A Theoretical Analysis of the Effects of Tumor‐Treating Electric Fields on Single Cells

Abstract

Tumor-treating fields (TTFields) are low-intensity and intermediate-frequency alternating electric fields that have been found to inhibit tumor cell growth. While effective, the mechanism by which TTFields affect cell growth is not yet clearly understood. Although numerous mathematical studies on the effects of electromagnetic fields on single cells exist, the effect of TTFields on single cells have been analyzed less frequently. The goal of this study is to explore through a mathematical analysis the effects of TTFields on single cells, with particular emphasis on the thermal effect. We examine herein two singlecell models, a simplified spheroidal model and a simulation of a U-87 MG glioblastoma cell model obtained from microscopic images. A finite element method is used to analyze the electric field distribution, electromagnetic loss, and thermal field distribution. The results further prove that the electric field in the cytoplasm is too weak and its thermal damage can be excluded as a mechanism for cell death in TTFields. Bioelectromagnetics. 2020;41:438-446.

Permeabilizing Cell Membranes with Electric Fields

“…A second piece of evidence supporting TTFields’ effects on cell membranes comes from finite element modeling in which a modified Schwan equation was the governing model for membrane depolarization (along with the Laplace equation for electric field distribution). Li et al [ 51 ] predicted that TTFields depolarize the cell membrane by 10-17%, which may be enough to open membrane Ca v 2+ channels [ 51 ] and, at TTFields’ frequency, would likely ‘freeze’ the channels in an open state.…”

“…Various studies have shown the effectiveness of using irreversible electroporation to induce tumor ablation and suggest that its ability to target malignant cells is due to plasma membrane differences between cancer and non-cancer cells [ 67 , 68 ]. The V m of both non-cancer and cancer cells depolarizes during proliferation, to about −15 mV, but post-mitotic non-cancer cells return to a typical resting V m of −70 mV whereas post-mitotic cancer cells achieve a resting V m of −25 mV [ 51 , 69 ]. The depolarized resting V m in cancer cells relative to that in non-cancer cells is thought to be caused by altered lipid and sterol membrane composition, which results in an influx of sodium ions into the cell and a collection of negative charges on the cell coat [ 70 ].…”

“…To illustrate, DNA itself possesses intrinsic dipole moments and recent investigations have revealed that TTFields may have effects on DNA damage response and replication stress, ER stress, membrane permeability, autophagy, and immune response [ 5 ]. In addition, recent modeling studies in the context of dipole alignment suggest that the magnitude of the electric field caused by TTFields may not be sufficient to overcome Brownian motion inherent within the cytoplasm of single cancer cells [ 51 , 69 ]. TTFields have been shown to affect other cellular structures.…”

“…Augmentation of field strength in adjacent membrane regions of densely packed cells (i.e., the tissue level) may lead to values that would be concordant with either the bioelectrorheological or electroporation models. Indeed, research by some of us (co-authors TM and ZB, personal communication) shows that finite element modeling predicts that when cells are in close proximity to each other, electric field lines are concentrated between the contact points in a frequency-dependent manner [ 51 , 69 ]. The unexpectedly high field strengths achieved in these regions may remove the obstacle of electric field strength being insufficient for bioelectrorheological and electroporative processes to be able to explain the empirical observation of membrane fenestration due to TTFields [ 27 ].…”

“…Since resting cancer cells are relatively depolarized compared to non-cancer cells, the same phenomenon likewise provides an explanation for TTFields’ effect on cancer but not non-cancer cells as the former needs less field strength concentrations to trigger an effect. Certainly, the recent work of Li et al [ 51 , 69 ] suggests that the membrane potential could serve as an important read-out to monitor in studies of TTFields. This may not be surprising given that the resting V m of cancer cells is depolarized relative to that of non-cancer cells [ 28 , 29 , 30 , 31 , 73 , 74 , 75 ].…”