Oscillation in cycle length induces transient discordant and steady-state concordant alternans in the heart

Long-term changes in heart rate and electrical remodeling contribute to alternans formation in heart failure: a patient-specific in silico study

Individuals with chronic heart failure (CHF) have an increased risk of ventricular arrhythmias, which has been linked to pathological cellular remodeling and may also be mediated by changes in heart rate. Heart rate typically fluctuates on a timescale ranging from seconds to hours, termed heart rate variability (HRV). This variability is reduced in CHF, and this HRV reduction is associated with a greater risk for arrhythmias. Furthermore, variations in heart rate influence the formation of proarrhythmic alternans, a beat-to-beat alternation in the action potential duration (APD), or intracellular calcium (Ca). In this study, we investigate how long-term changes in heart rate and electrical remodeling associated with CHF influence alternans formation. We measure key statistical properties of the RR-interval sequences from ECGs of individuals with normal sinus rhythm (NSR) and CHF. Patient-specific RR-interval sequences and synthetic sequences (randomly generated to mimicking these statistical properties) are used as the pacing protocol for a discrete time-coupled map model that governs APD and intracellular Ca handling of a single cardiac myocyte, modified to account for pathological electrical remodeling in CHF. Patient-specific simulations show that beat-to-beat differences in APD vary temporally in both populations, with alternans formation more prevalent in CHF. Parameter studies using synthetic sequences demonstrate that increasing the autocorrelation time or mean RR-interval reduces APD alternations, whereas increasing the RR-interval standard deviation leads to higher alternans magnitudes. Importantly, we find that although both the CHF-associated changes in heart rate and electrical remodeling influence alternans formation, variations in heart rate may be more influential.NEW & NOTEWORTHY Using patient-specific data, we show that both the changes in heart rate and electrical remodeling associated with chronic heart failure influence the formation of proarrhythmic alternans in the heart.

Ventricular Repolarization and Calcium Transient Show Resonant Behavior under Oscillatory Pacing Rate

Cardiac EC coupling is triggered by rhythmic depolarizing current fronts originating from the sino-atrial node, and the way variability in rhythm is associated with variability in action potential duration (APD) and, in turn, in the variability of calcium transient amplitude (CTA) and contraction is a key determinant of beating stability. Sinusoidal-varying pacing rate is adopted here in order to establish whether APD and CTA oscillations, elicited in a human ventricular AP model (OR) under oscillatory pacing, are consistent with the dynamics of two coupled harmonic oscillators, e.g., a two-degree-of-freedom system of mass and springs (MS model). I show evidence that this is the case, and that the MS model, preliminarily fitted to OR behavior, retains key features of the physiological system, such as the dependence of APD and CTA oscillation amplitudes from average value and from beat-to-beat changes in pacing rate, and the phase relationship between them. The bi-directionality of coupling between APD and CTA makes it difficult to discriminate which one leads EC coupling dynamics under variable pacing. The MS model suggests that the calcium cycling, with its greater inertia chiefly determined by the SR calcium release, is the leading mechanism. I propose the present approach to also be relevant at the whole organ level, where the need of compact representations of electromechanical interaction, particularly in clinical practice, remains urgent.

Global vs local control of cardiac alternans in a 1D numerical model of human ventricular tissue

Cardiac alternans is a proarrhythmic state in which the action potential duration (APD) of cardiac myocytes alternate between long and short values and often occurs under conditions of rapid pacing of cardiac tissue. In the ventricles, alternans is especially dangerous due to the life-threatening risk of developing arrhythmias, such as ventricular fibrillation. Alternans can be formed in periodically paced tissue as a result of pacing itself. Recently, it has been demonstrated that this pacing-induced alternans can be prevented by performing constant diastolic interval (DI) pacing, in which DI is independent of APD. However, constant DI pacing is difficult to implement in experimental settings since it requires the real-time measurement of APD. A more practical way was proposed based on electrocardiograms (ECGs), which give an indirect measure of the global DI relaxation period through the TR interval assessment. Previously, we demonstrated that constant TR pacing prevented alternans formation in isolated Langendorff-perfused rabbit hearts. However, the efficacy of "local" constant DI pacing vs "global" constant TR pacing in preventing alternans formation has never been investigated. Thus, the purpose of this study was to implement an ECG-based constant TR pacing in a 1D numerical model of human ventricular tissue and to compare the dynamical behavior of cardiac tissue with that resulted from a constant DI pacing. The results showed that both constant TR and constant DI pacing prevented the onset of alternans until lower basic cycle length when compared to periodic pacing. For longer cable lengths, constant TR pacing was shown to exhibit greater control on alternans than constant DI pacing.

Restitution and Stability of Human Ventricular Action Potential at High and Variable Pacing Rate

Despite the key role of beat-to-beat action potential (AP) variability in the onset of ventricular arrhythmias at high pacing rate, the knowledge of the involved dynamics and of effective prognostic parameters is largely incomplete. Electrical restitution (ER), the way AP duration (APD) senses changes in preceding cycle length (CL), has been used to monitor transition to arrhythmias. The use of standard ER (sER), though, is controversial, not always suitable for in vivo and only rarely for clinical applications. By means of simulations on a human ventricular AP model, I investigate the dynamics of APD at high pacing rate under sinusoidally, saw-tooth, and randomly variable pacing CLs. AP sequences were compared in terms of beat-to-beat restitution (btb-ER) and of the collections of sER curves generated from each beat. A definition of APD stability is also proposed, based on successive APD changes introduced in an AP sequence by a premature beat. The explored CL range includes values leading to APD alternans under constant pacing. Three different types of response to CL variability were found, corresponding to progressively higher rate of beat-to-beat CL changes. Low rates (∼1 ms/beat) generate a btb-ER dominated by steady-state rate dependence of APD (type 1), intermediate rates (∼5 ms/beat) lead to a btb-ER similar to a single sER (type 2), and high rates (∼20 ms/beat) to hysteretic btb-ER under periodic pacing and to a vertically spread btb-ER in the case of random pacing (type 3). Stability of AP repolarization always increases with the rate of CL changes. Thus, rather than looking at sER slope, which requires additional interventions during the recording of cardiac electrical activity, this study provides rationale for the use of btb-ER representations as predictors of repolarization stability under extreme pacing conditions, known to be critical for the arrhythmia development.

Ephaptic coupling rescues conduction failure in weakly coupled cardiac tissue with voltage-gated gap junctions

Electrical conduction in cardiac tissue is usually considered to be primarily facilitated by gap junctions, providing a pathway between the intracellular spaces of neighboring cells. However, recent studies have highlighted the role of coupling via extracellular electric fields, also known as ephaptic coupling, particularly in the setting of reduced gap junction expression. Further, in the setting of reduced gap junctional coupling, voltage-dependent gating of gap junctions, an oft-neglected biophysical property in computational studies, produces a positive feedback that promotes conduction failure. We hypothesized that ephaptic coupling can break the positive feedback loop and rescue conduction failure in weakly coupled cardiac tissue. In a computational tissue model incorporating voltage-gated gap junctions and ephaptic coupling, we demonstrate that ephaptic coupling can rescue conduction failure in weakly coupled tissue. Further, ephaptic coupling increased conduction velocity in weakly coupled tissue, and importantly, reduced the minimum gap junctional coupling necessary for conduction, most prominently at fast pacing rates. Finally, we find that, although neglecting gap junction voltage-gating results in negligible differences in well coupled tissue, more significant differences occur in weakly coupled tissue, greatly underestimating the minimal gap junctional coupling that can maintain conduction. Our study suggests that ephaptic coupling plays a conduction-preserving role, particularly at rapid heart rates.

Memory in a fractional-order cardiomyocyte model alters properties of alternans and spontaneous activity

Cardiac memory is the dependence of electrical activity on the prior history of one or more system state variables, including transmembrane potential (V_m), ionic current gating, and ion concentrations. While prior work has represented memory either phenomenologically or with biophysical detail, in this study, we consider an intermediate approach of a minimal three-variable cardiomyocyte model, modified with fractional-order dynamics, i.e., a differential equation of order between 0 and 1, to account for history-dependence. Memory is represented via both capacitive memory, due to fractional-order V_m dynamics, that arises due to non-ideal behavior of membrane capacitance; and ionic current gating memory, due to fractional-order gating variable dynamics, that arises due to gating history-dependence. We perform simulations for varying V_m and gating variable fractional-orders and pacing cycle length and measure action potential duration (APD) and incidence of alternans, loss of capture, and spontaneous activity. In the absence of ionic current gating memory, we find that capacitive memory, i.e., decreased V_m fractional-order, typically shortens APD, suppresses alternans, and decreases the minimum cycle length (MCL) for loss of capture. However, in the presence of ionic current gating memory, capacitive memory can prolong APD, promote alternans, and increase MCL. Further, we find that reduced V_m fractional order (typically less than 0.75) can drive phase 4 depolarizations that promote spontaneous activity. Collectively, our results demonstrate that memory reproduced by a fractional-order model can play a role in alternans formation and pacemaking, and in general, can greatly increase the range of electrophysiological characteristics exhibited by a minimal model.

Impaired Sarcoplasmic Reticulum Calcium Uptake and Release Promote Electromechanically and Spatially Discordant Alternans: A Computational Study

Cardiac electrical dynamics are governed by cellular-level properties, such as action potential duration (APD) restitution and intracellular calcium (Ca) handling, and tissue-level properties, including conduction velocity restitution and cell-cell coupling. Irregular dynamics at the cellular level can lead to instabilities in cardiac tissue, including alternans, a beat-to-beat alternation in the action potential and/or the intracellular Ca transient. In this study, we incorporate a detailed single cell coupled map model of Ca cycling and bidirectional APD-Ca coupling into a spatially extended tissue model to investigate the influence of sarcoplasmic reticulum (SR) Ca uptake and release properties on alternans and conduction block. We find that an intermediate SR Ca uptake rate and larger SR Ca release resulted in the widest range of stimulus periods that promoted alternans. However, both reduced SR Ca uptake and release promote arrhythmogenic spatially and electromechanically discordant alternans, suggesting a complex interaction between SR Ca handling and alternans characteristics at the cellular and tissue level.

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.

Control of cardiac alternans by mechanical and electrical feedback

A persistent alternation in the cardiac action potential duration has been linked to the onset of ventricular arrhythmia, which may lead to sudden cardiac death. A coupling between these cardiac alternans and the intracellular calcium dynamics has also been identified in previous studies. In this paper, the system of PDEs describing the small amplitude of alternans and the alternation of peak intracellular Ca(2+) are stabilized by optimal boundary and spatially distributed actuation. A simulation study demonstrating the successful annihilation of both alternans on a one-dimensional cable of cardiac cells by utilizing the full-state feedback controller is presented. Complimentary to these studies, a three variable Nash-Panfilov model is used to investigate alternans annihilation via mechanical (or stretch) perturbations. The coupled model includes the active stress which defines the mechanical properties of the tissue and is utilized in the feedback algorithm as an independent input from the pacing based controller realization in alternans annihilation. Simulation studies of both control methods demonstrate that the proposed methods can successfully annihilate alternans in cables that are significantly longer than 1 cm, thus overcoming the limitations of earlier control efforts.

Stochastic cardiac pacing increases ventricular electrical stability--a computational study

The ventricular tissue is activated in a stochastic rather than in a deterministic rhythm due to the inherent heart rate variability (HRV). Low HRV is a known predictor for arrhythmia events and traditionally is attributed to autonomic nervous system tone damage. Yet, there is no model that directly assesses the antiarrhythmic effect of pacing stochasticity per se. One-dimensional (1D) and two-dimensional (2D) human ventricular tissues were modeled, and both deterministic and stochastic pacing protocols were applied. Action potential duration restitution (APDR) and conduction velocity restitution (CVR) curves were generated and analyzed, and the propensity and characteristics of action potential duration (APD) alternans were investigated. In the 1D model, pacing stochasticity was found to sustain a moderating effect on the APDR curve by reducing its slope, rendering the tissue less arrhythmogenic. Moreover, stochasticity was found to be a significant antagonist to the development of concordant APD alternans. These effects were generally amplified with increased variability in the pacing cycle intervals. In addition, in the 2D tissue configuration, stochastic pacing exerted a protective antiarrhythmic effect by reducing the spatial APD heterogeneity and converting discordant APD alternans to concordant ones. These results suggest that high cardiac pacing stochasticity is likely to reduce the risk of cardiac arrhythmias in patients.

Can body surface microvolt T-wave alternans distinguish concordant and discordant intracardiac alternans?

INTRODUCTION

There is convincing experimental evidence that cellular action potential duration (APD) alternans is arrhythmogenic but its relationship with body surface microvolt T-wave alternans (MTWA) remains unclear. We investigated the relationship between MTWA and APD alternans induced by alternating cycle length (CL) pacing in a pig model.

METHODS

In 10 pigs, catheters in the right atrium (RA) and right (RV) and left ventricle (LV) allowed pacing and recording of monophasic action potentials (MAP). During RA pacing at stable 500-ms CL, LV was paced at alternating CL (505 ms and 495 ms). Changing the alternating LV (A-LV) pacing delay changes the size of the region with alternating ventricular activation. Spectral analysis of intracardiac MAP was correlated with body surface MTWA. In a similar setup (during alternating pacing in RV and LV), we investigated concordant versus discordant APD alternans.

RESULTS

Pacing the LV with subtle alternating cycle lengths at short A-LV delay leads to broad QRS (97 ± 10 ms), body surface MTWA (mean Valt 4.2 ± 1.8 µV), and positive RR-interval alternans. At longer A-LV delay, not resulting in QRS widening (68 ± 5 ms), body surface RR alternans was absent but MTWA remained detectable and was even more pronounced (8.7 ± 5.1 µV, P < 0.01). During both concordant and discordant pacing MTWA was present. The precordial leads were better for detecting discordant APD alternans (8.0 ± 2.9 µV and 12.8 ± 4.52 µV, P = 0.02).

CONCLUSION

MTWA is a potent technique to detect subtle and isolated intracardiac APD alternans that is artificially induced by alternating pacing. In the same model, discordant activation alternans can only be discriminated from concordant when using a quantifying approach of MTWA analysis.

Defibrillation success with high frequency electric fields is related to degree and location of conduction block

BACKGROUND

We recently demonstrated that high frequency alternating current (HFAC) electric fields can reversibly block propagation in the heart by inducing an oscillating, elevated transmembrane potential (Vm) that maintains myocytes in a refractory state for the field duration and can terminate arrhythmias, including ventricular fibrillation (VF).

OBJECTIVES

To quantify and characterize conduction block (CB) induced by HFAC fields and to determine whether the degree of CB can be used to predict defibrillation success.

METHODS

Optical mapping was performed in adult guinea pig hearts (n = 14), and simulations were performed in an anatomically accurate rabbit ventricular model. HFAC fields (50-500 Hz) were applied to the ventricles. A novel power spectrum metric of CB-the loss of spectral power in the 1-30 Hz range, termed loss of conduction power (LCP)-was assessed during the HFAC field and compared with defibrillation success and VF vulnerability.

RESULTS

LCP increased with field strength and decreased with frequency. Optical mapping experiments conducted on the epicardial surface showed that LCP and the size of CB regions were significantly correlated with VF initiation and termination. In simulations, subsurface myocardial LCP and CB sizes were more closely correlated with VF termination than surface values. Multilinear regression analysis of simulation results revealed that while CB on both the surface and the subsurface myocardium was predictive, subsurface myocardial CB was the better predictor of defibrillation success.

CONCLUSIONS

HFAC fields induce a field-dependent state of CB, and defibrillation success is related to the degree and location of the CB.