The mechanics of biological growth: a study through the vertex model

This thesis work aims to investigate the mechanical behavior of biological tissues composed of polygonal cells, tightly arranged in networks, and how their behavior is influenced by the geometric and mechanical properties of each cell. This understanding is vital for the modeling of biological processes like tissue growth, wound healing, and cancer progression. Specifically, the study employs the so-called vertex model, a computational framework that describes cells as polygons, with vertices as cell junctions and edges as cell boundaries, and which attributes to each cell a quadratic elastic energy, describing a penalization from target values of area and perimeter. This model incorporates physical properties such as area stiffness, perimeter stiffness, and line tension to simulate tissue mechanics under various conditions.