# Hybrid cell-centred/vertex model for multicellular systems with equilibrium-preserving remodelling

## TL;DR

This paper introduces a hybrid vertex and cell-centred model for simulating planar cellular monolayers, focusing on cell remodelling while preserving mechanical equilibrium through an innovative mapping technique.

## Contribution

The paper presents a novel hybrid modeling approach combining vertex and cell-centred methods with an equilibrium-preserving remodelling technique for cellular systems.

## Key findings

- The model accurately simulates cell reorganisation and wound healing.
- The equilibrium-preserving mapping maintains mechanical stability during remodelling.
- The technique seamlessly transitions between vertex and cell-centred models.

## Abstract

We present a hybrid vertex/cell-centred model for mechanically simulating planar cellular monolayers undergoing cell reorganisation. Cell centres are represented by a triangular nodal network, while the cell boundaries are formed by an associated vertex network. The two networks are coupled through a kinematic constraint which we allow to relax progressively. Special attention is paid to the change of cell-cell connectivity due to cell reorganisation or remodelling events. We handle these situations by using a variable resting length and applying an Equilibrium-Preserving Mapping (EPM) on the new connectivity, which computes a new set of resting lengths that preserve nodal and vertex equilibrium. We illustrate the properties of the model by simulating monolayers subjected to imposed extension and during a wound healing process. The evolution of forces and the EPM are analysed during the remodelling events. As a by-product, the proposed technique enables to recover fully vertex or fully cell-centred models in a seamlessly manner by modifying a numerical parameter of the model.