Radiofrequency ablation (RFA) is increasingly being used to treat unresectable liver tumors. Complete ablation of the tumor and a safety margin is necessary to prevent local recurrence.With current electrodes, size and shape of the ablation zone are highly variable leading to unsatisfactory local recurrence rates, especially for tumors > 3 cm. In order to improve Table 6: outcome of the ex vivo bovine liver experiments: comparison according to the number of electrodes activated at the same time.

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.

Radiofrequency ablation (RFA) is a widely used thermal treatment for liver tumors. Knowledge about the resistivity of liver is a prerequisite for the predictability of producible thermo-necrosis with RFA. Most research to date has focused on performing specific experiments to determine the resistivity of a given liver. This work aims to determine the resistivity from the time course of impedance obtained in RFA. We assume that the liver resistivity obeys a piecewise function of temperature. We determine in this work the means and standard derivations of parameters in the resistivity function with finite element analysis of ex vivo bipolar RFA. We experimentally found the temperature at the electrode equal to 125.2 °C. This finding validates a parameter in the function relating to the temperature at which the resistivity starts to rise exponentially. We conclude that it is feasible and reliable to characterize the resistivity function of liver in using the time course of impedance from RFA. This work opens a pathway for the automatic determination of the patient specific resistivity of in vivo liver.