Origin and Characteristics of High Shannon Entropy at the Pivot of Locally Stable Rotors: Insights from Computational Simulation

Background

Rotors are postulated to maintain cardiac fibrillation. Despite the importance of bipolar electrograms in clinical electrophysiology, few data exist on the properties of bipolar electrograms at rotor sites. The pivot of a spiral wave is characterized by relative uncertainty of wavefront propagation direction compared to the periphery. The bipolar electrograms used in electrophysiology recording encode information on both direction and timing of approaching wavefronts.

Objective

To test the hypothesis that bipolar electrograms from the pivot of rotors have higher Shannon entropy (ShEn) than electrograms recorded at the periphery due to the spatial dynamics of spiral waves.

Methods and Results

We studied spiral wave propagation in 2-dimensional sheets constructed using a simple cell automaton (FitzHugh-Nagumo), atrial (Courtemanche-Ramirez-Nattel) and ventricular (Luo-Rudy) myocyte cell models and in a geometric model spiral wave. In each system, bipolar electrogram recordings were simulated, and Shannon entropy maps constructed as a measure of electrogram information content. ShEn was consistently highest in the pivoting region associated with the phase singularity of the spiral wave. This property was consistently preserved across; (i) variation of model system (ii) alterations in bipolar electrode spacing, (iii) alternative bipolar electrode orientation (iv) bipolar electrogram filtering and (v) in the presence of rotor meander. Directional activation plots demonstrated that the origin of high ShEn at the pivot was the directional diversity of wavefront propagation observed in this location.

Conclusions

The pivot of the rotor is consistently associated with high Shannon entropy of bipolar electrograms despite differences in action potential model, bipolar electrode spacing, signal filtering and rotor meander. Maximum ShEn is co-located with the pivot for rotors observed in the bipolar electrogram recording mode, and may be an intrinsic property of spiral wave dynamic behaviour.     

High-density activation map of atrial tachycardia within left atrial appendage

Identification of the critical isthmus of the reentrant tachycardia is essential to maximize the effect of catheter ablation (CA) and to minimize the myocardial injury of CA. An 81-year-old woman presented recurrent palpitations after CA of atrial fibrillation (AF) and atrial tachycardia (AT). She had moderate aortic valve stenosis and coronary artery disease. She had received a pulmonary vein isolation, left atrial (LA) posterior wall isolation, and LA anterior linear ablation for atrial fibrillation 1 year prior. At the start of the procedure, she was in sinus rhythm. Atrial burst pacing induced an AT (230msec). High-density mapping revealed a figure-of-eight activation pattern within the LA appendage (LAA), accounting for 99% of the tachycardia cycle length. The critical isthmus was identified at the mid LAA and the local electrogram of the critical isthmus was not fractionated. A single radiofrequency application at the critical isthmus of the AT, terminated the AT. She was free from any ATs for 28 months.Radiofrequency ablation of the localized reentrant AT was usually performed targeting long fractionated electrograms. In our case, the local electrogram at the critical isthmus was not fragmented compared with the LAA distal part. Long fractionated electrograms were recorded at a more distal part of the LAA than the common isthmus and we could avoid the potential risk of a perforation. A recent developed 3-dimensional electro-anatomical mapping system can identify the critical isthmus and allow us to select a new therapeutic strategy for a critical isthmus ablation of an AT within the LAA.     

Characterization of fibrillatory rhythms by ensemble vector directional analysis

Recent studies have demonstrated that fibrillatory rhythms are not random phenomena but have definable patterns. However, standard mapping techniques may have limitations in their ability to identify the organization of fibrillation. The purpose of this study was to develop and apply a method, "ensemble vector mapping," for characterizing the spatiotemporal organization of fibrillation. Ventricular fibrillation was induced by burst pacing in normal mongrel dogs. In a separate protocol, atrial fibrillation was induced by epicardial aconitine application. Epicardial electrograms were recorded from a 112-electrode plaque array using a computerized mapping system. Vectors were created by summing orthogonal bipolar electrograms. The magnitude of the vectors was transformed using a logarithmic function, integrated over time, and normalized for local electrogram amplitude to produce an "ensemble vector" index whose magnitude is high when beat-to-beat activation direction is consistent and low when activation direction is variable. The mean index was 137 +/- 36 mV/s during ventricular pacing at a cycle length of 300 ms but only 39 +/- 23 mV/s during ventricular fibrillation (P < 0.001). The ensemble vector index was also lower during atrial fibrillation (60 +/- 54 mV/s) than during atrial pacing (115 +/- 27 mV/s, P < 0.01 vs. atrial fibrillation) but not as low as during ventricular fibrillation (P < 0.05, atrial vs. ventricular fibrillation). The index was also capable of distinguishing atrial tachycardia from atrial fibrillation. Ensemble vector mapping produces an objective assessment of the consistency of myocardial activation during fibrillation. The consistency of activation direction differs in different models of fibrillation and is higher during atrial than ventricular fibrillation. This technique has the potential to rapidly characterize repetitive activation patterns in fibrillatory rhythms and may help distinguish among different characteristics of fibrillatory rhythms.     

A Three-Dimensional Human Atrial Model with Fiber Orientation. Electrograms and Arrhythmic Activation Patterns Relationship

The most common sustained cardiac arrhythmias in humans are atrial tachyarrhythmias, mainly atrial fibrillation. Areas of complex fractionated atrial electrograms and high dominant frequency have been proposed as critical regions for maintaining atrial fibrillation; however, there is a paucity of data on the relationship between the characteristics of electrograms and the propagation pattern underlying them. In this study, a realistic 3D computer model of the human atria has been developed to investigate this relationship. The model includes a realistic geometry with fiber orientation, anisotropic conductivity and electrophysiological heterogeneity. We simulated different tachyarrhythmic episodes applying both transient and continuous ectopic activity. Electrograms and their dominant frequency and organization index values were calculated over the entire atrial surface. Our simulations show electrograms with simple potentials, with little or no cycle length variations, narrow frequency peaks and high organization index values during stable and regular activity as the observed in atrial flutter, atrial tachycardia (except in areas of conduction block) and in areas closer to ectopic activity during focal atrial fibrillation. By contrast, cycle length variations and polymorphic electrograms with single, double and fragmented potentials were observed in areas of irregular and unstable activity during atrial fibrillation episodes. Our results also show: 1) electrograms with potentials without negative deflection related to spiral or curved wavefronts that pass over the recording point and move away, 2) potentials with a much greater proportion of positive deflection than negative in areas of wave collisions, 3) double potentials related with wave fragmentations or blocking lines and 4) fragmented electrograms associated with pivot points. Our model is the first human atrial model with realistic fiber orientation used to investigate the relationship between different atrial arrhythmic propagation patterns and the electrograms observed at more than 43000 points on the atrial surface.     

A case of successful radiofrequency catheter ablation for atrial tachycardia originating from the inferior vena cava using high-resolution mapping

A 60-year-old man presented with sustained supraventricular tachycardia. Atrial tachycardia (AT), with the earliest atrial activation (EAA) occurring at the ostium of the coronary sinus, was reproducibly induced.Three-dimensional electroanatomical mapping (3DEAM) using a 3.5-mm distal electrode tip linear catheter (Thermocool) and radiofrequency energy (RF) was performed at the fractionated atrial electrogram site. It preceded at 30 ms to the EAA but did not terminate AT. Further 3DEAM using a multielectrode mapping catheter (Pentaray) demonstrated a centrifugal propagation pattern at the boundary zone between the right atrium and inferior vena cava. RF application here terminated AT, which then became non-inducible.     

Ventricular fibrillation in myopathic human hearts: mechanistic insights from in vivo global endocardial and epicardial mapping

Ventricular fibrillation (VF) is an important cause of sudden cardiac death and cardiovascular mortality in patients with cardiomyopathy. Although it was generally believed that chaotic reentrant wavefronts underlie VF in humans, there is emerging evidence of spatiotemporal organization during early VF. The mechanism of this organization of electrical activity in early VF is unknown in myopathic hearts. We studied early VF in vivo, intraoperatively in five cardiomyopathic patients. Simultaneous electrograms were obtained from the epicardium and endocardium in left ventricular cardiomyopathy and from the endocardium in right ventricular myopathy. The Hilbert transform was used to derive the phase of the electrograms. Rotors were identified by isolating phase singularity points. Rotors were present in all of the myopathic hearts studied during VF and cumulatively lasted a mean of 3.2 +/- 2.0 s of the 7.0 +/- 4.0 s of the VF segments analyzed. For each surface mapped, 3.6 +/- 2.9 rotors were identified for the duration mapped. The average number of cycles completed by these rotors was 4.9 +/- 4.9. The longest rotor lasted 10.2 +/- 6.2 rotations and lasted 2.0 +/- 1.2 s. The rotors on the endocardium had a cycle length of 192 +/- 33 ms compared with 220 +/- 15 ms on the epicardium (P=0.08). There is centrifugal activation of electrical activity from these rotors, and they give rise to domains that activate at faster rates with evidence of conduction block at the border with slower domains. These rotors frequently localized to border regions of myocardium with bipolar electrogram amplitude of <0.5 mV. The organization of electrical activity during early VF in myopathic human hearts is characterized by wavefronts emanating from a few rotors.     

Automated detection and mapping of electrical activation when electrogram morphology is complex

BackgroundMapping of cardiac electrical activity can be difficult when electrogram morphology is complex. Complex morphology (multiple and changing deflections) causes activation maps to vary when constructed by different analysts, particularly at areas with spatially varying conduction pattern. An algorithm was developed to automatically detect electrogram activation time which is robust to complex morphology.MethodElectrograms, many of which were complex, were collected from 320 canine epicardial border zone sites in five experiments. A library of electrogram activation times were manually marked a priori by two expert analysts. Then an algorithm which combined correlation and error functions was used to compare each input electrogram to library electrogram patterns. The closest match of input to library electrogram was used to estimate activation time. Once activation times at 320 sites were determined, activation maps were automatically constructed on a computerized grid. The algorithm was validated by comparison with activation times determined by the analysts.ResultsThe mean difference between manual and automated marking of activation time in electrograms acquired during reentrant ventricular tachycardia was 2.1 ± 3.9 ms. The mean sensitivity and positive predictive value were 95.9% and 83.8% respectively. The computer-automated marking process was completed within a few seconds and was robust to fractionated electrograms. Measurement error was mostly attributable to 60 Hz noise, which can be rectified with filtering.ConclusionsThe automated algorithm is useful for rapid and accurate automatic marking of multichannel electrograms, some of which may be fractionated, as well as for real-time display of activation maps in clinical electrophysiology or research studies.     

Lifetimes of epicardial rotors in panoramic optical maps of fibrillating swine ventricles

During ventricular fibrillation (VF), electrical activation waves are fragmented, and the heart cannot contract in synchrony. It has been proposed that VF waves emanate from stable periodic sources (often called "mother rotors"). The objective of the present study was to determine if stable rotors are consistently present on the epicardial surface of hearts comparable in size to human hearts. Using new optical mapping technology, we imaged VF from nearly the entire ventricular surface of six isolated swine hearts. Using newly developed pattern analysis algorithms, we identified and tracked VF wave fronts and phase singularities (PS; the pivot point of a reentrant wave front). We introduce the notion of a compound rotor in which the rotor's central PS can change and describe an algorithm for automatically identifying such patterns. This prevents rotor lifetimes from being inappropriately abbreviated by wave front fragmentation and collision events near the PS. We found that stable epicardial rotors were not consistently present during VF: only 1 of 17 VF episodes contained a compound rotor that lasted for the entire mapped interval of 4 s. However, shorter-lived rotors were common; 12.2 (SD 3.3) compound rotors with lifetime >200 ms were visible on the epicardium at any given instant. We conclude that epicardial mother rotors do not drive VF in this experimental model; if mother rotors do exist, they are intramural or septal. This paucity of persistent rotors suggests that individual rotors will eventually terminate by themselves and therefore that the continual formation of new rotors is critical for VF maintenance.     

Ionic determinants of functional reentry in a 2-D model of human atrial cells during simulated chronic atrial fibrillation

Recent studies suggest that atrial fibrillation (AF) is maintained by fibrillatory conduction emanating from a small number of high-frequency reentrant sources (rotors). Our goal was to study the ionic correlates of a rotor during simulated chronic AF conditions. We utilized a two-dimensional (2-D), homogeneous, isotropic sheet (5 x 5 cm(2)) of human atrial cells to create a chronic AF substrate, which was able to sustain a stable rotor (dominant frequency approximately 5.7 Hz, rosette-like tip meander approximately 2.6 cm). Doubling the magnitude of the inward rectifier K(+) current (I(K1)) increased rotor frequency ( approximately 8.4 Hz), and reduced tip meander (approximately 1.7 cm). This rotor stabilization was due to a shortening of the action potential duration and an enhanced cardiac excitability. The latter was caused by a hyperpolarization of the diastolic membrane potential, which increased the availability of the Na(+) current (I(Na)). The rotor was terminated by reducing the maximum conductance (by 90%) of the atrial-specific ultrarapid delayed rectifier K(+) current (I(Kur)), or the transient outward K(+) current (I(to)), but not the fast or slow delayed rectifier K(+) currents (I(Kr)/I(Ks)). Importantly, blockade of I(Kur)/I(to) prolonged the atrial action potential at the plateau, but not at the terminal phase of repolarization, which led to random tip meander and wavebreak, resulting in rotor termination. Altering the rectification profile of I(K1) also slowed down or abolished reentrant activity. In combination, these simulation results provide novel insights into the ionic bases of a sustained rotor in a 2-D chronic AF substrate.     

Detection of focal source and arrhythmogenic substrate from body surface potentials to guide atrial fibrillation ablation

Focal sources (FS) are believed to be important triggers and a perpetuation mechanism for paroxysmal atrial fibrillation (AF). Detecting FS and determining AF sustainability in atrial tissue can help guide ablation targeting. We hypothesized that sustained rotors during FS-driven episodes indicate an arrhythmogenic substrate for sustained AF, and that non-invasive electrical recordings, like electrocardiograms (ECGs) or body surface potential maps (BSPMs), could be used to detect FS and AF sustainability. Computer simulations were performed on five bi-atrial geometries. FS were induced by pacing at cycle lengths of 120–270 ms from 32 atrial sites and four pulmonary veins. Self-sustained reentrant activities were also initiated around the same 32 atrial sites with inexcitable cores of radii of 0, 0.5 and 1 cm. FS fired for two seconds and then AF inducibility was tested by whether activation was sustained for another second. ECGs and BSPMs were simulated. Equivalent atrial sources were extracted using second-order blind source separation, and their cycle length, periodicity and contribution, were used as features for random forest classifiers. Longer rotor duration during FS-driven episodes indicates higher AF inducibility (area under ROC curve = 0.83). Our method had accuracy of 90.6±1.0% and 90.6±0.6% in detecting FS presence, and 93.1±0.6% and 94.2±1.2% in identifying AF sustainability, and 80.0±6.6% and 61.0±5.2% in determining the atrium of the focal site, from BSPMs and ECGs of five atria. The detection of FS presence and AF sustainability were insensitive to vest placement (±9.6%). On pre-operative BSPMs of 52 paroxysmal AF patients, patients classified with initiator-type FS on a single atrium resulted in improved two-to-three-year AF-free likelihoods (p-value < 0.01, logrank tests). Detection of FS and arrhythmogenic substrate can be performed from ECGs and BSPMs, enabling non-invasive mapping towards mechanism-targeted AF treatment, and malignant ectopic beat detection with likely AF progression.     

Mother rotor anchoring in branching tissue with heterogeneous membrane properties.

Abstract Current understanding of atrial fibrillation is based on the co-existence of multiple re-entrant waves propagating randomly throughout the tissue. However, recent experimental results indicate that in many cases one or a small number of periodic, high-frequency re-entrant sources (mother rotors) can drive the arrhythmia. Owing to the high activation rate, mother rotors seem to be located in regions of shortened action potential duration. In this study a computer model of cardiac propagation was applied to investigate mechanisms leading to the formation and maintenance of such mother rotors. For this purpose, a region of short action potential duration was generated by varying the acetylcholine concentration across the tissue. A mother rotor initiated in the center of this region drifts away, and the activation terminates. If an additional heterogeneity such as a bundle is included into the model, a further drift mechanism directed to the bundle is observed and the rotor can be stabilized. Therefore, bundle insertions may play an important role in the maintenance of mother rotors. The influence of the driving rotor on the activation pattern was studied in a three-dimensional model of rectangular shape and a monolayer model of anatomically correct atrial geometry.     

Non-linear coupling of atrial activation processes during atrial fibrillation in humans

The activation patterns underlying the electrical activity of the heart during atrial fibrillation (AF) are not entirely random. The aim of this study was to assess the local organization of the activation processes during AF by estimating the non-linear coupling between activation sequences (ASs) in two atrial sites. To quantitatively estimate the degree of non-linear coupling we extracted two indices based on a multivariate embedding procedure and on the estimation of the correlation dimension (CD) and correlation entropy (CE), termed independence of complexity and of independence of predictability, respectively. We analysed AS in two atrial sites in 30 informed subjects during chronic AF of type I, II and III (Wells' classification), ten 6-s-long episodes of each type. Surrogates were used to reject the hypothesis that the time series were generated by linear stochastic dynamics. We estimated CD and CE according to the coarse-grained approach, which leads to a fixed high value for the embedding dimension in all the analysed ASs, and a typical value for the distance between the two ASs in the phase space. Various degrees of organization, ranging from completely synchronized to fully de-coupled signals, were observed: significant degrees of non-linear coupling were found in segments belonging in types I and II AF, whereas type III electrograms always turned out to be weakly coupled. This finding links the morphology of single electrograms to the synchronization between pairs of closely spaced electrograms. Our bivariate approach suggests that the measurement of organization during AF should be based on the estimation of the non-linear coupling between two sites. This approach appears to be more reliable and sensitive than non-linear analysis of single electrograms or linear analysis of their coupling.     

Assessment of spatial organization in the atria during paroxysmal atrial fibrillation and adrenergic stimulation.

Non-linear parameters were computed to assess the extent of spatial organization in the atria in terms of coupling/synchronization between electrograms recorded in different atrial sites. Recordings of 9 patients suffering from paroxysmal atrial fibrillation were tested during four clinical experimental conditions: sinus rhythm and atrial fibrillation, both before and after isoproterenol infusion, a drug mimicking adrenergic activation. Two non-linear metrics were investigated: an index of non-linear association (NLA) and a synchronization (S) index based on the cross-conditional entropy. Results evidence the presence of reduced coupling after drug infusion in both sinus rhythm and atrial fibrillation. Moreover, passing from the NLA to the S index, the capability of the parameter to capture the subtle changes due to isoproterenol administration increased.     

What are the post-ablation insular residual electrograms in the posterior left pulmonary veins electrically connected to?

A 67-year-old man underwent a third ablation procedure for a recurrent atrial tachycardia (AT) after an extensive pulmonary vein (PV) isolation, linear ablation along the left atrial (LA) roof and posterolateral mitral isthmus (MI), and defragmentation of persistent atrial fibrillation and an induced perimitral AT. High-resolution mapping during the clinical AT using the Rhythmia system (Boston Scientific) suggested that the AT was a ridge-related reentrant AT and exhibited a reconnection of the left PVs (LPVs). The residual electrograms in the posterior LPVs were surrounded by endocardial scar, which was like an island consisting of residual LPV electrograms. Retrograde venography of the vein of Marshall (VOM) demonstrated that the VOM reached the posterior left superior PV through the ridge between the LA appendage and left inferior PV and then the LPV carina. An ethanol infusion into the VOM resulted in a simultaneous AT termination and complete electrical isolation of the LPVs, that is, the disappearance of the residual LPV electrograms. The insular residual LPV electrograms in the present case did not appear to be endocardially connected to the LA, because the LPV electrograms were surrounded by endocardial scar and there was a large time gap between the earliest activation in the posterior LPVs and activation in the surrounding area. The VOM course on the venography and elimination of the residual LPV electrograms with an ethanol infusion into the VOM suggested that the insular residual LPV electrograms were electrically connected to the posterolateral LA via the VOM and its branches.     

Transitions among atrial fibrillation, atrial flutter, and sinus rhythm during procainamide infusion and vagal stimulation in dogs with sterile pericarditis

The mechanism of atrial flutter and fibrillation induced by rapid pacing in 22 dogs with 3-day-old sterile pericarditis was investigated by computerized epicardial mapping of atrial activation before and after administration of agents known to modify atrial electrophysiologic properties: procainamide, isoproterenol, and electrical stimulation of the vagosympathetic trunks. Before the administration of any of these agents, a total of 30 episodes of sustained atrial flutter (greater than 1 min duration, monomorphic; regular cycle length, 127 +/- 12 ms, mean +/- SD) was induced in 15 out of 22 dogs and 9 episodes of unstable atrial flutter (duration, less than 1 min; cycle length, 129 +/- 34 ms; monomorphic, alternating with fibrillation) were induced in the remaining 7 preparations. In the latter, administration of procainamide transformed unstable atrial flutter and atrial fibrillation to sustained atrial flutter (cycle length, 142 +/- 33 ms; n = 9 episodes). During control atrial flutter, atrial maps displayed circus movement of excitation in the right atrial free wall with faster conduction parallel to the orientation of intra-atrial myocardial bundles. Vagal stimulation changed atrial flutter to atrial fibrillation in 32 of 73 trials; this was associated with acceleration of conduction in the lower right atrium, leading to fragmentation of the major wave front. Isoproterenol produced a 6-25% increase of the atrial rate in 6 out of 14 trials of atrial flutter and induced atrial fibrillation in 4. After procainamide, the reentrant pathway was lengthened and conduction was slowed further in the right atrium. Maps obtained during unstable atrial flutter showed incomplete circuits involving the right atrium. Following procainamide infusion, the area of functional dissociation or block was enlarged and a stable circus movement pattern, which was similar to the pattern seen in control atrial flutter, was established in the right atrium. We conclude that (1) the transitions among atrial fibrillation, atrial flutter, and sinus rhythm occur between different functional states of the same circus movement substratum primarily located in the lower right atrial free wall, and (2) the anisotropic conduction properties of the right atrium may contribute to these reentrant arrhythmias and may be potentiated by acute pericarditis.     

Automatic mode switching in atrial fibrillation

Automatic mode switching (AMS) algorithms were designed to prevent tracking of atrial tachyarrhythmias (ATA) or other rapidly occurring signals sensed by atrial channels, thereby reducing the adverse hemodynamic and symptomatic consequences of a rapid ventricular response. The inclusion of an AMS function in most dual chamber pacemaker now provides optimal management of atrial arrhythmias and allows the benefit of atrioventricular synchrony to be extended to a population with existing atrial fibrillation. Appropriate AMS depends on several parameters: a) the programmed parameters; b) the characteristics of the arrhythmia; c) the characteristics of the AMS algorithm. Three qualifying aspects constitute an AMS algorithm: onset, AMS response, and resynchronization. Since AMS programs also provide data on the time of onset and duration of AMS episodes, AMS data may be interpreted as a surrogate marker of ATAs recurrence. Recently, stored electrograms corresponding to episodes of ATAs have been introduced, thus clarifying the accuracy of AMS in detecting ATAs Clinically this information may be used to assess the efficacy of an antiarrhythmic intervention or the risk of thromboembolic events, and it may serve as a valuable research tool for evaluating the natural history and burden of ATAs.     

Attraction of Rotors to the Pulmonary Veins in Paroxysmal Atrial Fibrillation: A Modeling Study

Maintenance of paroxysmal atrial fibrillation (AF) by fast rotors in the left atrium (LA) or at the pulmonary veins (PVs) is not fully understood. To gain insight into this dynamic and complex process, we studied the role of the heterogeneous distribution of transmembrane currents in the PVs and LA junction (PV-LAJ) in the localization of rotors in the PVs. We also investigated whether simple pacing protocols could be used to predict rotor drift in the PV-LAJ. Experimentally observed heterogeneities in I_K1, I_Ks, I_Kr, I_to, and I_CaL in the PV-LAJ were incorporated into two- and pseudo three-dimensional models of Courtemanche-Ramirez-Nattel-Kneller human atrial kinetics to simulate various conditions and investigate rotor drifting mechanisms. Spatial gradients in the currents resulted in shorter action potential duration, minimum diastolic potential that was less negative, and slower upstroke and conduction velocity for rotors in the PV region than in the LA. Rotors under such conditions drifted toward the PV and stabilized at the shortest action potential duration and less-excitable region, consistent with drift direction under intercellular coupling heterogeneities and regardless of the geometrical constraint in the PVs. Simulations with various I_K1 gradient conditions and current-voltage relationships substantiated its major role in the rotor drift. In our 1:1 pacing protocol, we found that among various action potential properties, only the minimum diastolic potential gradient was a rate-independent predictor of rotor drift direction. Consistent with experimental and clinical AF studies, simulations in an electrophysiologically heterogeneous model of the PV-LAJ showed rotor attraction toward the PV. Our simulations suggest that I_K1 heterogeneity is dominant compared to other currents in determining the drift direction through its impact on the excitability gradient. These results provide a believed novel framework for understanding the complex dynamics of rotors in AF.     

Substrate size as a determinant of fibrillatory activity maintenance in a mathematical model of canine atrium

Tissue size has been considered an important determinant of atrial fibrillation (AF), but recent work has questioned the critical size hypothesis. Here, we use a previously developed mathematical model of the two-dimensional canine atrium with realistic action potential, ionic, and conduction properties to address substrate size effects on the maintenance of fibrillatory activity. Cholinergic AF was simulated at different acetylcholine (ACh) concentrations ([ACh]) and distributions, with substrate area varied 11.1-fold. Automated phase singularity detection was used to facilitate the analysis of arrhythmic activity. The duration of activity induced by a single extrastimulus increased with increasing substrate dimensions. Two general mechanisms underlying activity were observed and were differentially affected by substrate size. For large mean [ACh], single primary rotors anchored in low-[ACh] zones maintained activity and substrate dimensions were not critical. At lower mean [ACh], extensive spiral wave meander prevented the emergence of single stable rotors. Prolonged activity was favored when substrate size permitted a sufficiently large number of simultaneous longer-lasting rotors that extinction of all was unlikely. Thus either single dominant rotor or multiple reentrant spiral generator mechanisms could maintain fibrillatory activity in this model and were differentially dependent on substrate size. These results speak to recent debates about the role in AF of single driver rotors versus multiple reentrant circuit mechanisms by suggesting that either may maintain fibrillatory atrial activity depending on atrial size and electrophysiological properties.     

Signal processing methods for information enhancement in atrial fibrillation: Spectral analysis and non-linear parameters

Recently, the research efforts in the context of electrocardiographical recording during atrial fibrillation (AF) has been directed to broaden the understandings on the electrophysiological and structural remodelling occurring during the arrhythmia and on characterizing the different types of AF. Following this line, both surface ECG and endocardial electrograms have been thoroughly studied and a series of linear and non-linear parameters were computed either directly on the electrograms or on the derived activation series.

In this paper, we reviewed some signal processing methods used to characterize surface ECG and endocardial electrograms during AF, focusing on spectral and non-linear analysis. In particular, parametric and non-parametric methods for spectral analysis of the residual ECG, i.e. atrial waves obtained from surface ECG after removing ventricular activity, and endocardial recordings are described. The different purposes of spectral analysis (exploring autonomic functions, analysis of spontaneous AF behaviour and predicting therapeutic effects) are illustrated with some examples. In addition, we described some more recent non-linear methods applied to AF, assessing the organization of atrial signals as well as ventricular response in AF. In particular, methods derived from embedding time series and based on entropy computation are illustrated and exemplified.     

First Case of Automatic His Potential Detection With a Novel Ultra High-density Electroanatomical Mapping System for AV Nodal Ablation

A 74-year old was considered for atrioventricular (AV) nodal ablation in view of atrial fibrillation (AF) with poorly controlled ventricular rate despite being on amiodarone. Targeted AV nodal ablation was successfully performed after identifying the target site for ablation by reviewing an ultra high-density map of the His region produced by automatic electrogram annotation.Key words: His bundle, atrioventricular node, cardiac mapping, catheter ablation