Distributions of the potential and electric field of an electrode elliptic array used in tumor electrotherapy. Analytical and numerical solutions

Electrotherapy on Cancer: Experiment and Mathematical Modeling

“…sources and radial arrays of electrodes with finite length. The results of the simulations reveal as these distributions in the tumor and its surrounding healthy tissue change in function of the tumor size, the positioning, number and polarity of the electrodes, and the difference of electrical conductivity between both tissues for, in agreement with previous theoretical studies [Aguilera et al, 2009;Aguilera et al 2010;Čorović et al, 2007;Jiménez et al, 2011;Joa, 2010;Reberšek et al, 2008;Šel et al, 2003] and experimental reports [Chou et al, 1997;Ren et al, 2001;Serša et al, 1997;Turler et al, 2000;Xin et al, 1994;Yoon et al, 2007]. 3D-analytical expressions for the potential, electric field intensity and electric current density generated by wires completely inserted in the tumor along their diameters (plane y = 0 cm) are directly obtained from the application of this mathematical theorem and the parametric form of the curve given in equation (3).…”

“…Also, the mathematical modeling constitutes a rapid way to propose an optimum electrodes array or close to it, in function of their parameters and those of tumor (localization, size, shape and consistency), using both analytical and numerical solutions. This allows the visualization of the potential, electric field intensity and electric current density distributions generated electrodes arrays in two-dimensional (2D) and three-dimensional (3D) tumors, in order to induce the highest electrotherapy effectiveness (higher tumor destruction with the minimum damage to the organism) [Aguilera et al, 2009;Aguilera et al, 2010;Čorović et al, 2007;Dev et al, 2003;Jiménez et al, 2011;Joa, 2010;Reberšek et al, 2008;Šel et al, 2003]. This later increases our understanding about the current flow inside tumor during direct current application.…”

“…We support that the direct current strength and its form of distribution, through electrodes, have potential biomedical applications and a decisive role in the electrotherapy effectiveness Jiménez et al, 2011]. 2D-electrode arrays are useful for planar tumors (basal cell carcinoma of the skin, cutaneous lymphoma, gastric cancer in its form of delinitis, and melanoma in clinical superficial extension) and the potential, electric field strength and electric current density distributions that these induce in the tumor are reported for electrodes circular array [Čorović et al, 2007;Dev et al, 2003;Šel et al, 2003] and electrodes elliptical array [Aguilera et al, 2009;Aguilera et al, 2010]. The explicit dependence of how electric current density distributions depend on the ellipse eccentricity, the ratio between the electric conductivities of the solid tumor (σ 1 ) and the surrounding healthy tissue (σ 2 ), named σ 1 /σ 2 ratio, and positioning of the electrodes with respect to tumor-surrounding healthy tissue interface is shown in Figures 3 and 4 for an electrodes circular array (eccentricity = 0) and an electrodes elliptical array (eccentricity = 0.85), respectively .…”

Modified Gompertz Equation for Electrotherapy Murine Tumor Growth Kinetics: Predictions and New Hypotheses

“…As a result an optimal electrode distribution has not been determined for ET, nor has the dose-response relationship been established. For this reason, we pay special attention to these two factors [16,17].…”

Analytical and Numerical Solutions of the Potential and Electric Field Generated by Different Electrode Arrays in a Tumor Tissue under Electrotherapy

“…The proposal for electrode arrays that efficiently distribute the electric field (electric current density) in a tumor and its surrounding healthy tissue is one of the most stimulating problems in the electrotherapy-cancer theme because the tumor may significantly be destroyed with the minimum damage in the organism. Different studies reveal that the electric field (electric current density) spatial distribution in tumor and its surrounding healthy tissue strongly depends on the tumor size, electrodes array parameters (applied voltage on the electrodes, number, positioning, size, shape, and polarity of them) and the electric field orientation [11][12][13][14][15][16]. Also, these distributions depend explicitly on the difference of conductivities of both tissues [13,15,16].…”