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

3D printing combined with biopredictive dissolution and PBPK/PD modeling optimization and personalization of pharmacotherapy: Are we there yet?

Precision medicine requires selecting the appropriate dosage regimen for a patient using the right drug, at the right time. Model-Informed Precision Dosing (MIPD) is a concept suggesting utilization of model-based prediction methods for optimizing the treatment benefit-harm balance, based on individual characteristics of the patient, disease, treatment method, and other factors. Here, we discuss a theoretical workflow comprising several elements, beginning from the physiologically based pharmacokinetic/pharmacodynamic (PBPK/PD) models, through 3D printed tablets with the model proposed dose, information range and flow, and the patient themselves. We also describe each of these elements, and the connection between them, highlighting challenges and potential obstacles.

A mathematical model with aberrant growth correction in tissue homeostasis and tumor cell growth

Cancer is usually considered a genetic disease caused by alterations in genes that control cellular behaviors, especially growth and division. Cancer cells differ from normal tissue cells in many ways that allow them to grow out of control and become invasive. However, experiments have shown that aberrant growth in many tissues burdened with varying numbers of mutant cells can be corrected, and wild-type cells are required for the active elimination of mutant cells. These findings reveal the dynamic cellular behaviors that lead to a tissue homeostatic state when faced with mutational and nonmutational insults. The current study was motivated by these observations and established a mathematical model of how a tissue copes with the aberrant behavior of mutant cells. The proposed model depicts the interaction between wild-type and mutant cells through a system of two delay differential equations, which include the random mutation of normal cells and the active extrusion of mutant cells. Based on the proposed model, we performed qualitative analysis to identify the conditions of either normal tissue homeostasis or uncontrolled growth with varying numbers of abnormal mutant cells. Bifurcation analysis suggests the conditions of bistability with either a small or large number of mutant cells, the coexistence of bistable steady states can be clinically beneficial by driving the state of mutant cell predominance to the attraction basin of the state with a low number of mutant cells. This result is further confirmed by the treatment strategy obtained from optimal control theory.

A Quantitative Systems Pharmacology Framework for Optimal Doxorubicin Granulocyte Colony-Stimulating Factor Regimens in Triple-Negative Breast Cancer

INTRODUCTION

To mitigate the risk of neutropenia during chemotherapy treatment of triple-negative breast cancer, prophylactic and supportive therapy with granulocyte colony-stimulating factor (G-CSF) is administered concomitant to chemotherapy. The proper timing of combined chemotherapy and G-CSF is crucial for treatment outcomes.

METHODS

Leveraging our established mathematical model of neutrophil production by G-CSF, we developed quantitative systems pharmacology (QSP) framework to investigate how modulating chemotherapy dose frequency and intensity can maximize antitumour effects. To establish schedules that best control tumour size while minimizing neutropenia, we combined Gompertzian tumour growth with pharmacokinetic/pharmacodynamic models of doxorubicin and G-CSF, and our QSP model of neutrophil production.

RESULTS

We optimized a range of chemotherapeutic cycle lengths and dose sizes to establish regimens that simultaneously reduced tumour burden while minimizing neutropenia. Our results suggest that cytotoxic chemotherapy with doxorubicin 45 mg/m2 every 14 days provides effective control of tumour growth while mitigating neutropenic risks.

CONCLUSION

This work suggests future avenues for optimal regimens of chemotherapy with prophylactic G-CSF support. Importantly, the algorithmic approach that we developed can aid in balancing the anticancer and the neutropenic effects of both drugs, and therefore contributes to rational considerations in clinical decision-making in triple-negative breast cancer.

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.

Translational approaches to treating dynamical diseases through in silico clinical trials

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

Engineering in Medicine To Address the Challenge of Cancer Drug Resistance: From Micro- and Nanotechnologies to Computational and Mathematical Modeling

Drug resistance has profoundly limited the success of cancer treatment, driving relapse, metastasis, and mortality. Nearly all anticancer drugs and even novel immunotherapies, which recalibrate the immune system for tumor recognition and destruction, have succumbed to resistance development. Engineers have emerged across mechanical, physical, chemical, mathematical, and biological disciplines to address the challenge of drug resistance using a combination of interdisciplinary tools and skill sets. This review explores the developing, complex, and under-recognized role of engineering in medicine to address the multitude of challenges in cancer drug resistance. Looking through the "lens" of intrinsic, extrinsic, and drug-induced resistance (also referred to as "tolerance"), we will discuss three specific areas where active innovation is driving novel treatment paradigms: (1) nanotechnology, which has revolutionized drug delivery in desmoplastic tissues, harnessing physiochemical characteristics to destroy tumors through photothermal therapy and rationally designed nanostructures to circumvent cancer immunotherapy failures, (2) bioengineered tumor models, which have benefitted from microfluidics and mechanical engineering, creating a paradigm shift in physiologically relevant environments to predict clinical refractoriness and enabling platforms for screening drug combinations to thwart resistance at the individual patient level, and (3) computational and mathematical modeling, which blends in silico simulations with molecular and evolutionary principles to map mutational patterns and model interactions between cells that promote resistance. On the basis that engineering in medicine has resulted in discoveries in resistance biology and successfully translated to clinical strategies that improve outcomes, we suggest the proliferation of multidisciplinary science that embraces engineering.

IL-6 -572C>G and CARD8 304T>A Genetic Polymorphisms are Associated with the Absolute Neutrophil Count in Patients with Hematological Malignancies Under Chemotherapy: An Application of Multilevel Models to a Preliminary Pharmacogenetic Study

Purpose

Neutropenia is a common event in patients undergoing cytotoxic chemotherapy for the treatment of a hematological malignancy. Some polymorphisms, as IL-6 -572C>G (rs1800796), IL-1β -31 G>A (rs1143627), and CARD8 304T>A (rs2043211), in genes related to the inflammatory process, could affect the level of absolute neutrophil count (ANC) after chemotherapy. Since an efficient inflammatory process enhances neutrophil survival, we hypothesize that these polymorphisms are associated with ANC.

Patients and Methods

We carried out a prospective cohort study in two hospitals in Santiago, Chile. The patients included were adults diagnosed with acute myeloblastic leukemia, acute lymphoblastic leukemia, or non-Hodgkin's lymphoma, undergoing cytotoxic chemotherapy. We use a multilevel linear regression model to test our hypothesis. The best model was selected using the Akaike's information criterion (AIC).

Results

We analyzed 1726 hemograms and ANCs from 172 hospitalizations from 32 patients. The results show that CC and CG genotypes of IL-6 -572 C>G polymorphism are associated with higher ANCs compared with the GG genotype (Ln (ANC) ~ 0.81 IC95% 0.02-1.55). Similarly, TT and AT genotypes of CARD8 304T>A polymorphism were related to higher ANCs compared with AA (Ln (ANC) ~ 0.95 IC95% 0.02-1.82). IL-1β genetic polymorphism had no statistically significant association with ANC.

Conclusion

IL-6 rs1800796 -572C>G and CARD8 rs2043211 304T>A polymorphisms are associated with the absolute neutrophil count in patients undergoing cytotoxic chemotherapy for treatment of hematological malignancies. Our findings might be useful to improve the safety of chemotherapy through predictive ANC models.

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.

The timing of cyclic cytotoxic chemotherapy can worsen neutropenia and neutrophilia

Despite recent advances in immunotherapies, cytotoxic chemotherapy continues to be a first-line treatment option for the majority of cancers. Unfortunately, a common side effect in patients undergoing chemotherapy treatment is neutropenia. To mitigate the risk of neutropenia and febrile neutropenia, prophylactic treatment with granulocyte-colony stimulating factor (G-CSF) is administered. Extensive pharmacokinetic/pharmacodynamic modelling of myelosuppression during chemotherapy has suggested avenues for therapy optimization to mitigate this neutropenia. However, the issue of resonance, whereby neutrophil oscillations are induced by the periodic administration of cytotoxic chemotherapy and the coadministration of G-CSF, potentially aggravating a patient's neutropenic/neutrophilic status, is not well-characterized in the clinical literature. Here, through analysis of neutrophil data from young acute lymphoblastic leukaemia patients, we find that resonance is occurring during cyclic chemotherapy treatment in 26% of these patients. Motivated by these data and our previous modelling studies on adult lymphoma patients, we examined resonance during treatment with or without G-CSF. Using our quantitative systems pharmacology model of granulopoiesis, we show that the timing of cyclic chemotherapy can worsen neutropenia or neutrophilia, and suggest clinically-actionable schedules to reduce the resonant effect. We emphasize that delaying supportive G-CSF therapy to 6-7 days after chemotherapy can mitigate myelosuppressive effects. This study therefore highlights the importance of quantitative systems pharmacology for the clinical practice for developing rational therapeutic strategies.

Periodic hematological disorders: Quintessential examples of dynamical diseases

This paper summarizes the evidence supporting the classification of cyclic neutropenia as a dynamical disease and periodic chronic myelogenous leukemia is also considered. The unsatisfactory state of knowledge concerning the genesis of cyclic thrombocytopenia and periodic autoimmune hemolytic anemia is detailed.

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 models for cytarabine-derived myelosuppression in acute myeloid leukaemia

We investigate the personalisation and prediction accuracy of mathematical models for white blood cell (WBC) count dynamics during consolidation treatment using intermediate or high-dose cytarabine (Ara-C) in acute myeloid leukaemia (AML). Ara-C is the clinically most relevant cytotoxic agent for AML treatment. We extend a mathematical model of myelosuppression and a pharmacokinetic model of Ara-C with different hypotheses of Ara-C's pharmacodynamic effects. We cross-validate the 12 model variations using dense WBC count measurements from 23 AML patients. Surprisingly, the prediction accuracy remains satisfactory in each of the models despite different modelling hypotheses. Therefore, we compare average clinical and calculated WBC recovery times for different Ara-C schedules as a successful methodology for model discrimination. As a result, a new hypothesis of a secondary pharmacodynamic effect on the proliferation rate seems plausible. Furthermore, we demonstrate the impact of treatment timing on subsequent nadir values based on personalised predictions as a possibility for influencing/controlling myelosuppression.

Response of an oscillatory differential delay equation to a periodic stimulus

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

Understanding Hematological Toxicities Using Mathematical Modeling

Balancing antitumor efficacy with toxicity is a significant challenge, and drug-induced myelosuppression is a common dose-limiting toxicity of cancer treatments. Mathematical modeling has proven to be a powerful ally in this field, scaling results from animal models to humans, and designing optimized treatment regimens. Here we outline existing mathematical approaches for studying bone marrow toxicity, identify gaps in current understanding, and make future recommendations to advance this vital field of safety research further.

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.

Model-based optimization of G-CSF treatment during cytotoxic chemotherapy

PURPOSE

Although G-CSF is widely used to prevent or ameliorate leukopenia during cytotoxic chemotherapies, its optimal use is still under debate and depends on many therapy parameters such as dosing and timing of cytotoxic drugs and G-CSF, G-CSF pharmaceuticals used and individual risk factors of patients.

METHODS

We integrate available biological knowledge and clinical data regarding cell kinetics of bone marrow granulopoiesis, the cytotoxic effects of chemotherapy and pharmacokinetics and pharmacodynamics of G-CSF applications (filgrastim or pegfilgrastim) into a comprehensive model. The model explains leukocyte time courses of more than 70 therapy scenarios comprising 10 different cytotoxic drugs. It is applied to develop optimized G-CSF schedules for a variety of clinical scenarios.

RESULTS

Clinical trial results showed validity of model predictions regarding alternative G-CSF schedules. We propose modifications of G-CSF treatment for the chemotherapies 'BEACOPP escalated' (Hodgkin's disease), 'ETC' (breast cancer), and risk-adapted schedules for 'CHOP-14' (aggressive non-Hodgkin's lymphoma in elderly patients).

CONCLUSIONS

We conclude that we established a model of human granulopoiesis under chemotherapy which allows predictions of yet untested G-CSF schedules, comparisons between them, and optimization of filgrastim and pegfilgrastim treatment. As a general rule of thumb, G-CSF treatment should not be started too early and patients could profit from filgrastim treatment continued until the end of the chemotherapy cycle.

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.

Steady-state volume of distribution of two-compartment models with simultaneous linear and saturated elimination

The model-independent estimation of physiological steady-state volume of distribution ([Formula: see text]), often referred to non-compartmental analysis (NCA), is historically based on the linear compartment model structure with central elimination. However the NCA-based steady-state volume of distribution ([Formula: see text]) cannot be generalized to more complex models. In the current paper, two-compartment models with simultaneous first-order and Michaelis-Menten elimination are considered. In particular, two indistinguishable models [Formula: see text] and [Formula: see text], both having central Michaelis-Menten elimination, while first-order elimination exclusively either from central or peripheral compartment, are studied. The model-based expressions of the steady-state volumes of distribution [Formula: see text] and their relationships to NCA-based [Formula: see text] are derived. The impact of non-linearity and peripheral elimination is explicitly delineated in the formulas. Being concerned with model identifiability and indistinguishability issues, an interval estimate of [Formula: see text] is suggested.

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.

PLAG (1-palmitoyl-2-linoleoyl-3-acetyl-rac-glycerol) augments the therapeutic effect of pegfilgrastim on gemcitabine-induced neutropenia

Granulocyte colony-stimulating factor (G-CSF) is widely used for preventing neutropenia during chemotherapy. Polyethylene glycol-conjugated granulocyte colony-stimulating factor (PEG-G-CSF, pegfilgrastim) serves the same purpose but has a longer half-life and greater stability than G-CSF. In this study, we investigated whether 1-palmitoyl-2-linoleoyl-3-acetyl-rac-glycerol, acetylated diglyceride (PLAG), augments the therapeutic effect of pegfilgrastim on chemotherapy-induced neutropenia. We compared neutrophil counts in four groups of mice: control mice, gemcitabine-treated mice, gemcitabine/pegfilgrastim-treated mice, and gemcitabine/pegfilgrastim/PLAG-treated mice. PLAG (50 mg/kg) was orally administered every day during the treatment course. CBC analysis showed that the group treated with PLAG experienced a dramatically increased neutrophil counts on the third day following pegfilgrastim treatment. PLAG had no effect on blood cell apoptosis and neutrophil release from bone marrow. Additionally, pegfilgrastim-induced CXCR2 expression in neutrophils was markedly decreased in PLAG-treated animals. These results suggest that PLAG plays a role in inhibiting neutrophil extravasation, giving rise to an increased number of circulating neutrophils when used with pegfilgrastim during gemcitabine treatment. These data support the potential for PLAG to be used with pegfilgrastim to treat or prevent chemotherapy-induced neutropenia by modulating neutrophil transmigration.

Approaching Pharmacometrics as a Paleontologist Would: Recovering the Links Between Drugs and the Body Through Reconstruction

Our knowledge of dinosaurs comes primarily from the fossil record. Notwithstanding the condition of these vestiges, paleontologists reconstruct early reptilian life by comparison to previously discovered specimens. When relics are missing, reasonable deductions are used to fill in the gaps.

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.

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.