On continuum modeling of cell aggregation phenomena

TL;DR

This paper introduces a novel continuum mechanics and finite element simulation framework to model cellular aggregate formation, focusing on bacterial colonies as active phase separation phenomena, with insights into parameter influences on dynamics.

Contribution

It presents a new Lagrangian continuum model and finite element approach for simulating cell aggregation, incorporating gradient-enhanced methods for stability and efficiency.

Findings

The model successfully captures the dynamics of bacterial colony formation.

Parameter variations significantly affect aggregation behavior.

The framework provides a versatile tool for studying non-equilibrium cellular systems.

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. 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.