Bubbly vertex dynamics: a dynamical and geometrical model for epithelial tissues with curved cell shapes

TL;DR

This paper introduces a novel vertex model for epithelial tissues that incorporates cell boundary curvatures and pressures, providing a more accurate mathematical and physical representation of tissue dynamics.

Contribution

It develops a new vertex model that explicitly includes cell boundary curvatures and pressures, enhancing the realism of tissue simulations.

Findings

Model successfully incorporates curvature and pressure effects.

Simulation algorithm for the new model is provided.

Potential extensions and applications discussed.

Abstract

In order to describe two-dimensionally packed cells in epithelial tissues both mathematically and physically, there have been developed several sorts of geometrical models, such as the vertex model, the finite element model, the cell-centered model, the cellular Potts model. So far, in any case, pressures have not neatly been dealt with and curvatures of the cell boundaries have been even omitted through their approximations. We focus on these quantities and formulate them on the vertex model. Thus, a model with the curvatures is constructed and its algorithm is given for simulation. Its possible extensions and applications will also be discussed.