Number Of Phase Singularities Research Articles

Chaos control in cardiac dynamics: terminating chaotic states with local minima pacing.

Current treatments of cardiac arrhythmias like ventricular fibrillation involve the application of a high-energy electric shock, that induces significant electrical currents in the myocardium and therefore involves severe side effects like possible tissue damage and post-traumatic stress. Using numerical simulations on four different models of 2D excitable media, this study demonstrates that low energy pulses applied shortly after local minima in the mean value of the transmembrane potential provide high success rates. We evaluate the performance of this approach for ten initial conditions of each model, ten spatially different stimuli, and different shock amplitudes. The investigated models of 2D excitable media cover a broad range of dominant frequencies and number of phase singularities, which demonstrates, that our findings are not limited to a specific kind of model or parameterization of it. Thus, we propose a method that incorporates the dynamics of the underlying system, even during pacing, and solely relies on a scalar observable, which is easily measurable in numerical simulations.

Abstract 14702: Roles of Atrial Mass Reduction and Gaps on the Anti-Atrial Fibrillatory Effects of Pulmonary Vein Isolation: A Computational Modeling Study

Background: Although pulmonary vein isolation (PVI) is the basis of atrial fibrillation (AF) catheter ablation (AFCA), the conditional changes of an anti-AF effect and the wave-dynamic mechanism are poorly understood. Therefore, we compared the effects of PVI based on the ablation circumference, width, and number or locations of gaps with or without amiodarone at the same condition in realistic computational modeling of human AF. Hypothesis: An anatomical level of PVI and characteristics of the PVI gap would affect the anti-AF effects of the AFCA. Methods: We included 50 patients (76.0% persistent AF) who underwent AFCA. Realistic AF modeling reflecting the computed tomography (CT) and the electroanatomical map was performed on each patient. We compared the AF defragmentation rate (DeFR; change to atrial tachycardia (AT) or termination), termination rate (TnR), and changes in the dominant frequency (DF) and the number of phase singularities (PSs) based on the PVI level (antral vs. ostial), PVI width (single vs. 3х width), number and location of 2-mm PVI gaps with or without amiodarone (10mM). We randomly assigned the number and location of the PVI gaps to the AF models. Results: The antral PVI had a significantly higher DeFR (p for trend <0.001) and TnR (p for trend <0.001) than the ostial PVI, PVI gaps, or baseline AF. However, there was no difference depending on PVI width. Among the PVI gaps, the DeFR (p for trend<0.001) decreased as the gap number increased. Additional amiodarone increased DeFR (p=0.003) and TnR (p=0.034) and reduced DF (p<0.001) and the number of PSs (p<0.001) with PVI-gap, especially with a single PVI-gap. Conclusions: In this realistic computational modeling study with integrated patients’ atrial anatomy and electrophysiology, the atrial mass reduction depending on the anatomical PVI level, number of PVI gaps, and additional antiarrhythmic drug significantly affected the AF maintenance mechanisms.

PO-02-147 THE ANTIARRHYTHMIC EFFECTS OF MIRABEGRON IN ISOLATED RABBIT HEARTS

β-3 adrenoceptor (AR) activation opposes the effects of β-1 and β-2 AR activation and rescues the effects of excessive catecholamines. BRL37344 (beta3-AR agonist) is antiarrhythmic in canine models. Mirabegron is a β-3 agonist approved by the FDA for the treatment of overactive bladder. A previous study showed that isoproterenol activates the small conductance Ca-activated K current more in female than in male ventricles. To test the hypothesis that mirabegron reduces the proarrhythmic effects of isoproterenol more effectively in female than in male ventricles. We performed optical mapping studies in 6 male and 6 female Langendorff-perfused rabbit hearts first at baseline, then sequentially after isoproterenol (ISO, 100 nM), mirabegron (1000 nM), apamin (100 nM) administration and washout in study 1. In study 2 (5 males and 5 females), we studied at baseline, then after adding mirabegron (250 nM, 500 nM, 750 nM, and 1000 nM), followed by isoproterenol and washout. All hearts underwent 10 attempts of ventricular fibrillation (VF) induction with a ventricular burst (20 Hz for 10 s) pacing at each stage of the experiment. The number of phase singularities (PSs) was determined per episode of VF (PSs/VF). In study 1, mirabegron reduced the VF inducibility (number of VF after 10 attempts) during isoproterenol infusion by an average of -2.75 (p = 0.026). When VF was induced, the PSs/VF increased by 2.4±2.1 in males and 6.6±3.3 in females (p=0.03, Figure A). Mirabegron significantly reduced the PSs/VF in both sexes and eliminated the sex differences. Apamin given after mirabegron in the presence of isoproterenol did not further change PSs/VF (p=0.63) (Figure B). The conduction velocity (CV), estimated by the inverse of the total activation time (1/s), was 16±2.7 for all hearts at baseline and 35±10 after ISO, respectively (p=0.0006). ISO did not increase CV differentially by sex (p=0.93). Mirabegron reduced the CV by an average of 15.6 (from 34±11.4 to 18±3.9) in females, which was significantly (p=0.043) more than 5.1 (from 35±8.7 to 31±9.3) in males. Figure C shows a summary of study 2. Mirabegron significantly reduced PSs/VF at 750 nM in female (p=0.015 vs. baseline) and at 1000 nM in male (p=0.033 vs. baseline) hearts. The addition of ISO did not increase PSs/VF. During ISO infusion, mirabegron reduces the CV and the PSs/VF more in females than males during VF. These data suggest that the β3 agonist is a sex-specific antiarrhythmic agent.

Sodium-Glucose cotransporter 2 inhibitor empagliflozin decreases ventricular arrhythmia susceptibility by alleviating electrophysiological remodeling post-myocardial-infarction in mice.

Background: Recent clinical trials indicate that sodium–glucose cotransporter 2 (SGLT2) inhibitors improve cardiovascular outcomes in myocardial infarction (MI) patients, but the underlying mechanisms remain unknown. As arrhythmia often occurs during myocardial infarction, it is the main cause of death. Objective: The purpose of this study was to investigate the influence of empagliflozin (EMPA), an SGLT2 inhibitor, on cardiac electrophysiological remodeling and arrhythmia susceptibility of myocardial infarction mice. Methods: ECG was obtained from mice 1 week after MI to determine the QT interval. In an electrophysiological study and optical mapping was performed to evaluate the function of EMPA and underlying mechanisms of post-myocardial-infarction in mice. Results: EMPA treatment significantly reduced the QT interval of MI mice (MI + EMPA 50.24 ms vs. MI 64.68 ms). The membrane potential and intracellular Ca [Cai] were mapped from 13 MI hearts and five normal hearts using an optical mapping technique. A dynamic pacing protocol was used to determine action potential duration and [Cai] at baseline and after EMPA (10 umol/L) infusion. EMPA perfusion did not change the APD80 and CaT80 in normal ventricles while shortening them in an infarct zone, bordering zone, and remote zone of MI hearts at 200 ms, 150 ms, 120 ms, and 100 ms pacing cycle length. The conduction velocity of infarcted ventricles was 0.278 m/s and 0.533 m/s in normal ventricles at baseline (p < 0.05). After EMPA administration, the conduction velocity of infarcted ventricles increased to 0.363 m/s, whereas no significant changes were observed in normal ventricles. The action potential rise time, CaT rise time, and CaT tau time were improved after EMPA perfusion in infarcted ventricles, whereas no significant changes were observed in normal ventricles. EMPA decreases early afterdepolarizations premature ventricular beats, and ventricular fibrillation (VF) in infarcted ventricles. The number of phase singularities (baseline versus EMPA, 6.26 versus 3.25), dominant frequency (20.52 versus 10.675 Hz), and ventricular fibrillation duration (1.072 versus 0.361 s) during ventricular fibrillation in infarcted ventricles were all significantly decreased by EMPA. Conclusion: Treatment with EMPA improved post-MI electrophysiological remodeling and decreased substrate for VF of MI mice. The inhibitors of SGLT2 may be a new class of agents for the prevention of ventricle arrhythmia after chronic MI.

Predicting the duration of chaotic transients in excitable media

The spatiotemporal dynamics of excitable media may exhibit chaotic transients. We investigate this transient chaos in the 2D Fenton–Karma model describing the propagation of electrical excitation waves in cardiac tissue and compute the average duration of chaotic transients in dependence on model parameter values. Furthermore, other characteristics like the dominant frequency, the size of the excitable gap, pseudo ECGs, the number of phase singularities and parameters characterizing the action potential duration restitution curve are determined and it is shown that these quantities can be used to predict the average transient time using polynomial regression.

Propagation-invariant laser beams with an array of phase singularities

In this work, we investigate multivortex beams with an infinite topological charge. Such optical vortices contain an array of an infinite, but countable, number of phase singularities (isolated intensity nulls), which typically have the unitary topological charge and are located either uniformly (or not uniformly) on a straight line (or on several crossing straight lines) in the beam transverse cross section. Such optical vortices are form invariant and their transverse intensity distribution is conserved on propagation, changing only in scale and rotation. The orbital angular momentum of such optical vortices is finite, since only a finite number of screw dislocations is located within the area of the notable intensity of the Gaussian beam, while the other phase singularities are in the periphery (and in the infinity), where the intensity is very small. Increasing the Gaussian beam waist radius leads to a parabolic growth of the orbital angular momentum of such beams.

Proinflammatory Cytokine Modulates Intracellular Calcium Handling and Enhances Ventricular Arrhythmia Susceptibility.

Background: The mechanism of Interleukin-17 (IL-17) induced ventricular arrhythmia (VA) remains unclear. This study aimed to investigate the effect of intracellular calcium (Cai) handling and VA susceptibility by IL-17.Methods: The electrophysiological properties of isolated perfused rabbit hearts under IL-17 (20 ng/ml, N = 6) and the IL-17 with neutralizer (0.4 μg/ml, N = 6) were evaluated using an optical mapping system. The action potential duration (APD) and Cai transient duration (CaiTD) were examined, and semiquantitative reverse transcriptase-polymerase chain reaction analysis of ion channels was performed.Results: There were longer APD80, CaiTD80 and increased thresholds of APD and CaiTD alternans, the maximum slope of APD restitution and induction of VA threshold in IL-17 group compared with those in IL-17 neutralizer and baseline groups. During ventricular fibrillation, the number of phase singularities and dominant frequency were both significantly greater in IL-17 group than in baseline group. The mRNA expressions of the Na+/Ca2+ exchanger, phospholamban, and ryanodine receptor Ca2+ release channel were upregulated, and the subunit of L-type Ca2+ current and sarcoplasmic reticulum Ca2+-ATPase 2a were significantly reduced in IL-17 group compared to baseline and IL-17 neutralizer group.Conclusions: IL-17 enhanced CaiTD and APD alternans through disturbances in calcium handling, which may increase VA susceptibility.

Diffraction phenomenon description method based on by the topological objects set and the algorithm for distinguishing the minimum from zero intensity

Diffraction phenomenon describing method based on the topological objects set by means of system analysis was developed in the work. Diffraction field topological objects are maximum, minimum and zero intensity, which is identical to the phase singularity or optical vortex. Topological objects mathematical representation by standard extremum search function methods was considered. The algorithm for distinguishing the minimum has been developed and zero intensity at the experimental images due to the algorithm the diffractive optical images classification possibility by the number of phase singularities without further interference analysis was shown. To increase the speed of data analyses the image segmentation method is suggested. Otained results and recommendations applying is possible in various fields of medicine and technology, which use laser radiation.

Poincare sphere noise filtering for singularities in dynamic speckle activity: Application to paint drying time measurement

We present an approach based on optical vortex density to characterize a dynamic process. The proposal is tested in real experiments involving the drying of paint as case study. In this case, speckle patterns are generated by coherent light scattered from the sample. The dynamic behavior of the speckle pattern during the paint drying is evaluated by using Time History of Speckle Pattern (THSP). The THSP's pseudo-phase representation is calculated via a two-dimensional Laguerre Gauss transform algorithm. The singular points in the pseudo-phase are then identified, then the number of phase singularities are evaluated over all the pseudo-phase representations of the THSP sequence.A comparison between the number of the phase singularities in THSP sequences and the gravimetric curve shows that the results are in good agreement for the active period. However, for very low activity periods noise vortices are obtained. The noise vortices are originated in the camera recoding and digitalization process. We propose the use of Stokes Parameters to configure a Vortex-Filter in order to eliminate noise vortices in each paint-drying measurement, this filter is represented using Poincare Sphere for visualization purposes. In all cases, the drying evolution curve obtained by using the optical vortex density and the Poincare Sphere filter present a good agreement with gravimetric curve, indicating that the proposed method is a valid measuring alternative.

Role of Apamin-Sensitive Calcium-Activated Small-Conductance Potassium Currents on the Mechanisms of Ventricular Fibrillation in Pacing-Induced Failing Rabbit Hearts.

Ventricular fibrillation (VF) during heart failure is characterized by stable reentrant spiral waves (rotors). Apamin-sensitive small-conductance calcium-activated potassium currents (IKAS) are heterogeneously upregulated in failing hearts. We hypothesized that IKAS influences the location and stability of rotors during VF. Optical mapping was performed on 9 rabbit hearts with pacing-induced heart failure. The epicardial right ventricular and left ventricular surfaces were simultaneously mapped in a Langendorff preparation. At baseline and after apamin (100 nmol/L) infusion, the action potential duration (APD80) was determined, and VF was induced. Areas with a >50% increase in the maximum action potential duration (ΔAPD) after apamin infusion were considered to have a high IKAS distribution. At baseline, the distribution density of phase singularities during VF in high IKAS distribution areas was higher than in other areas (0.0035±0.0011 versus 0.0014±0.0010 phase singularities/pixel; P=0.004). In addition, high dominant frequencies also colocalized to high IKAS distribution areas (26.0 versus 17.9 Hz; P=0.003). These correlations were eliminated during VF after apamin infusion, as the number of phase singularities (17.2 versus 11.0; P=0.009) and dominant frequencies (22.1 versus 16.2 Hz; P=0.022) were all significantly decreased. In addition, reentrant spiral waves became unstable after apamin infusion, and the duration of VF decreased. The IKAS current influences the mechanism of VF in failing hearts as phase singularities, high dominant frequencies, and reentrant spiral waves all correlated to areas of high IKAS. Apamin eliminated this relationship and reduced VF vulnerability.

Modelling methodology of atrial fibrosis affects rotor dynamics and electrograms

Catheter ablation is an effective technique for terminating atrial arrhythmia. However, given a high atrial fibrillation (AF) recurrence rate, optimal ablation strategies have yet to be defined. Computer modelling can be a powerful aid but modelling of fibrosis, a major factor associated with AF, is an open question. Several groups have proposed methodologies based on imaging data, but no comparison to determine which methodology best corroborates clinically observed reentrant behaviour has been performed. We examined several methodologies to determine the best method for capturing fibrillation dynamics. Patient late gadolinium-enhanced magnetic resonance imaging data were transferred onto a bilayer atrial computer model and used to assign fibrosis distributions. Fibrosis was modelled as conduction disturbances (lower conductivity, edge splitting, or percolation), transforming growth factor-β1 ionic channel effects, myocyte-fibroblast coupling, and combinations of the preceding. Reentry was induced through pulmonary vein ectopy and the ensuing rotor dynamics characterized. Non-invasive electrocardiographic imaging data of the patients in AF was used for comparison. Electrograms were computed and the fractionation durations measured over the surface. Edge splitting produced more phase singularities from wavebreaks than the other representations. The number of phase singularities seen with percolation was closer to the clinical values. Addition of fibroblast coupling had an organizing effect on rotor dynamics. Simple tissue conductivity changes with ionic changes localized rotors over fibrosis which was not observed with clinical data. The specific representation of fibrosis has a large effect on rotor dynamics and needs to be carefully considered for patient specific modelling.

Stable vortex solitons in a ring-shaped partially-PT-symmetric potential.

We address the existence and stability of vortex solitons in a ring-shaped partially-parity-time (pPT) configuration. In sharp contrast to the reported nonlinear modes in PT- or pPT-symmetric systems, stable vortex solitons with different topological charges can be supported by the proposed pPT potential, despite the system always being beyond the symmetry-breaking point. Vortex solitons are characterized by the number of phase singularities which equals the corresponding topological charge. At higher power, unstable higher-charged vortices degenerate into stable vortices with lower charges. Robust nonlinear vortices can be easily excited by an input Gaussian beam. Our results provide, to the best of our knowledge, the first example of stable solitons in a symmetry-breaking system.

56-02: Spatially-discordant alternans phase islands promote arrhythmogenesis

Purpose: Two key features of ventricular remodeling are fibrosis and reduced gap junctional coupling. These are associated with abnormalities in electrical impulse generation and propagation, which predispose to reentrant tachyarrhythmias. In the absence of structural remodeling, high-frequency impulse generation can also induce such arrhythmias, via the development of dynamic electrical instabilities. However, owing to the complex and stochastic nature of arrhythmias, the combined mechanistic influences of structural and dynamical perturbations on arrhythmogenesis remain incompletely understood. Methods: Arrhythmogenesis was studied using in vitro and in silico monolayer models of neonatal rat ventricular tissue with 30% randomly distributed cardiac myofibroblasts and systematically lowered intercellular coupling achieved in vitro through graded knockdown of connexin43 expression. Summary of Results: Arrhythmia incidence and complexity (i.e., number of phase singularities) increased with decreasing intercellular coupling efficiency, at pacing frequencies > 3Hz. This coincided with the onset of a special type of spatially discordant action potential duration (APD) alternans characterized by island-like areas of opposite alternans phase (APIs). The degree of electrotonic dyssynchrony (number of APIs) correlated positively with the degree of Cx43 knockdown and arrhythmia complexity. At higher myofibroblast densities, more APIs were formed and reentrant arrhythmias were more easily induced. Conclusion: Downregulation of intercellular coupling and presence of myofibroblasts give rise to spatially-discordant APD alternans in simulated and cultured monolayers of rat ventricular cells. This study reveals islands of oppositely phased APD alternans to be important determinants of reentrant tachyarrhythmia initiation and complexity.

18-02: Fibrosis explains increased epicardial breakthrough in AF

Introduction: Recent work has shown that the transition from persistent to permanent AF in goats coincides with an increase in fibrosis in the outer millimeter of the atrial wall. Macroscopically this leads to reduced electrical conductivity orthogonal to the dominant fiber orientation. A causal relation has not been established yet. Our purpose was to test if subepicardial fibrosis can explain the increased incidence of epicardial breakthroughs, which is also observed in permanent AF. Methods: We constructed a detailed geometry of the human atria including all major bundle structures and two layers of fiber orientation. Computer simulations were run with a mesh of 0.2 mm resolution and an ionic current formulation specific for the human atrial myocyte. Subepicardial fibrosis was modeled by assigning zero transverse conductivity to a random selection of model elements. Simulations were performed with 0, 50, and 70% affected elements. Fibrillation was induced with incremental rapid pacing. Simulations were repeated with 10 different pacing locations, for a total of 30 simulations of 5 seconds each. We tested in the first place whether AF was induced by this protocol. In those simulations where fibrillation occurred, we computed the number of waves, number of phase singularities, percentage dyssynchrony, and number of breakthroughs in the 3 seconds after pacing. Conclusion: Subepicardial fibrosis can account for an increased susceptibility for AF as well as for the remarkable increase in epicardial breakthrough observed in experimental studies.

Phase singularities and energy fluxes of a noncanonical vortex dipole Airy beam in the far field

Based on the vector angular spectrum representation and stationary phase method, analytical far-field vectorial expressions of a noncanonical vortex dipole Airy beam, namely, a pair of noncanonical vortices with opposite charges embedded in an Airy beam are derived and used to investigate the phase singularities and energy flux distributions of the corresponding beam in the far-field regime, where the noncanonical characteristic of vortex is stressed. It is shown that the noncanonical strength, off-axis distance, and aperture coefficient affect the position and number of phase singularities, and the motion, creation, and annihilation of phase singularities are found by adjusting these parameters. For a low aperture coefficient, the energy flux distributions exhibit different numbers and orientations of lobes by varying the noncanonical strength. With increasing aperture coefficient, the symmetries of lobes are broken, and the energy flux distributions gradually become ellipses and the directions of their major axes vary with different noncanonical strengths. Finally, the energy flux distributions of an Airy beam carrying a single noncanonical vortex are discussed and compared.

Computation and projection of spiral wave trajectories during atrial fibrillation: a computational study.

To show how atrial fibrillation rotor activity on the heart surface manifests as phase on the torso, fibrillation was induced on a geometrically accurate computer model of the human atria. The Hilbert transform, time embedding, and filament detection were compared. Electrical activity on the epicardium was used to compute potentials on different surfaces from the atria to the torso. The Hilbert transform produces erroneous phase when pacing for longer than the action potential duration. The number of phase singularities, frequency content, and the dominant frequency decreased with distance from the heart, except for the convex hull.

Ptychographical imaging of the phase vortices in the x-ray beam formed by nanofocusing lenses

We present the ptychographical reconstruction of the x-ray beam formed by nanofocusing lenses (NFLs) containing a number of phase singularities (vortices) in the vicinity of the focal plane. As a test object Siemens star pattern was used with the finest features of 50 nm for ptychographical measurements. The extended ptychographical iterative engine (ePIE) algorithm was applied to retrieve both complex illumination and object functions from the set of diffraction patterns. The reconstruction revealed the focus size of 91.4±1.1 nm in horizontal and 70±0.3 nm in vertical direction at full width at half maximum (FWHM). The complex probe function was propagated along the optical axis of the beam revealing the evolution of the phase singularities.

Apamin-Sensitive Potassium Current Modulates Action Potential Duration Restitution and Arrhythmogenesis of Failing Rabbit Ventricles

Apamin-sensitive K currents (I(KAS)) are upregulated in heart failure. We hypothesize that apamin can flatten action potential duration restitution (APDR) curve and can reduce ventricular fibrillation duration in failing ventricles. We simultaneously mapped membrane potential and intracellular Ca (Ca(i)) in 7 rabbit hearts with pacing-induced heart failure and in 7 normal hearts. A dynamic pacing protocol was used to determine APDR at baseline and after apamin (100 nmol/L) infusion. Apamin did not change APD(80) in normal ventricles, but prolonged APD(80) in failing ventricles at either long (≥300 ms) or short (≤170 ms) pacing cycle length, but not at intermediate pacing cycle length. The maximal slope of APDR curve was 2.03 (95% confidence interval, 1.73-2.32) in failing ventricles and 1.26 (95% confidence interval, 1.13-1.40) in normal ventricles at baseline (P=0.002). After apamin administration, the maximal slope of APDR in failing ventricles decreased to 1.43 (95% confidence interval, 1.01-1.84; P=0.018), whereas no significant changes were observed in normal ventricles. During ventricular fibrillation in failing ventricles, the number of phase singularities (baseline versus apamin, 4.0 versus 2.5), dominant frequency (13.0 versus 10.0 Hz), and ventricular fibrillation duration (160 versus 80 s) were all significantly (P<0.05) decreased by apamin. Apamin prolongs APD at long and short, but not at intermediate pacing cycle length in failing ventricles. I(KAS) upregulation may be antiarrhythmic by preserving the repolarization reserve at slow heart rate, but is proarrhythmic by steepening the slope of APDR curve, which promotes the generation and maintenance of ventricular fibrillation.

Interaction between two edge dislocations in the presence of a tilted lens

The interaction between two edge dislocations in the presence of a tilted lens is studied. It is shown that for the interaction between two off-axis edge dislocations, the edge dislocations vanish, and one or two noncanonical vortices appear under certain conditions. A noncanonical vortex appears for the interaction between the on-axis edge dislocation and off-axis edge dislocation. However, one or two edge dislocations may take place when two edge dislocations are perpendicular or parallel to each other in the initial plane. The variation of the tilt coefficient does not affect the type and number of phase singularities, but the relation between the transverse position of phase singularities and the tilt coefficient is linear. The three-dimensional trajectories of vortices are nonlinear while the center of the pair of vortices propagates along a line during propagation.

Studying semblances of a true killer: experimental model of human ventricular fibrillation

It is unknown whether ventricular fibrillation (VF) studied in experimental models represents in vivo human VF. First, we examined closed chest in vivo VF induced at defibrillation threshold testing (DFT) in four patients with ischemic cardiomyopathy pretransplantation. We examined VF in these same four hearts in an ex vivo human Langendorff posttransplantation. VF from DFT was compared with VF from the electrodes from a similar region in the right ventricular endocardium in the Langendorff using two parameters: the scale distribution width (extracted from continuous wavelet transform) and VF mean cycle length (CL). In a second substudy group where multielectrode phase mapping could be performed, we examined early VF intraoperatively (in vivo open chest condition) in three patients with left ventricular cardiomyopathy. We investigated early VF in the hearts of three patients in an ex vivo Langendorff and compared findings with intraoperative VF using two metrics: dominant frequency (DF) assessed by the Welch periodogram and the number of phase singularities (lasting >480 ms). Wavelet analysis (P = 0.9) and VF CL were similar between the Langendorff and the DFT groups (225 ± 13, 218 ± 24 ms; P = 0.9), indicating that wave characteristics and activation rate of VF was comparable between the two models. Intraoperative DF was slower but comparable with the Langendorff DF over the endocardium (4.6 ± 0.1, 5.0 ± 0.4 Hz; P = 0.9) and the epicardium (4.5 ± 0.2, 5.2 ± 0.4 Hz; P = 0.9). Endocardial phase singularity number (9.6 ± 5, 12.1 ± 1; P = 0.6) was lesser in number but comparable between in vivo and ex vivo VF. VF dynamics in the limited experimental human studies approximates human in vivo VF.