Approximation of 2D and 3D Models of Chemotactic Cell Movement in Vasculogenesis

Cell migration plays a central role in a wide variety of biological phenomena. In
the case of chemotaxis, cells (or an organism) move in response to a chemical
gradient. Chemotaxis underlies many events during embryo development and
in the adult body. An understanding of chemotaxis is not only gained through
laboratory experiments but also through the analysis of model systems, which
often are more amenable to manipulation. This work is concerned with the
relaxation schemes for the numerical approximation of a 2D and 3D model
for cell movement driven by chemotaxis. More precisely, we consider models
arising in the description of blood vessels formation and network formation
starting from a random cell distribution