Mechanical modelling of confined cell migration across constricted-curved micro-channels

Confined migration is a crucial phenomenon during embryogenesis, immune response and cancer. Here, a two-dimensional finite element model of a HeLa cell migrating across constricted-curved micro-channels is proposed. The cell is modelled as a continuum with embedded cytoplasm and nucleus, which are described by standard Maxwell viscoelastic models. The decomposition of the deformation gradient is employed to define the cyclic active strains of protrusion and contraction, which are synchronized with the adhesion forces between the cell and the substrate. The micro-channels are represented by two rigid walls and exert an additional viscous force on the cell boundaries. Five configurations have been tested: 1) top constriction, 2) top-bottom constriction, 3) shifted top-bottom constriction, 4) embedded obstacle and 5) bending micro-channel. Additionally, for the first four micro-channels both sub-cellular and sub-nuclear constrictions have been obtained, while for the fifth micro-channel three types of bending have been investigated ('curved', 'sharp' and 'sharper'). For each configuration, several parameters such as the cell behaviour, the covered distance, the migration velocity, the ratio between the cell and the nucleus area as well as the cell-substrate and cell-channel surfaces forces have been evaluated. The results show once more the fundamental role played by mechanics of both the cell and the environment.