  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.
