A pharmacodynamic model for the time course of tumor shrinkage by gemcitabine + carboplatin in non-small cell lung cancer patients

Tumor growth inhibition modeling in patients with second line biliary tract cancer and first line non-small cell lung cancer based on bintrafusp alfa trials

This analysis aimed to quantify tumor dynamics in patients receiving either bintrafusp alfa (BA) or pembrolizumab, by population pharmacokinetic (PK)-pharmacodynamic modeling, and investigate clinical and molecular covariates describing the variability in tumor dynamics by pharmacometric and machine-learning (ML) approaches. Data originated from two clinical trials in patients with biliary tract cancer (BTC; NCT03833661) receiving BA and non-small cell lung cancer (NSCLC; NCT03631706) receiving BA or pembrolizumab. Individual drug exposure was estimated from previously developed population PK models. Population tumor dynamics models were developed for each drug-indication combination, and covariate evaluations performed using nonlinear mixed-effects modeling (NLME) and ML (elastic net and random forest models) approaches. The three tumor dynamics' model structures all included linear tumor growth components and exponential tumor shrinkage. The final BTC model included the effect of drug exposure (area under the curve) and several covariates (demographics, disease-related, and genetic mutations). Drug exposure was not significant in either of the NSCLC models, which included two, disease-related, covariates in the BA arm, and none in the pembrolizumab arm. The covariates identified by univariable NLME and ML highly overlapped in BTC but showed less agreement in NSCLC analyses. Hyperprogression could be identified by higher tumor growth and lower tumor kill rates and could not be related to BA exposure. Tumor size over time was quantitatively characterized in two tumor types and under two treatments. Factors potentially related to tumor dynamics were assessed using NLME and ML approaches; however, their net impact on tumor size was considered as not clinically relevant.

Investigating the impact of target lesion selection on drug effect evaluation and tumour growth rate determination using tumour growth inhibition models: Example of malignant pleural mesothelioma patients treated with cisplatin alone or in combination with pemetrexed

In the last update of the RECIST criteria in 2009, it was proposed that the number of target lesions to be followed over time for response-to-treatment assessment be reduced from 10 to 5 lesions maximum, with up to 2 per organ. We explored the impact of reducing the number of target lesion on the assessment of drug effect in a randomised phase III clinical trial using a tumour growth inhibition (TGI) model. Tumour size measurements from 441 (out of 456) patients were used to build two datasets for which observations were the sum of longest diameters of all measurable lesions (ALL dataset) or following the RECIST 1.1 recommendations (R1.1 dataset). TGI models incorporating a categorical covariate for treatment group or a pharmacokinetic metric (i.e. dose; simulated area under the curve) were used to describe the longitudinal tumour size kinetics. Drug exposure was not superior to treatment group at describing drug effect. ALL and R1.1 individual estimates of drug effect appeared to be strongly correlated (r²=0.88). Including pharmacokinetic metrics in TGI models should be conducted carefully when no pharmacokinetic samples are available. Reducing the number of target lesion did not seem to compromise the determination of drug effect using TGI models.

Do we really understand how drug eluted from stents modulates arterial healing?

The advent of drug-eluting stents (DES) has revolutionised the treatment of coronary artery disease. These devices, coated with anti-proliferative drugs, are deployed into stenosed or occluded vessels, compressing the plaque to restore natural blood flow, whilst simultaneously combating the evolution of restenotic tissue. Since the development of the first stent, extensive research has investigated how further advancements in stent technology can improve patient outcome. Mathematical and computational modelling has featured heavily, with models focussing on structural mechanics, computational fluid dynamics, drug elution kinetics and subsequent binding within the arterial wall; often considered separately. Smooth Muscle Cell (SMC) proliferation and neointimal growth are key features of the healing process following stent deployment. However, models which depict the action of drug on these processes are lacking. In this article, we start by reviewing current models of cell growth, which predominantly emanate from cancer research, and available published data on SMC proliferation, before presenting a series of mathematical models of varying complexity to detail the action of drug on SMC growth in vitro. Our results highlight that, at least for Sodium Salicylate and Paclitaxel, the current state-of-the-art nonlinear saturable binding model is incapable of capturing the proliferative response of SMCs across a range of drug doses and exposure times. Our findings potentially have important implications on the interpretation of current computational models and their future use to optimise and control drug release from DES and drug-coated balloons.

Artificial Intelligence and Mechanistic Modeling for Clinical Decision Making in Oncology

The amount of "big" data generated in clinical oncology, whether from molecular, imaging, pharmacological, or biological origin, brings novel challenges. To mine efficiently this source of information, mathematical models able to produce predictive algorithms and simulations are required, with applications for diagnosis, prognosis, drug development, or prediction of the response to therapy. Such mathematical and computational constructs can be subdivided into two broad classes: biologically agnostic, statistical models using artificial intelligence techniques, and physiologically based, mechanistic models. In this review, recent advances in the applications of such methods in clinical oncology are outlined. These include machine learning applied to big data (omics, imaging, or electronic health records), pharmacometrics and quantitative systems pharmacology, as well as tumor kinetics and metastasis modeling. Focus is set on studies with high potential of clinical translation, and particular attention is given to cancer immunotherapy. Perspectives are given in terms of combinations of the two approaches: "mechanistic learning."

Progress and Opportunities to Advance Clinical Cancer Therapeutics Using Tumor Dynamic Models

There is a need for new approaches and endpoints in oncology drug development, particularly with the advent of immunotherapies and the multiple drug combinations under investigation. Tumor dynamics modeling, a key component to oncology "model-informed drug development," has shown a growing number of applications and a broader adoption by drug developers and regulatory agencies in the past years to support drug development and approval in a variety of ways. Tumor dynamics modeling is also being investigated in personalized cancer therapy approaches. These models and applications are reviewed and discussed, as well as the limitations and issues open for further investigations. A close collaboration between stakeholders like clinical investigators, statisticians, and pharmacometricians is warranted to advance clinical cancer therapeutics.

Linking Tumor Growth Dynamics to Survival in Ipilimumab-Treated Patients With Advanced Melanoma Using Mixture Tumor Growth Dynamic Modeling

Early tumor assessments have been widely used to predict overall survival (OS), with potential application to dose selection and early go/no‐go decisions. Most published tumor dynamic models assume a uniform pattern of tumor growth dynamics (TGDs). We developed a mixture TGD model to characterize different patterns of longitudinal tumor sizes. Data from 688 patients with advanced melanoma who received ipilimumab 3 or 10 mg/kg every 3 weeks in a phase III study (NCT01515189) were used in a TGD‐OS analysis. The mixture model described TGD profiles using three subpopulations (no‐growth, intermediate, and fast). The TGD model showed a positive exposure/dose‐response (i.e., a higher proportion of patients in no/intermediate growth subpopulations and a lower tumor growth rate with ipilimumab 10 mg/kg relative to the 3 mg/kg dose). Finally, the mixture TGD model‐based measures of tumor response provided better predictions of OS compared with the nonmixture model.

Challenging the dose-response-time data approach: Analysis of a complex system

This study presents an extensive dose-response-time (DRT) meta-analysis of the nicotinic acid-induced inhibition of free fatty acids and insulin release. The purpose was to quantify the implications of lacking exposure data when analysing complex pharmacodynamic systems. The DRT model successfully characterised various response behaviours-including time-delays, rebound, feedback mechanisms, and adaptation-on both the individual and the population level. Comparing the fitted DRT model to an exposure-driven reference analysis showed that bias and uncertainty were introduced in the parameter estimates. However, most estimates were within one standard error from the reference. In both approaches, a few parameters suffered from practical identifiability issues, likely due to large differences in half-lives of the different rate processes. Moreover, the optimal dosing strategies predicted by the DRT model differed slightly from those of the exposure-driven analysis, having a lower optimal steady-state reduction of free fatty acids exposure.

Assessing Similarity Among Individual Tumor Size Lesion Dynamics: The CICIL Methodology

Mathematical models of tumor dynamics generally omit information on individual target lesions (iTLs), and consider the most important variable to be the sum of tumor sizes (TS). However, differences in lesion dynamics might be predictive of tumor progression. To exploit this information, we have developed a novel and flexible approach for the non‐parametric analysis of iTLs, which integrates knowledge from signal processing and machine learning. We called this new methodology ClassIfication Clustering of Individual Lesions (CICIL). We used CICIL to assess similarities among the TS dynamics of 3,223 iTLs measured in 1,056 patients with metastatic colorectal cancer treated with cetuximab combined with irinotecan, in two phase II studies. We mainly observed similar dynamics among lesions within the same tumor site classification. In contrast, lesions in anatomic locations with different features showed different dynamics in about 35% of patients. The CICIL methodology has also been implemented in a user‐friendly and efficient Java‐based framework.

Predicting tumour growth and its impact on survival in gemcitabine-treated patients with advanced pancreatic cancer

The aim of this evaluation was to characterize the impact of the tumour size (TS) effects driven by the anticancer drug gemcitabine on overall survival (OS) in patients with advanced pancreatic cancer by building and validating a predictive semi-mechanistic joint TS-OS model. TS and OS data were obtained from one phase II and one phase III study where gemcitabine was administered (1000-1250 mg/kg over 30-60 min i.v infusion) as single agent to patients (n = 285) with advanced pancreatic cancer. Drug exposure, TS and OS were linked using the population approach with NONMEM 7.3. Pancreatic tumour progression was characterized by exponential growth (doubling time = 67 weeks), and tumour response to treatment was described as a function of the weekly area under the gemcitabine triphosphate concentration vs time curve (AUC), including treatment-related resistance development. The typical predicted percentage of tumour growth inhibition with respect to no treatment was 22.3% at the end of 6 chemotherapy cycles. Emerging resistance elicited a 57% decrease in drug effects during the 6th chemotherapy cycle. Predicted TS profile was identified as main prognostic factor of OS, with tumours responders' profiles improving median OS by 30 weeks compared to stable-disease TS profiles. Results of NCT00574275 trial were predicted using this modelling framework, thereby validating the approach as a prediction tool in clinical development. Our analyses show that despite the advanced stage of the disease in this patient population, the modelling framework herein can be used to predict the likelihood of treatment success using early clinical data.

Exposure-Response Analysis of Necitumumab Efficacy in Squamous Non-Small Cell Lung Cancer Patients

We sought to describe the exposure-response relationship of necitumumab efficacy in squamous non-small cell lung cancer patients and evaluate intrinsic and extrinsic patient descriptors that may guide dosing. SQUIRE was a phase III study comparing necitumumab in combination with gemcitabine and cisplatin vs. gemcitabine and cisplatin alone in 1,014 patients. An integrated model for tumor size dynamics and overall survival was developed, where reduction in tumor size results in a decrease in survival hazard. The change in tumor size was characterized using linear growth and first-order shrinkage. Overall survival was described using a combination of a Weibull function and Gompertz function for the hazard, with dynamic tumor size being a predictor for the hazard. Although body weight resulted in higher clearance and lower exposure, simulations showed that an 800 mg flat dose provided optimal response regardless of body weight.

Identification of the Serine Biosynthesis Pathway as a Critical Component of BRAF Inhibitor Resistance of Melanoma, Pancreatic, and Non-Small Cell Lung Cancer Cells

Metastatic melanoma cells commonly acquire resistance to BRAF V600E inhibitors (BRAFi). In this study, we identified serine biosynthesis as a critical mechanism of resistance. Proteomic assays revealed differential protein expression of serine biosynthetic enzymes PHGDH, PSPH, and PSAT1 following vemurafenib (BRAFi) treatment in sensitive versus acquired resistant melanoma cells. Ablation of PHGDH via siRNA sensitized acquired resistant cells to vemurafenib. Inhibiting the folate cycle, directly downstream of serine synthesis, with methotrexate also displayed similar sensitization. Using the DNA-damaging drug gemcitabine, we show that gemcitabine pretreatment sensitized resistant melanoma cells to BRAFis vemurafenib and dabrafenib. We extended our findings to BRAF WT tumor cell lines that are intrinsically resistant to vemurafenib and dabrafenib. Pretreatment of pancreatic cancer and non-small cell lung cancer cell lines with sublethal doses of 50 and 5 nmol/L of gemcitabine, respectively, enhanced killing by both vemurafenib and dabrafenib. The novel aspects of this study are the direct identification of serine biosynthesis as a critical mechanism of BRAF V600E inhibitor resistance and the first successful example of using gemcitabine + BRAFis in combination to kill previously drug-resistant cancer cells, creating the translational potential of pretreatment with gemcitabine prior to BRAFi treatment of tumor cells to reverse resistance within the mutational profile and the WT. Mol Cancer Ther; 16(8); 1596-609. ©2017 AACR.

A Review of Modeling Approaches to Predict Drug Response in Clinical Oncology

Model-based approaches have emerged as important tools for quantitatively understanding temporal relationships between drug dose, concentration, and effect over the course of treatment, and have now become central to optimal drug development and tailored drug treatment. In oncology, the therapeutic index of a chemotherapeutic drug is typically narrow and a full dose-response relationship is not available, often because of treatment failure. Noting the benefits of model-based approaches and the low therapeutic index of oncology drugs, in recent years, modeling approaches have been increasingly used to streamline oncologic drug development through early identification and quantification of dose-response relationships. With this background, this report reviews publications that used model-based approaches to evaluate drug treatment outcome variables in oncology therapeutics, ranging from tumor size dynamics to tumor/biomarker time courses and survival response.

Preclinical PK/PD model for combined administration of erlotinib and sunitinib in the treatment of A549 human NSCLC xenograft mice

AIM

Combined therapy of EGFR TKI and VEGFR TKI may produce a greater therapeutic benefit and overcome EGFR TKI-induced resistance. However, a previous study shows that a combination of EGFR TKI erlotinib (ER) with VEGFR TKI sunitinib (SU) did not improve the overall survival in patients with non-small-cell lung cancer (NSCLC). In this study we examined the anticancer effect of ER, SU and their combination in the treatment of A549 human NSCLC xenograft mice, and conducted PK/PD modeling and simulations to optimize the dose regimen.

METHODS

ER (20, 50 mg·kg(-1)·d(-1)) or SU (5, 10, 20 mg·kg(-1)·d(-1)) alone, or their combination were administered to BALB/c nude mice bearing A549 tumors for 22 days. The tumor size and body weight were recorded daily. The experimental data were used to develop PK/PD models describing the quantitative relationship between the plasma concentrations and tumor suppression in different dose regimens. The models were further evaluated and validated, and used to predict the efficacy of different combination regimens and to select the optimal regimen.

RESULTS

The in vivo anticancer efficacy of the combination groups was much stronger than that of either drug administered alone. A PK/PD model was developed with a combination index (φ) of 4.4, revealing a strong synergistic effect between ER and SU. The model simulation predicted the tumor growth in different dosage regimens, and showed that the dose of SU played a decisive role in the combination treatment, and suggested that a lower dose of ER (≤5 mg·kg(-1)·d(-1)) and adjusting the dose of SU might yield a better dosage regimen for clinical research.

CONCLUSION

The experimental data and modeling confirm synergistic anticancer effect of ER and SU in the treatment of A549 xenograft mice. The optimal dosage regimen determined by the PK/PD modeling and simulation can be used in future preclinical study and provide a reference for clinical application.

Population pharmacokinetic-pharmacodynamic modelling in oncology: a tool for predicting clinical response

In oncology trials, overall survival (OS) is considered the most reliable and preferred endpoint to evaluate the benefit of drug treatment. Other relevant variables are also collected from patients for a given drug and its indication, and it is important to characterize the dynamic effects and links between these variables in order to improve the speed and efficiency of clinical oncology drug development. However, the drug-induced effects and causal relationships are often difficult to interpret because of temporal differences. To address this, population pharmacokinetic–pharmacodynamic (PKPD) modelling and parametric time-to-event (TTE) models are becoming more frequently applied. Population PKPD and TTE models allow for exploration towards describing the data, understanding the disease and drug action over time, investigating relevance of biomarkers, quantifying patient variability and in designing successful trials. In addition, development of models characterizing both desired and adverse effects in a modelling framework support exploration of risk-benefit of different dosing schedules. In this review, we have summarized population PKPD modelling analyses describing tumour, tumour marker and biomarker responses, as well as adverse effects, from anticancer drug treatment data. Various model-based metrics used to drive PD response and predict OS for oncology drugs and their indications are also discussed.

Preclinical Modeling of Tumor Growth and Angiogenesis Inhibition to Describe Pazopanib Clinical Effects in Renal Cell Carcinoma

The objective was to leverage tumor size data from preclinical experiments to propose a model of tumor growth and angiogenesis inhibition for the analysis of pazopanib efficacy in renal cell carcinoma (RCC) patients. We analyzed tumor data in mice with RCC CAKI‐2 cell line treated with pazopanib. Clinical tumor size data obtained in a subset of patients with RCC were also analyzed. A model accounting for the processes of tumor growth, angiogenesis, and drug effect was developed. The final tumor model was composed of two variables: the tumor and its vasculature. Our results show that, both in mice and in humans, pazopanib exhibits a dual mechanism of action, and parameter estimation values highlight the inherent difference between mice and humans on the time scale of tumor size response. We developed a semimechanistic tumor growth inhibition model that takes into account tumor angiogenesis in order to describe the effects of pazopanib in mice. Analyzing rich preclinical data with a semimechanistic model may be a relevant approach to facilitate the description of sparse clinical longitudinal tumor size data and to provide insights for the understanding of the drug mechanisms of action in patients.

Population pharmacokinetics and pharmacodynamics of BYL719, a phosphoinositide 3-kinase antagonist, in adult patients with advanced solid malignancies

AIMS

The aim was to characterize the population pharmacokinetics of BYL719 in cancer patients and assess the time course of tumour response in relation to drug exposure and dosing schedule.

METHODS

Plasma samples and longitudinal tumour size measurements were collected from 60 patients with advanced solid malignancies who received oral BYL719 once daily (30-450 mg) or twice daily at 120 mg or 200 mg. Non-linear mixed effect modelling was employed to develop the population pharmacokinetic and pharmacodynamic model.

RESULTS

The pharmacokinetics were best described by a one compartment disposition model and transit compartments accounting for the lag time in absorption. The typical population oral clearance and volume of distribution estimates with their between-subject variability (BSV) were 10 l h(-1) (BSV 26%) and 108 l (BSV 28%), respectively. The estimated optimal number of transit compartments was 8.1, with a mean transit time to the absorption compartment of 1.28 h (BSV 32%). The between-occasion variability in the rate and extent of absorption was 46% and 26%, respectively. Tumour growth was modelled using a turnover model characterized by a zero order growth rate of 0.581 cm week(1) and a first order death rate of 0.0123 week(-1) . BYL719 inhibited tumour growth with an IC50 of 100 ng ml(-1) (BSV 154%). Model-based predictions showed potential for additional anti-tumour activity of twice daily dosing at total daily dose below 400 mg, but a loss of efficacy if administered less frequently than once daily.

CONCLUSIONS

The proposed model provides a valuable approach for planning future clinical studies and for designing optimized dosing regimens with BYL719.

Developing Exposure/Response Models for Anticancer Drug Treatment: Special Considerations

Anticancer agents often have a narrow therapeutic index (TI), requiring precise dosing to ensure sufficient exposure for clinical activity while minimizing toxicity. These agents frequently have complex pharmacology, and combination therapy may cause schedule-specific effects and interactions. We review anticancer drug development, showing how integration of modeling and simulation throughout development can inform anticancer dose selection, potentially improving the late-phase success rate. This article has a companion article in Clinical Pharmacology & Therapeutics with practical examples.

Clinical pharmacology = disease progression + drug action

Clinical pharmacology is concerned with understanding how to use medicines to treat disease. Pharmacokinetics and pharmacodynamics have provided powerful methodologies for describing the time course of concentration and effect in individuals and in populations. This population approach may also be applied to describing the progression of disease and the action of drugs to change disease progress. Quantitative models for symptomatic and disease-modifying effects of drugs are valuable not only for describing drugs and diseases but also for identifying criteria to distinguish between types of drug actions, with implications for regulatory decisions and long-term patient care.

A review of mixed-effects models of tumor growth and effects of anticancer drug treatment used in population analysis

Population modeling of tumor size dynamics has recently emerged as an important tool in pharmacometric research. A series of new mixed-effects models have been reported recently, and we present herein a synthetic view of models with published mathematical equations aimed at describing the dynamics of tumor size in cancer patients following anticancer drug treatment. This selection of models will constitute the basis for the Drug Disease Model Resources (DDMoRe) repository for models on oncology.

The systems biology simulation core algorithm

BACKGROUND

With the increasing availability of high dimensional time course data for metabolites, genes, and fluxes, the mathematical description of dynamical systems has become an essential aspect of research in systems biology. Models are often encoded in formats such as SBML, whose structure is very complex and difficult to evaluate due to many special cases.

RESULTS

This article describes an efficient algorithm to solve SBML models that are interpreted in terms of ordinary differential equations. We begin our consideration with a formal representation of the mathematical form of the models and explain all parts of the algorithm in detail, including several preprocessing steps. We provide a flexible reference implementation as part of the Systems Biology Simulation Core Library, a community-driven project providing a large collection of numerical solvers and a sophisticated interface hierarchy for the definition of custom differential equation systems. To demonstrate the capabilities of the new algorithm, it has been tested with the entire SBML Test Suite and all models of BioModels Database.

CONCLUSIONS

The formal description of the mathematics behind the SBML format facilitates the implementation of the algorithm within specifically tailored programs. The reference implementation can be used as a simulation backend for Java™-based programs. Source code, binaries, and documentation can be freely obtained under the terms of the LGPL version 3 from http://simulation-core.sourceforge.net. Feature requests, bug reports, contributions, or any further discussion can be directed to the mailing list simulation-core-development@lists.sourceforge.net.

In vivo mathematical modeling of tumor growth from imaging data: soon to come in the future?

The future challenges in oncology imaging are to assess the response to treatment even earlier. As an addition to functional imaging, mathematical modeling based on the imaging is an alternative, cross-disciplinary area of development. Modeling was developed in oncology not only in order to understand and predict tumor growth, but also to anticipate the effects of targeted and untargeted therapies. A very wide range of these models exist, involving many stages in the progression of tumors. Few models, however, have been proposed to reproduce in vivo tumor growth because of the complexity of the mechanisms involved. Morphological imaging combined with "spatial" models appears to perform well although functioning imaging could still provide further information on metabolism and the micro-architecture. The combination of imaging and modeling can resolve complex problems and describe many facets of tumor growth or response to treatment. It is now possible to consider its clinical use in the medium term. This review describes the basic principles of mathematical modeling and describes the advantages, limitations and future prospects for this in vivo approach based on imaging data.

Pathway-based pharmacogenomics of gemcitabine pharmacokinetics in patients with solid tumors

AIM

The aim of this study was to evaluate the association of gemcitabine pathway SNPs with detailed pharmacokinetic measures obtained from solid tumor patients receiving gemcitabine-based therapy.

MATERIALS & METHODS

SNPs within nine gemcitabine pathway genes, namely CDA, CMPK, DCK, DCTD, NT5C2, NT5C3, SLC28A1, SLC28A3 and SLC29A1 were analyzed for association with gemcitabine pharmacokinetics.

RESULTS

Significant association of gemcitabine clearance with SNPs in NT5C2 was identified. Clearance of 2´,2´-difluorodeoxyuridine, a gemcitabine metabolite was significantly predicted by CDA, SLC29A1 and NT5C2 SNPs. This study reports an association of formation clearance of 2´,2´-difluoro-2´-deoxycytidine triphosphate, an active form of gemcitabine with SNPs within uptake transporters SLC28A1, SLC28A3 and SLC29A1.

CONCLUSION

Genetic variation in gemcitabine pathway genes is associated with its pharmacokinetics and hence could influence gemcitabine response. Our study identified pharmacogenetic markers that could be further tested in larger patient cohorts and could open up opportunities to individualize therapy in solid tumor patients.

Modeling NSCLC progression: recent advances and opportunities available

Non-small cell lung cancer (NSCLC) is one of the leading causes of death around the world with an estimated 5-year relative survival rate of 16% at diagnosis. Development of drugs treating NSCLC is not easy, and the success rate for an anticancer treatment to pass through the whole clinical development process is as low as 5%. Modeling and simulation lend themselves as tools which can potentially streamline drug development. A critical component of the models developed is a description of how the disease progresses over time and how a treatment would affect its trajectory. Our aim was to review the literature to present the models and growth functions which have been used for describing NSCLC dynamics, and how anticancer treatments can affect such dynamics, both in animals and in humans. Only a limited set of models were identified for such a purpose. Most of the models which have been used were descriptive of tumor growth, yet there were attempts to account for the underlying processes, especially in animals where it is more feasible to collect data needed for developing such models. Moreover, we discuss how modeling and simulation can aid in decision making across the different stages of drug development. Based on some encouraging results from trials of other cancer types where modeling tumor dynamics has played an important role, we propose further exploration of NSCLC using model-based techniques and further use of these techniques in designing and evaluating NSCLC trials.

Supporting SBML as a model exchange format in software applications

This chapter describes the Systems Biology Markup Language (SBML) from its origins. It describes the rationale behind and importance of having a common language when it comes to representing models. This chapter mentions the development of SBML and outlines the structure of an SBML model. It provides a section on libSBML, a useful application programming interface (API) library for reading, writing, manipulating and validating content expressed in the SBML format. Finally the chapter also provides a description of the SBML Toolbox which provides a means of facilitating the import and export of SBML from both MATLAB and Octave ( http://www.gnu.org/software/octave/) environments.

Estimation of renal cell carcinoma treatment effects from disease progression modeling

To improve future drug development efficiency in renal cell carcinoma (RCC), a disease-progression model was developed with longitudinal tumor size data from a phase III trial of sorafenib in RCC. The best-fit model was externally evaluated on 145 placebo-treated patients in a phase III trial of pazopanib; the model incorporated baseline tumor size, a linear disease-progression component, and an exponential drug effect (DE) parameter. With the model-estimated effect of sorafenib on RCC growth, we calculated the power of randomized phase II trials between sorafenib and hypothetical comparators over a range of effects. A hypothetical comparator with 80% greater DE than sorafenib would have 82% power (one-sided α = 0.1) with 50 patients per arm. Model-based quantitation of treatment effect with computed tomography (CT) imaging offers a scaffold on which to develop new, more efficient, phase II trial end points and analytic strategies for RCC.

Algorithmic modeling quantifies the complementary contribution of metabolic inhibitions to gemcitabine efficacy

Gemcitabine (2,2-difluorodeoxycytidine, dFdC) is a prodrug widely used for treating various carcinomas. Gemcitabine exerts its clinical effect by depleting the deoxyribonucleotide pools, and incorporating its triphosphate metabolite (dFdC-TP) into DNA, thereby inhibiting DNA synthesis. This process blocks the cell cycle in the early S phase, eventually resulting in apoptosis. The incorporation of gemcitabine into DNA takes place in competition with the natural nucleoside dCTP. The mechanisms of indirect competition between these cascades for common resources are given with the race for DNA incorporation; in clinical studies dedicated to singling out mechanisms of resistance, ribonucleotide reductase (RR) and deoxycytidine kinase (dCK) and human equilibrative nucleoside transporter1 (hENT1) have been associated to efficacy of gemcitabine with respect to their roles in the synthesis cascades of dFdC-TP and dCTP. However, the direct competition, which manifests itself in terms of inhibitions between these cascades, remains to be quantified. We propose an algorithmic model of gemcitabine mechanism of action, verified with respect to independent experimental data. We performed in silico experiments in different virtual conditions, otherwise difficult in vivo, to evaluate the contribution of the inhibitory mechanisms to gemcitabine efficacy. In agreement with the experimental data, our model indicates that the inhibitions due to the association of dCTP with dCK and the association of gemcitabine diphosphate metabolite (dFdC-DP) with RR play a key role in adjusting the efficacy. While the former tunes the catalysis of the rate-limiting first phosphorylation of dFdC, the latter is responsible for depletion of dCTP pools, thereby contributing to gemcitabine efficacy with a dependency on nucleoside transport efficiency. Our simulations predict the existence of a continuum of non-efficacy to high-efficacy regimes, where the levels of dFdC-TP and dCTP are coupled in a complementary manner, which can explain the resistance to this drug in some patients.

Modelling non-homogeneous stochastic reaction-diffusion systems: the case study of gemcitabine-treated non-small cell lung cancer growth

Background

Reaction-diffusion based models have been widely used in the literature for modeling the growth of solid tumors. Many of the current models treat both diffusion/consumption of nutrients and cell proliferation. The majority of these models use classical transport/mass conservation equations for describing the distribution of molecular species in tumor spheroids, and the Fick's law for describing the flux of uncharged molecules (i.e oxygen, glucose). Commonly, the equations for the cell movement and proliferation are first order differential equations describing the rate of change of the velocity of the cells with respect to the spatial coordinates as a function of the nutrient's gradient. Several modifications of these equations have been developed in the last decade to explicitly indicate that the tumor includes cells, interstitial fluids and extracellular matrix: these variants provided a model of tumor as a multiphase material with these as the different phases. Most of the current reaction-diffusion tumor models are deterministic and do not model the diffusion as a local state-dependent process in a non-homogeneous medium at the micro- and meso-scale of the intra- and inter-cellular processes, respectively. Furthermore, a stochastic reaction-diffusion model in which diffusive transport of the molecular species of nutrients and chemotherapy drugs as well as the interactions of the tumor cells with these species is a novel approach. The application of this approach to he scase of non-small cell lung cancer treated with gemcitabine is also novel.

Methods

We present a stochastic reaction-diffusion model of non-small cell lung cancer growth in the specification formalism of the tool Redi, we recently developed for simulating reaction-diffusion systems. We also describe how a spatial gradient of nutrients and oncological drugs affects the tumor progression. Our model is based on a generalization of the Fick's first diffusion law that allows to model diffusive transport in non-homogeneous media. The diffusion coefficient is explicitly expressed as a function depending on the local conditions of the medium, such as the concentration of molecular species, the viscosity of the medium and the temperature. We incorporated this generalized law in a reaction-based stochastic simulation framework implementing an efficient version of Gillespie algorithm for modeling the dynamics of the interactions between tumor cell, nutrients and gemcitabine in a spatial domain expressing a nutrient and drug concentration gradient.

Results

Using the mathematical framework of model we simulated the spatial growth of a 2D spheroidal tumor model in response to a treatment with gemcitabine and a dynamic gradient of oxygen and glucose. The parameters of the model have been taken from recet literature and also inferred from real tumor shrinkage curves measured in patients suffering from non-small cell lung cancer. The simulations qualitatively reproduce the time evolution of the morphologies of these tumors as well as the morphological patterns follow the growth curves observed in patients.

Conclusions

s This model is able to reproduce the observed increment/decrement of tumor size in response to the pharmacological treatment with gemcitabine. The formal specification of the model in Redi can be easily extended in an incremental way to include other relevant biophysical processes, such as local extracellular matrix remodelling, active cell migration and traction, and reshaping of host tissue vasculature, in order to be even more relevant to support the experimental investigation of cancer.

Dynamic tumor modeling of the dose-response relationship for everolimus in metastatic renal cell carcinoma using data from the phase 3 RECORD-1 trial

Background

The phase 3 RECORD-1 trial (NCT00410124) established the efficacy and safety of everolimus in patients with metastatic renal cell carcinoma (mRCC) who progress on sunitinib or sorafenib. In RECORD-1, patients received 10 mg everolimus daily, with dose reduction to 5 mg daily allowed for toxicity. We have developed a model of tumor growth dynamics utilizing serial measurements of the sum of the longest tumor diameters (SLD) from individual RECORD-1 patients to define the dose–response relationship of everolimus.

Results

The model predicts that after 1 year of continuous dosing, the change in SLD of target lesions will be +142.1% ± 98.3%, +22.4% ± 17.2%, and –15.7% ± 11.5% in the average patient treated with placebo, 5 mg everolimus, and 10 mg everolimus, respectively. This nonlinear, mixed-effects modeling approach can be used to describe the dynamics of each individual patient, as well as the overall population. This allows evaluation of how an actual dosing history and individual covariates impact on the observed drug effect, and offers the possibility of predicting clinical observations as a function of time.

Conclusions

In this pharmacodynamic model of tumor response, everolimus more effectively shrinks target lesions in mRCC when dosed 10 mg daily versus 5 mg daily, although a 5-mg dose still shows an antitumor effect. These data support earlier studies that established 10 mg daily as the preferred clinical dose of everolimus, and improve our understanding of the everolimus dose–response relationship.

A tumor growth inhibition model for low-grade glioma treated with chemotherapy or radiotherapy

PURPOSE

To develop a tumor growth inhibition model for adult diffuse low-grade gliomas (LGG) able to describe tumor size evolution in patients treated with chemotherapy or radiotherapy.

EXPERIMENTAL DESIGN

Using longitudinal mean tumor diameter (MTD) data from 21 patients treated with first-line procarbazine, 1-(2-chloroethyl)-3-cyclohexyl-l-nitrosourea, and vincristine (PCV) chemotherapy, we formulated a model consisting of a system of differential equations, incorporating tumor-specific and treatment-related parameters that reflect the response of proliferative and quiescent tumor tissue to treatment. The model was then applied to the analysis of longitudinal tumor size data in 24 patients treated with first-line temozolomide (TMZ) chemotherapy and in 25 patients treated with first-line radiotherapy.

RESULTS

The model successfully described the MTD dynamics of LGG before, during, and after PCV chemotherapy. Using the same model structure, we were also able to successfully describe the MTD dynamics in LGG patients treated with TMZ chemotherapy or radiotherapy. Tumor-specific parameters were found to be consistent across the three treatment modalities. The model is robust to sensitivity analysis, and preliminary results suggest that it can predict treatment response on the basis of pretreatment tumor size data.

CONCLUSIONS

Using MTD data, we propose a tumor growth inhibition model able to describe LGG tumor size evolution in patients treated with chemotherapy or radiotherapy. In the future, this model might be used to predict treatment efficacy in LGG patients and could constitute a rational tool to conceive more effective chemotherapy schedules.

[Population pharmacokinetics of gemcitabine applied to personalize the dosage used in cancer patients]

OBJECTIVE

To develop and internally validate a population pharmacokinetic model for gemcitabine and its metabolite 2',2'-difluorodeoxyuridine (dFdU); and to evaluate its predictive perfomance for personalizing the dosage used in cancer patients.

METHODS

Gemcitabine and dFdU plasma concentrations were determined in 18 cancer patients. A 2-compartment pharmacokinetic model was implemented in the NONMEN VI program to determine the appropriate pharmacokinetic parameters. The power to identify the parameters was assessed by parametric bootstrap, and the internal model validation was performed using nonparametric bootstrap and visual and numerical predictive check methods. The final predictive performance of the model was assessed for accuracy and precision during the first (a priori) and second (a posteriori) chemotherapy cycles.

RESULTS

The mean and interpatient variability of gemcitabine and dFdU clearance was 2.70 L/min (31.0%) and 0.0515 L/min (35.8%), respectively. The estimated distribution volume at steady state was 30 L for gemcitabine and 238 L for dFdU. Internal validation confirmed that the population pharmacokinetic model was appropriate for describing the plasma concentrations of gemcitabine and dFdU over time, as well as its variability in the study population. The accuracy and precision of a posteriori gemcitabine plasma concentrations improved by 67% and 46%, respectively, compared to the a priori prediction.

CONCLUSION

The population pharmacokinetic model adequately characterised the gemcitabine and dFdU plasma concentrations in the study population over time, and can be used to accurately and precisely optimise gemcitabine dosing regimens in cancer patients.

Mathematical modeling of tumor growth and tumor growth inhibition in oncology drug development

INTRODUCTION

Approaches aiming to model the time course of tumor growth and tumor growth inhibition following a therapeutic intervention have recently been proposed for supporting decision making in oncology drug development. When considered in a comprehensive model-based approach, tumor growth can be included in the cascade of quantitative and causally related markers that lead to the prediction of survival, the final clinical response.

AREAS COVERED

The authors examine articles dealing with the modeling of tumor growth and tumor growth inhibition in both preclinical and clinical settings. In addition, the authors review models describing how pharmacological markers can be used to predict tumor growth and models describing how tumor growth can be linked to survival endpoints.

EXPERT OPINION

Approaches and success stories of application of model-based drug development centered on tumor growth modeling are growing. It is also apparent that these approaches can answer practical questions on drug development more effectively than that in the past. For modeling purposes, some improvements are still needed related to study design and data quality. Further efforts are needed to encourage the mind shift from a simple description of data to the prediction of untested conditions that modeling approaches allow.

A phase II study of sunitinib in recurrent and/or metastatic adenoid cystic carcinoma (ACC) of the salivary glands: current progress and challenges in evaluating molecularly targeted agents in ACC

BACKGROUND

Vascular endothelial growth factor (VEGF) and c-kit are highly expressed in adenoid cystic carcinoma (ACC) and associated with biologic aggressiveness. This study aimed to assess the antitumor activity of sunitinib, a multi-targeted inhibitor of vascular endothelial growth factor receptor, c-kit, platelet-derived growth factor receptor, ret proto-oncogene (RET) and FMS-like tyrosine kinase 3 (FLT3), in ACC of the salivary gland.

PATIENTS AND METHODS

Patients with progressive, recurrent and/or metastatic ACC were treated with sunitinib 37.5 mg daily in this single-arm, two-stage phase II trial. Response was assessed every 8 weeks.

RESULTS

Fourteen patients were enrolled on to the study. Among 13 assessable patients, there were no objective responses, 11 patients had stable disease (SD), 8 patients had SD ≥ 6 months and 2 patients had progressive disease as best response. Median time to progression was 7.2 months. Median overall survival was 18.7 months. Toxic effects occurring in at least 50% of patients included fatigue, oral mucositis and hypophosphatemia usually of mild to moderate severity.

CONCLUSIONS

Although no responses were observed, sunitinib was well tolerated, with prolonged tumor stabilization of ≥ 6 months in 62% of assessable patients. The lack of responses is comparable with other trials of molecularly targeted agents in ACC and highlights the need for novel strategies in phase II clinical trial design.

The pharmacokinetic/pharmacodynamic pipeline: translating anticancer drug pharmacology to the clinic

Progress in an understanding of the genetic basis of cancer coupled to molecular pharmacology of potential new anticancer drugs calls for new approaches that are able to address key issues in the drug development process, including pharmacokinetic (PK) and pharmacodynamic (PD) relationships. The incorporation of predictive preclinical PK/PD models into rationally designed early-stage clinical trials offers a promising way to relieve a significant bottleneck in the drug discovery pipeline. The aim of the current review is to discuss some considerations for how quantitative PK and PD analyses for anticancer drugs may be conducted and integrated into a global translational effort, and the importance of examining drug disposition and dynamics in target tissues to support the development of preclinical PK/PD models that can be subsequently extrapolated to predict pharmacologic characteristics in patients. In this article, we describe three different physiologically based (PB) PK modeling approaches, i.e., the whole-body PBPK model, the hybrid PBPK model, and the two-pore model for macromolecules, as well as their applications. General conclusions are that greater effort should be made to generate more clinical data that could validate scaled preclinical PB-PK/PD tumor-based models and, thus, stimulate a framework for preclinical to clinical translation. Finally, given the innovative techniques to measure tissue drug concentrations and associated biomarkers of drug responses, development of predictive PK/PD models will become a standard approach for drug discovery and development.

A model of vascular tumour growth in mice combining longitudinal tumour size data with histological biomarkers

Optimising the delivery of antiangiogenic drugs requires the development of drug-disease models of vascular tumour growth that incorporate histological data indicative of cytostatic action. In this study, we formulated a model to analyse the dynamics of tumour progression in nude mice xenografted with HT29 or HCT116 colorectal cancer cells. In 30 mice, tumour size was periodically measured, and percentages of hypoxic and necrotic tissue were assessed using immunohistochemistry techniques on tumour samples after euthanasia. The simultaneous analysis of histological data together with longitudinal tumour size data prompted the development of a semi-mechanistic model integrating random effects of parameters. In this model, the peripheral non-hypoxic tissue proliferates according to a generalised-logistic equation where the maximal tumour size is represented by a variable called 'carrying capacity'. The ratio of the whole tumour size to the carrying capacity was used to define the hypoxic stress. As this stress increases, non-hypoxic tissue turns hypoxic. Hypoxic tissue does not stop proliferating, but hypoxia constitutes a transient stage before the tissue becomes necrotic. As the tumour grows, the carrying capacity increases owing to the process of angiogenesis. The model is shown to correctly predict tumour growth dynamics as well as percentages of necrotic and hypoxic tissues within the tumour. We show how the model can be used as a theoretical tool to investigate the effects of antiangiogenic treatments on tumour growth. This model provides a tool to analyse tumour size data in combination with histological biomarkers such as the percentages of hypoxic and necrotic tissue and is shown to be useful for gaining insight into the effects of antiangiogenic drugs on tumour growth and composition.

Population pharmacokinetic/pharmacodynamic modeling for the time course of tumor shrinkage by motesanib in thyroid cancer patients

OBJECTIVE

To develop a population pharmacokinetic/pharmacodynamic model describing the relationship between motesanib exposure and tumor response in a phase 2 study of motesanib in patients with advanced differentiated thyroid cancer or medullary thyroid cancer.

METHODS

Data from patients (n = 184) who received motesanib 125 mg once daily were used for population pharmacokinetic/pharmacodynamic modeling. Motesanib concentrations were fitted to a 2-compartment population pharmacokinetic model. Observed change in tumor size was the drug response measure for the pharmacodynamic model. Exposure measures in the pharmacokinetic/pharmacodynamic model included dose, plasma concentration profile, or steady-state area under the concentration versus time curve (AUC( ss )). A longitudinal exposure-tumor response model of drug effect on tumor growth dynamics was used.

RESULTS

Motesanib oral clearance in patients with medullary thyroid cancer was 67% higher than in patients with differentiated thyroid cancer patients (73.7 vs. 44 L/h). Patients' disease type (medullary thyroid cancer vs. differentiated thyroid cancer) was the most important covariate for explaining interpatient variability in clearance. The objective response rates were 14 versus 2% for differentiated thyroid cancer and medullary thyroid cancer, respectively. Motesanib exposure measures (AUC( ss ) or concentration profile) were better predictors of tumor response than motesanib dose. The estimated motesanib concentration yielding tumor stasis (1.9 ng/mL) was lower than the observed trough concentrations in differentiated thyroid cancer and medullary thyroid cancer patients.

CONCLUSIONS

Differences in motesanib pharmacokinetics likely explain the difference in tumor response observed between differentiated thyroid cancer and medullary thyroid cancer patients. The population pharmacokinetic/pharmacodynamic model provides a tool for predicting tumor response to the drug to support the dosing regimen of motesanib in thyroid cancer patients.