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

Abstract

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.

Fourier, hyperbolic and relativistic heat transfer equations: a comparative analytical study

“…The analytical solution of HHE was also obtained in López Molina et al [19], where was already demonstrated that lim λ→0 V H (ρ, ξ ) = V F (ρ, ξ ); i.e. the FHE solution is equal to the HHE solution in the case of zero thermal relaxation time.…”

“…These values have been used in previous modelling studies [19]. The dimensionless thermal relaxation time of the biological tissue for HHE was λ = 1.2963, which is equivalent to τ = 16 s. This value was initially suggested by Mitra et al [13] in processed meat.…”

“…The solution of this problem was previously presented in López Molina et al [19], and we can express it as follows: …”

“…This case was considered since experimental data have suggested that the thermal relaxation time in biological tissues could be significant [13]. The analytical solutions for the HHE and FHE were previously obtained [19]. In this study, we first obtained the analytical solution to RHE for RFA, and then compared the corresponding solutions in terms of computer temperature distributions.…”

Thermal convection in a magnetized conducting fluid with the Cattaneo–Christov heat-flow model

“…Hyperbolic heat-flow effects have a range of practical applications that extend beyond their foundational significance. For example, thermal waves are important in the study of thermal transport in nanomaterials and nanofluids [6,13], and thermal shocks in solids [14], and for heat transport in biological tissue and surgical operations [8,[15][16][17]. Similarly, thermal relaxation has been shown to impact on flow velocity profiles in Jeffrey fluids [18], and a number of thermal convection problems in fluids and porous media [19][20][21][22] (including thermo-haline convection [23,24]), while type-II flux laws analogous to equation (1.1) have found utility in related contexts involving advection-diffusion systems [25][26][27].…”