On continuum modeling of cell aggregation phenomena

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