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

Author (s): Mosaffa, P.; Rodríguez-Ferran, A.; Muñoz, J.J.
Journal: International Journal for Numerical Methods in Biomedical Engineering

Volume: 34
Pages: 1 – 28
Date: 2018

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 seamless manner by modifying a numerical parameter of the model.

Journal paper (from the publisher)  
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Bibtex:

@article{MOSAFFA2017,
title = "Hybrid cell-centred/vertex model for multicellular systems with equilibrium-preserving remodelling",
journal = "International Journal for Numerical Methods in Biomedical Engineering",
volume = “34”,
number = “3”,
pages = “e2928”,
year = "2018”,
note = "",
issn = “2040-7947",
doi = "",
url = "",
author = “Payman Mosaffa and Antonio Rodríguez-Ferran and José J Muñoz”,
keywords = "cell-centred",
keywords = "vertex model",
keywords = "remodelling",
keywords = "tessellation”,
keywords = "biomechanics”,
keywords = "tissues”,
}