Simulation study on electroporation of cancer cells in multicellular system

Electroporation (EP) of the normal cell and cancer cell both in single-cell and multicellular models was investigated by the meshed transport network method (MTNM) in this paper. The simulation results suggest that the cancer cell undergoes faster and more significant local EP than that of the corresponding normal cell induced by nanosecond pulsed electric fields (nsPEFs) both in single-cell and multicellular models. Furthermore, the results of the multicellular model indicate that there is a unidirectional neighboring effect in the multicellular model, meaning that cells at the center are affected and their pore formation is significantly reduced, but this effect is very weak for cells at the edges of the system. This means that the electric field selectively kills cells in different distribution locations. This work can provide guidance for the selection of parameters for the cancer cell EP process.

A microdosimetry analysis of reversible electroporation in scattered, overlapping, and cancerous cervical cells

We present a numerical method for studying reversible electroporation on normal and cancerous cervical cells. This microdosimetry analysis builds on a unique approach for extracting contours of free and overlapping cervical cells in the cluster from the Extended Depth of Field (EDF) images. The algorithm used for extracting the contours is a joint optimization of multiple-level set function along with the Gaussian mixture model and Maximally Stable Extremal Regions. These contours are then exported to a multi-physics domain solver, where a variable frequency pulsed electric field is applied. The trans-Membrane voltage (TMV) developed across the cell membrane is computed using the Maxwell equation coupled with a statistical approach, employing the asymptotic Smoluchowski equation. The numerical model was validated by successful replication of existing experimental configurations that employed low-frequency uni-polar pulses on the overlapping cells to obtain reversible electroporation, wherein, several overlapping clumps of cervical cells were targeted. For high-frequency calculation, a combination of normal and cancerous cells is introduced to the computational domain. The cells are assumed to be dispersive and the Debye dispersion equation is used for further calculations. We also present the resulting strength-duration relationship for achieving the threshold value of electroporation between the normal and cancerous cervical cells due to their size and conductivity differences. The dye uptake modulation during the high-frequency electric field electroporation is further advocated by a mathematical model.

Dispersive Modeling of Normal and Cancerous Cervical Cell Responses to Nanosecond Electric Fields in Reversible Electroporation Using a Drift-Step Rectifier Diode Generator

This paper creates an approximate three-dimensional model for normal and cancerous cervical cells using image processing and computer-aided design (CAD) tools. The model is then exposed to low-frequency electric pulses to verify the work with experimental data. The transmembrane potential, pore density, and pore radius evolution are analyzed. This work adds a study of the electrodeformation of cells under an electric field to investigate cytoskeleton integrity. The Maxwell stress tensor is calculated for the dispersive bi-lipid layer plasma membrane. The solid displacement is calculated under electric stress to observe cytoskeleton integrity. After verifying the results with previous experiments, the cells are exposed to a nanosecond pulsed electric field. The nanosecond pulse is applied using a drift-step rectifier diode (DSRD)-based generator circuit. The cells' transmembrane voltage (TMV), pore density, pore radius evolution, displacement of the membrane under electric stress, and strain energy are calculated. A thermal analysis of the cells under a nanosecond pulse is also carried out to prove that it constitutes a non-thermal process. The results showed differences in normal and cancerous cell responses to electric pulses due to changes in morphology and differences in the cells' electrical and mechanical properties. This work is a model-driven microdosimetry method that could be used for diagnostic and therapeutic purposes.

Engineering high post-electroporation viabilities and transfection efficiencies for elongated cells on suspended nanofiber networks

The impact of cell shape on cell membrane permeabilization by pulsed electric fields is not fully understood. For certain applications, cell survival and recovery post-treatment is either desirable, as in gene transfection, electrofusion, and electrochemotherapy, or is undesirable, as in tumor and cardiac ablations. Understanding of how morphology affects cell viability post-electroporation may lead to improved electroporation methods. In this study, we use precisely aligned nanofiber networks within a microfluidic device to reproducibly generate elongated cells with controlled orientations to an applied electric field. We show that cell viability is significantly dependent on cell orientation, elongation, and spread. Further, these trends are dependent on the external buffer conductivity. Additionally, we see that cell survival for elongated cells is still supported by the standard pore model of electroporation. Lastly, we see that manipulating the cell orientation and shape can be leveraged for increased transfection efficiencies when compared to spherical cells. An improved understanding of cell shape and pulsation buffer conductivity may lead to improved methods for enhancing cell viability post-electroporation by engineering the cell morphology, cytoskeleton, and electroporation buffer conditions.

The Importance of Subcellular Structures to the Modeling of Biological Cells in the Context of Computational Bioelectromagnetics Simulations

Numerical investigation of the interaction of electromagnetic fields with eukaryotic cells requires specifically adapted computer models. Virtual microdosimetry, used to investigate exposure, requires volumetric cell models, which are numerically challenging. For this reason, a method is presented here to determine the current and volumetric loss densities occurring in single cells and their distinct compartments in a spatially accurate manner as a first step toward multicellular models within the microstructure of tissue layers. To achieve this, 3D models of the electromagnetic exposure of generic eukaryotic cells of different shape (i.e. spherical and ellipsoidal) and internal complexity (i.e. different organelles) are performed in a virtual, finite element method-based capacitor experiment in the frequency range from 10 Hz to 100 GHz. In this context, the spectral response of the current and loss distribution within the cell compartments is investigated and any effects that occur are attributed either to the dispersive material properties of these compartments or to the geometric characteristics of the cell model investigated in each case. In these investigations, the cell is represented as an anisotropic body with an internal distributed membrane system of low conductivity that mimics the endoplasmic reticulum in a simplified manner. This will be used to determine which details of the cell interior need to be modeled, how the electric field and the current density will be distributed in this region, and where the electromagnetic energy is absorbed in the microstructure regarding electromagnetic microdosimetry. Results show that for 5 G frequencies, membranes make a significant contribution to the absorption losses. © 2023 The Authors. Bioelectromagnetics published by Wiley Periodicals LLC on behalf of Bioelectromagnetics Society.

Dielectric Dispersion Modulated Sensing of Yeast Suspension Electroporation

A specific pulsed electric field protocol can be used to induce electroporation. This is used in the food industry for yeast pasteurization, in laboratories for generic transfer and the medical field for cancer treatment. The sensing of electroporation can be done with simple ‘instantaneous’ voltage-current analysis. However, there are some intrinsic low-frequency phenomena superposing the electroporation current, such as electrode polarization. The biological media are non-homogeneous, giving them specific characterization in the broad frequency spectrum. For example, the cell barrier, i.e., cell membrane, causes so called β-dispersion in the frequency range of tens to thousands of kHz. Electroporation is a dynamic phenomenon characterized by altering the cell membrane permeability. In this work, we show that the impedance measurement at certain frequencies could be used to detect the occurrence of electroporation, i.e., dielectric dispersion modulated sensing. This approach may be used for the design and implementation of electroporation systems. Yeast suspension electroporation is simulated to show changes in the frequency spectrum. Moreover, the alteration depends on characteristics of the system. Three types of external buffers and their characteristics are evaluated.

Polymer Nanoparticles Enhance Irreversible Electroporation In Vitro

Expanding the volume of an irreversible electroporation treatment typically necessitates an increase in pulse voltage, number, duration, or repetition. This study investigates the addition of polyethylenimine nanoparticles (PEI-NP) to pulsed electric field treatments, determining their combined effect on ablation size and voltages. U118 cells in an in vitro 3D cell culture model were treated with one of three pulse parameters (with and without PEI-NPs) which are representative of irreversible electroporation (IRE), high frequency irreversible electroporation (H-FIRE), or nanosecond pulsed electric fields (nsPEF). The size of the ablations were compared and mapped onto an electric field model to describe the electric field required to induce cell death. Analysis was conducted to determine the role of PEI-NPs in altering media conductivity, the potential for PEI-NP degradation following pulsed electric field treatment, and PEI-NP uptake. Results show there was a statistically significant increase in ablation diameter for IRE and H-FIRE pulses with PEI-NPs. There was no increase in ablation size for nsPEF with PEI-NPs. This all occurs with no change in cell media conductivity, no observable degradation of PEI-NPs, and moderate particle uptake. These results demonstrate the synergy of a combined cationic polymer nanoparticle and pulsed electric field treatment for the ablation of cancer cells. These results set the foundation for polymer nanoparticles engineered specifically for irreversible electroporation.

Reversible electroporation study of realistic normal and cancerous cervical cells model using avalanche transistor-based nano pulse generator

In this paper, we study the reversible electroporation process on normal and cancerous cervical cells. The 2D contour of the cervical cells is extracted using image processing techniques from the Pap smear images. The conductivity change in the cancer cell model has been used to differentiate the effects of the high-frequency electric field on normal and cancerous cells. The cells' dielectric constant modulates when this high-frequency pulse is applied based on the Debye relaxation. To computationally visualize the effects of the electroporation on the cell membrane, the Smoluchowski equation is employed to estimate pore density, and Maxwell equations are used to determine the electric potential developed across the membrane of the cervical cell. The results demonstrate the suitability of this mathematical model for studying the response of normal and cancerous cells under electric stress. The electric field is supplied with the help of a realistic pulse generator which is designed on the principle of Marx circuit and avalanche transistor-based operations to produce a Gaussian pulse. The paper here uses a strength-duration curve to differentiate the electric field and time in nanoseconds required to electroporate normal and cancerous cells.

Experimental and Numerical Study of Electroporation Induced by Long Monopolar and Short Bipolar Pulses on Realistic 3D Irregularly Shaped Cells

In this article, the reversible electroporation induced by rectangular long unipolar and short bipolar voltage pulses on 3D cells is studied. The cell geometry was reconstructed from 3D images of real cells obtained using the confocal microscopy technique. A numerical model based on the Maxwell and the asymptotic Smoluchowski equations has been developed to calculate the induced transmembrane voltage and pore density on the plasma membrane of real cells exposed to the pulsed electric field. Moreover, in the case of the high-frequency pulses, the dielectric dispersion of plasma membranes has been taken into account using the second-order Debye-based relationship. Several numerical simulations were performed and we obtained suitable agreement between the numerical and experimental results.

Electroporation Modelling of Irregular Nucleated Cells Including Pore Radius Dynamics

When high-amplitude, short-duration electric pulses are applied to cells the permeability of their membranes is increased. From the biological point of view, the phenomenon is quite well understood, however, it is important to develop accurate numerical models to investigate the electroporation effectiveness in terms of electrical, geometrical and physical parameters. To this aim, in this paper, we illustrate a spatio–temporal, non-linear, and dispersive multiphysics approach to study the electroporation in irregularly nucleated shaped cells. The model couples the Maxwell equations with the partial differential equation describing the creation and closure of pores as well as the evolution of the pore size. The dispersive properties of biological media and the irregular geometries of the membranes have been described using the multi-relaxation Debye-based relationship and the Gielis superformula, respectively. Numerical simulations highlight the importance to include in the model the spatial and temporal evolution of the pore radius. In fact, the obtained numerical results show significant discrepancies between our model and the one in which the pore radius dynamics is negligible.

Design of Electroporation Process in Irregularly Shaped Multicellular Systems

Electroporation technique is widely used in biotechnology and medicine for the transport of various molecules through the membranes of biological cells. Different mathematical models of electroporation have been proposed in the literature to study pore formation in plasma and nuclear membranes. These studies are mainly based on models using a single isolated cell with a canonical shape. In this work, a space–time (x,y,t) multiphysics model based on quasi-static Maxwell’s equations and nonlinear Smoluchowski’s equation has been developed to investigate the electroporation phenomenon induced by pulsed electric field in multicellular systems having irregularly shape. The dielectric dispersion of the cell compartments such as nuclear and plasmatic membranes, cytoplasm, nucleoplasm and external medium have been incorporated into the numerical algorithm, too. Moreover, the irregular cell shapes have been modeled by using the Gielis transformations.