Polarisation and membrane voltage of ellipsoidal particle with a constant membrane thickness: a series expansion approach

The estimation of the membrane voltage and the polarisation factor of biological cells provide a base for the study of bio-manipulation techniques, such as dielectrophoresis, electroporation or electrofusion. To model a biological cell, an ellipsoidal particle with an insulating membrane is sometimes employed, but due to the limitation of the confocal nature of the coordinate system, the membrane thickness is assumed to vary with the position, despite the fact that the lipid bilayer membrane has a uniform thickness. The authors present a method to rigorously treat the uniform-thickness condition in a system having an axial symmetry. The method is based on the harmonic expansion of the field, to include the condition of the uniform- membrane thickness as a series expansion of the geometrical factor, and to solve the field problem as an interaction of the harmonic components. The conventional variable thickness model has been identified as being equivalent to neglecting the harmonic interactions in the uniform-thickness model. Numerical calculations are done of the membrane voltage and the polarisation factor, and it has been found that the discrepancy between the proposed rigorous model and the conventional variable thickness model becomes significant when field deformation is large due to the high axial ratio of the ellipsoid.