A methodology for constraining power in finite element modeling of radiofrequency ablation

Abstract

Radiofrequency ablation (RFA) is a minimally invasive thermal therapy for the treatment of cancer, hyperopia, and cardiac tachyarrhythmia. In RFA, the power delivered to the tissue is a key parameter. The objective of this study was to establish a methodology for the finite element modeling of RFA with constant power. Because of changes in the electric conductivity of tissue with temperature, a nonconventional boundary value problem arises in the mathematic modeling of RFA: neither the voltage (Dirichlet condition) nor the current (Neumann condition), but the power, that is, the product of voltage and current was prescribed on part of boundary. We solved the problem using Lagrange multiplier: the product of the voltage and current on the electrode surface is constrained to be equal to the Joule heating. We theoretically proved the equality between the product of the voltage and current on the surface of the electrode and the Joule heating in the domain. We also proved the well-posedness of the problem of solving the Laplace equation for the electric potential under a constant power constraint prescribed on the electrode surface. The Pennes bioheat transfer equation and the Laplace equation for electric potential augmented with the constraint of constant power were solved simultaneously using the Newton-Raphson algorithm. Three problems for validation were solved. Numerical results were compared either with an analytical solution deduced in this study or with results obtained by ANSYS or experiments. This work provides the finite element modeling of constant power RFA with a firm mathematical basis and opens pathway for achieving the optimal RFA power.

Safety and effect on ablation size of hydrochloric acid-perfused radiofrequency ablation in animal livers

“…[12,13]. Several studies have also reported that the volume of the ablation zone tended to increase as the power output during RFA increased and that the power output was higher when RFA was done with HCl rather than saline [21,22]. Also, others have shown that the conductivity of HCl runs about 3-6 times higher than that of normal saline at the same concentrations [23], providing an explanation for why the ablation zone in HCl-RFA tends to be larger than in NS-RFA.…”

A computational model of open‐irrigated radiofrequency catheter ablation accounting for mechanical properties of the cardiac tissue

“…For a constant‐power ablation mode, Equation is augmented with a constant‐power constraint where Ω is the computational domain and P is the constant power imposed.…”

Radiofrequency ablation with four electrodes as a building block for matrix radiofrequency ablation: Ex vivo liver experiments and finite element method modelling. Influence of electric and activation mode on coagulation size and geometry

“…RAFEM-2 was an updated version taking into account the temperature dependence of electric and thermal conductivity [139][140][141] and has been described in detail before [51,142,152].…”