Dynamic approximate entropy electroanatomic maps detect rotors in a simulated atrial fibrillation model

RESEARCH ARTICLE Dynamic Approximate Entropy Electroanatomic Maps Detect Rotors in a Simulated Atrial Fibrillation Model Juan P. Ugarte 1 *, Andre´s Orozco-Duque 1 , Catalina Tobo´n 2 , Vaclav Kremen 3,4 , Daniel Novak 3 , Javier Saiz 5 , Tobias Oesterlein 6 , Clauss Schmitt 7 , Armin Luik 7 , John Bustamante 1 1. Centro de Bioingenierı´a, Universidad Pontificia Bolivariana, Medellı´n, Colombia, 2. GI 2 B, Instituto Tecnolo´gico Metropolitano, Medellı´n, Colombia, 3. Czech Institute of Informatics, Robotics and Cybernetics, Czech Technical University in Prague, Prague, Czech Republic, 4. Department of Cybernetics, Faculty of Electrical Engineering, Czech Technical University in Prague, Prague, Czech Republic, 5. I3BH, Universitat Polite`cnica de Vale`ncia, Valencia, Spain, 6. Institute of Biomedical Engineering, Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany, 7. Medizinische Klinik IV, Staedtisches Klinikum Karlsruhe, Karlsruhe, Germany *[email protected].edu.co Abstract There is evidence that rotors could be drivers that maintain atrial fibrillation. Complex fractionated atrial electrograms have been located in rotor tip areas. However, the concept of electrogram fractionation, defined using time intervals, is still controversial as a tool for locating target sites for ablation. We hypothesize that the fractionation phenomenon is better described using non-linear dynamic measures, such as approximate entropy, and that this tool could be used for locating the rotor tip. The aim of this work has been to determine the relationship between approximate entropy and fractionated electrograms, and to develop a new tool for rotor mapping based on fractionation levels. Two episodes of chronic atrial fibrillation were simulated in a 3D human atrial model, in which rotors were observed. Dynamic approximate entropy maps were calculated using unipolar electrogram signals generated over the whole surface of the 3D atrial model. In addition, we optimized the approximate entropy calculation using two real multicenter databases of fractionated electrogram signals, labeled in 4 levels of fractionation. We found that the values of approximate entropy and the levels of fractionation are positively correlated. This allows the dynamic approximate entropy maps to localize the tips from stable and meandering rotors. Furthermore, we assessed the optimized approximate entropy using bipolar electrograms generated over a vicinity enclosing a rotor, achieving rotor detection. Our results suggest that high approximate entropy values are able to detect a high level of fractionation and OPEN ACCESS Citation: Ugarte JP, Orozco-Duque A, Tobo´n C, Kremen V, Novak D, et al. (2014) Dynamic Approximate Entropy Electroanatomic Maps Detect Rotors in a Simulated Atrial Fibrillation Model. PLoS ONE 9(12): e114577. doi:10.1371/ journal.pone.0114577 Editor: Alexander V. Panfilov, Gent University, Belgium Received: June 13, 2014 Accepted: November 11, 2014 Published: December 9, 2014 Copyright: ß2014 Ugarte et al. This is an openaccess article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Data Availability: The authors confirm that all data underlying the findings are fully available without restriction. The data are available at https://github. com/andresfod/Atrial_Electrograms_ApEn. Funding: JPU, CT, and JB were partially supported by Departamento Administrativo de Ciencia, Tecnologı´a e Innovacio´n de la Republica de Colombia (www.colciencias.gov.co), project #121056933647; AO was supported by the Programa de Formacio´n de Investigadores Francisco Jose de Caldas (www.colciencias.gov. co); VK and DN were partially supported by research project #MSM6840770012 Interdisciplinary Biomedical Engineering Research II from the Ministry of Education (www.msmt.cz), Youth and Sports of the Czech Republic, and VK was partially supported by post-doctoral research project GACR #P103/11/P106 of the Czech Science Foundation (www.gacr.cz). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript. Competing Interests: The authors have declared that no competing interests exist. PLOS ONE | DOI:10.1371/journal.pone.0114577 December 9, 2014 1/19 to locate rotor tips in simulated atrial fibrillation episodes. We suggest that dynamic approximate entropy maps could become a tool for atrial fibrillation rotor mapping. Introduction Catheter ablation based on mapping procedures has revolutionized the treatment of atrial fibrillation (AF). Electroanatomical mapping for guided AF ablation provides a 3D reconstruction of the cardiac chambers together with electrical information obtained from electrograms (EGM). Mappings of activation waves, voltage, dominant frequency and complex fractionated atrial electrograms (CFAE) are used to localize target sites for ablation. However, there are limitations with these techniques, which depend heavily on the expertise of the electrophysiologist [1]. CFAE mapping is still a debated technique [2]. CFAE is a physiopathological concept that was introduced by Nademanee [3]. However, this concept is broadly and unclearly defined, and involves inherent subjectivity [4]. This can lead to incorrect detection of target sites for ablation, mistaking EGM that are fractionated and functional in nature [5]. It also makes studies difficult to compare. While the concept of CFAE has made a relevant contribution to the study of AF, it may fail to describe the wide range of EGM fractionation that occurs in specific cases. In addition, inconsistent results have been found using the CFAE concept. Taking this into account, recent studies have helped to understand the concept of CFAE as a nonlinear phenomenon for quantifying various CFAE patterns, without using cycle length criteria [6–8]. Studies have shown that sites representing AF substrates are characterized by a high degree of disorganization in EGM [9], and, accordingly, methods for EGM signal processing are being designed to quantify the degree of fractionation of EGM [7,8]. The relationship between CFAE and the rotor tip has been reported in recent studies [7,10–13], but automatic rotor mapping methods have not been fully established. The rotor hypothesis described in [14] proposes that in a significant number of patients, a rotor or a small number of rotors are drivers which maintain the arrhythmia. A rotor is a vortex of a spiral wave rotating around an unexcitable core. Narayan et al have provided evidence that human AF can be sustained by localized rotors [15,16]. Based on the rotor hypothesis, which surmises that sustained AF depends on uninterrupted periodic activity of the discrete reentrant site, and on evidence that a high degree of irregularity is present in EGM signals at the rotor tip, we hypothesized that 1) the level of fractionation on EGM can be measured using a non-linear index such as Approximate Entropy (ApEn), and 2) high levels of ApEn can be used to localize the rotor tip. Dynamic ApEn Maps in Atrial Fibrillation PLOS ONE | DOI:10.1371/journal.pone.0114577 December 9, 2014 2/19 Materials and Methods We present dynamic ApEn maps as a new tool for rotor detection. ApEn values for each EGM recorded from the atrial surface are used to construct a color map. We assess the method in a 3D computational model of human atria. Fig. 1A schematically illustrates the methodology used in this work, as follows. First, two AF episodes were simulated: a chronic AF episode in which two stable rotors were found, and a chronic AF episode in which a meandering rotor was found. Second, ApEn measurements, using standard parameters, are calculated over virtual EGM recorded from the 3D model to construct dynamic ApEn maps. Third, the ApEn parameters were optimized using real measured bipolar EGM from multi-center databases. Fourth, dynamic ApEn maps were generated using optimized parameters. Next, the rotors tips are identified by analyzing local activation time maps and dynamic ApEn maps. The details of each step are presented in the following sections. Chronic atrial fibrillation model A realistic 3D model of human atria including the main anatomical structures, fiber orientation, electrophysiological and conduction heterogeneity and anisotropy, was developed in an earlier work [17]. It includes 52906 hexahedral elements and 100554 nodes. The Courtemanche-Ramirez-Nattel-Kneller membrane formalism [18,19] was implemented to reproduce the human atrial cellular electrical activity. The monodomain model of the electrical propagation of the action potential along the tissue is described by a reaction-diffusion equation, and is solved using a finite element method [17]. To reproduce atrial electrical remodeling, changes in the maximum conductance and kinetics of different ionic channels of human atrial cells observed in experimental studies of chronic AF [20–22] have been incorporated into the atrial cellular model. The following parameters were altered [23]: the maximum conductance of IK1was increased by 100%, while the maximum conductance values of ICaL and Ito were decreased by 70% and by 50%, respectively. Simulation protocol Two AF episodes were generated by the S1–S2 protocol as follows: a train of stimuli with a basic cycle length of 1000 ms was applied for a period of 5 seconds in the sinus node area to simulate the sinus rhythm (S1). After the last beat of the sinus stimulus, a burst of 6 ectopic beats (S2) to high frequency were delivered into the right superior pulmonary vein, for the first AF episode; and they were delivered into the posterior wall of the left atrium near to the right pulmonary veins, for the second episode. Virtual electrograms Unipolar EGM in different points of the atria surface under conditions of uniform intracellular anisotropic resistivity was simulated, as previously described [24]. Dynamic ApEn Maps in Atrial Fibrillation PLOS ONE | DOI:10.1371/journal.pone.0114577 December 9, 2014 3/19 The extracellular potential (we) is given by the following equation: we(r)~{ 1 4p si seððð+Vm(r’):+1 r’{r  dv ð1Þ where +Vmis the spatial gradient of transmembrane potential Vm,siis the intracellular conductivity, seis the extracellular conductivity, ris the distance from the source point (x,y,z)to the measuring point (x’,y’,z’)and dv is the differential volume. EGM signals were recorded at 1kHz. Bipolar EGM were calculated by subtracting two 1-mm-spaced adjacent unipolar EGM. Numerical and computational methods A hexahedral mesh was built from the three-dimensional anatomical model using Femap from Siemens PLM software. Equations were numerically solved using EMOS software [25]. EMOS is a parallel code (mpibased) that implements the finite element method and Operator Splitting for solving the monodomain model. The time step was fixed to 0.001 ms. Simulation of 10 seconds of atrial activity took 14 hours on a computing node with two 6-core Intel Xeon X5650 clocked at 2.66 GHz and 48GB DDR3 RAM. Isochrone activation maps A method was developed as an arrangement of the isochrone map method [26], where the local activation times (LAT) are represented in a color map. To build an activation map, it is necessary to detect the local activation waves. An algorithm based on the Continuous Wavelet Transform was implemented to detect local activation waves. After a peak has been detected, an isochrone map is constructed with the LAT information. In order to ensure that one complete activation cycle is scanned, it is necessary to visualize the LAT minimum for a period of 100 ms. The Fig. 1. Experimental setup. A: Simulated episode of chronic AF in a 3D model of human atria. A local activation time map was constructed as an alternative method for detecting rotors. A pseudo-EGM signal was calculated from the 3D model. ApEn was calculated in pseudo-EGM signals recorded over the whole atrial surface. ApEn maps were constructed in order to observe the relation between ApEn values and rotor locations. B: Examples of EGM signals of DBCZ-DE. Representatives from the four levels of complexity proposed for the purposes of the study are shown from C0 to C3. These signals were used for ApEn parameter optimization. doi:10.1371/journal.pone.0114577.g001 Dynamic ApEn Maps in Atrial Fibrillation PLOS ONE | DOI:10.1371/journal.pone.0114577 December 9, 2014 4/19 points at which the activation waves are spinning can be observed; these points correspond to the rotor tip. This procedure was used as a gold standard for comparison with our results. Approximate entropy and parameter optimization Approximate Entropy (ApEn) is a nonlinear statistic proposed by Pincus [27]. It quantifies the degree of complexity of signals. The calculation of ApEn depends on three parameters: number of data points N, embedding dimension mand threshold r.ApEn(m,r,N)allows to measure regularity by calculating the probability that patterns of length mremain close on next incremental comparisons within a signal of length N, with mvN[28]. ApEn is theoretically defined as the value dependent on mand r, considering N??. This value cannot be reached but can be approximated. The approximation is well suited when a significant number of patterns, determined by m, are acquired [29]. Pincus stated that small values of mare needed in order to converge to the real value of ApEn [28]. Specifically, he suggested m~2, r[½0:1,0:25as standard parameters. We evaluate ApEn(2,0:1,1000)and ApEn(2,0:1,500)from standard parameters. Furthermore, we propose mand rvalues derived from an optimization procedure using a dataset of EGM. This dataset has already been applied to other studies aimed at developing signal processing tools for CFAE [30,31]. Dataset We used two different EGM databases, independently recorded from AF patients, and independently evaluated. The databases were ranked by different electrophysiology teams, with different equipment, from two different countries. The 542 signals in the databases were classified using the same criteria divided into four classes: fractionated signals were categorized by experts into three levels of fractionation (C1, C2 and C3), and nonfractionated EGM signals were considered as level 0 (C0). The four fractionation classes, see Fig. 1B, are: NC0: Nonfractionated EGM and also high frequency EGM. NC1: Fractionated EGM with periodic activity. NC2: A mixture of periodic fractionated and periodic nonfractionated EGM. NC3: High frequency EGM with continuous activity. No regular activation can be seen. The entire database constitutes a retrospective-offline analysis. For further information about the acquisition and classification of this database, refer to [32,33]. The database is available at https://github.com/andresfod/Atrial_ Electrograms_ApEn. Optimization process ApEn parameters mand rwere set using real data from the database, to obtain optimal values. The variation of mwas limited to 5, as recommended by Pincus [27]. Parameter rvaried from 0.02 to 0.6, increasing in steps of 0.02. The database Dynamic ApEn Maps in Atrial Fibrillation PLOS ONE | DOI:10.1371/journal.pone.0114577 December 9, 2014 5/19 was organized into four levels of fractionation (C0, C1, C2 and C3). Each level contains the entire set of signals of the corresponding level of fractionation. The first 500 and 1000 ms of each EGM were considered. The numbers of EGM signals were as follows: 175 signals in C0, 117 signals in C1, 184 signals in C2, and 66 signals in C3. From now on, we refer to this database organization as DB-CZ-GE. For each combination of mand r,ApEn was calculated for each EGM from DBCZ-GE and a boxplot was constructed, assigning a box to each level. In the interest of minimizing the scatter of each class and maximizing the distances between the ApEn measures of the classes, two criteria were considered in the optimization procedure: interclass percentile distance d1and interclass minimum-maximum distance d2, which were defined as follows: d1~X 3 i~1 Q1(Ciz1){Q3(Ci)½ ð2Þ d2~X 3 i~1 min(Ciz1){max(Ci)½ ð3Þ where Q1and Q3are the first and third quantile, respectively. To select the parameters to be used for ApEn, an optimization function Jbp was constructed by equal weighting of criteria d1and d2from (2) and (3): Jbp~d1zd2ð4Þ In order to validate the ApEn parameters obtained in the optimization procedure and to avoid overtraining, K-cross validation was performed. Randomly generated partitions were selected from full DB-CZ-GE. K~10 subsets were formed. Dynamic ApEn mapping In order to generate a dynamic ApEn map over the surface of the atrial model, the standard ApEn parameters m~2and r~0:1, as suggested by Pincus [27,28,34] and the parameters of ApEn obtained in the optimization procedure, were used. ApEn was calculated for virtual unipolar EGM signals, using moving windows of 500 and 1000 points, without overlapping. The range of ApEn, over the entire set of virtual EGM, was applied to a color scale, where red color corresponds to max (ApEn)and blue color corresponds to 0. Each virtual EGM is related to an element in the model. A 1000-point window was applied for tracking stable rotors. A 500-point window was applied for tracking meandering rotors. Unipolar EGM over the entire surface of the atria were analyzed, with the exception of the meandering rotor case, in which an observation area was selected in order to evaluate the behavior of the optimized ApEn during the presence and absence of the tip of the rotor. Dynamic ApEn Maps in Atrial Fibrillation PLOS ONE | DOI:10.1371/journal.pone.0114577 December 9, 2014 6/19 Bipolar-EGM based dynamic ApEn maps were also constructed for the stable rotor case. An observation area, in which the rotor tip is anchored, was selected. The ApEn values of bipolar EGM were calculated using the optimized parameters and the 1000-point window. Shannon Entropy (ShEn) maps were also generated, through a 4-second window and bins of 0.01 mV, in accordance with the work of Ganesan et al [7]. The ShEn performance in unipolar EGM was also assessed. Results CFAE mapping of stable rotors during AF simulation applying ApEn with standard parameters An AF propagation pattern over the atria was generated in the 3D model of human atria, see the action potential propagation in S1 Video. During AF activity initiated by an ectopic focus applied into the right superior pulmonary vein, two stable rotors were observed in the simulation. One is located in the posterior wall of the left atrium, near the left pulmonary vein, named R1, and the other is located in the superior vena cava, named R2. Fig. 2A shows the action potential wavefronts delimited by contour lines from the interval between 1 s and 2 s of AF simulation. Rotors R1 and R2, and a block line located over the inferior right pulmonary vein, named B1, have been marked. 42835 EGM were calculated in the whole atrial surface of the 3D model, over a four-second window. For all EGM signals, the ApEn measurements were calculated using the standard parameters (m~2,r~0:1). The ApEn values were used to generate a color map over the anatomic structure of the atria in a 3D model. In this manner, a dynamic ApEn map was obtained and the frame corresponding to the time interval from 1 s to 2 s is depicted in Fig. 2B. Red color areas, corresponding to high ApEn values (0:3285+0:0202), include B1 and the coronary sinus (CS) and also R1 and R2. Optimization of ApEn parameters (mand r) The optimization procedure resulted in m~3,r~0:38, for N~1000 and m~3, r~0:30, for N~500.Fig. 3A shows the boxplots for ApEn(3,0:38,1000)and for ApEn(3,0:30,500), respectively, applied to DB-CZ-GE. In addition, the Spearman correlation coefficient rSbetween ApEn and the corresponding level of fractionation was calculated. CFAE mapping of stable rotors during AF simulation applying ApEn with optimized parameters A dynamic ApEn(3,0:38,1000)map was generated using unipolar EGM, and the frame corresponding to the time interval 1 s to 2 s is depicted in Fig. 2C, see S1 Video. The dynamic ApEn map reveals two areas of high ApEn values (0:3285+0:0202), corresponding to rotors R1 and R2. In addition, the third area with lower ApEn values (0:2724+0:0238) corresponds to B1, taking into account Dynamic ApEn Maps in Atrial Fibrillation PLOS ONE | DOI:10.1371/journal.pone.0114577 December 9, 2014 7/19 that passive activation regions have ApEn values lower than 0.1. A ShEn map was also generated and is shown in Fig. 2D. Red color areas, corresponding to high ShEn values (8:375+0:125), include small vicinities near to R1 and near to B1, along other zones, e.g. CS, the inferior wall of the left atria, the left and right appendage and the lateral wall near to the left appendage. The LAT method was applied as a reference method, see S2 Video.Fig. 3B shows isochronic maps from R1 and R2. The rotor tip is defined by the converging points of the colored waves. These waves represent the local activation. Green color indicates early activation points. Table 1 shows the spatial location of R1 and R2 found using the LAT method and the dynamic ApEn mapping method. The last column corresponds to the Euclidean distance between the spatial coordinates from the rotor tip, identified using both methods. The maximum distance is 1.66 mm. Unipolar EGM extracted from rotor sites R1 and R2, and near to block area B1, are shown in Fig. 3C. ApEn values are also presented. The EGM corresponding to rotor activity (top) have low voltage and irregular morphology. The EGM corresponding to the block line (below left) presents fractionation, but activation Fig. 2. Comparison between tools for rotor mapping. A. Action potential wavefront delimited by contour lines over the 3D Human Atria Model extracted from the interval between 1 s and 2 s of simulation. The spinning wavefronts around one point define stable rotors R1 and R2. Line block B1 can be seen at the right inferior pulmonary vein. B. Dynamic ApEn map calculated using standard parameters and unipolar EGM. C. Dynamic ApEn map calculated from the optimized parameters obtained in our work, using unipolar EGM. D. Shannon entropy map, using unipolar EGM. Note that map C shows better sensitivity for localizing rotor tips. E. Dynamic ApEn map calculated from optimized parameters using bipolar EGM with horizontal and vertical orientation. The region corresponds to the vicinity of rotor R1. F. ShEn map calculated using the bipolar EGM obtained from the vicinity of rotor R1. doi:10.1371/journal.pone.0114577.g002 Dynamic ApEn Maps in Atrial Fibrillation PLOS ONE | DOI:10.1371/journal.pone.0114577 December 9, 2014 8/19 patterns are visible and their amplitudes are similar to non-fractionated EGM (below right). The highest ApEn values correspond to R1 and R2. A circular area containing R1 was selected. Bipolar EGM were calculated using horizontal and vertical bipole orientation. 636 EGM were obtained for each orientation. Fig. 2E shows the dynamic ApEn(3,0:38,1000)maps for horizontal and vertical bipolar orientation, in the time interval between seconds 1 and 2. High ApEn values correspond with the tip of the rotor in both cases. Fig. 2F shows the ShEn maps. The vertical bipolar orientation map presents a region of Fig. 3. Localization of stable rotors. A: Results of the optimization procedure. Boxplots of ApEn normalized values using optimized parameters: ApEn(1000,3,0:38)(left) and ApEn(500,3,0:30)(right). The Spearman correlation coefficient calculated over DB-CZ-GE for each boxplot is shown. B: Activation isochronic maps corresponding to R1 (below) and R2 (top). The rotor tip is indicated where the colors converge. C: EGM generated by the model in the areas of stable rotors and the block for the time interval between 2 s and 3 s. EGM corresponding to the R1, R2, B1 and plane activation wavefront areas. D: Bipolar EGM corresponding to R1 and plane activation wavefront area. ApEn values for each EGM are shown. doi:10.1371/journal.pone.0114577.g003 Dynamic ApEn Maps in Atrial Fibrillation PLOS ONE | DOI:10.1371/journal.pone.0114577 December 9, 2014 9/19 genic mechanisms besides rotors, should be studied. In order to fully validate the results of our optimization procedure with DB-CZ-GE, although good performance has been achieved for rotor detection in the 3D model, future studies should involve collecting more AF EGM samples from other databases in order to achieve equally distributed fractionation levels. Additionally, real unipolar EGM must be included. In conclusion, we have provided evidence for postulating dynamic ApEn maps as a supporting tool in AF ablation procedures. ApEn calculation over atrial EGM signals can be used to build an electroanatomical map with continuous ApEn values represented in colors that can identify rotor tip locations without prespecifying thresholds. This property makes the method adaptable to specific electrophysiological cases. A combination of all this could help to improve ablation procedures. We suggest that dynamic ApEn color maps could become a tool for AF rotor mapping. The methodology proposed here needs to be validated by experimental models and by clinical studies to evaluate ablation procedures guided by dynamic ApEn maps. Supporting Information S1 Video. Stable rotors. Left: Simulation of an AF episode induced by six transitory ectopic beats applied in the ostium of the right pulmonary vein, sustained by multiple reentrant waves. Two rotors can be observed: in the posterior wall of the left atria posterior wall, and in the superior cava vein. Right: A dynamic ApEn map using optimized parameters. Red areas correspond to the tips of rotors R1 and R2. doi:10.1371/journal.pone.0114577.s001 (MP4) S2 Video. Isochrone map. Isochrone maps for rotors R1 and R2 for the time interval between 1500 ms and 2000 ms. doi:10.1371/journal.pone.0114577.s002 (MP4) S3 Video. Meandering rotor. Left: Simulation of an AF episode induced by six transitory ectopic beats applied in the posterior wall of the left atrium near to the right pulmonary veins, sustained by multiple reentrant waves. One meandering rotor can be observed in the posterior wall of the left atria. Right: A dynamic ApEn map using optimized parameters. Note that, when a plane activation wavefront is present within the observation area, the dynamic ApEn map shows low values (green). Red zones appear when the rotor tip is within the observation area (e.g. the time interval between 2500 ms and 3000 ms). doi:10.1371/journal.pone.0114577.s003 (MP4) Author Contributions Conceived and designed the experiments: JPU AO CT JS JB. Performed the experiments: JPU AO CT VK DN JB. Analyzed the data: JPU AO CT VK DN AL JB. 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