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Mathematical Problems in Engineering
Volume 2017 (2017), Article ID 9021616, 12 pages
https://doi.org/10.1155/2017/9021616
Research Article

An Analytical Solution for Radiofrequency Ablation with a Cooled Cylindrical Electrode

1Facultad de Ingeniería, Universidad Autónoma de San Luis Potosí, Manuel Nava No. 8, Zona Universitaria, 78290 San Luis Potosí, SLP, Mexico
2Biomedical Synergy, Department of Electronic Engineering, Universitat Politècnica de València, Camí de Vera, 46022 Valencia, Spain

Correspondence should be addressed to Ricardo Romero-Méndez; xm.plsau@moremorr

Received 19 December 2016; Accepted 26 January 2017; Published 6 March 2017

Academic Editor: Alessio Gizzi

Copyright © 2017 Ricardo Romero-Méndez and Enrique Berjano. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We present an analytical solution to the electrothermal mathematical model of radiofrequency ablation of biological tissue using a cooled cylindrical electrode. The solution presented here makes use of the method of separation of variables to solve the problem. Green’s functions are used for the handling of nonhomogeneous terms, such as effect of electrical currents circulation and the nonhomogeneous boundary condition due to cooling at the electrode surface. The transcendental equation for determination of eigenvalues of this problem is solved using Newton’s method, and the integrals that appear in the solution of the problem are obtained by Simpson’s rule. The solution obtained here has the possibility of handling different functional dependencies of the source term and nonhomogeneous boundary condition. The solution provides a tool to understand the physics of the problem, as it shows how the solution depends on different parameters, to provide mathematical tools for the design of surgical procedures and to validate other modeling techniques, such as the numerical methods that are frequently used to solve the problem.