Dynamical mechanism of atrial fibrillation: a topological approach

While spiral wave breakup has been implicated in the emergence of atrial fibrillation, its role in maintaining this complex type of cardiac arrhythmia is less clear. We used the Karma model of cardiac excitation to investigate the dynamical mechanisms that sustain atrial fibrillation once it has been established. The results of our numerical study show that spatiotemporally chaotic dynamics in this regime can be described as a dynamical equilibrium between topologically distinct types of transitions that increase or decrease the number of wavelets, in general agreement with the multiple wavelets hypothesis. Surprisingly, we found that the process of continuous excitation waves breaking up into discontinuous pieces plays no role whatsoever in maintaining spatiotemporal complexity. Instead this complexity is maintained as a dynamical balance between wave coalescence -- a unique, previously unidentified, topological process that increases the number of wavelets -- and wave collapse -- a different topological process that decreases their number.Comment: 15 pages, 14 figure

Modeling the Heart as a Communication System

Electrical communication between cardiomyocytes can be perturbed during arrhythmia, but these perturbations are not captured by conventional electrocardiographic metrics. We developed a theoretical framework to quantify electrical communication using information theory metrics in 2-dimensional cell lattice models of cardiac excitation propagation. The time series generated by each cell was coarse-grained to 1 when excited or 0 when resting. The Shannon entropy for each cell was calculated from the time series during four clinically important heart rhythms: normal heartbeat, anatomical reentry, spiral reentry, and multiple reentry. We also used mutual information to perform spatial profiling of communication during these cardiac arrhythmias. We found that information sharing between cells was spatially heterogeneous. In addition, cardiac arrhythmia significantly impacted information sharing within the heart. Entropy localized the path of the drifting core of spiral reentry, which could be an optimal target of therapeutic ablation. We conclude that information theory metrics can quantitatively assess electrical communication among cardiomyocytes. The traditional concept of the heart as a functional syncytium sharing electrical information cannot predict altered entropy and information sharing during complex arrhythmia. Information theory metrics may find clinical application in the identification of rhythm-specific treatments which are currently unmet by traditional electrocardiographic techniques.Comment: 26 pages (including Appendix), 6 figures, 8 videos (not uploaded due to size limitation

Dynamics of filaments of scroll waves

This has been written as a chapter for "Engineering Chemical Complexity II", and as such does not have an abstract.Comment: 18 pages, 10 figure

Characterisation of re-entrant circuit (or rotational activity) in vitro using the HL1-6 myocyte cell line

Fibrillation is the most common arrhythmia observed in clinical practice. Understanding of the mechanisms underlying its initiation and maintenance remains incomplete. Functional re-entries are potential drivers of the arrhythmia. Two main concepts are still debated, the “leading circle” and the “spiral wave or rotor” theories. The homogeneous subclone of the HL1 atrial-derived cardiomyocyte cell line, HL1-6, spontaneously exhibits re-entry on a microscopic scale due to its slow conduction velocity and the presence of triggers, making it possible to examine re-entry at the cellular level. We therefore investigated the re-entry cores in cell monolayers through the use of fluorescence optical mapping at high spatiotemporal resolution in order to obtain insights into the mechanisms of re-entry. Re-entries in HL1-6 myocytes required at least two triggers and a minimum colony area to initiate (3.5 to 6.4 mm2). After electrical activity was completely stopped and re-started by varying the extracellular K+ concentration, re-entries never returned to the same location while 35% of triggers re-appeared at the same position. A conduction delay algorithm also allows visualisation of the core of the re-entries. This work has revealed that the core of re-entries is conduction blocks constituted by lines and/or groups of cells rather than the round area assumed by the other concepts of functional re-entry. This highlights the importance of experimentation at the microscopic level in the study of re-entry mechanisms

Model of unidirectional block formation leading to reentrant ventricular tachycardia in the infarct border zone of postinfarction canine hearts

AbstractBackgroundWhen the infarct border zone is stimulated prematurely, a unidirectional block line (UBL) can form and lead to double-loop (figure-of-eight) reentrant ventricular tachycardia (VT) with a central isthmus. The isthmus is composed of an entrance, center, and exit. It was hypothesized that for certain stimulus site locations and coupling intervals, the UBL would coincide with the isthmus entrance boundary, where infarct border zone thickness changes from thin-to-thick in the travel direction of the premature stimulus wavefront.MethodA quantitative model was developed to describe how thin-to-thick changes in the border zone result in critically convex wavefront curvature leading to conduction block, which is dependent upon coupling interval. The model was tested in 12 retrospectively analyzed postinfarction canine experiments. Electrical activation was mapped for premature stimulation and for the first reentrant VT cycle. The relationship of functional conduction block forming during premature stimulation to functional block during reentrant VT was quantified.ResultsFor an appropriately placed stimulus, in accord with model predictions: 1. The UBL and reentrant VT isthmus lateral boundaries overlapped (error: 4.8±5.7mm). 2. The UBL leading edge coincided with the distal isthmus where the center-entrance boundary would be expected to occur. 3. The mean coupling interval was 164.6±11.0ms during premature stimulation and 190.7±20.4ms during the first reentrant VT cycle, in accord with model calculations, which resulted in critically convex wavefront curvature and functional conduction block, respectively, at the location of the isthmus entrance boundary and at the lateral isthmus edges.DiscussionReentrant VT onset following premature stimulation can be explained by the presence of critically convex wavefront curvature and unidirectional block at the isthmus entrance boundary when the premature stimulation interval is sufficiently short. The double-loop reentrant circuit pattern is a consequence of wavefront bifurcation around this UBL followed by coalescence, and then impulse propagation through the isthmus. The wavefront is blocked from propagating laterally away from the isthmus by sharp increases in border zone thickness, which results in critically convex wavefront curvature at VT cycle lengths

Evolution of spiral and scroll waves of excitation in a mathematical model of ischaemic border zone

Abnormal electrical activity from the boundaries of ischemic cardiac tissue is recognized as one of the major causes in generation of ischemia-reperfusion arrhythmias. Here we present theoretical analysis of the waves of electrical activity that can rise on the boundary of cardiac cell network upon its recovery from ischaemia-like conditions. The main factors included in our analysis are macroscopic gradients of the cell-to-cell coupling and cell excitability and microscopic heterogeneity of individual cells. The interplay between these factors allows one to explain how spirals form, drift together with the moving boundary, get transiently pinned to local inhomogeneities, and finally penetrate into the bulk of the well-coupled tissue where they reach macroscopic scale. The asymptotic theory of the drift of spiral and scroll waves based on response functions provides explanation of the drifts involved in this mechanism, with the exception of effects due to the discreteness of cardiac tissue. In particular, this asymptotic theory allows an extrapolation of 2D events into 3D, which has shown that cells within the border zone can give rise to 3D analogues of spirals, the scroll waves. When and if such scroll waves escape into a better coupled tissue, they are likely to collapse due to the positive filament tension. However, our simulations have shown that such collapse of newly generated scrolls is not inevitable and that under certain conditions filament tension becomes negative, leading to scroll filaments to expand and multiply leading to a fibrillation-like state within small areas of cardiac tissue.Comment: 26 pages, 13 figures, appendix and 2 movies, as accepted to PLoS ONE 2011/08/0

Role of wavefront curvature in propagation of cardiac impulse

It is traditionally assumed that impulse propagation in cardiac muscle is determined by the combination of two factors: (1) the active properties of cardiac cell membranes and (2) the passive electrical characteristics of the network formed by cardiac cells. However, advances made recently in the theory of generic excitable media suggest that an additional factor—the geometry of excitation wavefronts—may play an important role. In particular, impulse propagation strongly depends on the wavefront curvature on a small spatial scale. In the heart, excitation wavefronts have pronounced curvatures in several situations including waves initiated by small electrodes, waves emerging from narrow tissue structures, and waves propagating around the sharp edges of anatomical obstacles or around a zone of functional conduction block during spiral wave rotation. In this short review we consider the theoretical background relating impulse propagation to wavefront curvature and we estimate the role of wavefront curvature in electrical stimulation, formation of conduction block, and the dynamic behavior of spiral wave

Virtual cardiac monolayers for electrical wave propagation

The complex structure of cardiac tissue is considered to be one of the main determinants of an arrhythmogenic substrate. This study is aimed at developing the first mathematical model to describe the formation of cardiac tissue, using a joint in silico-in vitro approach. First, we performed experiments under various conditions to carefully characterise the morphology of cardiac tissue in a culture of neonatal rat ventricular cells. We considered two cell types, namely, cardiomyocytes and fibroblasts. Next, we proposed a mathematical model, based on the Glazier-Graner-Hogeweg model, which is widely used in tissue growth studies. The resultant tissue morphology was coupled to the detailed electrophysiological Korhonen-Majumder model for neonatal rat ventricular cardiomyocytes, in order to study wave propagation. The simulated waves had the same anisotropy ratio and wavefront complexity as those in the experiment. Thus, we conclude that our approach allows us to reproduce the morphological and physiological properties of cardiac tissue

Studies on the dynamics of chaotic multi-wavelet reentrant propagation using a hybrid cellular automaton model of excitable tissue

There is a compelling body of evidence implicating continuous propagation (reentry) sustained by multiple meandering wavelets in the pathology of advanced human atrial fibrillation (AF). This forms the basis for many current therapies such as the Cox MAZE procedure and its derivatives, which aim to create non-conducting lesions in order to "transect" these circuits before they form. Nevertheless, our ability to successfully treat persistent and permanent AF using catheter ablation remains inadequate due to current limitations of clinical mapping technology as well as an incomplete understanding of how to place lesions in order to maximize circuit transection and, more importantly, minimize AF burden. Here, we used a hybrid cellular automaton model to study the dynamics of chaotic, multi-wavelet reentry (MWR) in excitable tissue. First, we used reentry as an exemplar to investigate a hysteretic disease mechanism in a multistable nonlinear system. We found that certain interactions with the environment can cause persistent changes to system behavior without altering its structure or properties, thus leading to a disconnect between clinical symptoms and the underlying state of disease. Second, we developed a novel analytical method to characterize the spatiotemporal dynamics of MWR. We identified a heterogeneous spatial distribution of reentrant pathways that correlated with the spatial distribution of cell activation frequencies. Third, we investigated the impact of topological and geometrical substrate alterations on the dynamics of MWR. We demonstrated a multi-phasic relationship between obstacle size and the fate of individual episodes. Notably, for a narrow range of sizes, obstacles appeared to play an active role in rapidly converting MWR to stable structural reentry. Our studies indicate that reentrant-pathway distributions are non-uniform in heterogeneous media (such as the atrial myocardium) and suggest a clinically measurable correlate for identifying regions of high circuit density, supporting the feasibility of patient-specific targeted ablation. Moreover, we have elucidated the key mechanisms of interaction between focal obstacles and MWR, which has implications for the use of spot ablation to treat AF as some recent studies have suggested

Quantification of the transmural dynamics of atrial fibrillation by simultaneous endocardial and epicardial optical mapping in an acute sheep model

BACKGROUND: Therapy strategies for atrial fibrillation based on electrical characterization are becoming viable personalized medicine approaches to treat a notoriously difficult disease. In light of these approaches that rely on high-density surface mapping, this study aims to evaluate the presence of three-dimensional electrical substrate variations within the transmural wall during acute episodes of atrial fibrillation. METHODS AND RESULTS: Optical signals were simultaneously acquired from the epicardial and endocardial tissue during acute fibrillation in ovine isolated left atria. Dominant frequency, regularity index, propagation angles and phase dynamics were assessed and correlated across imaging planes to gauge the synchrony of the activation patterns compared to paced rhythms. Static frequency parameters were well correlated spatially between the endocardium and the epicardium (dominant frequency, 0.79+/-0.06 and regularity index, 0.93+/-0.009). However, dynamic tracking of propagation vectors and phase singularity trajectories revealed discordant activity across the transmural wall. The absolute value of the difference in the number, spatial stability, and temporal stability of phase singularities between the epicardial and endocardial planes was significantly greater than 0 with a median difference of 1.0, 9.27%, and 19.75%, respectively. The number of wavefronts with respect to time was significantly less correlated and the difference in propagation angle was significantly larger in fibrillation compared to paced rhythms. CONCLUSIONS: Atrial fibrillation substrates are dynamic three-dimensional structures with a range of discordance between the epicardial and endocardial tissue. The results of this study suggest that transmural propagation may play a role in AF maintenance mechanisms