Selma Čorović

Modeling of electric field distribution in tissues during electroporation

BackgroundElectroporation based therapies and treatments (e.g. electrochemotherapy, gene electrotransfer for gene therapy and DNA vaccination, tissue ablation with irreversible electroporation and transdermal drug delivery) require a precise prediction of the therapy or treatment outcome by a personalized treatment planning procedure. Numerical modeling of local electric field distribution within electroporated tissues has become an important tool in treatment planning procedure in both clinical and experimental settings. Recent studies have reported that the uncertainties in electrical properties (i.e. electric conductivity of the treated tissues and the rate of increase in electric conductivity due to electroporation) predefined in numerical models have large effect on electroporation based therapy and treatment effectiveness. The aim of our study was to investigate whether the increase in electric conductivity of tissues needs to be taken into account when modeling tissue response to the electroporation pulses and how it affects the local electric distribution within electroporated tissues.MethodsWe built 3D numerical models for single tissue (one type of tissue, e.g. liver) and composite tissue (several types of tissues, e.g. subcutaneous tumor). Our computer simulations were performed by using three different modeling approaches that are based on finite element method: inverse analysis, nonlinear parametric and sequential analysis. We compared linear (i.e. tissue conductivity is constant) model and non-linear (i.e. tissue conductivity is electric field dependent) model. By calculating goodness of fit measure we compared the results of our numerical simulations to the results of in vivo measurements.ResultsThe results of our study show that the nonlinear models (i.e. tissue conductivity is electric field dependent: σ(E)) fit experimental data better than linear models (i.e. tissue conductivity is constant). This was found for both single tissue and composite tissue. Our results of electric field distribution modeling in linear model of composite tissue (i.e. in the subcutaneous tumor model that do not take into account the relationship σ(E)) showed that a very high electric field (above irreversible threshold value) was concentrated only in the stratum corneum while the target tumor tissue was not successfully treated. Furthermore, the calculated volume of the target tumor tissue exposed to the electric field above reversible threshold in the subcutaneous model was zero assuming constant conductivities of each tissue.Our results also show that the inverse analysis allows for identification of both baseline tissue conductivity (i.e. conductivity of non-electroporated tissue) and tissue conductivity vs. electric field (σ(E)) of electroporated tissue.ConclusionOur results of modeling of electric field distribution in tissues during electroporation show that the changes in electrical conductivity due to electroporation need to be taken into account when an electroporation based treatment is planned or investigated. We concluded that the model of electric field distribution that takes into account the increase in electric conductivity due to electroporation yields more precise prediction of successfully electroporated target tissue volume. The findings of our study can significantly contribute to the current development of individualized patient-specific electroporation based treatment planning.

Analytical and numerical quantification and comparison of the local electric field in the tissue for different electrode configurations

BackgroundElectrochemotherapy and gene electrotransfer are novel promising treatments employing locally applied high electric pulses to introduce chemotherapeutic drugs into tumor cells or genes into target cells based on the cell membrane electroporation. The main focus of this paper was to calculate analytically and numerically local electric field distribution inside the treated tissue in two dimensional (2D) models for different plate and needle electrode configurations and to compare the local electric field distribution to parameter U/d, which is widely used in electrochemotherapy and gene electrotransfer studies. We demonstrate the importance of evaluating the local electric field distribution in electrochemotherapy and gene electrotransfer.MethodsWe analytically and numerically analyze electric field distribution based on 2D models for electrodes and electrode configurations which are most widely used in electrochemotherapy and gene electrotransfer. Analytical calculations were performed by solving the Laplace equation and numerical calculations by means of finite element method in two dimensions.ResultsWe determine the minimal and maximal E inside the target tissue as well as the maximal E over the entire treated tissue for the given electrode configurations. By comparing the local electric field distribution calculated for different electrode configurations to the ratio U/d, we show that the parameter U/d can differ significantly from the actual calculated values of the local electric field inside the treated tissue. By calculating the needed voltage to obtain E > U/d inside the target tissue, we showed that better electric field distribution can be obtained by increasing the number and changing the arrangement of the electrodes.ConclusionBased on our analytical and numerical models of the local electric field distribution we show that the applied voltage, configuration of the electrodes and electrode position need to be chosen specifically for each individual case, and that numerical modeling can be used to optimize the appropriate electrode configuration and adequate voltage. Using numerical models we further calculate the needed voltage for a specific electrode configuration to achieve adequate E inside the target tissue while minimizing damages of the surrounding tissue. We present also analytical solutions, which provide a convenient, rapid, but approximate method for a pre-analysis of electric field distribution in treated tissue.

Numerical Modeling and Optimization of Electric Field Distribution in Subcutaneous Tumor Treated With Electrochemotherapy Using Needle Electrodes

Electrochemotherapy (ECT) is an effective antitumor treatment employing locally applied high-voltage electric pulses in combination with chemotherapeutic drugs. For successful ECT, the entire tumor volume needs to be subjected to a sufficiently high local electric field, whereas, in order to prevent damage, the electric field within the healthy tissue has to be as low as possible. To determine the optimum electrical parameters and electrode configuration for the ECT of a subcutaneous tumor, we combined a 3-D finite element numerical tumor model with a genetic optimization algorithm. We calculated and compared the local electric field distributions obtained with different geometrical and electrical parameters and different needle electrode geometries that have been used in research and clinics in past years. Based on this, we established which model parameters had to be taken into account for the optimization of the local electric field distribution and included them in the optimization algorithm. Our results showed that parallel array electrodes are the most suitable for the spherical tumor geometry, because the whole tumor volume is subjected to sufficiently high electric field while requiring the least electric current and causing the least tissue damage. Our algorithm could be a useful tool in the treatment planning of clinical ECT as well as in other electric field mediated therapies, such as gene electrotransfer, transdermal drug delivery, and irreversible tissues ablation.

Optimization of electrode position and electric pulse amplitude in electrochemotherapy

Optimization of electrode position and electric pulse amplitude in electrochemotherapy Background. In addition to the chemotherapeutic drug being present within the tumor during electric pulse delivery, successful electrochemotherapy requires the entire tumor volume to be subjected to a sufficiently high electric field, while the electric field in the surrounding healthy tissue is as low as possible to prevent damage. Both can be achieved with appropriate positioning of the electrodes and appropriate amplitude of electric pulses. Methods. We used 3D finite element numerical models and a genetic optimization algorithm to determine the optimum electrode configuration and optimum amplitude of electric pulses for treatment of three subcutaneous tumor models of different shapes and sizes and a realistic brain tumor model acquired from medical images. Results. In all four tumor cases, parallel needle electrode arrays were a better choice than hexagonal needle electrode arrays, since their utilization required less electric current and caused less healthy tissue damage. In addition, regardless of tumor geometry or needle electrode configuration, the optimum depth of electrode insertion was in all cases deeper than the deepest part of the tumor. Conclusions. Our optimization algorithm was able to determine the best electrode configuration in all four presented models and with further improvement it could be a useful tool in clinical electrochemotherapy treatment planning.

The effect of electroporation pulses on functioning of the heart

Electrochemotherapy is an effective antitumor treatment currently applied to cutaneous and subcutaneous tumors. Electrochemotherapy of tumors located close to the heart could lead to adverse effects, especially if electroporation pulses were delivered within the vulnerable period of the heart or if they coincided with arrhythmias of some types. We examined the influence of electroporation pulses on functioning of the heart of human patients by analyzing the electrocardiogram. We found no pathological morphological changes in the electrocardiogram; however, we demonstrated a transient RR interval decrease after application of electroporation pulses. Although no adverse effects due to electroporation have been reported so far, the probability for complications could increase in treatment of internal tumors, in tumor ablation by irreversible electroporation, and when using pulses of longer durations. We evaluated the performance of our algorithm for synchronization of electroporation pulse delivery with electrocardiogram. The application of this algorithm in clinical electroporation would increase the level of safety for the patient and suitability of electroporation for use in anatomical locations presently not accessible to existing electroporation devices and electrodes.

Electroporator with automatic change of electric field direction improves gene electrotransfer in-vitro

BackgroundGene electrotransfer is a non-viral method used to transfer genes into living cells by means of high-voltage electric pulses. An exposure of a cell to an adequate amplitude and duration of electric pulses leads to a temporary increase of cell membrane permeability. This phenomenon, termed electroporation or electropermeabilization, allows various otherwise non-permeant molecules, including DNA, to cross the membrane and enter the cell. The aim of our research was to develop and test a new system and protocol that would improve gene electrotransfer by automatic change of electric field direction between electrical pulses.MethodsFor this aim we used electroporator (EP-GMS 7.1) and developed new electrodes. We used finite-elements method to calculate and evaluate the electric field homogeneity between these new electrodes. Quick practical test was performed on confluent cell culture, to confirm and demonstrate electric field distribution. Then we experimentally evaluated the effectiveness of the new system and protocols on CHO cells. Gene transfection and cell survival were evaluated for different electric field protocols.ResultsThe results of in-vitro gene electrotransfer experiments show that the fraction of transfected cells increases by changing the electric field direction between electrical pulses. The fluorescence intensity of transfected cells and cell survival does not depend on electric field protocol. Moreover, a new effect a shading effect was observed during our research. Namely, shading effect is observed during gene electrotransfer when cells are in clusters, where only cells facing negative electro-potential in clusters become transfected and other ones which are hidden behind these cells do not become transfected.ConclusionOn the basis of our results we can conclude that the new system can be used in in-vitro gene electrotransfer to improve cell transfection by changing electric field direction between electrical pulses, without affecting cell survival.

Importance of Contact Surface between Electrodes and Treated Tissue in Electrochemotherapy

Electrochemotherapy is an effective antitumor treatment employing locally applied high voltage electric pulses delivered through conductive electrodes to the tumor in combination with chemotherapeutic drugs. The efficiency of electrochemotherapy strongly depends on the local electric field distribution inside the target tissue. For successful therapy the entire target tissue has to be exposed to the local electric field strength above the reversible threshold. The aim of this study is to demonstrate the influence of the contact surface between electrode and treated tissue on the coverage of the tumor tissue by sufficiently high local electric field. The electric field distribution is calculated by means of numerical modeling using finite element method. Numerical results are confirmed with in vivo experiments. We demonstrated that the placement of electrodes giving larger electrode-tissue contact surface leads to improved electrochemotherapy outcome. Our results provide guidance on electrochemotherapy for treatment of protruding cutaneous tumors using parallel plate electrodes.

Numerical optimization of gene electrotransfer into muscle tissue.

BackgroundElectroporation-based gene therapy and DNA vaccination are promising medical applications that depend on transfer of pDNA into target tissues with use of electric pulses. Gene electrotransfer efficiency depends on electrode configuration and electric pulse parameters, which determine the electric field distribution. Numerical modeling represents a fast and convenient method for optimization of gene electrotransfer parameters. We used numerical modeling, parameterization and numerical optimization to determine the optimum parameters for gene electrotransfer in muscle tissue.MethodsWe built a 3D geometry of muscle tissue with two or six needle electrodes (two rows of three needle electrodes) inserted. We performed a parametric study and optimization based on a genetic algorithm to analyze the effects of distances between the electrodes, depth of insertion, orientation of electrodes with respect to muscle fibers and applied voltage on the electric field distribution. The quality of solutions were evaluated in terms of volumes of reversibly (desired) and irreversibly (undesired) electroporated muscle tissue and total electric current through the tissue.ResultsLarge volumes of reversibly electroporated muscle with relatively little damage can be achieved by using large distances between electrodes and large electrode insertion depths. Orienting the electrodes perpendicular to muscle fibers is significantly better than the parallel orientation for six needle electrodes, while for two electrodes the effect of orientation is not so pronounced. For each set of geometrical parameters, the window of optimal voltages is quite narrow, with lower voltages resulting in low volumes of reversibly electroporated tissue and higher voltages in high volumes of irreversibly electroporated tissue. Furthermore, we determined which applied voltages are needed to achieve the optimal field distribution for different distances between electrodes.ConclusionThe presented numerical study of gene electrotransfer is the first that demonstrates optimization of parameters for gene electrotransfer on tissue level. Our method of modeling and optimization is generic and can be applied to different electrode configurations, pulsing protocols and different tissues. Such numerical models, together with knowledge of tissue properties can provide useful guidelines for researchers and physicians in selecting optimal parameters for in vivo gene electrotransfer, thus reducing the number of animals used in studies of gene therapy and DNA vaccination.

Electrode commutation sequence for honeycomb arrangement of electrodes in electrochemotherapy and corresponding electric field distribution

Electrochemotherapy is a treatment based on combination of chemotherapeutic drug and electroporation. It is used in clinics for treatment of solid tumours. For electrochemotherapy of larger tumours multiple needle electrodes were already suggested. We developed and tested electrode commutation circuit, which controls up to 19 electrodes independently. Each electrode can be in one of three possible states: on positive or negative potential or in the state of high impedance. In addition, we tested a pulse sequence using seven electrodes for which we also calculated electric field distribution in tumour tissue by means of finite-elements method. Electrochemotherapy, performed by multiple needle electrodes and tested pulse sequence on large subcutaneous murine tumour model resulted in tumour growth delay and 57% complete responses, thus demonstrating that the tested electrode commutation sequence is efficient.

Modeling of Microvascular Permeability Changes after Electroporation

Vascular endothelium selectively controls the transport of plasma contents across the blood vessel wall. The principal objective of our preliminary study was to quantify the electroporation-induced increase in permeability of blood vessel wall for macromolecules, which do not normally extravasate from blood into skin interstitium in homeostatic conditions. Our study combines mathematical modeling (by employing pharmacokinetic and finite element modeling approach) with in vivo measurements (by intravital fluorescence microscopy). Extravasation of fluorescently labeled dextran molecules of two different sizes (70 kDa and 2000 kDa) following the application of electroporation pulses was investigated in order to simulate extravasation of therapeutic macromolecules with molecular weights comparable to molecular weight of particles such as antibodies and plasmid DNA. The increase in blood vessel permeability due to electroporation and corresponding transvascular transport was quantified by calculating the apparent diffusion coefficients for skin microvessel wall (D [μm2/s]) for both molecular sizes. The calculated apparent diffusion coefficients were D = 0.0086 μm2/s and D = 0.0045 μm2/s for 70 kDa and 2000 kDa dextran molecules, respectively. The results of our preliminary study have important implications in development of realistic mathematical models for prediction of extravasation and delivery of large therapeutic molecules to target tissues by means of electroporation.