Differences in the Electric Field Distribution Predicted with a Mathematical Model of Cylindrical Electrodes of Finite Length vs. Infinite Length: A Comparison Based on Analytical Solution

Abstract

Cylindrical-shaped metal electrodes are used in numerous medical specialties to force an electric field into the surrounding tissue (e.g., in electrical stimulation and electroporation). Although these electrodes have a limited length in reality, previous mathematical modeling studies have simplified the physical situation and have built a model geometry based on a cylindrical electrode of infinite length, which allows for reducing the model from 2D to 1D. Our objective was to quantify the differences in the electric field values between the finite and infinite electrode cases and assess the adequacy of the mentioned simplification for different values of electrode diameter and length. We used analytical solutions for the electric field distribution. We found that the electric field distribution is substantially different for both cases, not only near the edges of the electrode (when finite length is assumed) and in close locations (<1 mm), but even in the central area and at distances greater than 2 mm. Our work presents analytical solutions for both cases (finite and infinite length), which, despite the oscillations derived from computational limitations, could be used by researchers involved in electric field modeling in biological tissues, in order to quantify the possible error generated with simple models in geometric terms that assume infinite length.