Vulnerable window for conduction block in a one-dimensional cable of cardiac cells, 2: multiple extrasystoles

Unidirectional conduction block of premature extrasystoles can lead to initiation of cardiac reentry, causing lethal arrhythmias including ventricular fibrillation. Multiple extrasystoles are often more effective at inducing unidirectional conduction block and reentry than a single extrasystole. Since the substrate for conduction block is spatial dispersion of refractoriness, in this study we investigate how the first extrasystole modulates this dispersion to influence the "vulnerable window" for conduction block by subsequent extrasystoles, particularly in relation to action potential duration restitution and conduction velocity restitution properties. Using a kinematic model to represent wavefront-waveback interactions and simulations with the Luo-Rudy model in a one-dimensional cable of cardiac cells, we show that in homogeneous tissue, a premature extrasystole can create a large dispersion of refractoriness leading to conduction block of a subsequent extrasystole. In heterogeneous tissue, however, a premature extrasystole can either reduce or enhance the dispersion of refractoriness depending on its propagation direction with respect to the previous beat. With multiple extrasystoles at random coupling intervals, vulnerability to conduction block is proportional to their number. In general, steep action potential duration restitution and broad conduction velocity restitution promote dispersion of refractoriness in response to multiple extrasystoles, and thus enhance vulnerability to conduction block. These restitution properties also promote spatially discordant alternans, a setting which is particularly prone to conduction block. The equivalent dispersion of refractoriness created dynamically in homogeneous tissue by spatially discordant alternans is more likely to cause conduction block than a comparable degree of preexisting dispersion in heterogeneous tissue.     

Effects of Na(+) channel and cell coupling abnormalities on vulnerability to reentry: a simulation study

The role of dynamic instabilities in the initiation of reentry in diseased (remodeled) hearts remains poorly explored. Using computer simulations, we studied the effects of altered Na(+) channel and cell coupling properties on the vulnerable window (VW) for reentry in simulated two-dimensional cardiac tissue with and without dynamic instabilities. We related the VW for reentry to effects on conduction velocity, action potential duration (APD), effective refractory period dispersion and restitution, and concordant and discordant APD alternans. We found the following: 1). reduced Na(+) current density and slowed recovery promoted postrepolarization refractoriness and enhanced concordant and discordant APD alternans, which increased the VW for reentry; 2). uniformly reduced cell coupling had little effect on cellular electrophysiological properties and the VW for reentry. However, randomly reduced cell coupling combined with decoupling promoted APD dispersion and alternans, which also increased the VW for reentry; 3). the combination of decreased Na(+) channel conductance, slowed Na(+) channel recovery, and cellular uncoupling synergistically increased the VW for reentry; and 4) the VW for reentry was greater when APD restitution slope was steep than when it was flat. In summary, altered Na(+) channel and cellular coupling properties increase vulnerability to reentrant arrhythmias. In remodeled hearts with altered Na(+) channel properties and cellular uncoupling, dynamic instabilities arising from electrical restitution exert important influences on the VW for reentry.     

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.     

The pinwheel experiment revisited: effects of cellular electrophysiological properties on vulnerability to cardiac reentry

In normal heart, ventricular fibrillation can be induced by a single properly timed strong electrical or mechanical stimulus. A mechanism first proposed by Winfree and coined the "pinwheel experiment" emphasizes the timing and strength of the stimulus in inducing figure-of-eight reentry. However, the effects of cellular electrophysiological properties on vulnerability to reentry in the pinwheel scenario have not been investigated. In this study, we extend Winfree's pinwheel experiment to show how the vulnerability to reentry is affected by the graded action potential responses induced by a strong premature stimulus, action potential duration (APD), and APD restitution in simulated monodomain homogeneous two-dimensional tissue. We find that a larger graded response, longer APD, or steeper APD restitution slope reduces the vulnerable window of reentry. Strong graded responses and long APD promote tip-tip interactions at long coupling intervals, causing the two initiated spiral wave tips to annihilate. Steep APD restitution promotes wave front-wave back interaction, causing conduction block in the central common pathway of figure-of-eight reentry. We derive an analytical treatment that shows good agreement with numerical simulation results.     

How different two almost identical action potentials can be: A model study on cardiac repolarization

Spatial heterogeneity in the properties of ion channels generates spatial dispersion of ventricular repolarization, which is modulated by gap junctional coupling. However, it is possible to simulate conditions in which local differences in excitation properties are electrophysiologically silent and only play a role in pathological states. We use a numerical procedure on the Luo-Rudy phase 1 model of the ventricular action potential (AP1) in order to find a modified set of model parameters which generates an action potential profile (AP2) almost identical to AP1. We show that, although the two waveforms elicited from resting conditions as a single AP are very similar and belong to membranes sharing similar passive electrical properties, the modified membrane generating AP2 is a weaker current source than the one generating AP1, has different sensitivity to up/down-regulation of ion channels and to extracellular potassium, and a different electrical restitution profile. We study electrotonic interaction of AP1- and AP2 - type membranes in cell pairs and in cable conduction, and find differences in source-sink properties which are masked in physiological conditions and become manifest during intercellular uncoupling or partial block of ion channels, leading to unidirectional block and spatial repolarization gradients. We provide contour plot representations that summarize differences and similarities. The present report characterizes an inverse problem in cardiac cells, and strengthen the recently emergent notion that a comprehensive characterization and validation of cell models and their components are necessary in order to correctly understand simulation results at higher levels of complexity.     

L-type Ca2+ channel mutations and T-wave alternans: a model study

A number of mutations have been linked to diseases for which the underlying mechanisms are poorly understood. An example is Timothy Syndrome (TS), a multisystem disorder that includes severe cardiac arrhythmias. Here we employ theoretical simulations to examine the effects of a TS mutation in the L-type Ca(2+) channel on cardiac dynamics over multiple scales, from a gene mutation to protein, cell, tissue, and finally the ECG, to connect a defective Ca(2+) channel to arrhythmia susceptibility. Our results indicate that 1) the TS mutation disrupts the rate-dependent dynamics in a single cardiac cell and promotes the development of alternans; 2) in coupled tissue, concordant alternans is observed at slower heart rates in mutant tissue than in normal tissue and, once initiated, rapidly degenerates into discordant alternans and conduction block; and 3) the ECG computed from mutant-simulated tissue exhibits prolonged QT intervals at physiological rates and with small increases in pacing rate, T-wave alternans, and alternating T-wave inversion. At the cellular level, enhanced Ca(2+) influx due to the TS mutation causes electrical instabilities. In tissue, the interplay between faulty Ca(2+) influx and steep action potential duration restitution causes arrhythmogenic discordant alternans. The prolongation of action potentials causes spatial dispersion of the Na(+) channel excitability, leading to inhomogeneous conduction velocity and large action potential spatial gradients. Our model simulations are consistent with the ECG patterns from TS patients, which suggest that the TS mutation is sufficient to cause the clinical phenotype and allows for the revelation of the complex interactions of currents underlying it.     

Alternans Resonance and Propagation Block during Supernormal Conduction in Cardiac Tissue with Decreased [K]o

Cardiac restitution is an important factor in arrhythmogenesis. Steep positive action potential duration and conduction velocity (CV) restitution slopes promote alternans and reentrant arrhythmias. We examined the consequences of supernormal conduction (characterized by a negative CV restitution slope) on patterns of conduction and alternans in strands of Luo-Rudy model cells and in cultured cardiac cell strands. Interbeat intervals (IBIs) were analyzed as a function of distance during S1S2 protocols and during pacing at alternating cycle lengths. Supernormal conduction was induced by decreasing [K⁺]_o. In control [K⁺]_o simulations, S1S2 intervals converged toward basic cycle length with a length constant determined by both CV and the CV restitution slope. During alternant pacing, the amplitude of IBI alternans converged with a shorter length constant, determined also by the action potential duration restitution slope. In contrast, during supernormal conduction, S1S2 intervals and the amplitude of alternans diverged. This amplification (resonance) led to phase-locked or more complex alternans patterns, and then to distal conduction block. The convergence/divergence of IBIs was verified in the cultured strands, in which naturally occurring tissue heterogeneities resulted in prominent discontinuities of the spatial IBI profiles. We conclude that supernormal conduction potentiates alternans and spatial analysis of IBIs represents a powerful method to locate tissue heterogeneities.     

Rate-dependent effects of lidocaine on cardiac dynamics: Development and analysis of a low-dimensional drug-channel interaction model

State-dependent sodium channel blockers are often prescribed to treat cardiac arrhythmias, but many sodium channel blockers are known to have pro-arrhythmic side effects. While the anti and proarrhythmic potential of a sodium channel blocker is thought to depend on the characteristics of its rate-dependent block, the mechanisms linking these two attributes are unclear. Furthermore, how specific properties of rate-dependent block arise from the binding kinetics of a particular drug is poorly understood. Here, we examine the rate-dependent effects of the sodium channel blocker lidocaine by constructing and analyzing a novel drug-channel interaction model. First, we identify the predominant mode of lidocaine binding in a 24 variable Markov model for lidocaine-sodium channel interaction by Moreno et al. Specifically, we find that (1) the vast majority of lidocaine bound to sodium channels is in the neutral form, i.e., the binding of charged lidocaine to sodium channels is negligible, and (2) neutral lidocaine binds almost exclusively to inactivated channels and, upon binding, immobilizes channels in the inactivated state. We then develop a novel 3-variable lidocaine-sodium channel interaction model that incorporates only the predominant mode of drug binding. Our low-dimensional model replicates an extensive amount of the voltage-clamp data used to parameterize the Moreno et al. model. Furthermore, the effects of lidocaine on action potential upstroke velocity and conduction velocity in our model are similar to those predicted by the Moreno et al. model. By exploiting the low-dimensionality of our model, we derive an algebraic expression for level of rate-dependent block as a function of pacing frequency, restitution properties, diastolic and plateau potentials, and drug binding rate constants. Our model predicts that the level of rate-dependent block is sensitive to alterations in restitution properties and increases in diastolic potential, but it is insensitive to variations in the shape of the action potential waveform and lidocaine binding rates.     

Electrophysiological heterogeneity and stability of reentry in simulated cardiac tissue

Generation of wave break is a characteristic feature of cardiac fibrillation. In this study, we investigated how dynamic factors and fixed electrophysiological heterogeneity interact to promote wave break in simulated two-dimensional cardiac tissue, by using the Luo-Rudy (LR1) ventricular action potential model. The degree of dynamic instability of the action potential model was controlled by varying the maximal amplitude of the slow inward Ca(2+) current to produce spiral waves in homogeneous tissue that were either nearly stable, meandering, hypermeandering, or in breakup regimes. Fixed electrophysiological heterogeneity was modeled by randomly varying action potential duration over different spatial scales to create dispersion of refractoriness. We found that the degree of dispersion of refractoriness required to induce wave break decreased markedly as dynamic instability of the cardiac model increased. These findings suggest that reducing the dynamic instability of cardiac cells by interventions, such as decreasing the steepness of action potential duration restitution, may still have merit as an antifibrillatory strategy.     

The canine virtual ventricular wall: a platform for dissecting pharmacological effects on propagation and arrhythmogenesis

We have constructed computational models of canine ventricular cells and tissues, ultimately combining detailed tissue architecture and heterogeneous transmural electrophysiology. The heterogeneity is introduced by modifying the Hund–Rudy canine cell model in order to reproduce experimentally reported electrophysiological properties of endocardial, midmyocardial (M) and epicardial cells. These models are validated against experimental data for individual ionic current and action potential characteristics, and their rate dependencies. 1D and 3D heterogeneous virtual tissues are constructed, with detailed tissue architecture (anisotropy and orthotropy, due to fibre orientation and sheet structure) of the left ventricular wall wedge extracted from a diffusion tensor imaging data set. The models are used to study the effects of tissue heterogeneity and class III drugs on transmural propagation and tissue vulnerability to re-entry.

We have determined relationships between the transmural dispersion of action potential duration (APD) and the vulnerable window in the 1D virtual ventricular wall, and demonstrated how changes in the transmural heterogeneity, and hence tissue vulnerability, can lead to generation of re-entry in the 3D ventricular wedge. Two class III drugs with opposite qualitative effects on transmural APD heterogeneity are considered: d-sotalol that increases transmural APD dispersion, and amiodarone that decreases it. Simulations with the 1D virtual ventricular wall show that under d-sotalol conditions the vulnerable window is substantially wider compared to amiodarone conditions, primarily in the epicardial region where unidirectional conduction block persists until the adjacent M cells are fully repolarised.

Further simulations with the 3D ventricular wedge have shown that ectopic stimulation of the epicardial region results in generation of sustained re-entry under d-sotalol conditions, but not under amiodarone conditions or in control. Again, APD increase in M cells was identified as the major contributor to tissue vulnerability—re-entry was initiated primarily due to ectopic excitation propagating around the unidirectional conduction block in the M cell region. This suggests an electrophysiological mechanism for the anti- and proarrhythmic effects of the class III drugs: the relative safety of amiodarone in comparison to d-sotalol can be explained by relatively low transmural APD dispersion, and hence, a narrow vulnerable window and low probability of re-entry in the tissue.     

Repolarisation and vulnerability to re-entry in the human heart with short QT syndrome arising from KCNQ1 mutation--a simulation study

Idiopathic short QT syndrome (SQTS) is a recently identified, genetically heterogeneous condition characterised by abbreviated QT intervals and an increased susceptibility to arrhythmia and sudden death. This simulation study identifies mechanisms by which cellular electrophysiological changes in the SQT2 (slow delayed rectifier, I_Ks, -linked) SQTS variant increases arrhythmia risk. The channel kinetics of the V307L mutation of the KCNQ1 subunit of the I_Ks channel were incorporated into human ventricular action potential (AP) models and into 1D and 2D transmural tissue simulations. Incorporating the V307L mutation into simulations reproduced defining features of the SQTS: abbreviation of the QT interval, and increases in T wave amplitude and T_peak–T_end duration. In the single-cell model, the V307L mutation abbreviated ventricular cell AP duration at 90% repolarisation (APD₉₀) and increased the maximal transmural voltage heterogeneity (δV) during APs; this resulted in augmented transmural heterogeneity of APD₉₀ and of the effective refractory period (ERP). In the intact tissue model, the vulnerable window for unidirectional conduction block was also increased. In 2D tissue the V307L mutation facilitated and maintained reentrant excitation. Thus, in SQT2 increases in transmural heterogeneity of APD, δV, ERP and an increased vulnerable window for unidirectional conduction block generate an electrical substrate favourable to reentrant arrhythmia.     

Effects of Na(+) and K(+) channel blockade on vulnerability to and termination of fibrillation in simulated normal cardiac tissue

Na(+) and K(+) channel-blocking drugs have anti- and proarrhythmic effects. Their effects during fibrillation, however, remain poorly understood. We used computer simulation of a two-dimensional (2-D) structurally normal tissue model with phase I of the Luo-Rudy action potential model to study the effects of Na(+) and K(+) channel blockade on vulnerability to and termination of reentry in simulated multiple-wavelet and mother rotor fibrillation. Our main findings are as follows: 1) Na(+) channel blockade decreased, whereas K(+) channel blockade increased, the vulnerable window of reentry in heterogeneous 2-D tissue because of opposing effects on dynamical wave instability. 2) Na(+) channel blockade increased the cycle length of reentry more than it increased refractoriness. In multiple-wavelet fibrillation, Na(+) channel blockade first increased and then decreased the average duration or transient time () of fibrillation. In mother rotor fibrillation, Na(+) channel blockade caused peripheral fibrillatory conduction block to resolve and the mother rotor to drift, leading to self-termination or sustained tachycardia. 3) K(+) channel blockade increased dynamical instability by steepening action potential duration restitution. In multiple-wavelet fibrillation, this effect shortened because of enhanced wave instability. In mother rotor fibrillation, this effect converted mother rotor fibrillation to multiple-wavelet fibrillation, which then could self-terminate. Our findings help illuminate, from a theoretical perspective, the possible underlying mechanisms of termination of different types of fibrillation by antiarrhythmic drugs.     

An analytical study of the physiology and pathology of the propagation of cardiac action potentials

Many cardiac diseases are caused by the abnormal propagation of electrical waves. Previous experimental and modelling work is reviewed, then a detailed study of the mathematics of cardiac propagation is presented. Pathologies are examined in the context of the models by varying parameters in the models to mimic different pathological states. Ionic models of cells are simplified to form analytically tractable models of the propagation of electrical cardiac waves. The roles that sodium channel activation and inactivation play in determining the conduction velocity are studied in detail, and the roles of resting potential currents in conduction block are calculated. The effect of curvature on the conduction velocity is examined, and the conditions in which curvature leads to conduction block and fibrillation are discussed. Hyperkalaemia (important during ischaemia) is modelled, and the model correctly describes the bi-phasic relation between propagation velocity and extracellular potassium.     

A Quantitative Comparison of the Behavior of Human Ventricular Cardiac Electrophysiology Models in Tissue

Numerical integration of mathematical models of heart cell electrophysiology provides an important computational tool for studying cardiac arrhythmias, but the abundance of available models complicates selecting an appropriate model. We study the behavior of two recently published models of human ventricular action potentials, the Grandi-Pasqualini-Bers (GPB) and the O''Hara-Virág-Varró-Rudy (OVVR) models, and compare the results with four previously published models and with available experimental and clinical data. We find the shapes and durations of action potentials and calcium transients differ between the GPB and OVVR models, as do the magnitudes and rate-dependent properties of transmembrane currents and the calcium transient. Differences also occur in the steady-state and S1–S2 action potential duration and conduction velocity restitution curves, including a maximum conduction velocity for the OVVR model roughly half that of the GPB model and well below clinical values. Between single cells and tissue, both models exhibit differences in properties, including maximum upstroke velocity, action potential amplitude, and minimum diastolic interval. Compared to experimental data, action potential durations for the GPB and OVVR models agree fairly well (although OVVR epicardial action potentials are shorter), but maximum slopes of steady-state restitution curves are smaller. Although studies show alternans in normal hearts, it occurs only in the OVVR model, and only for a narrow range of cycle lengths. We find initiated spiral waves do not progress to sustained breakup for either model. The dominant spiral wave period of the GPB model falls within clinically relevant values for ventricular tachycardia (VT), but for the OVVR model, the dominant period is longer than periods associated with VT. Our results should facilitate choosing a model to match properties of interest in human cardiac tissue and to replicate arrhythmia behavior more closely. Furthermore, by indicating areas where existing models disagree, our findings suggest avenues for further experimental work.     

Asymptotics of Conduction Velocity Restitution in Models of Electrical Excitation in the Heart

We extend a non-Tikhonov asymptotic embedding, proposed earlier, for calculation of conduction velocity restitution curves in ionic models of cardiac excitability. Conduction velocity restitution is the simplest non-trivial spatially extended problem in excitable media, and in the case of cardiac tissue it is an important tool for prediction of cardiac arrhythmias and fibrillation. An idealized conduction velocity restitution curve requires solving a non-linear eigenvalue problem with periodic boundary conditions, which in the cardiac case is very stiff and calls for the use of asymptotic methods. We compare asymptotics of restitution curves in four examples, two generic excitable media models, and two ionic cardiac models. The generic models include the classical FitzHugh–Nagumo model and its variation by Barkley. They are treated with standard singular perturbation techniques. The ionic models include a simplified “caricature” of Noble (J. Physiol. Lond. 160:317–352, 1962) model and Beeler and Reuter (J. Physiol. Lond. 268:177–210, 1977) model, which lead to non-Tikhonov problems where known asymptotic results do not apply. The Caricature Noble model is considered with particular care to demonstrate the well-posedness of the corresponding boundary-value problem. The developed method for calculation of conduction velocity restitution is then applied to the Beeler–Reuter model. We discuss new mathematical features appearing in cardiac ionic models and possible applications of the developed method.     

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.     

Spatially discordant alternans in cardiomyocyte monolayers

Repolarization alternans is a harbinger of sudden cardiac death, particularly when it becomes spatially discordant. Alternans, a beat-to-beat alternation in the action potential duration (APD) and intracellular Ca (Cai), can arise from either tissue heterogeneities or dynamic factors. Distinguishing between these mechanisms in normal cardiac tissue is difficult because of inherent complex three-dimensional tissue heterogeneities. To evaluate repolarization alternans in a simpler two-dimensional cardiac substrate, we optically recorded voltage and/or Cai in monolayers of cultured neonatal rat ventricular myocytes during rapid pacing, before and after exposure to BAY K 8644 to enhance dynamic factors promoting alternans. Under control conditions (n = 37), rapid pacing caused detectable APD alternans in 81% of monolayers, and Cai transient alternans in all monolayers, becoming spatially discordant in 62%. After BAY K 8644 (n = 28), conduction velocity restitution became more prominent, and APD and Cai alternans developed and became spatially discordant in all monolayers, with an increased number of nodal lines separating out-of-phase alternating regions. Nodal lines moved closer to the pacing site with faster pacing rates and changed orientation when the pacing site was moved, as predicted for the dynamically generated, but not heterogeneity-based, alternans. Spatial APD gradients during spatially discordant alternans were sufficiently steep to induce conduction block and reentry. These findings indicate that spatially discordant alternans severe enough to initiate reentry can be readily induced by pacing in two-dimensional cardiac tissue and behaves according to predictions for a predominantly dynamically generated mechanism.     

Reentry in heterogeneous cardiac tissue described by the Luo-Rudy ventricular action potential model

Heterogeneity of cardiac tissue is an important factor determining the initiation and dynamics of cardiac arrhythmias. In this paper, we studied the effects of gradients of electrophysiological heterogeneity on reentrant excitation patterns using computer simulations. We investigated the dynamics of spiral waves in a two-dimensional sheet of cardiac tissue described by the Luo-Rudy phase 1 (LR1) ventricular action potential model. A gradient of action potential duration (APD) was imposed by gradually varying the local current density of K(+) current or inward rectifying K(+) current along one axis of the tissue sheet. We show that a gradient of APD resulted in spiral wave drift. This drift consisted of two components. The longitudinal (along the gradient) component was always directed toward regions of longer spiral wave period. The transverse (perpendicular to the gradient) component had a direction dependent on the direction of rotation of the spiral wave. We estimated the velocity of the drift as a function of the magnitude of the gradient and discuss its implications.     

A computationally efficient electrophysiological model of human ventricular cells

Recent experimental and theoretical results have stressed the importance of modeling studies of reentrant arrhythmias in cardiac tissue and at the whole heart level. We introduce a six-variable model obtained by a reformulation of the Priebe-Beuckelmann model of a single human ventricular cell. The reformulated model is 4.9 times faster for numerical computations and it is more stable than the original model. It retains the action potential shape at various frequencies, restitution of action potential duration, and restitution of conduction velocity. We were able to reproduce the main properties of epicardial, endocardial, and M cells by modifying selected ionic currents. We performed a simulation study of spiral wave behavior in a two-dimensional sheet of human ventricular tissue and showed that spiral waves have a frequency of 3.3 Hz and a linear core of approximately 50-mm diameter that rotates with an average frequency of 0.62 rad/s. Simulation results agreed with experimental data. In conclusion, the proposed model is suitable for efficient and accurate studies of reentrant phenomena in human ventricular tissue.     

Mechanoelectric feedback leads to conduction slowing and block in acutely dilated atria: a modeling study of cardiac electromechanics

Atrial fibrillation, a common cardiac arrhythmia, is promoted by atrial dilatation. Acute atrial dilatation may play a role in atrial arrhythmogenesis through mechanoelectric feedback. In experimental studies, conduction slowing and block have been observed in acutely dilated atria. In the present study, the influence of the stretch-activated current (I(sac)) on impulse propagation is investigated by means of computer simulations. Homogeneous and inhomogeneous atrial tissues are modeled by cardiac fibers composed of segments that are electrically and mechanically coupled. Active force is related to free Ca(2+) concentration and sarcomere length. Simulations of homogeneous and inhomogeneous cardiac fibers have been performed to quantify the relation between conduction velocity and I(sac) under stretch. In our model, conduction slowing and block are related to the amount of stretch and are enhanced by contraction of early-activated segments. Conduction block can be unidirectional in an inhomogeneous fiber and is promoted by a shorter stimulation interval. Slowing of conduction is explained by inactivation of Na(+) channels and a lower maximum upstroke velocity due to a depolarized resting membrane potential. Conduction block at shorter stimulation intervals is explained by a longer effective refractory period under stretch. Our observations are in agreement with experimental results and explain the large differences in intra-atrial conduction, as well as the increased inducibility of atrial fibrillation in acutely dilated atria.