Approches mathématiques multi-niveaux pour l'étude de la croissance des tumeurs : Application à la morphogenèse du cancer du sein et ciblage thérapeutique de l'angiogenèse du cancer du côlon

Cancer is one of the leading causes of death in Europe. The mechanisms involved in tumour growth are qualitatively known, but we are still unable to precisely predict how a given tumour will evolve, nor estimate with certainty the optimal therapeutic protocol for each patient.It is well understood that mathematical modelling could give part of the answer to these questions. That is why during this thesis we considered the building of mathematical formalisms to describe tumour growth and the action of anti-cancer treatments. In particular, we investigated the molecular to tissular mechanisms of cancer development and angiogenesis through the building of a continuous multi-scale model. We were able to reproduce the effect of anti- angiogenesis treatments on tumour growth, and qualitatively study an optimal therapeutic protocol of anti-angiogenic combined with cytotoxic drugs. This multi-scale model integrates a mathematical representation of the signalling pathways of VEGF (Vascular Endothelial Growth Factor). We detail the development of this model which is based solely on information available in the literature and dedicated databases. In another approach, we considered a discrete, cell-based model to reproduce the development of spheroid structures of mammary epithelial cells. This model considers the behaviour of these cells when observed while grown in vitro in an appropriate medium. We were able to highlight the different mechanisms involved in the morphogenesis of wild and mutated cells structures.This work shows the importance of the multi-scale formalism we used to integrate the knowledge and data related to the study of cancer treatment.Les cancers sont l’une des causes majeures de mortalité dans le monde. Les mécanismes en jeu dans la croissance tumorale sont qualitativement connus, mais on se sait pas à l’heure actuelle prédire précisément quel sera le développement d’une tumeur donnée, ni estimer de façon certaine le protocole thérapeutique optimal pour chaque patient. Il est entendu que la modélisation mathématique pourrait apporter des éléments de réponse à ces questions. Durant cette thèse on s'est alors intéressé à la construction de formalismes mathématiques pour décrire la croissance tumorale et l’action de traitement anti-cancéreux. En particulier, on s'est intéressé à la prise en compte des mécanismes aussi bien moléculaires que cellulaires et tissulaires, par la construction d’un modèle continu, multi-échelles, de croissance de tumeur solide et d’angiogenèse. A partir de ce modèle, nous a pu envisager de façon qualitative un protocole optimal de combinaison entre un anti-angiogénique et une chimiothérapie.Le modèle multi-échelles inclut une représentation mathématique des voies de signalisation du VEGF dont on détaille la construction.Dans une autre approche, on a considéré un modèle discret, cellule-centré, reproduisant le développement de sphéroïdes de cellules épithéliales mammaires telles qu’observées lorsque ces cellules sont cultivées in vitro. On a pu mettre en évidence les différents mécanismes cellulaires impliqués dans la morphogenèse de structures composées de cellules saines, et celles composées de cellules mutées.Ces contributions montrent l’intérêt du formalisme multi-échelles adopté pour intégrer les connaissances et données sous-jacentes à l’étude du traitement des tumeurs

Approches mathématiques multi-niveaux pour l'étude de la croissance des tumeurs (Application à la morphogenèse du cancer du sein et ciblage thérapeutique de l'angiogenèse du cancer du côlon)

Les cancers sont l une des causes majeures de mortalité dans le monde. Les mécanismes en jeu dans la croissance tumorale sont qualitativement connus, mais on se sait pas à l heure actuelle prédire précisément quel sera le développement d une tumeur donnée, ni estimer de façon certaine le protocole thérapeutique optimal pour chaque patient. Il est entendu que la modélisation mathématique pourrait apporter des éléments de réponse à ces questions. Durant cette thèse on s'est alors intéressé à la construction de formalismes mathématiques pour décrire la croissance tumorale et l action de traitement anti-cancéreux. En particulier, on s'est intéressé à la prise en compte des mécanismes aussi bien moléculaires que cellulaires et tissulaires, par la construction d un modèle continu, multi-échelles, de croissance de tumeur solide et d angiogenèse. A partir de ce modèle, nous a pu envisager de façon qualitative un protocole optimal de combinaison entre un anti-angiogénique et une chimiothérapie.Le modèle multi-échelles inclut une représentation mathématique des voies de signalisation du VEGF dont on détaille la construction.Dans une autre approche, on a considéré un modèle discret, cellule-centré, reproduisant le développement de sphéroïdes de cellules épithéliales mammaires telles qu observées lorsque ces cellules sont cultivées in vitro. On a pu mettre en évidence les différents mécanismes cellulaires impliqués dans la morphogenèse de structures composées de cellules saines, et celles composées de cellules mutées.Ces contributions montrent l intérêt du formalisme multi-échelles adopté pour intégrer les connaissances et données sous-jacentes à l étude du traitement des tumeurs.Cancer is one of the leading causes of death in Europe. The mechanisms involved in tumour growth are qualitatively known, but we are still unable to precisely predict how a given tumour will evolve, nor estimate with certainty the optimal therapeutic protocol for each patient.It is well understood that mathematical modelling could give part of the answer to these questions. That is why during this thesis we considered the building of mathematical formalisms to describe tumour growth and the action of anti-cancer treatments. In particular, we investigated the molecular to tissular mechanisms of cancer development and angiogenesis through the building of a continuous multi-scale model. We were able to reproduce the effect of anti- angiogenesis treatments on tumour growth, and qualitatively study an optimal therapeutic protocol of anti-angiogenic combined with cytotoxic drugs. This multi-scale model integrates a mathematical representation of the signalling pathways of VEGF (Vascular Endothelial Growth Factor). We detail the development of this model which is based solely on information available in the literature and dedicated databases. In another approach, we considered a discrete, cell-based model to reproduce the development of spheroid structures of mammary epithelial cells. This model considers the behaviour of these cells when observed while grown in vitro in an appropriate medium. We were able to highlight the different mechanisms involved in the morphogenesis of wild and mutated cells structures.This work shows the importance of the multi-scale formalism we used to integrate the knowledge and data related to the study of cancer treatment.LYON-ENS Sciences (693872304) / SudocSudocFranceF

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

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

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 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

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

Multi-scale mathematical approaches for the study of tumour growth : Application to breast cancer morphogenesis and the therapeutic targeting of colon cancer angiogenesis

Les cancers sont l’une des causes majeures de mortalité dans le monde. Les mécanismes en jeu dans la croissance tumorale sont qualitativement connus, mais on se sait pas à l’heure actuelle prédire précisément quel sera le développement d’une tumeur donnée, ni estimer de façon certaine le protocole thérapeutique optimal pour chaque patient. Il est entendu que la modélisation mathématique pourrait apporter des éléments de réponse à ces questions. Durant cette thèse on s'est alors intéressé à la construction de formalismes mathématiques pour décrire la croissance tumorale et l’action de traitement anti-cancéreux. En particulier, on s'est intéressé à la prise en compte des mécanismes aussi bien moléculaires que cellulaires et tissulaires, par la construction d’un modèle continu, multi-échelles, de croissance de tumeur solide et d’angiogenèse. A partir de ce modèle, nous a pu envisager de façon qualitative un protocole optimal de combinaison entre un anti-angiogénique et une chimiothérapie.Le modèle multi-échelles inclut une représentation mathématique des voies de signalisation du VEGF dont on détaille la construction.Dans une autre approche, on a considéré un modèle discret, cellule-centré, reproduisant le développement de sphéroïdes de cellules épithéliales mammaires telles qu’observées lorsque ces cellules sont cultivées in vitro. On a pu mettre en évidence les différents mécanismes cellulaires impliqués dans la morphogenèse de structures composées de cellules saines, et celles composées de cellules mutées.Ces contributions montrent l’intérêt du formalisme multi-échelles adopté pour intégrer les connaissances et données sous-jacentes à l’étude du traitement des tumeurs.Cancer is one of the leading causes of death in Europe. The mechanisms involved in tumour growth are qualitatively known, but we are still unable to precisely predict how a given tumour will evolve, nor estimate with certainty the optimal therapeutic protocol for each patient.It is well understood that mathematical modelling could give part of the answer to these questions. That is why during this thesis we considered the building of mathematical formalisms to describe tumour growth and the action of anti-cancer treatments. In particular, we investigated the molecular to tissular mechanisms of cancer development and angiogenesis through the building of a continuous multi-scale model. We were able to reproduce the effect of anti- angiogenesis treatments on tumour growth, and qualitatively study an optimal therapeutic protocol of anti-angiogenic combined with cytotoxic drugs. This multi-scale model integrates a mathematical representation of the signalling pathways of VEGF (Vascular Endothelial Growth Factor). We detail the development of this model which is based solely on information available in the literature and dedicated databases. In another approach, we considered a discrete, cell-based model to reproduce the development of spheroid structures of mammary epithelial cells. This model considers the behaviour of these cells when observed while grown in vitro in an appropriate medium. We were able to highlight the different mechanisms involved in the morphogenesis of wild and mutated cells structures.This work shows the importance of the multi-scale formalism we used to integrate the knowledge and data related to the study of cancer treatment

A structural model of the VEGF signalling pathway: Emergence of robustness and redundancy properties.

International audienceThe vascular endothelial growth factor (VEGF) is known as one of the main promoter of angiogenesis - the process of blood vessel formation. Angiogenesis has been recognized as a key stage for cancer development and metastasis. In this paper, we propose a structural model of the main molecular pathways involved in the endothelial cells response to VEGF stimuli. The model, built on qualitative information from knowledge databases, is composed of 38 ordinary differential equations with 78 parameters and focuses on the signalling driving endothelial cell proliferation, migration and resistance to apoptosis. Following a VEGF stimulus, the model predicts an increase of proliferation and migration capability, and a decrease in the apoptosis activity. Model simulations and sensitivity analysis highlight the emergence of robustness and redundancy properties of the pathway. If further calibrated and validated, this model could serve as tool to analyse and formulate new hypothesis on th e VEGF signalling cascade and its role in cancer development and treatment

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

Abstract 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 $$\mu \mathrm{g}/\mathrm{mL}$$ μ g / mL 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