title: 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.
authors.affiliation: Department of Radiology, Gasthuisberg University Hospital, Herestraat 49, Leuven, 3000, Belgium.
authors.forename: Yansheng
authors.initials: Y
authors.lastname: Jiang
authors.affiliation: Applied Mechanics Group, Graduate Program in Engineering, Federal University of Pampa, Av. Tiarajú 810, Ibirapuitã, CEP 97546-550, Alegrete, Rio Grande do Sul, Brazil.
authors.forename: Ricardo
authors.initials: R
authors.lastname: Possebon
authors.affiliation: Department of Radiology, Gasthuisberg University Hospital, Herestraat 49, Leuven, 3000, Belgium.|Department of Surgery, Leopold Park Clinic, CHIREC Cancer Institute, Froissartstraat 38, Brussels, 1040, Belgium.
authors.forename: Stefaan
authors.initials: S
authors.lastname: Mulier
authors.affiliation: Applied Mechanics Group, Graduate Program in Engineering, Federal University of Pampa, Av. Tiarajú 810, Ibirapuitã, CEP 97546-550, Alegrete, Rio Grande do Sul, Brazil.
authors.forename: Chong
authors.initials: C
authors.lastname: Wang
authors.affiliation: University of Zhe Jiang, Hang Zhou, China.
authors.forename: Feng
authors.initials: F
authors.lastname: Chen
authors.affiliation: Department of Radiology, Gasthuisberg University Hospital, Herestraat 49, Leuven, 3000, Belgium.
authors.forename: Yuanbo
authors.initials: Y
authors.lastname: Feng
authors.affiliation: Renji Hospital, Shanghai, China.
authors.forename: Qian
authors.initials: Q
authors.lastname: Xia
authors.affiliation: Department of Radiology, Gasthuisberg University Hospital, Herestraat 49, Leuven, 3000, Belgium.
authors.forename: Yewei
authors.initials: Y
authors.lastname: Liu
authors.affiliation: Department of Radiology, Gasthuisberg University Hospital, Herestraat 49, Leuven, 3000, Belgium.
authors.forename: Ting
authors.initials: T
authors.lastname: Yin
authors.affiliation: Department of Radiology, Gasthuisberg University Hospital, Herestraat 49, Leuven, 3000, Belgium.
authors.forename: Raymond
authors.initials: R
authors.lastname: Oyen
authors.affiliation: Department of Radiology, Gasthuisberg University Hospital, Herestraat 49, Leuven, 3000, Belgium.
authors.forename: Yicheng
authors.initials: Y
authors.lastname: Ni
mesh_terms: D017115:Catheter Ablation; D004553:Electric Conductivity; D004566:Electrodes; D020342:Finite Element Analysis; D006358:Hot Temperature; D006801:Humans
keywords: Lagrange multiplier; finite element; power constraint; radiofrequency ablation