Electrophysiological heterogeneity and stability of reentry in simulated cardiac tissue

Atrial Fibrillation and Underlying Structural and Electrophysiological Heterogeneity

As atrial fibrillation (AF) progresses from initial paroxysmal episodes to the persistent phase, maintaining sinus rhythm for an extended period through pharmacotherapy and catheter ablation becomes difficult. A major cause of the deteriorated treatment outcome is the atrial structural and electrophysiological heterogeneity, which AF itself can exacerbate. This heterogeneity exists or manifests in various dimensions, including anatomically segmental structural features, the distribution of histological fibrosis and the autonomic nervous system, sarcolemmal ion channels, and electrophysiological properties. All these types of heterogeneity are closely related to the development of AF. Recognizing the heterogeneity provides a valuable approach to comprehending the underlying mechanisms in the complex excitatory patterns of AF and the determining factors that govern the seemingly chaotic propagation. Furthermore, substrate modification based on heterogeneity is a potential therapeutic strategy. This review aims to consolidate the current knowledge on structural and electrophysiological atrial heterogeneity and its relation to the pathogenesis of AF, drawing insights from clinical studies, animal and cell experiments, molecular basis, and computer-based approaches, to advance our understanding of the pathophysiology and management of AF.

Meander pattern of spiral wave and the spatial distribution of its cycle length

One of the most interesting dynamics of rotating spiral waves in an excitable medium is meandering. The tip of a meandering spiral wave moves along a complex trajectory, which often takes the shape of an epitrochoid or hypotrochoid with inward or outward petals. The cycle lengths (CLs) of a meandering spiral wave are not constant; rather, they depend on the meandering dynamics. In this paper, we show that the CLs take two mean values, outside T^{out} and inside T^{in} the meandering trajectory with a ratio of T^{in}/T^{out}=(n+1)/n for the inward and (n-1)/n for the outward petals, where n is the number of petals in the tip trajectory. We illustrate this using four models of excitable media and prove this result. These formulas are shown to be suitable for a meandering spiral wave in an anatomical model of the heart. We also show that the effective periods of overdrive pacing of meandering spiral waves depend on the electrode location relative to the tip trajectory. Overall, our approach can be used to study the meandering pattern from the CL data; it should work for any type of dynamics that produces complex tip trajectories of the spiral wave, for example, for a drift due to heterogeneity.

The transient outward potassium current plays a key role in spiral wave breakup in ventricular tissue

Spiral wave reentry as a mechanism of lethal ventricular arrhythmias has been widely demonstrated in animal experiments and recordings from human hearts. It has been shown that in structurally normal hearts spiral waves are unstable, breaking up into multiple wavelets via dynamical instabilities. However, many of the second-generation action potential models give rise only to stable spiral waves, raising issues regarding the underlying mechanisms of spiral wave breakup. In this study, we carried out computer simulations of two-dimensional homogeneous tissues using five ventricular action potential models. We show that the transient outward potassium current (Ito), although it is not required, plays a key role in promoting spiral wave breakup in all five models. As the maximum conductance of Ito increases, it first promotes spiral wave breakup and then stabilizes the spiral waves. In the absence of Ito, speeding up the L-type calcium kinetics can prevent spiral wave breakup, however, with the same speedup kinetics, spiral wave breakup can be promoted by increasing Ito. Increasing Ito promotes single-cell dynamical instabilities, including action potential duration alternans and chaos, and increasing Ito further suppresses these action potential dynamics. These cellular properties agree with the observation that increasing Ito first promotes spiral wave breakup and then stabilizes spiral waves in tissue. Implications of our observations to spiral wave dynamics in the real hearts and action potential model improvements are discussed.NEW & NOTEWORTHY Spiral wave breakup manifesting as multiple wavelets is a mechanism of ventricular fibrillation. It has been known that spiral wave breakup in cardiac tissue can be caused by a steeply sloped action potential duration restitution curve, a property mainly determined by the recovery of L-type calcium current. Here, we show that the transient outward potassium current (Ito) is another current that plays a key role in spiral wave breakup, that is, spiral waves can be stable for low and high maximum Ito conductance but breakup occurs for intermediate maximum Ito conductance. Since Ito is present in normal hearts of many species and required for Brugada syndrome, it may play an important role in the spiral wave stability and arrhythmogenesis under both normal condition and Brugada syndrome.

Anisotropic shortening in the wavelength of electrical waves promotes onset of electrical turbulence in cardiac tissue: An in silico study

Several pathological conditions introduce spatial variations in the electrical properties of cardiac tissue. These variations occur as localized or distributed gradients in ion-channel functionality over extended tissue media. Electrical waves, propagating through such affected tissue, demonstrate distortions, depending on the nature of the ionic gradient in the diseased substrate. If the degree of distortion is large, reentrant activity may develop, in the form of rotating spiral (2d) and scroll (3d) waves of electrical activity. These reentrant waves are associated with the occurrence of lethal cardiac rhythm disorders, known as arrhythmias, such as ventricular tachycardia (VT) and ventricular fibrillation (VF), which are believed to be common precursors of sudden cardiac arrest. By using state-of-the-art mathematical models for generic, and ionically-realistic (human) cardiac tissue, we study the detrimental effects of these ionic gradients on electrical wave propagation. We propose a possible mechanism for the development of instabilities in reentrant wave patterns, in the presence of ionic gradients in cardiac tissue, which may explain how one type of arrhythmia (VT) can degenerate into another (VF). Our proposed mechanism entails anisotropic reduction in the wavelength of the excitation waves because of anisotropic variation in its electrical properties, in particular the action potential duration (APD). We find that the variation in the APD, which we induce by varying ion-channel conductances, imposes a spatial variation in the spiral- or scroll-wave frequency ω. Such gradients in ω induce anisotropic shortening of wavelength of the spiral or scroll arms and eventually leads to instabilitites.

Pro-Arrhythmogenic Effects of Heterogeneous Tissue Curvature - A Suggestion for Role of Left Atrial Appendage in Atrial Fibrillation

BACKGROUND

The arrhythmogenic role of complex atrial morphology has not yet been clearly elucidated. We hypothesized that bumpy tissue geometry can induce action potential duration (APD) dispersion and wavebreak in atrial fibrillation (AF). Methods and Results: We simulated a 2D-bumpy atrial model by varying the degree of bumpiness, and 3D-left atrial (LA) models integrated by LA computed tomographic (CT) images taken from 14 patients with persistent AF. We also analyzed wave-dynamic parameters with bipolar electrograms during AF and compared them with LA-CT geometry in 30 patients with persistent AF. In the 2D-bumpy model, APD dispersion increased (P<0.001) and wavebreak occurred spontaneously when the surface bumpiness was greater, showing phase transition-like behavior (P<0.001). The bumpiness gradient 2D-model showed that spiral wave drifted in the direction of higher bumpiness, and phase singularity (PS) points were mostly located in areas with higher bumpiness. In the 3D-LA model, PS density was higher in the LA appendage (LAA) compared with other parts of the LA (P<0.05). In 30 persistent-AF patients, the surface bumpiness of LAA was 5.8-fold that of other LA parts (P<0.001), and exceeded critical bumpiness to induce wavebreak. Wave dynamics complexity parameters were consistently dominant in the LAA (P<0.001).

CONCLUSIONS

Bumpy tissue geometry promoted APD dispersion, wavebreak, and spiral wave drift in in-silico human atrial tissue, and corresponded to clinical electroanatomical maps.

Cardiac spiral wave drifting due to spatial temperature gradients - A numerical study

Cardiac rotors are believed to be a major driver source of persistent atrial fibrillation (AF), and their spatiotemporal characterization is essential for successful ablation procedures. However, electrograms guided ablation have not been proven to have benefit over empirical ablation thus far, and there is a strong need of improving the localization of cardiac arrhythmogenic targets for ablation. A new approach for characterize rotors is proposed that is based on induced spatial temperature gradients (STGs), and investigated by theoretical study using numerical simulations. We hypothesize that such gradients will cause rotor drifting due to induced spatial heterogeneity in excitability, so that rotors could be driven towards the ablating probe. Numerical simulations were conducted in single cell and 2D atrial models using AF remodeled kinetics. STGs were applied either linearly on the entire tissue or as a small local perturbation, and the major ion channel rate constants were adjusted following Arrhenius equation. In the AF-remodeled single cell, recovery time increased exponentially with decreasing temperatures, despite the marginal effect of temperature on the action potential duration. In 2D models, spiral waves drifted with drifting velocity components affected by both temperature gradient direction and the spiral wave rotation direction. Overall, spiral waves drifted towards the colder tissue region associated with global minimum of excitability. A local perturbation with a temperature of T = 28 °C was found optimal for spiral wave attraction for the studied conditions. This work provides a preliminary proof-of-concept for a potential prospective technique for rotor attraction. We envision that the insights from this study will be utilize in the future in the design of a new methodology for AF characterization and termination during ablation procedures.

Dispersion of Recovery and Vulnerability to Re-entry in a Model of Human Atrial Tissue With Simulated Diffuse and Focal Patterns of Fibrosis

Fibrosis in atrial tissue can act as a substrate for persistent atrial fibrillation, and can be focal or diffuse. Regions of fibrosis are associated with slowed or blocked conduction, and several approaches have been used to model these effects. In this study a computational model of 2D atrial tissue was used to investigate how the spatial scale of regions of simulated fibrosis influenced the dispersion of action potential duration (APD) and vulnerability to re-entry in simulated normal human atrial tissue, and human tissue that has undergone remodeling as a result of persistent atrial fibrillation. Electrical activity was simulated in a 10 × 10 cm square 2D domain, with a spatially varying diffusion coefficient as described below. Cellular electrophysiology was represented by the Courtemanche model for human atrial cells, with the model parameters set for normal and remodeled cells. The effect of fibrosis was modeled with a smoothly varying diffusion coefficient, obtained from sampling a Gaussian random field (GRF) with length scales of between 1.25 and 10.0 mm. Twenty samples were drawn from each field, and used to allocate a value of diffusion coefficient between 0.05 and 0.2 mm²/ms. Dispersion of APD was assessed in each sample by pacing at a cycle length of 1,000 ms, followed by a premature beat with a coupling interval of 400 ms. Vulnerability to re-entry was assessed with an aggressive pacing protocol with pacing cycle lengths decreasing from 450 to 250 ms in 25 ms intervals for normal tissue and 300–150 ms for remodeled tissue. Simulated fibrosis at smaller spatial scales tended to lengthen APD, increase APD dispersion, and increase vulnerability to sustained re-entry relative to fibrosis at larger spatial scales. This study shows that when fibrosis is represented by smoothly varying tissue diffusion, the spatial scale of fibrosis has important effects on both dispersion of recovery and vulnerability to re-entry.

Quantitative systems models illuminate arrhythmia mechanisms in heart failure: Role of the Na+ -Ca2+ -Ca2+ /calmodulin-dependent protein kinase II-reactive oxygen species feedback

Quantitative systems modeling aims to integrate knowledge in different research areas with models describing biological mechanisms and dynamics to gain a better understanding of complex clinical syndromes. Heart failure (HF) is a chronic complex cardiac disease that results from structural or functional disorders impairing the ability of the ventricle to fill with or eject blood. Highly interactive and dynamic changes in mechanical, structural, neurohumoral, metabolic, and electrophysiological properties collectively predispose the failing heart to cardiac arrhythmias, which are responsible for about a half of HF deaths. Multiscale cardiac modeling and simulation integrate structural and functional data from HF experimental models and patients to improve our mechanistic understanding of this complex arrhythmia syndrome. In particular, they allow investigating how disease-induced remodeling alters the coupling of electrophysiology, Ca²⁺ and Na⁺ handling, contraction, and energetics that lead to rhythm derangements. The Ca²⁺ /calmodulin-dependent protein kinase II, which expression and activity are enhanced in HF, emerges as a critical hub that modulates the feedbacks between these various subsystems and promotes arrhythmogenesis. This article is categorized under: Physiology > Mammalian Physiology in Health and Disease Models of Systems Properties and Processes > Mechanistic Models Models of Systems Properties and Processes > Cellular Models Models of Systems Properties and Processes > Organ, Tissue, and Physiological Models.

Computational Cardiac Modeling Reveals Mechanisms of Ventricular Arrhythmogenesis in Long QT Syndrome Type 8: CACNA1C R858H Mutation Linked to Ventricular Fibrillation

Functional analysis of the L-type calcium channel has shown that the CACNA1C R858H mutation associated with severe QT interval prolongation may lead to ventricular fibrillation (VF). This study investigated multiple potential mechanisms by which the CACNA1C R858H mutation facilitates and perpetuates VF. The Ten Tusscher-Panfilov (TP06) human ventricular cell models incorporating the experimental data on the kinetic properties of L-type calcium channels were integrated into one-dimensional (1D) fiber, 2D sheet, and 3D ventricular models to investigate the pro-arrhythmic effects of CACNA1C mutations by quantifying changes in intracellular calcium handling, action potential profiles, action potential duration restitution (APDR) curves, dispersion of repolarization (DOR), QT interval and spiral wave dynamics. R858H “mutant” L-type calcium current (I_CaL) augmented sarcoplasmic reticulum calcium content, leading to the development of afterdepolarizations at the single cell level and focal activities at the tissue level. It also produced inhomogeneous APD prolongation, causing QT prolongation and repolarization dispersion amplification, rendering R858H “mutant” tissue more vulnerable to the induction of reentry compared with other conditions. In conclusion, altered I_CaL due to the CACNA1C R858H mutation increases arrhythmia risk due to afterdepolarizations and increased tissue vulnerability to unidirectional conduction block. However, the observed reentry is not due to afterdepolarizations (not present in our model), but rather to a novel blocking mechanism.

Role of abnormal repolarization in the mechanism of cardiac arrhythmia

In cardiac patients, life-threatening tachyarrhythmia is often precipitated by abnormal changes in ventricular repolarization and refractoriness. Repolarization abnormalities typically evolve as a consequence of impaired function of outward K⁺ currents in cardiac myocytes, which may be caused by genetic defects or result from various acquired pathophysiological conditions, including electrical remodelling in cardiac disease, ion channel modulation by clinically used pharmacological agents, and systemic electrolyte disorders seen in heart failure, such as hypokalaemia. Cardiac electrical instability attributed to abnormal repolarization relies on the complex interplay between a provocative arrhythmic trigger and vulnerable arrhythmic substrate, with a central role played by the excessive prolongation of ventricular action potential duration, impaired intracellular Ca²⁺ handling, and slowed impulse conduction. This review outlines the electrical activity of ventricular myocytes in normal conditions and cardiac disease, describes classical electrophysiological mechanisms of cardiac arrhythmia, and provides an update on repolarization-related surrogates currently used to assess arrhythmic propensity, including spatial dispersion of repolarization, activation-repolarization coupling, electrical restitution, TRIaD (triangulation, reverse use dependence, instability, and dispersion), and the electromechanical window. This is followed by a discussion of the mechanisms that account for the dependence of arrhythmic vulnerability on the location of the ventricular pacing site. Finally, the review clarifies the electrophysiological basis for cardiac arrhythmia produced by hypokalaemia, and gives insight into the clinical importance and pathophysiology of drug-induced arrhythmia, with particular focus on class Ia (quinidine, procainamide) and Ic (flecainide) Na⁺ channel blockers, and class III antiarrhythmic agents that block the delayed rectifier K⁺ channel (dofetilide).

Increased Late Sodium Current Contributes to the Electrophysiological Effects of Chronic, but Not Acute, Dofetilide Administration

BACKGROUND

Drugs are screened for delayed rectifier potassium current (IKr) blockade to predict long QT syndrome prolongation and arrhythmogenesis. However, single-cell studies have shown that chronic (hours) exposure to some IKr blockers (eg, dofetilide) prolongs repolarization additionally by increasing late sodium current (INa-L) via inhibition of phosphoinositide 3-kinase. We hypothesized that chronic dofetilide administration to intact dogs prolongs repolarization by blocking IKr and increasing INa-L.

METHODS AND RESULTS

We continuously infused dofetilide (6-9 μg/kg bolus+6-9 μg/kg per hour IV infusion) into anesthetized dogs for 7 hours, maintaining plasma levels within the therapeutic range. In separate experiments, myocardial biopsies were taken before and during 6-hour intravenous dofetide infusion, and the level of phospho-Akt was determined. Acute and chronic dofetilide effects on action potential duration (APD) were studied in canine left ventricular subendocardial slabs using microelectrode techniques. Dofetilide monotonically increased QTc and APD throughout 6.5-hour exposure. Dofetilide infusion during ≥210 minutes inhibited Akt phosphorylation. INa-L block with lidocaine shortened QTc and APD more at 6.5 hours than at 50 minutes (QTc) or 30 minutes (APD) dofetilide administration. In comparison, moxifloxacin, an IKr blocker with no effects on phosphoinositide 3-kinase and INa-L prolonged APD acutely but no additional prolongation occurred on chronic superfusion. Lidocaine shortened APD equally during acute and chronic moxifloxacin superfusion.

CONCLUSIONS

Increased INa-L contributes to chronic dofetilide effects in vivo. These data emphasize the need to include time and INa-L in evaluating the phosphoinositide 3-kinase inhibition-derived proarrhythmic potential of drugs and provide a mechanism for benefit from lidocaine administration in clinical acquired long QT syndrome.

Computational rabbit models to investigate the initiation, perpetuation, and termination of ventricular arrhythmia

Current understanding of cardiac electrophysiology has been greatly aided by computational work performed using rabbit ventricular models. This article reviews the contributions of multiscale models of rabbit ventricles in understanding cardiac arrhythmia mechanisms. This review will provide an overview of multiscale modeling of the rabbit ventricles. It will then highlight works that provide insights into the role of the conduction system, complex geometric structures, and heterogeneous cellular electrophysiology in diseased and healthy rabbit hearts to the initiation and maintenance of ventricular arrhythmia. Finally, it will provide an overview on the contributions of rabbit ventricular modeling on understanding the mechanisms underlying shock-induced defibrillation.

Ventricular fibrillation: triggers, mechanisms and therapies

Ventricular fibrillation (VF) is a common, life-threatening arrhythmia responsible for significant morbidity and mortality. Due to challenges in safely mapping VF, a comprehensive understanding of its mechanisms remains elusive. Recent findings have provided new insights into mechanisms that sustain early VF. Notably, the central role of electrical rotors and catheter-based ablation of VF rotor substrate have been recently reported. In this article, we will review data regarding four stages of VF: initiation, transition, maintenance and evolution. We will discuss the particular mechanisms for each stage and therapies targeting these mechanisms. We also examine inherited arrhythmia syndromes, including the mechanisms and therapies specific to each. We hope that the overview of VF outlined in this work will assist other investigators in designing future therapies to interrupt this life-threatening arrhythmia.

Using Skewness and the First-Digit Phenomenon to Identify Dynamical Transitions in Cardiac Models

Disruptions in the normal rhythmic functioning of the heart, termed as arrhythmia, often result from qualitative changes in the excitation dynamics of the organ. The transitions between different types of arrhythmia are accompanied by alterations in the spatiotemporal pattern of electrical activity that can be measured by observing the time-intervals between successive excitations of different regions of the cardiac tissue. Using biophysically detailed models of cardiac activity we show that the distribution of these time-intervals exhibit a systematic change in their skewness during such dynamical transitions. Further, the leading digits of the normalized intervals appear to fit Benford's law better at these transition points. This raises the possibility of using these observations to design a clinical indicator for identifying changes in the nature of arrhythmia. More importantly, our results reveal an intriguing relation between the changing skewness of a distribution and its agreement with Benford's law, both of which have been independently proposed earlier as indicators of regime shift in dynamical systems.

Nonlinear and Stochastic Dynamics in the Heart

In a normal human life span, the heart beats about 2 to 3 billion times. Under diseased conditions, a heart may lose its normal rhythm and degenerate suddenly into much faster and irregular rhythms, called arrhythmias, which may lead to sudden death. The transition from a normal rhythm to an arrhythmia is a transition from regular electrical wave conduction to irregular or turbulent wave conduction in the heart, and thus this medical problem is also a problem of physics and mathematics. In the last century, clinical, experimental, and theoretical studies have shown that dynamical theories play fundamental roles in understanding the mechanisms of the genesis of the normal heart rhythm as well as lethal arrhythmias. In this article, we summarize in detail the nonlinear and stochastic dynamics occurring in the heart and their links to normal cardiac functions and arrhythmias, providing a holistic view through integrating dynamics from the molecular (microscopic) scale, to the organelle (mesoscopic) scale, to the cellular, tissue, and organ (macroscopic) scales. We discuss what existing problems and challenges are waiting to be solved and how multi-scale mathematical modeling and nonlinear dynamics may be helpful for solving these problems.

The logical operator map identifies novel candidate markers for critical sites in patients with atrial fibrillation

The identification of suitable markers for critical patterns during atrial fibrillation (AF) may be crucial to guide an effective ablation treatment. Single parameter maps, based on dominant frequency and complex fractionated electrograms, have been proposed as a tool for electrogram-guided ablation, however the specificity of these markers is debated. Experimental studies suggest that AF critical patterns may be identified on the basis of specific rate and organization features, where rapid organized and rapid fragmented activities characterize respectively localized sources and critical substrates. In this paper we introduce the logical operator map, a novel mapping tool for a point-by-point identification and localization of AF critical sites. Based on advanced signal and image processing techniques, the approach combines in a single map electrogram-derived rate and organization features with tomographic anatomical detail. The construction of the anatomically-detailed logical operator map is based on the time-domain estimation of atrial rate and organization in terms of cycle length and wave-similarity, the logical combination of these indexes to obtain suitable markers of critical sites, and the multimodal integration of electrophysiological and anatomical information by segmentation and registration techniques. Logical operator maps were constructed in 14 patients with persistent AF, showing the capability of the combined rate and organization markers to identify with high selectivity the subset of electrograms associated with localized sources and critical substrates. The precise anatomical localization of these critical sites revealed the confinement of rapid organized sources in the left atrium with organization and rate gradients towards the surrounding tissue, and the presence of rapid fragmented electrograms in proximity of the sources. By merging in a single map the most relevant electrophysiological and anatomical features of the AF process, the logical operator map may have significant clinical impact as a direct, comprehensive tool to understand arrhythmia mechanisms in the single patient and guide more conservative, step-wise ablation.

Unpinning of rotating spiral waves in cardiac tissues by circularly polarized electric fields

Spiral waves anchored to obstacles in cardiac tissues may cause lethal arrhythmia. To unpin these anchored spirals, comparing to high-voltage side-effect traditional therapies, wave emission from heterogeneities (WEH) induced by the uniform electric field (UEF) has provided a low-voltage alternative. Here we provide a new approach using WEH induced by the circularly polarized electric field (CPEF), which has higher success rate and larger application scope than UEF, even with a lower voltage. And we also study the distribution of the membrane potential near an obstacle induced by CPEF to analyze its mechanism of unpinning. We hope this promising approach may provide a better alternative to terminate arrhythmia.

The emergence of subcellular pacemaker sites for calcium waves and oscillations

Calcium (Ca(2+)) waves generating oscillatory Ca(2+) signals are widely observed in biological cells. Experimental studies have shown that under certain conditions, initiation of Ca(2+) waves is random in space and time, while under other conditions, waves occur repetitively from preferred locations (pacemaker sites) from which they entrain the whole cell. In this study, we use computer simulations to investigate the self-organization of Ca(2+) sparks into pacemaker sites generating Ca(2+) oscillations. In both ventricular myocyte experiments and computer simulations of a heterogeneous Ca(2+) release unit (CRU) network model, we show that Ca(2+) waves occur randomly in space and time when the Ca(2+) level is low, but as the Ca(2+) level increases, waves occur repetitively from the same sites. Our analysis indicates that this transition to entrainment can be attributed to the fact that random Ca(2+) sparks self-organize into Ca(2+) oscillations differently at low and high Ca(2+) levels. At low Ca(2+), the whole cell Ca(2+) oscillation frequency of the coupled CRU system is much slower than that of an isolated single CRU. Compared to a single CRU, the distribution of interspike intervals (ISIs) of the coupled CRU network exhibits a greater variation, and its ISI distribution is asymmetric with respect to the peak, exhibiting a fat tail. At high Ca(2+), however, the coupled CRU network has a faster frequency and lesser ISI variation compared to an individual CRU. The ISI distribution of the coupled network no longer exhibits a fat tail and is well-approximated by a Gaussian distribution. This same Ca(2+) oscillation behaviour can also be achieved by varying the number of ryanodine receptors per CRU or the distance between CRUs. Using these results, we develop a theory for the entrainment of random oscillators which provides a unified explanation for the experimental observations underlying the emergence of pacemaker sites and Ca(2+) oscillations.

Spiral-wave dynamics in a mathematical model of human ventricular tissue with myocytes and fibroblasts

Cardiac fibroblasts, when coupled functionally with myocytes, can modulate the electrophysiological properties of cardiac tissue. We present systematic numerical studies of such modulation of electrophysiological properties in mathematical models for (a) single myocyte-fibroblast (MF) units and (b) two-dimensional (2D) arrays of such units; our models build on earlier ones and allow for zero-, one-, and two-sided MF couplings. Our studies of MF units elucidate the dependence of the action-potential (AP) morphology on parameters such as , the fibroblast resting-membrane potential, the fibroblast conductance , and the MF gap-junctional coupling . Furthermore, we find that our MF composite can show autorhythmic and oscillatory behaviors in addition to an excitable response. Our 2D studies use (a) both homogeneous and inhomogeneous distributions of fibroblasts, (b) various ranges for parameters such as , and , and (c) intercellular couplings that can be zero-sided, one-sided, and two-sided connections of fibroblasts with myocytes. We show, in particular, that the plane-wave conduction velocity decreases as a function of , for zero-sided and one-sided couplings; however, for two-sided coupling, decreases initially and then increases as a function of , and, eventually, we observe that conduction failure occurs for low values of . In our homogeneous studies, we find that the rotation speed and stability of a spiral wave can be controlled either by controlling or . Our studies with fibroblast inhomogeneities show that a spiral wave can get anchored to a local fibroblast inhomogeneity. We also study the efficacy of a low-amplitude control scheme, which has been suggested for the control of spiral-wave turbulence in mathematical models for cardiac tissue, in our MF model both with and without heterogeneities.

Quinidine elicits proarrhythmic changes in ventricular repolarization and refractoriness in guinea-pig

Quinidine is a class Ia Na+ channel blocker that prolongs cardiac repolarization owing to the inhibition of IKr, the rapid component of the delayed rectifier current. Although quinidine may induce proarrhythmia, the contributing mechanisms remain incompletely understood. This study examined whether quinidine may set proarrhythmic substrate by inducing spatiotemporal abnormalities in repolarization and refractoriness. The monophasic action potential duration (APD), effective refractory periods (ERPs), and volume-conducted electrocardiograms (ECGs) were assessed in perfused guinea-pig hearts. Quinidine was found to produce the reverse rate-dependent prolongation of ventricular repolarization, which contributed to increased steepness of APD restitution. Throughout the epicardium, quinidine elicited a greater APD increase in the left ventricular chamber compared with the right ventricle, thereby enhancing spatial repolarization heterogeneities. Quinidine prolonged APD to a greater extent than ERP, thus extending the vulnerable window for ventricular re-excitation. This change was attributed to increased triangulation of epicardial action potential because of greater APD lengthening at 90% repolarization than at 30% repolarization. Over the transmural plane, quinidine evoked a greater ERP prolongation at endocardium than epicardium and increased dispersion of refractoriness. Premature ectopic beats and monomorphic ventricular tachycardia were observed in 50% of quinidine-treated heart preparations. In summary, abnormal changes in repolarization and refractoriness contribute greatly to proarrhythmic substrate upon quinidine infusion.

Synchronization of early afterdepolarizations and arrhythmogenesis in heterogeneous cardiac tissue models

Early afterdepolarizations (EADs) are linked to both triggered arrhythmias and reentrant arrhythmias by causing premature ventricular complexes (PVCs), focal excitations, or heterogeneous tissue substrates for reentry formation. However, a critical number of cells that synchronously exhibit EADs are needed to result in arrhythmia triggers and substrates in tissue. In this study, we use mathematical modeling and computer simulations to investigate EAD synchronization and arrhythmia induction in tissue models with random cell-to-cell variations. Our major observations are as follows. Random cell-to-cell variations in action potential duration without EAD presence do not cause large dispersion of refractoriness in well-coupled tissue. In the presence of phase-2 EADs, the cells may synchronously exhibit the same number of EADs or no EADs with a very small dispersion of refractoriness, or synchronize regionally to result in large dispersion of refractoriness. In the presence of phase-3 EADs, regional synchronization leads to propagating EADs, forming PVCs in tissue. Interestingly, even though the uncoupled cells exhibit either no EAD or only a single EAD, when these cells are coupled to form a tissue, more than one PVC can occur. When the PVCs occur at different locations and time, multifocal arrhythmias are triggered, with the foci shifting in space and time in an irregular manner. The focal arrhythmias either spontaneously terminate or degenerate into reentrant arrhythmias due to heterogeneities and spatiotemporal chaotic dynamics of the foci.

Abnormal restitution property of action potential duration and conduction delay in Brugada syndrome: both repolarization and depolarization abnormalities

AIMS

This study sought to examine the action potential duration restitution (APDR) property and conduction delay in Brugada syndrome (BrS) patients. A steeply sloped APDR curve and conduction delay are known to be important determinants for the occurrence of ventricular fibrillation (VF).

METHODS AND RESULTS

Endocardial monophasic action potential was obtained from 39 BrS patients and 9 control subjects using the contact electrode method. Maximum slopes of the APDR curve were obtained at both the right ventricular outflow tract (RVOT) and the right ventricular apex (RVA). The onset of activation delay (OAD) after premature stimulation was examined as a marker of conduction delay. Maximum slope of the APDR curve in BrS patients was significantly steeper than that in control subjects at both the RVOT and the RVA (0.77 +/- 0.21 vs. 058 +/- 0.14 at RVOT, P = 0.009; 0.98 +/- 0.23 vs. 0.62 +/- 0.16 at RVA, P = 0.001). The dispersion of maximum slope of the APDR curve between the RVOT and the RVA was also larger in BrS patients than in control subjects. The OAD was significantly longer in BrS patients than in control subjects from the RVOT to RVA and from the RVA to RVOT (from RVOT to RVA: 256 +/- 12 vs. 243 +/- 7 ms, P = 0.003; from RVA to RVOT: 252 +/- 11 vs. 241 +/- 9 ms, P = 0.01).

CONCLUSIONS

Abnormal APDR properties and conduction delay were observed in BrS patients. Both repolarization and depolarization abnormalities are thought to be related to the development of VF in BrS patients.

Centrifugal gradients of rate and organization in human atrial fibrillation

INTRODUCTION

Animal studies show that atrial fibrillation (AF) may emanate from sites of high rate and regularity, with fibrillatory conduction to adjacent areas. We used simultaneous mapping to find evidence for potential drivers in human AF defined as sites with higher rate and regularity than surrounding tissue.

MATERIALS AND METHODS

In 24 patients (age 61+/-10 years; 12 persistent), we recorded AF simultaneously from 32 left atrial bipolar basket electrodes in addition to pulmonary veins (PV), coronary sinus, and right atrial electrodes. We measured AF cycle length (CL) by Fourier transform and electrogram regularity at each electrode, referenced to patient-specific atrial anatomy.

RESULTS

We analyzed 10,298 electrode-periods. Evidence for potential AF drivers was found in 11 patients (five persistent). In persistent AF, these sites lay at the coronary sinus and left atrial roof but not PVs, while in paroxysmal AF six of nine sites lay at PVs (P<0.05). During ablation, a subset of patients experienced AF CL prolongation or termination with a focal lesion; in each case this lesion mapped to potential driver sites on blinded analysis. Conversely, sequential mapping failed to reveal these sites, possibly due to fluctuations in dominant frequency at driver locations in the context of migratory AF.

CONCLUSIONS

Simultaneous multisite recordings in human AF reveal evidence for drivers that lie near PVs in paroxysmal but not persistent AF, and were sites where ablation slowed or terminated AF in a subset of patients. The future work should determine if real-time ablation of AF-maintaining regions defined in this fashion eliminates AF.

Reexcitation mechanisms in epicardial tissue: role of I(to) density heterogeneities and I(Na) inactivation kinetics

Dispersion of action potential repolarization is known to be an important arrhythmogenic factor in cardiopathies such as Brugada syndrome. In this work, we analyze the effect of a variation in sodium current (I(Na)) inactivation and a heterogeneous rise of transient outward current (I(to)) in the probability of reentry in epicardial tissue. We use the Luo-Rudy model of epicardial ventricular action potential to study wave propagation in a one-dimensional fiber. Spatial dispersion in repolarization is introduced by splitting the fiber into zones with different strength of I(to). We then analyze the pro-arrhythmic effect of a variation in the relaxation time and steady-state of the sodium channel fast inactivating gate h. We quantify the probability of reentry measuring the percentage of reexcitations that occurs in 200 beats. We find that, for high stimulation rates, this percentage is negligible, but increases notably for pacing periods above 700ms. Surprisingly, with decreasing I(Na) inactivation time, the percentage of reexcitations does not grow monotonically, but presents vulnerable windows, separated by values of the I(Na) inactivation speed-up where reexcitation does not occur. By increasing the strength of L-type calcium current I(CaL) above a certain threshold, reexcitation disappears. Finally, we show the formation of reentry in stimulated two-dimensional epicardial tissue with modified I(Na) kinetics and I(to) heterogeneity. Thus, we confirm that while I(to) dispersion is necessary for phase-2 reentry, altered sodium inactivation kinetics influences the probability of reexcitation in a highly nonlinear fashion.

Spiral-wave turbulence and its control in the presence of inhomogeneities in four mathematical models of cardiac tissue

Regular electrical activation waves in cardiac tissue lead to the rhythmic contraction and expansion of the heart that ensures blood supply to the whole body. Irregularities in the propagation of these activation waves can result in cardiac arrhythmias, like ventricular tachycardia (VT) and ventricular fibrillation (VF), which are major causes of death in the industrialised world. Indeed there is growing consensus that spiral or scroll waves of electrical activation in cardiac tissue are associated with VT, whereas, when these waves break to yield spiral- or scroll-wave turbulence, VT develops into life-threatening VF: in the absence of medical intervention, this makes the heart incapable of pumping blood and a patient dies in roughly two-and-a-half minutes after the initiation of VF. Thus studies of spiral- and scroll-wave dynamics in cardiac tissue pose important challenges for in vivo and in vitro experimental studies and for in silico numerical studies of mathematical models for cardiac tissue. A major goal here is to develop low-amplitude defibrillation schemes for the elimination of VT and VF, especially in the presence of inhomogeneities that occur commonly in cardiac tissue. We present a detailed and systematic study of spiral- and scroll-wave turbulence and spatiotemporal chaos in four mathematical models for cardiac tissue, namely, the Panfilov, Luo-Rudy phase 1 (LRI), reduced Priebe-Beuckelmann (RPB) models, and the model of ten Tusscher, Noble, Noble, and Panfilov (TNNP). In particular, we use extensive numerical simulations to elucidate the interaction of spiral and scroll waves in these models with conduction and ionic inhomogeneities; we also examine the suppression of spiral- and scroll-wave turbulence by low-amplitude control pulses. Our central qualitative result is that, in all these models, the dynamics of such spiral waves depends very sensitively on such inhomogeneities. We also study two types of control schemes that have been suggested for the control of spiral turbulence, via low amplitude current pulses, in such mathematical models for cardiac tissue; our investigations here are designed to examine the efficacy of such control schemes in the presence of inhomogeneities. We find that a local pulsing scheme does not suppress spiral turbulence in the presence of inhomogeneities; but a scheme that uses control pulses on a spatially extended mesh is more successful in the elimination of spiral turbulence. We discuss the theoretical and experimental implications of our study that have a direct bearing on defibrillation, the control of life-threatening cardiac arrhythmias such as ventricular fibrillation.

Modeling ventricular repolarization: effects of transmural and apex-to-base heterogeneities in action potential durations

Heterogeneities in the densities of membrane ionic currents of myocytes cause regional variations in action potential duration (APD) at various intramural depths and along the apico-basal and circumferential directions in the left ventricle. This work extends our previous study of cartesian slabs to ventricular walls shaped as an ellipsoidal volume and including both transmural and apex-to-base APD heterogeneities. Our 3D simulation study investigates the combined effect on repolarization sequences and APD distributions of: (a) the intrinsic APD heterogeneity across the wall and along the apex-to-base direction, and (b) the electrotonic currents that modulate the APDs when myocytes are embedded in a ventricular wall with fiber rotation and orthotropic anisotropy. Our findings show that: (i) the transmural and apex-to-base heterogeneities have only a weak influence on the repolarization patterns on myocardial layers parallel to the epicardium; (ii) the patterns of APD distribution on the epicardial surface are mostly affected by the apex-to-base heterogeneities and do not reveal the APD transmural heterogeneity; (iii) the transmural heterogeneity is clearly discernible in both repolarization and APD patterns only on transmural sections; (iv) the apex-to-base heterogeneity is clearly discernible only in APD patterns on layers parallel to the epicardium. Thus, in our orthotropic ellipsoidal wall, the complex 3D electrotonic modulation of APDs does not fully mix the effects of the transmural and apex-to-base heterogeneity. The intrinsic spatial heterogeneity of the APDs is unmasked in the modulated APD patterns only in the appropriate transmural or intramural sections. These findings are independent of the stimulus location (epicardial, endocardial) and of Purkinje involvement.

Ventricular repolarization restitution properties in patients exhibiting type 1 Brugada electrocardiogram with and without inducible ventricular fibrillation

OBJECTIVES

This study aimed to elucidate the contribution of the repolarization restitution property to the sustained ventricular fibrillation (VF) in Brugada syndrome.

BACKGROUND

Although phase 2 re-entry develops as the trigger of VF, the other precipitating factors have remained unclear.

METHODS

Twenty-one patients with a type 1 Brugada electrocardiogram underwent programmed electrical stimulation. Before the VF induction, single extrastimuli were delivered at 3 basic drive cycle lengths (BCLs) (400 ms, 600 ms, and 750 ms) from the right ventricular apex (RVA) and outflow tract (RVOT), and the activation recovery interval (ARI) was measured at 5-mm vicinity of the pacing site. The maximum ARI restitution slope was determined using the overlapping least-squares linear segments.

RESULTS

We found that VF was inducible in 10 patients. A repeated-measure analysis of variance revealed that the slope in the RVA was steeper in patients with inducible VF than in those without but that in the RVOT was similar. The slope was steeper at longer BCLs and also steeper in the RVA than RVOT at BCLs of 600 and 750 ms. In patients with inducible VF, the percentage of patients exhibiting a slope >1 was 0%, 20%, and 75% in the RVA and 0%, 0%, and 14% in the RVOT at BCLs of 400 ms, 600 ms, and 750 ms, respectively. No patients without inducible VF had a slope >1.

CONCLUSIONS

These results suggest the repolarization restitution property is a contributing factor to the propensity for VF in Brugada syndrome and, regarding this property, the RVA plays more important role than the RVOT.

Cardiac mechano-electric feedback and electrical restitution in humans

Electrical restitution in the heart is the property whereby the action potential duration and conduction velocity of a beat of altered cycle length vary according to its immediacy to the preceding basic beat--the coupling interval, usually the diastolic interval. In general, action potential duration (APD) increases with increasing coupling interval, and the relation between action potential duration and the preceding diastolic interval describes the APD restitution curve. The latter has recently been the focus of considerable interest since the steepness of the initial part of the restitution curve plays an important role in electrical stability and arrhythmogenesis. Mechanical stretch has been shown to alter APD and hence refractoriness either through stretch activated channels or by influencing calcium cycling. Such an effect on refractoriness has been proposed as a mechanism of arrhythmogenesis particularly if spatially inhomogeneities manifest within the heart. Here, we review (1) the spatial and temporal characteristics of APD restitution in humans; (2) previously reported work showing that mechanical loading differentially effects APD of interpolated beats of altered cycle length, and hence alters the slope of the APD restitution curve; and (3) evidence that inhomogeneity of APD restitution slope may be an important factor in arrhythmogenesis.

Effect of heterogeneous APD restitution on VF organization in a model of the human ventricles

The onset of ventricular fibrillation (VF) has been associated with steep action potential duration restitution in both clinical and computational studies. Recently, detailed clinical restitution properties in cardiac patients were reported showing a substantial degree of heterogeneity in restitution slopes at the epicardium of the ventricles. The aim of the present study was to investigate the effect of heterogeneous restitution properties in a three-dimensional model of the ventricles using these clinically measured restitution data. We used a realistic model of the human ventricles, including detailed descriptions of cell electrophysiology, ventricular anatomy, and fiber direction anisotropy. We extended this model by mapping the clinically observed epicardial restitution data to our anatomic representation using a diffusion-based algorithm. Restitution properties were then fitted by regionally varying parameters of the electrophysiological model. We studied the effects of restitution heterogeneity on the organization of VF by analyzing filaments and the distributions of excitation periods. We found that the number of filaments and the excitation periods were both dependent on the extent of heterogeneity. An increased level of heterogeneity leads to a greater number of filaments and a broader distribution of excitation periods, thereby increasing the complexity and dynamics of VF. Restitution heterogeneity may play an important role in providing a substrate for cardiac arrhythmias.

An unconditionally stable numerical method for the Luo–Rudy 1 model used in simulations of defibrillation

Numerical simulations of defibrillation using the Bidomain model coupled to a model of membrane kinetics represent a serious numerical challenge. This is because very high voltages close to defibrillation electrodes demand that extreme time step restrictions be placed on standard numerical schemes, e.g. the forward Euler scheme. A common solution to this problem is to modify the cell model by simple if-tests applied to several equations and rate functions. These changes are motivated by numerical problems rather than physiology, and should therefore be avoided whenever possible. The purpose of this paper is to present a numerical scheme that handles the original model without modifications and which is unconditionally stable for the Luo-Rudy phase 1 model. This also shows that the cell model is mathematically well-behaved, even in the presence of very high voltages. Our theoretical results are illustrated by numerical computations.

Steeper restitution slopes across right ventricular endocardium in patients with cardiomyopathy at high risk of ventricular arrhythmias

Steep action potential duration (APD) restitution slopes (>1) and spatial APD restitution heterogeneity provide the substrate for ventricular fibrillation in computational models and experimental studies. Their relationship to ventricular arrhythmia vulnerability in human cardiomyopathy has not been defined. Patients with cardiomyopathy [left ventricular (LV) ejection fraction <40%] and no history of ventricular arrhythmias underwent risk stratification with programmed electrical stimulation or T wave alternans (TWA). Low-risk patients ( n = 10) had no inducible ventricular tachycardia (VT) or negative TWA, while high-risk patients ( n = 8) had inducible VT or positive TWA. Activation recovery interval (ARI) restitution slopes were measured simultaneously from 10 right ventricular (RV) endocardial sites during an S1-S2 pacing protocol. ARI restitution slope heterogeneity was defined as the coefficient of variation of slopes. Mean ARI restitution slope was significantly steeper in the high-risk group compared with the low-risk group [1.16 (SD 0.31) vs. 0.59 (SD 0.19), P = 0.0002]. The proportion of endocardial recording sites with a slope >1 was significantly larger in the high-risk patients [47% (SD 35) vs. 13% (SD 21), P = 0.022]. Spatial heterogeneity of ARI restitution slopes was similar between the two groups [29% (SD 16) vs. 39% (SD 34), P = 0.48]. There was an inverse linear relationship between the ARI restitution slope and the minimum diastolic interval ( P < 0.001). In cardiomyopathic patients at high risk of ventricular arrhythmias, ARI restitution slopes along the RV endocardium are steeper, but restitution slope heterogeneity is similar compared with those at low risk. Steeper ARI restitution slopes may increase the propensity for ventricular arrhythmias in patients with impaired left ventricular function.

Arrhythmogenesis in the heart: Multiscale modeling of the effects of defibrillation shocks and the role of electrophysiological heterogeneity

The mechanisms of initiation of ventricular arrhythmias as well as those behind the complex spatiotemporal wave dynamics and its filament organization during ventricular fibrillation (VF) are the topic of intense research and debate. Mechanistic inquiry into the various mechanisms that lead to arrhythmia initiation and VF maintenance is hampered by the inability of current experimental techniques to resolve, with sufficient accuracy, electrical behavior confined to the depth of the ventricles. The objective of this article is to demonstrate that realistic 3D simulations of electrical activity in the heart are capable of bringing a new level of understanding of the mechanisms that underlie arrhythmia initiation and subsequent organization. The article does this by presenting the results of two multiscale simulation studies of ventricular electrical behavior. The first study aims to uncover the mechanisms responsible for rendering the ventricles vulnerable to electric shocks during a specific interval of time, the vulnerable window. The second study focuses on elucidating the role of electrophysiological heterogeneity, and specifically, differences in action potential duration in various ventricular structures, in VF organization. Both studies share common multiscale modeling approaches and analysis, including characterization of scroll-wave filament dynamics.

A case of short-coupled variant of torsade de pointes characterized by spatial heterogeneity of action potential duration and its restitution kinetics

A 21-year-old male experienced frequent episodes of polymorphic ventricular tachycardia (PVT) initiated by a closely coupled premature ventricular complex (PVC) in the absence of QT prolongation and structural heart disease. Programmed stimulation at right ventricular apex (RVA), but not at the outflow tract (RVOT), provoked PVT degenerating into ventricular fibrillation (VF). Monophasic action potential duration (MAPD) was significantly shorter at RVA than RVOT. The maximum slope of MAPD restitution was much steeper at RVA than RVOT (1.91 versus 0.50). Such spatial heterogeneities of MAPD and its restitution may facilitate wavebreak and functional reentry predisposing to PVT and VF.

Effects of transmural electrical heterogeneities and electrotonic interactions on the dispersion of cardiac repolarization and action potential duration: A simulation study

It has been shown in the literature that myocytes isolated from the ventricular walls at various intramural depths have different action potential durations (APDs). When these myocytes are embedded in the ventricular wall, their inhomogeneous properties affect the sequence of repolarization and the actual distribution of the APDs in the entire wall. In this article, we implement a mathematical model to simulate the combined effect of (a) the non-homogeneous intrinsic membrane properties (in particular the non-homogeneous APDs) and (b) the electrotonic currents that modulate the APDs when the myocytes are embedded in the ventricular myocardium. In particular, we study the effect of (a) and (b) on the excitation and repolarization sequences and on the distribution of APDs in the ventricles. We implement a Monodomain tissue representation that includes orthotropic anisotropy, transmural fiber rotation and homogeneous or heterogeneous transmural intrinsic membrane properties, modeled according to the phase I Luo-Rudy membrane ionic model. Three-dimensional simulations are performed in a cartesian slab with a parallel finite element solver employing structured isoparametric trilinear finite elements in space and a semi-implicit adaptive method in time. Simulations of excitation and repolarization sequences elicited by epicardial or endocardial pacing show that in a homogeneous slab the repolarization pathways approximately follow the activation sequence. Conversely, in the heterogeneous cases considered in this study, we observed two repolarization wavefronts that started from the epi and the endocardial faces respectively and collided in the thickness of the wall and in one case an additional repolarization wave starting from an intramural site. Introducing the heterogeneities along the transmural epi-endocardial direction affected both the repolarization sequence and the APD dispersion, but these effects were clearly discernible only in transmural planes. By contrast, in planes parallel to epi- and endocardium the APD distribution remained remarkably similar to that observed in the homogeneous model. Therefore, the patterns of the repolarization sequence and APD dispersion on the epicardial surface (or any other intramural surface parallel to it) do not reveal the uniform transmural heterogeneity.

Activation sequence as a key factor in spatio-temporal optimization of myocardial function

Using one-dimensional models of myocardial tissue, implemented as chains of virtual ventricular muscle segments that are kinematically connected in series, we studied the role of the excitation sequence in spatio-temporal organization of cardiac function. Each model element was represented by a well-verified mathematical model of cardiac electro-mechanical activity. We found that homogeneous chains, consisting of identical elements, respond to non-simultaneous stimulation by generation of complex spatio-temporal heterogeneities in element deformation. These are accompanied by the establishment of marked gradients in local electro-mechanical properties of the elements (heterogeneity in action potential duration, Ca2+ transient characteristics and sarcoplasmic reticulum Ca2+ loading). In heterogeneous chains, composed of elements simulating fast and slow contracting cardiomyocytes from different transmural layers, we found that only activation sequences where stimulation of the slower elements preceded that of faster ones gave rise to optimization of the system's electro-mechanical function, which was confirmed experimentally. Based on the results obtained, we hypothesize that the sequence of activation of cardiomyocytes in different ventricular layers is one of the key factors of spatio-temporal organization of myocardium. Moreover, activation sequence and regional differences in intrinsic electro-mechanical properties of cardiac muscle must be matched in order to optimize myocardial function.

The role of heterogeneities and intercellular coupling in wave propagation in cardiac tissue

Electrical heterogeneities play a role in the initiation of cardiac arrhythmias. In certain pathological conditions such as ischaemia, current sinks can develop in the diseased cardiac tissue. In this study, we investigate the effects of changing the amount of heterogeneity and intercellular coupling on wavefront stability in a cardiac cell culture system and a mathematical model of excitable media. In both systems, we observe three types of behaviour: plane wave propagation without breakup, plane wave breakup into spiral waves and plane wave block. In the theoretical model, we observe a linear decrease in propagation velocity as the number of heterogeneities is increased, followed by a rapid, nonlinear decrease to zero. The linear decrease results from the heterogeneities acting independently on the wavefront. A general scaling argument that considers the degree of system heterogeneity and the properties of the excitable medium is used to derive a dimensionless parameter that describes the interaction of the wavefront with the heterogeneities.

Effects of rapid and slow potassium repolarization currents and calcium dynamics on hysteresis in restitution of action potential duration

We used a mathematical model to investigate effects of repolarizing currents I(kr) and I(ks), calcium (Ca) current I(CaL), and Ca dynamics in network sarcoplasmic reticulum and junctional sarcoplasmic reticulum (JSR) on hysteresis in restitution of action potential duration. Enhanced I(kr) increased slope of restitution, hysteresis loop thickness, and delay between peaks of diastolic intervals and action potential duration. Increase in I(ks) decreased loop thickness and peak delay. Decrease in I(CaL) had effects similar to increasing I(kr), except slope of restitution decreased markedly. Uptake of Ca into the network sarcoplasmic reticulum had less effect on hysteresis than transfer of Ca into JSR. Faster transfer of Ca into JSR markedly decreased loop thickness and peak delay. Our results provide insight into mechanisms responsible for this newly identified property of restitution. Such information will be valuable in studies where modification of hysteresis is used to investigate its role in arrhythmogenesis.

Whole heart action potential duration restitution properties in cardiac patients: a combined clinical and modelling study

Steep action potential duration (APD) restitution has been shown to facilitate wavebreak and ventricular fibrillation. The global APD restitution properties in cardiac patients are unknown. We report a combined clinical electrophysiology and computer modelling study to: (1) determine global APD restitution properties in cardiac patients; and (2) examine the interaction of the observed APD restitution with known arrhythmia mechanisms. In 14 patients aged 52-85 years undergoing routine cardiac surgery, 256 electrode epicardial mapping was performed. Activation-recovery intervals (ARI; a surrogate for APD) were recorded over the entire ventricular surface. Mono-exponential restitution curves were constructed for each electrode site using a standard S1-S2 pacing protocol. The median maximum restitution slope was 0.91, with 27% of all electrode sites with slopes<0.5, 29% between 0.5 and 1.0, and 20% between 1.0 and 1.5. Eleven per cent of restitution curves maintained slope>1 over a range of diastolic intervals of at least 30 ms; and 0.3% for at least 50 ms. Activation-recovery interval restitution was spatially heterogeneous, showing regional organization with multiple discrete areas of steep and shallow slope. We used a simplified computer model of 2-D cardiac tissue to investigate how heterogeneous APD restitution can influence vulnerability to, and stability of re-entry. Our model showed that heterogeneity of restitution can act as a potent arrhythmogenic substrate, as well as influencing the stability of re-entrant arrhythmias. Global epicardial mapping in humans showed that APD restitution slopes were organized into regions of shallow and steep slopes. This heterogeneous organization of restitution may provide a substrate for arrhythmia.

Hybrid duplex: a novel method to study the contractile function of heterogeneous myocardium

In an earlier study, we experimentally mimicked the effects of mechanical interaction between different regions of the ventricular wall by allowing pairs of independently maintained cardiac muscle fibers to interact mechanically in series or in parallel. This simple physiological model of heterogeneous myocardium, which has been termed “duplex,” has provided new insight into basic effects of cardiac electromechanical heterogeneity. Here, we present a novel “hybrid duplex,” where one of the elements is an isolated cardiac muscle and the other a “virtual cardiac muscle.” The virtual muscle is represented by a computational model of cardiomyocyte electromechanical activity. We present in detail the computer-based digital control system that governs the mechanical interaction between virtual and biological muscle, the software used for data analysis, and working implementations of the model. Advantages of the hybrid duplex method are discussed, and experimental recordings are presented for illustration and as proof of the principle.

Critical mass hypothesis revisited: role of dynamical wave stability in spontaneous termination of cardiac fibrillation

The tendency of atrial or ventricular fibrillation to terminate spontaneously in finite-sized tissue is known as the critical mass hypothesis. Previous studies have shown that dynamical instabilities play an important role in creating new wave breaks that maintain cardiac fibrillation, but its role in self-termination, in relation to tissue size and geometry, is not well understood. This study used computer simulations of two- and three-dimensional tissue models to investigate qualitatively how, in relation to tissue size and geometry, dynamical instability affects the spontaneous termination of cardiac fibrillation. The major findings are as follows: 1) Dynamical instability promotes wave breaks, maintaining fibrillation, but it also causes the waves to extinguish, facilitating spontaneous termination of fibrillation. The latter effect predominates as dynamical instability increases, so that fibrillation is more likely to self-terminate in a finite-sized tissue. 2) In two-dimensional tissue, the average duration of fibrillation increases exponentially as tissue area increases. In three-dimensional tissue, the average duration of fibrillation decreases initially as tissue thickness increases as a result of thickness-induced instability but then increases after a critical thickness is reached. Therefore, in addition to tissue mass and geometry, dynamical instability is an important factor influencing the maintenance of cardiac fibrillation.

The effect of vagally induced dispersion of action potential duration on atrial arrhythmogenesis

OBJECTIVE

The purpose of this study is to ascertain the effects of spatially variable ACh distributions on arrhythmogenesis in a morphologically realistic computer model of canine atria.

BACKGROUND

Vagal stimulation releases acetylcholine (ACh), which causes a dose-dependent reduction in action potential duration (APD) in the atria. Due to the nonuniform distribution of nerve endings, APD dispersion may result, which has been shown to play a role in the breakup of activity.

METHODS

Reentry was initiated in a computationally efficient, morphologically realistic computer model of the atria. Discrete regions corresponding to ACh release sites, referred to as islands, were assigned shortened APDs in an ACh-dependent fashion. Island APD was varied as well as the basal APD. The window of vulnerability for ectopic beat-induction of sustained reentry was determined for both left atrial(LA) and right atrial (RA) stimulation. The resulting reentries were categorized based on type and location.

RESULTS

1) Atrial geometry severely restricts the formation of reentrant circuits. 2) Wave fractionation only occurred for large differences between island and basal APD. 3) Small ACh concentration differences produced stable figure-of-8 reentrant patterns. 4) Large islands displayed more wave breakup but could sometimes anchor reentries.

CONCLUSIONS

Large APD gradients produced by ACh heterogeneity can lead to a breakdown of organized activity.

Dispersion of cardiac action potential duration and the initiation of re-entry: a computational study

BACKGROUND

The initiation of re-entrant cardiac arrhythmias is associated with increased dispersion of repolarisation, but the details are difficult to investigate either experimentally or clinically. We used a computational model of cardiac tissue to study systematically the association between action potential duration (APD) dispersion and susceptibility to re-entry.

METHODS

We simulated a 60 x 60 mm2 D sheet of cardiac ventricular tissue using the Luo-Rudy phase 1 model, with maximal conductance of the K+ channel gKmax set to 0.004 mS mm(-2). Within the central 40 x 40 mm region we introduced square regions with prolonged APD by reducing gKmax to between 0.001 and 0.003 mS mm(-2). We varied (i) the spatial scale of these regions, (ii) the magnitude of gKmax in these regions, and (iii) cell-to-cell coupling.

RESULTS

Changing spatial scale from 5 to 20 mm increased APD dispersion from 49 to 102 ms, and the susceptible window from 31 to 86 ms. Decreasing gKmax in regions with prolonged APD from 0.003 to 0.001 mS mm-2 increased APD dispersion from 22 to 70 ms, and the susceptible window from <1 to 56 ms. Decreasing cell-to-cell coupling by changing the diffusion coefficient from 0.2 to 0.05 mm2 ms(-1) increased APD dispersion from 57 to 88 ms, and increased the susceptible window from 41 to 74 ms.

CONCLUSION

We found a close association between increased APD dispersion and susceptibility to re-entrant arrhythmias, when APD dispersion is increased by larger spatial scale of heterogeneity, greater electrophysiological heterogeneity, and weaker cell-to-cell coupling.

Dynamical effects of diffusive cell coupling on cardiac excitation and propagation: a simulation study

Cell coupling is considered to be important for cardiac action potential propagation and arrhythmogenesis. We carried out computer simulations to investigate the effects of stimulation strength and cell-to-cell coupling on action potential duration (APD) restitution, APD alternans, and stability of reentry in models of isolated cell, one-dimensional cable, and two-dimensional tissue. Phase I formulation of the Luo and Rudy action potential model was used. We found that stronger stimulation resulted in a shallower APD restitution curve and onset of APD alternans at a faster pacing rate. Reducing diffusive coupling between cells prolonged APD. Weaker diffusive currents along the direction of propagation steepened APD restitution and caused APD alternans to occur at a slower pacing rate in tissue. Diffusive current due to curvature changed APD but had little effect on APD restitution slope and onset of instability. Heterogeneous cell coupling caused APD inhomogeneities in space. Reduction in coupling strength either uniformly or randomly had little effect on the rotation period and stability of a reentry, but random cell decoupling slowed the rotation period and, thus, stabilized the reentry, preventing it from breaking up into multiple waves. Therefore, in addition to its effects on action potential conduction velocity, diffusive cell coupling also affects APD in a rate-dependent manner, causes electrophysiological heterogeneities, and thus modulates the dynamics of cardiac excitation. These effects are brought about by the modulation of ionic current activation and inactivation.

Regular and alternant spiral waves of contractile motion on rat ventricle cell cultures

We demonstrate that meandering as well as regular spiral waves can form in a well-controlled culture layer of rat ventricle cells and that the meandering spiral wave, in particular, can generate an alternant rhythm. These observations are made possible by a newly developed, noninvasive phase contrast macro-optics that is simple but highly effective in visualizing the contractile motion of the populations of cardiac cells.

Restitution of Action Potential Duration During Sequential Changes in Diastolic Intervals Shows Multimodal Behavior

Restitution of action potential duration (APD) is thought to be critical in activation instability. Although restitution is used to predict APD during sequential changes in diastolic interval (DI), currently used protocols to determine restitution do not use sequential changes in DI. We explored restitution using a new pacing protocol to change DI sequentially and independently of APD. Transmembrane potentials were recorded from right ventricular endocardial tissue isolated from six dogs. We used three patterns of DIs: oscillatory, to demonstrate differences in APDs depending on previous activation history; random, to minimize effects of previous activation history, each DI preceding an APD had an equal probability of being short or long; and linear, to compare restitution relationship obtained during sequential changes in DI with those obtained using currently used protocols; DIs mimicked those that resulted using currently used protocols, except that they changed in sequence. During oscillatory DIs, restitution showed bimodal trajectory similar to hysteresis. Decrease in APD during decreasing DIs was faster than increase in APD during increasing DIs. When effects of previous activation history were minimized, we observed that for a given DI there were multiple values of APD. Restitution relationship obtained during sequential changes in DI was shallower than those obtained using currently used protocols. Our results show that the new pacing protocol may permit direct evaluation of effects of memory on APD. Sequential and explicit control of DI suggests that use of a unimodal relationship to predict APD when DIs change in sequence may not be appropriate.

Combined phase singularity and wavefront analysis for optical maps of ventricular fibrillation

Much of the research into the mechanisms of ventricular fibrillation (VF) employs high-resolution mapping of electrical activation and recovery patterns. We previously developed a method for analyzing electrically mapped VF patterns that was based on identifying individual VF wavefronts. We now introduce a related method designed to take into account the information on repolarization that is present in optically mapped VF data. The new method first converts raw fluorescence data to an angular variable that tracks the phase of the mapped tissue through the depolarization-repolarization cycle. We define wavefronts in this context as isolines of phase that terminate either at boundaries or at singular points within the phase field. These singularities are the pivots of functional reentry and are important determinants of VF patterns. We parameterize VF by constructing data structures that describe wavefronts and singularities and also maintain wavefront-wavefront, wavefront-singularity, and singularity-singularity relationships. We describe one important application of this parameterization, which is to identify, localize, and characterize the importance of occurrences of propagation block during VF.

Novel approaches to identifying antiarrhythmic drugs

Currently, device therapy with implantable cardioverter-defibrillators is the only proven effective therapy for sudden cardiac death. However, new insights into the mechanisms of ventricular fibrillation, particularly the role of dynamic factors that cause wave instability, are providing conceptual advances toward developing effective new pharmacotherapy.

Spatial distribution of phase singularities in ventricular fibrillation

BACKGROUND

Multiple excitation wavelets are present during ventricular fibrillation (VF). The underlying wavelet organization of VF is unclear. Phase singularities (PSs)-locations of ambiguous activation state-underlie reentry and wavelet splitting and represent the sources of VF. Understanding the mechanisms of PS formation might be important in the development of effective therapies for sudden death.

METHODS AND RESULTS

We performed voltage, phase, and PS mapping in fibrillating ventricles, applying an automated PS detection algorithm to optically recorded fibrillation signals. PS clustering was noted along epicardial vessels, ridges of endocardial trabeculae, and papillary muscle insertions. Microscopically, these locations correlated with areas of apposition of fibers with different angulations and intramural vessels. A total of 83.2% of PSs were formed at and meandered about these anatomic structures, which acted as stabilizers: PSs colocalizing at anatomic substrates had longer life spans than nonanatomic PS (82.46+/-60.8 versus 40.5+/-31.9 ms, P<0.01). The RV endocardium had a higher PS incidence than the epicardium (42.3+/-9.2 versus 23.5+/-11.6 PS/s, P<0.01). Autocorrelation showed that irregular behavior was spatially restricted to anatomic heterogeneities compared with other areas, which had nearly periodic behaviors. Simple spatial PS distributions underlay complex and variable activation patterns attributable to variable PS behaviors, life spans, and inter-PS interactions.

CONCLUSIONS

PSs occur in a nonrandom spatial distribution and colocalize with normal anatomic heterogeneities. Varying PS behaviors and life spans but stable PS spatial distributions cause ever-changing activation patterns that characterize VF.