Modeling of Transmembrane Potential in Realistic Multicellular Structures before Electroporation

Abstract

Many approaches for studying the transmembrane potential (TMP) induced during the treatment of biological cells with pulsed electric fields have been reported. From the simple analytical models to more complex numerical models requiring significant computational resources, a gamut of methods have been used to recapitulate multicellular environments in silico. Cells have been modeled as simple shapes in two dimensions as well as more complex geometries attempting to replicate realistic cell shapes. In this study, we describe a method for extracting realistic cell morphologies from fluorescence microscopy images to generate the piecewise continuous mesh used to develop a finite element model in two dimensions. The preelectroporation TMP induced in tightly packed cells is analyzed for two sets of pulse parameters inspired by clinical irreversible electroporation treatments. We show that high-frequency bipolar pulse trains are better, and more homogeneously raise the TMP of tightly packed cells to a simulated electroporation threshold than conventional irreversible electroporation pulse trains, at the expense of larger applied potentials. Our results demonstrate the viability of our method and emphasize the importance of considering multicellular effects in the numerical models used for studying the response of biological tissues exposed to electric fields.

Membrane permeabilization of mammalian cells using bursts of high magnetic field pulses

“…The non-homogeneous sample conductivity could be addressed by applying, high-frequency bipolar pulse protocols (H-FIRE) which mitigate the impedance differences (Bhonsle et al, 2015; Sano et al, 2015) but unfortunately require delivery of higher energy than longer unipolar irreversible electroporation (IRE) pulses (Murovec et al, 2016; Sweeney et al, 2016). However, universal protocols, which allow countering or optimising all the limitations described above, are still not available (Pakhomova et al, 2011; Blumrosen et al, 2016; Yildirim et al, 2016).…”

Simulation of the influence of voltage level and pulse spacing on the efficiency, aggressiveness and uniformity of the electroporation process in tissues using meshless techniques

“…At the microscopic cell level, an increase in pulse amplitude leads to an increase of the local electric field at a determined point of the tissue, with the corresponding increment of the TMP of the cells. As mentioned in Murovec et al, electroporation is possible when TMP exceeds a cell/tissue‐type dependent threshold. Thereby, at the cellular level, TMP is a commonly used parameter to quantify the influence of the pulse amplitude .…”

“…As mentioned in Murovec et al, electroporation is possible when TMP exceeds a cell/tissue‐type dependent threshold. Thereby, at the cellular level, TMP is a commonly used parameter to quantify the influence of the pulse amplitude . At the macroscopic tissue level, the pulse amplitude can be quantified as the voltage level applied between plates (Δ V ) or as the corresponding average magnitude of electric field ( E av ), as related by where D represents the tissue thickness.…”

“…Thereby, at the cellular level, TMP is a commonly used parameter to quantify the influence of the pulse amplitude. 8,53,56,92 At the macroscopic tissue level, the pulse amplitude can be quantified as the voltage level applied between plates (ΔV) or as the corresponding average magnitude of electric field (E av ), as related by…”

Assessing the electro-deformation and electro-poration of biological cells using a three-dimensional finite element model

“…However, most of the existing numerical and analytical studies have tackled the modelling of this phenomenon based on various assumptions and constraints to predict and evaluate cell and tissue EP. [1][2][3][4][5][6][7][8][9][10][11][12][13][14] Typically, EP takes place when the transmembrane potential (TMP) exceeds a threshold V ep above which electrically conductive pores start forming in the membrane. [1][2][3] Experimental estimates for V ep fall in the range of 0.5-1.2 V but theoretical estimates point to V ep ¼ 0.258 V. 15 Most of the existing studies have so far assumed that cell membranes are rigid.…”