Effect of skin electrode location on radiofrequency ablation lesions: an in vivo and a three-dimensional finite element study

Simulating radiofrequency ablation of hepatocellular carcinomas proximal to bare area of liver

PURPOSE

To numerically assess the significance of dextrose 5% in water (D5W) thermo-protection during radiofrequency ablation (RFA) of hepatocellular carcinomas (HCCs) located near the 'bare area of liver'.

MATERIAL AND METHODS

This study utilises quasi-anatomical structures extracted from CT images. A multi-tine electrode, deployed inside the extracted organs and operated under temperature-controlled mode was used as the source of ablation. Geometrically, D5W was modelled around the 'bare area' and sandwiched between the liver and diaphragm. RFA at different sites relative to the 'bare area' was simulated to answer when to consider modelling D5W.

RESULTS

For targets near the edge of 'bare area' and at 0.5 mm gap (between the electrode and the 'bare area'), ignoring D5W and using ground conditions could result in underestimation of ablation volume by almost 25%. The importance of D5W becomes negligible for ablations near the centre of the 'bare area'.

CONCLUSIONS

Consideration of D5W during RFA of HCCs proximal to the 'bare area' can significantly influence the ablation outcome, especially when ablation is performed near the edge of the 'bare area'.

Effects of Pulsed Radiofrequency Source on Cardiac Ablation

Heart arrhythmia is caused by abnormal electrical conduction through the myocardium, which in some cases, can be treated with heat. One of the challenges is to reduce temperature peaks-by still guaranteeing an efficient treatment where desired-to avoid any healthy tissue damage or any electrical issues within the device employed. A solution might be employing pulsed heat, in which thermal dose is given to the tissue with a variation in time. In this work, pulsed heat is used to modulate induced temperature fields during radiofrequency cardiac ablation. A three-dimensional model of the myocardium, catheter and blood flow is developed. Porous media, heat conduction and Navier-Stokes equations are, respectively, employed for each of the investigated domains. For the electric field, solved via Laplace equation, it is assumed that the electrode is at a fixed voltage. Pulsed heating effects are considered with a cosine time-variable pulsed function for the fixed voltage by constraining the product between this variable and time. Different dimensionless frequencies are considered and applied for different blood flow velocity and sustained voltages. Results are presented for different pulsed conditions to establish if a reasonable ablation zone, known from the obtained temperature profiles, can be obtained without any undesired temperature peaks.

Effect of Baseline Impedance in Radiofrequency Delivery on Lesion Characteristics and the Relationship Between Impedance and Steam Pops

Objective

To explore the effects of baseline impedance (R) and power (P) on radiofrequency ablation (RFA) lesion characteristics and their correlation with steam pops using ThermoCool SmartTouch-SF (STSF) catheters in the porcine heart.

Method

A porcine left ventricle was submerged in 37°C saline ex vivo, and the experiment was performed with various P (P = 30, 40, 50, and 60 W) and multiple R loads (R = 80–100, 100–140, 140–180, and 180–220 Ω) to reach the target ablation index (AI; AI = 350, 450, and 500) or reach the target ablation time using a fixed contact force (CF; CF = 10–15 g) and the same saline irrigation (30 W/8 ml/min or 40–60 W/15 ml/min), repeated five times under each condition.

Results

The surface diameter, maximum diameter, depth, and volume of the lesions were strongly correlated with the AI (P = 40 W, R = 100–140 Ω, CF = 10–15 g) (r = 0.5412; r = 0.7889; r = 0.9366; and r = 0.913, respectively; all p < 0.05). As the value of R increased, the maximum diameter, depth, and volume of the lesions significantly increased (AI = 350, P = 30 W). Moreover, the higher the baseline value of R, the greater the absolute value of the R decrease (r = 0.9035, p < 0.05, Y = 0.2759 × X – 18.33). Under high power and high impedance, the occurrence rate of steam pops was high (P = 60 W, R = 180–220 Ω, AI when a steam pop occurred: 480 ± 26.5, ablation time: 11.29 ± 1.04 s).

Conclusion

Radiofrequency catheter ablation (RFCA) in power-controlled mode resulted in various lesion characteristics that were related to diverse baseline Rs. In addition, the incidence of steam pops was strongly correlated with high baseline R and high P.

Impact of baseline impedance of pulmonary vein antrum on success of catheter ablation for paroxysmal atrial fibrillation guided by ablation index

Objective

Ablation index (AI) is an effective ablation quality marker. Impedance is also an important factor for lesion formation. The present study evaluated the influence of the baseline impedance in the effect of ablation for atrial fibrillation (AF) guided by AI.

Methods

This was a retrospective study. 101 patients with paroxysmal AF (PAF) were enrolled. All patients underwent radiofrequency ablation guided by the same AI strategy. The ablation strategy was pulmonary vein (PV) isolation with non-PV triggers ablation. The baseline impedance of the ablation points was recorded. The patients were followed up every 3 months or so.

Results

During a median follow-up of 12 (4–14) months, freedom from AF/atrial tachycardia recurrence were 82.2%. No difference existed in baseline characteristics between the success group and the recurrence group. The average baseline impedance was 124.3 ± 9.7 Ω. The baseline impedance of the ablation points in success group was lower compared to the recurrence group (122.9 ± 9.4 vs. 130.5 ± 8.8 Ω, P < 0.01). The ratio of impedance drop in the success group was higher than the recurrence group ([8.8 ± 1.4]% vs. [8.1 ± 1.2]%, P = 0.03). Multivariate analysis revealed that baseline impedance, PAF duration and AI were the independent predictors of AF recurrence. The cumulative free of recurrence rate of low-impedance group (≤ 124 Ω, n = 54) was higher than that of high-impedance group.

Conclusion

Baseline impedance correlates with clinical outcome of radiofrequency ablation for PAF guided by AI. Higher impedance in the same AI strategy may result in an ineffective lesion which probably causes recurrence.

Supplementary Information

The online version contains supplementary material available at 10.1186/s12872-022-02530-y.

Computer modeling of radiofrequency cardiac ablation: 30 years of bioengineering research

This review begins with a rationale of the importance of theoretical, mathematical and computational models for radiofrequency (RF) catheter ablation (RFCA). We then describe the historical context in which each model was developed, its contribution to the knowledge of the physics of RFCA and its implications for clinical practice. Next, we review the computer modeling studies intended to improve our knowledge of the biophysics of RFCA and those intended to explore new technologies. We describe the most important technical details of the implementation of mathematical models, including governing equations, tissue properties, boundary conditions, etc. We discuss the utility of lumped element models, which despite their simplicity are widely used by clinical researchers to provide a physical explanation of how RF power is absorbed in different tissues. Computer model verification and validation are also discussed in the context of RFCA. The article ends with a section on the current limitations, i.e. aspects not yet included in state-of-the-art RFCA computer modeling and on future work aimed at covering the current gaps.

Mini Electrodes on Ablation Catheters: Valuable Addition or Redundant Information?-Insights from a Computational Study

Radiofrequency ablation has become a first-line approach for curative therapy of many cardiac arrhythmias. Various existing catheter designs provide high spatial resolution to identify the best spot for performing ablation and to assess lesion formation. However, creation of transmural and nonconducting ablation lesions requires usage of catheters with larger electrodes and improved thermal conductivity, leading to reduced spatial sensitivity. As trade-off, an ablation catheter with integrated mini electrodes was introduced. The additional diagnostic benefit of this catheter is still not clear. In order to solve this issue, we implemented a computational setup with different ablation scenarios. Our in silico results show that peak-to-peak amplitudes of unipolar electrograms from mini electrodes are more suitable to differentiate ablated and nonablated tissue compared to electrograms from the distal ablation electrode. However, in orthogonal mapping position, no significant difference was observed between distal electrode and mini electrodes electrograms in the ablation scenarios. In conclusion, catheters with mini electrodes bring about additional benefit to distinguish ablated tissue from nonablated tissue in parallel position with high spatial resolution. It is feasible to detect conduction gaps in linear lesions with this catheter by evaluating electrogram data from mini electrodes.

Computational Modeling of Open-Irrigated Electrodes for Radiofrequency Cardiac Ablation Including Blood Motion-Saline Flow Interaction

Radiofrequency catheter ablation (RFCA) is a routine treatment for cardiac arrhythmias. During RFCA, the electrode-tissue interface temperature should be kept below 80 °C to avoid thrombus formation. Open-irrigated electrodes facilitate power delivery while keeping low temperatures around the catheter. No computational model of an open-irrigated electrode in endocardial RFCA accounting for both the saline irrigation flow and the blood motion in the cardiac chamber has been proposed yet. We present the first computational model including both effects at once. The model has been validated against existing experimental results. Computational results showed that the surface lesion width and blood temperature are affected by both the electrode design and the irrigation flow rate. Smaller surface lesion widths and blood temperatures are obtained with higher irrigation flow rate, while the lesion depth is not affected by changing the irrigation flow rate. Larger lesions are obtained with increasing power and the electrode-tissue contact. Also, larger lesions are obtained when electrode is placed horizontally. Overall, the computational findings are in close agreement with previous experimental results providing an excellent tool for future catheter research.

Development of a computational simulation tool to design a protocol for treating prostate tumours using transurethral laser photothermal therapy

OBJECTIVES

The objective of this study was to design laser treatment protocols to induce sufficient thermal damage to a tumour embedded in a prostate model, while protecting the surrounding healthy tissue.

METHODS

A computational Monte Carlo simulation algorithm of light transport in a spherical prostatic tumour containing gold nanorods was developed to determine laser energy deposition. The laser energy absorption was then used to simulate temperature elevations in the tumour embedded in an elliptical human prostate model. The Arrhenius integral was coupled with the heat transfer model to identify heating protocols to induce 100% damage to the tumour, while resulting in less than 5% damage to the surrounding sensitive prostatic tissue.

RESULTS

Heating time to achieve 100% damage to the tumour was identified to be approximately 630 s when using a laser irradiance of 7 W/cm2 incident on the prostatic urethral surface. Parametric studies were conducted to show how the local blood perfusion rate and urethral surface cooling affect the heating time to achieve the same thermal dosage. The heating time was shorter when cooling at the urethra was not applied and/or with heat-induced vasculature damage. The identified treatment protocols were acceptable since the calculated percentages of the damaged healthy tissue volume to the healthy prostatic volume were approximately 2%, less than the threshold of 5%. The approach and results from this study can be used to design individualised treatment protocols for patients suffering from prostatic cancer.

Evaluation of thermal injury to liver, pancreas and kidney during irreversible electroporation in an in vivo experimental model

BACKGROUND

Irreversible electroporation (IRE) is a new technique for tumour cell ablation that is reported to involve non-thermal-based energy using high voltage at short microsecond pulse lengths. In vivo assessment of the thermal energy generated during IRE has not been performed. Thermal injury can be predicted using a critical temperature model. The aim of this study was to assess the potential for thermal injury during IRE in an in vivo porcine model.

METHODS

In vivo continuous temperature assessments of 86 different IRE procedures were performed on porcine liver, pancreas, kidney and retroperitoneal tissue. Tissue temperature was measured continuously throughout IRE by means of two thermocouples placed at set distances (0·5 cm or less, and 1 cm) from the IRE probes within the treatment field. Thermal injury was defined as a tissue temperature of 54°C lasting at least 10 s. Tissue type, pulse length, probe exposure length, number of probes and retreatment were evaluated for associations with thermal injury. In addition, IRE ablation was performed with metal clips or metal stents within the ablation field to determine their effect on thermal injury.

RESULTS

An increase in tissue temperature above the animals' baseline temperature (median 36·0°C) was generated during IRE in all tissues studied, with the greatest increase found at the thermocouple placed within 0·5 cm in all instances. On univariable and multivariable analysis, ablation in kidney tissue (maximum temperature 62·8°C), ablation with a pulse length setting of 100 µs (maximum 54·7°C), probe exposure of at least 3·0 cm (maximum 52·0°C) and ablation with metal within the ablation field (maximum 65·3°C) were all associated with a significant risk of thermal injury.

CONCLUSION

IRE can generate thermal energy, and even thermal injury, based on tissue type, probe exposure lengths, pulse lengths and proximity to metal. Awareness of probe placement regarding proximity to critical structures as well as probe exposure length and pulse length are necessary to ensure safety and prevent thermal injury. A probe exposure of 2·5 cm or less for liver IRE, and 1·5 cm or less for pancreas, with maximum pulse length of 90 µs will result in safe and non-thermal energy delivery with spacing of 1·5-2·3 cm between probe pairs.

Direct thermography-a new in vitro method to characterize temperature kinetics of ablation catheters

PURPOSE

For the treatment of increasingly complex cardiac arrhythmias, new catheter designs as well as alternative energy sources are constantly being developed. However, there is presently no in vitro method available for assessment of the temperature changes induced at various myocardial levels during energy delivery. Therefore, our study was aimed at developing an in vitro model to record and display the temperature kinetics during ablation in the entire muscle cross section.

METHODS AND RESULTS

A sapphire glass pane was inserted into one wall of the in vitro experimental set-up. Due to its thermodynamic properties, the temperature distribution in an adjacent cross section of the cardiac muscle can be measured exactly ( 1 °C) through this pane by means of a thermography camera. Computer-supported image processing enables the colour-coded and two-dimensional display of the temperature kinetics during the energy application at any location of the myocardial cross section (± 0.5 mm). This new measuring methodology was validated by direct temperature measurements utilizing several intramyocardial thermo elements.

CONCLUSION

This new method allows a temporal and spatial analysis of the temperature phenomena during ablation without the interference and spatial limitation of intramyocardial temperature probes. New ablation technologies can thus be evaluated, independent of the catheter configuration or source of energy used.

RF field visualization of RF ablation at the Larmor frequency

Radio-frequency ablation (RFA) is an effective minimally invasive treatment for tumors. One primary source of difficulty is monitoring and controlling the ablation region. Currently, RFA is performed at 460 kHz, for which magnetic resonance imaging (MRI) could play a role given its capability for temperature monitoring and tumor visualization. If instead the ablation were to be performed at the MRI Larmor frequency, then the MR capability for B(1) field mapping could be used to directly visualize the radio-frequency (RF) fields created by the ablation currents. Visualizing the RF fields may enable better control of the ablation currents, enabling better control of lesion shape and size and improving repeatability. We demonstrate the feasibility of performing RFAs at 64 MHz and show preliminary results from imaging the RF fields from the ablation. The post-ablation RF fields show an increase in current density in the ablated region, consistent with an increase in conductivity of the ablated tissue.

Considerations for Thermal Injury Analysis for RF Ablation Devices

Background:

The estimation of lesion size is an integral part of treatment planning for the clinical applications of radiofrequency ablation. However, to date, studies have not directly evaluated the impact of different computational estimation techniques for predicting lesion size. In this study, we focus on three common methods used for predicting tissue injury: (1) iso-temperature contours, (2) Cumulative equivalent minutes, (3) Arrhenius based thermal injury.

Methods:

We created a geometric model of a multi-tyne ablation electrode and simulated thermal and tissue injury profiles that result from three calculation methods after 15 minutes exposure to a constant RF voltage source. A hybrid finite element technique was used to calculate temperature and tissue injury. Time-temperature curves were used in the assessment of iso-temperature thresholds and the method of cumulative equivalent minutes. An Arrhenius-based formulation was used to calculate sequential and recursive thermal injury to tissues.

Results:

The data demonstrate that while iso-temperature and cumulative equivalent minute contours are similar in shape, these two methodologies grossly over-estimate the amount of tissue injury when compared to recursive thermal injury calculations, which have previously been shown to correlate closely with in vitro pathologic lesion volume measurement. In addition, Arrhenius calculations that do not use a recursive algorithm result in a significant underestimation of lesion volume. The data also demonstrate that lesion width and depth are inadequate means of characterizing treatment volume for multi-tine ablation devices.

Conclusions:

Recursive thermal injury remains the most physiologically relevant means of computationally estimating lesion size for hepatic tumor applications. Iso-thermal and cumulative equivalent minute approaches may produce significant errors in the estimation of lesion size.

Considerations for thermal injury analysis for RF ablation devices

BACKGROUND

The estimation of lesion size is an integral part of treatment planning for the clinical applications of radiofrequency ablation. However, to date, studies have not directly evaluated the impact of different computational estimation techniques for predicting lesion size. In this study, we focus on three common methods used for predicting tissue injury: (1) iso-temperature contours, (2) Cumulative equivalent minutes, (3) Arrhenius based thermal injury.

METHODS

We created a geometric model of a multi-tyne ablation electrode and simulated thermal and tissue injury profiles that result from three calculation methods after 15 minutes exposure to a constant RF voltage source. A hybrid finite element technique was used to calculate temperature and tissue injury. Time-temperature curves were used in the assessment of iso-temperature thresholds and the method of cumulative equivalent minutes. An Arrhenius-based formulation was used to calculate sequential and recursive thermal injury to tissues.

RESULTS

The data demonstrate that while iso-temperature and cumulative equivalent minute contours are similar in shape, these two methodologies grossly over-estimate the amount of tissue injury when compared to recursive thermal injury calculations, which have previously been shown to correlate closely with in vitro pathologic lesion volume measurement. In addition, Arrhenius calculations that do not use a recursive algorithm result in a significant underestimation of lesion volume. The data also demonstrate that lesion width and depth are inadequate means of characterizing treatment volume for multi-tine ablation devices.

CONCLUSIONS

Recursive thermal injury remains the most physiologically relevant means of computationally estimating lesion size for hepatic tumor applications. Iso-thermal and cumulative equivalent minute approaches may produce significant errors in the estimation of lesion size.

Esophageal temperature during radiofrequency-catheter ablation of left atrium: a three-dimensional computer modeling study

INTRODUCTION

There is current interest in finding a way to minimize thermal injury in the esophagus during radiofrequency-catheter ablation of the left atrium. Despite the fact that the esophageal temperature is now being monitored during ablation, the influence of different anatomic and technical factors on the temperature rise remains unknown.

METHODS AND RESULTS

We implemented a three-dimensional computational model that included atrial tissue, epicardial fat, esophagus, aorta, and lung, all linked by connective tissue. The finite-element method was used to calculate the esophageal temperature distribution during a procedure of constant-temperature ablation with an 8-mm electrode, under different tissue conditions. Results showed that the distance between electrode and esophagus was the most important anatomic factor in predicting the esophageal temperature rise, the composition of the different tissues being of lesser importance. The measurement of the esophageal temperature in different sites of the lumen offered differences up to 3.7 degrees C, especially for a short electrode-esophagus distance (5 mm). The difference in the convective cooling by circulating blood around electrode and endocardium did not show a significant influence on the esophageal temperature rise.

CONCLUSION

Computer results suggest that (1) the electrode-esophagus distance is the most important anatomic factor; (2) the incorrect positioning of an esophageal temperature probe could give a low reading for the maximum temperature reached in the esophagus; and (3) the different cooling effect of the circulating blood flow at different atrial sites has little impact on the esophageal temperature rise.

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.

What affects esophageal injury during radiofrequency ablation of the left atrium? An engineering study based on finite-element analysis

Recent studies on intraoperative radiofrequency ablation of atrial fibrillation have reported some cases of injury to the esophagus. The aim of this study was to perform computer simulations using a theoretical model in order to investigate the effect of different factors on the temperature distributions in the esophagus during ablation. A three-dimensional model was built to include an active electrode, atrial tissue, epicardial fat layer and a fragment of esophagus, aorta and lung, all linked by connective tissue. The finite-element method was used to calculate the temperature distribution during a procedure of constant-temperature ablation. The lesion geometry was assessed using a 50 degrees C isotherm. Our results show that the electrical power directly applied to the esophagus is insignificant and hence the esophageal injury is exclusively due to thermal conduction from the atrium. The esophageal lesion is mainly influenced by the thickness of connective tissue. Both the programmed target temperature of the electrode and the duration of the ablation also have a significant effect on the lesion in the esophagus. In contrast, the epicardial fat layer (0.9 mm thickness) did not show a significant influence. In conclusion, this theoretical model allows us to study the effect of different factors on the thermal injury in the esophagus during intraoperative radiofrequency ablation of atrial tissue.

Finite element modelling and simulations in cardiovascular mechanics and cardiology: A bibliography 1993–2004

The paper gives a bibliographical review of the finite element modelling and simulations in cardiovascular mechanics and cardiology from the theoretical as well as practical points of views. The bibliography lists references to papers, conference proceedings and theses/dissertations that were published between 1993 and 2004. At the end of this paper, more than 890 references are given dealing with subjects as: Cardiovascular soft tissue modelling; material properties; mechanisms of cardiovascular components; blood flow; artificial components; cardiac diseases examination; surgery; and other topics.

Effect of electrode locations and respiration in the characterization of myocardial tissue using a transcatheter impedance method

Our objective is to evaluate whether it is possible to characterize the passive electrical properties of myocardial tissue in contact with the electrocatheters used in arrhythmia diagnosis or radio frequency ablation techniques. To characterize the tissue, we propose the use of electrical impedance spectroscopy to measure the impedance between the catheter tip and an external electrode, assuming a three-electrode method. We constructed a 3D finite-element model of the thorax to estimate the impedance as measured in different situations. We defined an area on the anterior wall of the left ventricle in which we simulated three tissue states: healthy, acute ischaemic and scar. We studied the effect of the following parameters on the measured impedance spectrum: the position of the external electrode, the position and orientation of the catheter tip and the overall effect of the subject's respiration. Results show that the highest frequency phase (around 300 kHz) yields the best differentiation of tissue states and that it is less sensitive to respiration than the impedance magnitude. The phase is also less influenced by the catheter tip position (either touching the wall or floating) and the orientation of the catheter inside the left ventricle. The best position for the external electrode is on the chest; this position is less affected by breathing and is more sensitive to tissue changes. One can still distinguish between tissue states if the external electrode is placed on the back, but the effect of respiration is higher.

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.

Epicardial mapping and radiofrequency catheter ablation of ischemic ventricular tachycardia using a three-dimensional nonfluoroscopic mapping system

Endocardial radiofrequency catheter ablation of ischemic left ventricular tachycardia has been of variable success due to multiple factors. Two such factors include the location of the reentrant circuit in the deep myocardium or on the epicardial surface and the inherent limitations of fluoroscopy as a guide for target localization. We report a patient in whom successful epicardial mapping and radiofrequency catheter ablation of an ischemic left ventricular tachycardia was performed using pericardial access and the CARTO electroanatomic mapping system.

Temperature-controlled and constant-power radio-frequency ablation: what affects lesion growth?

Radio-frequency (RF) catheter ablation is the primary interventional therapy for the treatment of many cardiac tachyarrhythmias. Three-dimensional finite element analysis of constant-power (CPRFA) and temperature-controlled RF ablation (TCRFA) of the endocardium is performed. The objectives are to study: 1) the lesion growth with time and 2) the effect of ground electrode location on lesion dimensions and ablation efficiency. The results indicate that: a) for TCRFA: i) lesion growth was fastest during the first 20 s, subsequently the lesion growth slowed reaching a steady state after 100 s, ii) positioning the ground electrode directly opposite the catheter tip (optimal) produced a larger lesion, and iii) a constant tip temperature maintained a constant maximum tissue temperature; b) for CPRFA: i) the lesion growth was fastest during the first 20 s and then the lesion growth slowed; however, the lesion size did not reach steady state even after 600 s suggesting that longer durations of energy delivery may result in wider and deeper lesions, ii) the temperature-dependent electrical conductivity of the tissue is responsible for this continuous lesion growth, and iii) an optimal ground electrode location resulted in a slightly larger lesion and higher ablation efficiency.