Oliver Jensen

Harmonic fields and the mechanical response of a cellular monolayer to ablation

The vertex model is a popular discrete framework with which to simulate multicellular tissues. It is widely used to investigate epithelia, cell layers that coat developing embryos or provide protective barriers within the body. Based on simple constitutive assumptions, the model relates the shapes of individual cells (which are easily measurable) to their mechanical environment (which is generally measured invasively). Following ablation of a single cell in a monolayer, vertex-model simulations predict that perturbation stress and displacement fields show an inverse square decay rate and long-range coherence, respectively. Seeking to explain these observations, we use tools of discrete exterior calculus to evaluate stress potentials, including the harmonic vector field of a punctured monolayer. This approach illustrates how some familiar continuum modelling techniques can be adapted to describe disordered microstructured materials.