Distributions of the potential and electric field of an electrode elliptic array used in tumor electrotherapy: Analytical and numerical solutions Original Research Article

To estimate the potential and electric field generated by any electrode array is very useful in effective tumor destruction. At present, an electrode array that takes into account the ellipsoidal geometry of the solid tumors has not been proposed. We present both analytical and numerical solutions for the potential and electric field in a solid tumor established by an electrode array with elliptic shape which may be used in vitro, in vivo and in clinical studies for cancer treatment with electrotherapy. These analytical and numerical solutions are obtained using multipole expansion and the finite difference method. Distributions of potential and electric field magnitudes are computed in function of the eccentricity of an elliptical array and compared with those obtained with a circular array of electrode. Maximum difference and Root Means Square Error are used to compare the distributions of the potential and electric field in leading-order and first-order correction and between the analytical and numerical solutions. The results show a good agreement between these distributions in both orders and the analytical and numerical solutions. It was concluded that the mathematical approach presented in this study is a tool for a rapid design of electrode elliptical arrays in order to induce the maximum destruction of the tumor. Moreover, it is shown that, for all values of eccentricity, there is a good correspondence between the distributions of the potential and the electric field for leading-order and first-order correction and for both the analytical and numerical solutions.