Modeling of electric field distribution in tissues during electroporation

Abstract

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 investigate...

Evaluation of the Electroporation Efficiency of a Grid Electrode for Electrochemotherapy

“…However, the electroporation effect occurring in the cells or in the tissues depends on cell characteristics because cells have different conductivity, shape, orientation, size, and electroporation threshold. 27,[48][49][50][51][52] Other authors have proposed numerical models that take into account the electrical properties of the tissue as a function of the local electric field. 27,51,52 Nevertheless, in this work, simulation results are useful to characterize and compare different electrodes in terms of distribution of electric field.…”

“…2,18,[27][28][29][31][32][33][34][35] Figure 2 shows the model geometry, a parallelepiped (eg, sizes 5 Â 3.5 Â 3.5 cm 3 ) with 2 cylinders that simulate the stainless steel needles, 1.2 cm long and 0.5 mm diameter. The gray parallelepiped represents a homogeneous material characterized by the electrical resistivity of the tissue in this example is 5 Ωm (conductivity of 0.2 S/m).…”

Histological and Mathematical Analysis of the Irreversibly Electroporated Liver Tissue

“…These properties can cause distortions in the homogeneous distribution of the electric field within the tissue, resulting in an insufficient delivery of electric energy needed to produce an irreversible transmembrane potential. 34 The injured spots for the electrodes in Figure 3 were asymmetrical, and noninfluenced areas were observed in the ablated tissue. 35 Also, the effect of conductivity change with time as electroporation progresses, or dynamic conductivity, should be explored.…”

Maximizing Local Access to Therapeutic Deliveries in Glioblastoma. Part V: Clinically Relevant Model for Testing New Therapeutic Approaches

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