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

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Abstract

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).

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Abbreviations

B o :

Intensity of the time-varying magnetic field (T)

E :

Intensity of the electric field induced by time-varying magnetic field (V/m)

ρ s01 :

Surface charge density on the medium/membrane interface (C/m2)

ρ s12 :

Surface charge density on the membrane/cytoplasm interface (C/m2)

Q s01 :

Net induced surface charges on the medium/membrane interface (C)

Q s12 :

Net induced surface charges on the membrane/cytoplasm interface (C)

P r01 :

Surface pressure on the medium/membrane interface (N/m2)

P r12 :

Surface pressure on the membrane/cytoplasm interface (N/m2)

P r :

Net surface pressure on the cell membrane (N/m2)

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Acknowledgments

The authors thank the Research Support Grant from Loyola University Chicago. Amanda Steiger assisted with the revision of the manuscript.

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  1. Department of Biology, Quinlan Life Sciences Education and Research Center, Loyola University Chicago, 1032 W. Sheridan Rd., Chicago, IL, 60660, USA

    Hui Ye

  2. Department of Physics, Loyola University Chicago, 1032 W. Sheridan Rd., Chicago, IL, 60660, USA

    Austen Curcuru

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Correspondence to Hui Ye.

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Ye, H., Curcuru, A. Biomechanics of cell membrane under low-frequency time-varying magnetic field: a shell model. Med Biol Eng Comput 54, 1871–1881 (2016). https://doi.org/10.1007/s11517-016-1478-9

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