Ablation Pattern Guided by Approximate Entropy Maps to Prevent Chronic Atrial Fibrillation: A Simulation Study C. Tobón1,2, E.A. Cardona1, L.C. Palacio1, J.E. Duque1, J.P. Ugarte2, A. Orozco-Duque2, M.A. Becerra3, and J. Bustamante2 1
GI2B, Instituto Tecnológico Metropolitano, Medellín, Colombia Centro de Bioingeniería, Universidad Pontificia Bolivariana, Medellín, Colombia 3 Grupo de Electrónica y Automática, Instituto Universitario Salazar y Herrera, Medellín, Colombia {migb2b,andresfod}@gmail.com,
[email protected], {cripton80,laura-sarca116,catatobonz,estebanacq}@hotmail.com,
[email protected] 2
Abstract— Atrial fibrillation (AF) is the most prevalent cardiac arrhythmia. Experimental and clinical evidence suggest that AF are maintained by rotors, which are targets for ablation. Some studies suggest that complex fractionated atrial electrograms (CFAE) are generated by rotor tips. Approximate entropy (ApEn) can be used as a measurement that quantifies the complexity of a signal. It has been demonstrated that the ApEn can locate rotors. We hypothesized that simple ablation patterns guided by high ApEn regions can prevent and/or terminate chronic AF. An episode of chronic AF was simulated in a 3D human atrial model, in which 2 rotors were observed. Dynamic approximate entropy maps were calculated using electrogram signals generated over the whole surface of the model. ApEn map localized the tips from stable rotors. The ablation pattern developed in this work and guided by ApEn map, was able to convert AF into atrial tachycardia (AT) when it was applied during AF episode; moreover, when it was applied during sinus rhythm, AF could not be generated. The results suggest that simple ablation pattern guided by ApEn maps could prevent chronic AF or convert it into a more regular and less chaotic arrhythmia as atrial tachyarrhythmia. Keywords— Ablation, approximate entropy, chronic atrial fibrillation, virtual models. I. INTRODUCTION
Atrial fibrillation (AF) is the most prevalent cardiac arrhythmia. AF provokes disabling symptoms and severe complications such as heart failure and stroke [1]. Experimental and clinical evidence suggest that AF are maintained by high frequency small reentrant sources (rotors), which are stable over time and thus suitable targets for ablation [2]. A rotor is characterized as a spiral wave turning around the pivot point (tip). Rotor modulation guided ablation substantially improved long-term freedom from AF over conventional ablation alone [3]. Analyses of dominant frequency and regularity indexes have proven to be effective to localize arrhythmogenic sources during paroxysmal AF, but no on chronic AF [4]. Further, it has not been demonstrated its efficacy on rotors localization during AF. Some studies suggest that complex fractionated atrial electrograms (CFAE) are generated by rotor tips [5].
Approximate entropy (ApEn) is a non-linear statistic that can be used as a measurement that quantifies the complexity of a signal [6]. In previous work [7] we demonstrated that the ApEn can locate rotors, by means of quantification of irregularity degree of CFAE. We hypothesized that simple ablation patterns guided by high ApEn regions can prevent and/or terminate chronic AF. II. MATERIALS AND METHODS
A. Atrial Fibrillation in a 3D Model of Human Atria We used the Courtemanche-Ramirez-Nattel-Kneller [8, 9] membrane formalism. A 0.005 μM of acetylcholine (ACh) concentration was simulated. To reproduce the atrial electrical remodeling generated by chronic AF, changes in conductance of different ionic channels of human atrial cells observed in experimental studies of AF [10, 11] have been incorporated in the electrophysiological model. Several parameters were changed: the conductance for both IKur and Ito was decreased by 50%, the conductance for ICaL was decreased by 70%, while the conductance for IK1 was increased by 100% We used a 3D model of human atria developed previously [5]. The model comprises the main anatomical structures and three different pathways for inter-atrial conduction of electrical propagation. The model includes realistic fiber orientation, electrophysiological heterogeneity and anisotropy. The model includes 52906 hexahedral elements and 100554 nodes. The chronic AF electrophysiological model was coupled in the virtual model of human atria. The monodomain model was used to simulate the electrical propagation of the action potential along the virtual atrial model [5]. The conductivity values were assigned in order to obtain conduction velocities within the ranges reported by literature [12]. B. Stimulation Protocol Chronic AF episodes were generated by S1-S2 protocol in the virtual model as follows: a train of stimuli with a
© Springer International Publishing Switzerland 2015 A. Braidot and A. Hadad (eds.), VI Latin American Congress on Biomedical Engineering CLAIB 2014, Paraná, Argentina 29, 30 & 31 October 2014, IFMBE Proceedings 49, DOI: 10.1007/978-3-319-13117-7_143
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Ablation Pattern Guided by Approximate Entropy Maps to Prevent Chronic Atrial Fibrillation: A Simulation Study
basic cycle length (BCL) of 1000 ms was applied during 5 seconds in the sinoatrial node area to simulate the sinus rhythm (S1). After the last beat of the sinus nodal stimulus, a continuous ectopic focus (S2) to high frequency was delivered into the superior right pulmonary vein. All simulations were completed within 10 seconds. Equations were numerically solved using the software EMOS, which is a parallel code (mpibased) that implements the finite element method (FEM) for solving the monodomain model. The time step was fixed to 0.001 ms. C. Unipolar Atrial Electrograms Pseudo-unipolar atrial electrograms were simulated in the atrial surface. The extracellular potential (Фe) is given by the following equation: e o
1 i 4 e
'V
m
o' '
1 dv o'o
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E. Ablation Pattern Linear transmural lesions caused by ablation procedures are modelled by selecting elements of the virtual atrial model, which were assigned zero conductivity in order to become real obstacles to the activation fronts. Base on the result (next section), we developed a ablation pattern that consists of: 1) two circular patterns that enclose the tip of the rotors, located one on the posterior wall of the left atrium and the other in the right atrial wall; and 2) ablation lines connecting the circular patterns with conduction boundaries (superior pulmonary veins and superior and inferior vena cava) (Fig. 1). This pattern was applied before and after to AF initiation.
(1)
where ’Vm is the spatial gradient of transmembrane potential, i is the intracellular conductivity, e is the extracellular conductivity, o is the distance from the source point (x, y, z) to the measuring point (x’, y’, z’) and dv is the differential volume. Electrograms were computed each one millisecond and outside the mesh 0.2 mm away. CFAE were defined by reported criteria [13]. Fig. 1 Ablation pattern.
D. Approximate Entropy Approximate Entropy (ApEn) is a nonlinear statistic proposed by [6]. It quantifies the degree of complexity of signals. The calculation of ApEn(m, r, N) depends on three parameters: number of data points N, embedding dimension m and threshold r. ApEn is defined as: 1 (r ) N ( m 1) m
N ( m 1)
ln(Crm ( r ))
(2)
i 1
ApEn(m, r, N ) m (r ) m 1 (r )
(3)
Ci m(r) is a measure, within a tolerance r, of the regularity (or frequency) of patterns similar to a given pattern i, and is calculated as described in [6]. Pincus stated that small values of m are needed in order to converge to the real value of ApEn. We used m = 2, r = 0.1 for N = 5000, values suggested by [6]. Care must be taken here in the interpretation of parameters m and r, being as they are not the same [14] as that interpretation used in attractor reconstruction [15-17]. Since ApEn calculation is made in the time domain and does not require to unfold the attractor (i.e. the state space) we did not estimate the embedding lag τ. Moreover, we applied the default choice of τ = 1[6] as the autocorrelation function of the dynamics of the time series we used, decays rapidly [14].
III. RESULTS
A. Simulated AF Episode and Rotor’s Tip Location The ectopic focus applied into the superior right pulmonary vein, generated reentrant activity leading to fibrillatory conduction. During AF, two stable rotors were observed, one located in posterior wall of the left atrium near to left pulmonary veins and the other in superior vena cava (Fig 2 A). Fig. 2 B shows the ApEn map, there are two areas with high ApEn values (ApEn>0.5), which matched with the rotor tip. Low ApEn values were observed in the rest of the atria. B. Ablation Pattern The ablation pattern applied after to AF initiation (5 seconds after the ectopic focus activity), did not terminate the AF episode, but the rotor activity finished and AF became atrial tachycardia (AT). AT was maintained by a macroreentry around the left atrium (Fig. 3 A).
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Fig. 2 A) Chronic AF activity, rotors are shown. B) ApEn map showing high values in the rotor tips.
On the other hand, when the ablation pattern was applied before to AF initiation (during sinus rhythm), the AF episode could not be generated by the ectopic focus activity, the wave fronts propagated and collided around the whole atria and became extinct at 1080 ms (Fig. 3 B).
mental and clinical studies [18, 19], that shows the role of focal activation (into the pulmonary veins mainly) in the initiation of AF. Two stable rotors were generated spontaneously, which is in agreement with the rotor hypothesis [2]. Several studies have shown that FA in humans can be sustained by localized rotors [2, 3, 20]. There are evidence that a high degree of disorganization is present in EGM signals (CFAE) at the rotor tip [21, 22], and their fractionation can be measured using a non-linear index such as Approximate Entropy (ApEn) [7], as our results show. Then, areas with high ApEn could be targets for ablation. Experimental and clinical evidence suggest that rotors are suitable targets for ablation [2, 3]. Narayan et al. [3] demonstrated that rotor guided ablation substantially improved long-term freedom from AF over conventional ablation alone. An ideal pattern should be able to prevent AF with a limited number of ablation lines of minimal length, while allowing for maintenance or recovery of mechanical activity of both atria during sinus rhythm. Different lesion patterns have been suggested [2325], however, this ideal ablation pattern is still unknown. The ablation procedure can be applied in patients with chronic AF during AF episode or during sinus rhythm. The ablation pattern developed in this work and guided by approximate entropy map, was able to convert AF into AT when it was applied during AF episode; moreover, when it was applied during sinus rhythm, AF could not be generated. After ablation of chronic atrial fibrillation (AF) by simplified methods, often new postoperative supraventricular arrhythmias appear, as typical and atypical atrial flutter, and right or left reentrant tachycardia [26-28], requiring more than one ablation procedure or pharmacological interventions. Its incidence is not usually documented in surgical studies, however reaches percentages of 4 - 43% [29]. Faustino et al. [30] in a prospective study with 400 patients who underwent catheter ablation for persistent AF (4.6±2.4 months) observed that AF was terminated by radiofrequency application directly into sinus rhythm in 135 patients and passing through AT into sinus rhythm in 195 patients. V.
Fig. 3 A) AF become AT, after ablation pattern application during AF. B) AF can not be initiated by ectopic activity, after ablation pattern application during sinus rhythm.
CONCLUSIONS
Simple ablation pattern guided by approximate entropy maps could prevent chronic AF or convert it into a more regular and less chaotic arrhythmia as AT.
ACKNOWLEDGMENT IV. DISCUSSION
In this work, we initiated AF episode by an ectopic focus into the pulmonary veins, which is accord with experi-
This work was supported by the "Departamento Administrativo de Ciencia, Tecnologa e Innovación COLCIENCIAS" of Colombia, by research project
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#121056933647; and by the project with ITM code P14112 and IUSH code 250.
CONFLICT OF INTEREST The authors declare that they have no conflict of interest.
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