Abstract
BackgroundElectrotherapy is a relatively well established and efficient method of tumor treatment. In this paper we focus on analytical and numerical calculations of the potential and electric field distributions inside a tumor tissue in a two-dimensional model (2D-model) generated by means of electrode arrays with shapes of different conic sections (ellipse, parabola and hyperbola).MethodsAnalytical calculations of the potential and electric field distributions based on 2D-models for different electrode arrays are performed by solving the Laplace equation, meanwhile the numerical solution is solved by means of finite element method in two dimensions.ResultsBoth analytical and numerical solutions reveal significant differences between the electric field distributions generated by electrode arrays with shapes of circle and different conic sections (elliptic, parabolic and hyperbolic). Electrode arrays with circular, elliptical and hyperbolic shapes have the advantage of concentrating the electric field lines in the tumor.ConclusionThe mathematical approach presented in this study provides a useful tool for the design of electrode arrays with different shapes of conic sections by means of the use of the unifying principle. At the same time, we verify the good correspondence between the analytical and numerical solutions for the potential and electric field distributions generated by the electrode array with different conic sections.
Highlights
Electrotherapy is a relatively well established and efficient method of tumor treatment
Two modes are used with similar results: voltage mode and current mode
It illustrates how the electric field distributions in the tissue depend on the shape of the electrodes array and that the highest electric field strengths are obtained in the neighborhood of the electrodes
Summary
Electrotherapy is a relatively well established and efficient method of tumor treatment. Electrotherapy of a low-level direct current is used to treat the cancer (target tissue) through two or more platinum (platinum-iridium 90/10, stainless steel) electrodes placed in or near the malignant tumor. In this therapy, two modes are used with similar results: voltage mode (voltage keeps constant and direct current intensity varies due to changes in the tumor resistance) and current mode (direct current intensity keeps constant for voltage variations because the tumor resistance is altered). As a result of these studies, 6 V may be considered as an irreversible threshold
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