Three-Dimensional Continuum Model of Lumen Formation in a Cluster of Cells Immersed in an Extracellular Matrix: The Role of Mechanical Factors

The extent of participation of mechanisms such as the active interactions of cells with each other and with the extracellular matrix, the increased hydrostatic pressure in intercellular fluid, and enzymatic activity of cells that lead to the destruction of the extracellular matrix in the process of formation of cavities in clusters of cells formed during cluster vasculogenesis is studied. The problem of evolution of a single cluster of cells immersed in a deformable extracellular matrix is solved within the framework of a previously developed continuum multiphase model of the medium formed by two actively interacting solid phases and a fluid and the role of various cellular mechanisms discussed in the formation of hollow structures is studied. The calculations showed that the dominance of active interactions of the cell-matrix type over the intercellular interactions leads to a displacement of cells towards the outer boundary of the cluster and the creation of conditions for the formation of a cavity inside the cluster. The enzymatic activity of cells helps to free up a headroom for compaction of the cluster, due to the active intercellular interactions, and to slow down the formation of the increasing concentration profile of the cellular phase. An increase in the fluid pressure in the area occupied by cells leads to acceleration of the redistribution of concentrations of the cellular phase and matrix. The fluid pressure promotes accumulation of the cellular phase near the cluster boundary and increase in the matrix concentration in its central part. And only the joint participation of all the mechanisms considered leads to the formation of a structure in which a layer formed by the cellular phase surrounds a fluid-occupied cavity, while the matrix concentration in the cavity demonstrates the trend to its complete disappearance.