The induction of transmembrane potentials (Δϕ) by an external field is the basis of numerous applications in biotechnology, cell-technology and medicine. We have developed new, simplified analytical equations that avoid the complicated description by the depolarizing factors. The equations apply to the Δϕ induced in cells resembling ellipsoids of rotation, i.e. spheroids by homogeneous dc or ac fields. They will be especially useful for experimental scientists. The equations describe the dependence of the Δϕ on the electric media properties, the field frequency and the axis ratio for oblate and prolate spheroids for which the symmetry semiaxis (c) is shorter and longer than the other two semiaxes (a and b, with a = b), respectively. According to the Schwan equation, an electric field E may induce a maximum Δϕ of 1.5aE at the poles of a spherical cell. For the poles of spheroidal cells, the maxima can be easily described by Δϕ = (a + 2c)E/2 and Δϕ = a(a + 2c)E/(a + c) for fields oriented along and perpendicular to the symmetry axis, respectively. For practically important shapes the error in the magnitude of Δϕ is smaller than 5% except along the c-axis for axis ratios larger than 2. Nevertheless, the errors vanish for the three limiting shapes of infinitely thin disc, sphere and cylinder.
Electrorotation experiments are conducted in harmonic rotating fields to characterize the passive electric properties of cells or particles by their frequency-dependent rotation speed. The torque of the objects is proportional to the square of the field strength. Therefore, a rotating field of constant amplitude is desirable over a large area of the measuring chamber for reproducible measurements. In this study, the field distribution in chip chambers was analyzed using numerical field simulation in combination with analytical post-processing. The electric field distribution was compared for various electrode shapes. For the center, correction factors could be calculated, relating the actual field strength to the quotient of electrode voltage and distance. Apart from the center, the field was elliptically polarized with an eccentricity increasing with the distance from the center. A spherical model object has been assumed to derive a theoretical expression for the torque induced by an elliptical field. This model allowed us to consider the torque deviation for each site with respect to the torque induced by the circular center-field. Various electrode shapes have been checked for minimum deviations of the torque. We found the optimal chip design for electrorotation to feature electrodes with round tips.
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