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

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