Theoretical analysis of transmembrane potential of cells exposed to nanosecond pulsed electric field

Abstract

Purpose: Intracellular electroporation occurs when the cells are exposed to nanosecond pulsed electric field (nsPEF). It is believed the electroporation (formation and extension of pores on the membrane induced by external electric field) is affected significantly by the transmembrane potential. This paper analyzed transmembrane potential induced by nsPEF in the term of pulse frequency spectrum, aiming to provide a theoretical explanation to intracellular bio-effects.

Methods: Based on the double-shelled spherical cell model, the frequency dependence of transmembrane potential was obtained by solving Laplace’s equation, while the time course of transmembrane potential was obtained by a method combined with discrete Fourier transform and Laplace transform. First-order Debye equation was used to describe the dielectric relaxation of the cell medium.

Results: Frequency-domain analysis showed that when the electric field frequency was higher than 10⁵ Hz, the transmembrane potential on the organelle membrane (ΔΦ_o) was increasing to exceed the transmembrane potential on the cellular membrane (ΔΦ_c). In the time-domain analysis, transmembrane potentials induced by four nsPEF (short trapezoid, long trapezoid, bipolar and sine shapes) with the same field strength were compared with each other. It showed that ΔΦ_o is obviously larger than ΔΦ_c if the curve of the normalized frequency spectrum of the pulse is more similar with the curve of normalized ΔΦ_o in frequency domain. Pulses with major frequency components higher than 10⁸ Hz lead to both small ΔΦ_o and ΔΦ_c. This may explain why high power pulsed microwave lead to unobvious bio-effects of cells than nsPEF with trapezoid form.

Conclusion: Through the pulse frequency spectrum it is clearer to understand the relationship between nsPEF and the transmembrane potential.

Keywords:

• Computational model
• Debye dispersion
• frequency spectrum
• time-domain

Disclosure statement

The authors report no conflicts of interest. The authors alone are response for the content and writing of the paper.

Funding

This work is funded by the National Natural Science Foundation of China (NSFC), grant 61101032 and the National Basic Research Program of China (973 Program), grant 2011CB503706.