Biomechanics of cell membrane under low-frequency time-varying magnetic field: a shell model

Cell membrane deforms in the electromagnetic field, suggesting an interesting control of cellular physiology by the field. Previous research has focused on the biomechanical analysis of membrane deformation under electric fields that are generated by electrodes. An alternative, noninvasive method to generate an electric field is the use of electromagnetic induction with a time-varying magnetic field, such as that used for transcranial magnetic stimulation (TMS). Although references reporting the magnetic control of cellular mechanics have recently emerged, theoretical analysis of the membrane biomechanics under a time-varying magnetic field is inadequate. We developed a cell model that included the membrane as a low-conductive, capacitive shell and investigated the electric pressure generated on the membrane by a low-frequency magnetic field (0-200 kHz). Our results show that externally applied magnetic field induced surface charges on both sides of the membrane. The charges interacted with the induced electric field to produce a radial pressure upon the membrane. Under the low-frequency range, the radial pressure pulled the cell membrane along the axis that was defined by the magnetically induced electric field. The radial pressure was a function of the field frequency, the conductivity ratio of the cytoplasm to the medium, and the size of the cell. It is quantitatively insignificant in deforming the membrane at the frequency used in TMS, but could be significant at a relatively higher-frequency range (>100 kHz).