Dynamical modeling of tissue electroporation

Electroporation enhances cell death in 3D scaffold-based MDA-MB-231 cells treated with metformin

Triple-negative breast cancer (TNBC), the most aggressive subtype of breast cancer lacks estrogen, progesterone, and HER2 receptors and hence, is therapeutically challenging. Towards this, we studied an alternate therapy by repurposing metformin (FDA-approved type-2 diabetic drug with anticancer properties) in a 3D-scaffold culture, with electrical pulses. 3D cell culture was used to simulate the tumor microenvironment more closely and MDA-MB-231, human TNBC cells, treated with both 5 mM metformin (Met) and 8 electrical pulses at 2500 V/cm, 10 µs (EP1) and 800 V/cm, 100 µs (EP2) at 1 Hz were studied in 3D and 2D. They were characterized using cell viability, reactive oxygen species (ROS), glucose uptake, and lactate production assays at 24 h. Cell viability, as low as 20 % was obtained with EP1 + 5 mM Met. They exhibited 1.65-fold lower cell viability than 2D with EP1 + 5 mM Met. ROS levels indicated a 2-fold increase in oxidative stress for EP1 + 5 mM Met, while the glucose uptake was limited to only 9 %. No significant change in the lactate production indicated glycolytic arrest and a non-conducive environment for MDA-MB-231 growth. Our results indicate that 3D cell culture, with a more realistic tumor environment that enhances cell death using metformin and electrical pulses could be a promising approach for TNBC therapeutic intervention studies.

Characterizing reversible, irreversible, and calcium electroporation to generate a burst-dependent dynamic conductivity curve

The relationships between burst number, reversible, irreversible, and calcium electroporation have not been comprehensively evaluated in tumor tissue-mimics. Our findings indicate that electroporation effects saturate with a rate constant (τ) of 20 bursts for both conventional and high frequency waveforms (R2 > 0.88), with the separation between reversible and irreversible electroporation thresholds converging at 50 bursts. We find the lethal thresholds for calcium electroporation are statistically similar to reversible electroporation (R2 > 0.99). We then develop a burst-dependent dynamic conductivity curve that now incorporates electroporation effects due to both the electric field magnitude and burst number. Simulated ablation and thermal damage volumes vary significantly between finite element models using either the conventional or new burst-dependent dynamic conductivity curve (p < 0.05). Lastly, for clinically relevant protocols, thermal damage is indicated to not begin until 50 bursts, with maximum nonthermal ablation volumes at 100 bursts (1.5-13% thermal damage by volume). We find that >100 bursts generated negligible increases in ablation volumes with 40-70% thermal damage by volume at 300 bursts. Our results illustrate the need for considering burst number in minimizing thermal damage, choosing adjuvant therapies, and in modeling electroporation effects at low burst numbers.

Musa acuminata as electroporation model

Electrochemotherapy (ECT) and Irreversible electroporation (IRE) are cancer treatments based on electric field distribution in tissues. Solanum tuberosum (potato tissue) phantom is known to mimic changes in the electrical conductivity that occur in animal tissues during electroporation (EP). Electric field distribution is assessed through enzymatic staining. However, the 24-h wait for this assessment could slow agile response scenarios. We developed and validated the Musa acuminata (cavendish banana) conductivity model, which quickly evaluates EP by tissue staining. We investigated the frequency response of the tissue using impedance spectroscopy analysis, conductivity changes, and enzymatic staining. We optimized three usual EP models: adapted Gompertz, smoothed Heaviside, and the sigmoid or logistic function. We found dielectric parameters in banana tissue similar to those in potato (electrical conductivity of 0.035 S/m and relative permittivity of 4.1×104). The coefficients of determination R2 were 99.94% (Gompertz), 99.85% (Heaviside), and 99.58% (sigmoid). The sigmoid and Heaviside functions described the calibration and validation electric currents with 95% confidence. We observed the electroporated areas in bananas 3h30m after EP. Staining was significant after 450 V/cm. The conductivity model of Musa acuminata suits treatment planning, hardware development, and training scenarios. Banana phantom supports the 3Rs practice and is a reliable alternative for potato in EP studies.

Influence of electric pulse characteristics on the cellular internalization of chemotherapeutic drugs and cell survival fraction in electroporated and vasoconstricted cancer tissues using boundary element techniques

Electroporation has emerged as a suitable technique to induce the pore formation in the cell membrane of cancer tissues, facilitating the cellular internalization of chemotherapeutic drugs. An adequate selection of the electric pulse characteristics is crucial to guarantee the efficiency of this technique, minimizing the adverse effects. In the present work, the dual reciprocity boundary element method (DR-BEM) is applied for the simulation of drug transport in the extracellular and intracellular space of cancer tissues subjected to the application of controlled electric pulses, using a continuum tumour cord approach, and considering both the electro-permeabilization and vasoconstriction phenomena. The developed DR-BEM algorithm is validated with numerical and experimental results previously published, obtaining a satisfactory accuracy and convergence. Using the DR-BEM code, a study about the influence of the magnitude of electric field (E) and pulse spacing (dpulses) on the time behavior and spatial distribution of the internalized drug, as well as on the cell survival fraction, is carried out. In general, the change of drug concentration, drug exposure and cell survival fraction with the parameters E and dpulses is ruled by two important factors: the balance between the electro-permeabilization and vasoconstriction phenomena, and the relative importance of the sources of cell death (electric pulses and drug cytotoxicity); these two factors, in turn, significantly depend on the reversible and irreversible thresholds considered for the electric field.

Effects of pulse repetition rate in static electrochemotherapy models

Electroporation alters cell membrane structure and tissue electrical properties by short and intense pulsed electric fields (PEF). Static mathematical models are often used to explain the change in electrical properties of tissues caused by electroporation. Electric pulse repetition rate may play an important role, as tissue dielectric dispersion, electroporation dynamics, and Joule heating may affect the electrical properties. In this work, we investigate the effects on the magnitude of the electric current when the repetition rate of the standard electrochemotherapy protocol is increased. Liver, oral mucosa, and muscle tissues were studied. Ex vivo animal experiments show that the magnitude of the electric current increases when the repetition rate is changed from 1 Hz to 5 kHz (10.8% for liver, 5.8% for oral mucosa, and 4.7% for muscle). Although a correction factor could reduce the error to less than 1%, dynamic models seem to be necessary to analyze different protocol signatures. Authors should be aware that static models and experimental results can only be compared if they use exactly the same PEF signature. The repetition rate is a key information to consider in the pretreatment computer study because the current at 1 Hz PEF differs from a 5 kHz PEF.

Nanoporous electroporation needle for localized intracellular delivery in deep tissues

The exogenous control of intracellular drug delivery has been shown to improve the overall efficacy of therapies by reducing nonspecific off-target toxicity. However, achieving a precise on-demand dosage of a drug in deep tissues with minimal damage is still a challenge. In this study, we report an electric-pulse-driven nanopore-electroporation (nEP) system for the localized intracellular delivery of a model agent in deep tissues. Compared with conventional bulk electroporation, in vitro nEP achieved better transfection efficiency (>60%) with a high cell recovery rate (>95%) under a nontoxic low electroporation condition (40 V). Furthermore, in vivo nEP using a nanopore needle electrode with a side drug-releasing compartment offered better control over the dosage release, time, and location of propidium iodide, which was used as a model agent for intracellular delivery. In a pilot study using experimental animals, the nEP system exhibited two times higher transfection efficiency of propidium iodide in the thigh muscle tissue, while minimizing tissue damage (<20%) compared to that of bulk electroporation. This tissue-penetrating nEP platform can provide localized, safe, and effective intracellular delivery of diverse therapeutics into deep tissues in a controlled manner.

Microarray Chip and Method for Simultaneous and Highly Consistent Electroporation of Multiple Cells of Different Sizes

Cell electroporation is an important cell manipulation technology to artificially transfer specific extracellular components into cells. However, the consistency of substance transport during the electroporation process is still an issue due to the wide size distribution of the natural cells. In this study, a cell electroporation microfluidic chip based on a microtrap array is proposed. The microtrap structure was optimized for single-cell capture and electric field focusing. The effects of the cell size on the cell electroporation in the microchip were investigated through simulation and experiment methods using the giant unilamellar vesicle as the simplified cell model, and a numerical model of a uniform electric field was used as a comparison. Compared with the uniform electric field, a lower threshold electric field is required to induce electroporation and produces a higher transmembrane voltage on the cell under a specific electric field in the microchip, showing an improvement in cell viability and electroporation efficiency. The larger perforated area produced on the cells in the microchip under a specific electric field allows a higher substance transfer efficiency, and the electroporation results are less affected by the cell size, which is beneficial for improving substance transfer consistency. Furthermore, the relative perforation area increases with the decrease of the cell diameter in the microchip, which is exactly opposite to that in a uniform electric field. By manipulating the electric field applied to the microtrap individually, a consistent proportion of substance transfer during electroporation of cells with different sizes can be achieved.

Real-Time Temperature Rise Estimation during Irreversible Electroporation Treatment through State-Space Modeling

To evaluate the feasibility of real-time temperature monitoring during an electroporation-based therapy procedure, a data-driven state-space model was developed. Agar phantoms mimicking low conductivity (LC) and high conductivity (HC) tissues were tested under the influences of high (HV) and low (LV) applied voltages. Real-time changes in impedance, measured by Fourier Analysis SpecTroscopy (FAST) along with the known tissue conductivity and applied voltages, were used to train the model. A theoretical finite element model was used for external validation of the model, producing model fits of 95.8, 88.4, 90.7, and 93.7% at 4 mm and 93.2, 58.9, 90.0, and 90.1% at 10 mm for the HV-HC, LV-LC, HV-LC, and LV-HC groups, respectively. The proposed model suggests that real-time temperature monitoring may be achieved with good accuracy through the use of real-time impedance monitoring.

An Investigation for Large Volume, Focal Blood-Brain Barrier Disruption with High-Frequency Pulsed Electric Fields

The treatment of CNS disorders suffers from the inability to deliver large therapeutic agents to the brain parenchyma due to protection from the blood-brain barrier (BBB). Herein, we investigated high-frequency pulsed electric field (HF-PEF) therapy of various pulse widths and interphase delays for BBB disruption while selectively minimizing cell ablation. Eighteen male Fisher rats underwent craniectomy procedures and two blunt-tipped electrodes were advanced into the brain for pulsing. BBB disruption was verified with contrast T1W MRI and pathologically with Evans blue dye. High-frequency irreversible electroporation cell death of healthy rodent astrocytes was investigated in vitro using a collagen hydrogel tissue mimic. Numerical analysis was conducted to determine the electric fields in which BBB disruption and cell ablation occur. Differences between the BBB disruption and ablation thresholds for each waveform are as follows: 2-2-2 μs (1028 V/cm), 5-2-5 μs (721 V/cm), 10-1-10 μs (547 V/cm), 2-5-2 μs (1043 V/cm), and 5-5-5 μs (751 V/cm). These data suggest that HF-PEFs can be fine-tuned to modulate the extent of cell death while maximizing peri-ablative BBB disruption. Furthermore, numerical modeling elucidated the diffuse field gradients of a single-needle grounding pad configuration to favor large-volume BBB disruption, while the monopolar probe configuration is more amenable to ablation and reversible electroporation effects.

TUB and ZNF532 Promote the Atoh1-Mediated Hair Cell Regeneration in Mouse Cochleae

Hair cell (HC) regeneration is a promising therapy for permanent sensorineural hearing loss caused by HC loss in mammals. Atoh1 has been shown to convert supporting cells (SCs) to HCs in neonatal cochleae; its combinations with other factors can improve the efficiency of HC regeneration. To identify additional transcription factors for efficient Atoh1-mediated HC regeneration, here we optimized the electroporation procedure for explant culture of neonatal mouse organs of Corti and tested multiple transcription factors, Six2, Ikzf2, Lbh, Arid3b, Hmg20 a, Tub, Sall1, and Znf532, for their potential to promote Atoh1-mediated conversion of SCs to HCs. These transcription factors are expressed highly in HCs but differentially compared to the converted HCs based on previous studies, and are also potential co-reprograming factors for Atoh1-mediated SC-to-HC conversion by literature review. P0.5 cochlear explants were electroporated with these transcription factors alone or jointly with Atoh1. We found that Sox2+ progenitors concentrated within the lateral greater epithelial ridge (GER) can be electroporated efficiently with minimal HC damage. Atoh1 ectopic expression promoted HC regeneration in Sox2+ lateral GER cells. Transcription factors Tub and Znf532, but not the other six tested, promoted the HC regeneration mediated by Atoh1, consistent with previous studies that Isl1 promotes Atoh1-mediated HC conversionex vivo and in vivo and that both Tub and Znf532 are downstream targets of Isl1. Thus, our studies revealed an optimized electroporation method that can transfect the Sox2+ lateral GER cells efficiently with minimal damage to the endogenous HCs. Our results also demonstrate the importance of the Isl1/Tub/Znf532 pathway in promoting Atoh1-mediated HC regeneration.

Modeling methods for treatment planning in overlapping electroporation treatments

OBJECTIVE

Irreversible electroporation (IRE) is a non thermal tissue ablation therapy which is induced by applying high voltage waveforms across electrode pairs. When multiple electrode pairs are sequentially used, the treatment volume (TV) is typically computed as the geometric union of the TVs of individual pairs. However, this method neglects that some regions are exposed to overlapping treatments. Recently, a model describing cell survival probability was introduced which effectively predicted TV with overlapping fields in vivo. However, treatment overlap has yet to be quantified. This study characterizes TV overlap in a controlled in vitro setup with the two existing methods which are compared to an adapted logistic model proposed here.

METHODS

CHO cells were immobilized in agarose gel. Initially, we characterized the electric field threshold and the cell survival probability for overlapping treatments. Subsequently, we created a 2D setup where we compared and validated the accuracy of the different methods in predicting the TV.

RESULTS

Overlap can reduce the electric field threshold required to induce cell death, particularly for treatments with low pulse number. However, it does not have a major impact on TV in the models assayed here, and all the studied methods predict TV with similar accuracy.

CONCLUSION

Treatment overlap has a minor influence in the TV for typical protocols found in IRE therapies.

SIGNIFICANCE

This study provides evidence that the modeling method used in most pre-clinical and clinical studies seems adequate.

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.

Rapid Impedance Spectroscopy for Monitoring Tissue Impedance, Temperature, and Treatment Outcome During Electroporation-Based Therapies

OBJECTIVE

Electroporation-based therapies (EBTs) employ high voltage pulsed electric fields (PEFs) to permeabilize tumor tissue; this results in changes in electrical properties detectable using electrical impedance spectroscopy (EIS). Currently, commercial potentiostats for EIS are limited by impedance spectrum acquisition time (  ∼ 10 s); this timeframe is much larger than pulse periods used with EBTs (  ∼ 1 s). In this study, we utilize rapid EIS techniques to develop a methodology for characterizing electroporation (EP) and thermal effects associated with high-frequency irreversible EP (H-FIRE) in real-time by monitoring inter-burst impedance changes.

METHODS

A charge-balanced, bipolar rectangular chirp signal is proposed for rapid EIS. Validation of rapid EIS measurements against a commercial potentiostat was conducted in potato tissue using flat-plate electrodes and thereafter for the measurement of impedance changes throughout IRE treatment. Flat-plate electrodes were then utilized to uniformly heat potato tissue; throughout high-voltage H-FIRE treatment, low-voltage inter-burst impedance measurements were used to continually monitor impedance change and to identify a frequency at which thermal effects are delineated from EP effects.

RESULTS

Inter-burst impedance measurements (1.8 kHz - 4.93 MHz) were accomplished at 216 discrete frequencies. Impedance measurements at frequencies above  ∼ 1 MHz served to delineate thermal and EP effects in measured impedance.

CONCLUSION

We demonstrate rapid-capture ( 1 s) EIS which enables monitoring of inter-burst impedance in real-time. For the first time, we show impedance analysis at high frequencies can delineate thermal effects from EP effects in measured impedance.

SIGNIFICANCE

The proposed waveform demonstrates the potential to perform inter-burst EIS using PEFs compatible with existing pulse generator topologies.

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.

Physiological changes may dominate the electrical properties of liver during reversible electroporation: Measurements and modelling

This study presents electrical measurements (both conductivity during the pulses and impedance spectroscopy before and after) performed in liver tissue of mice during electroporation with classical electrochemotherapy conditions (8 pulses of 100 µs duration). A four-needle electrode arrangement inserted in the tissue was used for the measurements. The undesirable effects of the four-electrode geometry, notably concerning its sensitivity, were quantified and discussed showing how the electrode geometry chosen for the measurements can impact the results. Numerical modelling was applied to the information collected during the pulse, and to the impedance spectra acquired before and after the pulses sequence. Our results show that the numerical results were not consistent, suggesting that other collateral phenomena not considered in the model are at work during electroporation in vivo. We show how the modification in the volume of the intra and extra cellular media, likely caused by the vascular lock effect, could at least partially explain the recorded impedance evolution. In the present study we demonstrate the significant impact that physiological effects have on impedance changes following electroporation at the tissue scale and the potential need of introducing them into the numerical models. The code for the numerical model is publicly available at https://gitlab.inria.fr/poignard/4-electrode-system.

Development of a Multi-Pulse Conductivity Model for Liver Tissue Treated With Pulsed Electric Fields

Pulsed electric field treatment modalities typically utilize multiple pulses to permeabilize biological tissue. This electroporation process induces conductivity changes in the tissue, which are indicative of the extent of electroporation. In this study, we characterized the electroporation-induced conductivity changes using all treatment pulses instead of solely the first pulse as in conventional conductivity models. Rabbit liver tissue was employed to study the tissue conductivity changes caused by multiple, 100 μs pulses delivered through flat plate electrodes. Voltage and current data were recorded during treatment and used to calculate the tissue conductivity during the entire pulsing process. Temperature data were also recorded to quantify the contribution of Joule heating to the conductivity according to the tissue temperature coefficient. By fitting all these data to a modified Heaviside function, where the two turning points (E₀, E₁) and the increase factor (A) are the main parameters, we calculated the conductivity as a function of the electric field (E), where the parameters of the Heaviside function (A and E₀) were functions of pulse number (N). With the resulting multi-factor conductivity model, a numerical electroporation simulation can predict the electrical current for multiple pulses more accurately than existing conductivity models. Moreover, the saturating behavior caused by electroporation can be explained by the saturation trends of the increase factor A in this model. The conductivity change induced by electroporation has a significant increase at about the first 30 pulses, then tends to saturate at 0.465 S/m. The proposed conductivity model can simulate the electroporation process more accurately than the conventional conductivity model. The electric field distribution computed using this model is essential for treatment planning in biomedical applications utilizing multiple pulsed electric fields, and the method proposed here, relating the pulse number to the conductivity through the variables in the Heaviside function, may be adapted to investigate the effect of other parameters, like pulse frequency and pulse width, on electroporation.

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.

Numerical workflow of irreversible electroporation for deep-seated tumor

The paper provides a numerical workflow, based on the 'real-life' clinical workflow of irreversible electroporation (IRE) performed for the treatment of deep-seated liver tumors. Thanks to a combination of numerical modeling, image registration algorithm and clinical data, our numerical workflow enables to provide the distribution of the electric field as effectively delivered by the clinical IRE procedure. As a proof of concept, we show on a specific clinical case of IRE ablation of liver tumor that clinical data could be advantageously combined to numerical simulations in a near future, in order to give to the interventional radiologists information on the effective IRE ablation. We also corroborate the simulated treated region with the post-treatment MRI performed 3 d after the treatment.

Histopathological and Ultrastructural Changes after Electroporation in Pig Liver Using Parallel-Plate Electrodes and High-Performance Generator

Irreversible electroporation (IRE) has gained attention as a new non-thermal therapy for ablation with important benefits in terms of homogeneous treatment and fast recovery. In this study, a new concept of high voltage generator is used, enabling irreversible electroporation treatment in large tissue volume using parallel plates. Unlike currently available generators, the proposed versatile structure enables delivering high-voltage high-current pulses. To obtain homogeneous results, 3-cm parallel-plates electrodes have also been designed and implemented. IRE ablation was performed on six female pigs at 2000 V/cm electric field, and the results were analysed after sacrifice three hours, three days and seven days after ablation. Histopathological and ultrastructural studies, including transmission and scanning electron microscopy, were carried out. The developed high-voltage generator has proved to be effective for homogeneous IRE treatment using parallel plates. The destruction of the membrane of the hepatocytes and the alterations of the membranes of the cellular organelles seem incompatible with cell death by apoptosis. Although endothelial cells also die with electroporation, the maintenance of vascular scaffold allows repairing processes to begin from the third day after IRE as long as the blood flow has not been interrupted. This study has opened new direction for IRE using high performance generators and highlighted the importance of taking into account ultrastructural changes after IRE by using electron microscopy analysis.

Time-Dependent Finite Element Analysis of In Vivo Electrochemotherapy Treatment

Electrochemotherapy and irreversible electroporation are gaining importance in clinical practice for the treatment of solid tumors. For successful treatment, it is extremely important that the coverage and exposure time of the treated tumor to the electric field are within the specified range. In order to ensure successful coverage of the entire target volume with sufficiently strong electric fields, numerical treatment planning has been proposed and its use has also been demonstrated in practice. Most of numerical models in treatment planning are based on charge conservation equation and are not able to provide time course of electric current, electrical conductivity, or electric field distribution changes established in the tissue during pulse delivery. Recently, a model based on inverse analysis of experimental data that delivers time course of tissue electroporation has been introduced. The aim of this study was to apply the previously reported time-dependent numerical model to a complex in vivo example of electroporation with different tissue types and with a long-term follow-up. The model, consisting of a tumor placed in the liver with 2 needle electrodes inserted in the center of the tumor and 4 around the tumor, was validated by comparison of measured and calculated time course of applied electric current. Results of simulations clearly indicated that proposed numerical model can successfully capture transient effects, such as evolution of electric current during each pulse, and effects of pulse frequency due to electroporation effects in the tissue. Additionally, the model can provide evolution of electric field amplitude and electrical conductivity in the tumor with consecutive pulse sequences.

Characterization of Cell Membrane Permeability In Vitro Part II: Computational Model of Electroporation-Mediated Membrane Transport

Electroporation is the process by which applied electric fields generate nanoscale defects in biological membranes to more efficiently deliver drugs and other small molecules into the cells. Due to the complexity of the process, computational models of cellular electroporation are difficult to validate against quantitative molecular uptake data. In part I of this two-part report, we describe a novel method for quantitatively determining cell membrane permeability and molecular membrane transport using fluorescence microscopy. Here, in part II, we use the data from part I to develop a two-stage ordinary differential equation model of cellular electroporation. We fit our model using experimental data from cells immersed in three buffer solutions and exposed to electric field strengths of 170 to 400 kV/m and pulse durations of 1 to 1000 μs. We report that a low-conductivity 4-(2-hydroxyethyl)-1 piperazineethanesulfonic acid buffer enables molecular transport into the cell to increase more rapidly than with phosphate-buffered saline or culture medium-based buffer. For multipulse schemes, our model suggests that the interpulse delay between two opposite polarity electric field pulses does not play an appreciable role in the resultant molecular uptake for delays up to 100 μs. Our model also predicts the per-pulse permeability enhancement decreases as a function of the pulse number. This is the first report of an ordinary differential equation model of electroporation to be validated with quantitative molecular uptake data and consider both membrane permeability and charging.