Purpose: Although theoretical modeling is widely used to study different aspects of radiofrequency ablation (RFA) its utility is directly related to its realism. An important factor in this realism is the use of mathematical functions to model the temperaturedependence of tissue thermal (k) and electrical () conductivities. Our aim was to review the piecewise mathematical functions most commonly used for modeling the temperaturedependence of k and  in RFA computational modeling. Materials and methods:We built a hepatic RFA theoretical model of a cooled electrode and compared lesion dimensions and impedance evolution with combinations of mathematical functions proposed in previous studies We employed the thermal damage contour D63 to compute the lesion dimension contour, which corresponds to Ω= 1, Ω being local thermal damage assessed by the Arrhenius damage model. Results:The results were very similar in all cases in terms of impedance evolution and lesion size after 6 minutes of ablation. Although the relative differences between cases in terms of time to first roll-off (abrupt increase in impedance) were as much as 12%, the maximum relative differences in terms of the short lesion (transverse) diameter were below 3.5%. Conclusions:The findings suggest that the different methods of modeling temperature dependence of k and  reported in the literature do not significantly affect the computed lesion diameter.3

The objective of this study was to compare three different heat transfer models for radiofrequency ablation of in vivo liver tissue using a cooled electrode and three different voltage levels. The comparison was between the simplest but less realistic Pennes’ equation and two porous media-based models, i.e. the Local Thermal Non-Equilibrium (LTNE) equations and Local Thermal Equilibrium (LTE) equation, both modified to take into account two-phase water vaporization (tissue and blood). Different blood volume fractions in liver were considered and the blood velocity was modeled to simulate a vascular network. Governing equations with the appropriate boundary conditions were solved with Comsol Multiphysics finite-element code. The results in terms of coagulation transverse diameters and temperature distributions at the end of the application showed significant differences, especially between Pennes and the modified LTNE and LTE models. The new modified porous media-based models covered the ranges found in the few in vivo experimental studies in the literature and they were closer to the published results with similar in vivo protocol. The outcomes highlight the importance of considering the three models in the future in order to improve thermal ablation protocols and devices and adapt the model to different organs and patient profiles.

Berjano, E. (2012). Relationship between roll-off occurrence and spatial distribution of dehydrated tissue during RF ablation with cooled electrodes. International Journal of Hyperthermia. 28 (1) AbstractPurpose: To study the relationship between roll-off (sudden increase in impedance) and spatial distribution of dehydrated tissue during RF ablation using a cooled electrode (temperatures around 100ºC). Methods:We used a double approach: 1) theoretical modeling based on the Finite Element Method; and 2) 20 ablations using an experimental study on ex-vivo excised bovine liver in which we measured impedance progress and temperature at three points close to the electrode surface: 0.5 (T1), 1.5 (T2) and 2.5 (T3) mm from the tip. T2 was located exactly at the center of the 30 mm long electrode.Results: Temperatures at T1 and T3 quickly rose to 100ºC (at ≈ 20 and 40 s, respectively), while at the rise at T2 was somewhat slower, stabilized around 50 s and reached a maximum value of 99ºC at about 60 s. Impedance reached a minimum of 65  (plateau), began increasing at 50 s and continued rising throughout the procedure, reaching a value equal to the initial value at 70 s. Likewise, computed impedance dropped to ≈73  (plateau), began increasing at 50 s and reached an impedance value equal to the initial value at ≈78 s, which approximately coincided with the time when the entire zone surrounding the electrode was within the 100ºC isotherm. Conclusion:There is a close relationship between the moment at which roll-off occurs and the time when the entire electrode is completely encircled by the dehydrated tissue. The midelectrode zone is the last in which tissue dessication occurs.

For the same delivered energy, the new protocol significantly increases the magnitude of the applied electric field, which may be the reason why it is clinically more effective in achieving pain relief.

Koruth, J.; Berjano, E. (2014). Radiofrequency cardiac ablation with catheters placed on opposing sides of the ventricular wall: Computer modelling comparing bipolar and unipolar modes. International Journal of Hyperthermia. 30 (6) Materials and methods:We built computational models to study the temperature distributions and lesion dimensions created by BM and UM on IVS and VFW during RFA. Two different UM types were considered: sequential (SEUM) and simultaneous (SIUM). The effect of ventricular wall thickness, catheter misalignment, epicardial fat, and presence of air in the epicardial space were also studied.Results: As regards IVS ablation, BM created transmural and symmetrical lesions for wall thicknesses up to 15 mm. SEUM and SIUM were not able to create transmural lesions with IVS thicknesses ≥ 12.5 and 15 mm, respectively. Lesions were asymmetrical only with SEUM. For VFW ablation, BM also created transmural lesions for wall thicknesses up to 15 mm. However, with SEUM and SIUM transmurality was obtained for VFW thicknesses ≤ 7.5 and 12.5 mm, respectively. With the three modes VFW lesions were always asymmetrical. In the scenario with air or a fat tissue layer on the epicardial side, only SIUM was capable of creating transmural lesions. Overall, BM was superior to UM in IVS and VFW ablation when the catheters were not aligned. Conclusions:Our findings suggest that BM is more effective than UM in achieving transmurality across both ventricular sites, except in the situation of the epicardial catheter tip surrounded by air or placed over a fat tissue layer.

Purpose: To develop computer models to mimic the impedance-controlled pulsing protocol implemented in RF generators used for clinical practice of radiofrequency ablation (RFA), and to assess the appropriateness of the models by comparing the computer results with those obtained in previous experimental studies.Methods: A 12-minute RFA was modeled using a cooled electrode (17G, 3 cm tip) inserted in hepatic tissue. The short (transverse) diameter of the coagulation zone was assessed under in vivo (with blood perfusion and considering clamping) and ex vivo (at 21ºC) conditions.The computer results obtained by programming voltage pulses were compared with current pulses.Results: The differences between voltage and current pulses protocol were noticeable: using current instead of voltage allows larger coagulation zones to be created, due to the higher energy applied by current pulses. If voltage pulses are employed, the model can accurately predict number of roll-offs, although the waveform of the applied power is clearly not realistic. If current voltages are employed, the applied power waveform matches well with those reported experimentally, but there are significantly fewer roll-offs. Our computer results were overall into the ranges of experimental ones. Conclusions:The proposed models reproduce reasonably well the electrical-thermal performance and coagulation zone size obtained during an impedance-controlled pulsing protocol.

Results: Rehydration and increased electrical conductivity were responsible for an increase in coagulation zone size and a delay (or absence) in the occurrence of abrupt increases in electrical impedance (roll-off). While the increased electrical conductivity had a remarkable effect on enlarging the coagulation zone (an increase of 0.74 cm for differences in electrical conductivity of 0.31 S/m), rehydration considerably affected the delay in roll-off, which, in fact, was absent with a sufficiently high rehydration level. In contrast, thermal convection had an insignificant effect for the flow rates considered (0.05 and 1 mL/min). Conclusions:Computer results suggest that rehydration and increased electrical conductivity were mainly responsible for the absence of roll-off and increased size of the coagulation zone, respectively, and in combination allow the thermal and electrical performance of ICW electrodes to be modeled during RFA.

In modern surgery, a multitude of minimally intrusive operational techniques are used which are based on the punctual heating of target zones of human tissue via laser or radio-frequency currents. Traditionally, these processes are modeled by the bioheat equation introduced by Pennes, who considers Fourier's theory of heat conduction. We present an alternative and more realistic model established by the hyperbolic equation of heat transfer. To demonstrate some features and advantages of our proposed method, we apply the obtained results to different types of tissue heating with high energy fluxes, in particular radiofrequency heating and pulsed laser treatment of the cornea to correct refractive errors. Hopefully, the results of our approach help to refine surgical interventions in this novel field of medical treatment. (M. M. Tung), matrugui@mat.upv.es (M. Trujillo), jalopez@mat.upv.es (J.A. López Molina), mjrivera@mat.upv.es (M.J. Rivera), eberjano@eln.upv.es (E.J. Berjano).