A mechanistic mathematical model of temozolomide myelosuppression in children with high-grade gliomas

Myelotoxicity of Temozolomide Treatment in Patients with Glioblastoma Is It Time for a More Mechanistic Approach?

Glioblastoma multiforme is the most common primary central nervous system tumor, with an incidence of 3 [...].

Improving cancer treatments via dynamical biophysical models

Despite significant advances in oncological research, cancer nowadays remains one of the main causes of mortality and morbidity worldwide. New treatment techniques, as a rule, have limited efficacy, target only a narrow range of oncological diseases, and have limited availability to the general public due their high cost. An important goal in oncology is thus the modification of the types of antitumor therapy and their combinations, that are already introduced into clinical practice, with the goal of increasing the overall treatment efficacy. One option to achieve this goal is optimization of the schedules of drugs administration or performing other medical actions. Several factors complicate such tasks: the adverse effects of treatments on healthy cell populations, which must be kept tolerable; the emergence of drug resistance due to the intrinsic plasticity of heterogeneous cancer cell populations; the interplay between different types of therapies administered simultaneously. Mathematical modeling, in which a tumor and its microenvironment are considered as a single complex system, can address this complexity and can indicate potentially effective protocols, that would require experimental verification. In this review, we consider classical methods, current trends and future prospects in the field of mathematical modeling of tumor growth and treatment. In particular, methods of treatment optimization are discussed with several examples of specific problems related to different types of treatment.

Drug Exposure to Establish Pharmacokinetic-Response Relationships in Oncology

In the oncology field, understanding the relationship between the dose administered and the exerted effect is particularly important because of the narrow therapeutic index associated with anti-cancer drugs and the high interpatient variability. Therefore, in this review, we provide a critical perspective of the different methods of characterising treatment exposure in the oncology setting. The increasing number of modelling applications in oncology reflects the applicability and the impact of pharmacometrics on all phases of the drug development process and patient management as well. Pharmacometric modelling is a worthy component within the current paradigm of model-based drug development, but pharmacometric modelling techniques are also accessible for the clinician in the optimisation of current oncology therapies. Consequently, the application of population models in a hospital setting by generating close collaborations between physicians and pharmacometricians is highly recommended, providing a systematic means of developing and assessing model-based metrics as 'drivers' for various responses to treatments, which can then be evaluated as predictors for treatment success. Characterising the key determinants of variability in exposure is of particular importance for anticancer agents, as efficacy and toxicity are associated with exposure. We present the different strategies to describe and predict drug exposure that can be applied depending on the data available, with the objective of obtaining the most useful information in the patients' favour throughout the full drug cycle. Therefore, the objective of the present article is to review the different approaches used to characterise a patient's exposure to oncology drugs, which will result in a better understanding of the time course of the response and the magnitude of interpatient variability.

A physiological model of granulopoiesis to predict clinical drug induced neutropenia from in vitro bone marrow studies: with application to a cell cycle inhibitor

Neutropenia is one of the most common dose-limiting toxocities associated with anticancer drug therapy. The ability to predict the probability and severity of neutropenia based on in vitro studies of drugs in early drug development will aid in advancing safe and efficacious compounds to human testing. Toward this end, a physiological model of granulopoiesis and its regulation is presented that includes the bone marrow progenitor cell cycle, allowing for a mechanistic representation of the action of relevant anticancer drugs based on in vitro studies. Model development used data from previously reported tracer kinetic studies of granulocyte disposition in healthy humans to characterize the dynamics of neutrophil margination in the presence of endogenous granulocyte-colony stimulating factor (G-CSF). In addition, previously published data from healthy volunteers following pegfilgrastim and filgrastim were used to quantify the regulatory effects of support G-CSF therapies on granulopoiesis. The model was evaluated for the cell cycle inhibitor palbociclib, using an in vitro system of human bone marrow mononuclear cells to quantify the action of palbociclib on proliferating progenitor cells, including its inhibitory effect on G1 to S phase transition. The in vitro results were incorporated into the physiological model of granulopoiesis and used to predict the time course of absolute neutrophil count (ANC) and the incidence of neutropenia observed in three previously reported clinical trials of palbociclib. The model was able to predict grade 3 and 4 neutropenia due to palbociclib treatment with 86% accuracy based on in vitro data.

ACT001 modulates the NF-κB/MnSOD/ROS axis by targeting IKKβ to inhibit glioblastoma cell growth

Glioblastomas are high-grade brain tumors with poor prognoses, and new therapeutic approaches for these tumors are critically needed. This study revealed the underlying mechanisms of a new orphan drug, ACT001, that is currently in clinical trials for the treatment of advanced glioblastoma in Australia and China. ACT001 significantly suppressed glioma cell proliferation and induced apoptosis and cell cycle arrest in vitro, as determined by Cell Counting Kit-8 assays and flow cytometry. In addition, U-118 MG cells with high expression of p-IKKβ were sensitive to ACT001. Changes in the oxidative stress pathway in U-118 MG cells were detected with the isobaric tags for relative and absolute quantitation (iTRAQ) method. We further verified that ACT001 elevated the levels of reactive oxygen species (ROS) by regulating NF-κB-targeted MnSOD. ACT001 markedly inhibited NF-κB activation by directly binding IKKβ and inhibiting its phosphorylation. Overexpression of IKKβ markedly attenuated the changes in MnSOD and NOX1, indicating that ACT001 increased the levels of ROS by reducing the protein expression of p-IKKβ. Furthermore, ACT001 reduced cyclin B1/CDC2 expression and triggered G₂/M phase arrest by increasing ROS production. ACT001 also upregulated the expression of Bax and Bim and induced apoptosis in a ROS-dependent manner. ACT001 effectively suppressed the growth of U-118 MG tumors in BALB/c nude mice and GL-261-luciferase tumors in C57BL/6 J mice. Finally, ACT001 downregulated the expression of p-p65, MnSOD, cyclin B1, CDC2, and Ki67 in U-118 MG tumor tissues. Patients with activated NF-κB signaling should thus be given priority for enrollment in future phase II clinical trials. KEY MESSAGES: ACT001 directly bind to IKKβ and inhibited its phosphorylation. The inhibition of p-IKKβ induced the generation of ROS. ACT001 promoted the generation of ROS by regulating MnSOD expression to induce G₂/M phase arrest.

Optimization of Cancer Treatment in the Frequency Domain

Thorough exploration of alternative dosing frequencies is often not performed in conventional pharmacometrics approaches. Quantitative systems pharmacology (QSP) can provide novel insights into optimal dosing regimen and drug behaviors which could add a new dimension to the design of novel treatments. However, methods for such an approach are currently lacking. Recently, we illustrated the utility of frequency-domain response analysis (FdRA), an analytical method used in control engineering, using several generic pharmacokinetic-pharmacodynamic case studies. While FdRA is not applicable to models harboring ever increasing variables such as those describing tumor growth, studying such models in the frequency domain provides valuable insight into optimal dosing frequencies. Through the analysis of three distinct tumor growth models (cell cycle-specific, metronomic, and acquired resistance), we demonstrate the application of a simulation-based analysis in the frequency domain to optimize cancer treatments. We study the response of tumor growth to dosing frequencies while simultaneously examining treatment safety, and found for all three models that above a certain dosing frequency, tumor size is insensitive to an increase in dosing frequency, e.g., for the cell cycle-specific model, one dose per 3 days, and an hourly dose yield the same reduction of tumor size to 3% of the initial size after 1 year of treatment. Additionally, we explore the effect of drug elimination rate changes on the tumor growth response. In summary, we show that the frequency-domain view of three models of tumor growth dynamics can help in optimizing drug dosing regimen to improve treatment success.

Artificial Intelligence in Drug Treatment

The most common applications of artificial intelligence (AI) in drug treatment have to do with matching patients to their optimal drug or combination of drugs, predicting drug-target or drug-drug interactions, and optimizing treatment protocols. This review outlines some of the recently developed AI methods aiding the drug treatment and administration process. Selection of the best drug(s) for a patient typically requires the integration of patient data, such as genetics or proteomics, with drug data, like compound chemical descriptors, to score the therapeutic efficacy of drugs. The prediction of drug interactions often relies on similarity metrics, assuming that drugs with similar structures or targets will have comparable behavior or may interfere with each other. Optimizing the dosage schedule for administration of drugs is performed using mathematical models to interpret pharmacokinetic and pharmacodynamic data. The recently developed and powerful models for each of these tasks are addressed, explained, and analyzed here.

A STRATEGY OF OPTIMAL EFFICACY OF T11 TARGET STRUCTURE IN THE TREATMENT OF BRAIN TUMOR

We report a mathematical model depicting gliomas and immune system interactions by considering the role of immunotherapeutic drug T11 target structure (T11TS). The mathematical model comprises a system of coupled nonlinear ordinary differential equations involving glioma cells, macrophages, activated cytotoxic T-lymphocytes (CTLs), immunosuppressive cytokine transforming growth factor-[Formula: see text] (TGF-[Formula: see text]), immunostimulatory cytokine interferon-[Formula: see text] (IFN-[Formula: see text]) and the concentrations of immunotherapeutic agent T11TS. For the better understanding of the circumstances under which the gliomas can be eradicated from a patient, we use optimal control strategy. We design the objective functional by considering the biomedical goal, which minimizes the glioma burden and maximizes the macrophages and activated CTLs. The existence and the characterization for the optimal control are established. The uniqueness of the quadratic optimal control problem is also analyzed. We demonstrate numerically that the optimal treatment strategies using T11TS reduce the glioma burden and increase the cell count of activated CTLs and macrophages.

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.

Optimal dynamic regimens with artificial intelligence: The case of temozolomide

We determine an optimal protocol for temozolomide using population variability and dynamic optimization techniques inspired by artificial intelligence. We use a Pharmacokinetics/Pharmacodynamics (PK/PD) model based on Faivre and coauthors (Faivre, et al., 2013) for the pharmacokinetics of temozolomide, as well as the pharmacodynamics of its efficacy. For toxicity, which is measured by the nadir of the normalized absolute neutrophil count, we formalize the myelosuppression effect of temozolomide with the physiological model of Panetta and coauthors (Panetta, et al., 2003). We apply the model to a population with variability as given in Panetta and coauthors (Panetta, et al., 2003). Our optimization algorithm is a variant in the class of Monte-Carlo tree search algorithms. We do not impose periodicity constraint on our solution. We set the objective of tumor size minimization while not allowing more severe toxicity levels than the standard Maximum Tolerated Dose (MTD) regimen. The protocol we propose achieves higher efficacy in the sense that –compared to the usual MTD regimen– it divides the tumor size by approximately 7.66 after 336 days –the 95% confidence interval being [7.36–7.97]. The toxicity is similar to MTD. Overall, our protocol, obtained with a very flexible method, gives significant results for the present case of temozolomide and calls for further research mixing operational research or artificial intelligence and clinical research in oncology.

Administration of temozolomide: Comparison of conventional and metronomic chemotherapy regimens

PURPOSE

We compare the Maximum Tolerated Dose (MTD) and Metronomic Chemotherapy (MC) protocols for temozolomide administration. We develop an innovative methodology for characterizing optimal chemotherapy regimens.

METHODS

We use a PK/PD model based on Faivre et al. (2013) for the pharmacokinetics of temozolomide, as well as the pharmacodynamics of its efficacy. For toxicity, which is measured by the nadir of the normalized absolute neutrophil count, we formalize the myelosuppression effect of temozolomide with the physiological model of Panetta et al. (2003b). We introduce a multi-criteria tool for comparing protocols along their efficacy and toxicity dimensions.

RESULTS

We show that the toxicity of the MC regimen proposed by Faivre et al. (2013) can greatly be reduced without affecting its efficacy, while the standard MTD protocol efficacy cannot be improved without impairing its toxicity. We also show that for any acceptable toxicity level, the optimal protocol remains closely related to standard MTD.

CONCLUSIONS

Overall, our new method enables a rich comparison between protocols along multiple dimensions. We can rank protocols for temozolomide administration. It is a first step toward building optimal individual protocols.

Pharmacodynamic modeling of adverse effects of anti-cancer drug treatment

Purpose

Adverse effects related to anti-cancer drug treatment influence patient’s quality of life, have an impact on the realized dosing regimen, and can hamper response to treatment. Quantitative models that relate drug exposure to the dynamics of adverse effects have been developed and proven to be very instrumental to optimize dosing schedules. The aims of this review were (i) to provide a perspective of how adverse effects of anti-cancer drugs are modeled and (ii) to report several model structures of adverse effect models that describe relationships between drug concentrations and toxicities.

Methods

Various quantitative pharmacodynamic models that model adverse effects of anti-cancer drug treatment were reviewed.

Results

Quantitative models describing relationships between drug exposure and myelosuppression, cardiotoxicity, and graded adverse effects like fatigue, hand-foot syndrome (HFS), rash, and diarrhea have been presented for different anti-cancer agents, including their clinical applicability.

Conclusions

Mathematical modeling of adverse effects proved to be a helpful tool to improve clinical management and support decision-making (especially in establishment of the optimal dosing regimen) in drug development. The reported models can be used as templates for modeling a variety of anti-cancer-induced adverse effects to further optimize therapy.

Semimechanistic cell-cycle type-based pharmacokinetic/pharmacodynamic model of chemotherapy-induced neutropenic effects of diflomotecan under different dosing schedules

The current work integrates cell-cycle dynamics occurring in the bone marrow compartment as a key element in the structure of a semimechanistic pharmacokinetic/pharmacodynamic model for neutropenic effects, aiming to describe, with the same set of system- and drug-related parameters, longitudinal data of neutropenia gathered after the administration of the anticancer drug diflomotecan (9,10-difluoro-homocamptothecin) under different dosing schedules to patients (n = 111) with advanced solid tumors. To achieve such an objective, the general framework of the neutropenia models was expanded, including one additional physiologic process resembling cell cycle dynamics. The main assumptions of the proposed model are as follows: within the stem cell compartment, proliferative and quiescent cells coexist, and only cells in the proliferative condition are sensitive to drug effects and capable of following the maturation chain. Cell cycle dynamics were characterized by two new parameters, FProl (the fraction of proliferative [Prol] cells that enters into the maturation chain) and kcycle (first-order rate constant governing cell cycle dynamics within the stem cell compartment). Both model parameters were identifiable as indicated by the results from a bootstrap analysis, and their estimates were supported by date from the literature. The estimates of FProl and kcycle were 0.58 and 1.94 day(-1), respectively. The new model could properly describe the neutropenic effects of diflomotecan after very different dosing scenarios, and can be used to explore the potential impact of dosing schedule dependencies on neutropenia prediction.

Parameter identification of hematopoiesis mathematical model - periodic chronic myelogenous leukemia

Periodic chronic myelogenous leukemia (PCML) is a dynamic hematopoietic disease which causes oscillations of circulating leukocytes, platelets and reticulocytes. Mathematical modeling is an invaluable tool to help in predicting hematopoiesis behavior. In this paper we modify the existing models based on improving the parameters of the model. Also more parameters are estimated regarding the proposed model. It is our major intention to construct a physiological model which can map major identified mechanisms of leukopoiesis to provide a deeper insight into this complex biological process. In the proposed model the leukocytes line has been modeled more precisely. In fact, precursor cells have been considered as two separate groups: proliferating precursor cells and non-proliferating precursor cells. As a result, more parameters have appeared in the model and identifying the new parameters has resulted in a better fit of clinical data and the data extracted from the model for both platelets and leukocytes. That is, the new model describes the leukocytes and platelets of the system in a way that is closer to clinical data, so the proposed model can be more useful for predicting the behavior of leukocytes and platelets for PCML disease. Compared with the previous works, it is shown that the new model has a better fit of the quantitative data on leukocytes and platelets.

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

PURPOSE

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

METHODS

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

RESULTS

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

CONCLUSION

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

OPTIMAL CONTROL OF MIXED IMMUNOTHERAPY AND CHEMOTHERAPY OF TUMORS

We investigate a mathematical population model of tumor-immune interactions. The populations involved are tumor cells, specific and non-specific immune cells, and concentrations of therapeutic treatments. We establish the existence of an optimal control for this model and provide necessary conditions for the optimal control triple for simultaneous application of chemotherapy, tumor infiltrating lymphocyte (TIL) therapy, and interleukin-2 (IL-2) treatment. We discuss numerical results for the combination of the chemo-immunotherapy regimens. We find that the qualitative nature of our results indicates that chemotherapy is the dominant intervention with TIL interacting in a complementary fashion with the chemotherapy. However, within the optimal control context, the interleukin-2 treatment does not become activated for the estimated parameter ranges.

Optimizing cancer pharmacotherapeutics using mathematical modeling and a systems biology approach

Research in mathematics and in mathematical biology on cancer and its treatments has been soaring in the past 10 years at an unprecedented speed. Such thriving is likely due as much to new findings in fundamental biology as to an emerging general interest from mathematicians and engineers towards applications in biology and medicine and to their subsequently designed representations and predictions of tumor processes that are now allowed by modern means of computation and simulation. This article, which does not claim the status of an extended review paper on mathematical models of cancer and its treatment, is focused on modeling in a systems biology perspective. I will list here the most necessary mathematical methods, in my opinion, which, while enforcing already existing methods, should be further developed towards designing and applying optimized individualized treatments of cancer in the clinic.

Semi-mechanistic population pharmacokinetic/pharmacodynamic model for neutropenia following therapy with the Plk-1 inhibitor BI 2536 and its application in clinical development

PURPOSE

(1) To describe the neutropenic response of BI 2536 a polo-like kinase 1 inhibitor in patients with cancer using a semi-mechanistic model. (2) To explore by simulations (a) the neutropenic effects for the maximum tolerated dose (MTD) and the dose at which dose-limiting toxicity occurred, (b) the possibility to reduce the cycle duration without increasing neutropenia substantially, and (c) the impact of the initial absolute neutrophil count (ANC) on the degree of neutropenia for different doses.

EXPERIMENTAL DESIGN

BI 2536 was administered as intravenous infusion over 60 min in the dose range from 25 to 250 mg. Three different administration schedules were explored: (a) day 1, (b) days 1, 2, and 3 or (c) days 1 and 8 within a 3 week treatment cycle. BI 2536 plasma concentrations and ANC obtained during the first treatment cycle from 104 patients were analysed using the population approach with NONMEM VI.

RESULTS

Neutropenia was described by a semi-mechanistic model resembling proliferation at the stem cell compartment, maturation, degradation, and homeostatic regulation. BI 2536 acts decreasing proliferation rate. Simulations showed that (1) all MTD doses showed an acceptable risk of neutropenia, (2) when BI 2536 is given as 200 mg single administration, cycle duration can be reduced from 3 to 2 weeks, and (3) baseline ANC might be considered to individualise the dose of BI 2536.

CONCLUSIONS

A semi-mechanistic population model was applied to describe the neutropenic effects of BI 2536. The model was used for simulations to support further clinical development.

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

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

Mathematical model for G-CSF administration after chemotherapy

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

Using synchronization for prediction of high-dimensional chaotic dynamics

We experimentally observe the nonlinear dynamics of an optoelectronic time-delayed feedback loop designed for chaotic communication using commercial fiber optic links, and we simulate the system using delay differential equations. We show that synchronization of a numerical model to experimental measurements provides a new way to assimilate data and forecast the future of this time-delayed high-dimensional system. For this system, which has a feedback time delay of 22 ns, we show that one can predict the time series for up to several delay periods, when the dynamics is about 15 dimensional.

Using pharmacokinetic and pharmacodynamic modeling and simulation to evaluate importance of schedule in topotecan therapy for pediatric neuroblastoma

PURPOSE

The study aims to use mathematical modeling and simulation to assess the relative contribution of topotecan systemic exposure and scheduling in the activity and myelosuppression of topotecan in pediatric patients with neuroblastoma.

EXPERIMENTAL DESIGN

Pharmacokinetic and pharmacodynamic data were obtained from a phase II study for pediatric patients with high-risk neuroblastoma. The topotecan dosage was individualized to attain a topotecan lactone area under the plasma concentration-time curve between 80 and 120 ng/mL h and given over a protracted schedule (i.e., 10 days). Four mathematical models describing topotecan pharmacokinetics, tumor growth, and neutrophil and platelet dynamics were developed. The models were combined to simulate and compare different topotecan treatment strategies with respect to systemic exposure and schedule.

RESULTS

The median change in tumor volume was significantly different between schedules (5% increase for D x 5 versus 60% decrease for D x 5 x 2; P < 0.0001) when administering the same total systemic exposure. Whereas protracted schedules showed increased neutropenia (median of 7 versus 12 days below an absolute neutrophil count of 500/microL; P < 0.0001) and thrombocytopenia (median of 3 versus 10 days below a platelet count of 20,000/microL; P < 0.00001), simulations showed that delays in topotecan therapy would not be required. Simulations showed that an increase in topotecan exposure on the D x 5 schedule by 2.4-fold resulted in a modest decrease in tumor volume (i.e., median percentage change tumor volume of 24% versus 3%).

CONCLUSIONS

The present mathematical model gave an innovative approach to determining relevant topotecan schedules for possible evaluation in the clinic, which could lead to improved tumor response with minimized toxicities.

Contribution of modelling chemotherapy-induced hematological toxicity for clinical practice

Anticancer chemotherapies are responsible for numerous adverse events. Among these, hematological toxicity is one of the main causes for ending treatment. These toxicities decrease production of red blood cells (anemia), production of white blood cells (neutropenia or granulocytopenia), and production of platelets (thrombocytopenia), which may be life-threatening to the patient. Preventing such discontinuation would be valuable for treating patients more effectively. In order to achieve this goal, numerous mathematical and physiological or semiphysiological models have been developed. The complexity of models has increased over the years, from empiric E(max) models to mechanistic models including physiological mechanisms such as feedback control. This review discusses several approaches of modelling hematological toxicities illustrated with some examples: pharmacodynamic models for the hematological toxicity of 5-fluorouracil, epirubicin, melphalan, paclitaxel, topotecan, and indisulam.

G-CSF Control of Neutrophils Dynamics in the Blood

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

Compartmental architecture and dynamics of hematopoiesis

Background

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

Methodology/Significant Finding

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

Conclusions

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

A Microenvironment Based Model of Antimitotic Therapy of Gompertzian Tumor Growth

A model of tumor growth, based on two-compartment cell population dynamics, and an overall Gompertzian growth has been previously developed. The main feature of the model is an inter-compartmental transfer function that describes the net exchange between proliferating (P) and quiescent (Q) cells and yields Gompertzian growth for tumor cell population N = P + Q. Model parameters provide for cell reproduction and cell death. This model is further developed here and modified to simulate antimitotic therapy. Therapy decreases the reproduction-rate constant and increases the death-rate constant of proliferating cells with no direct effect on quiescent cells. The model results in a system of two ODE equations (in N and P/N) that has an analytical solution. Net tumor growth depends on support from the microenvironment. Indirectly, this is manifested in the transfer function, which depends on the proliferation ratio, P/N. Antimitotic therapy will change P/N, and the tumor responds by slowing the transfer rate from P to Q. While the cellular effects of therapy are modeled as dependent only on antimitotic activity of the drug, the tumor response also depends on the tumor age and any previous therapies--after therapy, it is not the same tumor. The strength of therapy is simulated by the parameter lambda, which is the ratio of therapy induced net proliferation rate constant versus the original. A pharmacodynamic factor inversely proportional to tumor size is implemented. Various chemotherapy regimens are simulated and the outcomes of therapy administered at different time points in the life history of the tumor are explored. Our analysis shows: (1) for a constant total dose administered, a decreasing dose schedule is marginally superior to an increasing or constant scheme, with more pronounced benefit for faster growing tumors, (2) the minimum dose to stop tumor growth is age dependent, and (3) a dose-dense schedule is favored. Faster growing tumors respond better to dose density.

Successful therapy must eradicate cancer stem cells

Despite significant improvements in cancer therapy, tumor recurrence is frequent and can be due to a variety of mechanisms, including the evolution of resistance and tumor progression. Cancer stem cells have been postulated to maintain tumor growth similar to normal stem cells maintaining tissue homeostasis. Recently, the existence of these malignant stem cells has been proven for hematological as well as some solid tumors. Tumor stem cells are not targeted by standard therapy and might be responsible for treatment failure and tumor recurrence in many patients. We designed a simple mathematical model to demonstrate the importance of eliminating tumor stem cells. We explored different therapeutic scenarios to illustrate the properties required from novel therapeutic agents for successful tumor treatment. We show that successful therapy must eradicate tumor stem cells.

Development of a pharmacokinetic limited sampling model for temozolomide and its active metabolite MTIC

PURPOSE

To develop a pharmacokinetic limited sampling model (LSM) for temozolomide and its metabolite MTIC in infants and children.

METHODS

LSMs consisting of either two or four samples were determined using a modification of the D-optimality algorithm. This accounted for prior distribution of temozolomide and MTIC pharmacokinetic parameters based on full pharmacokinetic sampling from 38 patients with 120 pharmacokinetic studies (dosage range 145-200 mg/m(2) per day orally). Accuracy and bias of each LSM were determined relative to the full sampling method. We also assessed the predictive performance of the LSMs using Monte-Carlo simulations.

RESULTS

The four strategies generated from the D-optimality algorithm were as follows: LSM 1=0.25, 1.25, and 3 h; LSM 2=0.25, 1.25, and 6 h; LSM 3=0.25, 0.5, 1.25, and 3 h; LSM 4=0.25, 0.5, 1.25, and 6 h. LSM 2 demonstrated the best combination of low bias [0.1% (-8.9%, 11%) and 11% (4.3%, 15%)] and high accuracy [-1.0% (-12%, 24%) and 14% (7.9%, 37%)] for temozolomide clearance and MTIC AUC, respectively. Furthermore, adding a fourth sample (e.g., LSM 4) did not substantially decrease the bias or increase the accuracy for temozolomide clearance or MTIC AUC. Results from Monte-Carlo simulations also revealed that LSM 2 had the best combination of lowest bias (0.1+/-6.1% and -0.8+/-6.5%), and the highest accuracy (4.5+/-4.1% and 5.0+/-4.3%) for temozolomide clearance and MTIC apparent clearance, respectively.

CONCLUSIONS

Using data derived from our population analysis, the sampling times for a limited sample pharmacokinetic model for temozolomide and MTIC in children are prior to the temozolomide dose, and 15 min, 1.25 h and 6 h after the dose.