We introduce a phenomenological model for anti-angiogenic therapy in the treatment of metastatic cancers. It is a structured transport equation with a nonlocal boundary condition describing the evolution of the density of metastases that we analyze first at the continuous level. We present the numerical analysis of a lagrangian scheme based on the characteristics whose convergence establishes existence of solutions. Then we prove an error estimate and use the model to perform interesting simulations...

We introduce a phenomenological model for anti-angiogenic therapy in the treatment of metastatic cancers. It is a structured transport equation with a nonlocal boundary condition describing the evolution of the density of metastases that we analyze first at the continuous level. We present the numerical analysis of a lagrangian scheme based on the characteristics whose convergence establishes existence of solutions. Then we prove an error estimate and use the model to perform interesting simulations...

We introduce a phenomenological model for anti-angiogenic therapy in the treatment of metastatic cancers. It is a structured transport equation with a nonlocal boundary condition describing the evolution of the density of metastases that we analyze first at the continuous level. We present the numerical analysis of a lagrangian scheme based on the characteristics whose convergence establishes existence of solutions. Then we prove an error estimate and use the model to perform interesting simulations...

This article is devoted to the construction of a mathematical model describing the early formation of atherosclerotic lesions. The early stage of atherosclerosis is an inflammatory process that starts with the penetration of low density lipoproteins in the intima and with their oxidation. This phenomenon is closely linked to the local blood flow dynamics. Extending a previous work [5] that was mainly restricted to a one-dimensional setting, we couple...

We study a class of parabolic-ODE systems modeling tumor growth, its mathematical modeling and the global in time existence of the solution obtained by the method of Lyapunov functions.

The paper is devoted to mathematical modelling and numerical computations of a nonstationary free boundary problem. The model is based on processes of molecular diffusion of some products of chemical decomposition of a solid organic substance concentrated in bottom sediments. It takes into account non-stationary multi-component and multi-stage chemical decomposition of organic substances and the processes of sorption desorption under aerobic and anaerobic conditions. Such a model allows one to...

In this article, we propose an integrated model for oxygen transfer into the blood, coupled with a lumped mechanical model for the ventilation process. Objectives. We aim at investigating oxygen transfer into the blood at rest or exercise. The first task consists in describing nonlinear effects of the oxygen transfer under normal conditions. We also include the possible diffusion limitation in oxygen transfer observed in extreme regimes involving parameters such as alveolar and venous blood oxygen...

In this paper we are interested in a mathematical model of migration of grass eels in an estuary. We first revisit a previous model proposed by O. Arino and based on a degenerate convection-diffusion equation of parabolic-hyperbolic type with time-varying subdomains. Then, we propose an adapted mathematical framework for this model, we prove a result of existence of a weak solution and we propose some numerical simulations.

Plant growth occurs due to cell proliferation in the meristem. We model the case of apical meristem specific for branch growth and the case of basal meristem specific for bulbous plants and grass. In the case of apical growth, our model allows us to describe the variety of plant forms and lifetimes, endogenous rhythms and apical domination. In the case of basal growth, the spatial structure, which corresponds to the appearance of leaves, results...

Over the past decade or so, there have been a large number of modelling approaches aimed at elucidating the most important mechanisms affecting the formation of new capillaries from parent blood vessels — a process known as angiogenesis. Most studies have focussed upon the way in which capillary sprouts are initiated and migrate in response to diffusible chemical stimuli supplied by hypoxic stromal cells and leukocytes in the contexts of solid tumour...

We study molecular motor-induced microtubule self-organization in dilute and semi-dilute filament solutions. In the dilute case, we use a probabilistic model of microtubule interaction via molecular motors to investigate microtubule bundle dynamics. Microtubules are modeled as polar rods interacting through fully inelastic, binary collisions. Our model indicates that initially disordered systems of interacting rods exhibit an orientational instability...

We examine the theoretical and applications-specific issues relating to modeling the temporal and spatial dynamics of forest ecosystems, based on the principles of investigating dynamical models. When developing the predictive dynamical models of forest resources, there is a possibility of achieving uniqueness of the solutions to equations by taking into account the initial and boundary conditions of the solution, and the conditions of the geographical environment. We present the results of a computer...