# 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
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