Study And Calculation Of Transmembrane Voltage Induced By The External Electric Field

Exposure of biological cells to electric fields can lead to a variety of biophysical and biochemical responses. Applications based on these responses can roughly be divided into two groups. The first group uses electric fields as a tool to modify various properties of the cells. Herein are the applications that utilize the increase in membrane permeability caused by electric fields for introduction of various molecules into cells, insertion of molecules into cell membranes, and fusion of cells. The second group of applications uses electric fields and currents as tools to characterize various properties of biological cells or their constituents, both in suspensions and in tissues. Among the most important approaches in such characterization is the evaluation of cell's response to electric fields at different frequencies.Consequently, various physical quantities of biological cell can be determined that are difficult to assess by direct measurement (e.g., conductivity and capacitance of the membrane and the cytoplasm). The basic mechanism underlying majority of these methods is the inducement of potential difference across the membrane by the external electric field, which results in the trans-membrane potential (TMP) and membrane electric field.The trans-membrane potential of the cells is a suitable parameter reflecting the life activity and function of cells. During the exposure to an electric field, the change of the trans-membrane potential can cause the remotion of the ions through the membrane. Then, the balance state of the ions which is necessary to keep the normal life activity is broken, and the physiological and biochemical state of the cells will be changed. Therefore, it is very important to build the analytical models for trans-membrane potential induced on cells in biological and medical fields. The analytical model for trans-membrane potential on a single cell exposed to an external electrical field has been well known for a long time. However, due to the asymmetrical distribution of conductivity and the interactions among the cells exposed to an external electric field, the analytical model for trans-membrane potential on suspension cells is too complicated to obtain. Thus, in this paper, the approximate equivalence method is used to resolve this problem. Firstly, the average field inside the suspensions is calculated according to the effective medium theory. Secondly, the average strength of electric field inside the suspensions is analyzed by using Laplace formula, and the condition under which the local electric field of an unit cell in suspensions is approximately similar to that of a single cell exposed to external field was investigated. Finally, based on the analytical solution of a single cell, some analytical models for the trans-membrane potential on the cells in suspensions are built.The model of trans-membrane potential proves feasible by discussing the consistency of numerical and analytical results with different cell volume fractions. The distributed power dissipation in membrane of the single cell is discussed. The results show that the power dissipation depends on the cell volume fraction, the symmetry, maximum and minimum. The equation may provide a plausible basis for studying the mechanism of the bio-electromagnetic effects. The trans-membrane potentials of normal and cancer cells are analyzed with different frequencies as to different physical parameters.Analytical descriptions of trans-membrane potential induced on spheroidal cells with zero membrane conductivity are deduced: DC steady state polarization of an oriented spheroidal cell; the parallel orientation of the symmetry axis and the field and the perpendicular orientation of the symmetry axis and the field. The well-known Schwan formula for calculation of single-cell TMV in DC field proves feasible.For the simplified cell properties assumed, it is possible to drive closed, analytical trans-membrane expressions in a very straightforward manner. In principle, such expressions have already existed for a long time. From a physical point of view, the equations describe the potential distribution on the surface of a spheroidal cavity in a dielectric. But they lack physiological cell properties. The deduced equations in the paper help study on the complex physiological conditions and external electric field.