regimen containing bevacizumab applied i.v. in combination with once-weekly docetaxel would be more efficacious in the MCS patient than all other simulated schedules. Weekly docetaxel in the patient resulted in stable metastatic disease and relief of pancytopenia due to tumor infiltration. We suggest that the advantage of weekly docetaxel on the triweekly regimen is directly related to the angiogenesis rate of the tumor. Further validation of this conclusion, and the theranostic method we provide, may facilitate personalization of solid cancer pharmacotherapy.

Mathematical model for G-CSF administration after chemotherapy

Granulocyte-colony stimulating factor (G-CSF) is used clinically for treating chemotherapy-induced neutropenia (low neutrophil levels). Here we present a delay differential equation model for the regulation of neutrophil production that accounts for the effects of G-CSF. Using a combination of analysis and numerical simulations, we use this model to study the effects of delaying G-CSF treatment following chemotherapy for two recombinant forms of G-CSF (filgrastim and pegfilgrastim). We also examine the consequences of varying the duration of filgrastim treatment. We found that varying the starting day or the duration of G-CSF treatment can lead to different qualitative responses in the neutrophil count. These changes can be explained by the coexistence of two stable solutions in the mathematical model.

Perspectives on Mathematical Modeling for Receptor-Mediated Processes

Mathematical modeling is a potent in silico tool that can help investigate, interpret, and predict the behavior of biological systems. The first step is to develop a working hypothesis of the biology. Then by "translating" the biological phenomena into equations, models can harness the power of mathematical analysis techniques to explore the dynamics and interactions of the biological components. Models can be used together with traditional experimental models to help design new experiments, test hypotheses, identify mechanisms, and predict outcomes. This article reviews the process of building, calibrating, and using mathematical models in the context of the kinetics of receptor and signal transduction biology. An example model related to the androgen receptor-mediated regulation of the prostate is presented to illustrate the steps in the modeling process and to highlight the potential for mathematical modeling in this area.

Mathematical properties and parameter estimation for transit compartment pharmacodynamic models

One feature of recent research in pharmacodynamic modelling has been the move towards more mechanistically based model structures. However, in all of these models there are common sub-systems, such as feedback loops and time-delays, whose properties and contribution to the model behaviour merit some mathematical analysis. In this paper a common pharmacodynamic model sub-structure is considered: the linear transit compartment. These models have a number of interesting properties as the length of the cascade chain is increased. In the limiting case a pure time-delay is achieved [Milsum, J.H., 1966. Biological Control Systems Analysis. McGraw-Hill Book Company, New York] and the initial behaviour becoming increasingly sensitive to parameter value perturbation. It is also shown that the modelled drug effect is attenuated, though the duration of action is longer. Through this analysis the range of behaviours that such models are capable of reproducing are characterised. The properties of these models and the experimental requirements are discussed in order to highlight how mathematical analysis prior to experimentation can enhance the utility of mathematical modelling.

Genetic heterogeneity in severe congenital neutropenia: how many aberrant pathways can kill a neutrophil?

PURPOSE OF REVIEW

Severe congenital neutropenia is a primary immunodeficiency in which lack of neutrophils causes inadequate innate immune host response to bacterial infections. Severe congenital neutropenia occurs with sporadic, autosomal dominant, autosomal recessive and X-linked recessive inheritance, as well as in a variety of multisystem syndromes. A principal stimulus for this review is the identification of novel genetic defects and pathophysiological insights into the role of neutrophil apoptosis.

RECENT FINDINGS

The recent findings include identification of mutations in HAX1 in autosomal recessive severe congenital neutropenia (Kostmann disease), a large epidemiological study estimating the risk of progression from severe congenital neutropenia to leukemia, a better understanding of how heterozygous mutations in neutrophil elastase (ELA2) cause severe congenital neutropenia, molecular characterization of a novel syndromic form of severe congenital neutropenia called p14 deficiency and new animal models for several syndromic forms of severe congenital neutropenia.

SUMMARY

We consider the numerous genes mutated in severe congenital neutropenia, the many attempts to make animal models of severe congenital neutropenia, and the results from both human and mouse studies investigating the molecular mechanisms of neutrophil apoptosis. Investigations of how severe congenital neutropenia genes and apoptosis pathways are connected should lead to a better understanding of the pathogenesis of neutropenia and apoptosis pathways relevant to many cell types.

G-CSF Control of Neutrophils Dynamics in the Blood

White blood cell neutrophil is a key component in the fast initial immune response against bacterial and fungal infections. Granulocyte colony stimulating factor (G-CSF) which is naturally produced in the body, is known to control the neutrophils production in the bone marrow and the neutrophils delivery into the blood. In oncological practice, G-CSF injections are widely used to treat neutropenia (dangerously low levels of neutrophils in the blood) and to prevent the infectious complications that often follow chemotherapy. However, the accurate dynamics of G-CSF neutrophil interaction has not been fully determined and no general scheme exists for an optimal G-CSF application in neutropenia. Here we develop a two-dimensional ordinary differential equation model for the G-CSF-neutrophil dynamics in the blood. The model is built axiomatically by first formally defining from the biology the expected properties of the model, and then deducing the dynamic behavior of the resulting system. The resulting model is structurally stable, and its dynamical features are independent of the precise form of the various rate functions. Choosing a specific form for these functions, three complementary parameter estimation procedures for one clinical (training) data set are utilized. The fully parameterized model (6 parameters) provides adequate predictions for several additional clinical data sets on time scales of several days. We briefly discuss the utility of this relatively simple and robust model in several clinical conditions.

G-CSF treatment of canine cyclical neutropenia: A comprehensive mathematical model

OBJECTIVE

To study the effects of different G-CSF temporal treatment schemes using a comprehensive mathematical model of the mammalian hematopoietic system that couples the pharmacokinetics of granulocyte colony-stimulating factor (G-CSF) to the hematopoietic stem cell, neutrophil, platelet, and erythrocyte dynamics.

MATERIALS AND METHODS

Data from cyclical neutropenic (CN) grey collies are used to build an extended model that reproduces the dynamics of circulating blood cells found in laboratory data from the dogs with and without daily G-CSF therapy. The effects of varying the treatment initiation time, and whether injections are given daily, every other day, or every three days, are examined.

RESULTS

The mathematical model is able to reproduce the large variation in data that occurs from one dog to another. Different drug delivery times, with no other changes in the model parameters, can have significant long-term effects on neutrophil numbers. The frequency of drug delivery also has long-term effects on the oscillations.

CONCLUSION

Using a realistic representation of the effects of G-CSF on the tissue-level hematopoietic system, the model matches a wide range of laboratory data. This implies that it would be possible to generate individualized predictions for specific dogs if data were available in real time. The proposed interventions are practical and may reduce the amount of G-CSF required while potentially maintaining or even improving the treatment effects.

Compartmental architecture and dynamics of hematopoiesis

Background

Blood cell formation is maintained by the replication of hematopoietic stem cells (HSC) that continuously feed downstream “compartments” where amplification and differentiation of cells occurs, giving rise to all blood lineages. Whereas HSC replicate slowly, committed cells replicate faster as they become more differentiated.

Methodology/Significant Finding

We propose a multi-compartment model of hematopoiesis, designed on the principle of cell flow conservation under stationary conditions. Cells lost from one compartment due to differentiation are replaced by cells from the upstream compartment. We assume that there is a constant relationship between cell input and output in each compartment and fix the single parameter of the model using data available for granulocyte maturation. We predict that ∼31 mitotic events separate the HSC from the mature cells observed in the circulation. Besides estimating the number of compartments, our model allows us to estimate the size of each compartment, the rate of cell replication within each compartment, the mean time a given cell type contributes to hematopoiesis, the amplification rate in each compartment, as well as the mean time separating stem-cell replication and mature blood-cell formation.

Conclusions

Despite its simplicity, the model agrees with the limited in vivo data available and can make testable predictions. In particular, our prediction of the average lifetime of a PIG-A mutated clone agrees closely with the experimental results available for the PIG-A gene mutation in healthy adults. The present elucidation of the compartment structure and dynamics of hematopoiesis may prove insightful in further understanding a variety of hematopoietic disorders.

Model-based design of chemotherapeutic regimens that account for heterogeneity in leucopoenia

Patients treated with multicycle chemotherapy can exhibit large interindividual heterogeneity of haematotoxicity. We describe how a biomathematical model of human granulopoiesis can be used to design risk-adapted dose-dense chemotherapies, leading to more similar leucopoenias in the population. Calculations were performed on a large data set for cyclophosphamide/doxorubicin/vincristine/prednisone (CHOP)-like chemotherapies for aggressive non-Hodgkin lymphoma. Age, gender, Eastern Cooperative Oncology Group performance status, lactate dehydrogenase and the degree of leucopoenia within the first therapy cycle were used to stratify patients into groups with different expected severity of leucopoenia. We estimated risk-specific bone marrow toxicities depending on the drug doses administered. These toxicities were used to derive risk-adapted therapy schedules. We determined different doses of cyclophosphamide and additional etoposide for patients treated with CHOP-14. Alternatively, the model predicted that further reductions of cycle duration were feasible in groups with low toxicity. We also used the model to identify appropriate granulocyte colony-stimulating factor (G-CSF) schedules. In conclusion, we present a method to estimate the potential of risk-specific dose adaptation of different cytotoxic drugs in order to design chemotherapy protocols that result in decreased diversity of leucopoenia between patients, to develop dose-escalation strategies in cases of low leucopoenic reaction and to determine optimal G-CSF support.