Electric field-induced deformation of biological cells

Biological cells in general, and erythrocytes in particular, have been experimentally observed to undergo pronounced shape changes (or deformation) in the presence of an electric field. At high field strengths, deformation is believed to be caused by the mechanical rupture of the membranes, leading to the formation of pores that allow water and other small ions to enter the cells\u27 interiors which subsequently become swollen. At low field strengths the magnitude of the potential that develops across a cell membrane may be too small to cause mechanical rupture. This suggests that the mechanism for deformation may be due to another cause. The cell is modelled as an ellipsoid with shell and the surface stress distribution calculated by means of the Maxwell Stress Tensor. The cell membrane is treated as incompressible material having both bending and shear energies of deformation. Employing the principle of virtual work, cell volume (and hence shape) is computed as a function of the external field strength and orientation with respect to the field. The following results were obtained: (1) The surface stresses that develop on the cell membrane are distributed having both normal and tangential components that act together to produce a rounding of the cell. (2) If the tangential component of the stress is ignored, then higher field strengths are needed to produce similar deformation (shape change) of cells. (3) The threshold value of the applied field, i.e, the field strength at which the volume (shape) of the cell changes abruptly, occurs at approximately 55V/cm. Above the threshold value further increases in the applied field produce small changes in the cell volume (shape). (4) Ellipsoid-to-sphere transformation of the cell is independent of the orientation of the field with respect to the major semi-axis. (5) The hydrostatic pressure increases and the osmotic pressure decreases as the membrane becomes semi-permeable with increasing volume. At the equilibrium volume both pressures are equal. (6) Deformation of the cell can be accounted for, at least partially, by the mechanical stresses that develop across the membrane due to the application of the electric field