Assessment of Hyperbolic Heat Transfer Equation in Theoretical Modeling for Radiofrequency Heating Techniques

Abstract

Theoretical modeling is a technique widely used to study the electrical-thermal performance of different surgical procedures based on tissue heating by use of radiofrequency (RF) currents. Most models employ a parabolic heat transfer equation (PHTE) based on Fourier’s theory, which assumes an infinite propagation speed of thermal energy. We recently proposed a one-dimensional model in which the electrical-thermal coupled problem was analytically solved by using a hyperbolic heat transfer equation (HHTE), i.e. by considering a non zero thermal relaxation time. In this study, we particularized this solution to three typical examples of RF heating of biological tissues: heating of the cornea for refractive surgery, cardiac ablation for eliminating arrhythmias, and hepatic ablation for destroying tumors. A comparison was made of the PHTE and HHTE solutions. The differences between their temperature profiles were found to be higher for lower times and shorter distances from the electrode surface. Our results therefore suggest that HHTE should be considered for RF heating of the cornea (which requires very small electrodes and a heating time of 0.6 s), and for rapid ablations in cardiac tissue (less than 30 s).

Non-Fourier based thermal-mechanical tissue damage prediction for thermal ablation

“…Table 1 shows the thermal and mechanical parameters used for the cubic tissue under thermal loads. [13][14][15][16][17][18] The boundary of the cubic model is fixed and its temperature is set to 310 K. The cubic model has the initial temperature of 310 K at the rest state.…”

Pre-treatment planning for hepatic radiofrequency ablation

“…Internal heat generation due to resistive heating and heat loss due to blood perfusion are represented as a distributed source q and sink Q p , respectively. Tissue heating in RF ablation is a resistive heating process, modeled by the Joule heating relationship [22], [23], [24], [12],…”

“…Next, we solve (21), which is a linear non-homogeneous first order ordinary differential equation, to obtain a n (t) e λnαt da n (t) dt + λ n αa n (t) = d dt a n (t)e λnαt = q n αe λnαt (22) where e λnαt is the integrating factor. Then integrating (22) from 0 to t, we find a n (t)e λnαt − a n (0) = t 0 q n αe λnατ dτ (23) ⇒ a n (t) = a n (0) − q n λ n e −λnαt + q n λ n .…”

“…Then integrating (22) from 0 to t, we find a n (t)e λnαt − a n (0) = t 0 q n αe λnατ dτ (23) ⇒ a n (t) = a n (0) − q n λ n e −λnαt + q n λ n .…”

Ultra-structure changes and survivin expression in uterine fibroids after radiofrequency ablation

“…Radiofrequency (RF) ablation makes use of a high frequency alternating current to produce biological heating to 85-100 C, which in turn causes coagulative necrosis in the target tissue and in situ inactivation of the diseased tissue [1]. RF ablation is widely used to treat many solid tumours.…”