Cell membrane electroporation modeling: A multiphysics approach

A Model for Reversible Electroporation to Deliver Drugs into Diseased Tissues

Drug delivery through electroporation could be highly beneficial for the treatment of different types of diseased tissues within the human body. In this work, a mathematical model of reversible tissue electroporation is presented for injecting drug into the diseased cells. The model emphasizes the tissue boundary where the drug is injected as a point source. In addition, the effect of drug loss at tissue boundaries through extracellular space is studied elaborately. Multiple pulses are applied to deliver a sufficient amount of drug into the targeted cells. The set of differential equations that model the physical circumstances are solved numerically. This model obtains a mass transfer coefficient (MTC), in terms of pore fraction coefficient and drug permeability that controls the drug transport from extracellular to intracellular space. The drug penetration throughout the tissue is captured for the application of different pulses. The boundary effects on drug concentration are highlighted in this study. The advocated model is able to perform homogeneous drug transport into the cells so that the affected tissue is treated completely. This model can be applied to optimize clinical experiments by avoiding the lengthy and costly in vivo and in vitro experiments.

Considering Joule heating in coupled electroporation and electrodeformation modeling of glioblastoma cells

Cells exposed to a pulsed electric field undergo electroporation(EP) and electrodeformation(ED) under electric field stress, and a coupled model of EP and ED of glioblastoma(GBM) taking into account Joule heating is proposed. The model geometry is extracted from real cell boundaries, and the effects of Joule heating-induced temperature rise on the EP and ED processes are considered. The results show that the temperature rise will increase the cell's local conductivity, leading to a decrease in the transmembrane potential(TMP). The temperature rise also causes a decrease in the dynamic Young's modulus of the cell membrane, making the cell less resistant to deformation. In addition, GBM cells are more susceptible to EP in the middle portion of the cell and ED in the three tentacle portions under pulsed electric fields, and the cells undergo significant positional shifts. The ED of the nucleus is similar to spherical cells, but the degree of ED is smaller.

Analysis of In Situ Electroporation Utilizing Induced Electric Field at a Wireless Janus Microelectrode

In situ electroporation, a non-invasive technique for enhancing the permeability of cell membranes, has emerged as a powerful tool for intracellular delivery and manipulation. This method allows for the precise introduction of therapeutic agents, such as nucleic acids, drugs, and proteins, directly into target cells within their native tissue environment. Herein, we introduce an innovative electroporation strategy that employs a Janus particle (JP)-based microelectrode to generate a localized and controllable electric field within a microfluidic chip. The microfluidic device is engineered with an indium tin oxide (ITO)-sandwiched microchannel, where the electric field is applied, and suspended JP microelectrodes that induce a stronger localized electric field. The corresponding simulation model is developed to better understand the dynamic electroporation process. Numerical simulations for both single-cell and chain-assembled cell electroporation have been successfully conducted. The effects of various parameters, including pulse voltage, duration medium conductivity, and radius of Janus microelectrode, on cell membrane permeabilization are systematically investigated. Our findings indicate that the enhanced electric intensity near the poles of the JP microelectrode significantly contributes to the electroporation process. In addition, the distribution for both transmembrane voltage and the resultant nanopores can be altered by conveniently adjusting the relative position of the JP microelectrode, demonstrating a selective and in situ electroporation technique for spatial control over the delivery area. Moreover, the obtained differences in the distribution of electroporation between chain cells can offer insightful directives for the electroporation of tissues or cell populations, enabling the precise and targeted modulation of specific cell populations. As a proof of concept, this work can provide a robust alternative technique for the study of complex and personalized cellular processes.

Calculating transmembrane voltage on the electric pulse-affected cancerous cell membrane: using molecular dynamics and finite element simulations

CONTEXT

Electroporation is a technique that creates electrically generated pores in the cell membrane by modifying transmembrane potential. In this work, the finite element method (FEM) was used to examine the induced transmembrane voltage (ITV) of a spherical-shaped MCF-7 cell, allowing researchers to determine the stationary ITV. A greater ITV than the critical value causes permeabilization of the membrane. Furthermore, the present study shows how a specific surface conductivity can act as a stand-in for the thin layer that constitutes a cell membrane as the barrier between extracellular and intracellular environments. Additionally, the distribution of ITV on the cell membrane and its maximum value were experimentally evaluated for a range of applied electric fields. Consequently, the entire cell surface area was electroporated 66% and 68% for molecular dynamics (MD) simulations and FEM, respectively, when the external electric field of 1500 V/cm was applied to the cell suspension using the previously indicated numerical methods. Furthermore, the lipid bilayers' molecular structure was changed, which led to the development of hydrophilic holes with a radius of 1.33 nm. Applying MD and FEM yielded threshold values for transmembrane voltage of 700 and 739 mV, respectively.

METHOD

Using MD simulations of palmitoyloleoyl-phosphatidylcholine (POPC), pores in cell membranes exposed to external electric fields were numerically investigated. The dependence on the electric field was estimated and developed, and the amount of the electroporated cell surface area matches the applied external electric field. To investigate more, a mathematical model based on an adaptive neuro-fuzzy inference system (ANFIS) is employed to predict the percent cell viability of cancerous cells after applying four pulses during electroporation. For MD simulations, ArgusLab, VMD, and GROMACS software packages were used. Moreover, for FEM analysis, COMSOL software package was used. Also, it is worth mentioning that for mathematical model, MATLAB software is used.

An experimental and theoretical study on cell swelling for osmotic imbalance induced by electroporation

The cellular membrane serves as a pivotal barrier in regulating intra- and extracellular matter exchange. Disruption of this barrier through pulsed electric fields (PEFs) induces the transmembrane transport of ions and molecules, creating a concentration gradient that subsequently results in the imbalance of cellular osmolality. In this study, a multiphysics model was developed to simulate the electromechanical response of cells exposed to microsecond pulsed electric fields (μsPEFs). Within the proposed model, the diffusion coefficient of the cellular membrane for various ions was adjusted based on electropore density. Cellular osmolality was governed and described using Van't Hoff theory, subsequently converted to loop stress to dynamically represent the cell swelling process. Validation of the model was conducted through a hypotonic experiment and simulation at 200 mOsm/kg, revealing a 14.2% increase in the cell's equivalent radius, thereby confirming the feasibility of the cell mechanical model. With the transmembrane transport of ions induced by the applied μsPEF, the hoop stress acting on the cellular membrane reached 179.95 Pa, and the cell equivalent radius increased by 11.0% when the extra-cellular medium was supplied with normal saline. The multiphysics model established in this study accurately predicts the dynamic changes in cell volume resulting from osmotic imbalance induced by PEF action. This model holds theoretical significance, offering valuable references for research on drug delivery and tumor microenvironment modulation.

Research frontiers of electroporation-based applications in cancer treatment: a bibliometric analysis

OBJECTIVES

Electroporation, the breakdown of the biomembrane induced by external electric fields, has increasingly become a research hotspot for its promising related methods in various kinds of cancers.

CONTENT

In this article, we utilized CiteSpace 6.1.R2 to perform a bibliometric analysis on the research foundation and frontier of electroporation-based applications in cancer therapy. A total of 3,966 bibliographic records were retrieved from the Web of Science Core Collection for the bibliometric analysis. Sersa G. and Mir L. M. are the most indispensable researchers in this field, and the University of Ljubljana of Slovenia is a prominent institution. By analyzing references and keywords, we found that, with a lower recurrence rate, fewer severe adverse events, and a higher success rate, irreversible electroporation, gene electrotransfer, and electrochemotherapy are the three main research directions that may influence the future treatment protocol of cancers.

SUMMARY

This article visualized relevant data to synthesize scientific research on electroporation-based cancer therapy, providing helpful suggestions for further investigations on electroporation.

OUTLOOK

Although electroporation-based technologies have been proven as promising tools for cancer treatment, its radical mechanism is still opaque and their commercialization and universalization need further efforts from peers.

Enhanced Drug Uptake on Application of Electroporation in a Single-Cell Model

Electroporation method is a useful tool for delivering drugs into various diseased tissues in the human body. As a result of an applied electric field, drug particles enter the intracellular compartment through the temporarily permeabilized cell membrane. Consequently, electroporation method allows better penetration of the drug into the diseased tissue and improves treatment clinically. In this study, a more generalized model of drug transport in a single cell is proposed. The model is able to capture non-homogeneous drug transport in the cell due to non-uniform cell membrane permeabilization. Several numerical experiments are conducted to understand the effects of electric field and drug permeability on drug uptake into the cell. Through investigation, the appropriate electric field and drug permeability are identified, which lead to sufficient drug uptake into the cell. This model can be used by experimentalists to get information prior to conduct any experiment, and it may help reduce the number of actual experiments that might be conducted otherwise.

A Comprehensive Review on Barium Titanate Nanoparticles as a Persuasive Piezoelectric Material for Biomedical Applications: Prospects and Challenges

Stimulation of cells with electrical cues is an imperative approach to interact with biological systems and has been exploited in clinical practices over a wide range of pathological ailments. This bioelectric interface has been extensively explored with the help of piezoelectric materials, leading to remarkable advancement in the past two decades. Among other members of this fraternity, colloidal perovskite barium titanate (BaTiO₃ ) has gained substantial interest due to its noteworthy properties which includes high dielectric constant and excellent ferroelectric properties along with acceptable biocompatibility. Significant progression is witnessed for BaTiO₃ nanoparticles (BaTiO₃ NPs) as potent candidates for biomedical applications and in wearable bioelectronics, making them a promising personal healthcare platform. The current review highlights the nanostructured piezoelectric bio interface of BaTiO₃ NPs in applications comprising drug delivery, tissue engineering, bioimaging, bioelectronics, and wearable devices. Particular attention has been dedicated toward the fabrication routes of BaTiO₃ NPs along with different approaches for its surface modifications. This review offers a comprehensive discussion on the utility of BaTiO₃ NPs as active devices rather than passive structural unit behaving as carriers for biomolecules. The employment of BaTiO₃ NPs presents new scenarios and opportunity in the vast field of nanomedicines for biomedical applications.

Plant-based model for the visual evaluation of electroporated area after irreversible electroporation and its comparison to in-vivo animal data

Electroporation (EP) is widely used in medicine, such as cancer treatment, in form of electrochemotherapy or irreversible electroporation (IRE). For EP device testing, living cells or tissue inside a living organism (including animals) are needed. Plant-based models seem to be a promising alternative to substitute animal models in research. The aim of this study is to find a suitable plant-based model for visual evaluation of IRE, and to compare the geometry of electroporated areas with in-vivo animal data.For this purpose, a variety of fruit and vegetables were selected and visually evaluated after 0/1/2/4/6/8/12/16/24 h post-EP. Apple and potato were found to be suitable models as they enabled a visual evaluation of the electroporated area. For these models, the size of the electroporated area was determined after 0/1/2/4/6/8/12/16/24 h. For apples, a well-defined electroporated area was visual within two hours, while in potatoes it reached a plateau after eight hours only. The electroporated area of apple, which showed the fastest visual results was then compared to a retrospectively evaluated swine liver IRE dataset which had been obtained for similar conditions. The electroporated area of the apple and swine liver both showed a spherical geometry of comparable size. For all experiments, the standard protocol for human liver IRE was followed. To conclude, potato and apple were found to be suitable plant-based models for the visual evaluation of electroporated area after irreversible EP, with apple being the best choice for fast visual results. Given the comparable range, the size of the electroporated area of the apple may be promising as a quantitative predictor in animal tissue. Even if plant-based models cannot completely replace animal experiments, they can be used in the early stages of EP device development and testing, decreasing animal experiments to the necessary minimum.

Comprehensive single-shot biophysical cytometry using simultaneous quantitative phase imaging and Brillouin spectroscopy

Single-cell analysis, or cytometry, is a ubiquitous tool in the biomedical sciences. Whereas most cytometers use fluorescent probes to ascertain the presence or absence of targeted molecules, biophysical parameters such as the cell density, refractive index, and viscosity are difficult to obtain. In this work, we combine two complementary techniques-quantitative phase imaging and Brillouin spectroscopy-into a label-free image cytometry platform capable of measuring more than a dozen biophysical properties of individual cells simultaneously. Using a geometric simplification linked to freshly plated cells, we can acquire the cellular diameter, volume, refractive index, mass density, non-aqueous mass, fluid volume, dry volume, the fractional water content of cells, both by mass and by volume, the Brillouin shift, Brillouin linewidth, longitudinal modulus, longitudinal viscosity, the loss modulus, and the loss tangent, all from a single acquisition, and with no assumptions of underlying parameters. Our methods are validated across three cell populations, including a control population of CHO-K1 cells, cells exposed to tubulin-disrupting nocodazole, and cells under hypoosmotic shock. Our system will unlock new avenues of research in biophysics, cell biology, and medicine.

Effects of solution conductivity on macropore size dynamics in electroporated lipid vesicle membranes

Using fast imaging microscopy, we investigate in detail the expansion of micron-sized pores occurring in individual electroporated giant unilamellar vesicles composed of the phospholipid 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (POPC). To infer pore dynamics on the electrodeformed and electropermeabilized vesicles, we develop a computational approach and provide for the first time a direct evidence of quantitative agreement between experimental data and the well-established theoretical prediction of Smith, Neu and Krassowska (SNK). The analysis we describe also provides an extension to the current theoretical literature on how the conductivity ratio of the internal and the external vesicle solution plays a determinant role in the definition of the electrical force driving pore expansion kinetics.

Modeling cell membrane electrodeformation by alternating electric fields

With the aim of characterizing and gaining insight into the frequency response of cells suspended in a fluid medium and deformed with a controlled alternating electric field, a continuum-based analysis is presented for modeling electrodeformation (ED) via Maxwell stress tensor (MST) calculation. Our purpose here is to apply this approach to explain the fact that the electric field anisotropy and electrical conductivity ratio Λ of the cytoplasm and the extracellular medium significantly impact the MST exerted on the cytoplasm-membrane interface. One important finding is that the modulation of electrical cues and MST force by the frequency of the applied electric field provides an extremely rich tool kit for manipulating cells. We show the extreme sensitivity of proximity-induced capacitive coupling arising concomitantly when the magnitude of the MST increases as the distance between cells is decreased and the spatial anisotropy becomes important. Moreover, our model highlights the strongly localized character of the electrostatic field effect emanating from neighboring cells and suggests the possibility of exploiting cell distribution as a powerful tool to engineer the functional performance of cell assemblies by controlling ED and capacitive coupling. We furthermore show that frequency has a significant impact on the attenuation-amplification transition of MST, suggesting that shape anisotropy has a much weaker influence on ED of the cell membrane compared to the anisotropy induced by the orientation angle itself.

Translocation of silica nanospheres through giant unilamellar vesicles (GUVs) induced by a high frequency electromagnetic field

Membrane model systems capable of mimicking live cell membranes were used for the first time in studying the effects arising from electromagnetic fields (EMFs) of 18 GHz where membrane permeability was observed following exposure. A present lack of understanding of the mechanisms that drive such a rapid change in membrane permeabilization as well as any structural or dynamic changes imparted on biomolecules affected by high-frequency electromagnetic irradiation limits the use of 18 GHz EMFs in biomedical applications. A phospholipid, 1,2-dioleoyl-sn-glycero-3-phosphocholine (DOPC) labelled with a fluorescent marker 1,2-dioleoyl-sn-glycero-3-phosphoethanolamine-N-(lissamine rhodamine B sulfonyl) (rhodamine-DOPE) was used in constructing the giant unilamellar vesicles (GUVs). After three cycles of exposure, enhanced membrane permeability was observed by the internalisation of hydrophilic silica nanospheres of 23.5 nm and their clusters. All-atom molecular dynamics simulations of 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (POPC) membranes exposed to high frequency electric fields of different field strengths showed that within the simulation timeframe only extremely high strength fields were able to cause an increase in the interfacial water dynamics characterized by water dipole realignments. However, a lower strength, high frequency EMF induced changes of the water hydrogen bond network, which may contribute to the mechanisms that facilitate membrane permeabilization in a longer timeframe.

Dynamic Electroporation Model Evaluation on Rabbit Tissues

Biological electroporation is a process of opening pores in the cell membrane when exposed to intense electric fields. This work provides results for validation of a dynamic model of electroporation on biological tissues. Computational simulations were carried out and results for the electrical current through the tissue and increase of the tissue temperature were compared to experimental results. Two calculation methods were used: Equivalent Circuit Method and Finite Element Method. With Equivalent Circuit Method the dielectric dispersion present in biological tissues was included. Liver, kidney and heart of rabbit were used in the experiments. Voltage pulse protocols and voltage ramps were applied using stainless steel needles electrodes. There is good agreement between the simulated and experimental results with mean errors below 15%, with the simulated results within the experimental standard deviation. Only for the protocol with fundamental frequency of 50 kHz, the simulation performed by the Finite Element Method using a commercial software did not correctly represent the current, with errors reaching 50%. The justification for the error found is due to the dielectric dispersion that was not included in this simulator.

Multiphysics modelling of electroporation under uni- or bipolar nanosecond pulse sequences

A nonlinear dispersive multiphysics model of single-cell electroporation was proposed in this paper. The time-domain Debye model was utilised to describe the membrane dispersion while the dynamic pore radius function was deployed to modify the plasma membrane conductivity. The dynamic spatial distributions of the ion concentration were dominated by the Nernst-Planck function. First, a single nanosecond pulsed electric field was applied to verify our model and to explore the effects of dispersion and dynamic pore radius on the redistribution of the electric field. The dispersive membrane was found to increase the transmembrane potential, expedite the electroporation process, and weaken the membrane permeability; however, adding the dynamic pore radius function had the opposite effect on transmembrane potential and membrane permeability. The responses of the cells exposed to unipolar and bipolar nanosecond pulse sequences were subsequently simulated. During the application of unipolar pulse sequences, the pore radius and perforation area showed a step-like accumulation, and significant increases in the perforation area and intracellular ion concentration were observed with higher frequency pulse sequences and wider subpulse intervals. The bipolar cancellation effect was also observed in terms of membrane permeability and pore radius.

Single-cell electroporation with high-frequency nanosecond pulse bursts: Simulation considering the irreversible electroporation effect and experimental validation

To study the electroporation characteristics of cells under high-frequency nanosecond pulse bursts (HFnsPBs), the original electroporation mathematical model was improved. By setting a threshold value for irreversible electroporation (IRE) and considering the effect of an electric field on the surface tension of a cell membrane, a mathematical model of electroporation considering the effect of IRE is proposed for the first time. A typical two-dimensional cell system was discretized into nodes using MATLAB, and a mesh transport network method (MTNM) model was established for simulation. The dynamic processes of single-cell electroporation and molecular transport under the application of 50 unipolar HFnsPBs with field intensities of 9 kV cm^-1 and different frequencies (10 kHz, 100 kHz and 500 kHz) to the target system was simulated with a 300 s simulation time. The IRE characteristics and molecular transport were evaluated. In addition, a PI fluorescent dye assay was designed to verify the correctness of the model by providing time-domain and spatial results that were compared with the simulation results. The simulation achieved IRE and demonstrated the cumulative effects of multipulse bursts and intraburst frequency on irreversible pores. The model can also reflect the cumulative effect of multipulse bursts on reversible pores by introducing an assumption of stable reversible pores. The experimental results agreed qualitatively with the simulation results. A relative calibration of the fluorescence data gave time-domain molecular transport results that were quantitatively similar to the simulation results. This article reveals the cell electroporation characteristics under HFnsPBs from a mechanism perspective and has important guidance for fields involving the IRE of cells.

Coupled mathematical modeling of cisplatin electroporation

The use of electrochemotherapy (ECT) is a well-established technique to increase the cellular uptake of cytotoxic agents within certain cancer treatment strategies. The study of the mechanisms that take part in this complex process is of high interest to gain a deeper knowledge of it, enabling the improvement of these strategies. In this work, we present a coupled multi-physics electroporation model based on a related previous one, to describe the effect of a set of electric pulses on cisplatin transport across the plasma membrane. The model applies a system of partial differential equations that includes Poisson's equation for the electric field, Nernst-Planck's equation for species transport, Maxwell's tensor and mechanical equilibrium equation for membrane deformation and Smoluchowski's equation for pore creation dynamics. Our numerical results were compared with previous numerical and experimental published data with good qualitative and quantitative agreement. These results indicate that pore aperture is favored at the cell poles by the electric field and mechanical stress forces, giving support to the dominant hypothesis of hydrophilic pore creation as the main mechanism of drug entry during an ECT treatment.

Proximity-induced electrodeformation and membrane capacitance coupling between cells

Membrane capacitance and transmembrane potential are sensitive to the proximity of neighboring biological cells which eventually induces anisotropic perturbation of the local electric field distribution in a cell assembly and/or a tissue. The development of robust and reliable multiphysics approaches is essential to solve the challenge of analyzing proximity-induced capacitance coupling (CC) between cells. In this study, we ask to what extent this CC is a minor perturbation on the individual cells or whether it can fundamentally affect bio-electromechanical cues. A key component of our continuum electromechanical analysis is the consideration of elastic models of cells under steady state electric field excitation to characterize electrodeformation (ED). Analyzing the difference between the ED force for a pair of cells and its counterpart for a single reference cell allows us to determine a separation distance-orientation angle diagram providing evidence of a separation distance beyond which the electrostatic interactions between a pair of biological cells become inconsequential for the ED. An attenuation-amplification transition of ED force in this diagram suggests that anisotropy induced by the orientation angle of the cell pair relative to the applied electric field direction has a significant influence on ED and CC. We furthermore observe that the shape of this diagram changes when extracellular conductivity is varied. The results obtained are then contrasted with the corresponding diagrams of similar cell configurations under an oscillating electric field excitation below and above the α-dispersion frequency. This investigation may provide new opportunities for further assessment of electromechanical properties of engineered tissues.

Recent Advances in Electrochemotherapy

Electrochemotherapy is gaining recognition as an effective local therapy that uses systemically or intratumorally injected bleomycin or cisplatin with electroporation as a delivery system that brings drugs into the cells to exert their cytotoxic effects. Preclinical work is still ongoing, testing new drugs, seeking the best treatment combination with other treatment modalities, and exploring new sets of pulses for effective tissue electroporation. The applications of electrochemotherapy are being fully exploited in veterinary oncology, where electrochemotherapy, because of its simple execution, has a relatively good cost-benefit ratio and is used in the treatment of cutaneous tumors. In human oncology, electrochemotherapy is fully recognized as a local therapy for cutaneous tumors and metastases. Its effectiveness is being explored in combination with immunomodulatory drugs. However, the development of electrochemotherapy is directed into the treatment of deep-seated tumors with a percutaneous approach. Because of the vast number of reports, this review discusses the articles published in the past 5 years.

Exposure to high-frequency electromagnetic field triggers rapid uptake of large nanosphere clusters by pheochromocytoma cells

Background

Effects of man-made electromagnetic fields (EMF) on living organisms potentially include transient and permanent changes in cell behaviour, physiology and morphology. At present, these EMF-induced effects are poorly defined, yet their understanding may provide important insights into consequences of uncontrolled (e.g., environmental) as well as intentional (e.g., therapeutic or diagnostic) exposure of biota to EMFs. In this work, for the first time, we study mechanisms by which a high frequency (18 GHz) EMF radiation affects the physiology of membrane transport in pheochromocytoma PC 12, a convenient model system for neurotoxicological and membrane transport studies.

Methods and results

Suspensions of the PC 12 cells were subjected to three consecutive cycles of 30s EMF treatment with a specific absorption rate (SAR) of 1.17 kW kg^-1, with cells cooled between exposures to reduce bulk dielectric heating. The EMF exposure resulted in a transient increase in membrane permeability for 9 min in up to 90 % of the treated cells, as demonstrated by rapid internalisation of silica nanospheres (diameter d ≈ 23.5 nm) and their clusters (d ≈ 63 nm). In contrast, the PC 12 cells that received an equivalent bulk heat treatment behaved similar to the untreated controls, showing lack to minimal nanosphere uptake of approximately 1-2 %. Morphology and growth of the EMF treated cells were not altered, indicating that the PC 12 cells were able to remain viable after the EMF exposure. The metabolic activity of EMF treated PC 12 cells was similar to that of the heat treated and control samples, with no difference in the total protein concentration and lactate dehydrogenase (LDH) release between these groups.

Conclusion

These results provide new insights into the mechanisms of EMF-induced biological activity in mammalian cells, suggesting a possible use of EMFs to facilitate efficient transport of biomolecules, dyes and tracers, and genetic material across cell membrane in drug delivery and gene therapy, where permanent permeabilisation or cell death is undesirable.