Effective conductivity of cell suspensions

Synergistic effects of an atmospheric pressure plasma jet and pulsed electric field on cells and skin

Nonthermal atmospheric pressure plasmas produce reactive plasma species including charged particles and reactive oxygen nitrogen species, which are known to induce oxidative stress in living cells in liquid or tissue. In the meantime, pulsed electric fields have been widely used in reversible or irreversible electropermeabilization for either the delivery of plasmid DNA or inactivation of cancer cells. This work discusses the synergistic effects of nanosecond pulsed plasma jets and pulsed electric field on inactivation of pancreatic cancer cells in vitro and enhancement of plasmid DNA delivery to guinea pig skin in vivo. Higher inactivation rates of the cancer cells in suspension were obtained with combined treatment of 300-ns 50 kV/cm pulsed electric field and a 1-min exposure of a nanosecond pulsed, 250-μm plasma jet. Increased efficiency of gene electrotransfer to skin was also observed after a 3-min treatment of a nanosecond pulsed, 1-mm plasma jet. Application of the plasma alone at the same dosage did not have significant effect on gene delivery. These findings signify the dosage-dependent cell-response to both the electric fields and plasma. Importantly, the use of cold plasma to increase the sensitization of the biological cells in response to pulsed electric fields could be an effective approach to enhance the desired effects in electroporation-based applications.

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.

Sine wave electropermeabilization reveals the frequency-dependent response of the biological membranes

The permeabilization of biological membranes by electric fields, known as electroporation, has been traditionally performed with square electric pulses. These signals distribute the energy applied to cells in a wide frequency band. This paper investigates the use of sine waves, which are narrow band signals, to provoke electropermeabilization and the frequency dependence of this phenomenon. Single bursts of sine waves at different frequencies in the range from 8 kHz-130 kHz were applied to cells in vitro. Electroporation was studied in the plasma membrane and the internal organelles membrane using calcium as a permeabilization marker. Additionally, a double-shell electrical model was simulated to give a theoretical framework to our results. The electroporation efficiency shows a low pass filter frequency dependence for both the plasma membrane and the internal organelles membrane. The mismatch between the theoretical response and the observed behavior for the internal organelles membrane is explained by a two-step permeabilization process: first the permeabilization of the external membrane and afterwards that of the internal membranes. The simulations in the model confirm this two-step hypothesis when a variable plasma membrane conductivity is considered in the analysis. This study demonstrates how the use of narrow-band signals as sine waves is a suitable method to perform electroporation in a controlled manner. We suggest that the use of this type of signals could bring a simplification in the investigations of the very complex phenomenon of electroporation, thus representing an interesting option in future fundamental studies.

Frequency-dependent conductivity contrast for tissue characterization using a dual-frequency range conductivity mapping magnetic resonance method

Electrical conductivities of biological tissues show frequency-dependent behaviors, and these values at different frequencies may provide clinically useful diagnostic information. MR-based tissue property mapping techniques such as magnetic resonance electrical impedance tomography (MREIT) and magnetic resonance electrical property tomography (MREPT) are widely used and provide unique conductivity contrast information over different frequency ranges. Recently, a new method for data acquisition and reconstruction for low- and high-frequency conductivity images from a single MR scan was proposed. In this study, we applied this simultaneous dual-frequency range conductivity mapping MR method to evaluate its utility in a designed phantom and two in vivo animal disease models. Magnetic flux density and B(1)(+) phase map for dual-frequency conductivity images were acquired using a modified spin-echo pulse sequence. Low-frequency conductivity was reconstructed from MREIT data by the projected current density method, while high-frequency conductivity was reconstructed from MREPT data by B(1)(+) mapping. Two different conductivity phantoms comprising varying ion concentrations separated by insulating films with or without holes were used to study the contrast mechanism of the frequency-dependent conductivities related to ion concentration and mobility. Canine brain abscess and ischemia were used as in vivo models to evaluate the capability of the proposed method to identify new electrical properties-based contrast at two different frequencies. The simultaneous dual-frequency range conductivity mapping MR method provides unique contrast information related to the concentration and mobility of ions inside tissues. This method has potential to monitor dynamic changes of the state of disease.

Theoretical analyses of cellular transmembrane voltage in suspensions induced by high-frequency fields

A change of the transmembrane voltage is considered to cause biophysical and biochemical responses in cells. The present study focuses on the cellular transmembrane voltage (Δφ) induced by external fields. We detail analytical equations for the transmembrane voltage induced by external high-frequency (above the relaxation frequency of the cell membrane) fields on cells of a spherical shape in suspensions and layers. At direct current (DC) and low frequencies, the cell membrane was assumed to be non-conductive under physiologic conditions. However, with increasing frequency, the permittivity of the cytoplasm/extracellular medium and conductivity of the membrane must be accounted for. Our main work is to extend application of the analytical solution of Δφ to the high-frequency range. We first introduce the transmembrane voltage generated by DC and low-frequency exposures on a single cell. Then, we focus on cell suspensions exposed to high-frequency fields. Using the effective medium theory and the reasonable assumption, the approximate analytical solution of Δφ on cells in suspensions and layers can be derived. Phenomenological effective medium theory equations cannot be used to calculate the local electric field of cell suspensions, so we raised a possible solution based on the Bergman theory.

A three-dimensional in vitro tumor platform for modeling therapeutic irreversible electroporation

Irreversible electroporation (IRE) is emerging as a powerful tool for tumor ablation that utilizes pulsed electric fields to destabilize the plasma membrane of cancer cells past the point of recovery. The ablated region is dictated primarily by the electric field distribution in the tissue, which forms the basis of current treatment planning algorithms. To generate data for refinement of these algorithms, there is a need to develop a physiologically accurate and reproducible platform on which to study IRE in vitro. Here, IRE was performed on a 3D in vitro tumor model consisting of cancer cells cultured within dense collagen I hydrogels, which have been shown to acquire phenotypes and respond to therapeutic stimuli in a manner analogous to that observed in in vivo pathological systems. Electrical and thermal fluctuations were monitored during treatment, and this information was incorporated into a numerical model for predicting the electric field distribution in the tumors. When correlated with Live/Dead staining of the tumors, an electric field threshold for cell death (500 V/cm) comparable to values reported in vivo was generated. In addition, submillimeter resolution was observed at the boundary between the treated and untreated regions, which is characteristic of in vivo IRE. Overall, these results illustrate the advantages of using 3D cancer cell culture models to improve IRE-treatment planning and facilitate widespread clinical use of the technology.

Effective admittivity of biological tissues as a coefficient of elliptic PDE

The electrical properties of biological tissues can be described by a complex tensor comprising a simple expression of the effective admittivity. The effective admittivities of biological tissues depend on scale, applied frequency, proportions of extra- and intracellular fluids, and membrane structures. The effective admittivity spectra of biological tissue can be used as a means of characterizing tissue structural information relating to the biological cell suspensions, and therefore measuring the frequency-dependent effective conductivity is important for understanding tissue's physiological conditions and structure. Although the concept of effective admittivity has been used widely, it seems that its precise definition has been overlooked. We consider how we can determine the effective admittivity for a cube-shaped object with several different biologically relevant compositions. These precise definitions of effective admittivity may suggest the ways of measuring it from boundary current and voltage data. As in the homogenization theory, the effective admittivity can be computed from pointwise admittivity by solving Maxwell equations. We compute the effective admittivity of simple models as a function of frequency to obtain Maxwell-Wagner interface effects and Debye relaxation starting from mathematical formulations. Finally, layer potentials are used to obtain the Maxwell-Wagner-Fricke expression for a dilute suspension of ellipses and membrane-covered spheres.

Simultaneous imaging of dual-frequency electrical conductivity using a combination of MREIT and MREPT

PURPOSE

To propose a single magnetic resonance scan conductivity imaging technique providing dual-frequency characteristics of tissue conductivity.

METHODS

Using a modified spin-echo pulse sequence, the magnetic flux density induced by externally injected currents and the B1+ phase map with injected current effects removed were acquired simultaneously. The low-frequency conductivity was reconstructed from the measured magnetic flux density by the projected current density method, while the high-frequency conductivity was reconstructed using the B1+ maps. Three different conductivity phantoms were used to demonstrate low- and high-frequency conductivity characteristics.

RESULTS

A conductivity spectrum at two frequencies was successfully acquired with the proposed scheme. Magnetic resonance electrical impedance tomography is advantageous for seeing an anomaly itself wrapped with a thin insulating membrane. In addition, if the membrane is porous, the membrane property can be quantitatively visualized with magnetic resonance electrical impedance tomography. Magnetic resonance electrical properties tomography does not detect such membranes, which enable it to probe things inside an insulating membrane.

CONCLUSION

Considering these pros and cons and also the fact that the conductivity of biological tissue changes with frequency, a dual-frequency conductivity imaging incorporating both magnetic resonance electrical impedance tomography and magnetic resonance electrical properties tomography in future animal and human experiments is suggested.

Theoretical and experimental analysis of electroporated membrane conductance in cell suspension

An intense electric field can be applied to increase the membrane conductance G(m) and consequently, the conductivity of cell suspension. This phenomenon is called electroporation. This mechanism is used in a wide range of medical applications, genetic engineering, and therapies. Conductivity measurements of cell suspensions were carried out during application of electric fields from 40 to 165 kV/m. Experimental results were analyzed with two electroporation models: the asymptotic electroporation model was used to estimate G(m) at the beginning and at the end of electric field pulse, and the extended Kinosita electroporation model to increase G(m) linearly in time. The maximum G(m) was 1-7 × 10(4) S/m(2), and the critical angle (when the G(m) is insignificant) was 50°-65°. In addition, the sensitivity of electroporated membrane conductance to extracellular and cytoplasmatic conductivity and cell radius has been studied. This study showed that external conductivity and cell radius are important parameters affecting the pore-opening phenomenon. However, if the cell radius is larger than 7 μm in low conductivity medium, the cell dimensions are not so important.

Pore characteristics of chitosan scaffolds studied by electrochemical impedance spectroscopy

In this study, a novel approach, electrochemical impedance spectroscopy (EIS), was used to examine the pore characteristics of chitosan scaffolds under aqueous conditions. The EIS was run with a constant current of 0.1 mA with the frequency sweep of 10(6) to 10(-4) Hz. The resulting complex impedance measurement was then used to calculate porosity, which was determined to be 71%. Scanning electron microscopy (SEM) and mercury intrusion porosimetry (MIP), two commonly used methods for scaffold characterization, were used to independently evaluate the pore characteristics and compare with that of EIS. The SEM and MIP were performed and analyzed under standard conditions. The pore diameter values found by SEM and MIP are 107 mum and 82 mum, respectively, indicating that both the image-based (SEM) and pressure-based (MIP) analyses provide similar results. The porosity of 73% calculated by MIP is comparable to that of EIS. From these results, it can be suggested that EIS, a relatively nondestructive test, is able to obtain comparable data on pore characteristics, as compared to SEM and MIP. The advantage of the EIS as an nondestructive test is that it can be performed under physiologically relevant conditions, whereas SEM and MIP require dry samples and vacuum conditions for measurement. These benefits make EIS a viable option for the characterization and long-term observation of tissue-engineered scaffolds.

Improved numerical approach for electrical modeling of biological cell clusters

This article presents an efficient numerical approach to simulate the process of polarization and ion conduction in membranes of biological cells subjected to intense electric fields. The proposed method uses Coulomb's law to calculate the electric field on the surface of the cell membrane and the continuity equation for calculating the difference in electric potential between the faces of the membrane. The behavior of the membrane conductance is described by a model of electroporation proposed in literature. This method provides results that agree well with the analytical model of polarization of an isolated cell suspended in electrolytic solution and also provides results for the conductance of the membrane during electroporation of cells in concentrated suspensions that agree with experimental results already published.

Evaluation of a capillary measuring system for the characterisation of small tissue samples by impedance spectroscopy at higher frequencies

For the gentle and non-destructive characterisation of small tissue samples, non-invasive methods are required for biotechnological applications and medical diagnostics. One approach is the characterisation of small tissue samples by impedance spectroscopy using a measuring capillary. In this paper, the applicability of a capillary measuring system to record the impedance of a biological sample over a wide frequency range is evaluated using a suspension of human breast adenocarcinoma cells (MCF-7). Impedance spectra over a frequency range 1 Hz to 1.1 GHz were recorded. To describe the electrical properties of the cell suspensions, we use an equivalent circuit model containing advanced RC-elements. Changes of plasma membrane integrity of suspended cells were detectable.

Electroporation in dense cell suspension--theoretical and experimental analysis of ion diffusion and cell permeabilization

Electroporation is a process where increased permeability of cells exposed to an electric field is observed. It is used in many biomedical applications including electrogene transfection and electrochemotherapy. Although the increased permeability of the membrane is believed to be the result of pores due to an induced transmembrane voltage U(m), the exact molecular mechanisms are not fully explained. In this study we analyze transient conductivity changes during the electric pulses and increased membrane permeability for ions and molecules after the pulses in order to determine which parameters affect stabilization of pores, and to analyze the relation between transient pores and long-lived transport pores. By quantifying ion diffusion, fraction of transport pores f(per) was obtained. A simple model, which assumes a quadratic dependence of f(per) on E in the area where U(m)>U(c) very accurately describes experimental values, suggesting that f(per) increases with higher electric field due to larger permeabilized area and due to higher energy available for pore formation. The fraction of transport pores increases also with the number of pulses N, which suggest that each pulse contributes to formation of more and/or larger stable transport pores, whereas the number of transient pores does not depend on N.

Numerical study of the electrical conductivity and polarization in a suspension of spherical cells

The spatial distribution of electrical potential and current in a suspension of spherical cells under an applied electric field was numerically obtained using the equivalent circuit method (ECM). The effect of the proximity of the cells was studied in a set of simulations where the volumetric fraction varied from 0.24 to 0.66. The results show that the transmembrane potential for cells in the suspension is lower than the theoretically predicted value for a single dielectric membrane under a uniform electric field. It was also observed that as the volumetric fraction is increased, the transmembrane potential on the pole of the cells decreases linearly. Furthermore, the conductivity of the suspension was also observed to be a function of the volumetric fraction and this result is in a good agreement with the Maxwell's model for spherical particles suspended in a volume conductor.

Techniques of signal generation required for electropermeabilization. Survey of electropermeabilization devices

Electropermeabilization is a phenomenon that transiently increases permeability of the cell plasma membrane. In the state of high permeability, the plasma membrane allows ions, small and large molecules to be introduced into the cytoplasm, although the cell plasma membrane represents a considerable barrier for them in its normal state. Besides introduction of various substances to cell cytoplasm, permeabilized cell membrane allows cell fusion or insertion of proteins to the cell membrane. Efficiency of all these applications strongly depends on parameters of electric pulses that are delivered to the treated object using specially developed electrodes and electronic devices--electroporators. In this paper we present and compare most commonly used techniques of signal generation required for electropermeabilization. In addition, we present an overview of commercially available electroporators and electroporation systems that were described in accessible literature.

Effect of cell electroporation on the conductivity of a cell suspension

An increased permeability of a cell membrane during the application of high-voltage pulses results in increased transmembrane transport of molecules that otherwise cannot enter the cell. Increased permeability of a cell membrane is accompanied by increased membrane conductivity; thus, by measuring electric conductivity the extent of permeabilized tissue could be monitored in real time. In this article the effect of cell electroporation caused by high-voltage pulses on the conductivity of a cell suspension was studied by current-voltage measurements during and impedance measurement before and after the pulse application. At the same time the percentage of permeabilized and survived cells was determined and the extent of osmotic swelling measured. For a train of eight pulses a transient increase in conductivity of a cell suspension was obtained above permeabilization threshold in low- and high-conductive medium with complete relaxation in <1 s. Total conductivity changes and impedance measurements showed substantial changes in conductivity due to the ion efflux in low-conductive medium and colloid-osmotic swelling in both media. Our results show that by measuring electric conductivity during the pulses we can detect limit permeabilization threshold but not directly permeabilization level, whereas impedance measurements in seconds after the pulse application are not suitable.

Effective conductivity of a suspension of permeabilized cells: a theoretical analysis

During the electroporation cell membrane undergoes structural changes, which increase the membrane conductivity and consequently lead to a change in effective conductivity of a cell suspension. To correlate microscopic membrane changes to macroscopic changes in conductivity of a suspension, we analyzed the effective conductivity theoretically, using two different approaches: numerically, using the finite elements method; and analytically, by using the equivalence principle. We derived the equation, which connects membrane conductivity with effective conductivity of the cell suspension. The changes in effective conductivity were analyzed for different parameters: cell volume fraction, membrane and medium conductivity, critical transmembrane potential, and cell orientation. In our analysis we used a tensor form of the effective conductivity, thus taking into account the anisotropic nature of the cell electropermeabilization and rotation of the cells. To determine the effect of cell rotation, as questioned by some authors, the difference between conductivity of a cell suspension with normally distributed orientations and parallel orientation was also calculated, and determined to be <10%. The presented theory provides a theoretical basis for the analysis of measurements of the effective conductivity during electroporation.

Dependence of induced transmembrane potential on cell density, arrangement, and cell position inside a cell system

A nonuniform transmembrane potential (TMP) is induced on a cell membrane exposed to external electric field. If the induced TMP is above the threshold value, cell membrane becomes permeabilized in a reversible process called electropermeabilization. Studying electric potential distribution on the cell membrane 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 TMP. In the first part of our study, we studied dependence of potential distribution on cell arrangement and density in infinite cell suspensions where cells were organized into simple-cubic, body-centered cubic, and face-centered cubic lattice. In the second part of the study, we examined how induced TMP on a cell membrane is dependent on its position inside a three-dimensional cell cluster. Finally, the results for cells inside the cluster were compared to those in infinite lattice. We used numerical analysis for the study, specifically the finite-element method (FEM). The results for infinite cell suspensions show that the induced TMP depends on both: cell volume fraction and cell arrangement. We established from the results for finite volume cell clusters and layers, that there is no radial dependence of induced TMP for cells inside the cluster.