Mathematical model for G-CSF administration after chemotherapy

Continuous Intravenous Administration of Granulocyte-Colony-Stimulating Factors-A Breakthrough in the Treatment of Cancer Patients with Febrile Neutropenia

Background: Febrile neutropenia (FN) remains one of the most challenging problems in medical oncology and is a very severe side effect of chemotherapy. Its late consequences, when it is recurrent or of a severe grade, are dose reduction and therapy delays. Current guidelines allow the administration of granulocyte-colony-stimulating factors (G-CSF) for profound FN (except for the case when a pegylated form of G-CSF is administrated with prophylactic intention) in addition to antibiotics and supportive care. Methods: This is a prospective study that included 96 patients with confirmed malignancy, treated with chemotherapy, who developed FN during their oncological therapy, and were hospitalized. They received standard treatment plus a dose of G-CSF of 16 µg/Kg/day IV continuous infusion. Results: The gender distribution was almost symmetrical: Male patients made up 48.96% and 51.04% were female patients, with no significance on recovery from FN (p = 1.00). The patients who received prophylactic G-CSF made up 20.21%, but this was not a predictive or prognostic factor for the recovery time from aplasia (p = 0.34). The median chemotherapy line where patients with FN were included was two and the number of previous chemotherapy cycles before FN was three. The median serological number of neutrophils (PMN) was 450/mm³ and leucocytes (WBC) 1875/mm³ at the time of FN. Ten patients possess PMN less than 100/mm³. The median time to recovery was 25.5 h for 96 included patients, with one failure in which the patient possessed grade 5 FN. Predictive factors for shorter recovery time were lower levels of C reactive protein (p < 0.001) and procalcitonin (p = 0.002) upon hospital admission and higher WBC (p = 0.006) and PMN (p < 0.001) at the time of the provoking cycle of chemotherapy for FN. The best chance for a shorter duration of FN was a short history of chemotherapy regarding the number of cycles) (p < 0.0001). Conclusions: Continuous IV administration of G-CSF could be an alternative salvage treatment for patients with profound febrile neutropenia, with a very fast recovery time for neutrophiles.

Constant infusion case of one compartment pharmacokinetic model with simultaneous first-order and Michaelis-Menten elimination: analytical solution and drug exposure formula

The main objective of this article is to propose the closed-form solution of one-compartment pharmacokinetic model with simultaneous first-order and Michaelis-Menten elimination for the case of constant infusion. For the case of bolus administration, we have previously established a closed-form solution of the model through introducing a transcendent X function. In the same vein, we found here a closed-form solution of constant infusion could be realized through introducing another transcendent Y function. For the general case of constant infusion of limited duration, the closed-form solution is then fully expressed using both X and Y functions. As direct results, several important pharmacokinetic surrogates, such as peak concentration [Formula: see text] and total drug exposure AUC[Formula: see text], are found the closed-form expressions and ready to be analyzed. The new pharmacokinetic knowledge we have gained on these parameters, which largely exhibits in a nonlinear feature, is in clear contrast to that of the linear case. Finally, with a pharmacokinetic model adapted from that formerly reported on phenytoin, we numerically analyzed and illustrated the roles of different model parameters and discussed their influence on drug exposure. To conclude, the present findings elucidate the intrinsic quantitative structural properties of such pharmacokinetic model and provide a new avenue for future modelling and rational drug designs.

MATHEMATICAL CHARACTERIZATION OF HETEROGENEITY IN A CANCER STEM CELL DRIVEN TUMOR GROWTH MODEL WITH NONLINEAR SELF-RENEWAL

The detection, in a wide variety of cancer types, of a population of highly tumorigenic cells that exhibit self-renewal and multipotency, which are hallmarks of stem cells, has transformed the current view of tumor initiation, progression, and treatment. Here, we develop and analyze a mathematical model for tumor growth that is based on the current biological understanding of the processes that underlie cellular expansion under the hierarchical guidelines of the cancer stem cell (CSC) hypothesis. Important features of the model include (i) a nonlinear probability of CSC self-renewal that reflects the fact that this key type of stem cell division can be regulated by extrinsic and intrinsic chemical signaling as well as environmental (niche) constraints and (ii) an amplification factor that captures the transient amplifying divisions that are a defining characteristic of progenitor cells. We present a thorough mathematical analysis of the model and highlight the conditions required for tumors to evolve toward either bounded or exponential growth. Numerical simulations further illustrate the impact of the various parameters on the tumor growth rate and on the heterogeneous cellular composition, which varies during progression.

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.

Model-Based Optimal AML Consolidation Treatment

OBJECTIVE

Neutropenia is an adverse event commonly arising during intensive chemotherapy of acute myeloid leukemia (AML). It is often associated with infectious complications. Mathematical modeling, simulation, and optimization of the treatment process would be a valuable tool to support clinical decision making, potentially resulting in less severe side effects and deeper remissions. However, until now, there has been no validated mathematical model available to simulate the effect of chemotherapy treatment on white blood cell (WBC) counts and leukemic cells simultaneously.

METHODS

We developed a population pharmacokinetic/pharmacodynamic (PK/PD) model combining a myelosuppression model considering endogenous granulocyte-colony stimulating factor (G-CSF), a PK model for cytarabine (Ara-C), a subcutaneous absorption model for exogenous G-CSF, and a two-compartment model for leukemic blasts. This model was fitted to data of 44 AML patients during consolidation therapy with a novel Ara-C plus G-CSF schedule from a phase II controlled clinical trial. Additionally, we were able to optimize treatment schedules with respect to disease progression, WBC nadirs, and the amount of Ara-C and G-CSF.

RESULTS

The developed PK/PD model provided good prediction accuracies and an interpretation of the interaction between WBCs, G-CSF, and blasts. For 14 patients (those with available bone marrow blast counts), we achieved a median 4.2-fold higher WBC count at nadir, which is the most critical time during consolidation therapy. The simulation results showed that relative bone marrow blast counts remained below the clinically important threshold of 5%, with a median of 60% reduction in Ara-C.

CONCLUSION

These in silico findings demonstrate the benefits of optimized treatment schedules for AML patients.

SIGNIFICANCE

Until 2017, no new drug had been approved for the treatment of AML, fostering the optimal use of currently available drugs.

Analytical Solution and Exposure Analysis of a Pharmacokinetic Model with Simultaneous Elimination Pathways and Endogenous Production: The Case of Multiple Dosing Administration

In this paper, a typical pharmacokinetic (PK) model is studied for the case of multiple intravenous bolus-dose administration. This model, of one-compartment structure, not only exhibits simultaneous first-order and Michaelis-Menten elimination, but also involves a constant endogenous production. For the PK characterization of the model, we have established the closed-form solution of concentrations over time, the existence and local stability of the steady state. Using analytical approaches and the concept of corrected concentration, we have shown that the area under the curve ([Formula: see text]) at steady state is higher compared to that at the single dose ([Formula: see text]). Moreover, by splitting the dose and dosing interval into halves, we have revealed that it can result in a significant decrease in the steady-state average concentration. These model-based findings, which contrast with the current knowledge for linear PK, confirm the necessity to revisit drugs exhibiting nonlinear PK and to suggest a rational way of using mathematical analysis for the dosing regimen design.

Mathematical analysis and drug exposure evaluation of pharmacokinetic models with endogenous production and simultaneous first-order and Michaelis-Menten elimination: the case of single dose

Drugs with an additional endogenous source often exhibit simultaneous first-order and Michaelis-Menten elimination and are becoming quite common in pharmacokinetic modeling. In this paper, we investigate the case of single dose intravenous bolus administration for the one-compartment model. Relying on a formerly introduced transcendent function, we were able to analytically express the concentration time course of this model and provide the pharmacokinetic interpretation of its components. Using the concept of the corrected concentration, the mathematical expressions for the partial and total areas under the concentration time curve (AUC) were also given. The impact on the corrected concentration and AUC is discussed as well as the relative contribution of the exogenous part in presence of endogenous production. The present findings theoretically elucidate several pharmacokinetic issues for the considered drug compounds and provide guidance for the rational estimation of their pharmacokinetic parameters.

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.

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.

Closed form solutions and dominant elimination pathways of simultaneous first-order and Michaelis-Menten kinetics

The current study aims to provide the closed form solutions of one-compartment open models exhibiting simultaneous linear and nonlinear Michaelis-Menten elimination kinetics for single- and multiple-dose intravenous bolus administrations. It can be shown that the elimination half-time ([Formula: see text]) has a dose-dependent property and is upper-bounded by [Formula: see text] of the first-order elimination model. We further analytically distinguish the dominant role of different elimination pathways in terms of model parameters. Moreover, for the case of multiple-dose intravenous bolus administration, the existence and local stability of the periodic solution at steady state are established. The closed form solutions of the models are obtained through a newly introduced function motivated by the Lambert W function.

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 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.

Toward a universal treatment for cancer: cell inflation assisted chemotherapy

Cancers show considerable genetic and functional heterogeneity, preventing the development of a universal anticancer drug. Here, I argue that it is nevertheless possible to elaborate a therapeutic strategy that can be used in almost every cancer, exploiting the negative feedback effect of normal cells on the proliferation of their precursors. This method, termed cell inflation assisted chemotherapy, is aimed at blocking normal cell division prior to high-dose antimitotic chemotherapy. Evidence for a negative feedback effect on granulocyte production suggests that it is possible to prevent neutropenia by transfusion of autologous granulocytes. In a first step, this protocol will be devised to protect neutrophils and to prevent granulopenia in patients treated with intensive chemotherapy. In its simplest form, it will consist of a leukapheresis–storage–reinjection sequence just prior to drug administration. Then, if the proof of concept is established, a more systematic use of intensive cell cycle-specific chemotherapy, together with protection of other lineages through temporary mitotic blockade might be a treatment applicable for most cancers.

Negative feedback effect of normal cells on the proliferation of their precursors may be used to protect them from high-dose antimitotic chemotherapy, preventing myelosuppression. In its simplest form, cell inflation assisted chemotherapy will consist of a leukapheresis-storage-reinjection sequence just prior to drug administration.

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.

Lifespan based indirect response models

In the field of hematology, several mechanism-based pharmacokinetic-pharmacodynamic models have been developed to understand the dynamics of several blood cell populations under different clinical conditions while accounting for the essential underlying principles of pharmacology, physiology and pathology. In general, a population of blood cells is basically controlled by two processes: the cell production and cell loss. The assumption that each cell exits the population when its lifespan expires implies that the cell loss rate is equal to the cell production rate delayed by the lifespan and justifies the use of delayed differential equations for compartmental modeling. This review is focused on lifespan models based on delayed differential equations and presents the structure and properties of the basic lifespan indirect response (LIDR) models for drugs affecting cell production or cell lifespan distribution. The LIDR models for drugs affecting the precursor cell production or decreasing the precursor cell population are also presented and their properties are discussed. The interpretation of transit compartment models as LIDR models is reviewed as the basis for introducing a new LIDR for drugs affecting the cell lifespan distribution. Finally, the applications and limitations of the LIDR models are discussed.

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.

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.