Alternans resonance and propagation block during supernormal conduction in cardiac tissue with decreased [K(+)](o)

Synchronization of spatially discordant voltage and calcium alternans in cardiac tissue

The heart is an excitable medium which is excited by membrane potential depolarization and propagation. Membrane potential depolarization brings in calcium (Ca) through the Ca channels to trigger intracellular Ca release for contraction of the heart. Ca also affects voltage via Ca-dependent ionic currents, and thus, voltage and Ca are bidirectionally coupled. It has been shown that the voltage subsystem or the Ca subsystem can generate its own dynamical instabilities which are affected by their bidirectional couplings, leading to complex dynamics of action potential and Ca cycling. Moreover, the dynamics become spatiotemporal in tissue in which cells are diffusively coupled through voltage. A widely investigated spatiotemporal dynamics is spatially discordant alternans (SDA) in which action potential duration (APD) or Ca amplitude exhibits temporally period-2 and spatially out-of-phase patterns, i.e., APD-SDA and Ca-SDA patterns, respectively. However, the mechanisms of formation, stability, and synchronization of APD-SDA and Ca-SDA patterns remain incompletely understood. In this paper, we use cardiac tissue models described by an amplitude equation, coupled iterated maps, and reaction-diffusion equations with detailed physiology (the ionic model) to perform analytical and computational investigations. We show that, when the Ca subsystem is stable, the Ca-SDA pattern always follows the APD-SDA pattern, and thus, they are always synchronized. When the Ca subsystem is unstable, synchronization of APD-SDA and Ca-SDA patterns depends on the stabilities of both subsystems, their coupling strengths, and the spatial scales of the initial Ca-SDA patterns. Spontaneous (initial condition-independent) synchronization is promoted by enhancing APD instability and reducing Ca instability as well as stronger Ca-to-APD and APD-to-Ca coupling, a pattern formation caused by dynamical instabilities. When Ca is more unstable and APD is less unstable or APD-to-Ca coupling is weak, synchronization of APD-SDA and Ca-SDA patterns is promoted by larger initially synchronized Ca-SDA clusters, i.e., initial condition-dependent synchronization. The synchronized APD-SDA and Ca-SDA patterns can be locked in-phase, antiphase, or quasiperiodic depending on the coupling relationship between APD and Ca. These theoretical and simulation results provide mechanistic insights into the APD-SDA and Ca-SDA dynamics observed in experimental studies.

Stability of spatially discordant repolarization alternans in cardiac tissue

Cardiac alternans, a period-2 behavior of excitation and contraction of the heart, is a precursor of ventricular arrhythmias and sudden cardiac death. One form of alternans is repolarization or action potential duration alternans. In cardiac tissue, repolarization alternans can be spatially in-phase, called spatially concordant alternans, or spatially out-of-phase, called spatially discordant alternans (SDA). In SDA, the border between two out-of-phase regions is called a node in a one-dimensional cable or a nodal line in a two-dimensional tissue. In this study, we investigate the stability and dynamics of the nodes and nodal lines of repolarization alternans driven by voltage instabilities. We use amplitude equation and coupled map lattice models to derive theoretical results, which are compared with simulation results from the ionic model. Both conduction velocity restitution induced SDA and non-conduction velocity restitution induced SDA are investigated. We show that the stability and dynamics of the SDA nodes or nodal lines are determined by the balance of the tensions generated by conduction velocity restitution, convection due to action potential propagation, curvature of the nodal lines, and repolarization and coupling heterogeneities. Our study provides mechanistic insights into the different SDA behaviors observed in experiments.

Double-wave reentry in excitable media

A monolayer of chick embryo cardiac cells grown in an annular geometry supports two simultaneous reentrant excitation waves that circulate as a doublet. We propose a mechanism that can lead to such behavior. The velocity restitution gives the instantaneous velocity of a wave as a function of the time since the passage of the previous wave at a given point in space. Nonmonotonic restitution relationships will lead to situations in which various spacings between circulating waves are possible. In cardiology, the situation in which two waves travel in an anatomically defined circuit is referred to as double-wave reentry. Since double-wave reentry may arise as a consequence of pacing during cardiac arrhythmias, understanding the dynamic features of double-wave reentry may be helpful in understanding the physiological properties of cardiac tissue and in the design of therapy.

Dynamics of spatiotemporal line defects and chaos control in complex excitable systems

Spatiotemporal pattern formation governs dynamics and functions in various biological systems. In the heart, excitable waves can form complex oscillatory and chaotic patterns even at an abnormally higher frequency than normal heart beats, which increase the risk of fatal heart conditions by inhibiting normal blood circulation. Previous studies suggested that line defects (nodal lines) play a critical role in stabilizing those undesirable patterns. However, it remains unknown if the line defects are static or dynamically changing structures in heart tissue. Through in vitro experiments of heart tissue observation, we reveal the spatiotemporal dynamics of line defects in rotating spiral waves. We combined a novel signaling over-sampling technique with a multi-dimensional Fourier analysis, showing that line defects can translate, merge, collapse and form stable singularities with even and odd parity while maintaining a stable oscillation of the spiral wave in the tissue. These findings provide insights into a broad class of complex periodic systems, with particular impact to the control and understanding of heart diseases.

Myofibroblasts Electrotonically Coupled to Cardiomyocytes Alter Conduction: Insights at the Cellular Level from a Detailed In silico Tissue Structure Model

Fibrotic myocardial remodeling is typically accompanied by the appearance of myofibroblasts (MFBs). In vitro, MFBs were shown to slow conduction and precipitate ectopic activity following gap junctional coupling to cardiomyocytes (CMCs). To gain further mechanistic insights into this arrhythmogenic MFB-CMC crosstalk, we performed numerical simulations in cell-based high-resolution two-dimensional tissue models that replicated experimental conditions. Cell dimensions were determined using confocal microscopy of single and co-cultured neonatal rat ventricular CMCs and MFBs. Conduction was investigated as a function of MFB density in three distinct cellular tissue architectures: CMC strands with endogenous MFBs, CMC strands with coating MFBs of two different sizes, and CMC strands with MFB inserts. Simulations were performed to identify individual contributions of heterocellular gap junctional coupling and of the specific electrical phenotype of MFBs. With increasing MFB density, both endogenous and coating MFBs slowed conduction. At MFB densities of 5-30%, conduction slowing was most pronounced in strands with endogenous MFBs due to the MFB-dependent increase in axial resistance. At MFB densities >40%, very slow conduction and spontaneous activity was primarily due to MFB-induced CMC depolarization. Coating MFBs caused non-uniformities of resting membrane potential, which were more prominent with large than with small MFBs. In simulations of MFB inserts connecting two CMC strands, conduction delays increased with increasing insert lengths and block appeared for inserts >1.2 mm. Thus, electrophysiological properties of engineered CMC-MFB co-cultures depend on MFB density, MFB size and their specific positioning in respect to CMCs. These factors may influence conduction characteristics in the heterocellular myocardium.

Supernormal Conduction and Suppression of Spatially Discordant Alternans of Cardiac Action Potentials

Spatially discordant alternans (DA) of action potential durations (APD) is thought to be more pro-arrhythmic than concordant alternans. Super normal conduction (SNC) has been reported to suppress formation of DA. An increase in conduction velocity (CV) as activation rate increases, i.e., a negative CV restitution, is widely considered as hallmark of SNC. Our aim in this study is to show that it is not an increase in CV for faster rates that prevents formation of DA, rather, it is the ratio of the CV for the short relative to the long activation that is critical in DA suppression. To illustrate this subtlety, we simulated this phenomenon using two approaches; (1) by using the standard, i.e., S1S2 protocol to quantify restitution and disabling the slow inactivation gate j of the sodium current (I_Na), and (2) by using the dynamic, i.e., S1S1 protocol for quantification of restitution and increasing I_Na at different cycle lengths (CL). Even though both approaches produced similar CV restitution curves, DA was suppressed only during the first approach, where the CV of the short of the long-short action potential (AP) pattern was selectively increased. These results show that negative CV restitution, which is considered characteristic of SNC, per se, is not causal in suppressing DA, rather, the critical factor is a change in the ratio of the velocities of the short and the long APs.

Spatial discordance and phase reversals during alternate pacing in discrete-time kinematic and cardiomyocyte ionic models

Alternans, a beat-to-beat alternation in the cardiac action potential duration (APD), is a dynamical instability linked with the initiation of arrhythmias and sudden cardiac death, and arises via a period-doubling bifurcation when myocytes are stimulated at fast rates. In this study, we analyze the stability of a propagating electrical wave in a one-dimensional cardiac myocyte model in response to an arrhythmogenic rhythm known as alternate pacing. Using a discrete-time kinematic model and complex frequency (Z) domain analysis, we derive analytical expressions to predict phase reversals and spatial discordance in the interbeat interval (IBI) and APD, which, importantly, cannot be predicted with a model that neglects the influence of cell coupling on repolarization. We identify key dimensionless parameters that determine the transition from spatial concordance to discordance. Finally, we show that the theoretical predictions agree closely with numerical simulations of an ionic myocyte model, over a wide range of parameters, including variable IBI, altered ionic current gating, and reduced cell coupling. We demonstrate a novel approach to predict instability in cardiac tissue during alternate pacing and further illustrate how this approach can be generalized to more detail models of myocyte dynamics.

Titanium dioxide nanoparticles promote arrhythmias via a direct interaction with rat cardiac tissue

BACKGROUND

In light of recent developments in nanotechnologies, interest is growing to better comprehend the interaction of nanoparticles with body tissues, in particular within the cardiovascular system. Attention has recently focused on the link between environmental pollution and cardiovascular diseases. Nanoparticles <50 nm in size are known to pass the alveolar-pulmonary barrier, enter into bloodstream and induce inflammation, but the direct pathogenic mechanisms still need to be evaluated. We thus focused our attention on titanium dioxide (TiO₂) nanoparticles, the most diffuse nanomaterial in polluted environments and one generally considered inert for the human body.

METHODS

We conducted functional studies on isolated adult rat cardiomyocytes exposed acutely in vitro to TiO₂ and on healthy rats administered a single dose of 2 mg/Kg TiO₂ NPs via the trachea. Transmission electron microscopy was used to verify the actual presence of TiO₂ nanoparticles within cardiac tissue, toxicological assays were used to assess lipid peroxidation and DNA tissue damage, and an in silico method was used to model the effect on action potential.

RESULTS

Ventricular myocytes exposed in vitro to TiO₂ had significantly reduced action potential duration, impairment of sarcomere shortening and decreased stability of resting membrane potential. In vivo, a single intra-tracheal administration of saline solution containing TiO₂ nanoparticles increased cardiac conduction velocity and tissue excitability, resulting in an enhanced propensity for inducible arrhythmias. Computational modeling of ventricular action potential indicated that a membrane leakage could account for the nanoparticle-induced effects measured on real cardiomyocytes.

CONCLUSIONS

Acute exposure to TiO₂ nanoparticles acutely alters cardiac excitability and increases the likelihood of arrhythmic events.

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.

Effects of pacing site and stimulation history on alternans dynamics and the development of complex spatiotemporal patterns in cardiac tissue

Alternans of action potential duration has been associated with T wave alternans and the development of arrhythmias because it produces large gradients of repolarization. However, little is known about alternans dynamics in large mammalian hearts. Using optical mapping to record electrical activations simultaneously from the epicardium and endocardium of 9 canine right ventricles, we demonstrate novel arrhythmogenic complex spatiotemporal dynamics. (i) Alternans predominantly develops first on the endocardium. (ii) The postulated simple progression from normal rhythm to concordant to discordant alternans is not always observed; concordant alternans can develop from discordant alternans as the pacing period is decreased. (iii) In contrast to smaller tissue preparations, multiple stationary nodal lines may exist and need not be perpendicular to the pacing site or to each other. (iv) Alternans has fully three-dimensional dynamics and the epicardium and endocardium can show significantly different dynamics: multiple nodal surfaces can be transmural or intramural and can form concave/convex surfaces resulting in islands of discordant alternans. (v) The complex spatiotemporal patterns observed during alternans are very sensitive to both the site of stimulation and the stimulation history. Alternans in canine ventricles not only exhibit larger amplitudes and persist for longer cycle length regimes compared to those found in smaller mammalian hearts, but also show novel dynamics not previously described that enhance dispersion and show high sensitivity to initial conditions. This indicates some underlying predisposition to chaos and can help to guide the design of new drugs and devices controlling and preventing arrhythmic events.

A discrete electromechanical model for human cardiac tissue: effects of stretch-activated currents and stretch conditions on restitution properties and spiral wave dynamics

We introduce an electromechanical model for human cardiac tissue which couples a biophysical model of cardiac excitation (Tusscher, Noble, Noble, Panfilov, 2006) and tension development (adjusted Niederer, Hunter, Smith, 2006 model) with a discrete elastic mass-lattice model. The equations for the excitation processes are solved with a finite difference approach, and the equations of the mass-lattice model are solved using Verlet integration. This allows the coupled problem to be solved with high numerical resolution. Passive mechanical properties of the mass-lattice model are described by a generalized Hooke's law for finite deformations (Seth material). Active mechanical contraction is initiated by changes of the intracellular calcium concentration, which is a variable of the electrical model. Mechanical deformation feeds back on the electrophysiology via stretch-activated ion channels whose conductivity is controlled by the local stretch of the medium. We apply the model to study how stretch-activated currents affect the action potential shape, restitution properties, and dynamics of spiral waves, under constant stretch, and dynamic stretch caused by active mechanical contraction. We find that stretch conditions substantially affect these properties via stretch-activated currents. In constantly stretched medium, we observe a substantial decrease in conduction velocity, and an increase of action potential duration; whereas, with dynamic stretch, action potential duration is increased only slightly, and the conduction velocity restitution curve becomes biphasic. Moreover, in constantly stretched medium, we find an increase of the core size and period of a spiral wave, but no change in rotation dynamics; in contrast, in the dynamically stretching medium, we observe spiral drift. Our results may be important to understand how altered stretch conditions affect the heart's functioning.

Computational approaches to understand cardiac electrophysiology and arrhythmias

Cardiac rhythms arise from electrical activity generated by precisely timed opening and closing of ion channels in individual cardiac myocytes. These impulses spread throughout the cardiac muscle to manifest as electrical waves in the whole heart. Regularity of electrical waves is critically important since they signal the heart muscle to contract, driving the primary function of the heart to act as a pump and deliver blood to the brain and vital organs. When electrical activity goes awry during a cardiac arrhythmia, the pump does not function, the brain does not receive oxygenated blood, and death ensues. For more than 50 years, mathematically based models of cardiac electrical activity have been used to improve understanding of basic mechanisms of normal and abnormal cardiac electrical function. Computer-based modeling approaches to understand cardiac activity are uniquely helpful because they allow for distillation of complex emergent behaviors into the key contributing components underlying them. Here we review the latest advances and novel concepts in the field as they relate to understanding the complex interplay between electrical, mechanical, structural, and genetic mechanisms during arrhythmia development at the level of ion channels, cells, and tissues. We also discuss the latest computational approaches to guiding arrhythmia therapy.

Phase Relationship between Alternans of Early and Late Phases of Ventricular Action Potentials

BACKGROUND

Alternans of early phase and of duration of action potential (AP) critically affect dispersion of refractoriness through their influence on conduction and repolarization. We investigated the phase relationship between the two alternans and its effect on conduction.

METHODS AND RESULTS

Transmembrane potentials recorded from ventricles of eight swine and three canines during paced activation intervals of ≤300 ms were used to quantify alternans of maximum rate of depolarization (|dv/dt|(max)) and of action potential duration (APD). Incidence of APD alternans was 62 and 76% in swine and canines. Alternans of APD was frequently accompanied with alternans of |dv/dt|(max). Of these, 4 and 26% were out of phase in swine and canines, i.e., low |dv/dt|(max) preceded long APD. Computer simulations show that out of phase alternans attenuate variation of wavelength and thus minimize formation of spatially discordant alternans.

CONCLUSION

The spontaneous switching of phase relationship between alternans of depolarization and repolarization suggests that mechanisms underlying these alternans may operate independent of each other. The phase between these alternans can critically impact spatial dispersion of refractoriness and thus stability of conduction, with the in phase relation promoting transition from concord to discord while out of phase preventing formation of discord.

Conduction velocity restitution of the human atrium--an efficient measurement protocol for clinical electrophysiological studies

Conduction velocity (CV) and CV restitution are important substrate parameters for understanding atrial arrhythmias. The aim of this work is to (i) present a simple but feasible method to measure CV restitution in-vivo using standard circular catheters, and (ii) validate its feasibility with data measured during incremental pacing. From five patients undergoing catheter ablation, we analyzed eight datasets from sinus rhythm and incremental pacing sequences. Every wavefront was measured with a circular catheter and the electrograms were analyzed with a cosine-fit method that calculated the local CV. For each pacing cycle length, the mean local CV was determined. Furthermore, changes in global CV were estimated from the time delay between pacing stimulus and wavefront arrival. Comparing local and global CV between pacing at 500 and 300 ms, we found significant changes in seven of eight pacing sequences. On average, local CV decreased by 20 ± 15% and global CV by 17 ± 13%. The method allows for in-vivo measurements of absolute CV and CV restitution during standard clinical procedures. Such data may provide valuable insights into mechanisms of atrial arrhythmias. This is important both for improving cardiac models and also for clinical applications, such as characterizing arrhythmogenic substrates during sinus rhythm.

Supernormal conduction in cardiac tissue promotes concordant alternans and action potential bunching

Supernormal conduction (SNC) in excitable cardiac tissue refers to an increase of pulse (or action potential) velocity with decreasing distance to the preceding pulse. Here we employ a simple ionic model to study the effect of SNC on the propagation of action potentials (APs) and the phenomenology of alternans in excitable cardiac tissue. We use bifurcation analysis and simulations to study attraction between propagating APs caused by SNC that leads to AP pairs and bunching. It is shown that SNC stabilizes concordant alternans in arbitrarily long paced one-dimensional cables. As a consequence, spiral waves in two-dimensional tissue simulations exhibit straight nodal lines for SNC in contrast to spiraling ones in the case of normal conduction.