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.

Impedance measurement to assess epicardial fat prior to RF intraoperative cardiac ablation: a feasibility study using a computer model.

Radiofrequency (RF) cardiac ablation is used to treat certain types of arrhythmias. In the epicardial approach, efficacy of RF ablation is uncertain due to the presence of epicardial adipose tissue interposed between the ablation electrode and the atrial wall. We planned a feasibility study based on a theoretical model in order to assess a new technique to estimate the quantity of fat by conducting bioimpedance measurements using a multi-electrode probe. The finite element method was used to solve the electrical problem. The results showed that the measured impedance profile coincided approximately with the epicardial fat profile measured under the probe electrodes and also that the thicker the epicardial fat, the higher the impedance values. When the lateral fat width was less than 4.5 mm, the impedance values altered, suggesting that measurements should always be conducted over a sizeable fat layer. We concluded that impedance measurement could be a practical method of assessing epicardial fat prior to RF intraoperative cardiac ablation, i.e. 'to map' the amount of adipose tissue under the probe.

Black-box modeling to estimate tissue temperature during radiofrequency catheter cardiac ablation: Feasibility study on an agar phantom model.

The aim of this work was to study linear deterministic models to predict tissue temperature during radiofrequency cardiac ablation (RFCA) by measuring magnitudes such as electrode temperature, power and impedance between active and dispersive electrodes. The concept involves autoregressive models with exogenous input (ARX), which is a particular case of the autoregressive moving average model with exogenous input (ARMAX). The values of the mode parameters were determined from a least-squares fit of experimental data. The data were obtained from radiofrequency ablations conducted on agar models with different contact pressure conditions between electrode and agar (0 and 20 g) and different flow rates around the electrode (1, 1.5 and 2 L min(-1)). Half of all the ablations were chosen randomly to be used for identification (i.e. determination of model parameters) and the other half were used for model validation. The results suggest that (1) a linear model can be developed to predict tissue temperature at a depth of 4.5 mm during RF cardiac ablation by using the variables applied power, impedance and electrode temperature; (2) the best model provides a reasonably accurate estimate of tissue temperature with a 60% probability of achieving average errors better than 5 degrees C; (3) substantial errors (larger than 15 degrees C) were found only in 6.6% of cases and were associated with abnormal experiments (e.g. those involving the displacement of the ablation electrode) and (4) the impact of measuring impedance on the overall estimate is negligible (around 1 degrees C).

Mathematical modeling of epicardial RF ablation of atrial tissue with overlying epicardial fat.

The efficacy of treating atrial fibrillation by RF ablation on the epicardial surface is currently under question due to the presence of epicardial adipose tissue interposed between the ablation electrode and target site (atrial wall). The problem is probably caused by the electrical conductivity of the fat (0.02 S/m) being lower than that of the atrial tissue (0.4-0.6 S/m). Since our objective is to improve epicardial RF ablation techniques, we planned a study based on a two-dimensional mathematical model including an active electrode, a fragment of epicardial fat over a fragment of atrial tissue, and a section of atrium with circulating blood. Different procedures for applying RF power were studied, such as varying the frequency, using a cooled instead of a dry electrode, and different modes of controlling RF power (constant current, temperature and voltage) for different values of epicardial fat thickness. In general, the results showed that the epicardial fat layer seriously impedes the passage of RF current, thus reducing the effectiveness of atrial wall RF ablation.

In vivo assessment of a new method of pulsatile perfusion based on a centrifugal pump.

The aim of this study was to assess platelet dysfunction and damage to organs after extracorporeal circulation using a pump based on a new method that adds a pulsatile flow to the continuous flow provided by a centrifugal pump. The continuous component of the total flow (2-3 L/min) is created by a Bio-Pump centrifugal pump, while the pulsatile component is created by the pulsating of an inner membrane pneumatically controlled by an intra-aortic counterpulsation balloon console (systolic volume of 37.5 mL in an asynchronous way with a frequency of 60 bpm). Six pigs were subjected to a partial cardiopulmonary bypass lasting 180 min and were sacrificed 60 min after extracorporeal circulation was suspended. The hematological study included the measurement of hematocrit, hemoglobin, leukocytes, and platelet function. The new pump did not significantly alter either platelet count or platelet function. In contrast, hematocrit and hemoglobin were significantly reduced during extracorporeal circulation (approximately 5% P = 0.011, and 2 g/dL P = 0.01, respectively). The leukocyte count during extracorporeal circulation showed a tendency to decrease, but this was not significant. In general, the short-term use of the new pump (4 h) did not cause any serious morphological damage to the heart, lung, kidney, or liver. The results suggest that the hemodynamic performance of the new pump is similar to a conventional centrifugal pump and could therefore be appropriate for use in extracorporeal circulation.

Pulse wave velocity and digital volume pulse as indirect estimators of blood pressure: pilot study on healthy volunteers.

The purpose of the study was to asses the potential use of pulse wave velocity (PWV) and digital volume pulse (DVP) as estimators of systolic (SBP) and diastolic (DPB) blood pressure. Single and multiple correlation studies were conducted, including biometric parameters and risk factors. Brachial-ankle PWV (baPWV) and DVP signals were obtained from a Pulse Trace PWV and Pulse Trace PCA (pulse contour analysis), respectively. The DVP (obtained by photoplethysmography), allowed stiffness (SI) and reflection indexes (RI) to be derived. The first study on 47 healthy volunteers showed that both SBP and DPB correlated significantly both with baPWV and SI. Multiple regression models of the baPWV and the waist-to-hip ratio (WHR) allowed SBP and DBP to be modeled with r = 0.838 and r = 0.673, respectively. SI results also employed WHR and modeled SBP and DBP with r = 0.852 and r = 0.663, respectively. RI did not correlate either with SBP or DBP. In order to avoid the use of ultrasound techniques to measure PWV, we then developed a custom-built system to measure PWV by photoplethysmography and validated it against the Pulse Trace. With the same equipment we conducted a second pilot study with ten healthy volunteers. The best SBP multiple regression model for SBP achieved r = 0.997 by considering the heart-finger PWV (hfPWV measured between R-wave and index finger), WHR and heart rate. Only WHR was significant in the DBP model. Our findings suggest that the hfPWV photoplethysmography signal could be a reliable estimator of approximate SBP and could be used, for example, to monitor cardiac patients during physical exercise sessions in cardiac rehabilitation.

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.

Thermal modeling for pulsed radiofrequency ablation: analytical study based on hyperbolic heat conduction.

The objectives of this study were to model the temperature progress of a pulsed radiofrequency (RF) power during RF heating of biological tissue, and to employ the hyperbolic heat transfer equation (HHTE), which takes the thermal wave behavior into account, and compare the results to those obtained using the heat transfer equation based on Fourier theory (FHTE). A theoretical model was built based on an active spherical electrode completely embedded in the biological tissue, after which HHTE and FHTE were analytically solved. We found three typical waveforms for the temperature progress depending on the relations between the dimensionless duration of the RF pulse delta(a) and the expression square root of lambda(rho-1), with lambda as the dimensionless thermal relaxation time of the tissue and rho as the dimensionless position. In the case of a unique RF pulse, the temperature at any location was the result of the overlapping of two different heat sources delayed for a duration delta(a) (each heat source being produced by a RF pulse of limitless duration). The most remarkable feature in the HHTE analytical solution was the presence of temperature peaks traveling through the medium at a finite speed. These peaks not only occurred during the RF power switch-on period but also during switch off. Finally, a physical explanation for these temperature peaks is proposed based on the interaction of forward and reverse thermal waves. All-purpose analytical solutions for FHTE and HHTE were obtained during pulsed RF heating of biological tissues, which could be used for any value of pulsing frequency and duty cycle.

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.

Analytical thermal-optic model for laser heating of biological tissue using the hyperbolic heat transfer equation.

In this paper, we solve in an analytical way the thermal-optic coupled problem associated with a 1D model of non-perfused homogeneous biological tissue irradiated by a laser beam. We consider a laser pulse duration of 200 micros and study the temperatures of areas very close to the point of laser beam application. We consider that these values of the temporal and spatial variables mean that the problem has to be solved by means of the hyperbolic heat conduction model instead of the classic or parabolic model. We therefore obtain the solution using both models and apply the temperature profiles obtained to a specific biological tissue for comparison. Finally, we theoretically study the effect of the thermal relaxation time on the temperature profiles in the tissue for both heating and cooling phases (i.e. during and after laser application).

Reliability assessment of a cooled intraesophageal balloon to prevent thermal injury during RF cardiac ablation: an agar phantom study.

UNLABELLED: Cooled Balloon Prevents Thermal Injury During RF Ablation. INTRODUCTION: The use of a cooled intraesophageal balloon has recently been proposed to minimize the risk of thermal injury in the esophagus during radiofrequency (RF) ablation of the left atrium. However, the capacity of this device to adequately protect the esophagus under different procedural and anatomical conditions remains unknown. METHODS AND RESULTS: An agar phantom-based model was built that provided temperature readings not only on the cooled balloon (T(b)) but also at a hypothetical point between the esophageal lumen and myocardium at a distance of 2 mm (T(2-mm)). The RF ablations were conducted considering two anatomical factors (total distance between the electrode and balloon and flow rate around the electrode) and two procedural factors (angle and pressure between the electrode and agar surface). The results show that most of the parameters studied have no significant influence on the temperature measured on the cooled balloon (T(b)), the exception being a variation in the flow rate, which was found to influence the temperature. On the other hand, T(2-mm) was affected to a great extent by all the factors considered, the smallest influence being that of the contact pressure. The results also suggest that when an intraesophageal balloon is employed, the applied power is not a good predictor either of the temperature on the balloon or of the temperature measured at a distance 2 mm away. CONCLUSION: The results suggest that a cooled intraesophageal balloon provides effective thermal protection of the esophageal lumen. However, under certain circumstances, the temperature reached at a distance 2 mm away could possibly put at risk the integrity of the inner layers of the esophagus.

A new method of providing pulsatile flow in a centrifugal pump: assessment of pulsatility using a mock circulatory system.

Previous studies have demonstrated the potential advantages of pulsatile flow as compared with continuous flow. However, to date, physiologic pumps have been technically complex and their application has therefore remained in the experimental field. We have developed a new type of centrifugal pump, which can provide pulsatile as well as continuous flow. The inner wall of a centrifugal pump is pulsed by means of a flexible membrane, which can be accurately controlled by means of either a hydraulic or pneumatic driver. The aim of this study was to assess the hydraulic behavior of the new pump in terms of surplus hemodynamic energy (SHE). We conducted experiments using a mock circulatory system including a membrane oxygenator. No differences were found in the pressure-flow characteristics between the new pump and a conventional centrifugal pump, suggesting that the inclusion of the flexible membrane does not alter hydraulic performance. The value of SHE rose when systolic volume was increased. However, SHE dropped when the percentage of ejection time was reduced and also when the continuous flow (programmed by the centrifugal console) increased. Mean flow matched well with the continuous flow set by the centrifugal console, that is, the pulsatile component of the flow was exclusively controlled by the pulsatile console, and was therefore independent of the continuous flow programmed by the centrifugal console. The pulsatility of the new pump was approximately 25% of that created with a truly pulsatile pump.

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.

A cooled water-irrigated intraesophageal balloon to prevent thermal injury during cardiac ablation: experimental study based on an agar phantom.

A great deal of current research is directed to finding a way to minimize thermal injury in the esophagus during radiofrequency catheter ablation of the atrium. A recent clinical study employing a cooling intraesophageal balloon reported a reduction of the temperature in the esophageal lumen. However, it could not be determined whether the deeper muscular layer of the esophagus was cooled enough to prevent injury. We built a model based on an agar phantom in order to experimentally study the thermal behavior of this balloon by measuring the temperature not only on the balloon, but also at a hypothetical point between the esophageal lumen and myocardium (2 mm distant). Controlled temperature (55 degrees C) ablations were conducted for 120 s. The results showed that (1) the cooling balloon provides a reduction in the final temperature reached, both on the balloon surface and at a distance of 2 mm; (2) coolant temperature has a significant effect on the temperature measured at 2 mm from the esophageal lumen (it has a less effect on the temperature measured on the balloon surface) and (3) the pre-cooling period has a significant effect on the temperature measured on the balloon surface (the effect on the temperature measured 2 mm away is small). The results were in good agreement with those obtained in a previous clinical study. The study suggests that the cooling balloon gives thermal protection to the esophagus when a minimum pre-cooling period of 2 min is programmed at a coolant temperature of 5 degrees C or less.

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).