# American Institute of Mathematical Sciences

2009, 6(3): 611-627. doi: 10.3934/mbe.2009.6.611

## Theoretical modeling of RF ablation with internally cooled electrodes: Comparative study of different thermal boundary conditions at the electrode-tissue interface

 1 Instituto Universitario de Matemática Pura y Aplicada, Universidad Politécnica de Valencia, Camino de Vera s/n. 46022, Valencia, Spain, Spain, Spain 2 Institute for Research and Innovation on Bioengineering, Universidad Politécnica de Valencia, Camino de Vera s/n. 46022, Valencia, Spain

Received  September 2008 Revised  February 2009 Published  June 2009

Previous studies on computer modeling of RF ablation with cooled electrodes modeled the internal cooling circuit by setting surface temperature at the coolant temperature (i.e., Dirichlet condition, DC). Our objective was to compare the temperature profiles computed from different thermal boundary conditions at the electrode-tissue interface. We built an analytical one-dimensional model based on a spherical electrode. Four cases were considered: A) DC with uniform initial condition, B) DC with pre-cooling period, C) Boundary condition based on Newton's cooling law (NC) with uniform initial condition, and D) NC with a pre-cooling period. The results showed that for a long time ($120$ s), the profiles obtained with (Cases B and D) and without (Cases A and C) considering pre-cooling are very similar. However, for shorter times ($<30$ s), Cases A and C overestimated the temperature at points away from the electrode-tissue interface. In the NC cases, this overestimation was more evident for higher values of the convective heat transfer coefficient ($h$). Finally, with NC, when $h$ was increased the temperature profiles became more similar to those with DC. The results suggest that theoretical modeling of RF ablation with cooled electrodes should consider: 1) the modeling of a pre-cooling period, especially if one is interested in the thermal profiles registered at the beginning of RF application; and 2) NC rather than DC, especially for low flow in the internal circuit.
Citation: María J. Rivera, Juan A. López Molina, Macarena Trujillo, Enrique J. Berjano. Theoretical modeling of RF ablation with internally cooled electrodes: Comparative study of different thermal boundary conditions at the electrode-tissue interface. Mathematical Biosciences & Engineering, 2009, 6 (3) : 611-627. doi: 10.3934/mbe.2009.6.611
 [1] Harsh Vardhan Jain, Avner Friedman. Modeling prostate cancer response to continuous versus intermittent androgen ablation therapy. Discrete & Continuous Dynamical Systems - B, 2013, 18 (4) : 945-967. doi: 10.3934/dcdsb.2013.18.945 [2] J. A. López Molina, M. J. Rivera, E. Berjano. Electrical-thermal analytical modeling of monopolar RF thermal ablation of biological tissues: determining the circumstances under which tissue temperature reaches a steady state. Mathematical Biosciences & Engineering, 2016, 13 (2) : 281-301. doi: 10.3934/mbe.2015003 [3] Erik Grandelius, Kenneth H. Karlsen. The cardiac bidomain model and homogenization. Networks & Heterogeneous Media, 2019, 14 (1) : 173-204. doi: 10.3934/nhm.2019009 [4] Paolo Biscari, Chiara Lelli. DAD characterization in electromechanical cardiac models. Discrete & Continuous Dynamical Systems - A, 2013, 33 (7) : 2651-2665. doi: 10.3934/dcds.2013.33.2651 [5] Mounira Kesmia, Soraya Boughaba, Sabir Jacquir. New approach of controlling cardiac alternans. Discrete & Continuous Dynamical Systems - B, 2018, 23 (2) : 975-989. doi: 10.3934/dcdsb.2018051 [6] Mostafa Bendahmane, Fatima Mroue, Mazen Saad, Raafat Talhouk. Mathematical analysis of cardiac electromechanics with physiological ionic model. Discrete & Continuous Dynamical Systems - B, 2019, 24 (9) : 4863-4897. doi: 10.3934/dcdsb.2019035 [7] Fabrice Delbary, Rainer Kress. Electrical impedance tomography using a point electrode inverse scheme for complete electrode data. Inverse Problems & Imaging, 2011, 5 (2) : 355-369. doi: 10.3934/ipi.2011.5.355 [8] Micol Amar, Daniele Andreucci, Paolo Bisegna, Roberto Gianni. Homogenization limit and asymptotic decay for electrical conduction in biological tissues in the high radiofrequency range. Communications on Pure & Applied Analysis, 2010, 9 (5) : 1131-1160. doi: 10.3934/cpaa.2010.9.1131 [9] Jérémi Dardé, Harri Hakula, Nuutti Hyvönen, Stratos Staboulis. Fine-tuning electrode information in electrical impedance tomography. Inverse Problems & Imaging, 2012, 6 (3) : 399-421. doi: 10.3934/ipi.2012.6.399 [10] Erfang Ma. Integral formulation of the complete electrode model of electrical impedance tomography. Inverse Problems & Imaging, 2020, 14 (2) : 385-398. doi: 10.3934/ipi.2020017 [11] Alexandre Cornet. Mathematical modelling of cardiac pulse wave reflections due to arterial irregularities. Mathematical Biosciences & Engineering, 2018, 15 (5) : 1055-1076. doi: 10.3934/mbe.2018047 [12] Boris Andreianov, Mostafa Bendahmane, Kenneth H. Karlsen, Charles Pierre. Convergence of discrete duality finite volume schemes for the cardiac bidomain model. Networks & Heterogeneous Media, 2011, 6 (2) : 195-240. doi: 10.3934/nhm.2011.6.195 [13] Nuutti Hyvönen, Harri Hakula, Sampsa Pursiainen. Numerical implementation of the factorization method within the complete electrode model of electrical impedance tomography. Inverse Problems & Imaging, 2007, 1 (2) : 299-317. doi: 10.3934/ipi.2007.1.299 [14] Jiying Ma, Dongmei Xiao. Nonlinear dynamics of a mathematical model on action potential duration and calcium transient in paced cardiac cells. Discrete & Continuous Dynamical Systems - B, 2013, 18 (9) : 2377-2396. doi: 10.3934/dcdsb.2013.18.2377 [15] Mostafa Bendahmane, Kenneth H. Karlsen. Analysis of a class of degenerate reaction-diffusion systems and the bidomain model of cardiac tissue. Networks & Heterogeneous Media, 2006, 1 (1) : 185-218. doi: 10.3934/nhm.2006.1.185

2018 Impact Factor: 1.313