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.

Inclusion of memory effects in a dynamic model of electroporation in biological tissues.

This article presents experimental and computational results of electroporation in rat liver. The experiments were performed using different forms of electrodes and waveforms of applied electric pulses. For the numerical simulation, the electroporation model proposed by Ramos and Weinert in a previous publication was used. Dynamic adjustments were used for obtaining a good modeling of the electric current. A single set of model parameters was obtained to fit the simulated current response for different waveforms and electrodes. These parameters were obtained with the use of a genetic algorithm that minimized the error between the simulated and experimental currents. The electroporation model with dynamic adjustment proved to be an appropriate simulation tool to predict the tissue conductivity during stimulation by intense electrical fields.

Numerical model of dog mast cell tumor treated by electrochemotherapy.

Electrochemotherapy is a combination of high electric field and anticancer drugs. The treatment basis is electroporation or electropermeabilization of the cell membrane. Electroporation is a threshold phenomenon and, for efficient treatment, an adequate local distribution of electric field within the treated tissue is important. When this local electric field is not enough, there is a regrown tumor cell; however, if it is stronger than necessary, permanent damage to the tissue occurs. In the treatment of dogs, electrochemotherapy is not yet an established treatment for mast cell tumor in veterinary medicine, although there are studies showing evidence of its effectiveness. In this study, we examined electrochemotherapy of dog mast cell tumor with numerical simulation of local electric field distribution. The experimental result was used to validate the numerical models. The effect of tumor position and tissue thickness (tumor in different parts of dog body) was investigated using plate electrodes. Our results demonstrated that the electrochemotherapy is efficient and flexible, and even when the tumor extends into the subcutis, the treatment with plate electrode eliminated the tumor cells. This result suggests that electrochemotherapy is a suitable method to treat mast cell tumors in dog.

Sinusoidal signal analysis of electroporation in biological cells.

Conductivity measurements in suspensions of biological cells have been used since many years for electroporation effectiveness evaluation. However, conductivity modeling by means of instantaneous values of current and voltage during pulse application does not take into account the effects of the sample reactance and the dielectric dispersion of the medium. This can lead to misinterpretation in the electroporation analysis. The electrical modeling and characterization of electroporation using sinusoidal signal analysis at 10 kHz proposed in this paper allows us to avoid distortions due to reactive effects of the sample. A simple equation establishes the relation between suspension conductivity and membrane conductance. This model was used in experiments with suspensions of yeast cells and applied electric fields of up to 450 kV/m for 1 ms. The analysis using the proposed model resulted in membrane conductance values of up to 8000 S/m (2) and allowed estimating the distribution profile of conductance on the cell membrane.

Numerical sensitivity modeling for the detection of skin tumors by using tetrapolar probe.

The measurement of electrical impedance of skin using surface electrodes permits the assessment of changes in local properties of the skin and can be used in the detection of tumors. The sensitivity of this technique depends mainly on the geometry of the probe and the size of the tumor. In this article, the impedance method was used to estimate the sensitivity of a tetrapolar probe in detecting small regions of increased conductivity in a stratified model of human skin. The impedance method was used to model the potential distribution using fasorial analysis to solve the node equations of the equivalent circuit. Interpolation was applied to reduce discretization error. The skin was modeled as a three-layer structure with different conductivity and permittivity obtained from the literature. A tumor was modeled as a small volume with admittivity four times higher than the normal tissue. Sensitivity calculation was made as a function of electrode diameter and separation, tumor size, and excitation frequency. The simulations indicated that by inserting a one square millimeter tumor in the epidermis, the load impedance to the current source varies about 1% while the transfer impedance varied 8%. The sensitivity also increases nonlinearly with increasing tumor area and thickness. Additionally, it was found that the sensitivity of the transfer impedance has a maximum value when the electrodes are separated by 1.8 mm. The results show that transfer impedance measurements of the skin may detect small skin tumors with a reasonable sensitivity by using an appropriate tetrapolar probe.

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.

Numerical modeling of magnetic induction tomography using the impedance method.

This article discusses the impedance method in the forward calculation in magnetic induction tomography (MIT). Magnetic field and eddy current distributions were obtained numerically for a sphere in the field of a coil and were compared with an analytical model. Additionally, numerical and experimental results for phase sensitivity in MIT were obtained and compared for a cylindrical object in a planar array of sensors. The results showed that the impedance method provides results that agree very well with reality in the frequency range from 100 kHz to 20 MHz and for low conductivity objects (10 S/m or less). This opens the possibility of using this numerical approach in image reconstruction in MIT.

Improved numerical approach for electrical modeling of biological cell clusters.

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

Modeling environment for numerical simulation of applied electric fields on biological cells.

The application of electric pulses in cells increases membrane permeability. This phenomenon is called electroporation. Current electroporation models do not explain all experimental findings: part of this problem is due to the limitations of numerical methods. The Equivalent Circuit Method (ECM) was developed in an attempt to solve electromagnetic problems in inhomogeneous and anisotropic media. ECM is based on modeling of the electrical transport properties of the medium by lumped circuit elements as capacitance, conductance, and current sources, representing the displacement, drift, and diffusion current, respectively. The purpose of the present study was to implement a 2-D cell Model Development Environment (MDE) of ionic transport process, local anisotropy around cell membranes, biological interfaces, and the dispersive behaviour of tissues. We present simulations of a single cell, skeletal muscle, and polygonal cell arrangement. Simulation of polygonal form indicates that the potential distribution depends on the geometrical form of cell. The results demonstrate the importance of the potential distributions in biological cells to provide strong evidences for the understanding of electroporation.

Effect of the electroporation in the field calculation in biological tissues.

This article presents results from the field calculation in a model of biological tissue taking into account the electroporation process. The electroporation model used in this study was proposed and experimentally verified by Glaser et al. for planar membranes. The numerical method for field calculation is based on a two-step process: (1) a cell-scale analysis, used for obtaining the field and current in a small volume containing only one cell and its nearest neighbors; and (2) a tissue-scale analysis, based on averaged values of conductivity and permittivity (obtained from the cell-scale analysis) and used for field calculation in a large volume of the tissue. The results for a high voltage applied between two electrodes in a two-dimensional analysis show that the electric field in the porated tissue extends beyond the limits obtained when the electroporation process is not taken into account. Furthermore, due to the electroporation, the tissue conductivity increases in the space between the electrodes. These results show that the electroporation process cannot be ignored in the field calculation in biological tissues when high strength electric fields are present.

Numerical simulation of electroporation in spherical cells.

This article presents a numerical study of the electroporation process of spherical cells suspended in an electrolyte solution, using the equivalent circuit method (ECM) for field calculation proposed by Ramos et al. A model for the electric conductance of the cell membrane derived from the analytical and experimental results obtained by Glaser et al. for planar lipidic membranes was applied. The influence of the cell concentration and membrane properties (described in the model) on the membrane current, membrane potential, and dependence of the electrolyte conductivity on the applied electric field was studied. These results clarify the electric events connected with the pore opening process and allow the planning of experimental approaches to study reversible membrane rupture in real cells.

A new computational approach for electrical analysis of biological tissues.

A new computational approach for electrical analysis especially designed for application in biological tissues is presented. It is based on the modelling of the electrical properties of the medium by means of lumped circuit elements, such as capacitance, conductance and current sources. The cell scale model is suitable for modelling the local anisotropy around cell membranes. It permits to obtain the electric potential, ionic concentrations and current densities around cells in time steps in an iterative process. The tissue scale model utilises volume-averaged values of conductivity and permittivity and models suitably the dispersive characteristic of biological tissues. It permits to obtain potential and current distributions in large volumes of tissue in the time or frequency domain. An example of analysis of skeletal muscle is presented aiming to demonstrate the features of the method.

Indocianina verde vídeo-angiografia e oftalmoscopia de rastreamento a laser em neovascularizaçäo sub-retiniana / Indocyanine green angiography and scanning laser ophthalmoscopy in subretinal neovascularization

Objetivo: verificar a utilidade da indocianina verde vídeo-angiografia com oftalmoscopia de rastreamento a laser (ORL-ICG, V) na fotocoagulaçäo em pacientes com degeneraçäo macular relacionado à idade e outras causas de membranas neovasculares subretinianas (MNSR). Métodos: estudar retrospectivamente os prontuários de 90 pacientes consecutivos que foram submetidos ao exame de ORL-ICG, V, que apresentavam alguma doença retiniana relacionada ao desenvolvimento de membrana neovascular subretiniana. Resultados: os pacientes apresentavam degeneraçäo macular relacionada à idade (DMRI) (96,7 por cento), neovascularizaçäo subretiniana idiopática (1,11 por cento), síndrome da histoplasmose presumível (1,11 por cento) e estrias angióides (1,11 por cento). Nos pacientes com DMRI com a forma exsudativa houve indicaçäo de fotocoagulaçäo em 35 por cento dos casos. Conclusäo: o exame ORL-ICG, V aumenta a possibilidade de difinir melhor a neovascularizaçäo subretiniana para indicar a fotocoagulaçäo