Yohannes Shiferaw

From Pulsus to Pulseless The Saga of Cardiac Alternans

Computer simulations and nonlinear dynamics have provided invaluable tools for illuminating the underlying mechanisms of cardiac arrhythmias. Here, we review how this approach has led to major insights into the mechanisms of spatially discordant alternans, a key arrhythmogenic factor predisposing the heart to re-entry and lethal arrhythmias. During spatially discordant alternans, the action potential duration (APD) alternates out of phase in different regions of the heart, markedly enhancing dispersion of refractoriness so that ectopic beats have a high probability of inducing reentry. We show how, at the cellular level, instabilities in membrane voltage (ie, steep APD restitution slope) and intracellular Ca (Cai) cycling dynamics cause APD and the Cai transient to alternate and how the characteristics of alternans are affected by different “modes” of the bidirectional coupling between voltage and Cai. We illustrate how, at the tissue level, additional factors, such as conduction velocity restitution and ectopic beats, promote spatially discordant alternans. These insights have illuminated the mechanistic basis underlying the clinical association of cardiac alternans (eg, T wave alternans) with arrhythmia risk, which may lead to novel therapeutic approaches to avert sudden cardiac death.

Model of Intracellular Calcium Cycling in Ventricular Myocytes

We present a mathematical model of calcium cycling that takes into account the spatially localized nature of release events that correspond to experimentally observed calcium sparks. This model naturally incorporates graded release by making the rate at which calcium sparks are recruited proportional to the whole cell L-type calcium current, with the total release of calcium from the sarcoplasmic reticulum (SR) being just the sum of local releases. The dynamics of calcium cycling is studied by pacing the model with a clamped action potential waveform. Experimentally observed calcium alternans are obtained at high pacing rates. The results show that the underlying mechanism for this phenomenon is a steep nonlinear dependence of the calcium released from the SR on the diastolic SR calcium concentration (SR load) and/or the diastolic calcium level in the cytosol, where the dependence on diastolic calcium is due to calcium-induced inactivation of the L-type calcium current. In addition, the results reveal that the calcium dynamics can become chaotic even though the voltage pacing is periodic. We reduce the equations of the model to a two-dimensional discrete map that relates the SR and cytosolic concentrations at one beat and the previous beat. From this map, we obtain a condition for the onset of calcium alternans in terms of the slopes of the release-versus-SR load and release-versus-diastolic-calcium curves. From an analysis of this map, we also obtain an understanding of the origin of chaotic dynamics.

Spatially Discordant Alternans in Cardiac Tissue: Role of Calcium Cycling

Spatially discordant alternans, where the action potential duration (APD) and intracellular calcium transient (Cai) alternate with opposite phase in different regions of tissue, is known to promote wave break and reentry. However, this phenomenon is not completely understood. It is known that alternans at the cellular level can be caused by dynamical instabilities arising from either membrane voltage (Vm) attributable to steep APD restitution or to calcium (Ca) cycling. Here, we used a mathematical model of intracellular Ca cycling, coupled with membrane ion currents, to investigate the dynamics of Vm and Cai transient alternans in an isolated cell, in two electrotonically coupled cells, and in 1D spatially homogeneous tissue. Our main finding is a novel instability mechanism in which the bidirectional coupling of Vm and Cai can drive the Cai transient of two neighboring cells to be out of phase. This instability is manifested in cardiac tissue by the dynamical formation of spatially discordant alternans. In this case, Cai transient alternans can reverse phase over a length scale of one cell, whereas APD alternans reverses phase over a much longer length scale set by the electrotonic coupling. We analyze this mechanism in detail and show that it is a robust consequence of experimentally established properties of the bidirectional coupling between Ca cycling and Vm dynamics. Finally, we address the experimental relevance of these findings and suggest physiological conditions under which these patterns can be observed.

Coupled dynamics of voltage and calcium in paced cardiac cells

We investigate numerically and analytically the coupled dynamics of transmembrane voltage and intracellular calcium cycling in paced cardiac cells using a detailed physiological model, and its reduction to a three-dimensional discrete map. The results provide a theoretical framework to interpret various experimentally observed modes of instability ranging from electromechanically concordant and discordant alternans to quasiperiodic oscillations of voltage and calcium.

Variability in timing of spontaneous calcium release in the intact rat heart is determined by the time course of sarcoplasmic reticulum calcium load.

Background: Abnormalities in intracellular calcium (Ca) cycling during Ca overload can cause triggered activity because spontaneous calcium release (SCR) activates sufficient Ca-sensitive inward currents to induce delayed afterdepolarizations (DADs). However, little is known about the mechanisms relating SCR and triggered activity on the tissue scale. Methods and Results: Laser scanning confocal microscopy was used to measure the spatiotemporal properties of SCR within large myocyte populations in intact rat heart. Computer simulations were used to predict how these properties of SCR determine DAD magnitude. We measured the average and standard deviation of the latency distribution of SCR within a large population of myocytes in intact tissue. We found that as external [Ca] is increased, and with faster pacing rates, the average and SD of the latency distribution decreases substantially. This result demonstrates that the timing of SCR occurs with less variability as the sarcoplasmic reticulum (SR) Ca load is increased, causing more sites to release Ca within each cell. We then applied a mathematical model of subcellular Ca cycling to show that a decrease in SCR variability leads to a higher DAD amplitude and is dictated by the rate of SR Ca refilling following an action potential. Conclusions: Our results demonstrate that the variability of the timing of SCR in a population of cells in tissue decreases with SR load and is dictated by the time course of the SR Ca content.

Mechanisms Underlying the Formation and Dynamics of Subcellular Calcium Alternans in the Intact Rat Heart

Optical mapping of intact cardiac tissue reveals that, in some cases, intracellular calcium (Ca) release can alternate from one beat to the next in a large-small-large sequence, also referred to as Ca transient (CaT) alternans. CaT alternans can also become spatially phase-mismatched within a single cell, when one part of the cell alternates in a large-small-large sequence, whereas a different part alternates in a small-large-small sequence, a phenomenon known as subcellular discordant alternans. The mechanisms for the formation and spatiotemporal evolution of these phase-mismatched patterns are not known. We used confocal Ca imaging to measure CaT alternans at the sarcomeric level within individual myocytes in the intact rat heart. After a sudden change in cycle length (CL), 2 distinct spatial patterns of CaT alternans emerge. CaTs can form spatially phase-mismatched alternans patterns after the first few beats following the change in CL. The phase mismatch persists for many beats, after which it gradually becomes phase matched via the movement of nodes, which are junctures between phase-mismatched cell regions. In other examples, phase-matched alternans gradually become phase-mismatched, via the formation and movement of nodes. In these examples, we observed large beat-to-beat variations in the cell activation times, despite constant CL pacing. Using computer simulations, we explored the underlying mechanisms for these dynamical phenomena. Our results show how heterogeneity at the sarcomeric level, in conjunction with the dynamics of Ca cycling and membrane voltage, can lead to complex spatiotemporal phenomena within myocytes of the intact heart.

Intracellular Ca2+ waves, afterdepolarizations, and triggered arrhythmias

Clinical studies have shown that sudden death is initiated by an ill-timed propagated ectopic beat that leads to fibrillation.1–4 However, the mechanism underlying these focal excitations is not completely understood. Experimental studies have demonstrated that abnormal calcium (Ca2+) cycling is a critical factor in the development of focal excitations.5–9 These excitations can be caused by spontaneous Ca2+ release (SCR) in the form of intracellular Ca2+ waves. These waves are initiated when Ca2+ release from a few Ca2+ release units (CRUs) on the sarcoplasmic reticulum (SR) causes regenerative release in adjoining units via Ca2+-induced Ca2+ release (CICR), causing Ca2+ wave propagation. The resulting depolarizing inward current through the electrogenic Na+–Ca2+ exchanger (NCX) depolarizes the cell membrane to threshold, producing a triggered beat.10–14 The relationship between subcellular Ca2+ waves and focal excitations in cardiac tissue is, however, still not completely understood. The basic unanswered question is how Ca2+ release within a population of cardiac cells can induce sufficient inward current to overcome the electrotonic load of the neighbouring cells. In this paper, we will discuss some key ideas that are essential in answering this question, focusing on the probabilistic nature of SCR and the importance of measuring the timing distribution of Ca2+ waves in multicellular populations in tissue. We will also discuss our recent results showing that the likelihood of a triggered beat is determined by the variance of the timing distribution, which is dictated by the time course of SR reloading.15,16 In addition, we will discuss our observations of a form of Ca2+ wave that is distinct from SCR. These Ca2+ waves occur only during rapid pacing and occur with a latency …

Role of coupled gating between cardiac ryanodine receptors in the genesis of triggered arrhythmias

Mutations in the ryanodine receptor (RyR) have been linked to exercise-induced sudden cardiac death. However, the precise sequence of events linking RyR channel mutations to a whole heart arrhythmia is not completely understood. In this paper, we apply a detailed, mathematical model of subcellular calcium (Ca) release, coupled to membrane voltage, to study how defective RyR channels can induce arrhythmogenic-triggered activity. In particular, we show that subcellular Ca activity, such as spontaneous Ca sparks and Ca waves, is highly sensitive to coupled gating between RyR channels in clusters. We show that small changes in coupled gating can induce aberrant Ca release activity, which, under Ca overload conditions, can induce delayed afterdepolarization (DAD). We systematically investigate the properties of subcellular Ca during DAD induction and show that the voltage time course during a DAD is dependent on the timing and number of spontaneous Ca sparks that transition to Ca waves. These results provide a detailed mechanism for the role of coupled gating in the genesis of triggered arrhythmias.

Formation of spatially discordant alternans due to fluctuations and diffusion of calcium.

Spatially discordant alternans (SDA) of action potential duration (APD) is a phenomenon where different regions of cardiac tissue exhibit an alternating sequence of APD that are out-of-phase. SDA is arrhythmogenic since it can induce spatial heterogeneity of refractoriness, which can cause wavebreak and reentry. However, the underlying mechanisms for the formation of SDA are not completely understood. In this paper, we present a novel mechanism for the formation of SDA in the case where the cellular instability leading to alternans is caused by intracellular calcium (Ca) cycling, and where Ca transient and APD alternans are electromechanically concordant. In particular, we show that SDA is formed when rapidly paced cardiac tissue develops alternans over many beats due to Ca accumulation in the sarcoplasmic reticulum (SR). The mechanism presented here relies on the observation that Ca cycling fluctuations dictate Ca alternans phase since the amplitude of Ca alternans is small during the early stages of pacing. Thus, different regions of a cardiac myocyte will typically develop Ca alternans which are opposite in phase at the early stages of pacing. These subcellular patterns then gradually coarsen due to interactions with membrane voltage to form steady state SDA of voltage and Ca on the tissue scale. This mechanism for SDA is distinct from well-known mechanisms that rely on conduction velocity restitution, and a Turing-like mechanism known to apply only in the case where APD and Ca alternans are electromechanically discordant. Furthermore, we argue that this mechanism is robust, and is likely to underlie a wide range of experimentally observed patterns of SDA.

A mathematical model of spontaneous calcium release in cardiac myocytes.

In cardiac myocytes, calcium (Ca) can be released from the sarcoplasmic reticulum independently of Ca influx from voltage-dependent membrane channels. This efflux of Ca, referred to as spontaneous Ca release (SCR), is due to Ryanodine receptor fluctuations, which can induce spontaneous Ca sparks, which propagate to form Ca waves. This release of Ca can then induce delayed after-depolarizations (DADs), which can lead to arrhythmogenic-triggered activity in the heart. However, despite its importance, to date there is no mathematical model of SCR that accounts for experimentally observed features of subcellular Ca. In this article, we present an experimentally based model of SCR that reproduces the timing distribution of spontaneous Ca sparks and key features of the propagation of Ca waves emanating from these spontaneous sparks. We have coupled this model to an ionic model for the rabbit ventricular action potential to simulate SCR within several thousand cells in cardiac tissue. We implement this model to study the formation of an ectopic beat on a cable of cells that exhibit SCR-induced DADs.