A polarization model overcoming the geometric restrictions of the laplace solution for spheroidal cells: Obtaining new equations for field-induced forces and transmembrane potential

We present a new model for a variety of electric polarization effects on ob late and prolate homogeneous and single-shell spheroids. For homogeneous sp heroids the model is identical to the Laplace model. For single-shell spher es of cell-like geometry the calculated difference of the induced dipole mo ments is in the thousandths range. To solve Laplace's equation for nonspher ical single-shell objects it is necessary to assume a confocal shell, which results in different cell membrane properties in the pole and equator regi ons, respectively. Our alternative model addresses this drawback. It assume s that the disturbance of the external field due to polarization may projec t into the medium to a characteristic distance, the influential radius. Thi s parameter is related to the axis ratio of the spheroid over the depolariz ing factors and allows us to determine the geometry for a finite resistor-c apacitor model. From this model the potential at the spheroid's surface is obtained and, consequently, the local field inside a homogeneous spheroid i s determined. In the single-shell case, this is the effective local field o f an equivalent homogeneous spheroid. Finally, integration over the volume yields the frequency-dependent induced dipole moment. The resistor-capacito r approach allowed us to find simple equations for the critical and charact eristic frequencies, force plateaus and peak heights of deformation, dielec trophoresis and electrorotation for homogeneous and single-shell spheroids, and a more generalized equation for the induced transmembrane potential of spheroidal cells.