Research On Modeling The Transmembrane Voltage Induced On A Cell Membrane In Suspensions Exposed To External Electric Fields

The transmembrane voltage 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 transmembrane voltage 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 transmembrane voltage induced on cells in biological and medical fields. The analytical model for transmembrane voltage on a single cell exposed to an external electrical fiel 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 transmembrane voltage on suspension cells is too complicated to obtain. Thus, in this paper, we used the approximate equivalence method to resolve this problem. Firstly, the average field inside the suspensions is calculated according to the effective medium theory. Secondly, 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 transmembrane voltage on the cells in suspensions were built as the following: Based on Schwan euation for calculating the transmembrane voltage on a single cell, some analytical models for transmembrane voltage on a cell in suspensions exposed to external direct fields were built according to the Maxwell, Bruggeman, Tobias equations, respectively. Then the transmemrane voltage on a cell in suspensions is calculated by using the proposed analytical model, and the results are compared with those from numerical calculation using finite-element method. It is shown that the analytical results are in agreement with the numerical results. During the exposure to external alternating fields, the permitivity of the membrane, cytoplasm and external medium vare with the change of the frequency. At different cell concentrations, Maxwell-Wagner and Bruggeman-Hanai equations were used respectively to derive an analytical model for transmembrane voltage on a cell in symmetrical suspensions exposed to external fiels at different frequency. During the derivation of the models, the first-order, the second-order and the inhanced second-order analytical models for transmembrane voltage on a single cell exposed to external fields were considered for the frequency range: f ≤100KHz,100KHz≤f ≤100MHz and f ≥100MHz, respectively. Since the conductivity of the membrane cannot be ignored and its distribution is asymmetric, a permeabilized cell in suspensions was replaced with a spheral body with a symmetric conductivity. Then the average field was calculated by using Maxwell and Tobias equations for dilute and dense suspensions, respectively. Finally, based on the equation for the transmembrane voltage on a single permeabilized cell, some analytical solutions for transmembrane voltae on cells in symmetrical suspensions were derived. The analytical models mentioned above show that the transmebrane voltage induced on a cell membrane in suspensions exposed to an external field depends on some parameters such as the amplitude of the external field, the location of the membrane site under consideration, the cell arrangement and the cell volume fraction. For an alternating field, the transmebrane voltage also depends on the permitivity of the membrane, the conductivity of the cytoplasm and external medium. If the frequency is above 100KHz, the permitivity of cytoplasm and external medium should be accounted for. For a permeablized cell in suspensions, the critical angle of electroporation must be accounted for the calculating the transmembrane voltage. Based on the analytical models built in this paper, some theoretical evaluations of the distributed power...