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.     

Scroll wave dynamics in a three-dimensional cardiac tissue model: roles of restitution, thickness, and fiber rotation

Scroll wave (vortex) breakup is hypothesized to underlie ventricular fibrillation, the leading cause of sudden cardiac death. We simulated scroll wave behaviors in a three-dimensional cardiac tissue model, using phase I of the Luo-Rudy (LR1) action potential model. The effects of action potential duration (APD) restitution, tissue thickness, filament twist, and fiber rotation were studied. We found that APD restitution is the major determinant of scroll wave behavior and that instabilities arising from APD restitution are the main determinants of scroll wave breakup in this cardiac model. We did not see a "thickness-induced instability" in the LR1 model, but a minimum thickness is required for scroll breakup in the presence of fiber rotation. The major effect of fiber rotation is to maintain twist in a scroll wave, promoting filament bending and thus scroll breakup. In addition, fiber rotation induces curvature in the scroll wave, which weakens conduction and further facilitates wave break.     

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 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.     

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.     

Mechanism of anode break stimulation in the heart.

Anodal stimulation is routinely observed in cardiac tissue, but only recently has a mechanism been proposed. The bidomain cardiac tissue model proposes that virtual cathodes induced at sites distant from the electrode initiate the depolarization. In contrast, none of the existing cardiac action potential models (Luo-Rudy phase I and II, or Oxsoft) predict anodal stimulation at the single-cell level. To determine whether anodal stimulation has a cellular basis, we measured membrane potential and membrane current in mammalian ventricular myocytes by using whole-cell patch clamp. Anode break responses can be readily elicited in single ventricular cells. The basis of this anodal stimulation in single cells is recruitment of the hyperpolarization-activated inward current I(f). The threshold of activation for I(f) is -80 mV in rat cells and -120 mV in guinea pig or canine cells. Persistent I(f) "tail" current upon release of the hyperpolarization drives the transmembrane potential toward the threshold of sodium channels, initiating an action potential. Time-dependent block of the inward rectifier, I(K1), at hyperpolarized potentials decreases membrane conductance and thereby potentiates the ability of I(f) to depolarize the cell on the break of an anodal pulse. Inclusion of I(f), as well as the block and unblock kinetics of I(K1), in the existing Luo-Rudy action potential model faithfully reproduces anode break stimulation. Thus active cellular properties suffice to explain anode break stimulation in cardiac tissue.     

High resolution magnetic images of planar wave fronts reveal bidomain properties of cardiac tissue

We magnetically imaged the magnetic action field and optically imaged the transmembrane potentials generated by planar wavefronts on the surface of the left ventricular wall of Langendorff-perfused isolated rabbit hearts. The magnetic action field images were used to produce a time series of two-dimensional action current maps. Overlaying epifluorescent images allowed us to identify a net current along the wavefront and perpendicular to gradients in the transmembrane potential. This is in contrast to a traditional uniform double-layer model where the net current flows along the gradient in the transmembrane potential. Our findings are supported by numerical simulations that treat cardiac tissue as a bidomain with unequal anisotropies in the intra- and extracellular spaces. Our measurements reveal the anisotropic bidomain nature of cardiac tissue during plane wave propagation. These bidomain effects play an important role in the generation of the whole-heart magnetocardiogram and cannot be ignored.     

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.     

A kinetic model for determining the consequences of electrogenic active transport in cardiac muscle

When active transport is electrogenic in a tissue that is continuously active, such as cardiac muscle, the active transport current is as important in the generation of the action potential as are the passive currents. A thermodynamically constrained kinetic model of electrogenic active transport of sodium and potassium ions has been developed in which the influences of voltage and chemical composition are explicitly defined. This model is coupled to a system of passive permeabilities, of the minimum degree of complexity, to simulate the integrated activity of active and passive ion transport in the generation of the cardiac action potential. Results of preliminary simulations indicate that electrogenic active transport provides a mechanism for slowly changing currents both within the time scale of an action potential as well as of many action potentials. The presence of active transport also complicates the interpretation of isotopic flux measurements and the separation of currents.     

A Simulation Study of the Role of Mechanical Stretch in Arrhythmogenesis during Cardiac Alternans

The deformation of the heart tissue due to the contraction can modulate the excitation, a phenomenon referred to as mechanoelectrical feedback (MEF), via stretch-activated channels. The effects of MEF on the electrophysiology at high pacing rates are shown to be proarrhythmic in general. However, more studies need to be done to elucidate the underlying mechanism. In this work, we investigate the effects of MEF on cardiac alternans, which is an alternation in the width of the action potential that typically occurs when the heart is paced at high rates, using a biophysically detailed electromechanical model of cardiac tissue. We observe that the transition from spatially concordant alternans to spatially discordant alternans, which is more arrhythmogenic than concordant alternans, may occur in the presence of MEF and when its strength is sufficiently large. We show that this transition is due to the increase of the dispersion of conduction velocity. In addition, our results also show that the MEF effects, depending on the stretch-activated channels’ conductances and reversal potentials, can result in blocking action potential propagation.     

The statistics of calcium-mediated focal excitations on a one-dimensional cable

It is well known that various cardiac arrhythmias are initiated by an ill-timed excitation that originates from a focal region of the heart. However, up to now, it is not known what governs the timing, location, and morphology of these focal excitations. Recent studies have shown that these excitations can be caused by abnormalities in the calcium (Ca) cycling system. However, the cause-and-effect relationships linking subcellular Ca dynamics and focal activity in cardiac tissue is not completely understood. In this article, we present a minimal model of Ca-mediated focal excitations in cardiac tissue. This model accounts for the stochastic nature of spontaneous Ca release on a one-dimensional cable of cardiac cells. Using this model, we show that the timing of focal excitations is equivalent to a first passage time problem in a spatially extended system. In particular, we find that for a short cable the mean first passage time increases exponentially with the number of cells in tissue, and is critically dependent on the ratio of inward to outward currents near the threshold for an action potential. For long cables excitations occurs due to ectopic foci that occur on a length scale determined by the minimum length of tissue that can induce an action potential. Furthermore, we find that for long cables the mean first passage time decreases as a power law in the number cells. These results provide precise criteria for the occurrence of focal excitations in cardiac tissue, and will serve as a guide to determine the propensity of Ca-mediated triggered arrhythmias in the heart.     

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.     

Effects of simulated ischemia on spiral wave stability

Regional hyperkalemia during acute myocardial ischemia is a major factor promoting electrophysiological abnormalities leading to ventricular fibrillation (VF). However, steep action potential duration restitution, recently proposed to be a major determinant of VF, is typically decreased rather than increased by hyperkalemia and acute ischemia. To investigate this apparent contradiction, we simulated the effects of regional hyperkalemia and other ischemic components (anoxia and acidosis) on the stability of spiral wave reentry in simulated two-dimensional cardiac tissue by use of the Luo-Rudy ventricular action potential model. We found that the hyperkalemic "ischemic" area promotes wavebreak in the surrounding normal tissue by accelerating the rate of spiral wave reentry, even after the depolarized ischemic area itself has become unexcitable. Furthermore, wavebreak and fibrillation can be prevented if the dynamical instability of the normal tissue is reduced significantly by targeting electrical restitution properties, suggesting a novel therapeutic approach.     

Empirical Study of an Adaptive Multiscale Model for Simulating Cardiac Conduction

We modify and empirically study an adaptive multiscale model for simulating cardiac action potential propagation along a strand of cardiomyocytes. The model involves microscale partial differential equations posed over cells near the action potential upstroke and macroscale partial differential equations posed over the remainder of the tissue. An important advantage of the modified model of this paper is that, unlike our original model, it does not require perfect alignment between myocytes and the macroscale computational grid. We study the effects of gap-junctional coupling, ephaptic coupling, and macroscale grid spacing on the accuracy of the multiscale model. Our simulations reveal that the multiscale method accurately reproduces both the wavespeed and the waveform, including both upstroke and recovery, of fully microscale models. They also reveal that perfect alignment between myocytes and the macroscale grid is not necessary to reproduce the dynamics of a traveling action potential. Further, our simulations suggest that the macroscale grid spacing used in an adaptive multiscale model need not be much finer than the spatial width of an action potential. These results are demonstrated to hold under high, low, and zero gap-junctional coupling regimes.     

Proven cardiac changes during death-feigning (tonic immobility) in rabbits (Oryctolagus cuniculus)

Tonic immobility (TI) is a response to fear or threat by remaining motionless, principally when attacked by predators from which there is no possibility of escape. Thus, here we demonstrate a way of easily reproducing this phenomenon in a laboratory setting and characterize the cardiac electromechanical alterations during TI. We observed a significant decrease in heart rate (HR) and changes of rhythm in electrocardiogram during TI in rabbits. Echocardiogram showed a significant increase in the left ventricle chamber diameter during systole and a consequent decrease in fractional shortening and ejection fraction, in addition to the HR and rhythm changes. There was also a significant decrease in aortic and pulmonary artery blood flow. Diastolic functional changes included a significant decrease of the peak atrial contraction velocity (A peak) and consequent increase in the ratio of peak early diastolic velocity to A peak and increased isovolumetric relaxation time. We were able to prove that TI changes the cardiac function considerably. Although the “fight-or-flight” response is the most common response to fear, which is characterized by the action of sympathetic nervous system with tachycardia and increased physical activity, TI is an alternative anti-predator behavior causing cardiac changes opposite to the “fight-or-flight” phenomenon.     

Mathematical models of action potentials in the periphery and center of the rabbit sinoatrial node

Mathematical models of the action potential in the periphery and center of the rabbit sinoatrial (SA) node have been developed on the basis of published experimental data. Simulated action potentials are consistent with those recorded experimentally: the model-generated peripheral action potential has a more negative takeoff potential, faster upstroke, more positive peak value, prominent phase 1 repolarization, greater amplitude, shorter duration, and more negative maximum diastolic potential than the model-generated central action potential. In addition, the model peripheral cell shows faster pacemaking. The models behave qualitatively the same as tissue from the periphery and center of the SA node in response to block of tetrodotoxin-sensitive Na(+) current, L- and T-type Ca(2+) currents, 4-aminopyridine-sensitive transient outward current, rapid and slow delayed rectifying K(+) currents, and hyperpolarization-activated current. A one-dimensional model of a string of SA node tissue, incorporating regional heterogeneity, coupled to a string of atrial tissue has been constructed to simulate the behavior of the intact SA node. In the one-dimensional model, the spontaneous action potential initiated in the center propagates to the periphery at approximately 0.06 m/s and then into the atrial muscle at 0.62 m/s.     

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.     

The Interrelations among Stochastic Pacing,Stability, and Memory in the Heart

Low pacing variabilty in the heart has been clinically reported as a risk factor for lethal cardiac arrhythmias and arrhythmic death. In a previous simulation study, we demonstrated that stochastic pacing sustains an antiarrhythmic effect by moderating the slope of the action potential duration (APD) restitution curve, by reducing the propensity of APD alternans, converting discordant to concordant alternans, and ultimately preventing wavebreaks. However, the dynamic mechanisms relating pacing stochasticity to tissue stability are not yet known. In this work, we develop a mathematical framework to describe the APD signal using an autoregressive stochastic model, and we establish the interrelations between stochastic pacing, cardiac memory, and cardiac stability, as manifested by the degree of APD alternans. Employing stability analysis tools, we show that increased stochasticity in the ventricular tissue activation sequence works to lower the maximal absolute eigenvalues of the stochastic model, thereby contributing to increased stability. We also show that the memory coefficients of the autoregressive model are modulated by pacing stochasticity in a nonlinear, biphasic way, so that for exceedingly high levels of pacing stochasticity, the antiarrhythmic effect is hampered by increasing APD variance. This work may contribute to establishment of an optimal antiarrhythmic pacing protocol in a future study.     

The Interrelations among Stochastic Pacing,Stability, and Memory in the Heart

Low pacing variabilty in the heart has been clinically reported as a risk factor for lethal cardiac arrhythmias and arrhythmic death. In a previous simulation study, we demonstrated that stochastic pacing sustains an antiarrhythmic effect by moderating the slope of the action potential duration (APD) restitution curve, by reducing the propensity of APD alternans, converting discordant to concordant alternans, and ultimately preventing wavebreaks. However, the dynamic mechanisms relating pacing stochasticity to tissue stability are not yet known. In this work, we develop a mathematical framework to describe the APD signal using an autoregressive stochastic model, and we establish the interrelations between stochastic pacing, cardiac memory, and cardiac stability, as manifested by the degree of APD alternans. Employing stability analysis tools, we show that increased stochasticity in the ventricular tissue activation sequence works to lower the maximal absolute eigenvalues of the stochastic model, thereby contributing to increased stability. We also show that the memory coefficients of the autoregressive model are modulated by pacing stochasticity in a nonlinear, biphasic way, so that for exceedingly high levels of pacing stochasticity, the antiarrhythmic effect is hampered by increasing APD variance. This work may contribute to establishment of an optimal antiarrhythmic pacing protocol in a future study.     

Short-term cardiac memory and mother rotor fibrillation

Short-term cardiac memory refers to the effects of pacing history on action potential duration (APD). Although the ionic mechanisms for short-term memory occurring over many heartbeats (also called APD accommodation) are poorly understood, they may have important effects on reentry and fibrillation. To explore this issue, we incorporated a generic memory current into the Phase I Luo and Rudy action potential model, which lacks short-term memory. The properties of this current were matched to simulate quantitatively human ventricular monophasic action potential accommodation. We show that, theoretically, short-term memory can resolve the paradox of how mother rotor fibrillation is initiated in heterogeneous tissue by physiological pacing. In simulated heterogeneous two-dimensional tissue and three-dimensional ventricles containing an inward rectifier K(+) current gradient, short-term memory could spontaneously convert multiple wavelet fibrillation to mother rotor fibrillation or to a mixture of both fibrillation types. This was due to progressive acceleration and stabilization of rotors as accumulation of memory shortened APD and flattened APD restitution slope nonuniformly throughout the tissue.