Sequential Finite Element Model of Tissue Electropermeabilization

Abstract

Abstract-Permeabilization, when observed on a tissue level, is a dynamic process resulting from changes in membrane permeability when exposing biological cells to external electric field (E).In this paper we present a sequential finite element model of E distribution in tissue which considers local changes in tissue conductivity due to permeabilization. These changes affect the pattern of the field distribution during the high voltage pulse application.The presented model consists of a sequence of static models (steps), which describe E distribution at discrete time intervals during tissue permeabilization and in this way present the dynamics of electropermeabilization. The tissue conductivity for each static model in a sequence is determined based on E distribution from the previous step by considering a sigmoid dependency between specific conductivity and E intensity. Such a dependency was determined by parameter estimation on a set of current measurements, obtained by in vivo experiments. Another set of measurements was used for model validation. All experiments were performed on rabbit liver tissue with inserted needle electrodes. Model validation was carried out in four different ways: 1) by comparing reversibly permeabilized tissue computed by the model and the reversibly permeabilized area of tissue as obtained in the experiments; 2) by comparing the area of irreversibly permeabilized tissue computed by the model and the area where tissue necrosis was observed in experiments; 3) through the comparison of total current at the end of pulse and computed current in the last step of sequential electropermeabilization model; 4) by comparing total current during the first pulse and current computed in consecutive steps of a modeling sequence.The presented permeabilization model presents the first approach of describing the course of permeabilization on tissue level. Despite some approximations (ohmic tissue behavior) the model can predict the permeabilized volume of tissue, when exposed to electrical treatment. Therefore, the most important contribution and novelty of the model is its potentiality to be used as a tool for determining parameters for effective tissue permeabilization.

Can electroporation previous to radiofrequency hepatic ablation enlarge thermal lesion size? A feasibility study based on theoretical modelling andin vivoexperiments

“…DC conductivity at low electric field magnitudes (σ 0 = 0.08 S/m) and DC conductivity at very high fields (σ MAX = 0.31 S/m = σ 0 + Δσ) were obtained from [15]. The sigmoid behavior and the parameters that determine its shape were adjusted from data in [18]. Gompertz sigmoid function was chosen instead of other possible sigmoid functions, such as the sigmoid expression employed in [18], because its shape parameters are easily identifiable in the expression.…”

“…The sigmoid behavior and the parameters that determine its shape were adjusted from data in [18]. Gompertz sigmoid function was chosen instead of other possible sigmoid functions, such as the sigmoid expression employed in [18], because its shape parameters are easily identifiable in the expression.…”

Finite Element Modeling of in Vivo Electroporation

“…One is the increase in tissue conductivity (σ) due to increased electric field (E) causing cell membrane electroporation (Pliquett and Weaver, 1996;Pavselj et al, 2005;Sel et al, 2005). This change of material properties has two more nonlinear characteristics.…”

Comparison of Electroporation Threshold for Different Cell Lines in vitro

“…When using cell electroporation in clinics, e.g., for tumor and gene therapy, it is important to know in advance whether and how many of cells will become electroporated as a result of a particular electric treatment. This could be achieved by using theoretical models of electroporation [2], optimized by using real experimental data on cell electroporation [3,4].…”