Global Dormancy of Metastases Due to Systemic Inhibition of Angiogenesis

Autopsy studies of adults dying of non-cancer causes have shown that virtually all of us possess occult, cancerous lesions. This suggests that, for most individuals, cancer will become dormant and not progress, while only in some will it become symptomatic disease. Meanwhile, it was recently shown in animal models that a tumor can produce both stimulators and inhibitors of its own blood supply. To explain the autopsy findings in light of the preclinical research data, we propose a mathematical model of cancer development at the organism scale describing a growing population of metastases, which, together with the primary tumor, can exert a progressively greater level of systemic angiogenesis-inhibitory influence that eventually overcomes local angiogenesis stimulation to suppress the growth of all lesions. As a departure from modeling efforts to date, we look not just at signaling from and effects on the primary tumor, but integrate over this increasingly negative global signaling from all sources to track the development of total tumor burden. This in silico study of the dynamics of the tumor/metastasis system identifies ranges of parameter values where mutual angio-inhibitory interactions within a population of tumor lesions could yield global dormancy, i.e., an organism-level homeostatic steady state in total tumor burden. Given that mortality arises most often from metastatic disease rather than growth of the primary per se, this finding may have important therapeutic implications.Comment: 5 figures, 2 table

Optimization of sequential administration of bevacizumab plus cytotoxics in non-small cell lung cancer by combining in vivo experiments and mathematical modeling

International audienceConcomitant administration of bevacizumab and pemetrexed-cisplatin is a common treatment for advanced nonsquamous non-small cell lung cancer (NSCLC). Vascular normalization following bevacizumab administration may transiently enhance drug delivery, suggesting improved efficacy with sequential administration. To investigate optimal scheduling, we conducted a study in NSCLC-bearing mice that combined mathematical modeling with experimental investigations. First, experiments demonstrated improved efficacy when using sequential vs. concomitant scheduling of bevacizumab and chemotherapy. Combining this data with a mathematical model of tumor growth under therapy accounting for the normalization effect, we predicted an optimal delay of 2.8 days between bevacizumab and chemotherapy. This prediction was confirmed experimentally, with reduced tumor growth of 38% as compared to concomitant scheduling, and prolonged survival (74 vs. 70 days). Alternate sequencing of 8 days failed in achieving a similar increase in efficacy, thus emphasizing the utility of modeling support to identify optimal scheduling. The model could also be a useful tool in the clinic to personally tailor regimen sequences

Data-driven mechanistic modeling of metastasis: cancer at the organism scale

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Mathematical Modeling of Tumor-Tumor Distant Interactions Supports a Systemic Control of Tumor Growth

International audienceInteractions between different tumors within the same organism have major clinical implications, especially in the context of surgery and metastatic disease. Three main explanatory theories (competition, angiogenesis inhibition, and proliferation inhibition) have been proposed, but precise determinants of the phenomenon remain poorly understood. In this talk, I will present a formalized version of these theories into mathematical models and the results of biological experiments that were performed to test them against empirical data.The main experimental finding was that in syngeneic mice bearing two simultaneously implanted tumors, growth of one and only one of the tumors was significantly suppressed (61% size reduction at day 15, P < 0.05). At the theoretical level, the competition model had to be rejected, whereas the angiogenesis inhibition and proliferation inhibition models were able to describe the data.The proliferation inhibition model was identifiable and minimal (four parameters), and its descriptive power was validated against the data, including consistency in predictions of single tumor growth when no secondary tumor was present. This theory may also shed new light on single cancer growth insofar as it offers a biologically translatable picture of how local and global action may combine to control local tumor growth and, in particular, the role of tumor-tumor inhibition. This model offers a depiction of concomitant resistance that provides an improved theoretical basis for tumor growth control and may also find utility in therapeutic planning to avoid postsurgery metastatic acceleration

Quantitative modeling of metastasis: cancer at the organism scale

Doctora

Une comparaison des algorithmes d'apprentissage pour la survie avec donn\'ees manquantes

Survival analysis is an essential tool for the study of health data. An inherent component of such data is the presence of missing values. In recent years, researchers proposed new learning algorithms for survival tasks based on neural networks. Here, we studied the predictive performance of such algorithms coupled with different methods for handling missing values on simulated data that reflect a realistic situation, i.e., when individuals belong to unobserved clusters. We investigated different patterns of missing data. The results show that, without further feature engineering, no single imputation method is better than the others in all cases. The proposed methodology can be used to compare other missing data patterns and/or survival models. The Python code is accessible via the package survivalsim. -- L'analyse de survie est un outil essentiel pour l'\'etude des donn\'ees de sant\'e. Une composante inh\'erente \`a ces donn\'ees est la pr\'esence de valeurs manquantes. Ces derni\`eres ann\'ees, de nouveaux algorithmes d'apprentissage pour la survie, bas\'es sur les r\'eseaux de neurones, ont \'et\'e con\c{c}us. L'objectif de ce travail est d'\'etudier la performance en pr\'ediction de ces algorithmes coupl\'es \`a diff\'erentes m\'ethodes pour g\'erer les valeurs manquantes, sur des donn\'ees simul\'ees qui refl\`etent une situation rencontr\'ee en pratique, c'est-\`a dire lorsque les individus peuvent \^etre group\'es selon leurs covariables. Diff\'erents sch\'emas de donn\'ees manquantes sont \'etudi\'es. Les r\'esultats montrent que, sans l'ajout de variables suppl\'ementaires, aucune m\'ethode d'imputation n'est meilleure que les autres dans tous les cas. La m\'ethodologie propos\'ee peut \^etre utilis\'ee pour comparer d'autres mod\`eles de survie. Le code en Python est accessible via le package survivalsim.Comment: in French languag

On the growth and dissemination laws in a mathematical model of metastatic growth

International audienceMetastasis represents one of the main clinical challenge in cancer treatment since it is associated with the majority of deaths. Recent technological advances allow quantification of the dynamics of the process by means of noninvasive techniques such as longitudinal tracking of bioluminescent cells. The metastatic process was simplified here into two essential components – dissemination and colonization – which were mathematically formalized in terms of simple quantitative laws. The resulting mathematical model was confronted to in vivo experimental data of spontaneous metastasis after primary tumor resection. We discuss how much information can be inferred from confrontation of theories to the data with emphasis on identifiability issues. It is shown that two mutually exclusive assumptions for the secondary growth law (namely same or different from the primary tumor growth law) could fit equally well the data. Similarly, the fractal dimension coefficient in the dissemination law could not be uniquely determined from data on total metastatic burden only. Together, these results delimitate the range of information that can be recovered from fitting data of metastatic growth to already simplified mathematical models

Mathematical modeling of differential effects of neo-adjuvant Sunitinib on primary tumor and metastatic growth

International audienceSunitinib is a drug with anti-angiogenic activity used in the treatment of patients with metastases from renal cell carcinoma or gastrointestinal tumors. However, despite clear efficacy in reducing established tumor growth, recent preclinical studies have shown limited, or even opposing, efficacies in preventing metastatic spread [1, 2]. In this work, we evaluated a previously validated mechanistic mathematical model of metastasis [3] to describe primary tumor and metastatic dynamics in response to neoadjuvant anti-angiogenic treatment in clinically relevant mouse models of spontaneous metastatic breast and kidney cancers that develop after surgical removal of orthotopically implanted primary tumors. The data of more than 380 mice receiving either vehicle or sunitinib in the neoadjuvant (presurgical) setting according to different schedules was analyzed. The experimental datasets comprise measurements of primary tumor and metastatic burden kinetics as well as pre-surgical molecular and cellular biomarkers, including vascular cell Ki67 and CD31 expression, circulating tumor cells (CTCs) and myeloid derived suppressor cell counts (MDSCs). Estimation of the mathematical model's parameters was performed using a mixed-effects population approach. Population fits obtained modeling the effect of treatment only on primary tumor growth described well the experimental data of all the treated groups considered, suggesting a negligible effect of the neo-adjuvant treatment on early metastatic spread and growth. When inserting in the model the available biomarkers as covariates, measurements of Ki67+/CD31+, CTCs and granulocytic MDSCs were found significantly correlated with a specific model parameter expressing the metastatic aggressiveness of the tumor. Together, our mathematical model confirms a differential effect of sunitinib on primary (localized) tumors compared to secondary (metastatic) disease. Our results suggest that CTCs and MDSCs might help in predicting metastatic potential and provide a biologically-based computational model integrating these biomarkers into personalized predictions of metastatic benefit of pre-operative treatments. [1] Ebos, J. M. L., Lee, C. R., Cruz-Munoz, W., Bjarnason, G. A., Christensen, J. G., and Kerbel, R. S. (2009). Accelerated metastasis after short-term treatment with a potent inhibitor of tumor angiogenesis. Cancer Cell, 15(3):232-239

Pharmacometrics modeling coupled with machine learning for early prediction of survival following atezolizumab monotherapy in non-small cell lung cancer

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