Should fluid dynamics be included in computer models of RF cardiac ablation by irrigated-tip electrodes?
- Ana González-Suárez^{1}Email authorView ORCID ID profile,
- Juan J. Pérez^{2} and
- Enrique Berjano^{2}
Received: 7 November 2017
Accepted: 16 April 2018
Published: 20 April 2018
Abstract
Background
Although accurate modeling of the thermal performance of irrigated-tip electrodes in radiofrequency cardiac ablation requires the solution of a triple coupled problem involving simultaneous electrical conduction, heat transfer, and fluid dynamics, in certain cases it is difficult to combine the software with the expertise necessary to solve these coupled problems, so that reduced models have to be considered. We here focus on a reduced model which avoids the fluid dynamics problem by setting a constant temperature at the electrode tip. Our aim was to compare the reduced and full models in terms of predicting lesion dimensions and the temperatures reached in tissue and blood.
Results
The results showed that the reduced model overestimates the lesion surface width by up to 5 mm (i.e. 70%) for any electrode insertion depth and blood flow rate. Likewise, it drastically overestimates the maximum blood temperature by more than 15 °C in all cases. However, the reduced model is able to predict lesion depth reasonably well (within 0.1 mm of the full model), and also the maximum tissue temperature (difference always less than 3 °C). These results were valid throughout the entire ablation time (60 s) and regardless of blood flow rate and electrode insertion depth (ranging from 0.5 to 1.5 mm).
Conclusions
The findings suggest that the reduced model is not able to predict either the lesion surface width or the maximum temperature reached in the blood, and so would not be suitable for the study of issues related to blood temperature, such as the incidence of thrombus formation during ablation. However, it could be used to study issues related to maximum tissue temperature, such as the steam pop phenomenon.
Keywords
Background
Radiofrequency (RF) catheter ablation (RFCA) is a common and safe procedure used to eliminate cardiac arrhythmias in which RF current is delivered by a metal electrode embedded in the tip of a percutaneous catheter. The electrode design must be such that it achieves effective thermal necrosis of the target tissue (temperatures > 50 °C), while keeping its temperature below 80 °C to prevent the formation of thrombi in the blood [1]. Irrigated-tip electrodes have been proposed to meet both requirements [2]. These electrodes, which are in fact currently those most often used in clinical practice, allow continuous saline flushing through small holes distributed around the electrode tip to cool the blood-tissue interface [2].
Computer modeling is an analysis technique broadly used in studies on RFCA [3–12]. In order to obtain accurate results, the model has to be as realistic as possible, which implies ever more complicated mathematical formulations, especially in the case of modeling irrigated-tip electrodes for RFCA. In this case an accurate model should be based on a triple coupled problem involving simultaneous electrical conduction, heat transfer, and fluid dynamics [4], which is necessary to model the thermal effect of the circulating blood around the electrode placed on the endocardium and its interaction with the saline infused through the holes in its tip. Furthermore, the fluid dynamics problem forces the model to be three-dimensional, with the consequent additional computational cost. However, in certain cases it is difficult to have access to the adequate software and/or have the expertise necessary to be able to couple these three problems. Therefore, reduced models should be considered.
In this respect, a reduced model that dispenses with fluid dynamics is sometimes employed as an alternative [5–8]. In this case, the thermal cooling due to electrode irrigation is modeled by keeping a fixed temperature similar to that found in clinical practice in a zone of the electrode-tip. Although it has been suggested that this model could reproduce lesion depth reasonably well [8], the reduced and the full model have never been directly compared in terms of lesion dimensions and maximum temperatures reached in the blood and tissue. Our goal was thus to compare both models in terms of predicting thermal lesion dimensions and temperature distributions in blood and tissue. Since the full model had already been validated experimentally [4, 9], this study really sought to evaluate the worth of the reduced model by comparing its results with those obtained from the full model. In terms of clinical application, it is especially important that both models should accurately predict the lesion surface width and the maximum blood temperature achieved around the electrode tip, since it is known that these parameters are related to thrombus formation [1, 13, 14]. It is also important that they be able to predict the maximum temperature in the tissue, since values of around 100 °C are associated with the formation of steam pops [15, 16].
Methods
Description of the model geometry
Governing equations
At the frequencies used in RF heating (≈ 500 kHz) and over the distance of interest, the biological medium can be considered almost totally resistive, and a quasi-static approach can therefore be used to solve the electrical problem [24]. The distributed heat source q is then given by q = σ|E|^{ 2 }, where |E| is the magnitude of the vector electric field (V/m) and σ the electrical conductivity (S m^{−1}). E = − ∇Ф is calculated from the gradient of the voltage Φ (V), which, in absence of internal electric sources, satisfies ∇·(σ∇Ф) = 0.
Model properties and boundary conditions
Thermal and electrical characteristics of the elements employed in the models [3]: σ, electrical conductivity; k, thermal conductivity; ρ, density; and c, specific heat
Element/material | σ (S/m) | k (W/m K) | ρ (kg/m^{3}) | c (J/kg K) |
---|---|---|---|---|
Electrode/Pt–Ir | 4.6 × 10^{6} | 71 | 21,500 | 132 |
Catheter/Polyurethane | 10^{−5} | 0.026 | 70 | 1045 |
Cardiac Chamber/Blood | 0.667 | 0.541 | 1000 | 4180 |
Myocardium/Cardiac tissue | ||||
Liquid phase | σ _{ o } ^{a} | k _{ o } ^{a} | 1060 | 3111 |
Gas phase | ||||
370.44 | 2155.92 |
Figure 2b, c show the thermal and velocity boundary conditions. The effect of blood circulating inside the cardiac chamber and the saline irrigation were differently modeled for the reduced and the full model (see following subsection). In both cases, a null thermal flux was used on the symmetry plane and a constant temperature of 37 °C was fixed on the outer surfaces of the model.
Modeling the blood motion and saline interaction
Reduced model
The effect of blood circulating inside the cardiac chamber was modeled by thermal convection coefficients at the electrode–blood (h_{ E }) and the tissue–blood (h_{ T }) interfaces (see Fig. 2b), considering electrical conductivity of blood independent of temperature (as in Method 2 described by [3]). Each coefficient was calculated under conditions of high and low blood velocity flow, the value of blood velocity being 8.5 and 3 cm/s for the high and low flow rates, respectively [12]. From these velocity values we obtained values of h_{ E } = 3346 W/m^{2} K and h_{ T } = 610 W/m^{2} K for high blood flow, and h_{ E } = 2059 W/m^{2} K and h_{ T } = 265 W/m^{2} K for low blood flow [3].
The effect of saline irrigation through the holes at the electrode tip was modeled by fixing a constant temperature of 40 °C only in the cylindrical zone of the electrode tip (see Fig. 2b), leaving the semispherical tip inserted into the tissue free, as in previous computational studies [5–8]. This temperature value was chosen due to its similarity with that obtained with multi-hole electrodes in clinical practice [30].
Full model
Figure 2c shows the velocity boundary conditions applied to model the interaction of blood motion and saline flow. A no slip condition (non permeable surface, i.e. the fluid at the wall was not moving) was applied on the upper surfaces of the fluid volume and at the tissue-blood and electrode-blood interfaces. An inlet velocity boundary condition was applied to the left surface of the fluid volume to simulate the two blood velocities (in x-direction) of 8.5 and 3 cm/s for high and low flow rate, respectively. An outlet boundary condition of zero pressure was fixed on the right surface of the fluid volume. The saline irrigation flow was taken into account by an inlet velocity condition in the blood region, applied to a specific part of the electrode-blood interface surface where the holes were located, except in the part of the electrode tip inserted in the tissue [4]. The saline velocity condition was calculated as the ratio between the saline irrigation flow rate and the electrode area through which the saline flows (see violet zone in Fig. 1). We considered a saline irrigation flow rate of 8 mL/min, since this is the clinical value recommended by the manufacturer for a multi-hole electrode using power levels below 30 W [31]. The electrode area in which the saline velocity was applied changed according to the depth of electrode insertion into the tissue (D_{E}): 0.0105, 0.0123 and 0.0147 m/s for values of D_{E} of 0.5, 1 and 1.5 mm, respectively.
Output variables
As in previous studies, the thermal lesion shape was assessed by the 50 °C isotherm [3–7, 11], which is usually considered to reasonably represent the contour of irreversible myocardial injury in hyperthermic ablation. The thermal lesion shape was characterized using the following values (see Fig. 1) [2, 4, 31, 32]: maximum depth (D), maximum width (MW), depth at the maximum width (DW), and surface width (SW). We compared the thermal lesion dimensions and the maximum temperature values reached in the tissue and blood computed by the reduced model with those obtained by the full model. We also compared the lesion volumes at the end of ablation (60 s) computed using the formula described by [32]. We used the full model as a “ground truth” for comparison with the reduced model, since the full model had previously been validated against experimental data [4, 9]. We considered that the differences in lesion dimensions between both models were insignificant for values lower than 1 mm, since this value is approximately that of the deviation (± 0.5 mm) observed in experimental RFCA studies [3]. Likewise, the differences in maximum temperature reached in tissue and blood were considered to be insignificant for values lower than 4 °C, since this value is approximately that of the observed deviation (± 2 °C) [3].
Results
After the convergence tests conducted with the computational model we obtained the following optimum values: dimensions X = 80 mm and Y = 40 mm (Z = Y), grid size of 0.2 mm in the finest zone (electrode-tissue interface), and step time of 0.05 s. The model had nearly 50,000 tetrahedral elements.
Lesion volume (mm^{3}) computed at 60 s for both models and different conditions of blood flow and insertion depths
Model | Blood flow | Insertion depth (mm) | ||
---|---|---|---|---|
0.5 | 1.0 | 1.5 | ||
Reduced | Low | 390.2 | 516.2 | 593.1 |
High | 295.3 | 434.6 | 544.4 | |
Full | Low | 302.3 | 408.7 | 550.7 |
High | 290.5 | 400.7 | 526.8 |
Discussion
This computer modeling study assessed the ability of a reduced model that does not consider fluid dynamics to compute the temperature distributions in tissue and blood during RFCA by irrigated electrodes in a comparison with the full model, which had previously been validated by experimental data [4, 9]. The reduced model would be promising if it could be used instead of the full model in certain circumstances, as it greatly simplifies certain issues such as geometry (often allowing a two-dimensional model instead of a three-dimensional model), mathematical formulation (reducing the amount of governing equations and boundary conditions, since only the electrical-thermal problem is solved without including fluid dynamics equations), considerably reducing the computational cost. Indeed, up to six times less computational time was required to solve the reduce model than for the full one (5.29 min vs. 31.73 min). Note that although the results from the reduce model were obtained with a three-dimensional model, they would have been the same with a two-dimensional model, further reducing the computational cost.
However, our results show that the reduced model is not suitable for studying temperature distributions in the blood; as can be seen in Fig. 5, the value of the maximum blood temperature in the proximity of the electrode-tissue interface was over-estimated, reaching a value of ~ 100 °C in all the cases, while the maximum blood temperature obtained with the full model always remained below 80 °C, as in a previous experimental work [33] (see Fig. 5 of that work for the cases using an ambient temperature for saline irrigation, as in our case). Our findings also showed that the reduced model cannot adequately predict either surface lesion width or lesion volume, since the former was wider than that achieved with the full model (see Fig. 3).
Although it was possible to adjust the surface lesion width obtained with the reduced model by increasing the thermal convection coefficients applied at the electrode-blood and tissue-blood interfaces to simulate the effect of circulating blood, it was impossible to obtain a realistic blood temperature distribution in the vicinity of the electrode-tissue interface (the maximum blood temperature still reached approximately 100 °C, very different from that of the full method, as can be seen in Fig. 6).
On the other hand, our results showed that the reduced model is able to accurately predict lesion depth at all times during ablation (up to 60 s), and also the maximum temperature reached in the tissue. In practical terms, a modeling study focusing on issues related with overheating occurring in the tissue (e.g. steam pops which are associated with intra-tissue temperatures of around 100 °C) could benefit from the results obtained with the reduced model, since they show the reliability of the full model as long as there is no blood circulating around the electrode-tip.
This study characterized the differences between both models under different electrode insertion depths and blood flow rates. Had other conditions (such as variations in tissue properties, the arrangement of the infusion holes on the electrode surface, and contact angle between electrode and tissue surface) also been included we think that the conclusions reached would still have been valid. In future work, computer models offering a realistic distribution of cardiac flow [34–39] could be coupled to the full model in order to increase their accuracy.
Conclusions
The findings confirm that a reduced model that does not include the fluid dynamics is not suitable for predicting either temperature distributions in the blood or surface lesion width, which rules it out as a means of studying the factors involved in thrombi formation. The full model, which solves electrical conduction, heat transfer, and fluid dynamics simultaneously, should therefore be generally employed for simulating the performance of an RF irrigated electrode surrounded by circulating blood. The results indicate that both models give satisfactory results when predicting lesion depth and maximum tissue temperature, which indicates that the reduced model could be employed to study issues related to tissue temperature, such as the incidence of steam pops during ablation.
Declarations
Authors’ contributions
AGS, JJP, and EB conceived and designed the experiments. AGS and JJP performed the computer simulations. AGS, JJP, and EB analyzed the data. AGS and EB wrote the paper. All authors read and approved the final manuscript.
Acknowledgements
This work was supported by the Spanish Government under the “Plan Estatal de Investigación, Desarrollo e Innovación Orientada a los Retos de la Sociedad” Grant “TEC2014-52383-C3 (TEC2014-52383-C3-1-R)”. A. González-Suárez has a Postdoctoral Grant “Juan de la Cierva-formación” (FJCI-2015-27202) supported by the Spanish Ministerio de Economía, Industria y Competitividad. We also would like to appreciate the interesting comments by Dr. Oscar Camara about the limitations of the computational modeling.
Competing interests
The authors declare that they have no competing interests.
Ethics approval and consent to participate
Not applicable.
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References
- Matsudaira K, Nakagawa H, Wittkampf FH, Yamanashi WS, Imai S, Pitha JV, et al. High incidence of thrombus formation without impedance rise during radiofrequency ablation using electrode temperature control. Pacing Clin Electrophysiol. 2003;26(5):1227–37.View ArticleGoogle Scholar
- Yokoyama K, Nakagawa H, Wittkampf FH, Pitha JV, Lazzara R, Jackman WM. Comparison of electrode cooling between internal and open irrigation in radiofrequency ablation lesion depth and incidence of thrombus and steam pop. Circulation. 2006;113(1):11–9.View ArticleGoogle Scholar
- González-Suárez A, Berjano E. Comparative analysis of different methods of modeling the thermal effect of circulating blood flow during RF cardiac ablation. IEEE Trans Biomed Eng. 2016;63(2):250–9.View ArticleGoogle Scholar
- González-Suárez A, Berjano E, Guerra JM, Gerardo-Giorda L. Computational modeling of open-irrigated electrodes for radiofrequency cardiac ablation including blood motion-saline flow interaction. PLoS ONE. 2016;11(3):e0150356.View ArticleGoogle Scholar
- Pérez JJ, D’Avila A, Aryana A, Berjano E. Electrical and thermal effects of esophageal temperature probes on radiofrequency catheter ablation of atrial fibrillation: results from a computational modeling study. J Cardiovasc Electrophysiol. 2015;26(5):556–64.View ArticleGoogle Scholar
- Pérez JJ, D’Avila A, Aryana A, Trujillo M, Berjano E. Can fat deposition after myocardial infarction alter the performance of RF catheter ablation of scar-related ventricular tachycardia?: results from a computer modeling study. J Cardiovasc Electrophysiol. 2016;27(8):947–52.View ArticleGoogle Scholar
- Pérez JJ, González-Suárez A, Berjano E. Numerical analysis of thermal impact of intramyocardial capillary blood flow during radiofrequency cardiac ablation. Int J Hyperth. 2018;34(3):243–49.View ArticleGoogle Scholar
- Demazumder D, Mirotznik MS, Schwartzman D. Biophysics of radiofrequency ablation using an irrigated electrode. J Interv Card Electrophysiol. 2001;5(4):377–89.View ArticleGoogle Scholar
- González-Suárez A, Berjano E, Guerra JM, Gerardo-Giorda L. Computational model for prediction of the occurrence of steam pops during irrigated radiofrequency catheter ablation. Comput Cardiol. 2016;43:1117–20.Google Scholar
- Cao H, Speidel MA, Tsai JZ, Van Lysel MS, Vorperian VR, Webster JG. FEM analysis of predicting electrode-myocardium contact from RF cardiac catheter ablation system impedance. IEEE Trans Biomed Eng. 2002;49(6):520–6.View ArticleGoogle Scholar
- Schutt D, Berjano EJ, Haemmerich D. Effect of electrode thermal conductivity in cardiac radiofrequency catheter ablation : a computational modeling study. Int J Hyperth. 2009;25(2):99–107.View ArticleGoogle Scholar
- Jain MK, Wolf PD. A three-dimensional finite element model of radiofrequency ablation with blood flow and its experimental validation. Ann Biomed Eng. 2000;28(9):1075–84.View ArticleGoogle Scholar
- Demolin JM, Eick OJ, Münch K, Koullick E, Nakagawa H, Wittkampf FH. Soft thrombus formation in radiofrequency catheter ablation. Pacing Clin Electrophysiol. 2002;25(8):1219–22.View ArticleGoogle Scholar
- Weiss C, Antz M, Eick O, Eshagzaiy K, Meinertz T, Willems S. Radiofrequency catheter ablation using cooled electrodes: impact of irrigation flow rate and catheter contact pressure on lesion dimensions. Pacing Clin Electrophysiol. 2002;25(4 Pt 1):463–9.View ArticleGoogle Scholar
- Wood MA, Shaffer KM, Ellenbogen AL, Ownby ED. Microbubbles during radiofrequency catheter ablation: composition and formation. Heart Rhythm. 2005;2(4):397–403.View ArticleGoogle Scholar
- Thompson N, Lustgarten D, Mason B, Mueller E, Calame J, Bell S, Spector P. The relationship between surface temperature, tissue temperature, microbubble formation, and steam pops. Pacing Clin Electrophysiol. 2009;32(7):833–41.View ArticleGoogle Scholar
- d’Avila A, Houghtaling C, Gutierrez P, Vragovic O, Ruskin JN, Josephson ME, Reddy VY. Catheter ablation of ventricular epicardial tissue: a comparison of standard and cooled-tip radiofrequency energy. Circulation. 2004;109:2363–9.View ArticleGoogle Scholar
- Dukkipati SR, d’Avila A, Soejima K, Bala R, Inada K, Singh S, et al. Long-term outcomes of combined epicardial and endocardial ablation of monomorphic ventricular tachycardia related to hypertrophic cardiomyopathy. Circ Arrhythm Electrophysiol. 2011;4:185–94.View ArticleGoogle Scholar
- Watanabe I, Nuo M, Okumura Y, Ohkubo K, Ashino S, Kofune M, et al. Temperature-controlled cooled-tip radiofrequency ablation in left ventricular myocardium. Int Heart J. 2010;51:193–8.View ArticleGoogle Scholar
- Yokoyama K, Nakagawa H, Wittkampf FH, Pitha JV, Lazzara R, Jackman WM. Comparison of electrode cooling between internal and open irrigation in radiofrequency ablation lesion depth and incidence of thrombus and steam pop. Circulation. 2006;113:11–9.View ArticleGoogle Scholar
- Bin Choy Y, Cao H, Tungjitkusolmun S, Tsai JZ, Haemmerich D, Vorperian VR, Webster JG. Mechanical compliance of the endocardium. J Biomech. 2002;35(12):1671–6.View ArticleGoogle Scholar
- Abraham JP, Sparrow EM. A thermal-ablation bioheat model including liquid-to-vapor phase change, pressure- and necrosis-dependent perfusion, and moisture-dependent properties. Int J Heat Mass Transf. 2007;50(13–14):2537–44.View ArticleMATHGoogle Scholar
- Labonté S. Numerical model for radio-frequency ablation of the endocardium and its experimental validation. IEEE Trans Biomed Eng. 1994;41(2):108–15.View ArticleGoogle Scholar
- Doss JD. Calculation of electric fields in conductive media. Med Phys. 1982;9(4):566–73.View ArticleGoogle Scholar
- Haemmerich D, Chachati L, Wright AS, Mahvi DM, Lee FT, Webster JG. Hepatic radiofrequency ablation with internally cooled probes: effect of coolant temperature on lesion size. IEEE Trans Biomed Eng. 2003;50(4):493–9.View ArticleGoogle Scholar
- Berjano EJ. Theoretical modeling for radiofrequency ablation: state-of-the-art and challenges for the future. Biomed Eng Online. 2006;5:24.View ArticleGoogle Scholar
- Berjano E, d’Avila A. Lumped element electrical model based on three resistors for electrical impedance in radiofrequency cardiac ablation: estimations from analytical calculations and clinical data. Open Biomed Eng J. 2013;12(7):62–70.View ArticleGoogle Scholar
- Haemmerich D, Webster JG. Automatic control of finite element models for temperature-controlled radiofrequency ablation. Biomed Eng Online. 2005;14(4):42.View ArticleGoogle Scholar
- Jain MK, Wolf PD. Temperature-controlled and constant-power radio-frequency ablation: what affects lesion growth? IEEE Trans Biomed Eng. 1999;46(12):1405–12.View ArticleGoogle Scholar
- Winterfield JR, Jensen J, Gilbert T, Marchlinski F, Natale A, Packer D, Reddy V, Mahapatra S, Wilber DJ. Lesion size and safety comparison between the novel flex tip on the flexAbility ablation catheter and the solid tips on the thermocool and thermocool sf ablation catheters. J Cardiovasc Electrophysiol. 2016;27(1):102–9.View ArticleGoogle Scholar
- Moreno J, Quintanilla JG, Molina-Morúa R, García-Torrent MJ, Angulo-Hernández MJ, Curiel-Llamazares C, Ramiro-Bargueño J, González P, Caamaño AJ, Pérez-Castellano N, Rojo-Álvarez JL, Macaya C, Pérez-Villacastín J. Morphological and thermodynamic comparison of the lesions created by 4 open-irrigated catheters in 2 experimental models. J Cardiovasc Electrophysiol. 2014;25(12):1391–9.Google Scholar
- Guerra JM, Jorge E, Raga S, Gálvez-Montón C, Alonso-Martín C, Rodríguez-Font E, Cinca J, Viñolas X. Effects of open-irrigated radiofrequency ablation catheter design on lesion formation and complications: in vitro comparison of 6 different devices. J Cardiovasc Electrophysiol. 2013;24(10):1157–62.Google Scholar
- Squara F, Maeda S, Aldhoon B, Marginiere J, Santangeli P, Chik WW, Michele J, Zado E, Marchlinski FE. In vitro evaluation of ice-cold saline irrigation during catheter radiofrequency ablation. J Cardiovasc Electrophysiol. 2014;25(10):1125–32.View ArticleGoogle Scholar
- Wong KKL, Kelso RM, Worthley SG, Sanders P, Mazumdar J, Abbott D. Medical imaging and processing methods for cardiac flow reconstruction. J Mech Med Biol. 2009;9(01):1–20.View ArticleGoogle Scholar
- Wong KKL, Thavornpattanapong P, Cheung SCP, Tu JY. Biomechanical investigation of pulsatile flow in a three-dimensional atherosclerotic carotid bifurcation model. J Mech Med Biol. 2013;13(01):1350001.View ArticleGoogle Scholar
- Liu G, Wu J, Huang W, Wu W, Zhang H, Wong KKL, Ghista DN. Numerical simulation of flow in curved coronary arteries with progressive amounts of stenosis using fluid-structure interaction modelling. J Med Imaging Health Inform. 2014;4(4):605–11.View ArticleGoogle Scholar
- Wong KKL, Kelso RM, Worthley SG, Sanders P, Mazumdar J, Abbott D. Cardiac flow analysis applied to phase contrast magnetic resonance imaging of the heart. Ann Biomed Eng. 2009;37(8):1495–515.View ArticleGoogle Scholar
- Wong KKL, Tu J, Kelso RM, Worthley SG, Sanders P, Mazumdar J, Abbott D. Cardiac flow component analysis. Med Eng Phys. 2010;32(2):174–88.View ArticleGoogle Scholar
- Wong KK, Wang D, Ko JK, Mazumdar J, Le TT, Ghista D. Computational medical imaging and hemodynamics framework for functional analysis and assessment of cardiovascular structures. Biomed Eng Online. 2017;16(1):35.View ArticleGoogle Scholar