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

Can Stochastic Pacing Restore Heart Rate Variability in Diseased Hearts? An In-vivo Ovine Case Study

Heart rate variability (HRV) is an important clinical parameter that depicts the autonomic balance. Diminished HRV has been associated with diseased hearts and incorporating stochasticity in pacing has been investigated as a potential mechanism for restoring the altered autonomic balance and preventing cardiac arrhythmias. We studied the change in HRV with the development of chronic myocardial infarction (MI) in adult sheep (n=16). Next, we investigated the utility of stochastic pacing in modulating HRV in-vivo in both sham and MI hearts. The propensity of the heart to the development of cardiac alternans, a known precursor to tachyarrhythmias, was studied under three different pacing techniques, namely periodic pacing, stochastic pacing and constant diastolic interval (DI) pacing in one sham and one MI sheep. Autonomic balance was observed to be altered after 6 weeks of chronic MI. Increased heart rate, QTc interval, standard deviation of the R-R intervals and LF/HF ratio was observed in MI hearts. Stochastic pacing was found to be proarrhythmic and increased T-wave alternans burden was observed with increase in stochasticity. Maintaining a constant DI on every beat demonstrated reduced alternans levels compared to both periodic and stochastic pacing.Clinical Relevance-Our results demonstrate that precise control of the diastolic interval may be more beneficial in inhibiting arrhythmias than stochastic pacing.

An Automata-Based Cardiac Electrophysiology Simulator to Assess Arrhythmia Inducibility

Personalized cardiac electrophysiology simulations have demonstrated great potential to study cardiac arrhythmias and help in therapy planning of radio-frequency ablation. Its application to analyze vulnerability to ventricular tachycardia and sudden cardiac death in infarcted patients has been recently explored. However, the detailed multi-scale biophysical simulations used in these studies are very demanding in terms of memory and computational resources, which prevents their clinical translation. In this work, we present a fast phenomenological system based on cellular automata (CA) to simulate personalized cardiac electrophysiology. The system is trained on biophysical simulations to reproduce cellular and tissue dynamics in healthy and pathological conditions, including action potential restitution, conduction velocity restitution and cell safety factor. We show that a full ventricular simulation can be performed in the order of seconds, emulate the results of a biophysical simulation and reproduce a patient’s ventricular tachycardia in a model that includes a heterogeneous scar region. The system could be used to study the risk of arrhythmia in infarcted patients for a large number of scenarios.

Advances in Cardiac Pacing: Arrhythmia Prediction, Prevention and Control Strategies

Cardiac arrhythmias constitute a tremendous burden on healthcare and are the leading cause of mortality worldwide. An alarming number of people have been reported to manifest sudden cardiac death as the first symptom of cardiac arrhythmias, accounting for about 20% of all deaths annually. Furthermore, patients prone to atrial tachyarrhythmias such as atrial flutter and fibrillation often have associated comorbidities including hypertension, ischemic heart disease, valvular cardiomyopathy and increased risk of stroke. Technological advances in electrical stimulation and sensing modalities have led to the proliferation of medical devices including pacemakers and implantable defibrillators, aiming to restore normal cardiac rhythm. However, given the complex spatiotemporal dynamics and non-linearity of the human heart, predicting the onset of arrhythmias and preventing the transition from steady state to unstable rhythms has been an extremely challenging task. Defibrillatory shocks still remain the primary clinical intervention for lethal ventricular arrhythmias, yet patients with implantable cardioverter defibrillators often suffer from inappropriate shocks due to false positives and reduced quality of life. Here, we aim to present a comprehensive review of the current advances in cardiac arrhythmia prediction, prevention and control strategies. We provide an overview of traditional clinical arrhythmia management methods and describe promising potential pacing techniques for predicting the onset of abnormal rhythms and effectively suppressing cardiac arrhythmias. We also offer a clinical perspective on bridging the gap between basic and clinical science that would aid in the assimilation of promising anti-arrhythmic pacing strategies.

Dual regulation by subcellular calcium heterogeneity and heart rate variability on cardiac electromechanical dynamics

Heart rate constantly varies under physiological conditions, termed heart rate variability (HRV), and in clinical studies, low HRV is associated with a greater risk of cardiac arrhythmias. Prior work has shown that HRV influences the temporal patterns of electrical activity, specifically the formation of pro-arrhythmic alternans, a beat-to-beat alternation in the action potential duration (APD), or intracellular calcium (Ca) levels. We previously showed that HRV may be anti-arrhythmic by disrupting APD and Ca alternations in a homogeneous cardiac myocyte. Here, we expand on our previous work, incorporating variation in subcellular Ca handling (also known to influence alternans) into a nonlinear map model of a cardiac myocyte composed of diffusively coupled Ca release units (CRUs). Ca-related parameters and initial conditions of each CRU are varied to mimic subcellular Ca heterogeneity, and a stochastic pacing sequence reproduces HRV. We find that subcellular Ca heterogeneity promotes the formation of spatially discordant subcellular alternans patterns, which decreases whole cell Ca and APD alternation for low and moderate HRV, while high subcellular Ca heterogeneity and HRV both promote electromechanical desynchronization. Finally, we find that for low and moderate HRV, both the specific subcellular Ca-related parameters and the pacing sequences influence measures of electromechanical dynamics, while for high HRV, these measures depend predominantly on the pacing sequence. Our results suggest that pro-arrhythmic subcellular discordant alternans tend to form for low levels of HRV, while high HRV may be anti-arrhythmic due to mitigated influence from subcellular Ca heterogeneity and desynchronization of APD from Ca instabilities.

The control mechanisms of heart rate dynamics in a new heart rate nonlinear time series model

The control mechanisms and implications of heart rate variability (HRV) under the sympathetic (SNS) and parasympathetic nervous system (PNS) modulation remain poorly understood. Here, we establish the HR model/HRV responder using a nonlinear process derived from Newton's second law in stochastic self-restoring systems through dynamic analysis of physiological properties. We conduct model validation by testing, predictions, simulations, and sensitivity and time-scale analysis. We confirm that the outputs of the HRV responder can be accepted as the real data-generating process. Empirical studies show that the dynamic control mechanism of heart rate is a stable fixed point, rather than a strange attractor or transitions between a fixed point and a limit cycle; HR slope (amplitude) may depend on the ratio of cardiac disturbance or metabolic demand mean (standard deviation) to myocardial electrical resistance (PNS-SNS activity). For example, when metabolic demands remain unchanged, HR amplitude depends on PNS to SNS activity; when autonomic activity remains unchanged, HR amplitude during resting reflects basal metabolism. HR parameter alterations suggest that age-related decreased HRV, ultrareduced HRV in heart failure, and ultraelevated HRV in ST segment alterations refer to age-related decreased basal metabolism, impaired myocardial metabolism, and SNS hyperactivity triggered by myocardial ischemia, respectively.

A healthy dose of chaos: Using fractal frameworks for engineering higher-fidelity biomedical systems

Optimal levels of chaos and fractality are distinctly associated with physiological health and function in natural systems. Chaos is a type of nonlinear dynamics that tends to exhibit seemingly random structures, whereas fractality is a measure of the extent of organization underlying such structures. Growing bodies of work are demonstrating both the importance of chaotic dynamics for proper function of natural systems, as well as the suitability of fractal mathematics for characterizing these systems. Here, we review how measures of fractality that quantify the dose of chaos may reflect the state of health across various biological systems, including: brain, skeletal muscle, eyes and vision, lungs, kidneys, tumours, cell regulation, skin and wound repair, bone, vasculature, and the heart. We compare how reports of either too little or too much chaos and fractal complexity can be damaging to normal biological function, and suggest that aiming for the healthy dose of chaos may be an effective strategy for various biomedical applications. We also discuss rising examples of the implementation of fractal theory in designing novel materials, biomedical devices, diagnostics, and clinical therapies. Finally, we explain important mathematical concepts of fractals and chaos, such as fractal dimension, criticality, bifurcation, and iteration, and how they are related to biology. Overall, we promote the effectiveness of fractals in characterizing natural systems, and suggest moving towards using fractal frameworks as a basis for the research and development of better tools for the future of biomedical engineering.

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.

A Biased Diffusion Approach to Sleep Dynamics Reveals Neuronal Characteristics

We propose a biased diffusion model of accumulated subthreshold voltage fluctuations in wake-promoting neurons to account for stochasticity in sleep dynamics and to explain the occurrence of brief arousals during sleep. Utilizing this model, we derive four neurophysiological parameters related to neuronal noise level, excitability threshold, deep-sleep threshold, and sleep inertia. We provide the first analytic expressions for these parameters, and we show that there is good agreement between empirical findings from sleep recordings and our model simulation results. Our work suggests that these four parameters can be of clinical importance because we find them to be significantly altered in elderly subjects and in children with autism.

Stochastic vagus nerve stimulation affects acute heart rate dynamics in rats

Vagus nerve stimulation (VNS) is an approved therapy for treatment of epilepsy and depression. While also shown to be promising in several preclinical and clinical studies to treat cardiovascular diseases, optimal therapeutic stimulation paradigms are still under investigation. Traditionally, parameters such as frequency, current, and duty cycle are used to adjust the efficacy of VNS therapy. This study explored the effect of novel stochastic VNS (S-VNS) on acute heart rate (HR) dynamics. The effect of S-VNS was evaluated in Sprague Dawley rats by comparing the acute HR and HR variability (HRV) responses to standard, periodic VNS (P-VNS) across different frequencies (FREQs, 10-30 Hz). Our results demonstrate that both S-VNS and P-VNS produced negative chronotropic effects in a FREQ-dependent manner with S-VNS inducing a significantly smaller drop in HR at 10 Hz and 20 Hz compared to P-VNS (p<0.05). S-VNS demonstrated a FREQ-dependent drop in the SD1/SD2 ratio, a measure of HRV, which was absent in P-VNS, suggesting that S-VNS may acutely modulate the nonlinear relationship between short- and long-term HRV. In conclusion, S-VNS is a novel stimulation procedure that may provide different physiological outcomes from standard P-VNS, as indicated by our analysis of HR dynamics. Our study provides a rationale for further detailed investigations into the therapeutic potential of S-VNS as a novel neuromodulation technique.

Short-term action potential memory and electrical restitution: A cellular computational study on the stability of cardiac repolarization under dynamic pacing

Electrical restitution (ER) is a major determinant of repolarization stability and, under fast pacing rate, it reveals memory properties of the cardiac action potential (AP), whose dynamics have never been fully elucidated, nor their ionic mechanisms. Previous studies have looked at ER mainly in terms of changes in AP duration (APD) when the preceding diastolic interval (DI) changes and described dynamic conditions where this relationship shows hysteresis which, in turn, has been proposed as a marker of short-term AP memory and repolarization stability. By means of numerical simulations of a non-propagated human ventricular AP, we show here that measuring ER as APD versus the preceding cycle length (CL) provides additional information on repolarization dynamics which is not contained in the companion formulation. We focus particularly on fast pacing rate conditions with a beat-to-beat variable CL, where memory properties emerge from APD vs CL and not from APD vs DI and should thus be stored in APD and not in DI. We provide an ion-currents characterization of such conditions under periodic and random CL variability, and show that the memory stored in APD plays a stabilizing role on AP repolarization under pacing rate perturbations. The gating kinetics of L-type calcium current seems to be the main determinant of this safety mechanism. We also show that, at fast pacing rate and under otherwise identical pacing conditions, a periodically beat-to-beat changing CL is more effective than a random one in stabilizing repolarization. In summary, we propose a novel view of short-term AP memory, differentially stored between systole and diastole, which opens a number of methodological and theoretical implications for the understanding of arrhythmia development.

Stochastic Pacing Inhibits Spatially Discordant Cardiac Alternans

Depressed heart rate variability is a well-established risk factor for sudden cardiac death in survivors of acute myocardial infarction and for those with congestive heart failure. Although measurements of heart rate variability provide a valuable prognostic tool, it is unclear whether reduced heart rate variability itself is proarrhythmic or if it simply correlates with the severity of autonomic nervous system dysfunction. In this work, we investigate a possible mechanism by which heart rate variability could protect against cardiac arrhythmia. Specifically, in numerical simulations, we observe an inverse relationship between the variance of stochastic pacing and the occurrence of spatially discordant alternans, an arrhythmia that is widely believed to facilitate the development of cardiac fibrillation. By analyzing the effects of conduction velocity restitution, cellular dynamics, electrotonic coupling, and stochastic pacing on the nodal dynamics of spatially discordant alternans, we provide intuition for this observed behavior and propose control strategies to inhibit discordant alternans.

Pro-arrhythmic effect of heart rate variability during periodic pacing

Clinically, healthy hearts have been associated with a high ventricular heart rate variability (HRV) while diseased hearts have been known to exhibit low ventricular HRV. Hence, low HRV is suggested to be a marker of cardiac ventricular arrhythmias. Over the past few years, there has been considerable amount of interest in incorporating HRV in pacing to emulate healthy heart conditions and re-stabilize the electrical activity in diseased hearts. Recently, we used single cell numerical simulations to demonstrate that HRV incorporated into periodic pacing promotes alternans formation and thus, can be pro-arrhythmic. Here, we performed high-resolution optical mapping experiments on Langendorff perfused, healthy whole mice hearts to validate our numerical findings. Our results indeed demonstrate that HRV promoted the onset of cardiac alternans, which is believed to be a precursor of fatal cardiac rhythms. Hence, our present study suggests that incorporating HRV into periodic pacing while addressing several clinical needs may not be safe. There is a pressing need to better understand paced cardiac dynamics and develop anti-arrhythmic pacing techniques that would prevent cardiac arrhythmias.

Stochastic pacing reveals the propensity to cardiac action potential alternans and uncovers its underlying dynamics

KEY POINTS

Beat-to-beat alternation (alternans) of the cardiac action potential duration is known to precipitate life-threatening arrhythmias and can be driven by the kinetics of voltage-gated membrane currents or by instabilities in intracellular calcium fluxes. To prevent alternans and associated arrhythmias, suitable markers must be developed to quantify the susceptibility to alternans; previous theoretical studies showed that the eigenvalue of the alternating eigenmode represents an ideal marker of alternans. Using rabbit ventricular myocytes, we show that this eigenvalue can be estimated in practice by pacing these cells at intervals varying stochastically. We also show that stochastic pacing permits the estimation of further markers distinguishing between voltage-driven and calcium-driven alternans. Our study opens the perspective to use stochastic pacing during clinical investigations and in patients with implanted pacing devices to determine the susceptibility to, and the type of alternans, which are both important to guide preventive or therapeutic measures.

ABSTRACT

Alternans of the cardiac action potential (AP) duration (APD) is a well-known arrhythmogenic mechanism. APD depends on several preceding diastolic intervals (DIs) and APDs, which complicates the prediction of alternans. Previous theoretical studies pinpointed a marker called λalt that directly quantifies how an alternating perturbation persists over successive APs. When the propensity to alternans increases, λalt decreases from 0 to -1. Our aim was to quantify λalt experimentally using stochastic pacing and to examine whether stochastic pacing allows discriminating between voltage-driven and Ca(2+) -driven alternans. APs were recorded in rabbit ventricular myocytes paced at cycle lengths (CLs) decreasing progressively and incorporating stochastic variations. Fitting APD with a function of two previous APDs and CLs permitted us to estimate λalt along with additional markers characterizing whether the dependence of APD on previous DIs or CLs is strong (typical for voltage-driven alternans) or weak (Ca(2+) -driven alternans). During the recordings, λalt gradually decreased from around 0 towards -1. Intermittent alternans appeared when λalt reached -0.8 and was followed by sustained alternans. The additional markers detected that alternans was Ca(2+) driven in control experiments and voltage driven in the presence of ryanodine. This distinction could be made even before alternans was manifest (specificity/sensitivity >80% for -0.4 > λalt  > -0.5). These observations were confirmed in a mathematical model of a rabbit ventricular myocyte. In conclusion, stochastic pacing allows the practical estimation of λalt to reveal the onset of alternans and distinguishes between voltage-driven and Ca(2+) -driven mechanisms, which is important since these two mechanisms may precipitate arrhythmias in different manners.

Morning surge of ventricular arrhythmias in a new arrhythmogenic canine model of chronic heart failure is associated with attenuation of time-of-day dependence of heart rate and autonomic adaptation, and reduced cardiac chaos

Patients with chronic heart failure (CHF) exhibit a morning surge in ventricular arrhythmias, but the underlying cause remains unknown. The aim of this study was to determine if heart rate dynamics, autonomic input (assessed by heart rate variability (HRV)) and nonlinear dynamics as well as their abnormal time-of-day-dependent oscillations in a newly developed arrhythmogenic canine heart failure model are associated with a morning surge in ventricular arrhythmias. CHF was induced in dogs by aortic insufficiency & aortic constriction, and assessed by echocardiography. Holter monitoring was performed to study time-of-day-dependent variation in ventricular arrhythmias (PVCs, VT), traditional HRV measures, and nonlinear dynamics (including detrended fluctuations analysis α1 and α2 (DFAα1 & DFAα2), correlation dimension (CD), and Shannon entropy (SE)) at baseline, as well as 240 days (240 d) and 720 days (720 d) following CHF induction. LV fractional shortening was decreased at both 240 d and 720 d. Both PVCs and VT increased with CHF duration and showed a morning rise (2.5-fold & 1.8-fold increase at 6 AM-noon vs midnight-6 AM) during CHF. The morning rise in HR at baseline was significantly attenuated by 52% with development of CHF (at both 240 d & 720 d). Morning rise in the ratio of low frequency to high frequency (LF/HF) HRV at baseline was markedly attenuated with CHF. DFAα1, DFAα2, CD and SE all decreased with CHF by 31, 17, 34 and 7%, respectively. Time-of-day-dependent variations in LF/HF, CD, DFA α1 and SE, observed at baseline, were lost during CHF. Thus in this new arrhythmogenic canine CHF model, attenuated morning HR rise, blunted autonomic oscillation, decreased cardiac chaos and complexity of heart rate, as well as aberrant time-of-day-dependent variations in many of these parameters were associated with a morning surge of ventricular arrhythmias.

The interrelations among stochastic pacing, stability, and memory in the heart

Low pacing variability in the heart has been clinically reported as a risk factor for lethal cardiac arrhythmias and arrhythmic death. In ia 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.

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.