IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 62, NO. 2, FEBRUARY 2015
673
Fibrillation Number Based on Wavelength and Critical Mass in Patients Who Underwent Radiofrequency Catheter Ablation for Atrial Fibrillation Minki Hwang, Junbeum Park, Young-Seon Lee, Jae Hyung Park, Sung Hwan Choi, Eun Bo Shim, and Hui-Nam Pak∗
Abstract—The heart characteristic length, the inverse of conduction velocity (CV), and the inverse of the refractory period are known to determine vulnerability to cardiac fibrillation (fibrillation number, FibN) in in silico or ex vivo models. The purpose of this study was to validate the accuracy of FibN through in silico atrial modeling and to evaluate its clinical application in patients with atrial fibrillation (AF) who had undergone radiofrequency catheter ablation. We compared the maintenance duration of AF at various FibNA F values using in silico bidomain atrial modeling. Among 60 patients (72% male, 54 ± 13 years old, 82% with paroxysmal AF) who underwent circumferential pulmonary vein isolation (CPVI) for AF rhythm control, we examined the relationship between FibNA F and postprocedural AF inducibility or induction pacing cycle length (iPCL). Clinical FibNA F was calculated using left atrium (LA) dimension (echocardiogram), the inverse of CV, and the inverse of the atrial effective refractory periods measured at proximal and distal coronary sinus. In silico simulation found a positive correlation between AF maintenance duration and FibNA F (R = 0.90, p < 0.001). After clinical CPVI, FibNA F (0.296 ± 0.038 versus 0.192 ± 0.028, p < 0.001) was significantly higher in patients with postprocedural AF inducibility (n = 41) than in those without (n = 19). Among 41 patients with postprocedural AF inducibility, FibNA F (P = 0.935, p < 0.001) had excellent correlations with induction pacing cycle length. FibNA F , based on LA mass and wavelength, correlates well with AF maintenance in computational modeling and clinical AF inducibility after CPVI. Index Terms—Arrhythmogenecity, Atrial fibrillation (AF), critical mass, parameter, wavelength.
Manuscript received August 13, 2014; revised October 8, 2014; accepted October 12, 2014. Date of publication October 17, 2014; date of current version January 16, 2015. This work was supported by the Ministry of Trade, Industry, and Energy (MOTIE), Korea Institute for Advancement of Technology (KIAT), and Gangwon Institute for Regional Program Evaluation (GWIRPE) through the Leading Industry Development for Economic Region (A002200868), a grant (A085136) from the Korea Health 21 R&D Project, Ministry of Health and Welfare, and a grant (2012027176) from the National Research Foundation of Korea (NRF) funded by the Ministry of Science, ICT, and Future Planning (MSIP). Asterisk indicates corresponding author. M. Hwang, J. Park, Y.-S. Lee, and J. H. Park are with the Yonsei University Health System, Seoul 120-752, Korea (e-mail: [email protected]; [email protected]; [email protected]; [email protected]). S. H. Choi is with the CU Medical Systems Incorporation, Wonju 220-801, Korea (e-mail: [email protected]). E. B. Shim is with Kangwon National University, Chuncheon 200-701, Korea (e-mail: [email protected]). ∗ H.-N. Pak is with Yonsei University Health System, Seoul 120-752, Korea (e-mail: [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TBME.2014.2363669
I. INTRODUCTION TRIAL fibrillation (AF), one of the most common arrhythmia in clinical practice, is related to increasingly high rates of disability and mortality [1]. It is predicted that the number of individuals with AF would more than double by the year 2050 [2]. The prevalence of AF increases with age up to 9% among those 80 years or older [3]. As radiofrequency catheter ablation (RFCA) for AF has become a common practice for AF rhythm control, the pathophysiology of this multifactorial disease is gradually being uncovered through clinical studies. However, the mechanisms of cardiac fibrillation are still poorly understood [4]. While the focal source hypothesis [5] states that a relatively stable periodic source (“mother rotor”) with fibrillatory conduction maintains fibrillation, the multiple wavelet hypothesis [6] states that a continuous wavebreak and localized reentry may sustain fibrillation after the exclusion of arrhythmogenic triggers [7]–[9]. Probability of reentry is expressed by wavelength, proportional to the effective refractory period (ERP) and conduction velocity (CV). The cardiac chamber mass also has been found to play an important role in the maintenance of continuous wavebreak, which led to the critical mass hypothesis [10], [11]. Moe et al. [12] originally reported that the characteristic length of substrate, the inverse of CV, and the inverse of the refractory period determine vulnerability to fibrillation (fibrillation number, FibN) based on in silico study of AF. These results are similar in concept to the Reynolds number, which is related to turbulence in fluid flow. In this study, we tested FibN to validate its predictive value for AF maintenance in silico, as well as its clinical usefulness among patients with AF. We hypothesized that FibNAF reflects the vulnerability to AF maintenance in silico, and postprocedural inducibility of AF after clinical catheter ablation.
A
II. METHODS A. Two-Dimensional Fibrillation Modeling To test the effect of FibN on wave propagation in cardiac tissue, we simulated the action potential propagation in atrial tissue using an in silico model. Time-dependent voltage distribution on a two-dimensional (2-D) computational domain was obtained by solving the bidomain reaction–diffusion equation as described by Ashihara et al. [13]. The electrophysiological model of human atrial action potential developed by
0018-9294 © 2014 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications standards/publications/rights/index.html for more information.
674
IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 62, NO. 2, FEBRUARY 2015
TABLE I PATIENT CHARACTERISTICS
Male (%) Age (years) Paroxysmal AF (%) BSA (m2 ) BMI (kg/m2 ) CHADS2 score Heart failure Hypertension Age > 75 years Diabetes Stroke/TIA Echo Parameters LA diameter (mm) LA volume index (mL/m2 ) LV EF (%) E/Em LVMI (g/m2 ) Electrophysiologic Parameters CV (m/s) AERP (ms) FibNA F (LA diameter[ E c h o ] )
All (n = 60)
Negative Post-RFCA Inducibility (n = 19)
Positive Post-RFCA Inducibility (n = 41)
p-Value
71.7 54.2 ± 12.9 81.7 1.83 ± 0.18 25.2 ± 2.7 0.867 ± 1.016 1.7% 55.0% 1.7% 11.7% 16.6%
63.2 53.9 ± 16.1 84.2 1.80 ± 0.18 25.1 ± 2.7 0.737 ± 1.147 5.3% 42.1% 0% 15.8% 10.5%
75.6 54.4 ± 11.4 80.5 1.85 ± 0.17 25.2 ± 2.8 0.927 ± 0.959 0% 61.0% 2.4% 9.8% 19.5%
0.243 0.446 0.516 0.143 0.443 0.253 0.072 0.089 0.250 0.253 0.386
41.3 ± 5.3 31.6 ± 9.7 63.7 ± 6.6 10.1 ± 3.9 90.7 ± 17.8
40.8 ± 5.9 31.0 ± 12.4 63.6 ± 8.3 12.0 ± 4.2 71.4 ± 10.9
41.5 ± 5.1 31.9 ± 8.4 63.7 ± 5.7 9.24 ± 3.39 92.0 ± 18.2
0.339 0.374 0.478 0.004 0.226
0.680 ± 0.188 245 ± 23 0.263 ± 0.060
0.871 ± 0.143 249 ± 25 0.192 ± 0.028
0.591 ± 0.132 244 ± 23 0.296 ± 0.038
< 0.001 0.231 < 0.001
BSA: Body surface area; BMI: body mass index; LA: left atrium; EF: ejection fraction; E/Em: the ratio of peak velocity of early diastolic mitral inflow and early diastolic mitral annular velocities, representing estimated left ventricular filling pressure; LVMI: left ventricular mass index; CV: conduction velocity; AERP, atrial effective refractory period.
Courtemanche et al. [14] was used to determine ion channel currents in each cell at each time step. A 600 × 600 element cell array, with spatial discretization of 0.25 mm and temporal discretization of 0.05 ms, was used to simulate fibrillation wave dynamics. Finite element formulation based on the Galerkin method was used for discretization of the bidomain equations for electric wave propagation in tissue [15]. We chose diffusion coefficients of 0.091 mm2 /s for the intracellular domain and 0.064 mm2 /s for the extracellular domain, which are in the range of typically used values for cardiac simulation [16]. The resulting CV was 0.31 m/s. No flux condition was applied for all the boundaries of intra- and extracellular domains. For reentry initiation, we used the protocol of Clayton and Holden [17], which we have previously validated [15]. To induce fibrillation, Ito , ICaL , and IKur were reduced by 80%, 30%, and 90%, respectively, and IKr was increased by 50% as described by Jacquemet et al. [18] The resulting action potential duration (APD) was 216 ms at 600 ms cycle length, and the maximal slope of the APD restitution curve is 1.2 [18]. B. In Silico Validation of FibNA F Moe et al. [12] defined FibN, a measure of susceptibility to AF, based on the theoretical consideration of cardiac wave propagation L (1) APD · CV where L is the length scale of tissue size and APD is the action potential duration. To evaluate the effect of FibNAF on fibrillation wave dynamics, 2-D fibrillation wave dynamics simulation was performed for 16 different values of FibNAF determined by randomly generated length scale, APD, and CV. The length of the side of FibNAF =
the square computational domain was used for the length scale. The APD was varied by changing the conductance of IKr and IKs , and CV was decreased by reducing the diffusion coefficients. The range of the length scale was 87.5–150 mm, the range of refractory period was 216–290 ms, the range of CV was 0.26–0.31 m/s, and the resulting FibNAF values were between 1.21 and 2.22. For each FibNAF value, the time from reentry initiation to the termination of fibrillation was recorded C. Clinical Validation of FibNA F in Human AF The study protocol was approved by the Institutional Review Board and adhered to the Declaration of Helsinki. All patients provided written informed consent. We included consecutive 60 AF patients (71.7% male, 54.2 ± 12.9 years old, paroxysmal AF: persistent AF = 81.7%:18.3%; Table I) who underwent radiofrequency catheter ablation (RFCA) guided by computed tomography (CT) merged three-dimensional (3-D) NavX map. All patients maintained optimal anticoagulation status and had ceased all antiarrhythmic medications for five half-lives of the respective drugs. We examined all patients with 3-D spiral CT (64 Channel, Light Speed Volume CT, Philips, Brilliance 63, The Netherlands) to visually define the anatomy of the left atrium (LA). Intracardiac electrograms were recorded using a Prucka CardioLab Electrophysiology system (General Electric Health Care System Inc., Milwaukee, WI, USA). We generated 3-D spiral CT merged 3-D electroanatomic mapping (NavX system, St. Jude Medical Inc., Minneapolis, MN, USA) for RFCA. An open-irrigated 3.5-mm-tip deflectable catheter (Celsius, Johnson & Johnson Inc., Diamond Bar, CA, USA; 30–35 W; 47 °C) was used for RFCA. All patients underwent circumferential PV isolation (CPVI) at the LA antrum level. After CPVI, we generated a LA 3-D activation map by obtaining
HWANG et al.: FIBRILLATION NUMBER BASED ON WAVELENGTH AND CRITICAL MASS IN PATIENTS WHO UNDERWENT RFCA
675
Fig. 1. Fibrillation wave dynamics as a function of FibNA F (left panel) and maintenance duration of fibrillation represented by action potential curves (right panel). (A). Eight different conditions of fibrillation wave dynamics were generated by adjusting the refractory period, CV, and length scale in a 2-D bidomain atrial tissue model. (B). An example showing shorter AF maintenance duration with larger tissue size and lower FibNA F .
Fig. 2.
Linear correlation between FibN and duration of AF.
contact bipolar electrograms from 350 to 500 points of the LA endocardium during high right atrial (RA) pacing (cycle length 500 ms). The bipolar electrograms were filtered from 32 to 300 Hz. After acquiring the LA activation map, we measured atrial effective refractory periods (AERPs) at proximal and coronary sinus by S1–S2 pacing (S1 500 ms). AF inducibility test was performed with 10-s high current burst pacing (10 mA, pulse width 5 ms, Bloom Associates, Denver, CO, USA) from the high RA with starting pacing cycle length (PCL) of 250 ms. If AF could not be induced or maintained for > 3 min, the PCL was reduced serially to 200, 190, 180, 170, 160, and 150 ms with 1:1 atrial capture. Inducibility was defined as the presence of induced AF lasting for longer than 3 min, and the PCL of successful induction of AF was regarded as the induction PCL (iPCL; see Fig. 3).
For off-line analyses, color-coded activation maps were generated by recording bipolar electrograms and the activation time of negative (dV/dt)m ax . We analyzed the color-coded LA activation maps (see Fig. 3) as previously described [19]. The earliest activation site on the LA high septum was colored white, and the site of activation 80 ms later than the earliest activation was colored purple. The reference distance was measured using the interelectrode distances of coronary sinus catheters (duodecapolar catheter, St. Jude Medical Inc., Minnetonka, MN, USA.). Because of limited spatial resolution of LA activation map, we calculated CV by measuring the distances from the earliest activation site to the latest activation sites on LA appendage parallel to septoatrial bundle (AP view) and to LA posterior wall parallel to septoatrial bundle (PA view), based on histological isotrophy [20] using customized software (Image Pro) referenced to a color scale bar. The measured distance on the activation map was divided by the time difference, as measured using color codes, to calculate the local CV. The length scale of tissue size was represented by anterior–posterior diameter of LA measured using 2-D echocardiogram or LA volume measured using 3-D CT. We did not include RA in our electroanatomic mapping study, because AF drivers have been known to exist mostly in LA in experimental model and in human [21], [22]. We calculated FibNAF as follows and compared it with postRFCA inducibility and iPCL. Mean values of AERPs measured at proximal and distal coronary sinus were used for FibNAF calculation: FibNAF =
LA Diameter(Echo) L = . APD · CV AERP · CVNavX
(2)
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IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 62, NO. 2, FEBRUARY 2015
Fig. 3. Examples of iPCL (induction pacing cycle length) and inducibility after AF ablation. (a). A patient with a greater LA and more difficult to induce with lower FibNA F . LA: 45 mm, ERP: 293 ms, CV: 0.89 m/s, FibNA F = 0.17, iPCL / = 60 years old (from the Framingham Heart Study),” Amer. J. Cardiol., vol. 107, pp. 917e1–921e1, Mar. 15, 2011. [41] C. T. January, L. S. Wann, J. S. Alpert, H. Calkins, J. C. Cleveland, Jr., J. E. Cigarroa, J. B. Conti, P. T. Ellinor, M. D. Ezekowitz, M. E. Field, K. T. Murray, R. L. Sacco, W. G. Stevenson, P. J. Tchou, C. M. Tracy, and C. W. Yancy, “2014 AHA/ACC/HRS guideline for the management of patients with atrial fibrillation: A report of the American College of Cardiology/American Heart Association Task Force on Practice Guidelines and the Heart Rhythm Society,” J. Amer. Coll. Cardiol., Mar. 28, 2014. pii: S0735-1097(14)01740-9. doi: 10.1016/j.jacc.2014.03.022 [42] J. Shim, B. Joung, J. H. Park, J. S. Uhm, M. H. Lee, and H. N. Pak, “Long duration of radiofrequency energy delivery is an independent predictor of clinical recurrence after catheter ablation of atrial fibrillation: Over 500 cases experience,” Int. J. Cardiol., vol. 167, pp. 2667–2672, Sep. 10, 2013. [43] A. N. Iyer and R. A. Gray, “An experimentalist’s approach to accurate localization of phase singularities during reentry,” Ann. Biomed. Eng., vol. 29, pp. 47–59, Jan. 2001. [44] K. Nademanee, J. McKenzie, E. Kosar, M. Schwab, B. Sunsaneewitayakul, T. Vasavakul, C. Khunnawat, and T. Ngarmukos, “A new approach for catheter ablation of atrial fibrillation: Mapping of the electrophysiologic substrate,” J. Amer. Coll. Cardiol., vol. 43, pp. 2044–2453, Jun. 2, 2004. [45] S. M. Narayan, D. E. Krummen, K. Shivkumar, P. Clopton, W. J. Rappel, and J. M. Miller, “Treatment of atrial fibrillation by the ablation of localized sources: CONFIRM (conventional ablation for atrial fibrillation with or without focal impulse and rotor modulation) trial,” J. Amer. Coll. Cardiol., vol. 60, pp. 628–636, Aug. 14, 2012.
Authors’ photographs and biographies not available at the time of publication.
673
Fibrillation Number Based on Wavelength and Critical Mass in Patients Who Underwent Radiofrequency Catheter Ablation for Atrial Fibrillation Minki Hwang, Junbeum Park, Young-Seon Lee, Jae Hyung Park, Sung Hwan Choi, Eun Bo Shim, and Hui-Nam Pak∗
Abstract—The heart characteristic length, the inverse of conduction velocity (CV), and the inverse of the refractory period are known to determine vulnerability to cardiac fibrillation (fibrillation number, FibN) in in silico or ex vivo models. The purpose of this study was to validate the accuracy of FibN through in silico atrial modeling and to evaluate its clinical application in patients with atrial fibrillation (AF) who had undergone radiofrequency catheter ablation. We compared the maintenance duration of AF at various FibNA F values using in silico bidomain atrial modeling. Among 60 patients (72% male, 54 ± 13 years old, 82% with paroxysmal AF) who underwent circumferential pulmonary vein isolation (CPVI) for AF rhythm control, we examined the relationship between FibNA F and postprocedural AF inducibility or induction pacing cycle length (iPCL). Clinical FibNA F was calculated using left atrium (LA) dimension (echocardiogram), the inverse of CV, and the inverse of the atrial effective refractory periods measured at proximal and distal coronary sinus. In silico simulation found a positive correlation between AF maintenance duration and FibNA F (R = 0.90, p < 0.001). After clinical CPVI, FibNA F (0.296 ± 0.038 versus 0.192 ± 0.028, p < 0.001) was significantly higher in patients with postprocedural AF inducibility (n = 41) than in those without (n = 19). Among 41 patients with postprocedural AF inducibility, FibNA F (P = 0.935, p < 0.001) had excellent correlations with induction pacing cycle length. FibNA F , based on LA mass and wavelength, correlates well with AF maintenance in computational modeling and clinical AF inducibility after CPVI. Index Terms—Arrhythmogenecity, Atrial fibrillation (AF), critical mass, parameter, wavelength.
Manuscript received August 13, 2014; revised October 8, 2014; accepted October 12, 2014. Date of publication October 17, 2014; date of current version January 16, 2015. This work was supported by the Ministry of Trade, Industry, and Energy (MOTIE), Korea Institute for Advancement of Technology (KIAT), and Gangwon Institute for Regional Program Evaluation (GWIRPE) through the Leading Industry Development for Economic Region (A002200868), a grant (A085136) from the Korea Health 21 R&D Project, Ministry of Health and Welfare, and a grant (2012027176) from the National Research Foundation of Korea (NRF) funded by the Ministry of Science, ICT, and Future Planning (MSIP). Asterisk indicates corresponding author. M. Hwang, J. Park, Y.-S. Lee, and J. H. Park are with the Yonsei University Health System, Seoul 120-752, Korea (e-mail: [email protected]; [email protected]; [email protected]; [email protected]). S. H. Choi is with the CU Medical Systems Incorporation, Wonju 220-801, Korea (e-mail: [email protected]). E. B. Shim is with Kangwon National University, Chuncheon 200-701, Korea (e-mail: [email protected]). ∗ H.-N. Pak is with Yonsei University Health System, Seoul 120-752, Korea (e-mail: [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TBME.2014.2363669
I. INTRODUCTION TRIAL fibrillation (AF), one of the most common arrhythmia in clinical practice, is related to increasingly high rates of disability and mortality [1]. It is predicted that the number of individuals with AF would more than double by the year 2050 [2]. The prevalence of AF increases with age up to 9% among those 80 years or older [3]. As radiofrequency catheter ablation (RFCA) for AF has become a common practice for AF rhythm control, the pathophysiology of this multifactorial disease is gradually being uncovered through clinical studies. However, the mechanisms of cardiac fibrillation are still poorly understood [4]. While the focal source hypothesis [5] states that a relatively stable periodic source (“mother rotor”) with fibrillatory conduction maintains fibrillation, the multiple wavelet hypothesis [6] states that a continuous wavebreak and localized reentry may sustain fibrillation after the exclusion of arrhythmogenic triggers [7]–[9]. Probability of reentry is expressed by wavelength, proportional to the effective refractory period (ERP) and conduction velocity (CV). The cardiac chamber mass also has been found to play an important role in the maintenance of continuous wavebreak, which led to the critical mass hypothesis [10], [11]. Moe et al. [12] originally reported that the characteristic length of substrate, the inverse of CV, and the inverse of the refractory period determine vulnerability to fibrillation (fibrillation number, FibN) based on in silico study of AF. These results are similar in concept to the Reynolds number, which is related to turbulence in fluid flow. In this study, we tested FibN to validate its predictive value for AF maintenance in silico, as well as its clinical usefulness among patients with AF. We hypothesized that FibNAF reflects the vulnerability to AF maintenance in silico, and postprocedural inducibility of AF after clinical catheter ablation.
A
II. METHODS A. Two-Dimensional Fibrillation Modeling To test the effect of FibN on wave propagation in cardiac tissue, we simulated the action potential propagation in atrial tissue using an in silico model. Time-dependent voltage distribution on a two-dimensional (2-D) computational domain was obtained by solving the bidomain reaction–diffusion equation as described by Ashihara et al. [13]. The electrophysiological model of human atrial action potential developed by
0018-9294 © 2014 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications standards/publications/rights/index.html for more information.
674
IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 62, NO. 2, FEBRUARY 2015
TABLE I PATIENT CHARACTERISTICS
Male (%) Age (years) Paroxysmal AF (%) BSA (m2 ) BMI (kg/m2 ) CHADS2 score Heart failure Hypertension Age > 75 years Diabetes Stroke/TIA Echo Parameters LA diameter (mm) LA volume index (mL/m2 ) LV EF (%) E/Em LVMI (g/m2 ) Electrophysiologic Parameters CV (m/s) AERP (ms) FibNA F (LA diameter[ E c h o ] )
All (n = 60)
Negative Post-RFCA Inducibility (n = 19)
Positive Post-RFCA Inducibility (n = 41)
p-Value
71.7 54.2 ± 12.9 81.7 1.83 ± 0.18 25.2 ± 2.7 0.867 ± 1.016 1.7% 55.0% 1.7% 11.7% 16.6%
63.2 53.9 ± 16.1 84.2 1.80 ± 0.18 25.1 ± 2.7 0.737 ± 1.147 5.3% 42.1% 0% 15.8% 10.5%
75.6 54.4 ± 11.4 80.5 1.85 ± 0.17 25.2 ± 2.8 0.927 ± 0.959 0% 61.0% 2.4% 9.8% 19.5%
0.243 0.446 0.516 0.143 0.443 0.253 0.072 0.089 0.250 0.253 0.386
41.3 ± 5.3 31.6 ± 9.7 63.7 ± 6.6 10.1 ± 3.9 90.7 ± 17.8
40.8 ± 5.9 31.0 ± 12.4 63.6 ± 8.3 12.0 ± 4.2 71.4 ± 10.9
41.5 ± 5.1 31.9 ± 8.4 63.7 ± 5.7 9.24 ± 3.39 92.0 ± 18.2
0.339 0.374 0.478 0.004 0.226
0.680 ± 0.188 245 ± 23 0.263 ± 0.060
0.871 ± 0.143 249 ± 25 0.192 ± 0.028
0.591 ± 0.132 244 ± 23 0.296 ± 0.038
< 0.001 0.231 < 0.001
BSA: Body surface area; BMI: body mass index; LA: left atrium; EF: ejection fraction; E/Em: the ratio of peak velocity of early diastolic mitral inflow and early diastolic mitral annular velocities, representing estimated left ventricular filling pressure; LVMI: left ventricular mass index; CV: conduction velocity; AERP, atrial effective refractory period.
Courtemanche et al. [14] was used to determine ion channel currents in each cell at each time step. A 600 × 600 element cell array, with spatial discretization of 0.25 mm and temporal discretization of 0.05 ms, was used to simulate fibrillation wave dynamics. Finite element formulation based on the Galerkin method was used for discretization of the bidomain equations for electric wave propagation in tissue [15]. We chose diffusion coefficients of 0.091 mm2 /s for the intracellular domain and 0.064 mm2 /s for the extracellular domain, which are in the range of typically used values for cardiac simulation [16]. The resulting CV was 0.31 m/s. No flux condition was applied for all the boundaries of intra- and extracellular domains. For reentry initiation, we used the protocol of Clayton and Holden [17], which we have previously validated [15]. To induce fibrillation, Ito , ICaL , and IKur were reduced by 80%, 30%, and 90%, respectively, and IKr was increased by 50% as described by Jacquemet et al. [18] The resulting action potential duration (APD) was 216 ms at 600 ms cycle length, and the maximal slope of the APD restitution curve is 1.2 [18]. B. In Silico Validation of FibNA F Moe et al. [12] defined FibN, a measure of susceptibility to AF, based on the theoretical consideration of cardiac wave propagation L (1) APD · CV where L is the length scale of tissue size and APD is the action potential duration. To evaluate the effect of FibNAF on fibrillation wave dynamics, 2-D fibrillation wave dynamics simulation was performed for 16 different values of FibNAF determined by randomly generated length scale, APD, and CV. The length of the side of FibNAF =
the square computational domain was used for the length scale. The APD was varied by changing the conductance of IKr and IKs , and CV was decreased by reducing the diffusion coefficients. The range of the length scale was 87.5–150 mm, the range of refractory period was 216–290 ms, the range of CV was 0.26–0.31 m/s, and the resulting FibNAF values were between 1.21 and 2.22. For each FibNAF value, the time from reentry initiation to the termination of fibrillation was recorded C. Clinical Validation of FibNA F in Human AF The study protocol was approved by the Institutional Review Board and adhered to the Declaration of Helsinki. All patients provided written informed consent. We included consecutive 60 AF patients (71.7% male, 54.2 ± 12.9 years old, paroxysmal AF: persistent AF = 81.7%:18.3%; Table I) who underwent radiofrequency catheter ablation (RFCA) guided by computed tomography (CT) merged three-dimensional (3-D) NavX map. All patients maintained optimal anticoagulation status and had ceased all antiarrhythmic medications for five half-lives of the respective drugs. We examined all patients with 3-D spiral CT (64 Channel, Light Speed Volume CT, Philips, Brilliance 63, The Netherlands) to visually define the anatomy of the left atrium (LA). Intracardiac electrograms were recorded using a Prucka CardioLab Electrophysiology system (General Electric Health Care System Inc., Milwaukee, WI, USA). We generated 3-D spiral CT merged 3-D electroanatomic mapping (NavX system, St. Jude Medical Inc., Minneapolis, MN, USA) for RFCA. An open-irrigated 3.5-mm-tip deflectable catheter (Celsius, Johnson & Johnson Inc., Diamond Bar, CA, USA; 30–35 W; 47 °C) was used for RFCA. All patients underwent circumferential PV isolation (CPVI) at the LA antrum level. After CPVI, we generated a LA 3-D activation map by obtaining
HWANG et al.: FIBRILLATION NUMBER BASED ON WAVELENGTH AND CRITICAL MASS IN PATIENTS WHO UNDERWENT RFCA
675
Fig. 1. Fibrillation wave dynamics as a function of FibNA F (left panel) and maintenance duration of fibrillation represented by action potential curves (right panel). (A). Eight different conditions of fibrillation wave dynamics were generated by adjusting the refractory period, CV, and length scale in a 2-D bidomain atrial tissue model. (B). An example showing shorter AF maintenance duration with larger tissue size and lower FibNA F .
Fig. 2.
Linear correlation between FibN and duration of AF.
contact bipolar electrograms from 350 to 500 points of the LA endocardium during high right atrial (RA) pacing (cycle length 500 ms). The bipolar electrograms were filtered from 32 to 300 Hz. After acquiring the LA activation map, we measured atrial effective refractory periods (AERPs) at proximal and coronary sinus by S1–S2 pacing (S1 500 ms). AF inducibility test was performed with 10-s high current burst pacing (10 mA, pulse width 5 ms, Bloom Associates, Denver, CO, USA) from the high RA with starting pacing cycle length (PCL) of 250 ms. If AF could not be induced or maintained for > 3 min, the PCL was reduced serially to 200, 190, 180, 170, 160, and 150 ms with 1:1 atrial capture. Inducibility was defined as the presence of induced AF lasting for longer than 3 min, and the PCL of successful induction of AF was regarded as the induction PCL (iPCL; see Fig. 3).
For off-line analyses, color-coded activation maps were generated by recording bipolar electrograms and the activation time of negative (dV/dt)m ax . We analyzed the color-coded LA activation maps (see Fig. 3) as previously described [19]. The earliest activation site on the LA high septum was colored white, and the site of activation 80 ms later than the earliest activation was colored purple. The reference distance was measured using the interelectrode distances of coronary sinus catheters (duodecapolar catheter, St. Jude Medical Inc., Minnetonka, MN, USA.). Because of limited spatial resolution of LA activation map, we calculated CV by measuring the distances from the earliest activation site to the latest activation sites on LA appendage parallel to septoatrial bundle (AP view) and to LA posterior wall parallel to septoatrial bundle (PA view), based on histological isotrophy [20] using customized software (Image Pro) referenced to a color scale bar. The measured distance on the activation map was divided by the time difference, as measured using color codes, to calculate the local CV. The length scale of tissue size was represented by anterior–posterior diameter of LA measured using 2-D echocardiogram or LA volume measured using 3-D CT. We did not include RA in our electroanatomic mapping study, because AF drivers have been known to exist mostly in LA in experimental model and in human [21], [22]. We calculated FibNAF as follows and compared it with postRFCA inducibility and iPCL. Mean values of AERPs measured at proximal and distal coronary sinus were used for FibNAF calculation: FibNAF =
LA Diameter(Echo) L = . APD · CV AERP · CVNavX
(2)
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Fig. 3. Examples of iPCL (induction pacing cycle length) and inducibility after AF ablation. (a). A patient with a greater LA and more difficult to induce with lower FibNA F . LA: 45 mm, ERP: 293 ms, CV: 0.89 m/s, FibNA F = 0.17, iPCL / = 60 years old (from the Framingham Heart Study),” Amer. J. Cardiol., vol. 107, pp. 917e1–921e1, Mar. 15, 2011. [41] C. T. January, L. S. Wann, J. S. Alpert, H. Calkins, J. C. Cleveland, Jr., J. E. Cigarroa, J. B. Conti, P. T. Ellinor, M. D. Ezekowitz, M. E. Field, K. T. Murray, R. L. Sacco, W. G. Stevenson, P. J. Tchou, C. M. Tracy, and C. W. Yancy, “2014 AHA/ACC/HRS guideline for the management of patients with atrial fibrillation: A report of the American College of Cardiology/American Heart Association Task Force on Practice Guidelines and the Heart Rhythm Society,” J. Amer. Coll. Cardiol., Mar. 28, 2014. pii: S0735-1097(14)01740-9. doi: 10.1016/j.jacc.2014.03.022 [42] J. Shim, B. Joung, J. H. Park, J. S. Uhm, M. H. Lee, and H. N. Pak, “Long duration of radiofrequency energy delivery is an independent predictor of clinical recurrence after catheter ablation of atrial fibrillation: Over 500 cases experience,” Int. J. Cardiol., vol. 167, pp. 2667–2672, Sep. 10, 2013. [43] A. N. Iyer and R. A. Gray, “An experimentalist’s approach to accurate localization of phase singularities during reentry,” Ann. Biomed. Eng., vol. 29, pp. 47–59, Jan. 2001. [44] K. Nademanee, J. McKenzie, E. Kosar, M. Schwab, B. Sunsaneewitayakul, T. Vasavakul, C. Khunnawat, and T. Ngarmukos, “A new approach for catheter ablation of atrial fibrillation: Mapping of the electrophysiologic substrate,” J. Amer. Coll. Cardiol., vol. 43, pp. 2044–2453, Jun. 2, 2004. [45] S. M. Narayan, D. E. Krummen, K. Shivkumar, P. Clopton, W. J. Rappel, and J. M. Miller, “Treatment of atrial fibrillation by the ablation of localized sources: CONFIRM (conventional ablation for atrial fibrillation with or without focal impulse and rotor modulation) trial,” J. Amer. Coll. Cardiol., vol. 60, pp. 628–636, Aug. 14, 2012.
Authors’ photographs and biographies not available at the time of publication.
