Modeling of combination therapy to support drug discovery in oncology

Mathematical models based on ordinary differential equations, with impulses, are used to describe tumor growth after different treatment combinations, including chemicals as well as radiation. The models are calibrated, using a nonlinear mixed-effects framework, based on time series data of tumor volume from animal experiments. Important features incorporated into the models include natural cell death, and short-term as well as long-term response to radiation treatment, with or without co-treatment with a radiosensitizing compound. Tumor Static Exposure, defined as the treatment combinations that yield stability of the trivial solution to the system model, is introduced as a prediction tool that can also be used to compare and optimize combination therapies. The Tumor Static Exposure concept is illustrated practically, using calibrated models and data from animal experiments, as well as theoretically, using a linear cell cycle model to describe cancer growth subject to treatment with an arbitrary number of anticancer compounds

Model-based prediction of progression-free survival for combination therapies in oncology

Progression-free survival (PFS) is an important clinical metric for comparing and evaluating similar treatments for the same disease within oncology. After the completion of a clinical trial, a descriptive analysis of the patients\u27 PFS is often performed post hoc using the Kaplan–Meier estimator. However, to perform predictions, more sophisticated quantitative methods are needed. Tumor growth inhibition models are commonly used to describe and predict the dynamics of preclinical and clinical tumor size data. Moreover, frameworks also exist for describing the probability of different types of events, such as tumor metastasis or patient dropout. Combining these two types of models into a so-called joint model enables model-based prediction of PFS. In this paper, we have constructed a joint model from clinical data comparing the efficacy of FOLFOX against FOLFOX + panitumumab in patients with metastatic colorectal cancer. The nonlinear mixed effects framework was used to quantify interindividual variability (IIV). The model describes tumor size and PFS data well, and showed good predictive capabilities using truncated as well as external data. A machine-learning guided analysis was performed to reduce unexplained IIV by incorporating patient covariates. The model-based approach illustrated in this paper could be useful to help design clinical trials or to determine new promising drug candidates for combination therapy trials

Optimization of additive chemotherapy combinations for an in vitro cell cycle model with constant drug exposures

Proliferation of an in vitro population of cancer cells is described by a linear cell cycle model with n states, subject to provocation with m chemotherapeutic compounds. Minimization of a linear combination of constant drug exposures is considered, with stability of the system used as a constraint to ensure a stable or shrinking cell population. The main result concerns the identification of redundant compounds, and an explicit solution formula for the case where all exposures are nonzero. The orthogonal case, where each drug acts on a single and different stage of the cell cycle, leads to a version of the classic inequality between the arithmetic and geometric means. Moreover, it is shown how the general case can be solved by converting it to the orthogonal case using a linear invertible transformation. The results are illustrated with two examples corresponding to combination treatment with two and three compounds, respectively

Optimized scaling of translational factors in oncology: from xenografts to RECIST

Purpose: Tumor growth inhibition (TGI) models are regularly used to quantify the PK–PD relationship between drug concentration and\ua0in vivo\ua0efficacy in oncology. These models are typically calibrated with data from xenograft mice and before being used for clinical predictions, translational methods have to be applied. Currently, such methods are commonly based on replacing model components or scaling of model parameters. However, difficulties remain in how to accurately account for inter-species differences. Therefore, more research must be done before xenograft data can fully be utilized to predict clinical response. Method: To contribute to this research, we have calibrated TGI models to xenograft data for three drug combinations using the nonlinear mixed effects framework. The models were translated by replacing mice exposure with human exposure and used to make predictions of clinical response. Furthermore, in search of a better way of translating these models, we estimated an optimal way of scaling model parameters given the available clinical data. Results: The predictions were compared with clinical data and we found that clinical efficacy was overestimated. The estimated optimal scaling factors were similar to a standard allometric scaling exponent of − 0.25. Conclusions: We believe that given more data, our methodology could contribute to increasing the translational capabilities of TGI models. More specifically, an appropriate translational method could be developed for drugs with the same mechanism of action, which would allow for all preclinical data to be leveraged for new drugs of the same class. This would ensure that fewer clinically inefficacious drugs are tested in clinical trials

A Model Based Approach for Translation in Oncology - From Xenografts to RECIST

A major problem in drug development is translating results from preclinical studies to the clinical setting. Therefore, we evalu ate the translational potential of semi mechanistic tumor models (based on xenograft data) to predict clinical oncology results (RECISTdata). Two commonly used translational methods are evaluated: (1) replacement with human PK, and (2) allometric scaling of PD pa rameters. We then compute optimal scaling coefficients given the observed clinical data and relate them to the standard allom etr icexponents in method (2). The analysis is performed for three drug combinations: binimetinib/encorafenib (shown below), binime tin ib/ribociclib, and cetuximab/encorafenib

Population Modeling of Toxicological Combination Effects

Aim: Nonlinear mixed effects (NLME) modeling is currently the state-of-the-art mathematical framework for analyzing population data in medicine. We aim to illustrate how NLME modeling and the Tumor Static Exposure (TSE) concept can be beneficial for analyzing the effects of combined pollutants in marine life.\ua0Results:TSE is defined as all drug exposure that results in tumor stasis and therefore separates the space of all exposures into a region of tumor growth and a region of tumor shrinkage. TSE is derived from the equations of the NLME model and when two drugs are investigated the TSE for the median individual can be illustrated in a diagram with each axis representing the exposure of one of the drugs.We apply a similar approach to a toxicological model that describes the combined toxicological effects of two pollutants on marine animals. The model is based on a set of ordinary differential equations and from these, we derive a curve, similar to TSE, which describes all exposure combinations that result in a critical toxicological event. We use simulated data to calibrate the model and illustrate how predictions of toxicity can be made on a population level. \ua0Discussion/Conclusions:Since all possible combinations of pollutants cannot be tested experimentally the modified version of the TSE-curve can be useful to explore how different combinations affect marine life populations. Thus, it could be used to rank which pollutants are most important to reduce in the oceans. The NLME framework provides a powerful method for analyzing time-series data and could increase the statistical power when analyzing data from animal studies. In addition, it allows for simulation-based analysis, which could help reduce the number of animal experiments

Exposure-response modeling improves selection of radiation and radiosensitizer combinations

A central question in drug discovery is how to select drug candidates from a large number of available compounds. This analysis presents a model-based approach for comparing and ranking combinations of radiation and radiosensitizers. The approach is quantitative and based on the previously-derived Tumor Static Exposure (TSE) concept. Combinations of radiation and radiosensitizers are evaluated based on their ability to induce tumor regression relative to toxicity and other potential costs. The approach is presented in the form of a case study where the objective is to find the most promising candidate out of three radiosensitizing agents. Data from a xenograft study is described using a nonlinear mixed-effects modeling approach and a previously-published tumor model for radiation and radiosensitizing agents. First, the most promising candidate is chosen under the assumption that all compounds are equally toxic. The impact of toxicity in compound selection is then illustrated by assuming that one compound is more toxic than the others, leading to a different choice of candidate

Modeling of radiation therapy and radiosensitizing agents in tumor xenografts

III-36\ua0Tim\ua0Cardilin\ua0Modeling of radiation therapy and radiosensitizing agents in tumor xenografts\ua0Tim Cardilin (1,2), Joachim Almquist (1), Mats Jirstrand (1), Astrid Zimmermann (3), Floriane Lignet (4), Samer El Bawab (4), and Johan Gabrielsson (5)(1) Fraunhofer-Chalmers Centre, Gothenburg, Sweden, (2) Department of Mathematical Sciences, Chalmers University of Technology and Gothenburg University, Gothenburg, Sweden, (3) Merck, Translational Innovation Platform Oncology, Darmstadt, Germany, (4) Merck, Global Early Development - Quantitative Pharmacology, Darmstadt, Germany, (5) Division of Pharmacology and Toxicology, Department of Biomedical Sciences and Veterinary Public Health, Swedish University of Agricultural Sciences, Uppsala, SwedenObjectives:\ua0To conceptually and mathematically describe the treatment effects of radiation and radiosensitizing agents on tumor volume in xenografts with respect to short- and long-term effects.Methods:\ua0Data were generated in FaDu xenograft mouse models, where animals were treated with radiation given either as monotherapy (2 Gy per dose) or together with an early-discovery radiosensitizing agent (25 or 100 mg/kg per dose) that interferes with the repair of the DNA damage induced by irradiation. Animals received treatment following a clinically-relevant administration schedule with doses five days a week for six weeks. Tumor diameters were measured by caliper twice a week for up to 140 days. A pharmacodynamic tumor model was adapted from a previously-published model [1,2]. The improved model captures both short- and long-term treatment effects including tumor eradication and tumor regrowth. Short-term radiation effects are described by allowing lethally irradiated cells up to one more cell division before apoptosis. Long-term radiation effects are described by an irreversible decrease in tumor growth rate. The radiosensitizing agent was assumed to stimulate both processes. The model also includes a natural death rate of cancer cells. The model was calibrated to the xenograft data using a mixed-effects approach based on the FOCE method that was implemented in Mathematica [3]. Between-subject variability was accounted for in initial tumor volume, as well as in the short- and long-term radiation effects.Results:\ua0Data across all treatment groups were well-described by the model. All model parameters were estimated with acceptable precision and biologically reasonable values. Vehicle growth was approximately exponential during the observed time period with an estimated tumor doubling time of approximately 5 days. Tumor growth following radiation therapy resulted in significant tumor regression followed by either tumor eradication (2 animals) or slow regrowth (7 animals). The short- and long-term effects incorporated into the tumor model were able to account for both of these scenarios. A simple analysis shows that if the tumor growth rate is decreased below the natural death rate, the tumor will be eradicated. Otherwise, the tumor will regrow but at a slower rate compared to pre-treatment. The model predicts that each fraction of radiation (2 Gy) results in lethal damage in 15 % of viable cells, and that a total dose above 120 Gy will eradicate the tumor. Tumor growth following combination therapy with a lower dose (25 mg/kg) resulted in more cases of tumor eradication (6 animals) and fewer cases of regrowth (3 animals), whereas combination therapy with the higher dose (100 mg/kg) resulted in tumor eradication in all 9 animals. When radiation therapy was complemented by radiosensitizing treatment (100 mg/kg per dose), each fraction of 2 Gy was estimated to kill 25 % of viable cells, and the total radiation dose required for tumor eradication was decreased by a factor four to 30 Gy.Conclusions:\ua0A tumor model has been developed to describe the treatment effects of radiation therapy, as well as combination therapies involving radiation, in tumor xenografts. The model distinguishes between short- and long-term effects of radiation treatment and can describe different tumor dynamics, including tumor eradication and tumor regrowth at different rates. The novel tumor model can be used to predict treatment outcomes for a broad range of treatments including radiation therapy and combination therapies with different radiosensitizing agents.References:\ua0[1] Cardilin T, Almquist J, Jirstrand M, Zimmermann A, El Bawab S, Gabrielsson J. Model-based evaluation of radiation and radiosensitizing agents in oncology. CPT: Pharmacometrics & Syst. Pharmacol.\ua0(2017).[2] Cardilin T, Zimmermann A, Jirstrand M, Almquist J, El Bawab S, Gabrielsson J. Extending the Tumor Static Concentration Curve to average doses – a combination therapy example using radiation therapy. PAGE 25 (2016) Abstr 5975 [www.page-meeting.org/?abstract=5975].[3] Almquist J, Leander J, Jirstrand M. Using sensitivity equations for computing gradients of the FOCE and FOCEI approximations to the population likelihood. J Pharmacokinet Pharmacodyn (2015) 42: 191-209

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\ua0Gy, which is reduced to 80 or 30\ua0Gy with co-administration of 25 or 100\ua0mg\ua0kg\ua0−1\ua0of 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

Data-driven modeling of combination therapy in oncology

This thesis contains two manuscripts: Tumor Static Concentration Curves in Combination Therapy and Extending the Tumor Static Concentration Curve to Exposure - A Combination Therapy Example with Radiation Therapy. There is also an introductory chapter presenting some basic facts necessary to understand the appended manuscripts. The manuscripts share the common goal of developing model-based data-driven tools and techniques to quantitatively assess the effectiveness of anticancer combinations. The first paper presents a dynamical systems model for combination therapy with the anticancer drugs cetuximab and cisplatin. Using a mixed-effects approach the model is shown to adequately describe a preclinical dataset. The model is then analyzed by introducing the Tumor Static Concentration (TSC) curve, a curve of cetuximab-cisplatin concentration pairs all of which, if maintained, result in tumor stasis. The TSC analysis reveals a modest gain from combining the compounds. The variability of the TSC curve across the population is also explored. In the second paper we develop a dynamical systems model for combination therapy with ionizing radiation and a test compound. For this combination we introduce an extension of the TSC curve called the (average) Tumor Static Exposure (TSE) curve based on average, as opposed to pointwise, tumor stasis. The TSE analysis for combinations of radiation and the test compound demonstrates a large synergistic effect