Cell modelling with applications to cell-wall interactions

This thesis investigates the dynamics of cells in linear shear flow near a plane wall. The first part of the thesis focuses on a two-dimensional model of a tethered cell to elucidate the effects of cell aspect ratio and cell internal viscosity on cell dynamics. Over the parameter space examined, the cell initially elongates out into the flow and then slowly pivots towards the wall as the cell relaxes to a steady-state shape. The region of the cell membrane that would come into contact with the wall corresponds with a region of elevated shear stress. The effect of viscosity is found to be negligible at low shear rates, but at high shear rates an increase in internal viscosity leads to an increase in cell deformation and force on the tether. At low shear rates, cells with higher aspect ratios experience less force and deformation. Conversely, at high shear rates cells with higher aspect ratios experience greater force and deformation. The second part of the thesis presents the results for a three-dimensional model of a single cell moving in close proximity to a wall. The effect of cell height and cell deformability on the dynamics of the cell is determined. The deformability of the cell is controlled by the shear rate, area-dilation parameter and amount of membrane prestress. The shear-stress distribution on the vessel wall is described. The presence of a cell has a marked effect on the shear-stress distribution, with regions of elevated shear stress apparent both upstream and downstream of the cell. A stiff cell moves slower than a more deformable cell, allowing it to approach the wall more easily. A more deformable cell presents a larger surface to the wall and creates a larger region of elevated shear stress on the wall immediately upstream. The effect of the presence of multiple cells on cell dynamics is presented in the third part of the thesis. Cells moving side-by-side have a tendency to move away from one another. The presence of a downstream cell causes the upstream cell to move towards and below the downstream cell. The presence of a downstream cell also provides a larger region of elevated shear stress on the vessel wall. The presence of multiple cells in the flow increases the slip velocity of both cells markedly, independent of the configuration of the cells.