Исследование движения сферического фронта клеток в вязком матриксе: роль клеточных делений и взаимодействия клеток с матриксом при развитии опухолей

Известия РАН. Механика жидкости и газа. 2026. № 3. С. 59–75.

Logvenkov S. A.

The problem of the evolution of cell volume fraction in a spherical aggregate composed of cells,
extracellular matrix, and fluid is considered. The aggregate is surrounded by extracellular matrix. The
problem formulation employs a multiphase model of a biological continuum, previously developed by the
author, consisting of two actively interacting solid phases and a fluid. The propagation of a spherical cell front
in a viscous matrix, resulting from cell division and active cellmatrix interactions, is investigated. Effects
associated with the production of proteolytic enzymes are neglected. The calculations show that, in the
absence of cell division, the dominance of active cellcell interactions over cellmatrix interactions leads to
aggregate compaction and a decrease in its radius. When active cross interactions dominate over cellcell
interactions, the evolution scenario depends on the initial cell density. A robust feature of the evolution
of loose aggregates is the formation of a prepattern for a hollow cellular structure. The evolution of dense
aggregates results in the formation of cellular structures that, depending on the matrix concentration, are
characterized either by the detachment of a small group of cells from the main mass, or by the formation
of a dense core surrounded by an expanding spherically symmetric layer of cells with low volume fraction
a pattern typical, in particular, of glioblastoma. It is shown that the velocity of the cell front depends nonmonotonically
on the concentration of the surrounding matrix. Cell division alters the evolution of dense
aggregates with dominant cell-cell interactions: instead of compaction, the aggregate radius increases, and
the spatial distribution of the cell phase takes the form of a slowly propagating front that displaces the matrix
a behavior characteristic, in particular, of meningiomas.

Keywords: клеточные системы, cell systems, active media, активные среды, континуальное моделирование, continuum modeling, tumor development, развитие опухолей