Analytical validation of COMSOL Multiphysics for theoretical models of Radiofrequency ablation including the Hyperbolic Bioheat transfer equation.

In this paper we outline our main findings about the differences between the use of the Bioheat Equation and the Hyperbolic Bioheat Equation in theoretical models for Radiofrequency (RF) ablation. At the moment, we have been working on the analytical approach to solve both equations, but more recently, we have considered numerical models based on the Finite Element Method (FEM). As a first step to use FEM, we conducted a comparative study between the temperature profiles obtained from the analytical solutions and those obtained from FEM. Regarding the differences between both methods, we obtain agreement in less than 5% of relative differences. Then FEM is a good alternative to model heating of biological tissues using BE and HBE in, for example, more complex and realistic geometries.

Effect of electrode thermal conductivity in cardiac radiofrequency catheter ablation: a computational modeling study.

PURPOSE: Radiofrequency (RF ablation) is the treatment of choice for certain types of cardiac arrhythmias. Recent studies have suggested that using gold instead of platinum as the electrode material for cardiac catheter ablation leads to larger thermal lesions due to its higher thermal conductivity. In this study we created computer models to compare the effects of different electrode materials on lesion dimensions using different catheters, insertion depths, and flow rates. MATERIALS AND METHODS: Finite element method (FEM) models of two cardiac ablation electrodes (7Fr, length 4 mm and 8Fr, length 10 mm) made of platinum, gold, and copper were created with tissue insertion depths of 0.75, 1.25, and 2.5 mm. Convective cooling was applied to the electrode and tissue based on measurements from previous studies at different flow rates. RF ablations were simulated with both temperature control and constant power control algorithms to determine temperature profiles after 60 s. RESULTS: With the constant power algorithm there was no difference in lesion dimensions between the electrode materials over the range of parameters. With the temperature control algorithm, lesion width and depth were only marginally larger ( approximately 0.1-0.7 mm) with the gold and copper electrodes compared to the platinum electrode for all parameter combinations. CONCLUSION: Our computer modelling results show only minor increases in thermal lesion dimensions with electrode materials of higher thermal conductivity. These observed differences likely do not provide a significant advantage during clinical procedures.

Esophagus histological analysis after hyperthermia-induced injury: implications for cardiac ablation.

PURPOSE: To evaluate and numerically score histological alterations observed in the acute phase in the esophagus after being exposed to a hyperthermic dosage and subsequently to correlate the scores obtained with the hyperthermic treatment parameters (i.e. temperature (T) and time (t)). MATERIAL AND METHODS: Esophagus samples obtained from New Zealand white rabbits were immersed in a temperature-controlled saline bath at 40, 50, 60 and 70 degrees C for 30, 60 and 90 s. Samples were then processed for histological analysis (Masson Trichrome technique), and evaluated by searching for objective heat-damage signs. A numerical value was assigned to each sample for each finding. RESULTS: In general, all the layers were affected by the treatment, however, the greatest alterations were found in the epithelium and deeper muscular layers (circular and longitudinal). We found no damage (i.e. no differences to control) in all of the samples treated at 40 degrees C, and severe damage in treatments at 60 and 70 degrees C, regardless of exposure time. On the other hand, samples treated at 50 degrees C did show different results related to time: no damage for 30 s, light damage for 60 s, and moderate damage for 90 s. We assigned a score value to each hyperthermic dosage, and obtained the fitted equation based on a logarithmic transformation of the Arrhenius equation: Score = 130.7 - 40,851/(T + 273) + log t, (R(2) = 0.9326, P < 0.0001). CONCLUSIONS: Hyperthermic treatment mainly affects the epithelium and deeper muscular layers. The results suggest a damage threshold of 50 degrees C for treatments of 30-90 s. The proposed scoring system provides a good fit with the hyperthermic parameters.

Research and development of a new RF-assisted device for bloodless rapid transection of the liver: computational modeling and in vivo experiments.

BACKGROUND: Efficient and safe transection of biological tissue in liver surgery is strongly dependent on the ability to address both parenchymal division and hemostasis simultaneously. In addition to the conventional clamp crushing or finger fracture methods other techniques based on radiofrequency (RF) currents have been extensively employed to reduce intraoperative blood loss. In this paper we present our broad research plan for a new RF-assisted device for bloodless, rapid resection of the liver. METHODS: Our research plan includes computer modeling and in vivo studies. Computer modeling was based on the Finite Element Method (FEM) and allowed us to estimate the distribution of electrical power deposited in the tissue, along with assessing the effect of the characteristics of the device on the temperature profiles. Studies based on in vivo pig liver models provided a comparison of the performance of the new device with other techniques (saline-linked technology) currently employed in clinical practice. Finally, the plan includes a pilot clinical trial, in which both the new device and the accessory equipment are seen to comply with all safety requirements. RESULTS: The FEM results showed a high electrical gradient around the tip of the blade, responsible for the maximal increase of temperature at that point, where temperature reached 100 degrees C in only 3.85 s. Other hot points with lower temperatures were located at the proximal edge of the device. Additional simulations with an electrically insulated blade produced more uniform and larger lesions (assessed as the 55 degrees C isotherm) than the electrically conducting blade. The in vivo study, in turn, showed greater transection speed (3 +/- 0 and 3 +/- 1 cm2/min for the new device in the open and laparoscopic approaches respectively) and also lower blood loss (70 +/- 74 and 26 +/- 34 mL) during transection of the liver, as compared to saline-linked technology (2 +/- 1 cm2/min with P = 0.002, and 527 +/- 273 mL with P = 0.001). CONCLUSION: A new RF-assisted device for bloodless, rapid liver resection was designed, built and tested. The results demonstrate the potential advantages of this device over others currently employed.

Laparoscopic blood-saving liver resection using a new radiofrequency-assisted device: preliminary report of an in vivo study with pig liver.

BACKGROUND: The aim of any device designed for liver resection is to allow blood saving and quick resections. This may be optimized using a minimally invasive approach. A radiofrequency-assisted device is described that combines a cooled blunt-tip electrode with a sharp blade on one side in an in vivo preliminary study using hand-assisted laparoscopy to perform partial hepatectomies. METHODS: Eight partial hepatectomies were performed on pigs with hand-assisted laparoscopy using the radiofrequency-assisted device as the only method for transection and hemostasis. The main outcome measures were transection time, blood loss, transection area, transection speed, blood loss per transection area, and tissue coagulation depth. The risk for biliary leak also was assessed using the methylene blue test. RESULTS: The transection time was 13 +/- 7 min for a mean transected area of 34 +/- 11 cm(2). The mean total blood loss was 26 +/- 34 ml. The mean transection speed was 3 +/- 1 cm(2)/min, and the blood loss per transection area was 1 +/- 1 ml/cm(2). Abdominal examination showed no complications in nearby organs. One biliary leak was identified in one case using the methylene blue test. The transection surface was 34 +/- 11 cm(2), and the mean tissue coagulation depth was 9 +/- 2 mm. The inviability of the coagulated surface was assessed by adenine dinucleotide (NADH) staining. CONCLUSIONS: The radiofrequency-assisted device has shown with a laparoscopic approach that it can perform liver resections faster and with less blood loss using a single device in a minimally invasive manner without vascular control than other commercial devices. The results show no significant differences with the same device used in an open procedure.

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.

Assessment of hyperbolic heat transfer equation in theoretical modeling for radiofrequency heating techniques.

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).

Small ablation zones created previous to saline infusion result in enlargement of the coagulated area during perfusion RF ablation: an ex vivo experimental study.

One of the strategies for enlarging coagulation zone dimensions during RF ablation of liver tumours is to infuse saline solutions into the tissue during ablation. The aim of this study was to evaluate experimentally whether the creation of a small coagulation adjacent to a bipolar RF applicator and prior to perfused RF ablation would allow enlargement of the coagulation zone. Thirty bipolar RF ablations (group A, n = 15; group B, n = 15) were performed in excised bovine livers. Additionally, in group B a monopolar RF application (60 W, 20 s) was performed before bipolar ablation using three small additional electrodes. Electrical parameters and dimensions of the ablation zone were compared between groups. Despite the fact that all three ablation zone diameters were greater in group B, only one of the minor diameters was significantly longer (5.52 +/- 0.66 cm versus 4.87 +/- 0.47 cm). Likewise, volume was significantly bigger in group B (100.26 +/- 24.10 cm(3) versus 79.56 +/- 15.59 cm(3)). There were no differences in the impedance evolution, allowing a relatively high constant power in both groups (around 90 W). The efficacy of delivering energy (expressed as the delivered energy per coagulation volume) was significantly better in group B, showing a lower value (578 J cm(-3) versus 752 J cm(-3)). These results suggest that the creation of small ablation zones prior to saline infusion improves the performance of this perfusion system, and hence the total volume.

RF tumor ablation with internally cooled electrodes and saline infusion: what is the optimal location of the saline infusion?

BACKGROUND: Radiofrequency ablation (RFA) of tumors by means of internally cooled electrodes (ICE) combined with interstitial infusion of saline may improve clinical results. To date, infusion has been conducted through outlets placed on the surface of the cooled electrode. However, the effect of infusion at a distance from the electrode surface is unknown. Our aim was to assess the effect of perfusion distance (PD) on the coagulation geometry and deposited power during RFA using ICE. METHODS: Experiments were performed on excised bovine livers. Perfusion distance (PD) was defined as the shortest distance between the infusion outlet and the surface of the ICE. We considered three values of PD: 0, 2 and 4 mm. Two sets of experiments were considered: 1) 15 ablations of 10 minutes (n > or = 4 for each PD), in order to evaluate the effect of PD on volume and diameters of coagulation; and 2) 20 additional ablations of 20 minutes. The effect of PD on deposited power and relative frequency of uncontrolled impedance rises (roll-off) was evaluated using the results from the two sets of experiments (n > or = 7 for each PD). Comparisons between PD were performed by analysis of variance or Kruskal-Wallis test. Additionally, non-linear regression models were performed to elucidate the best PD in terms of coagulation volume and diameter, and the occurrence of uncontrolled impedance rises. RESULTS: The best-fit least square functions were always obtained with quadratic curves where volume and diameters of coagulation were maximum for a PD of 2 mm. A thirty per cent increase in volume coagulation was observed for this PD value compared to other values (P < 0.05). Likewise, the short coagulation diameter was nearly twenty five per cent larger for a 2 mm PD than for 0 mm. Regarding deposited power, the best-fit least square function was obtained by a quadratic curve with a 2 mm PD peak. This matched well with the higher relative frequency of uncontrolled impedance rises for PD of 0 and 4 mm. CONCLUSION: Saline perfusion at around 2 mm from the electrode surface while using an ICE in RFA improves deposition of energy and enlarges coagulation volume.

Improved perfusion system for bipolar radiofrequency ablation of liver: preliminary findings from a computer modeling study.

Current systems for radiofrequency ablation of liver tumors are unable to consistently treat tumors larger than 3 cm in diameter with a single electrode in a single application. One of the strategies for enlarging coagulation zone dimensions is to infuse saline solutions into the tissue through the active electrodes. Nevertheless, the uncontrolled and undirected diffusion of boiling saline into the tissue has been associated with irregular coagulation zones and severe complications, mainly due to reflux of saline along the electrode path. In order to improve the perfusion bipolar ablation method, we hypothesized that the creation of small monopolar coagulation zones adjacent to the bipolar electrodes and previous to the saline infusion would create preferential paths for the saline to concentrate on the targeted coagulation zone. Firstly, we conducted ex vivo experiments in order to characterize the monopolar coagulation zones. We observed that they are practically impermeable to the infused saline. On the basis of this finding, we built theoretical models and conducted computer simulations to assess the feasibility of our hypothesis. Temperature distributions during bipolar ablations with and without previous monopolar coagulation zones were obtained. The results showed that in the case of monopolar coagulation zones the temperature of the tissue took longer to reach 100 degrees C. Since this temperature value is related to rise of impedance, and the time necessary for this process is directly related to the volume of the coagulation zone, our results suggest that monopolar sealing would allow larger coagulation zones to be created. Future experimental studies should confirm this benefit.

Theoretical modeling for radiofrequency ablation: state-of-the-art and challenges for the future.

Radiofrequency ablation is an interventional technique that in recent years has come to be employed in very different medical fields, such as the elimination of cardiac arrhythmias or the destruction of tumors in different locations. In order to investigate and develop new techniques, and also to improve those currently employed, theoretical models and computer simulations are a powerful tool since they provide vital information on the electrical and thermal behavior of ablation rapidly and at low cost. In the future they could even help to plan individual treatment for each patient. This review analyzes the state-of-the-art in theoretical modeling as applied to the study of radiofrequency ablation techniques. Firstly, it describes the most important issues involved in this methodology, including the experimental validation. Secondly, it points out the present limitations, especially those related to the lack of an accurate characterization of the biological tissues. After analyzing the current and future benefits of this technique it finally suggests future lines and trends in the research of this area.

Modeling for radio-frequency conductive keratoplasty: implications for the maximum temperature reached in the cornea.

Conductive keratoplasty (CK) is a new surgical technique for steepening the contours of the cornea to reduce hyperopia. It has been emphasized that during CK, tissue resistance to radio-frequency electrical current flow generates a localized heat with temperatures between 65 and 75 degrees C; however, we hypothesize that the maximum temperature reached in the cornea may be higher. For this reason, we developed a finite-element model to estimate the temperature distributions in the cornea during CK. The time evolution of the impedance obtained from computer simulations was compared to that obtained in an experimental study previously published. Our results show that during a typical CK with a 60% setting power (equivalent to 200 V peak-to-peak), the cornea may reach temperatures over 100 degrees C at the electrode tip. On the other hand, the initial impedance of the cornea has a significant influence on the temperature distribution, while the initial temperature of the cornea is not a significant parameter. The results also suggest that low power settings (30-40%) do not produce temperatures over 100 degrees C. Finally, although the actual voltage waveform during CK is exponential and pulsed, our model based on a constant voltage (with a value equal to the root mean square value) provides a better agreement between the theoretical impedance time evolution and that obtained experimentally.

Thermal-electrical modeling for epicardial atrial radiofrequency ablation.

Epicardial radiofrequency ablation is increasingly being used for intraoperative treatment of atrial fibrillation. However, the effect of different parameters on the lesion characteristics has not been sufficiently characterized. We used a finite element model to calculate the temperature distribution in the atrial tissue under different conditions during a constant voltage radiofrequency ablation. Our simulation results show that although in the case of a thin atrium the lesion was less deep for a thin atrium, it was easier to achieve transmurality. While considering a thinner atrium, the location of the hottest point of the lesion shifted from the electrode tip to epicardial surface. This effect was due to the convective cooling of the circulating blood inside the atrium. This convective cooling phenomenon has almost negligible effects for atria thicker than 3 mm. The variability of the cooling values has no significant effect on the lesion, even for thin atria (1-2 mm). Increasing the electrode insertion depth (ID) in the tissue produced larger lesions. However, for thinner atria (thickness <2 mm), this increase in the ID reduced the lesion width. It was also proved that the presence of a fat layer between the electrode and the atrial tissue decreased significantly the lesion dimensions.

Long electrodes for radio frequency ablation: comparative study of surface versus intramural application.

There is increasing use of radio frequency (RF) ablation with long electrodes in the intraoperative treatment of atrial fibrillation. Nevertheless, the disparity in the lesion geometry in both depth and width is the major pitfall in the use of RF currents. The objective of this study was to differentiate the shape and size of long lesions created by three surface application electrodes (SAE) and two intramural electrodes (IE). The SAE included a standard multi-polar catheter, and two standard electrosurgical pencils. The IE consisted of a needle and a wire both intramurally buried. The lesions were created on fresh fragments of porcine ventricular tissue. The IE created lesions with a curved prism-like shape around the electrode body, with homogeneous characteristics along the lesion trajectory. On the contrary, the lesions created with the SAE were in the shape of an hourglass. They showed a different geometry between the central zone and the edge zone (p<0.001 for depth and surface width). Electrical impedance evolution was recorded during the RF heating. We observed a slow decrease of the impedance in all the electrodes, except in the wire electrode. In conclusion, the results suggest that the IE might be a more suitable option than SAE when it is necessary to create long and homogeneous thermal lesions.

Radio-frequency heating of the cornea: theoretical model and in vitro experiments.

We present a theoretical model for the study of cornea heating with radio-frequency currents. This technique is used to reshape the cornea to correct refractive disorders. Our numerical model has allowed the study of the temperature distributions in the cornea and to estimate the dimensions of the lesion. The model incorporates a fragment of cornea, aqueous humor, and the active electrode placed on the cornea surface. The finite element method has been used to calculate the temperature distribution in the cornea by solving a coupled electric-thermal problem. We analyzed by means of computer simulations the effect of: a) temperature influence on the tissue electrical conductivity; b) the dispersion of the biological characteristics; c) the anisotropy of the cornea thermal conductivity; d) the presence of the tear film; and e) the insertion depth of the active electrode in the cornea, and the results suggest that these effects have a significant influence on the temperature distributions and thereby on the lesion dimensions. However, the cooling of the aqueous humor in the endothelium or the realistic value of the cornea curvature did not have a significant effect on the temperature distributions. An experimental model based on the lesions created in rabbit eyes has been used in order to compare the theoretical and experimental results. There is a tendency toward the agreement between experimental and theoretical results, although we have observed that the theoretical model overestimates the lesion dimension.