Simulations of the electrostatic field, temperature, and tissue damage generated by multiple electrodes for electrochemical treatment

Abstract

Integrated analysis of the spatial distributions of the electric potential, electric field, temperature, and tissue damage generated by multiple arrays of straight needle electrodes inserted into tumors is highly significant for improving the effectiveness of electrochemical treatment. In this study, we simulated the spatial profiles generated by multiple electrodes inserted individually into a tumor and multiple pairs of straight needle electrodes inserted in a tumor surrounded by healthy tissue. Poisson nonlinear and Laplace equations were used to calculate the electric potential in the tumor and the surrounding healthy tissue, respectively. The stationary bioheat transfer equation of Pennes was used to calculate the temperature in both tissues. The percentage tissue damage was computed in each biological medium for each electrode array shape. Numerical simulations showed that the non-homogeneous spatial distributions of the temperature (above 40 °C) generated by different types of multiple pairs of straight needle electrodes covered the whole tumor volume. Spatial profiles of this physical magnitude were generated by multiple straight needle electrodes, which were individually inserted into the tumor and partially covered by its volume. In addition, the simulations showed that multiple pairs of electrodes led to tumor damage percentages above 80%. By contrast, multiple electrodes inserted individually in the tumor induced damage percentages below 25%. We conclude that multiple pairs of straight needle electrodes may be applied to deep-seated solid tumors in treatment with electrochemical therapy considering their theoretically calculated high tumor damage percentages.