Methodologies for Quantitative Systems Pharmacology (QSP) Models: Design and Estimation.

With the increased interest in the application of quantitative systems pharmacology (QSP) models within medicine research and development, there is an increasing need to formalize model development and verification aspects. In February 2016, a workshop was held at Roche Pharma Research and Early Development to focus discussions on two critical methodological aspects of QSP model development: optimal structural granularity and parameter estimation. We here report in a perspective article a summary of presentations and discussions.

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.

Challenges and Opportunities for Quantitative Clinical Pharmacology in Cancer Immunotherapy: Something Old, Something New, Something Borrowed, and Something Blue.

Cancer immunotherapy (CIT) initiates or enhances the host immune response against cancer. Following decades of development, patients with previously few therapeutic options may now benefit from CIT. Although the quantitative clinical pharmacology (qCP) of previous classes of anticancer drugs has matured during this time, application to CIT may not be straightforward since CIT acts via the immune system. Here we discuss where qCP approaches might best borrow or start anew for CIT.

Pharmacometrics Markup Language (PharmML): Opening New Perspectives for Model Exchange in Drug Development.

The lack of a common exchange format for mathematical models in pharmacometrics has been a long-standing problem. Such a format has the potential to increase productivity and analysis quality, simplify the handling of complex workflows, ensure reproducibility of research, and facilitate the reuse of existing model resources. Pharmacometrics Markup Language (PharmML), currently under development by the Drug Disease Model Resources (DDMoRe) consortium, is intended to become an exchange standard in pharmacometrics by providing means to encode models, trial designs, and modeling steps.

Modeling and predicting optimal treatment scheduling between the antiangiogenic drug sunitinib and irinotecan in preclinical settings.

We present a system of nonlinear ordinary differential equations used to quantify the complex dynamics of the interactions between tumor growth, vasculature generation, and antiangiogenic treatment. The primary dataset consists of longitudinal tumor size measurements (1,371 total observations) in 105 colorectal tumor-bearing mice. Mice received single or combination administration of sunitinib, an antiangiogenic agent, and/or irinotecan, a cytotoxic agent. Depending on the dataset, parameter estimation was performed either using a mixed-effect approach or by nonlinear least squares. Through a log-likelihood ratio test, we conclude that there is a potential synergistic interaction between sunitinib when administered in combination with irinotecan in preclinical settings. Model simulations were then compared to data from a follow-up preclinical experiment. We conclude that the model has predictive value in identifying the therapeutic window in which the timing between the administrations of these two drugs is most effective.

Prediction of Response to Temozolomide in Low-Grade Glioma Patients Based on Tumor Size Dynamics and Genetic Characteristics.

Both molecular profiling of tumors and longitudinal tumor size data modeling are relevant strategies to predict cancer patients' response to treatment. Herein we propose a model of tumor growth inhibition integrating a tumor's genetic characteristics (p53 mutation and 1p/19q codeletion) that successfully describes the time course of tumor size in patients with low-grade gliomas treated with first-line temozolomide chemotherapy. The model captures potential tumor progression under chemotherapy by accounting for the emergence of tissue resistance to treatment following prolonged exposure to temozolomide. Using information on individual tumors' genetic characteristics, in addition to early tumor size measurements, the model was able to predict the duration and magnitude of response, especially in those patients in whom repeated assessment of tumor response was obtained during the first 3 months of treatment. Combining longitudinal tumor size quantitative modeling with a tumor''s genetic characterization appears as a promising strategy to personalize treatments in patients with low-grade gliomas.

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.

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.

Ongoing and prolonged response in adult low-grade gliomas treated with radiotherapy.

The aim of the present study was to evaluate the impact of first-line radiotherapy on low-grade gliomas (LGGs) growth kinetics. The mean tumor diameter (MTD) of 39 LGGs was retrospectively measured on serial magnetic resonance images before (n = 16) and after radiotherapy onset (n = 39). After radiotherapy, a decrease of the MTD was observed in 37 patients. Median duration of the MTD decrease was 1.9 years (range 0-8.1 years). According to RANO criteria, the rates of partial and minor responses were 15 and 28 % at the first evaluation after radiotherapy and 36 and 34 % at the time of maximal MTD decrease. The presence of a 1p19q codeletion and the absence of p53 expression were associated with longer durations of MTD decrease (5.3 vs 1 years, p = 0.02 and 2.4 vs 1.8 years, p = 0.05, respectively) while no association was observed between IDH1-R132H expression and duration of MTD decrease. In most patients, MTD decrease after radiotherapy occurred in two phases: an initial phase of rapid MTD decrease followed by a second phase of slower MTD decrease. Patients with a high rate of MTD decrease during the initial phase (>7 mm/year) had both a shorter duration of response (1.9 vs 5.3 years, p = 0.003) and a shorter overall survival (5.5 vs 11.6 years, p = 0.0004). LGGs commonly display a prolonged and ongoing volume decrease after radiotherapy. However, patients who respond rapidly should be carefully monitored because they are at a higher risk of rapid progression.

Theoretical investigation of the efficacy of antiangiogenic drugs combined to chemotherapy in xenografted mice.

Antiangiogenic drugs were developed with the aim to inhibit the formation of intratumoral blood vessels and in consequence the growth of solid tumors. As these drugs are generally combined with classical cytotoxic drugs in the treatment of cancer patients, finding the optimal combinations remains a complex challenge due to possible interactions of the antiangiogenic compound with the hemodynamic property of the treated tumor. To analyze this problem, we developed a multi-scale model of vascular tumor growth combining a molecular model of VEGF signaling pathways and a tissue model of the tumor expansion including the dynamics of cellular and tissue processes of tumor growth and response to treatments. We addressed the potential impact of antiangiogenic drug by defining a new index of vasculature quality which depends on the balance between stable and unstable vessels within the tumor mass. Our goal was to investigate the interactions between a chemotherapy and a antiangiogenic treatment, and, by simulating the model, to identify the optimal delay of chemotherapy delivery after the administration of the antiangiogenic compound. This theoretical analysis could be used in the future to optimize antiangiogenic drug delivery in preclinical settings and to facilitate the translation from preclinical to clinical studies.

Time-course analysis of main markers of primary infection in cats with the feline immunodeficiency virus.

Studies of the response of the immune system to feline immunodeficiency virus (FIV) during primary infection have shown that a subpopulation of CD8(+) T-cells with an activated phenotype and reduced expression of the CD8ß chain (denoted CD8ß(low) T cells) expands to reach up to 80% of the total CD8(+) T cell count. The expansion of this subpopulation is considered to be a signature of FIV and an indicator of immune system alteration. We use a simple mathematical formalism to study the relationships over time between the dose of infection, the size of the CD8ß(low) population, and the circulating viral load in cats infected with FIV. Viremia profiles are described using a combination of two exponential laws, whereas the CD8ß(low) percentage (out of the total CD8(+) population) is represented by a Gompertz law including an expansion phase and a saturation phase. Model parameters are estimated with a population approach using data from 102 experimentally infected cats. We examine the dose of infection as a potential covariate of parameters. We find that the rates of increase of viral load and of CD8ß(low) percentage are both correlated with the dose of infection. Cats that develop strong acute viremia also show the largest degree of CD8ß(low) expansion. The two simple models are robust tools for analysing the time course of CD8ß(low) percentage and circulating viral load in FIV-infected cats and may be useful for generating new insights on the disease and on the design of therapeutic strategies, potentially applicable to HIV infection.

Combining epitope-distinct antibodies to HER2: cooperative inhibitory effects on invasive growth.

Monoclonal antibodies (mAbs) to HER2 are currently used to treat breast cancer, but low clinical efficacy, along with primary and acquired resistance to therapy, commonly limit clinical applications. We previously reported that combinations of antibodies directed at non-overlapping epitopes of HER2 are endowed with enhanced antitumor effects, probably due to accelerated receptor degradation. Here, we extend these observations to three-dimensional mammary cell models, and compare the effects of single mAbs with the effects of antibody combinations. Collectively, our in vitro assays and computational image analyses indicate that combining mAbs against different epitopes of HER2 better inhibits invasive growth. Importantly, while growth factors are able to reduce intraluminal apoptosis and induce an invasive phenotype, combinations of mAbs better than single mAbs can reverse the growth factor-induced phenotypes of HER2-overexpressing spheroids. In conclusion, our studies propose that mAb combinations negate the biological effects of growth factors on invasive growth of HER2-overexpressing cells. Hence, combining mAbs offers a therapeutic strategy, potentially able to enhance clinical efficacy of existing antireceptor immunotherapeutics.

Predictive values of hCG clearance for risk of methotrexate resistance in low-risk gestational trophoblastic neoplasias.

BACKGROUND: Early identification of patients at high risk for chemoresistance among those treated with methotrexate (MTX) for low-risk gestational trophoblastic neoplasia (GTN) is needed. We modeled human chorionic gonadotropin (hCG) decline during MTX therapy using a kinetic population approach to calculate individual hCG clearance (CL(hCG)) and assessed the predictive value of CL(hCG) for MTX resistance. PATIENTS AND METHODS: A total of 154 patients with low-risk GTN treated with 8-day MTX regimen were retrospectively studied. NONMEM was used to model hCG decrease equations between day 0 and day 40 of chemotherapy. Receiver operating characteristic curve analysis defined the best CL(hCG) threshold. Univariate/multivariate survival analyses determined the predictive value of CL(hCG) and compared it with published predictive factors. RESULTS: A monoexponential equation best modeled hCG decrease: hCG(t) = 3900 x e(-0.149 x t). Median CL(hCG) was 0.57 l/day (quartiles: 0.37-0.74). Only choriocarcinoma pathology [yes versus no: hazard ratio (HR) = 6.01; 95% confidence interval (CI) 2.2-16.6; P < 0.001] and unfavorable CL(hCG) quartile (< or =0.37 versus >0.37 l/day: HR = 6.75; 95% CI 2.7-16.8; P < 0.001) were significant independent predictive factors of MTX resistance risk. CONCLUSION: In the second largest cohort of low-risk GTN patients reported to date, choriocarcinoma pathology and CL(hCG) < or =0.37 l/day were major independent predictive factors for MTX resistance risk.

Chemotherapy may be delivered based on an integrated view of tumour dynamics.

The aim here was to explore the potential of pharmacokinetic (PK)/pharmacodynamic (PD) and physiopathological parameters in explaining the primary effects of an anti-cancer treatment that targets cells in a specific cell cycle phase. The authors applied a theoretical multi-scale disease model of tumour growth that integrates cancer processes at the cellular and tissue scales. The mathematical model at the cell level relies on a dynamic description of cell cycle regulation while the model at the tissue level is based on fluid mechanics considerations. Simulations show that the number of target cells oscillates as the tumour grows after a first cycle of chemotherapy. Both treatment effect and tumour growth processes drive these oscillations. Nonetheless, results indicate that parameters related to physiopathological processes may have greater relevance than classical drug-related parameters in determining the efficacy of a chemotherapy treatment protocol. Physiopathological parameters, in particular those related to cell cycle regulation, may be integrated in PK/PD models aimed at optimising the delivery of phase-specific cytotoxic treatments.

A multiscale mathematical model of avascular tumor growth to investigate the therapeutic benefit of anti-invasive agents.

With the aim of inhibiting cancer growth and reducing the risk of metastasis, pharmaceutical companies in the early 1990s developed anti-metastatic agents called inhibitors of metalloproteinases (MMPi). Despite the promising results obtained in pre-clinical studies, results of Phase III trials have been somewhat disappointing for late stage cancer patients. With the aim of mathematically investigating this therapeutic failure, we developed a mechanistically based model which integrates cell cycle regulation and macroscopic tumor dynamics. By simulating the model, we evaluated the efficacy of MMPi therapy. Simulation results predict the lack of efficacy of MMPi in advanced cancer patients. The theoretical model may aid in evaluating the efficacy of anti-metastatic therapies, thus benefiting the design of prospective clinical trials.

A mathematical model of Doxorubicin treatment efficacy for non-Hodgkin's lymphoma: investigation of the current protocol through theoretical modelling results.

Doxorubicin treatment outcomes for non-Hodgkin's lymphomas (NHL) are mathematically modelled and computationally analyzed. The NHL model includes a tumor structure incorporating mature and immature vessels, vascular structural adaptation and NHL cell-cycle kinetics in addition to Doxorubicin pharmacokinetics (PK) and pharmacodynamics (PD). Simulations provide qualitative estimations of the effect of Doxorubicin on high-grade (HG), intermediate-grade (IG) and low-grade (LG) NHL. Simulation results imply that if the interval between successive drug applications is prolonged beyond a certain point, treatment will be inefficient due to effects caused by heterogeneous blood flow in the system.