The Effective Conductivity and the Induced Transmembrane Potential in Dense Cell System Exposed to DC and AC Electric Fields

Abstract

Abstract-Studying electric potential distribution on the cell membrane and electric conductivity gives us an insight into the effects of the electric field on cells and tissues. Since cells are always surrounded by other cells, we studied how their interactions influence the induced transmembrane potential (TMP) and the effective conductivity in dense cell systems. We numerically and analytically studied the effect of cell organization on the induced TMP and the effective conductivity by organizing cells into simple-cubic, body-centered cubic, and face-centered infinite cubic lattices. We analyzed the general relation between the local quantities (electric field and the induced TMP) and the effective properties such as effective conductivity. We demonstrated that the effective conductivity mainly depends on cell volume fraction, while the induced TMP is affected by cell volume fraction as well as cell ordering. We show that in contrast to some reported results, the phenomenological effective medium theory (EMT) equations cannot be used to determine the local quantities (e.g., the induced TMP) in dense cell systems, whereas the effective properties (e.g., conductivity) can be readily analyzed with EMT equations. We further derive an analytical approximation for the induced TMP in dense cell system exposed to dc and ac electric fields, where dominant factors, which govern the local electric field and the induced TMP, are cell volume fraction and cell ordering. The presented theoretical analysis can be extended also to high frequencies or random distribution of cells.Index Terms-Dense cell system, effective conductivity, frequency domain, numerical methods, transmembrane potential (TMP).

An Overview of Sub-Cellular Mechanisms Involved in the Action of TTFields

“…Another important aspect is the frequency-dependency of the induced trans-membrane voltage and thus also the intracellular field strength, as predicted by the above-mentioned studies and additional research reported elsewhere [30,31,32,33,34]. For low frequencies, the intracellular space is shielded to a large degree from extracellular electric fields.…”

Fundamental study on a gene transfection methodology for mammalian cells using water-in-oil droplet deformation in a DC electric field

“…EP generates transient pores in the cell membrane when the transmembrane potential exceeds a critical threshold value, altering the permeability of the membrane by application of an external electric field [1] , [2] . Many theoretical [3] , [4] , [5] , [6] , [7] and experimental [6] , [7] , [8] , [9] , [10] , [11] approaches have been investigated in an attempt to explain the mechanisms underlying EP, especially those involved in gene transfer. Advanced EP devices have been developed by combining microfabrication techniques and microfluidics [12] , [13] , [14] , [15] , [16] , [17] , [18] , [19] .…”

Modelling extracellular electrical stimulation: III. Derivation and interpretation of neural tissue equations

“…Several previous studies have provided theoretical estimates of the electrical properties of tissue on the basis of their cellular composition. Several studies have considered tissue as a collection of cells sparsely suspended in an extracellular medium [15,30,31,44], however this is not the situation considered here of densely packed, elongated fibres, which is characteristic of neural tissue.…”