Electrical-thermal analytical modeling of monopolar RF thermal ablation of biological tissues: determining the circumstances under which tissue temperature reaches a steady state
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Applied Mathematics Department, Universitat Politècnica de València, Camino de Vera 46022 Valencia
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2.
Biomedical Synergy, Electronic Engineering Department, Universitat Politècnica de València, Camino de Vera 46022 Valencia
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Received:
01 March 2015
Accepted:
29 June 2018
Published:
25 November 2015
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MSC :
Primary: 92C50, 35K05; Secondary: 35K99.
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It has been suggested that during RF thermal ablation of biological tissue the thermal lesion could reach an equilibrium size after 1-2 minutes. Our objective was to determine under which circumstances of electrode geometry (needle-like vs. ball-tip), electrode type (dry vs. cooled) and blood perfusion the temperature will reach a steady state at any point in the tissue. We solved the bioheat equation analytically both in cylindrical and spherical coordinates and the resultant limit temperatures were compared. Our results demonstrate mathematically that tissue temperature reaches a steady value in all cases except for cylindrical coordinates without the blood perfusion term, both for dry and cooled electrodes, where temperature increases infinitely. This result is only true when the boundary condition far from the active electrode is considered to be at infinitum. In contrast, when a finite and sufficiently large domain is considered, temperature reaches always a steady state.
Citation: 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[J]. Mathematical Biosciences and Engineering, 2016, 13(2): 281-301. doi: 10.3934/mbe.2015003
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Abstract
It has been suggested that during RF thermal ablation of biological tissue the thermal lesion could reach an equilibrium size after 1-2 minutes. Our objective was to determine under which circumstances of electrode geometry (needle-like vs. ball-tip), electrode type (dry vs. cooled) and blood perfusion the temperature will reach a steady state at any point in the tissue. We solved the bioheat equation analytically both in cylindrical and spherical coordinates and the resultant limit temperatures were compared. Our results demonstrate mathematically that tissue temperature reaches a steady value in all cases except for cylindrical coordinates without the blood perfusion term, both for dry and cooled electrodes, where temperature increases infinitely. This result is only true when the boundary condition far from the active electrode is considered to be at infinitum. In contrast, when a finite and sufficiently large domain is considered, temperature reaches always a steady state.
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