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Continuous Intravenous Administration of Granulocyte-Colony-Stimulating Factors-A Breakthrough in the Treatment of Cancer Patients with Febrile Neutropenia. ACTA ACUST UNITED AC 2021; 57:medicina57070675. [PMID: 34208815 PMCID: PMC8305666 DOI: 10.3390/medicina57070675] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/06/2021] [Revised: 05/17/2021] [Accepted: 06/21/2021] [Indexed: 11/16/2022]
Abstract
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.
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Constant infusion case of one compartment pharmacokinetic model with simultaneous first-order and Michaelis-Menten elimination: analytical solution and drug exposure formula. J Pharmacokinet Pharmacodyn 2021; 48:495-508. [PMID: 33629256 DOI: 10.1007/s10928-021-09740-5] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/30/2020] [Accepted: 01/20/2021] [Indexed: 10/22/2022]
Abstract
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.
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NAZARI FERESHTEH, PEARSON ALEXANDERT, JACKSON TRACHETTEL. MATHEMATICAL CHARACTERIZATION OF HETEROGENEITY IN A CANCER STEM CELL DRIVEN TUMOR GROWTH MODEL WITH NONLINEAR SELF-RENEWAL. J BIOL SYST 2021. [DOI: 10.1142/s0218339021500029] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
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.
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Affiliation(s)
- FERESHTEH NAZARI
- Applied BioMath, 210 Broadway, Suite 201, Cambridge, MA 02139, USA
| | - ALEXANDER T PEARSON
- Department of Medicine, Section of Hematology/Oncology, The University of Chicago, Chicago, IL 60637, USA
| | - TRACHETTE L JACKSON
- Department of Mathematics, University of Michigan, 530 Church Street, Ann Arbor, MI 48108-1043, USA
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Mika B, Pełka M, Tkacz E. Mathematical modeling of the neutrophil production process supported by administration of glycoprotein. Biocybern Biomed Eng 2021. [DOI: 10.1016/j.bbe.2020.12.001] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
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5
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Cassidy T, Humphries AR, Craig M, Mackey MC. Characterizing Chemotherapy-Induced Neutropenia and Monocytopenia Through Mathematical Modelling. Bull Math Biol 2020; 82:104. [PMID: 32737602 DOI: 10.1007/s11538-020-00777-0] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/01/2020] [Accepted: 07/11/2020] [Indexed: 12/18/2022]
Abstract
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.
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Affiliation(s)
- Tyler Cassidy
- Theoretical Biology and Biophysics, Los Alamos National Laboratory, Los Alamos, NM, 87545, USA
| | - Antony R Humphries
- Department of Mathematics and Statistics, McGill University, Montréal, QC, H3A 0B9, Canada.,Department of Physiology, McGill University, Montréal, QC, H3A 0B9, Canada
| | - Morgan Craig
- Department of Mathematics and Statistics, Université de Montréal, Montréal, Canada. .,CHU Sainte-Justine Research Centre, University of Montreal, Montréal, Canada.
| | - Michael C Mackey
- Department of Physiology, McGill University, 3655 Drummond, Montréal, QC, H3G 1Y6, Canada.,Department of Mathematics and Statistics, McGill University, 3655 Drummond, Montréal, QC, H3G 1Y6, Canada.,Department of Physics, McGill University, 3655 Drummond, Montréal, QC, H3G 1Y6, Canada
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6
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Jost F, Schalk E, Weber D, Dohner H, Fischer T, Sager S. Model-Based Optimal AML Consolidation Treatment. IEEE Trans Biomed Eng 2020; 67:3296-3306. [PMID: 32406820 DOI: 10.1109/tbme.2020.2982749] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/05/2022]
Abstract
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.
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Wu X, Nekka F, Li J. Analytical Solution and Exposure Analysis of a Pharmacokinetic Model with Simultaneous Elimination Pathways and Endogenous Production: The Case of Multiple Dosing Administration. Bull Math Biol 2019; 81:3436-3459. [PMID: 31420841 DOI: 10.1007/s11538-019-00651-8] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/18/2018] [Accepted: 07/15/2019] [Indexed: 12/17/2022]
Abstract
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.
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Affiliation(s)
- Xiaotian Wu
- Department of Mathematics, Shanghai Maritime University, Shanghai, 201306, People's Republic of China
- Faculté de pharmacie, Université de Montréal, Montreal, QC, H3C 3J7, Canada
| | - Fahima Nekka
- Faculté de pharmacie, Université de Montréal, Montreal, QC, H3C 3J7, Canada
- Centre de Recherches Mathématiques, Université de Montréal, Montreal, QC, H3C 3J7, Canada
| | - Jun Li
- Faculté de pharmacie, Université de Montréal, Montreal, QC, H3C 3J7, Canada.
- Centre de Recherches Mathématiques, Université de Montréal, Montreal, QC, H3C 3J7, Canada.
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Wu X, Nekka F, Li J. 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. J Pharmacokinet Pharmacodyn 2018; 45:693-705. [PMID: 29987574 DOI: 10.1007/s10928-018-9599-4] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/08/2018] [Accepted: 06/30/2018] [Indexed: 01/06/2023]
Abstract
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.
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Affiliation(s)
- Xiaotian Wu
- Department of Mathematics, Shanghai Maritime University, Shanghai, 201306, People's Republic of China.,Faculté de pharmacie, Université de Montréal, Montréal, QC, H3C 3J7, Canada
| | - Fahima Nekka
- Faculté de pharmacie, Université de Montréal, Montréal, QC, H3C 3J7, Canada. .,Centre de recherches mathématiques, Université de Montréal, Montréal, QC, H3C 3J7, Canada.
| | - Jun Li
- Faculté de pharmacie, Université de Montréal, Montréal, QC, H3C 3J7, Canada.,Centre de recherches mathématiques, Université de Montréal, Montréal, QC, H3C 3J7, Canada
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9
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Transit and lifespan in neutrophil production: implications for drug intervention. J Pharmacokinet Pharmacodyn 2017; 45:59-77. [DOI: 10.1007/s10928-017-9560-y] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/22/2017] [Accepted: 12/06/2017] [Indexed: 01/08/2023]
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10
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Craig M. Towards Quantitative Systems Pharmacology Models of Chemotherapy-Induced Neutropenia. CPT Pharmacometrics Syst Pharmacol 2017; 6:293-304. [PMID: 28418603 PMCID: PMC5445232 DOI: 10.1002/psp4.12191] [Citation(s) in RCA: 26] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/09/2017] [Revised: 02/21/2017] [Accepted: 02/21/2017] [Indexed: 12/22/2022] Open
Abstract
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.
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Affiliation(s)
- M Craig
- Program for Evolutionary Dynamics, Harvard UniversityCambridgeMassachusettsUSA
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11
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Milton J, Wu J, Campbell SA, Bélair J. Outgrowing Neurological Diseases: Microcircuits, Conduction Delay and Childhood Absence Epilepsy. COMPUTATIONAL NEUROLOGY AND PSYCHIATRY 2017. [DOI: 10.1007/978-3-319-49959-8_2] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/26/2023]
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12
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Craig M, Humphries AR, Mackey MC. A Mathematical Model of Granulopoiesis Incorporating the Negative Feedback Dynamics and Kinetics of G-CSF/Neutrophil Binding and Internalization. Bull Math Biol 2016; 78:2304-2357. [PMID: 27324993 DOI: 10.1007/s11538-016-0179-8] [Citation(s) in RCA: 40] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/21/2015] [Accepted: 05/19/2016] [Indexed: 11/24/2022]
Abstract
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.
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Affiliation(s)
- M Craig
- Faculté de Pharmacie, Université de Montréal, Montréal, QC, H3T 1J4, Canada.
- Program for Evolutionary Dynamics, Harvard University, Cambridge, MA, 02138, USA.
| | - A R Humphries
- Department of Mathematics and Statistics, McGill University, Montréal, QC, H3A 0B9, Canada
| | - M C Mackey
- Departments of Mathematics, Physics and Physiology, McGill University, Montréal, QC, H3G 1Y6, Canada
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Prognostic Value of Neutrophil-Related Factors in Locally Advanced Cervical Squamous Cell Carcinoma Patients Treated with Cisplatin-Based Concurrent Chemoradiotherapy. DISEASE MARKERS 2016; 2016:3740794. [PMID: 27087737 PMCID: PMC4818798 DOI: 10.1155/2016/3740794] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 12/05/2015] [Accepted: 02/08/2016] [Indexed: 01/18/2023]
Abstract
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.
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Craig M, González-Sales M, Li J, Nekka F. Impact of Pharmacokinetic Variability on a Mechanistic Physiological Pharmacokinetic/Pharmacodynamic Model: A Case Study of Neutrophil Development, PM00104, and Filgrastim. SPRINGER PROCEEDINGS IN MATHEMATICS & STATISTICS 2016. [DOI: 10.1007/978-3-319-31323-8_6] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/21/2023]
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15
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Craig M, Humphries AR, Nekka F, Bélair J, Li J, Mackey MC. Neutrophil dynamics during concurrent chemotherapy and G-CSF administration: Mathematical modelling guides dose optimisation to minimise neutropenia. J Theor Biol 2015; 385:77-89. [PMID: 26343861 DOI: 10.1016/j.jtbi.2015.08.015] [Citation(s) in RCA: 31] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/26/2014] [Revised: 06/10/2015] [Accepted: 08/20/2015] [Indexed: 11/18/2022]
Abstract
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.
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Affiliation(s)
- Morgan Craig
- Faculté de Pharmacie, Université de Montréal, Montréal, QC, Canada H3C 3J7; Centre for Applied Mathematics in Bioscience and Medicine (CAMBAM), McGill University, Montreal, QC, Canada H3G 1Y6.
| | - Antony R Humphries
- Department of Mathematics and Statistics, McGill University, Montreal, QC, Canada H3A 0B9; Centre for Applied Mathematics in Bioscience and Medicine (CAMBAM), McGill University, Montreal, QC, Canada H3G 1Y6; Centre de recherches mathématiques, Université de Montréal, Montréal, QC, Canada H3C 3J7.
| | - Fahima Nekka
- Centre for Applied Mathematics in Bioscience and Medicine (CAMBAM), McGill University, Montreal, QC, Canada H3G 1Y6; Centre de recherches mathématiques, Université de Montréal, Montréal, QC, Canada H3C 3J7.
| | - Jacques Bélair
- Département de mathématiques et de statistique, Université de Montréal, Montréal, QC, Canada H3C 3J7; Centre for Applied Mathematics in Bioscience and Medicine (CAMBAM), McGill University, Montreal, QC, Canada H3G 1Y6; Centre de recherches mathématiques, Université de Montréal, Montréal, QC, Canada H3C 3J7.
| | - Jun Li
- Faculté de Pharmacie, Université de Montréal, Montréal, QC, Canada H3C 3J7; Centre for Applied Mathematics in Bioscience and Medicine (CAMBAM), McGill University, Montreal, QC, Canada H3G 1Y6; Centre de recherches mathématiques, Université de Montréal, Montréal, QC, Canada H3C 3J7.
| | - Michael C Mackey
- Department of Mathematics and Statistics, McGill University, Montreal, QC, Canada H3A 0B9; Centre for Applied Mathematics in Bioscience and Medicine (CAMBAM), McGill University, Montreal, QC, Canada H3G 1Y6; Departments of Physiology and Physics, McGill University, Montreal, QC, Canada H3G 1Y6.
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16
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Wu X, Li J, Nekka F. Closed form solutions and dominant elimination pathways of simultaneous first-order and Michaelis-Menten kinetics. J Pharmacokinet Pharmacodyn 2015; 42:151-61. [PMID: 25678215 DOI: 10.1007/s10928-015-9407-3] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/12/2014] [Accepted: 02/04/2015] [Indexed: 11/29/2022]
Abstract
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.
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Affiliation(s)
- Xiaotian Wu
- Department of Mathematics, Shanghai Maritime University, Shanghai, 201306, China
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Schirm S, Engel C, Loeffler M, Scholz M. Modelling chemotherapy effects on granulopoiesis. BMC SYSTEMS BIOLOGY 2014; 8:138. [PMID: 25539928 PMCID: PMC4302124 DOI: 10.1186/s12918-014-0138-7] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 09/02/2014] [Accepted: 12/11/2014] [Indexed: 02/05/2023]
Abstract
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.
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18
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Dale DC, Mackey MC. Understanding, treating and avoiding hematological disease: better medicine through mathematics? Bull Math Biol 2014; 77:739-57. [PMID: 25213154 DOI: 10.1007/s11538-014-9995-x] [Citation(s) in RCA: 20] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/19/2014] [Accepted: 07/08/2014] [Indexed: 10/24/2022]
Abstract
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.
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Affiliation(s)
- David C Dale
- Department of Medicine, University of Washington, Seattle, WA, 98195, USA,
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Schirm S, Engel C, Loeffler M, Scholz M. A combined model of human erythropoiesis and granulopoiesis under growth factor and chemotherapy treatment. Theor Biol Med Model 2014; 11:24. [PMID: 24886056 PMCID: PMC4046020 DOI: 10.1186/1742-4682-11-24] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/07/2014] [Accepted: 05/16/2014] [Indexed: 12/03/2022] Open
Abstract
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.
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Affiliation(s)
- Sibylle Schirm
- Institute for Medical Informatics, Statistics and Epidemiology, University of Leipzig, Leipzig, Germany
- LIFE Research Center of Civilization Diseases, University of Leipzig, Leipzig, Germany
| | - Christoph Engel
- Institute for Medical Informatics, Statistics and Epidemiology, University of Leipzig, Leipzig, Germany
| | - Markus Loeffler
- Institute for Medical Informatics, Statistics and Epidemiology, University of Leipzig, Leipzig, Germany
| | - Markus Scholz
- Institute for Medical Informatics, Statistics and Epidemiology, University of Leipzig, Leipzig, Germany
- LIFE Research Center of Civilization Diseases, University of Leipzig, Leipzig, Germany
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Agur Z, Elishmereni M, Kheifetz Y. Personalizing oncology treatments by predicting drug efficacy, side-effects, and improved therapy: mathematics, statistics, and their integration. WILEY INTERDISCIPLINARY REVIEWS-SYSTEMS BIOLOGY AND MEDICINE 2014; 6:239-53. [DOI: 10.1002/wsbm.1263] [Citation(s) in RCA: 27] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/30/2013] [Revised: 12/23/2013] [Accepted: 01/03/2014] [Indexed: 01/21/2023]
Affiliation(s)
- Zvia Agur
- Institute for Medical BioMathematics; Hate'ena Bene Ataroth Israel
- Optimata Ltd.; Zichron Ya'akov; Tel Aviv Israel
| | - Moran Elishmereni
- Institute for Medical BioMathematics; Hate'ena Bene Ataroth Israel
- Optimata Ltd.; Zichron Ya'akov; Tel Aviv Israel
| | - Yuri Kheifetz
- Institute for Medical BioMathematics; Hate'ena Bene Ataroth Israel
- Optimata Ltd.; Zichron Ya'akov; Tel Aviv Israel
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Understanding and Treating Cytopenia Through Mathematical Modeling. ADVANCES IN EXPERIMENTAL MEDICINE AND BIOLOGY 2014; 844:279-302. [DOI: 10.1007/978-1-4939-2095-2_14] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/24/2022]
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Model-Based Approach to Describe G-CSF Effects in Carboplatin-Treated Cancer Patients. Pharm Res 2013; 30:2795-807. [DOI: 10.1007/s11095-013-1099-z] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/20/2012] [Accepted: 06/04/2013] [Indexed: 11/25/2022]
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Corcos D. Toward a universal treatment for cancer: cell inflation assisted chemotherapy. Cancer Med 2013; 2:421-6. [PMID: 24156014 PMCID: PMC3799276 DOI: 10.1002/cam4.91] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/17/2013] [Revised: 03/28/2013] [Accepted: 04/17/2013] [Indexed: 12/22/2022] Open
Abstract
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.
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Affiliation(s)
- Daniel Corcos
- INSERM U955, Faculté de Médecine de Créteil 8 Rue du Général Sarrail, 94010, Créteil Cedex, France
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Brooks G, Provencher G, Lei J, Mackey MC. Neutrophil dynamics after chemotherapy and G-CSF: the role of pharmacokinetics in shaping the response. J Theor Biol 2012; 315:97-109. [PMID: 22981924 DOI: 10.1016/j.jtbi.2012.08.028] [Citation(s) in RCA: 26] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/19/2012] [Revised: 07/21/2012] [Accepted: 08/23/2012] [Indexed: 11/17/2022]
Abstract
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.
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Affiliation(s)
- Grace Brooks
- Department of Physiology, Centre for Applied Mathematics in Bioscience and Medicine, McGill University, Montreal, QC, Canada H4X 2C1
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Scholz M, Schirm S, Wetzler M, Engel C, Loeffler M. Pharmacokinetic and -dynamic modelling of G-CSF derivatives in humans. Theor Biol Med Model 2012; 9:32. [PMID: 22846180 PMCID: PMC3507764 DOI: 10.1186/1742-4682-9-32] [Citation(s) in RCA: 30] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/17/2012] [Accepted: 06/12/2012] [Indexed: 11/17/2022] Open
Abstract
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.
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Affiliation(s)
- Markus Scholz
- Institute for Medical Informatics, Statistics and Epidemiology, University of Leipzig, Haertelstrasse 16-18, 04107 Leipzig, Germany.
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Vainas O, Ariad S, Amir O, Mermershtain W, Vainstein V, Kleiman M, Inbar O, Ben-Av R, Mukherjee A, Chan S, Agur Z. Personalising docetaxel and G-CSF schedules in cancer patients by a clinically validated computational model. Br J Cancer 2012; 107:814-22. [PMID: 22814580 PMCID: PMC3425973 DOI: 10.1038/bjc.2012.316] [Citation(s) in RCA: 27] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/02/2022] Open
Abstract
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.
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Affiliation(s)
- O Vainas
- Optimata Ltd, 7 Abba Hillel Street, Ramat-Gan 52522, Israel
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Krzyzanski W, Perez Ruixo JJ. Lifespan based indirect response models. J Pharmacokinet Pharmacodyn 2012; 39:109-23. [PMID: 22212685 PMCID: PMC3684441 DOI: 10.1007/s10928-011-9236-y] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/20/2011] [Accepted: 12/15/2011] [Indexed: 01/18/2023]
Abstract
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.
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Affiliation(s)
- Wojciech Krzyzanski
- Department of Pharmaceutical Sciences, University at Buffalo, Buffalo, NY, USA.
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Zhuge C, Lei J, Mackey MC. Neutrophil dynamics in response to chemotherapy and G-CSF. J Theor Biol 2012; 293:111-20. [DOI: 10.1016/j.jtbi.2011.10.017] [Citation(s) in RCA: 26] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/07/2011] [Revised: 10/13/2011] [Accepted: 10/14/2011] [Indexed: 11/25/2022]
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Nakaoka S, Aihara K. Mathematical study on kinetics of hematopoietic stem cells--theoretical conditions for successful transplantation. JOURNAL OF BIOLOGICAL DYNAMICS 2011; 6:836-854. [PMID: 22873618 DOI: 10.1080/17513758.2011.588343] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/01/2023]
Abstract
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.
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Affiliation(s)
- Shinji Nakaoka
- FIRST, Aihara Innovative Mathematical Modelling Project, Japan Science and Technology Agency, Institute of Industrial Science, University of Tokyo, 4-6-1 Komaba, Meguro-ku, Tokyo, 153-8505, Japan.
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Krzyzanski W, Wiczling P, Lowe P, Pigeolet E, Fink M, Berghout A, Balser S. Population modeling of filgrastim PK-PD in healthy adults following intravenous and subcutaneous administrations. J Clin Pharmacol 2011; 50:101S-112S. [PMID: 20881223 DOI: 10.1177/0091270010376966] [Citation(s) in RCA: 40] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
Abstract
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.
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Affiliation(s)
- Wojciech Krzyzanski
- Department of Pharmaceutical Sciences, State University of New York at Buffalo, Buffalo, New York, USA.
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Dingli D, Pacheco JM. Modeling the architecture and dynamics of hematopoiesis. WILEY INTERDISCIPLINARY REVIEWS-SYSTEMS BIOLOGY AND MEDICINE 2010; 2:235-244. [DOI: 10.1002/wsbm.56] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/10/2022]
Affiliation(s)
- David Dingli
- Division of Hematology, Department of Molecular Medicine, College of Medicine, Mayo Clinic, Rochester, MN 55905, USA
- Biomathematics Research Group, College of Medicine, Mayo Clinic, Rochester, MN 55905, USA
| | - Jorge M. Pacheco
- Applied Theoretical Physics Group, Departamento de Fisica de Faculdade de Ciencias, Universidade de Lisboa, 1649‐003 Lisboa Codex, Portugal
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Scholz M, Ackermann M, Engel C, Emmrich F, Loeffler M, Kamprad M. A pharmacokinetic model of filgrastim and pegfilgrastim application in normal mice and those with cyclophosphamide-induced granulocytopaenia. Cell Prolif 2009; 42:813-22. [PMID: 19689472 DOI: 10.1111/j.1365-2184.2009.00638.x] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/14/2023] Open
Abstract
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.
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Affiliation(s)
- M Scholz
- Institute for Medical Informatics, Statistics and Epidemiology, University of Leipzig, Leipzig, Germany.
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