Mathematical modeling of the evolution of a spherical cell aggregate in a viscous matrix. Formation of cell structures

Mathematical modeling of the development of spherically symmetrical structures in a cell ag-gregate surrounded by a viscous extracellular matrix was performed. The problem statement uses our previously developed multiphase continuum model of a biological medium formed by two ac-tively interacting solid phases and a liquid. One of the solid phases is formed by cells, the other by the extracellular matrix. The change in the radius of the spherical surface bounding the aggregate is determined by conditions that take into account the redistribution of the load between the cell phase and the matrix phase on opposite sides of the aggregate boundary. The influence of active interactions of cells both among themselves and with the matrix, as well as the initial composition of the cell aggregate on the process of redistribution of the volume concentrations of cells and matrix, was studied. Processes associated with cell division and the production of proteolytic en-zymes are not considered. Numerical calculations have shown that in the case of dominance of intercellular active mechanical interactions over cross interactions between cells and the matrix, only compaction of both loose and dense aggregates occurs - non-invasive development. In the case of dominance of active cross interactions over intercellular ones, the scenario of the devel-opment of cell structures depends on the initial volume concentration of cell phase. In loose ag-gregates, a heterogeneous distribution of the concentration of the cell phase is formed, which un-der certain conditions can develop into a hollow cell structure. In dense aggregates, a dense core is formed and part of the cell phase detaches from the main mass.