On the generation of potential differences across the membranes of ellipsoidal cells in an alternating electrical field

Summary

Particles with a nonconducting membrane, oriented in an alternating electrical field, will show the behaviour of electrical dipoles. Across the membranes there will be generated alternating electrical potential differences, which may be calculated for confocal ellipsoidal cells by solving Laplace's equation. We have evaluated a formula valid generally for single confocal ellipsoidal cells under physiological conditions, the cells being placed with one of their semi-axes parallel to an external electrical field. The values of the generated potential difference, considered at the position of their maximum values, are dependent on the shape and size of the cells, on their orientation to the electrical field and on the frequency and strength of the field. The relaxation frequency depends also on cell shape, size and orientation, but furthermore on the membrane properties and on the conductivities inside and outside the cells. For simple cases like spheres and cylinders perpendicular to the electrical field, our formula will correspond to known expressions. Values for the generated potential differences, form-factors and relaxation frequencies are given for different types of spheroids and at different orientations. Of some practical importance are long prolate spheroids with their long semi-axes parallel to the external field, because only small field strengths are necessary in order to generate large potential differences which may evoke action potentialse.g. in muscle or nerve cells. The significance of this mechanism concerning the determination of protection and safeguard standards for the exposure to low-frequency electrical fields is discussed.