On continuum modeling of cell aggregation phenomena

Firooz, S., Kaessmair, S., Zaburdaev, V., Javili, A. and Steinmann, P. (2022) On continuum modeling of cell aggregation phenomena. Journal of the Mechanics and Physics of Solids, 167, 105004. (doi: 10.1016/j.jmps.2022.105004)

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Abstract

Cellular aggregates play a significant role in the evolution of biological systems such as tumor growth, tissue spreading, wound healing, and biofilm formation. Analysis of such biological systems, in principle, includes examining the interplay of cell–cell interactions together with the cell–matrix interaction. These two interaction types mainly drive the dynamics of cellular aggregates which is intrinsically out of equilibrium. Here we propose a non-linear continuum mechanics formulation and the corresponding finite element simulation framework to model the physics of cellular aggregate formation. As an example, we focus in particular on the process of bacterial colony formation as recently studied by Kuan et al. (2021). Thereby we describe the aggregation process as an active phase separation phenomenon. We develop a Lagrangian continuum description of the problem which yields a substantial simplification to the formulations of the governing equations. Due to the presence of spatial Hessian and Laplacian operators, a gradient-enhanced approach is required to incorporate C1 continuity. In addition, a robust and efficient finite element formulation of the problem is provided. Taylor–Hood finite elements are utilized for the implementation to avoid instabilities related to the LBB condition. Finally, through a set of numerical examples, the influence of various parameters on the dynamics of the cellular aggregate formation is investigated. Our proposed methodology furnishes a general framework for the investigation of the rheology and non-equilibrium dynamics of cellular aggregates.

Item Type:Articles
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Steinmann, Professor Paul
Authors: Firooz, S., Kaessmair, S., Zaburdaev, V., Javili, A., and Steinmann, P.
College/School:College of Science and Engineering > School of Engineering > Infrastructure and Environment
Journal Name:Journal of the Mechanics and Physics of Solids
Publisher:Elsevier
ISSN:0022-5096
ISSN (Online):1873-4782
Published Online:21 July 2022
Copyright Holders:Copyright © 2022 Elsevier Ltd.
First Published:First published in Journal of the Mechanics and Physics of Solids 167: 105004
Publisher Policy:Reproduced in accordance with the publisher copyright policy

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