Speaker
Description
The rate at which biological tissues grow is regulated by the interplay between geometry, cell mechanics, and cellular processes. In scenarios where tissue growth occurs primarily at the surface of a confined environment -- such as bone remodelling, wound healing, and tissue growth within engineered scaffolds -- cells compete for space as they deposit new material. This competition leads to cell crowding or spreading depending on substrate curvature and generates mechanical stresses that may influence cellular processes including proliferation, differentiation, and survival. We present a discrete mathematical model for simulating tissue growth in confined geometries. The tissue interface is represented as a chain of mechanically interacting cells (modelled as springs) that simultaneously generate new tissue material. To more accurately capture cell population dynamics during tissue growth, we incorporate cell proliferation, death, and embedment as stochastic processes. To describe the collective behaviour of the cell population, we derive a continuum limit by representing each cell with $m$ subcellular mechanical components and taking the limit as $m\to\infty$. This derivation yields a reaction–diffusion partial differential equation governing the evolution of cell density along a moving interface parameterised by arc length.
