Effect of the thermal wave in radiofrequency ablation modeling: an analytical study.

To date, all radiofrequency heating (RFH) theoretical models have employed Fourier's heat transfer equation (FHTE), which assumes infinite thermal energy propagation speed. Although this equation is probably suitable for modeling most RFH techniques, it may not be so for surgical procedures in which very short heating times are employed. In such cases, a non-Fourier model should be considered by using the hyperbolic heat transfer equation (HHTE). Our aim was to compare the temperature profiles obtained from the FHTE and HHTE for RFH modeling. We built a one-dimensional theoretical model based on a spherical electrode totally embedded and in close contact with biological tissue of infinite dimensions. We solved the electrical-thermal coupled problem analytically by including the power source in both equations. A comparison of the analytical solutions from the HHTE and FHTE showed that (1) for short times and locations close to the electrode surface, the HHTE produced temperatures higher than the FHTE, however, this trend became negligible for longer times, when both equations produced similar temperature profiles (HHTE always being higher than FHTE); (2) for points distant from the electrode surface and for very short times, the HHTE temperature was lower than the FHTE, however, after a delay time, this tendency inverted and the HHTE temperature increased to the maximum; (3) from a mathematical point of view, the HHTE solution showed cuspidal-type singularities, which were materialized as a temperature peak traveling through the medium at a finite speed. This peak rose at the electrode surface, and clearly reflected the wave nature of the thermal problem; (4) the differences between the FHTE and HHTE temperature profiles were smaller for the lower values of thermal relaxation time and locations further from the electrode surface.

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

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.