Atrial Rotor Dynamics Under Complex Fractional Order Diffusion.
ABSTRACT: The mechanisms of atrial fibrillation (AF) are a challenging research topic. The rotor hypothesis states that the AF is sustained by a reentrant wave that propagates around an unexcited core. Cardiac tissue heterogeneities, both structural and cellular, play an important role during fibrillatory dynamics, so that the ionic characteristics of the currents, their spatial distribution and their structural heterogeneity determine the meandering of the rotor. Several studies about rotor dynamics implement the standard diffusion equation. However, this mathematical scheme carries some limitations. It assumes the myocardium as a continuous medium, ignoring, therefore, its discrete and heterogeneous aspects. A computational model integrating both, electrical and structural properties could complement experimental and clinical results. A new mathematical model of the action potential propagation, based on complex fractional order derivatives is presented. The complex derivative order appears of considering the myocardium as discrete-scale invariant fractal. The main aim is to study the role of a myocardial, with fractal characteristics, on atrial fibrillatory dynamics. For this purpose, the degree of structural heterogeneity is described through derivatives of complex order ? = ? + j?. A set of variations for ? is tested. The real part ? takes values ranging from 1.1 to 2 and the imaginary part ? from 0 to 0.28. Under this scheme, the standard diffusion is recovered when ? = 2 and ? = 0. The effect of ? on the action potential propagation over an atrial strand is investigated. Rotors are generated in a 2D model of atrial tissue under electrical remodeling due to chronic AF. The results show that the degree of structural heterogeneity, given by ?, modulates the electrophysiological properties and the dynamics of rotor-type reentrant mechanisms. The spatial stability of the rotor and the area of its unexcited core are modulated. As the real part decreases and the imaginary part increases, simulating a higher structural heterogeneity, the vulnerable window to reentrant is increased, as the total meandering of the rotor tip. This in silico study suggests that structural heterogeneity, described by means of complex order derivatives, modulates the stability of rotors and that a wide range of rotor dynamics can be generated.
Project description:Radiofrequency ablation therapy of atrial fibrillation (AF) recently incorporated the analysis of dominant frequency (DF) and/or electrogram fractionation for guidance. However, the relationships between DF, fractionation, and spatiotemporal characteristics of the AF source remain unclear.We hypothesize that a meandering reentrant AF source contributes to the wave fractionation and is reflected in the power spectrum of local electrograms elsewhere in the rotor's surroundings.Meandering rotors as AF sources were simulated in 2-dimensional models of human atrial tissue and recorded in isolated sheep hearts. Nondominant elements of the signals were differentiated from the dominant elements using singular value decomposition, whereby the purely periodic constituent (PC) relating to the rotor's DF was eliminated rendering a residual constituent (RC) that consisted of all other activity.Spectral analysis of the decomposed constituents revealed peaks corresponding to the meandering frequency of the rotor tip, the magnitudes of which were proportional to the size of and the distance to the rotor core. Similar analyses on epicardial optical signals and electrograms from isolated sheep hearts, as well as human complex fractionated atrial electrograms, showed applicability of the approach.Increased meandering of the rotor driving AF reduces activation periodicity and increases fractionation. The spectral manifestation of the rotor activity beyond the meandering region makes it possible to characterize AF source stability, as well as DF in humans using electrode mapping.
Project description: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.
Project description:Atrial fibrillation (AF) usually manifests as reentrant circuits propagating through the whole atria creating chaotic activation patterns. Little is yet known about how differences in electrophysiological and ionic properties between patients modulate reentrant patterns in AF. The goal of this study is to quantify how variability in action potential duration (APD) at different stages of repolarization determines AF dynamics and their modulation by ionic block using a set of virtual whole-atria human models. Six human whole-atria models are constructed based on the same anatomical structure and fiber orientation, but with different electrophysiological phenotypes. Membrane kinetics for each whole-atria model are selected with distinct APD characteristics at 20, 50, and 90% repolarization, from an experimentally calibrated population of human atrial action potential models, including AF remodeling and acetylcholine parasympathetic effects. Our simulations show that in all whole-atria models, reentrant circuits tend to organize around the pulmonary veins and the right atrial appendage, thus leading to higher dominant frequency (DF) and more organized activation in the left atrium than in the right atrium. Differences in APD in all phases of repolarization (not only APD90) yielded quantitative differences in fibrillation patterns with long APD associated with slower and more regular dynamics. Long APD50 and APD20 were associated with increased interatrial conduction block and interatrial differences in DF and organization index, creating reentry instability and self-termination in some cases. Specific inhibitions of IK1, INaK, or INa reduce DF and organization of the arrhythmia by enlarging wave meandering, reducing the number of secondary wavelets, and promoting interatrial block in all six virtual patients, especially for the phenotypes with short APD at 20, 50, and/or 90% repolarization. This suggests that therapies aiming at prolonging the early phase of repolarization might constitute effective antiarrhythmic strategies for the pharmacological management of AF. In summary, simulations report significant differences in atrial fibrillatory dynamics resulting from differences in APD at all phases of repolarization.
Project description:Ablation of electrical drivers during atrial fibrillation (AF) has been proved as an effective therapy to prevent recurrence of fibrillatory episodes. This study presents a new methodology based on causality analysis that is able to identify the hierarchical dominance of atrial areas driving AF. Realistic mathematical models of the atrial electrical activity during AF were used to assess the validity of our method. Identification of the dominant atrial propagation patterns was achieved by computing causal relations between multiple electrogram signals. The causal relationships between atrial areas during the fibrillatory processes were summarized into a recurrence map, highlighting the hierarchy and dominant areas. Recurrence maps computed from causality analysis allowed the identification of sites responsible for maintenance of the arrhythmia. These maps were able to locate the position of the atrial driver in fibrillatory processes with a single rotor, with 2 rotors or with several drivers. Additionally, the correspondence between the nodal values of the recurrence map and the distance to the rotor core has been established. Causal analysis consistently estimated propagation patterns and location of atrial drivers during AF. This methodology could guide ablation procedures in AF patients.
Project description:Atrial remodeling as a result of long-standing persistent atrial fibrillation (AF) induces substrate modifications that lead to different perpetuation mechanisms than in paroxysmal AF and a reduction in the efficacy of antiarrhythmic treatments.The purpose of this study was to identify the ionic current modifications that could destabilize reentries during chronic AF and serve to personalize antiarrhythmic strategies.A population of 173 mathematical models of remodeled human atrial tissue with realistic intersubject variability was developed based on action potential recordings of 149 patients diagnosed with AF. The relationship of each ionic current with AF maintenance and the dynamics of functional reentries (rotor meandering, dominant frequency) were evaluated by means of 3-dimensional simulations.Self-sustained reentries were maintained in 126 (73%) of the simulations. AF perpetuation was associated with higher expressions of INa and ICaL (P <.01), with no significant differences in the remaining currents. ICaL blockade promoted AF extinction in 30% of these 126 models. The mechanism of AF termination was related with collisions between rotors because of an increase in rotor meandering (1.71 ± 2.01cm2) and presented an increased efficacy in models with a depressed INa (P <.01).Mathematical simulations based on a population of models representing intersubject variability allow the identification of ionic mechanisms underlying rotor dynamics and the definition of new personalized pharmacologic strategies. Our results suggest that the underlying mechanism of the diverging success of ICaL block as an antiarrhythmic strategy is dependent on the basal availability of sodium and calcium ion channel conductivities.
Project description:Background:Mechanical stretch increases Na+ inflow into myocytes, related to mechanisms including stretch-activated channels or Na+/H+ exchanger activation, involving Ca2+ increase that leads to changes in electrophysiological properties favoring arrhythmia induction. Ranolazine is an antianginal drug with confirmed beneficial effects against cardiac arrhythmias associated with the augmentation of I NaL current and Ca2+ overload. Objective:This study investigates the effects of mechanical stretch on activation patterns in atrial cell monolayers and its pharmacological response to ranolazine. Methods:Confluent HL-1 cells were cultured in silicone membrane plates and were stretched to 110% of original length. The characteristics of in vitro fibrillation (dominant frequency, regularity index, density of phase singularities, rotor meandering, and rotor curvature) were analyzed using optical mapping in order to study the mechanoelectric response to stretch under control conditions and ranolazine action. Results:HL-1 cell stretch increased fibrillatory dominant frequency (3.65 ± 0.69 vs. 4.35 ± 0.74 Hz, p < 0.01) and activation complexity (1.97 ± 0.45 vs. 2.66 ± 0.58 PS/cm2, p < 0.01) under control conditions. These effects were related to stretch-induced changes affecting the reentrant patterns, comprising a decrease in rotor meandering (0.72 ± 0.12 vs. 0.62 ± 0.12 cm/s, p < 0.001) and an increase in wavefront curvature (4.90 ± 0.42 vs. 5.68 ± 0.40 rad/cm, p < 0.001). Ranolazine reduced stretch-induced effects, attenuating the activation rate increment (12.8% vs. 19.7%, p < 0.01) and maintaining activation complexity-both parameters being lower during stretch than under control conditions. Moreover, under baseline conditions, ranolazine slowed and regularized the activation patterns (3.04 ± 0.61 vs. 3.65 ± 0.69 Hz, p < 0.01). Conclusion:Ranolazine attenuates the modifications of activation patterns induced by mechanical stretch in atrial myocyte monolayers.
Project description:Ablation is an effective therapy in patients with atrial fibrillation (AF) in which an electrical driver can be identified.The aim of this study was to present and discuss a novel and strictly noninvasive approach to map and identify atrial regions responsible for AF perpetuation.Surface potential recordings of 14 patients with AF were recorded using a 67-lead recording system. Singularity points (SPs) were identified in surface phase maps after band-pass filtering at the highest dominant frequency (HDF). Mathematical models of combined atria and torso were constructed and used to investigate the ability of surface phase maps to estimate rotor activity in the atrial wall.The simulations show that surface SPs originate at atrial SPs, but not all atrial SPs are reflected at the surface. Stable SPs were found in AF signals during 8.3% ± 5.7% vs. 73.1% ± 16.8% of the time in unfiltered vs. HDF-filtered patient data, respectively (P < .01). The average duration of each rotational pattern was also lower in unfiltered than in HDF-filtered AF signals (160 ± 43 ms vs. 342 ± 138 ms; P < .01), resulting in 2.8 ± 0.7 rotations per rotor. Band-pass filtering reduced the apparent meandering of surface HDF rotors by reducing the effect of the atrial electrical activity occurring at different frequencies. Torso surface SPs representing HDF rotors during AF were reflected at specific areas corresponding to the fastest atrial location.Phase analysis of surface potential signals after HDF filtering during AF shows reentrant drivers localized to either the left atrium or the right atrium, helping in localizing ablation targets.
Project description:Atrial fibrillation (AF) is the most common cardiac arrhytmia, characterized by the chaotic motion of electrical wavefronts in the atria. In clinical practice, AF is classified under two primary categories: paroxysmal AF, short intermittent episodes separated by periods of normal electrical activity; and persistent AF, longer uninterrupted episodes of chaotic electrical activity. However, the precise reasons why AF in a given patient is paroxysmal or persistent is poorly understood. Recently, we have introduced the percolation-based Christensen-Manani-Peters (CMP) model of AF which naturally exhibits both paroxysmal and persistent AF, but precisely how these differences emerge in the model is unclear. In this paper, we dissect the CMP model to identify the cause of these different AF classifications. Starting from a mean-field model where we describe AF as a simple birth-death process, we add layers of complexity to the model and show that persistent AF arises from reentrant circuits which exhibit an asymmetry in their probability of activation relative to deactivation. As a result, different simulations generated at identical model parameters can exhibit fibrillatory episodes spanning several orders of magnitude from a few seconds to months. These findings demonstrate that diverse, complex fibrillatory dynamics can emerge from very simple dynamics in models of AF.
Project description:The aim of this paper was to study mechanisms of formation of fractionated electrograms on the posterior left atrial wall (PLAW) in human paroxysmal atrial fibrillation (AF).The mechanisms responsible for complex fractionated atrial electrogram formation during AF are poorly understood.In 24 patients, we induced sustained AF by pacing from a pulmonary vein. We analyzed transitions between organized patterns and changes in electrogram morphology leading to fractionation in relation to interbeat interval duration (systolic interval [SI]) and dominant frequency. Computer simulations of rotors helped in the interpretation of the results.Organized patterns were recorded 31 ± 18% of the time. In 47% of organized patterns, the electrograms and PLAW activation sequence were similar to those of incoming waves during pulmonary vein stimulation that induced AF. Transitions to fractionation were preceded by significant increases in electrogram duration, spike number, and SI shortening (R(2) = 0.94). Similarly, adenosine infusion during organized patterns caused significant SI shortening leading to fractionated electrograms formation. Activation maps during organization showed incoming wave patterns, with earliest activation located closest to the highest dominant frequency site. Activation maps during transitions to fragmentation showed areas of slowed conduction and unidirectional block. Simulations predicted that SI abbreviation that heralds fractionated electrograms formation might result from a Doppler effect on wave fronts preceding an approaching rotor or by acceleration of a stationary or meandering, remotely located source.During induced AF, SI shortening after either drift or acceleration of a source results in intermittent fibrillatory conduction and formation of fractionated electrograms at the PLAW.
Project description:Atrial fibrillation (AF) often converts to and from atrial tachycardia (AT), but it is undefined if these rhythms are mechanistically related in such patients. We tested the hypothesis that critical sites for AT may be related to regional AF sources in patients with both rhythms, by mapping their locations and response to ablation on transitions to and from AF.From 219 patients undergoing spatial mapping of AF prior to ablation at 3 centers, we enrolled 26 patients in whom AF converted to AT by ablation (n=19) or spontaneously (n=7; left atrial size 42±6cm, 38% persistent AF). Both atria were mapped in both rhythms by 64-electrode baskets, traditional activation maps and entrainment.Each patient had a single mapped AT (17 reentrant, 9 focal) and 3.7±1.7 AF sources. The mapped AT spatially overlapped one AF source in 88% (23/26) of patients, in left (15/23) or right (8/23) atria. AF transitioned to AT by 3 mechanisms: (a) ablation anchoring AF rotor to AT (n=13); (b) residual, unablated AF source producing AT (n=6); (c) spontaneous slowing of AF rotor leaving reentrant AT at this site without any ablation (n=7). Electrogram analysis revealed a lower peak-to-peak voltage at overlapping sites (0.36±0.2mV vs 0.49±0.2mV p=0.03).Mechanisms responsible for AT and AF may arise in overlapping atrial regions. This mechanistic inter-relationship may reflect structural and/or functional properties in either atrium. Future work should delineate how acceleration of an organized AT may produce AF, and whether such regions can be targeted a priori to prevent AT recurrence post AF ablation.