Three-dimensional Finite-element Analysis of Joule Heating in Electrochemotherapy and in vivo Gene Electrotransfer

Electrochemotherapy and electrogene therapy are new methods in molecular medicine based on electroporation-mediated introduction of foreign molecules (chemotherapeutic drugs, DNA) into target cells
in vivo
. Electrochemotherapy involves the injection of chemotherapeutic agent followed by a local delivery of a train of short high-voltage pulses to the tumor nodule (i.e. 8 square-wave pulses of 100 μs duration delivered at the repetition frequency of 1 Hz or several kHz, with a voltage-to-distance ratio of up to 1500 V/cm). For the transfer of DNA across a cell membrane a train of long low-voltage pulses (i.e. 8 rectangular pulses of 50 ms duration delivered at the repetition rate of 1 Hz, with a voltage-to-distance ratio up to 250 V/cm) is much more effective due to the electrophoretic effect on DNA molecule. In this paper we present a comprehensive analysis of tissue heating as a potential side effect of electric pulses used for electroporation-based treatments. The analysis is based on a coupled electrothermal model using 3-D finite-element approach. We studied two electrode geometries: parallel plates and a pair of needles. By setting the appropriate boundary conditions, we simulated driving of electrodes with short, high-voltage, electropermeabilizing pulses and with longer, lower voltage, electrophoretic pulses. We obtained time dependent solutions for electric field and temperature distribution by FEM solver. Based on the numerical simulations we analyzed the influence of tissue electrical conductivity and parameters of electric pulses (amplitude, duration, number of pulses, pulse repetition frequency) on the temperature distribution within the tissue and the electrodes. Results of our simulations show that at specific pulse parameters at least locally tissue heating might be significant (i.e. tissue temperatures to grow in excess of 43°C). For electrochemotherapy, this is not critical, but DNA electrotransfer may be unsuccessful due to heating-related DNA damage or denaturation.