Competition effects in the dynamics of tumor cords

Modeling tumor cell shedding

Cell shedding is an important step in the development of tumor invasion and metastasis. It influences growth saturation, latency, and tumor surface roughness. In spite of careful experiments carried out using multicellular tumor spheroids (MTS), the effects of the shedding process are not yet completely understood. Using a simulational model, we study how the nature and intensity of cell shedding may influence tumor morphology and examine the dependence of the total number of shed cells with the relevant parameters, finding the ranges that maximize cell detachment. These ranges correspond to intermediate values of the adhesion, for which we observe the emergence of a rough tumor surface. They are also likely to maximize the probability of generating invasion and metastases. Using numerical values taken from experiments, we find that the shedding-induced reduction in the growth rate is not intense enough to lead to latency, except when cell adhesion is assumed to be very weak. This suggests that the presence of inhibitors is a necessary condition for the observed MTS growth saturation.

Cancer growth: predictions of a realistic model

Simulations of avascular cancer growth are performed using experimental values of the relevant parameters. This permits a realistic assessment of the influence of these parameters on cancer growth dynamics. In general, an early exponential growth phase is followed by a linear regime (as observed in recent experiments), while the thickness of the viable cell layer remains approximately constant. Contrary to some predictions, a transition to latency is not observed.

Persistence of instanton connections in chemical reactions with time-dependent rates

The evolution of a system of chemical reactions can be studied, in the eikonal approximation, by means of a Hamiltonian dynamical system. The fixed points of this dynamical system represent the different states in which the chemical system can be found, and the connections among them represent instantons or optimal paths linking these states. We study the relation between the phase portrait of the Hamiltonian system representing a set of chemical reactions with constant rates and the corresponding system when these rates vary in time. We show that the topology of the phase space is robust for small time-dependent perturbations in concrete examples and state general results when possible. This robustness allows us to apply some of the conclusions on the qualitative behavior of the autonomous system to the time-dependent situation.

Minimal model for tumor angiogenesis

In this work, we show a mathematical model for the angiogenesis by endothelial cells. We present the model at the level of partial differential equations, describing the spatiotemporal evolution of the cell population, the extracellular matrix macromolecules, the proteases, the tumor angiogenic factors, and the possible presence of inhibitors. We mainly focus, however, on a complementary, more physiologically realistic, hybrid approach in which the cells are treated as individual particles. We examine the model numerically in two-dimensional settings, discussing its comparison with experimental results.

Inhibition of vascularization in tumor growth

The transition to a vascular phase is a prerequisite for fast tumor growth. During the avascular phase, the neoplasm feeds only from the (relatively few) existing nearby blood vessels. During angiogenesis, the number of capillaries surrounding and infiltrating the tumor increases dramatically. A model which includes physical and biological mechanisms of the interactions between the tumor and vascular growth describes the avascular-vascular transition. Numerical results agree with clinical observations and predict the influence of therapies aiming to inhibit the transition.