The formation of vascular networks in vitro develops along two rather distinct stages: during the early migration-dominated stage the main features of the pattern emerge, later the mechanical interaction of the cells with the substratum stretches the network. Mathematical models in the relevant literature have been focusing just on either of the aspects of this complex system. In this paper, a unified view of the morphogenetic process is provided in terms of physical mechanisms and mathematical modeling.

This work reports on vehicular traffic modeling by methods of the discrete kinetic theory. The purpose is to detail a reference mathematical framework for some discrete velocity kinetic models recently introduced in the literature, which proved capable of reproducing interesting traffic phenomena without using experimental information as modeling assumptions. To this end, we firstly derive a general discrete velocity kinetic framework with binary nonlocal interactions.

In this work the phenomenon of contact inhibition of growth is studied by applying an individual based model and a continuum multiphase model to describe cell colony growth in vitro. The impact of different cell behavior in response to mechanical cues is investigated. The work aims at comparing the results from both models from the qualitative and, whenever possible, also the quantitative point of view. Crown Copyright © 2009.

In this paper, we systematically apply the mathematical structures by time-evolving measures developed in a previous work to the macroscopic modeling of pedestrian flows. We propose a discrete-time Eulerian model, in which the space occupancy by pedestrians is described via a sequence of Radon-positive measures generated by a push-forward recursive relation.

We present a multiphase mathematical model for tumor growth which incorporates the remodeling of the extracellular matrix and describes the formation of fibrotic tissue by tumor cells. We also detail a full qualitative analysis of the spatially homogeneous problem, and study the equilibria of the system in order to characterize the conditions under which fibrosis may occur. © 2010 Elsevier Ltd.

In this paper a macroscopic model of tumor cord growth is developed, relying on the mathematical theory of deformable porous media. Tumor is modeled as a saturated mixture of proliferating cells, extracellular fluid and extracellular matrix, that occupies a spatial region close to a blood vessel whence cells get the nutrient needed for their vital functions. Growth of tumor cells takes place within a healthy host tissue, which is in turn modeled as a saturated mixture of non-proliferating cells.

In this paper we propose a classification of crowd models in built environments based on the assumed pedestrian ability to foresee the movements of other walkers. At the same time, we introduce a new family of macroscopic models, which make it possible to tune the degree of predictiveness of the individuals.