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Papers by Frédérique Billy

Bulletin du cancer

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Mathematics and Computers in Simulation, 2014

Please cite this article in press as: F. Billy, et al. Synchronisation and control of proliferati... more Please cite this article in press as: F. Billy, et al. Synchronisation and control of proliferation in cycling cell population models with age structure, Math. Comput. Simul. (2012), http://dx.

Mathematical Biosciences and Engineering, 2012

Cell proliferation is controlled by many complex regulatory networks. Our purpose is to analyse, ... more Cell proliferation is controlled by many complex regulatory networks. Our purpose is to analyse, through mathematical modeling, the effects of growth factors on the dynamics of the division cycle in cell populations.

Journal of Theoretical Biology, 2009

Tumor angiogenesis is the process by which new blood vessels are formed and enhance the oxygenati... more Tumor angiogenesis is the process by which new blood vessels are formed and enhance the oxygenation and growth of tumors. As angiogenesis is recognized as being a critical event in cancer development, considerable efforts have been made to identify inhibitors of this process. Cytostatic treatments that target the molecular events of the angiogenesis process have been developed, and have met with some success. However, it is usually difficult to preclinically assess the effectiveness of targeted therapies, and apparently promising compounds sometimes fail in clinical trials. We have developed a multiscale mathematical model of angiogenesis and tumor growth. At the molecular level, the model focuses on molecular competition between pro- and anti-angiogenic substances modeled on the basis of pharmacological laws. At the tissue scale, the model uses partial differential equations to describe the spatio-temporal changes in cancer cells during three stages of the cell cycle, as well as those of the endothelial cells that constitute the blood vessel walls. This model is used to qualitatively assess how efficient endostatin gene therapy is. Endostatin is an anti-angiogenic endogenous substance. The gene therapy entails overexpressing endostatin in the tumor and in the surrounding tissue. Simulations show that there is a critical treatment dose below which increasing the duration of treatment leads to a loss of efficacy. This theoretical model may be useful to evaluate the efficacy of therapies targeting angiogenesis, and could therefore contribute to designing prospective clinical trials.

Journal of Theoretical Biology, 2013

Antiangiogenic drugs were developed with the aim to inhibit the formation of intratumoral blood v... more 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.

Discrete and Continuous Dynamical Systems - Series B, 2013

We review the main types of mathematical models that have been designed to represent and predict ... more We review the main types of mathematical models that have been designed to represent and predict the evolution of a cell population under the action of anti-cancer drugs that are in use in the clinic, with effects on healthy and cancer tissue growth, which from a cell functional point of view are classically divided between "proliferation, death and differentiation". We focus here on the choices of the drug targets in these models, aiming at showing that they must be linked in each case to a given therapeutic application. We recall some analytical results that have been obtained in using models of proliferation in cell populations with control in recent years. We present some simulations performed when no theoretical result is available and we state some open problems. In view of clinical applications, we propose possible ways to design optimal therapeutic strategies by using combinations of drugs, cytotoxic, cytostatic, or redifferentiating agents, depending on the type of cancer considered, acting on different targets at the level of cell populations.

Evolutionary Applications, 2013

Since the mid 1970s, cancer has been described as a process of Darwinian evolution, with somatic ... more Since the mid 1970s, cancer has been described as a process of Darwinian evolution, with somatic cellular selection and evolution being the fundamental processes leading to malignancy and its many manifestations (neoangiogenesis, evasion of the immune system, metastasis, and resistance to therapies). Historically, little attention has been placed on applications of evolutionary biology to understanding and controlling neoplastic progression and to prevent therapeutic failures. This is now beginning to change, and there is a growing international interest in the interface between cancer and evolutionary biology. The objective of this introduction is first to describe the basic ideas and concepts linking evolutionary biology to cancer. We then present four major fronts where the evolutionary perspective is most developed, namely laboratory and clinical models, mathematical models, databases, and techniques and assays. Finally, we discuss several of the most promising challenges and future prospects in this interdisciplinary research direction in the war against cancer.