Optimisation of cancer drug treatments using cell population dynamics

International audienceCancer is primarily a disease of the physiological control on cell population proliferation. Tissue proliferation relies on the cell division cycle: one cell becomes two after a sequence of molecular events that are physiologically controlled at each step of the cycle at so-called checkpoints, in particular at transitions between phases of the cycle [105]. Tissue proliferation is the main physiological process occurring in development and later in maintaining the permanence of the organism in adults, at that late stage mainly in fast renewing tissues such as bone marrow, gut and skin

Designing proliferating cell population models with functional targets for control by anti-cancer drugs

24 pagesInternational audienceWe 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

Modelling targets for anticancer drug control optimisation in physiologically structured cell population models

International audienceThe main two pitfalls of therapeutics in clinical oncology, that limit increasing drug doses, are unwanted toxic side effects on healthy cell populations and occurrence of resistance to drugs in cancer cell populations. Depending on the constraint considered in the control problem at stake, toxicity or drug resistance, we present two different ways to model the evolution of proliferating cell populations, healthy and cancer, under the control of anti-cancer drugs. In the first case, we use a McKendrick age-structured model of the cell cycle, whereas in the second case, we use a model of evolutionary dynamics, physiologically structured according to a continuous phenotype standing for drug resistance. In both cases, we mention how drug targets may be chosen so as to accurately represent the effects of cytotoxic and of cytostatic drugs, separately, and how one may consider the problem of optimisation of combined therapies

Synchronisation and control of proliferation in cycling cell population models with age structure

International audienceWe present and analyse in this article a mathematical question with a biological origin, the theoretical treatment of which may have far-reaching implications in the practical treatment of cancers. Starting from biological and clinical observations on cancer cells, tumourbearing laboratory rodents, and patients with cancer, we ask from a theoretical biology viewpoint questions that may be transcribed, using physiologically based modelling of cell proliferation dynamics, into mathematical questions. We then show how recent fluorescence-based image modelling techniques performed at the single cell level in proliferating cell populations allow to identify model parameters and how this may be applied to investigate healthy and cancer cell populations. Finally, we show how this modelling approach allows us to design original optimisation methods for anticancer therapeutics, in particular chronotherapeutics, by controlling eigenvalues of the differential operators underlying the cell proliferation dynamics, in tumour and in healthy cell populations. We propose a numerical algorithm to implement these principles

Age-structured cell population model to study the influence of growth factors on cell cycle dynamics.

17 pagesInternational audienceCell proliferation is controlled by many complex regulatory networks. Ourpurpose is to analyse, through mathematical modeling, the effects of growth factors on the dynamics of the division cycle in cell populations. Our work is based on an age-structured PDE model of the cell division cycle within a population of cells in a common tissue. Cell proliferation is at its first stages exponential and is thus characterised by its growth exponent, the first eigenvalue of the linear system we consider here, a growth exponent that we will explicitly evaluate from biological data. Moreover, this study relies on recent and innovative imaging data (fluorescence microscopy) that make us able to experimentally determine the parameters of the model and to validate numerical results. This model has allowed us to study the degree of simultaneity of phase transitions within a proliferating cell population and to analyse the role of an increased growth factor concentration in this process. This study thus aims at helping biologists to elicit the impact of growth factor concentration on cell cycle regulation, at making more precise the dynamics of key mechanisms controlling the division cycle in proliferating cell populations, and eventually at establishing theoretical bases for optimised combined anticancer treatments

New Mass and Radius Constraints on the LHS 1140 Planets -- LHS 1140 b is Either a Temperate Mini-Neptune or a Water World

The two-planet transiting system LHS 1140 has been extensively observed since its discovery in 2017, notably with $Spitzer$, HST, TESS, and ESPRESSO, placing strong constraints on the parameters of the M4.5 host star and its small temperate exoplanets, LHS 1140 b and c. Here, we reanalyse the ESPRESSO observations of LHS 1140 with the novel line-by-line framework designed to fully exploit the radial velocity content of a stellar spectrum while being resilient to outlier measurements. The improved radial velocities, combined with updated stellar parameters, consolidate our knowledge on the mass of LHS 1140 b (5.60$\pm$0.19 M$_{\oplus}$) and LHS 1140 c (1.91$\pm$0.06 M$_{\oplus}$) with unprecedented precision of 3%. Transits from $Spitzer$, HST, and TESS are jointly analysed for the first time, allowing us to refine the planetary radii of b (1.730$\pm$0.025 R$_{\oplus}$) and c (1.272$\pm$0.026 R$_{\oplus}$). Stellar abundance measurements of refractory elements (Fe, Mg and Si) obtained with NIRPS are used to constrain the internal structure of LHS 1140 b. This planet is unlikely to be a rocky super-Earth as previously reported, but rather a mini-Neptune with a $\sim$0.1% H/He envelope by mass or a water world with a water-mass fraction between 9 and 19% depending on the atmospheric composition and relative abundance of Fe and Mg. While the mini-Neptune case would not be habitable, a water-abundant LHS 1140 b potentially has habitable surface conditions according to 3D global climate models, suggesting liquid water at the substellar point for atmospheres with relatively low CO$_2$ concentration, from Earth-like to a few bars.Comment: 31 pages, 18 figures, accepted for publication in ApJ

Modélisation mathématique multi-échelle de l'angiogenèse tumorale : analyse de la réponse tumorale aux traitements anti-angiogéniques

Cancer is one of the main causes of death worldwide. Angiogenesis is the formation of new blood vessels from preexisting vessels. A cancerous tumor can induce angiogenesis in order to get essential additional oxygen and nutrients supply to grow. This thesis is about the development of a multiscale mathematical model of tumor-induced angiogenesis. This model takes into account the main mechanisms that occur at the tissue level and at the molecular level during angiogenesis. Coupled with a model of tumor growth, our model enables to simulate the e_ect of oxygen supply on tumor growth. On a mathematical point of view, these models of tumor-induced angiogenesis and tumor growth are based on reaction-di_usion and advection partial di_erential equations that govern the evolution of the densities of endothelial cells, that compose blood vessel wall, and tumor cells, and that of the tissue concentrations of pro- and anti-angiogenic substances and oxygen. At the molecular level, the binding of angiogenic substances to receptors located on the membrane of endothelial cells is modeled by use of pharmacological laws. Such bindings are key mechanisms of intercellular communication. This model makes it possible to reproduce in silico the main mechanisms of angiogenesis and to analyze their action on tumor growth. It also enables to simulate the action of several antiangiogenic therapies and to study their e_cacy on tumor growth in order to help therapeuticLe cancer est l'une des principales causes de décès dans le monde. L'angiogenèse tumorale est le processus de formation de nouveaux vaisseaux sanguins à partir de vaisseaux préexistants. Une tumeur cancéreuse peut induire l'angiogenèse afin de disposer d'apports supplémentaires en oxygène et nutriments, indispensables à la poursuite de son développement. Cette thèse consiste en l'élaboration d'un modèle mathématique multi-échelle de l'angiogenèse tumorale. Ce modèle intègre les principaux mécanismes intervenant aux échelles tissulaire et moléculaire. Couplé à un modèle de croissance tumorale, notre modèle permet d'étudier les effets de l'apport en oxygène sur la croissance tumorale. D'un point de vue mathématique, ces modèles d'angiogenèse et de croissance tumorale reposent sur des équations aux dérivées partielles de réaction-diffusion et d'advection régissant l'évolution spatio-temporelle des densités de cellules endothéliales, cellules constituant la paroi des vaisseaux sanguins, et tumorales, ainsi que celle des concentrations tissulaires en substances pro- et antiangiogéniques et en oxygène. A l'échelle moléculaire, la liaison des substances angiogéniques aux récepteurs membranaires des cellules endothéliales, mécanisme clé de la communication intercellulaire, est modélisée à l'aide de lois pharmacologiques. Ce modèle permet ainsi de reproduire in silico les principaux mécanismes de l'angiogenèse et d'analyser leur rôle dans la croissance tumorale. Il permet également de simuler l'action de différentes thérapies anti-angiogéniques, et d'étudier leur efficacité sur le développement tumoral afin d'aider à l'innovation thérapeutiqu

Multiscale mathematical modeling of tumor-induced angiogenesis : investigation of the tumoral response to anti-angiogenic therapies

Le cancer est l'une des principales causes de décès dans le monde. L'angiogenèse tumorale est le processus de formation de nouveaux vaisseaux sanguins à partir de vaisseaux préexistants. Une tumeur cancéreuse peut induire l'angiogenèse afin de disposer d'apports supplémentaires en oxygène et nutriments, indispensables à la poursuite de son développement. Cette thèse consiste en l'élaboration d'un modèle mathématique multi-échelle de l'angiogenèse tumorale. Ce modèle intègre les principaux mécanismes intervenant aux échelles tissulaire et moléculaire. Couplé à un modèle de croissance tumorale, notre modèle permet d'étudier les effets de l'apport en oxygène sur la croissance tumorale. D'un point de vue mathématique, ces modèles d'angiogenèse et de croissance tumorale reposent sur des équations aux dérivées partielles de réaction-diffusion et d'advection régissant l'évolution spatio-temporelle des densités de cellules endothéliales, cellules constituant la paroi des vaisseaux sanguins, et tumorales, ainsi que celle des concentrations tissulaires en substances pro- et antiangiogéniques et en oxygène. A l'échelle moléculaire, la liaison des substances angiogéniques aux récepteurs membranaires des cellules endothéliales, mécanisme clé de la communication intercellulaire, est modélisée à l'aide de lois pharmacologiques. Ce modèle permet ainsi de reproduire in silico les principaux mécanismes de l'angiogenèse et d'analyser leur rôle dans la croissance tumorale. Il permet également de simuler l'action de différentes thérapies anti-angiogéniques, et d'étudier leur efficacité sur le développement tumoral afin d'aider à l'innovation thérapeutiqueCancer is one of the main causes of death worldwide. Angiogenesis is the formation of new blood vessels from preexisting vessels. A cancerous tumor can induce angiogenesis in order to get essential additional oxygen and nutrients supply to grow. This thesis is about the development of a multiscale mathematical model of tumor-induced angiogenesis. This model takes into account the main mechanisms that occur at the tissue level and at the molecular level during angiogenesis. Coupled with a model of tumor growth, our model enables to simulate the e_ect of oxygen supply on tumor growth. On a mathematical point of view, these models of tumor-induced angiogenesis and tumor growth are based on reaction-di_usion and advection partial di_erential equations that govern the evolution of the densities of endothelial cells, that compose blood vessel wall, and tumor cells, and that of the tissue concentrations of pro- and anti-angiogenic substances and oxygen. At the molecular level, the binding of angiogenic substances to receptors located on the membrane of endothelial cells is modeled by use of pharmacological laws. Such bindings are key mechanisms of intercellular communication. This model makes it possible to reproduce in silico the main mechanisms of angiogenesis and to analyze their action on tumor growth. It also enables to simulate the action of several antiangiogenic therapies and to study their e_cacy on tumor growth in order to help therapeuti

Short-term responses of glass eels transported from UK to small Belgian streams

Restocking of inland waters with glass eels is one of the recovery options to prevent the decline of European eel Anguilla anguilla (L.) populations. We studied the growth, dispersion, density and habitat preferences in the imported glass eels from United-Kingdom and stocked in three typologically different small Belgian streams, using electrofishing surveys around the single release point, 1 year following stocking. Our results clearly support that the recaptured individuals stocked in our streams farther from the sea, survived, grew, dispersed upstream and downstream. Elvers exploited the complete transversal section of stream, with preference for the sheltered microhabitats near the banks with slower water velocity and low depth. Length-weight relationship was different between streams in terms of allometric coefficient (b). We assume that microhabitats and food availabilities lead to contrasted results in terms of growth and absolute occurrence. Restocking of glass eels in small middle-land streams was found to be an interesting and unconventional option that requires adequate stream and habitat selection