Electric Field-Induced Transmembrane Potential Depends on Cell Density and Organizatio

Cardiac ablation with pulsed electric fields: principles and biophysics

Pulsed electric fields (PEFs) have emerged as an ideal cardiac ablation modality. At present numerous clinical trials in humans are exploring PEF as an ablation strategy for both atrial and ventricular arrhythmias, with early data showing significant promise. As this is a relatively new technology there is limited understanding of its principles and biophysics. Importantly, PEF biophysics and principles are starkly different to current energy modalities (radiofrequency and cryoballoon). Given the relatively novel nature of PEFs, this review aims to provide an understanding of the principles and biophysics of PEF ablation. The goal is to enhance academic research and ultimately enable optimization of ablation parameters to maximize procedure success and minimize risk.

Revisiting the role of pulsed electric fields in overcoming the barriers to in vivo gene electrotransfer

Gene therapies are revolutionizing medicine by providing a way to cure hitherto incurable diseases. The scientific and technological advances have enabled the first gene therapies to become clinically approved. In addition, with the ongoing COVID-19 pandemic, we are witnessing record speeds in the development and distribution of gene-based vaccines. For gene therapy to take effect, the therapeutic nucleic acids (RNA or DNA) need to overcome several barriers before they can execute their function of producing a protein or silencing a defective or overexpressing gene. This includes the barriers of the interstitium, the cell membrane, the cytoplasmic barriers and (in case of DNA) the nuclear envelope. Gene electrotransfer (GET), i.e., transfection by means of pulsed electric fields, is a non-viral technique that can overcome these barriers in a safe and effective manner. GET has reached the clinical stage of investigations where it is currently being evaluated for its therapeutic benefits across a wide variety of indications. In this review, we formalize our current understanding of GET from a biophysical perspective and critically discuss the mechanisms by which electric field can aid in overcoming the barriers. We also identify the gaps in knowledge that are hindering optimization of GET in vivo.

mRNA-based CAR T-cells manufactured by miniaturized two-step electroporation produce selective cytotoxicity toward target cancer cells

There is a growing interest for viral vector-free chimeric antigen receptor (CAR) T-cells due to its ability to kill cancer cells without adverse side effects. A potential avenue for manufacturing viral-vector free CAR T-cells is to utilize mRNA electroporation. One of the major concerns with mRNA electroporated CAR T-cells is the shorter cytotoxic lifespan of a few days, which is insufficient or not ideal for therapy. To better understand this issue and develop a potential solution, this study focused on examining the translation of electroporated mRNA to CAR molecules, time dependent degradation of CAR molecules and cytotoxicity produced by CAR T-cells on cancer cells. It was found that the initial expression of CAR molecules dictates the cytotoxicity. Initial CAR expression could be controlled by the experimental parameters such as electroporation time and mRNA concentration in the electroporation buffer. Experiments were carried out using a novel two-step electroporation that allows for controlled and uniform transfection of T-cells. These technical advancements and subsequent findings could provide a viable path for producing CAR T-cells with longer cytotoxic lifespans.

Electrotherapies for Glioblastoma

Non-thermal, intermediate frequency (100-500 kHz) electrotherapies present a unique therapeutic strategy to treat malignant neoplasms. Here, pulsed electric fields (PEFs) which induce reversible or irreversible electroporation (IRE) and tumour-treating fields (TTFs) are reviewed highlighting the foundations, advances, and considerations of each method when applied to glioblastoma (GBM). Several biological aspects of GBM that contribute to treatment complexity (heterogeneity, recurrence, resistance, and blood-brain barrier(BBB)) and electrophysiological traits which are suggested to promote glioma progression are described. Particularly, the biological responses at the cellular and molecular level to specific parameters of the electrical stimuli are discussed offering ways to compare these parameters despite the lack of a universally adopted physical description. Reviewing the literature, a disconnect is found between electrotherapy techniques and how they target the biological complexities of GBM that make treatment difficult in the first place. An attempt is made to bridge the interdisciplinary gap by mapping biological characteristics to different methods of electrotherapy, suggesting important future research topics and directions in both understanding and treating GBM. To the authors' knowledge, this is the first paper that attempts an in-tandem assessment of the biological effects of different aspects of intermediate frequency electrotherapy methods, thus offering possible strategies toward GBM treatment.

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

Electroporation is a widely used method consisting of application of high-voltage, short-duration electric pulses to increase cell membrane permeability, allowing cellular internalization of medications. In this work, the influence of two primary parameters, voltage level (V) and pulse spacing (N), on electroporation efficiency, uniformity and aggressiveness, as quantified by the total mass transport to viable cells, intracellular concentration gradients and an aggressiveness factor introduced here, is studied by means of numerical simulations of drug transport in electroporated tissues. The global method of approximate particular solutions (Global MAPS) is used to solve the governing equations, together with domain scaling, singular value decomposition and smoothing algorithms, to address the ill-conditioning of the final system and suppress small scale oscillations. The accuracy of Global MAPS is evaluated by comparing the initial extracellular concentration, C_e , and final intracellular concentration, C_i , with previous finite volume method results, obtaining similar behavior of C_e and C_i along the tissue domain, with some differences for C_i in high-gradient zones. According to the Global MAPS results, the influence of V and N on C_i is only significant over a certain range, within which the largest drug transport to viable cells occurs. In general, both electroporation efficiency and aggressiveness change in nonuniform manner with V and decrease with N, whereas the electroporation uniformity decreases as V increases and N decreases. The contour plots obtained here can be considered useful tools to compare electroporation-based treatments in terms of their efficiency, aggressiveness and uniformity, assisting in the selection of a suitable treatment plan for cancer.

Influence of low voltage electric field stimulation on hydrogen generation from anaerobic digestion of waste activated sludge

Low voltage electric field is an important stimulation condition for biochemical metabolic of microorganism. But few literatures were available related to the effect of low voltage electric field on hydrogen production from anaerobic digestion of waste activated sludge (WAS). This study aims to explore such influencing thus carried a series experiments under 35 ± 1 °C and pH 7.0 ± 0.2. The experimental results showed that the hydrogen production increased from 28.1 to 32.5 mL/g VSS with electric field strengthening from 0 to 40 V/m. The mechanism explorations revealed that the yield of volatile fatty acids (VFAs) yield could reach 1.16-fold of control group when the highest-level electric field (40 V/m) forced in the anaerobic fermentation system with dextran as model substrate. Further analysis of relative activities of functional enzymes, such as NADH, acetate kinase, butyrate kinase and OAATC, showed that it was promoted by electric field stimulation as 2.09, 1.52, 1.28 and 1.16-fold of the control test, respectively. Meanwhile, the conductivity of fermentation liquor in presence of low voltage electric field stimulation increased 83% compared with the control group. This work verified the promotion of low voltage electric field stimulation on hydrogen production from anaerobic digestion of WAS and might provide a new sight for the green energy generation.

Successful Tumor Electrochemotherapy Using Sine Waves

OBJECTIVE

The purpose of this work is to assess the ability of sine waves to perform electrochemotherapy (ECT) and to study the dependence of the frequency of the applied sine wave on the treatment efficacy.

METHODS

A subcutaneous tumor model in mice was used, and the electric field was delivered in combination with bleomycin. Sinusoidal electric fields of different frequencies, amplitudes, and durations were compared to square waves. Computer simulations were additionally performed.

RESULTS

The results confirmed the ability of a sinusoidal electric field to obtain successful ECT responses. A strong dependence on frequency was obtained. The efficacy of the treatment decreased when the frequency of the sine waves was increased. At low sinusoidal frequency, the efficacy of the treatment is very similar to that obtained with a square wave. The collateral effects such as skin burns and muscle contractions decreased for the highest frequency assayed.

CONCLUSION

The use of sine wave burst represents a feasible option for the treatment of cancer by ECT.

SIGNIFICANCE

These results could have important implications for the treatment of cancer in the clinical world where ECT is performed with dc square pulses.

Impact of the number of electric pulses on cell electrochemotherapy in vitro: Limits of linearity and saturation

In this study the evolution in the efficiency of electrochemotherapy (reversible electroporation) with pulse number was assessed in vitro. Experiments were performed using 100 μs pulses at different electric field intensities and the chemotherapeutic agent bleomycin. Additionally, electrical impedance spectroscopy measurements were used as a different method to study in real time the changes produced on cells with pulse number during trains of consecutive pulses. Our results show that the relation between pulse number and the observed outcome is complex and difficult to fully characterize. This relation can display a highly linear behaviour up to a certain number of pulses and/or field intensity applied. However, the relation between the number of pulses and the observed outcome always evolves to a saturation or at least a reduction in the electric field effects that is displayed when either electric field intensity or pulse number are increased. An exponential model was found to best describe this relation within the range of experimental conditions considered. Electrical impedance measurements confirmed the results and gave a more precise quantification of this dependence. The study highlights the importance that pulse number has in the electrochemotherapy protocols and establishes some limits in the use of this parameter.

From Cell to Tissue Properties-Modeling Skin Electroporation With Pore and Local Transport Region Formation

Current models of tissue electroporation either describe tissue with its bulk properties or include cell level properties, but model only a few cells of simple shapes in low-volume fractions or are in two dimensions. We constructed a three-dimensional model of realistically shaped cells in realistic volume fractions. By using a 'unit cell' model, the equivalent dielectric properties of whole tissue could be calculated. We calculated the dielectric properties of electroporated skin. We modeled electroporation of single cells by pore formation on keratinocytes and on the papillary dermis which gave dielectric properties of the electroporated epidermis and papillary dermis. During skin electroporation, local transport regions are formed in the stratum corneum. We modeled local transport regions and increase in their radii or density which affected the dielectric properties of the stratum corneum. The final model of skin electroporation accurately describes measured electric current and voltage drop on the skin during electroporation with long low-voltage pulses. The model also accurately describes voltage drop on the skin during electroporation with short high-voltage pulses. However, our results indicate that during application of short high-voltage pulses additional processes may occur which increase the electric current. Our model connects the processes occurring at the level of cell membranes (pore formation), at the level of a skin layer (formation of local transport region in the stratum corneum) with the tissue (skin layers) and even level of organs (skin). Using a similar approach, electroporation of any tissue can be modeled, if the morphology of the tissue is known.

Shielding effects of myelin sheath on axolemma depolarization under transverse electric field stimulation

Axonal stimulation with electric currents is an effective method for controlling neural activity. An electric field parallel to the axon is widely accepted as the predominant component in the activation of an axon. However, recent studies indicate that the transverse component to the axolemma is also effective in depolarizing the axon. To quantitatively investigate the amount of axolemma polarization induced by a transverse electric field, we computed the transmembrane potential (Vm) for a conductive body that represents an unmyelinated axon (or the bare axon between the myelin sheath in a myelinated axon). We also computed the transmembrane potential of the sheath-covered axonal segment in a myelinated axon. We then systematically analyzed the biophysical factors that affect axonal polarization under transverse electric stimulation for both the bare and sheath-covered axons. Geometrical patterns of polarization of both axon types were dependent on field properties (magnitude and field orientation to the axon). Polarization of both axons was also dependent on their axolemma radii and electrical conductivities. The myelin provided a significant “shielding effect” against the transverse electric fields, preventing excessive axolemma depolarization. Demyelination could allow for prominent axolemma depolarization in the transverse electric field, via a significant increase in myelin conductivity. This shifts the voltage drop of the myelin sheath to the axolemma. Pathological changes at a cellular level should be considered when electric fields are used for the treatment of demyelination diseases. The calculated term for membrane polarization (Vm) could be used to modify the current cable equation that describes axon excitation by an external electric field to account for the activating effects of both parallel and transverse fields surrounding the target axon.

Connecting the in vitro and in vivo experiments in electrochemotherapy - a feasibility study modeling cisplatin transport in mouse melanoma using the dual-porosity model

In electrochemotherapy two conditions have to be met to be successful - the electric field of sufficient amplitude and sufficient uptake of chemotherapeutics in the tumor. Current treatment plans only take into account critical electric field to achieve cell membrane permeabilization. However, permeabilization alone does not guarantee uptake of chemotherapeutics and consequently successful treatment. We performed a feasibility study to determine whether the transport of cisplatin in vivo could be calculated based on experiments performed in vitro. In vitro, a spectrum of parameters can be explored without ethical issues. Mouse melanoma B16-F1 cell suspension and inoculated B16-F10 tumors were exposed to electric pulses in the presence of chemotherapeutic cisplatin. The uptake of cisplatin was measured by inductively coupled plasma mass spectrometry. We modeled the transport of cisplatin with the dual-porosity model, which is based on the diffusion equation, connects pore formation with membrane permeability, and includes transport between several compartments. In our case, there were three compartments - tumor cells, interstitial fraction and peritumoral region. Our hypothesis was that in vitro permeability coefficient could be introduced in vivo, as long as tumor physiology was taken into account. Our hypothesis was confirmed as the connection of in vitro and in vivo experiments was possible by introducing a transformation coefficient which took into account the in vivo characteristics, i.e., smaller available area of the plasma membrane for transport due to cell density, presence of cell-matrix in vivo, and reduced drug mobility. We thus show that it is possible to connect in vitro and in vivo experiments of electrochemotherapy. However, more experimental work is required for model validation.

Plasma membrane depolarization and permeabilization due to electric pulses in cell lines of different excitability

In electroporation-based medical treatments, excitable tissues are treated, either intentionally (irreversible electroporation of brain cancer, gene electrotransfer or ablation of the heart muscle, gene electrotransfer of skeletal muscles), or unintentionally (excitable tissues near the target area). We investigated how excitable and non-excitable cells respond to electric pulses, and if electroporation could be an effective treatment of the tumours of the central nervous system. For three non-excitable and one excitable cell line, we determined a strength-duration curve for a single pulse of 10ns-10ms. The threshold for depolarization decreased with longer pulses and was higher for excitable cells. We modelled the response with the Lapicque curve and the Hodgkin-Huxley model. At 1μs a plateau of excitability was reached which could explain why high-frequency irreversible electroporation (H-FIRE) electroporates but does not excite cells. We exposed cells to standard electrochemotherapy parameters (8×100μs pulses, 1Hz, different voltages). Cells behaved similarly which indicates that electroporation most probably occurs at the level of lipid bilayer, independently of the voltage-gated channels. These results could be used for optimization of electric pulses to achieve maximal permeabilization and minimal excitation/pain sensation. In the future, it should be established whether the in vitro depolarization correlates to nerve/muscle stimulation and pain sensation in vivo.

Recommendations and requirements for reporting on applications of electric pulse delivery for electroporation of biological samples

Electric field-induced membrane changes are an important approach in the life sciences. However, the developments in knowledge and translational applications face problems of reproducibility. Indeed, a quick survey of the literature reveals a lack of transparent and comprehensive reporting of essential technical information in many papers. Too many of the published scientific papers do not contain sufficient information for proper assessment of the presented results. The general rule/guidance in reporting experimental data should require details on exposure conditions such that other researchers are able to evaluate, judge and reproduce the experiments and data obtained. To enhance dissemination of information and reproducibility of protocols, it is important to agree upon nomenclature and reach a consensus on documentation of experimental methods and procedures. This paper offers recommendations and requirements for reporting on applications of electric pulse delivery for electroporation of biological samples in life science.

Energy-efficient biomass processing with pulsed electric fields for bioeconomy and sustainable development

Fossil resources-free sustainable development can be achieved through a transition to bioeconomy, an economy based on sustainable biomass-derived food, feed, chemicals, materials, and fuels. However, the transition to bioeconomy requires development of new energy-efficient technologies and processes to manipulate biomass feed stocks and their conversion into useful products, a collective term for which is biorefinery. One of the technological platforms that will enable various pathways of biomass conversion is based on pulsed electric fields applications (PEF). Energy efficiency of PEF treatment is achieved by specific increase of cell membrane permeability, a phenomenon known as membrane electroporation. Here, we review the opportunities that PEF and electroporation provide for the development of sustainable biorefineries. We describe the use of PEF treatment in biomass engineering, drying, deconstruction, extraction of phytochemicals, improvement of fermentations, and biogas production. These applications show the potential of PEF and consequent membrane electroporation to enable the bioeconomy and sustainable development.

A review of basic to clinical studies of irreversible electroporation therapy

The use of irreversible electroporation (IRE) for cancer treatment has increased sharply over the past decade. As a nonthermal therapy, IRE offers several potential benefits over other focal therapies, which include 1) short treatment delivery time, 2) reduced collateral thermal injury, and 3) the ability to treat tumors adjacent to major blood vessels. These advantages have stimulated widespread interest in basic through clinical studies of IRE. For instance, many in vitro and in vivo studies now identify treatment planning protocols (IRE threshold, pulse parameters, etc.), electrode delivery (electrode design, placement, intraoperative imaging methods, etc.), injury evaluation (methods and timing), and treatment efficacy in different cancer models. Therefore, this study reviews the in vitro, translational, and clinical studies of IRE cancer therapy based on major experimental studies particularly within the past decade. Further, this study provides organized data and facts to assist further research, optimization, and clinical applications of IRE.

Response of single cell with acute angle exposed to an external electric field

It is known that the electric field incurs effects on the living cells. Predicting the response of single cell or multilayer cells to induced alternative or static eclectic field has permanently been a challenge. In the present study a first order single cell with acute angle under the influence of external electric field is considered. The cell division stage or the special condition of reshaping is modelled with a cone being connected. In the case of cell divisions, anaphase, it can be considered with two cones that connected nose-to-nose. Each cone consists of two regions. The first is the membrane modelled with a superficial layer, and the second is cytoplasm at the core. A Laplace equation is written for this model and the distribution of its electric field is a sharp point in the single cell for which an acute angle model is calculated.

Mechanisms of transfer of bioactive molecules through the cell membrane by electroporation

A short review of biophysical mechanisms for electrotransfer of bioactive molecules through the cell membrane by using electroporation is presented. The concept of transient hydrophilic aqueous pores and membrane electroporation mechanisms of single cells and cells in suspension models are analyzed. Alongside the theoretical approach, some peculiarities of drug and gene electrotransfer into cells and applications in clinical trials are discussed.

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.

Cell-cell proximity effects in multi-cell electroporation

We report a fundamental study of how the electropermeabilization of a cell is affected by nearby cells. Previous researchers studying electroporation of dense suspensions of cells have observed, both theoretically and experimentally, that such samples cannot be treated simply as collections of independent cells. However, the complexity of those systems makes quantitative modeling difficult. We studied the change in the minimum applied electric field, the threshold field, required to affect electropermeabilization of a cell due to the presence of a second cell. Experimentally, we used optical tweezers to accurately position two cells in a custom fluidic electroporation device and measured the threshold field for electropermeabilization. We also captured video of the process. In parallel, finite element simulations of the electrostatic potential distributions in our systems were generated using the 3-layer model and the contact resistance methods. Reasonably good agreement with measurements was found assuming a model in which changes in a cell's threshold field were predicted from the calculated changes in the maximum voltage across the cell's membrane induced by the presence of a second cell. The threshold field required to electroporate a cell is changed ∼5%-10% by a nearby, nearly touching second cell. Cells aligned parallel to the porating field shield one another. Those oriented perpendicular to the field enhance the applied field's effect. In addition, we found that the dynamics of the electropermeabilization process are important in explaining observations for even our simple two-cell system.

Non-uniform distribution of outer hair cell transmembrane potential induced by extracellular electric field

Intracochlear electric fields arising out of sound-induced receptor currents, silent currents, or electrical current injected into the cochlea induce transmembrane potential along the outer hair cell (OHC) but its distribution along the cells is unknown. In this study, we investigated the distribution of OHC transmembrane potential induced along the cell perimeter and its sensitivity to the direction of the extracellular electric field (EEF) on isolated OHCs at a low frequency using the fast voltage-sensitive dye ANNINE-6plus. We calibrated the potentiometric sensitivity of the dye by applying known voltage steps to cells by simultaneous whole-cell voltage clamp. The OHC transmembrane potential induced by the EEF is shown to be highly nonuniform along the cell perimeter and strongly dependent on the direction of the electrical field. Unlike in many other cells, the EEF induces a field-direction-dependent intracellular potential in the cylindrical OHC. We predict that without this induced intracellular potential, EEF would not generate somatic electromotility in OHCs. In conjunction with the known heterogeneity of OHC membrane microdomains, voltage-gated ion channels, charge, and capacitance, the EEF-induced nonuniform transmembrane potential measured in this study suggests that the EEF would impact the cochlear amplification and electropermeability of molecules across the cell.

Predicting electroporation of cells in an inhomogeneous electric field based on mathematical modeling and experimental CHO-cell permeabilization to propidium iodide determination

High voltage electric pulses cause electroporation of the cell membrane. Consequently, flow of the molecules across the membrane increases. In our study we investigated possibility to predict the percentage of the electroporated cells in an inhomogeneous electric field on the basis of the experimental results obtained when cells were exposed to a homogeneous electric field. We compared and evaluated different mathematical models previously suggested by other authors for interpolation of the results (symmetric sigmoid, asymmetric sigmoid, hyperbolic tangent and Gompertz curve). We investigated the density of the cells and observed that it has the most significant effect on the electroporation of the cells while all four of the mathematical models yielded similar results. We were able to predict electroporation of cells exposed to an inhomogeneous electric field based on mathematical modeling and using mathematical formulations of electroporation probability obtained experimentally using exposure to the homogeneous field of the same density of cells. Models describing cell electroporation probability can be useful for development and presentation of treatment planning for electrochemotherapy and non-thermal irreversible electroporation.

Differential cellular effects of electroporation and electrochemotherapy in monolayers of human microvascular endothelial cells

In vivo electroporation of tumours shows disruption of blood flow and creates a vascular effect with an initial rapid and transient vasoconstriction phase and a much longer lasting phase with changed microvascular endothelium. These changes are not well understood but are presumed to involve the cytoskeleton. The paper presents for the first time differential in vitro effects describing cytoskeleton changes and monolayer integrity changes by both electroporation and electrochemotherapy of monolayers of human microvascular endothelial cells (HMEC-1). After the application of electric field pulses, the morphology of cells, and both the F-actin and Beta-tubulin cytoskeleton proteins were affected. During both electroporation and electrochemotherapy, the initial phase of cellular damage was noticed at 10 min as swollen cells and honeycomb-like actin bundles. The electroporation-induced cellular effects, observed from electric pulses >150 V, were voltage-dependent and within 24 hrs partly recoverable. The electrochemotherapy-induced cellular effects developed at 2 hrs in spindle-like cells, and more densely packed F-actin and Beta-tubulin were observed, which were dependent on the amount of bleomycin and the voltages applied (>50 V). In addition, for electrochemotherapy with electric pulses >150 V cellular changes were not recoverable within 24 hrs. The effects on monolayer integrity were reflected in the enhanced monolayer permeability, with the electrochemotherapy showing an earlier onset and synergy. We conclude that electrochemotherapy as compared to electroporation leads within 24 hrs to a quicker and more pronounced monolayer integrity damage and endothelial cell death, which together provide further insight into the cellular changes of the vascular disruption of electrochemotherapy.

Hyaluronidase and collagenase increase the transfection efficiency of gene electrotransfer in various murine tumors

One of the applications of electroporation/electropulsation in biomedicine is gene electrotransfer, the wider use of which is hindered by low transfection efficiency in vivo compared with viral vectors. The aim of our study was to determine whether modulation of the extracellular matrix in solid tumors, using collagenase and hyaluronidase, could increase the transfection efficiency of gene electrotransfer in histologically different solid subcutaneous tumors in mice. Tumors were treated with enzymes before electrotransfer of plasmid DNA encoding either green fluorescent protein or luciferase. Transfection efficiency was determined 3, 9, and 15 days posttransfection. We demonstrated that pretreatment of tumors with a combination of enzymes significantly increased the transfection efficiency of electrotransfer in tumors with a high extracellular matrix area (LPB fibrosarcoma). In tumors with a smaller extracellular matrix area and less organized collagen lattice, the increase was not so pronounced (SA-1 fibrosarcoma and EAT carcinoma), whereas in B16 melanoma, in which only traces of collagen are present, pretreatment of tumors with hyaluronidase alone was more efficient than pretreatment with both enzymes. In conclusion, our results suggest that modification of the extracellular matrix could improve distribution of plasmid DNA in solid subcutaneous tumors, demonstrated by an increase in transfection efficiency, and thus have important clinical implications for electrogene therapy.

Theoretical considerations of tissue electroporation with high-frequency bipolar pulses

This study introduces the use of high-frequency pulsed electric fields for tissue electroporation. Through the development of finite element models and the use of analytical techniques, electroporation with rectangular, bipolar pulses is investigated. The electric field and temperature distribution along with the associated transmembrane potential development are considered in a heterogeneous skin fold geometry. Results indicate that switching polarity on the nanosecond scale near the charging time of plasma membranes can greatly improve treatment outcomes in heterogeneous tissues. Specifically, high-frequency fields ranging from 500 kHz to 1 MHz are best suited to penetrate epithelial layers without inducing significant Joule heating, and cause electroporation in underlying cells.

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.

Transmembrane potential generated by a magnetically induced transverse electric field in a cylindrical axonal model

During the electrical stimulation of a uniform, long, and straight nerve axon, the electric field oriented parallel to the axon has been widely accepted as the major field component that activates the axon. Recent experimental evidence has shown that the electric field oriented transverse to the axon is also sufficient to activate the axon, by inducing a transmembrane potential within the axon. The transverse field can be generated by a time-varying magnetic field via electromagnetic induction. The aim of this study was to investigate the factors that influence the transmembrane potential induced by a transverse field during magnetic stimulation. Using an unmyelinated axon model, we have provided an analytic expression for the transmembrane potential under spatially uniform, time-varying magnetic stimulation. Polarization of the axon was dependent on the properties of the magnetic field (i.e., orientation to the axon, magnitude, and frequency). Polarization of the axon was also dependent on its own geometrical (i.e., radius of the axon and thickness of the membrane) and electrical properties (i.e., conductivities and dielectric permittivities). Therefore, this article provides evidence that aside from optimal coil design, tissue properties may also play an important role in determining the efficacy of axonal activation under magnetic stimulation. The mathematical basis of this conclusion was discussed. The analytic solution can potentially be used to modify the activation function in current cable equations describing magnetic stimulation.

Induced transmembrane voltage and its correlation with electroporation-mediated molecular transport

Exposure of a cell to an electric field results in inducement of a voltage across its membrane (induced transmembrane voltage, DeltaPsi (m)) and, for sufficiently strong fields, in a transient increase of membrane permeability (electroporation). We review the analytical, numerical and experimental methods for determination of DeltaPsi (m) and a method for monitoring of transmembrane transport. We then combine these methods to investigate the correlation between DeltaPsi (m) and molecular transport through an electroporated membrane for isolated cells of regular and irregular shapes, for cells in dense suspensions as well as for cells in monolayer clusters. Our experiments on isolated cells of both regular and irregular shapes confirm the theoretical prediction that the highest absolute values of DeltaPsi (m) are found in the membrane regions facing the electrodes and that electroporation-mediated transport is confined to these same regions. For cells in clusters, the location of transport regions implies that, at the field strengths sufficient for electroporation, the cells behave as electrically insulated (i.e., as individual) cells. In contrast, with substantially weaker, nonelectroporating fields, potentiometric measurements show that the cells in these same clusters behave as electrically interconnected cells (i.e., as one large cell). These results suggest that sufficiently high electric fields affect the intercellular pathways and thus alter the electric behavior of the cells with respect to their normal physiological state.

The influence of skeletal muscle anisotropy on electroporation: in vivo study and numerical modeling

The aim of this study was to theoretically and experimentally investigate electroporation of mouse tibialis cranialis and to determine the reversible electroporation threshold values needed for parallel and perpendicular orientation of the applied electric field with respect to the muscle fibers. Our study was based on local electric field calculated with three-dimensional realistic numerical models, that we built, and in vivo visualization of electroporated muscle tissue. We established that electroporation of muscle cells in tissue depends on the orientation of the applied electric field; the local electric field threshold values were determined (pulse parameters: 8 × 100 μs, 1 Hz) to be 80 V/cm and 200 V/cm for parallel and perpendicular orientation, respectively. Our results could be useful electric field parameters in the control of skeletal muscle electroporation, which can be used in treatment planning of electroporation based therapies such as gene therapy, genetic vaccination, and electrochemotherapy.

Kinetics of transmembrane transport of small molecules into electropermeabilized cells

The transport of propidium iodide into electropermeabilized Chinese hamster ovary cells was monitored with a photomultiplier tube during and after the electric pulse. The influence of pulse amplitude and duration on the transport kinetics was investigated with time resolutions from 200 ns to 4 ms in intervals from 400 micros to 8 s. The transport became detectable as early as 60 micros after the start of the pulse, continued for tens of seconds after the pulse, and was faster and larger for higher pulse amplitudes and/or longer pulse durations. With fixed pulse parameters, transport into confluent monolayers of cells was slower than transport into suspended cells. Different time courses of fluorescence increase were observed during and at various times after the pulse, reflecting different transport mechanisms and ongoing membrane resealing. The data were compared to theoretical predictions of the Nernst-Planck equation. After a delay of 60 micros, the time course of fluorescence during the pulse was approximately linear, supporting a mainly electrophoretic solution of the Nernst-Planck equation. The time course after the pulse agreed with diffusional solution of the Nernst-Planck equation if the membrane resealing was assumed to consist of three distinct components, with time constants in the range of tens of microseconds, hundreds of microseconds, and tens of seconds, respectively.

Theoretical and experimental analysis of conductivity, ion diffusion and molecular transport during cell electroporation--relation between short-lived and long-lived pores

Electroporation is usually described as a formation of transient pores in the cell membrane in the presence of a strong electric field, which enables transport of molecules and ions across the cell membrane. Several experimental studies of electroporation showed a complex dependence of the transport on pulse parameters. In only few studies, however, the actual transport across the membrane was quantified. Current theoretical studies can describe pore formation in artificial lipid membranes but still cannot explain mechanisms of formation and properties of long-lived pores which are formed during cell electroporation. The focus of our study is to connect theoretical description of pore formation during the electric pulses with experimental observation of increased transport after the pulses. By analyzing transient increase in conductivity during the pulses in parallel with ion efflux after the pulses the relation between short-lived and long-lived pores was investigated. We present a simple model that incorporates an increase in the fraction of long-lived pores with higher electric field due to larger area of the cell membrane exposed to above-critical voltage and due to higher energy which is available for pore formation. We also show that each consecutive pulse increases the probability for the formation of long-lived pores.

A numerical model of skin electropermeabilization based on in vivo experiments

As an alternative to viral methods that are controversial because of their safety issues, chemical and physical methods have been developed to enhance gene expression in tissues. Reversible increase of the cell membrane permeability caused by the electric field--electroporation--is currently one of the most efficient and simple non-viral methods of gene transfer. We performed a series of in vivo experiments, delivering plasmids to rat skin using external plate electrodes. The experiments showed that skin layers below stratum corneum can be permeabilized in this way. In order to study the course of skin tissue permeabilization by means of electric pulses, a numerical model using the finite element method was made. The model is based on the tissue-electrode geometry and electric pulses used in our in vivo experiments. We took into account the layered structure of skin and changes of its bulk electrical properties during electroporation, as observed in the in vivo experiments. We were using tissue conductivity values found in literature and experimentally determined electric field threshold values needed for tissue permeabilization. The results obtained with the model are in good agreement with the in vivo results of gene transfection in rat skin. With the model presented we used the available data to explain the mechanism of the tissue electropermeabilization propagation beyond the initial conditions dictated by the tissue initial conductivities, thus contributing to a more in-depth understanding of this process. Such a model can be used to optimize and develop electrodes and pulse parameters.

The effect of the histological properties of tumors on transfection efficiency of electrically assisted gene delivery to solid tumors in mice

Uniform DNA distribution in tumors is a prerequisite step for high transfection efficiency in solid tumors. To improve the transfection efficiency of electrically assisted gene delivery to solid tumors in vivo, we explored how tumor histological properties affected transfection efficiency. In four different tumor types (B16F1, EAT, SA-1 and LPB), proteoglycan and collagen content was morphometrically analyzed, and cell size and cell density were determined in paraffin-embedded tumor sections under a transmission microscope. To demonstrate the influence of the histological properties of solid tumors on electrically assisted gene delivery, the correlation between histological properties and transfection efficiency with regard to the time interval between DNA injection and electroporation was determined. Our data demonstrate that soft tumors with larger spherical cells, low proteoglycan and collagen content, and low cell density are more effectively transfected (B16F1 and EAT) than rigid tumors with high proteoglycan and collagen content, small spindle-shaped cells and high cell density (LPB and SA-1). Furthermore, an optimal time interval for increased transfection exists only in soft tumors, this being in the range of 5-15 min. Therefore, knowledge about the histology of tumors is important in planning electrogene therapy with respect to the time interval between DNA injection and electroporation.

Membrane perturbation by an external electric field: a mechanism to permit molecular uptake

Electropermeabilisation is a well established physical method, based on the application of electric pulses, which induces the transient permeabilisation of the cell membrane. External molecules, otherwise nonpermeant, can enter the cell. Electropermeabilisation is now in use for the delivery of a large variety of molecules, as drugs and nucleic acids. Therefore, the method has great potential in the fields of cancer treatment and gene therapy. However many open questions about the underlying physical mechanisms involved remain to be answered or fully elucidated. In particular, the induced changes by the effects of the applied field on the membrane structure are still far from being fully understood. The present review focuses on questions related to the current theories, i.e. the basic physical processes responsible for the electropermeabilisation of lipid membranes. It also addresses recent findings using molecular dynamics simulations as well as experimental studies of the effect of the field on membrane components.

The endothelial cytoskeleton as a target of electroporation-based therapies

Electroporation-based therapies, such as electrochemotherapy and electrogene therapy, result in the disruption of blood vessel networks in vivo and cause changes in blood flow and vascular permeability. The effects of electroporation on the cytoskeleton of cultured primary endothelial cells and on endothelial monolayer permeability were investigated to elucidate possible mechanisms involved. Human umbilical vein endothelial cells (HUVECs) were electroporated in situ and then immunofluorescence staining for filamentous actin, beta-tubulin, vimentin, and VE-cadherin as well as Western blotting analysis of levels of phosphorylated myosin light chain and cytoskeletal proteins were performed. Endothelial permeability was determined by monitoring the passage of FITC-coupled dextran through endothelial monolayers. Exposure of endothelial cells to electric pulses resulted in a profound disruption of microfilament and microtubule cytoskeletal networks, loss of contractility, and loss of vascular endothelial cadherin from cell-to-cell junctions immediately after electroporation. These effects were voltage dependent and reversible because cytoskeletal structures recovered within 60 min of electroporation with up to 40 V, without any significant loss of cell viability. The cytoskeletal effects of electroporation were paralleled by a rapid increase in endothelial monolayer permeability. These results suggest that the remodeling of the endothelial cytoskeleton and changes in endothelial barrier function could contribute to the vascular disrupting actions of electroporation-based therapies and provide an insight into putative mechanisms responsible for the observed increase in permeability and cessation of blood flow in vivo.

Hybrid finite element method for describing the electrical response of biological cells to applied fields

A novel hybrid finite element method (FEM) for modeling the response of passive and active biological membranes to external stimuli is presented. The method is based on the differential equations that describe the conservation of electric flux and membrane currents. By introducing the electric flux through the cell membrane as an additional variable, the algorithm decouples the linear partial differential equation part from the nonlinear ordinary differential equation part that defines the membrane dynamics of interest. This conveniently results in two subproblems: a linear interface problem and a nonlinear initial value problem. The linear interface problem is solved with a hybrid FEM. The initial value problem is integrated by a standard ordinary differential equation solver such as the Euler and Runge-Kutta methods. During time integration, these two subproblems are solved alternatively. The algorithm can be used to model the interaction of stimuli with multiple cells of almost arbitrary geometries and complex ion-channel gating at the plasma membrane. Numerical experiments are presented demonstrating the uses of the method for modeling field stimulation and action potential propagation.

Electropermeabilization of dense cell suspensions

This paper investigates the influence of cell density on cell membrane electropermeabilization. The experiments were performed on dense cell suspensions (up to 400 x 10(6) cells/ml), which represent a simple model for studying electropermeabilization of tissues. Permeabilization was assayed with a fluorescence test using Propidium iodide to obtain the mean number of permeabilized cells (i.e. fluorescence positive) and the mean fluorescence per cell (amount of loaded dye). In our study, as the cell density increased from 10 x 10(6) to 400 x 10(6) cells/ml, the fraction of permeabilized cells decreased by approximately 50%. We attributed this to the changes in the local electric field, which led to a decrease in the amplitude of the induced transmembrane voltage. To obtain the same fraction of cell permeabilization in suspensions with 10 x 10(6) and 400 x 10(6) cells/ml, the latter suspension had to be permeabilized with higher pulse amplitude, which is in qualitative agreement with numerical computations. The electroloading of the cells also decreased with cell density. The decrease was considerably larger than expected from the differences in the permeabilized cell fractions alone. The additional decrease in fluorescence was mainly due to cell swelling after permeabilization, which reduced extracellular dye availability to the permeabilized membrane and hindered the dye diffusion into the cells. We also observed that resealing of cells appeared to be slower in dense suspensions, which can be attributed to cell swelling resulting from electropermeabilization.

Three dimensional transport lattice model for describing action potentials in axons stimulated by external electrodes

Conditions that stimulate action potentials in one or more nerves is of widespread interest. Axon and nerve models are usually based on two dimensional pre-specified lumped equivalents that assume where currents will flow. In contrast, here we illustrate creation of three dimensional (3D) system models with a transport lattice of interconnected local models for external and internal electrolyte and axon membrane. The transport lattice solves Laplace's equation in the extracellular medium and is coupled to the Hodgkin-Huxley model at local membrane sites. These space-filling models incorporate the geometric scale, which allows explicit representation of confined axons and external electrodes. The present results demonstrate feasibility of the basic approach. These models are spatially coarse and approximate, but can be straightforwardly improved. The transport lattice system models are modular and multiscale (spatial scales ranging from the membrane thickness of 5 nm to the axon segment length of 2 cm).

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.

Model of a confined spherical cell in uniform and heterogeneous applied electric fields

Cells exposed to electric fields are often confined to a small volume within a solid tissue or within or near a device. Here we report on an approach to describing the frequency and time domain electrical responses of a spatially confined spherical cell by using a transport lattice system model. Two cases are considered: (1) a uniform applied field created by parallel plane electrodes, and (2) a heterogeneous applied field created by a planar electrode and a sharp microelectrode. Here fixed conductivities and dielectric permittivities of the extra- and intracellular media and of the membrane are used to create local transport models that are interconnected to create the system model. Consistent with traditional analytical solutions for spherical cells in an electrolyte of infinite extent, in the frequency domain the field amplification, G(m) (f) is large at low frequencies, f<1 MHz. G(m) (f) gradually decreases above 1 MHz and reaches a lower plateau at about 300 MHz, with the cell becoming almost "electrically invisible". In the time domain the application of a field pulse can result in altered localized transmembrane voltage changes due to a single microelectrode. The transport lattice approach provides modular, multiscale modeling capability that here ranges from cell membranes (5 nm scale) to the cell confinement volume ( approximately 40 microm scale).

Numerical Determination of Transmembrane Voltage Induced on Irregularly Shaped Cells

The paper presents an approach that reduces several difficulties related to the determination of induced transmembrane voltage (ITV) on irregularly shaped cells. We first describe a method for constructing realistic models of irregularly shaped cells based on microscopic imaging. This provides a possibility to determine the ITV on the same cells on which an experiment is carried out, and can be of considerable importance in understanding and interpretation of the data. We also show how the finite-thickness, nonzero-conductivity membrane can be replaced by a boundary condition in which a specific surface conductivity is assigned to the interface between the cell interior (the cytoplasm) and the exterior. We verify the results obtained using this method by a comparison with the analytical solution for an isolated spherical cell and a tilted oblate spheroidal cell, obtaining a very good agreement in both cases. In addition, we compare the ITV computed for a model of two irregularly shaped CHO cells with the ITV measured on the same two cells by means of a potentiometric fluorescent dye, and also with the ITV computed for a simplified model of these two cells.

Field stimulation of cells in suspension: use of a hybrid finite element method

Electric fields are used in a range of applications, including gene transfection, electrochemotherapy of tumors and cardiac defibrillation. Despite the widespread use of electric fields, most of the theoretical and computational studies on discrete cellular tissue have focused on a single cell. In this work, we propose a hybrid finite element method to simulate the effects of external electric fields on clusters of excitable cells. The method can be used to model cells of arbitrary cell geometries and non-linear membrane dynamics. The results show that the response of multiple cell, like a single cell, is a two-stage process consisting of the initial polarization that proceeds with cellular time constant (less than one microsecond) and the actual excitation of the cell membrane that proceeds with the membrane time constant (on the order of milliseconds). The results also show that the stimulation of a given cell depends in part on the arrangement of cells within the field and not simply the location within the field, suggesting that classical approaches that ignores the effect of the cells on the field do not adequately predict the cellular response.

Cylindrical cell membranes in uniform applied electric fields: validation of a transport lattice method

The frequency and time domain transmembrane voltage responses of a cylindrical cell in an external electric field are calculated using a transport lattice, which allows solution of a variety of biologically relevant transport problems with complex cell geometry and field interactions. Here we demonstrate the method for a cylindrical membrane geometry and compare results with known analytical solutions. Results of transport lattice simulations on a Cartesian lattice are found to have discrepancies with the analytical solutions due to the limited volume of the system model and approximations for the local membrane model on the Cartesian lattice. Better agreement is attained when using a triangular mesh to represent the geometry rather than a Cartesian lattice. The transport lattice method can be readily extended to more sophisticated cell, organelle, and tissue configurations. Local membrane models within a system lattice can also include nonlinear responses such as electroporation and ion-channel gating.

Transmembrane voltage induced on a cell membrane in suspensions exposed to an alternating field: A theoretical analysis

We present analytical equations for the transmembrane voltage (DeltaPsi) induced by an alternating field on spherical cells arranged in orderly suspensions. For physiologically normal cells, the cell membrane was assumed to be non-conductive. With increasing alternating field frequency, capacitive property of the cytoplasm and the external medium become increasingly important and thus must be accounted for. Considering the symmetry of the arrayed cells and the tiny volume of the unit cell compared to that of the suspensions, the influence exerted on a unit cell by other cells was posited to be approximately symmetrical with respect to the symmetrical axis. This implies that the shape of the equipotential plane of spherical cells in the suspensions is similar to that of the single cell exposed to the external field, though the value of the potential of both cells should be different. Therefore, the internal field of the cytoplasm and the equivalent body of a unit cell in the suspensions should be approximately constant. This allows for calculating the effective average field in the equivalent body with Maxwell-Wagner and Bruggeman-Hanai equations for low and high cell concentrations, respectively. We investigated the conditions, under which the local electric field of a unit cells in suspension is approximately equal to that of a single cell. Under these conditions the analytical solution for DeltaPsi induced by alternating fields on cells in suspensions can be derived from that of the single cell.