A diffuse interface framework for modelling the evolution of multi-cell aggregates as a soft packing problem driven by the growth and division of cells

TL;DR

This paper introduces a diffuse interface model for simulating multi-cell cluster evolution, capturing cell growth, division, and packing with deformability constraints and contact mechanics.

Contribution

It develops a novel diffuse interface framework incorporating cell deformability, growth, division, and contact interactions for modeling multi-cell aggregates.

Findings

Demonstrates evolution of multi-cell clusters under growth and division.

Shows the impact of cell deformability on packing and energy.

Validates the model with numerical simulations of cell cluster dynamics.

Abstract

We present a model for cell growth, division and packing under soft constraints that arise from the deformability of the cells as well as of a membrane that encloses them. Our treatment falls within the framework of diffuse interface methods, under which each cell is represented by a scalar phase field and the zero level set of the phase field represents the cell membrane. One crucial element in the treatment is the definition of a free energy density function that penalizes cell overlap, thus giving rise to a simple model of cell-cell contact. In order to properly represent cell packing and the associated free energy, we include a simplified representation of the anisotropic mechanical response of the underlying cytoskeleton and cell membrane through appropriate penalization of the cell shape change. Numerical examples are presented to demonstrate the evolution of multi-cell clusters, and the total free energy of the clusters as a consequence of growth, division and packing.