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%27s 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%27s method, and the integrals that appear in the solution of the problem are obtained by Simpson%27s 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. © 2017 Ricardo Romero-Méndez and Enrique Berjano.
• 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. © 2017 Ricardo Romero-Méndez and Enrique Berjano.

authors

• Berjano E.
• Romero Méndez Ricardo

publication date

• 2017-01-01

published in

• Mathematical Problems in Engineering  Journal

keywords

• Ablation; Boundary conditions; Eigenvalues and eigenfunctions; Electrodes; Newton-Raphson method; Numerical methods; Cylindrical electrodes; Functional dependency; Method of separation of variables; Non-homogeneous boundary conditions; Non-homogeneous terms; Radio-frequency Ablation; Surgical procedures; Transcendental equations; Problem solving

Digital Object Identifier (DOI)

• 10.1155/2017/9021616

start page

end page

volume

• 2017