A Microdosimetric Study of Electropulsation on Multiple Realistically Shaped Cells: Effect of Neighbours

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.

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.

Confocal Microscopy Improves 3D Microdosimetry Applied to Nanoporation Experiments Targeting Endoplasmic Reticulum

In the last years, microdosimetric numerical models of cells including intracellular compartments have been proposed, aiming to investigate the poration induced by the application of nanosecond pulsed electric fields (nsPEFs). A limitation of such models was the extremely approximate cell and organelle shapes, leading to an incorrect estimation of the electric field or transmembrane potential distribution in the studied domain. In order to obtain a reliable model of in vitro experiments and a one-to-one comparison between experimental and simulated results, here, a realistic model of 12 human mesenchymal stem cells was built starting from their optical microscopy images where different cell compartments were highlighted. The microdosimetric analysis of the cells group was quantified in terms of electric field and transmembrane potentials (TMPs) induced by an externally applied 10-ns trapezoidal pulse with rise and fall times of 2 ns, with amplitudes ranging from 2 to 30 MV/m. The obtained results showed that the plasma and endoplasmic reticulum (ER) membrane of each cell respond in a different way to the same electric field amplitude, depending on differences in shape, size, and position of the single cell with respect to the applied electric field direction. Therefore, also the threshold for an efficient electroporation is highly different from cell to cell. This difference was quantitatively estimated through the cumulative distribution function of the pore density for the plasma and ER membrane of each cell, representing the probability that a certain percentage of membrane has reached a specific value of pore density. By comparing the dose-response curves resulted from the simulations and those from the experimental study of De Menorval et al. (2016), we found a very good matching of results for plasma and ER membrane when 2% of the porated area is considered sufficient for permeabilizing the membrane. This result is worth of noting as it highlights the possibility to effectively predict the behavior of a cell (or of a population of cells) exposed to nsPEFs. Therefore, the microdosimetric realistic model described here could represent a valid tool in setting up more efficient and controlled electroporation protocols.

Microdosimetric Realistic Model of a Cell with Endoplasmic Reticulum

When investigating the biophysical effects induced by the interaction between electromagnetic fields and biological cells, it is crucial to estimate the electromagnetic field intensity at the microscopic scale (microdosimetry). This information allows to find a connection between the external applied field and the observed biological event required to establish related biomedical applications. Here, authors present a microdosimetric study based on a 2D realistic model of a cell and its endoplasmic reticulum. The microdosimetric analysis of the cell and endoplasmic reticulum was quantified in terms of electric field and transmembrane potential induced by an externally applied high amplitude 10-ns pulsed electric field. In addition, electroporated local membrane sites and pore densities were also evaluated. This study opens the way to numerically assist experimental applications of nanosecond pulsed electric fields for controlled bio-manipulation of cells and subcellular organelles.

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.

A wide-band bio-chip for real-time optical detection of bioelectromagnetic interactions with cells

The analytical and numerical design, implementation, and experimental validation of a new grounded closed coplanar waveguide for wide-band electromagnetic exposures of cells and their optical detection in real-time is reported. The realized device fulfills high-quality requirements for novel bioelectromagnetic experiments, involving elevated temporal and spatial resolutions. Excellent performances in terms of matching bandwidth (less than -10 dB up to at least 3 GHz), emission (below 1 × 10^-6 W/m²) and efficiency (around 1) have been obtained as revealed by both numerical simulations and experimental measurements. A low spatial electric field inhomogeneity (coefficient of variation of around 10 %) has been achieved within the cell solutions filling the polydimethylsiloxane reservoir of the conceived device. This original bio-chip based on the grounded closed coplanar waveguide concept opens new possibilities for the development of controlled experiments combining electromagnetic exposures and sophisticated imaging using optical spectroscopic techniques.

Technological and Theoretical Aspects for Testing Electroporation on Liposomes

Recently, the use of nanometer liposomes as nanocarriers in drug delivery systems mediated by nanoelectroporation has been proposed. This technique takes advantage of the possibility of simultaneously electroporating liposomes and cell membrane with 10-nanosecond pulsed electric fields (nsPEF) facilitating the release of the drug from the liposomes and at the same time its uptake by the cells. In this paper the design and characterization of a 10 nsPEF exposure system is presented, for liposomes electroporation purposes. The design and the characterization of the applicator have been carried out choosing an electroporation cuvette with 1 mm gap between the electrodes. The structure efficiency has been evaluated at different experimental conditions by changing the solution conductivity from 0.25 to 1.6 S/m. With the aim to analyze the influence of device performances on the liposomes electroporation, microdosimetric simulations have been performed considering liposomes of 200 and 400 nm of dimension with different inner and outer conductivity (from 0.05 to 1.6 S/m) in order to identify the voltage needed for their poration.

A microdosimetry study for a realistic shaped nucleus

In the last decades, the effects of ultrashort pulsed electric fields have been investigated demonstrating their capability to be involved in a great number of medical applications (e.g. cancer, gene electrotransfer, drug delivery, electrofusion). In particular, experiments in literature demonstrate that internal structures can be involved when pulse duration is reduced. Up to now, the mechanism that permits the electroporation phenomenon has not been completely understood and hence atomistic, microdosimetry and dosimetry models have been developed to help in this field. Aim of this work is to demonstrate the importance of realistically model also the internal organelles to obtain predictive results of effects at sub-cellular level with a microdosimetry model.