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

Mechanistic characterization of oscillatory patterns in unperturbed tumor growth dynamics: The interplay between cancer cells and components of tumor microenvironment

Mathematical modeling of unperturbed and perturbed tumor growth dynamics (TGD) in preclinical experiments provides an opportunity to establish translational frameworks. The most commonly used unperturbed tumor growth models (i.e. linear, exponential, Gompertz and Simeoni) describe a monotonic increase and although they capture the mean trend of the data reasonably well, systematic model misspecifications can be identified. This represents an opportunity to investigate possible underlying mechanisms controlling tumor growth dynamics through a mathematical framework. The overall goal of this work is to develop a data-driven semi-mechanistic model describing non-monotonic tumor growth in untreated mice. For this purpose, longitudinal tumor volume profiles from different tumor types and cell lines were pooled together and analyzed using the population approach. After characterizing the oscillatory patterns (oscillator half-periods between 8-11 days) and confirming that they were systematically observed across the different preclinical experiments available (p<10-9), a tumor growth model was built including the interplay between resources (i.e. oxygen or nutrients), angiogenesis and cancer cells. The new structure, in addition to improving the model diagnostic compared to the previously used tumor growth models (i.e. AIC reduction of 71.48 and absence of autocorrelation in the residuals (p>0.05)), allows the evaluation of the different oncologic treatments in a mechanistic way. Drug effects can potentially, be included in relevant processes taking place during tumor growth. In brief, the new model, in addition to describing non-monotonic tumor growth and the interaction between biological factors of the tumor microenvironment, can be used to explore different drug scenarios in monotherapy or combination during preclinical drug development.

Model-based assessment of combination therapies - ranking of radiosensitizing agents in oncology

BACKGROUND

To increase the chances of finding efficacious anticancer drugs, improve development times and reduce costs, it is of interest to rank test compounds based on their potential for human use as early as possible in the drug development process. In this paper, we present a method for ranking radiosensitizers using preclinical data.

METHODS

We used data from three xenograft mice studies to calibrate a model that accounts for radiation treatment combined with radiosensitizers. A nonlinear mixed effects approach was utilized where between-subject variability and inter-study variability were considered. Using the calibrated model, we ranked three different Ataxia telangiectasia-mutated inhibitors in terms of anticancer activity. The ranking was based on the Tumor Static Exposure (TSE) concept and primarily illustrated through TSE-curves.

RESULTS

The model described data well and the predicted number of eradicated tumors was in good agreement with experimental data. The efficacy of the radiosensitizers was evaluated for the median individual and the 95% population percentile. Simulations predicted that a total dose of 220 Gy (5 radiation sessions a week for 6 weeks) was required for 95% of tumors to be eradicated when radiation was given alone. When radiation was combined with doses that achieved at least 8 [Formula: see text] of each radiosensitizer in mouse blood, it was predicted that the radiation dose could be decreased to 50, 65, and 100 Gy, respectively, while maintaining 95% eradication.

CONCLUSIONS

A simulation-based method for calculating TSE-curves was developed, which provides more accurate predictions of tumor eradication than earlier, analytically derived, TSE-curves. The tool we present can potentially be used for radiosensitizer selection before proceeding to subsequent phases of the drug discovery and development process.

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.

Opportunities for Quantitative Translational Modeling in Oncology

A 2-day meeting was held by members of the UK Quantitative Systems Pharmacology Network () in November 2018 on the topic of Translational Challenges in Oncology. Participants from a wide range of backgrounds were invited to discuss current and emerging modeling applications in nonclinical and clinical drug development, and to identify areas for improvement. This resulting perspective explores opportunities for impactful quantitative pharmacology approaches. Four key themes arose from the presentations and discussions that were held, leading to the following recommendations: Evaluate the predictivity and reproducibility of animal cancer models through precompetitive collaboration. Apply mechanism of action (MoA) based mechanistic models derived from nonclinical data to clinical trial data. Apply MoA reflective models across trial data sets to more robustly quantify the natural history of disease and response to differing interventions. Quantify more robustly the dose and concentration dependence of adverse events through mathematical modelling techniques and modified trial design.

Tumor Growth Dynamic Modeling in Oncology Drug Development and Regulatory Approval: Past, Present, and Future Opportunities

Model‐informed drug development (MIDD) approaches have rapidly advanced in drug development in recent years. Additionally, the Prescription Drug User Fee Act (PDUFA) VI has specific commitments to further enhance MIDD. Tumor growth dynamic (TGD) modeling, as one of the commonly utilized MIDD approaches in oncology, fulfills the purposes to accelerate the drug development, to support new drug and biologics license applications, and to guide the market access. Increasing knowledge of TGD modeling methodologies, encouraging applications in clinical setting for patients’ survival, and complementing assessment of regulatory review for submissions, together fueled promising potentials for imminent enhancement of TGD in oncology. This review is to comprehensively summarize the history of TGD, and present case examples of the recent advance of TGD modeling (mixture model and joint model), as well as the TGD impact on regulatory decisions, thus illustrating challenges and opportunities. Additionally, this review presents the future perspectives for TGD approach.

A Review of Mathematical Models for Tumor Dynamics and Treatment Resistance Evolution of Solid Tumors

Increasing knowledge of intertumor heterogeneity, intratumor heterogeneity, and cancer evolution has improved the understanding of anticancer treatment resistance. A better characterization of cancer evolution and subsequent use of this knowledge for personalized treatment would increase the chance to overcome cancer treatment resistance. Model‐based approaches may help achieve this goal. In this review, we comprehensively summarized mathematical models of tumor dynamics for solid tumors and of drug resistance evolution. Models displayed by ordinary differential equations, algebraic equations, and partial differential equations for characterizing tumor burden dynamics are introduced and discussed. As for tumor resistance evolution, stochastic and deterministic models are introduced and discussed. The results may facilitate a novel model‐based analysis on anticancer treatment response and the occurrence of resistance, which incorporates both tumor dynamics and resistance evolution. The opportunities of a model‐based approach as discussed in this review can be of great benefit for future optimizing and personalizing anticancer treatment.

Modeling long-term tumor growth and kill after combinations of radiation and radiosensitizing agents

PURPOSE

Radiation therapy, whether given alone or in combination with chemical agents, is one of the cornerstones of oncology. We develop a quantitative model that describes tumor growth during and after treatment with radiation and radiosensitizing agents. The model also describes long-term treatment effects including tumor regrowth and eradication.

METHODS

We challenge the model with data from a xenograft study using a clinically relevant administration schedule and use a mixed-effects approach for model-fitting. We use the calibrated model to predict exposure combinations that result in tumor eradication using Tumor Static Exposure (TSE).

RESULTS

The model is able to adequately describe data from all treatment groups, with the parameter estimates taking biologically reasonable values. Using TSE, we predict the total radiation dose necessary for tumor eradication to be 110 Gy, which is reduced to 80 or 30 Gy with co-administration of 25 or 100 mg kg^-1 of a radiosensitizer. TSE is also explored via a heat map of different growth and shrinkage rates. Finally, we discuss the translational potential of the model and TSE concept to humans.

CONCLUSIONS

The new model is capable of describing different tumor dynamics including tumor eradication and tumor regrowth with different rates, and can be calibrated using data from standard xenograft experiments. TSE and related concepts can be used to predict tumor shrinkage and eradication, and have the potential to guide new experiments and support translations from animals to humans.

Clinical Pharmacokinetics and Pharmacodynamics of Pazopanib: Towards Optimized Dosing

Pazopanib is an inhibitor of the vascular endothelial growth factor receptor, platelet-derived growth factor receptor, fibroblast growth factor receptor and stem cell receptor c-Kit, and has been approved for the treatment of renal cell carcinoma and soft tissue sarcoma. The pharmacokinetics of pazopanib are complex and are characterized by pH-dependent solubility, large interpatient variability and low, non-linear and time-dependent bioavailability. Exposure to pazopanib is increased by both food and coadministration of ketoconazole, but drastically reduced by proton pump inhibitors. Studies have demonstrated relationships between systemic exposure to pazopanib and toxicity, such as hypertension. Furthermore, a strong relationship between pazopanib trough level ≥20 mg/L and both tumor shrinkage and progression-free survival has been established. At the currently approved daily dose of 800 mg, approximately 20% of patients do not reach this threshold and may be at risk of suboptimal treatment. As a result of this, clinical trials have explored individualized pazopanib dosing, which demonstrate the safety and feasibility of individualized pazopanib dosing based on trough levels. In summary, we provide an overview of the complex pharmacokinetic and pharmacodynamic profiles of pazopanib and, based on the available data, we propose optimized dosing strategies.

Pharmacokinetic/Pharmacodynamic Modeling of Schedule-Dependent Interaction between Docetaxel and Cabozantinib in Human Prostate Cancer Xenograft Models

In this work, a semimechanistic pharmacokinetic/pharmacodynamic (PK/PD) model to quantitatively describe the antitumor activity of docetaxel (Doc) and cabozantinib (Cab) under monotherapy, concurrent therapy, interval therapy, and different sequential therapy in mouse xenograft models of castration-resistant prostate cancer was developed and evaluated. The pharmacokinetics (PK) of Doc and Cab when administered separately and simultaneously were investigated in nude mice, and PD study was conducted in tumor-bearing mice treated with different dosing schedules. The PK interaction between Doc and Cab was expressed by adding the effect of Cab on the clearance of Doc in the PK model. And the PD interaction between the two drugs was demonstrated by the developed PK/PD model through the combination index "φ" Our results showed that the concurrent therapy and Doc followed by Cab (Doc ∼ Cab) sequential therapy exhibited better tumor inhibitory efficacy than monotherapy. The Cab followed by Doc (Cab ∼ Doc) sequential schedule was less effective than monotherapy, and the interval therapy did not enhance the antitumor efficacy compared with the concurrent therapy. The parameter φ estimated from the PK/PD model quantitatively characterized the action between Doc and Cab. There was no significant PD interaction between Doc and Cab in both the concurrent schedule and the interval schedule, whereas the effect of the two drugs in the "Doc ∼ Cab" and "Cab ∼ Doc" sequential schedule was synergistic and antagonistic, respectively. The proposed model properly described the antitumor effects of Doc and Cab under different treatment schedules and could be used for dose optimization through model-based simulation.

Current mathematical models for cancer drug discovery

INTRODUCTION

Pharmacometric models represent the most comprehensive approaches for extracting, summarizing and integrating information obtained in the often sparse, limited, and less-than-optimally designed experiments performed in the early phases of oncology drug discovery. Whilst empirical methodologies may be enough for screening and ranking candidate drugs, modeling approaches are needed for optimizing and making economically viable the learn-confirm cycles within an oncology research program and anticipating the dose regimens to be investigated in the subsequent clinical development. Areas covered: Papers appearing in the literature of approximately the last decade reporting modeling approaches applicable to anticancer drug discovery have been listed and commented. Papers were selected based on the interest in the proposed methodology or in its application. Expert opinion: The number of modeling approaches used in the discovery of anticancer drugs is consistently increasing and new models are developed based on the current directions of research of new candidate drugs. These approaches have contributed to a better understanding of new oncological targets and have allowed for the exploitation of the relatively sparse information generated by preclinical experiments. In addition, they are used in translational approaches for guiding and supporting the choice of dosing regimens in early clinical development.

Modeling Longitudinal Preclinical Tumor Size Data to Identify Transient Dynamics in Tumor Response to Antiangiogenic Drugs

Experimental evidence suggests that antiangiogenic therapy gives rise to a transient window of vessel normalization, within which the efficacy of radiotherapy and chemotherapy may be enhanced. Preclinical experiments that measure components of vessel normalization are invasive and expensive. We have developed a mathematical model of vascular tumor growth from preclinical time‐course data in a breast cancer xenograft model. We used a mixed‐effects approach for model parameterization, leveraging tumor size data to identify a period of enhanced tumor growth that could potentially correspond to the transient window of vessel normalization. We estimated the characteristics of the window for mice treated with an anti‐VEGF antibody (bevacizumab) or with a bispecific anti‐VEGF/anti‐angiopoietin‐2 antibody (vanucizumab). We show how the mathematical model could theoretically be used to predict how to coordinate antiangiogenic therapy with radiotherapy or chemotherapy to maximize therapeutic effect, reducing the need for preclinical experiments that directly measure vessel normalization parameters.