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.

Interbeat interval modulation in the sinoatrial node as a result of membrane current stochasticity-a theoretical and numerical study.

A single isolated sinoatrial pacemaker cell presents intrinsic interbeat interval (IBI) variability that is believed to result from the stochastic characteristics of the opening and closing processes of membrane ion channels. To our knowledge, a novel mathematical framework was developed in this work to address the effect of current fluctuations on the IBIs of sinoatrial pacemaker cells. Using statistical modeling and employing the Fokker-Planck formalism, our mathematical analysis suggests that increased stochastic current fluctuation variance linearly increases the slope of phase-4 depolarization, hence the rate of activations. Single-cell and two-dimensional computerized numerical modeling of the sinoatrial node was conducted to validate the theoretical predictions using established ionic kinetics of the rabbit pacemaker and atrial cells. Our models also provide, to our knowledge, a novel complementary or alternative explanation to recent experimental observations showing a strong reduction in the mean IBI of Cx30 deficient mice in comparison to wild-types, not fully explicable by the effects of intercellular decoupling.

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.

Mechanistic description of spontaneous loss of memory persistent activity based on neuronal synaptic strength.

Persistent neural activity associated with working memory (WM) lasts for a limited time duration. Current theories suggest that its termination is actively obtained via inhibitory currents, and there is currently no theory regarding the possibility of a passive memory-loss mechanism that terminates memory persistent activity. Here, we develop an analytical-framework, based on synaptic strength, and show via simulations and fitting to wet-lab experiments, that passive memory-loss might be a result of an ionic-current long-term plateau, i.e., very slow reduction of memory followed by abrupt loss. We describe analytically the plateau, when the memory state is just below criticality. These results, including the plateau, are supported by experiments performed on rats. Moreover, we show that even just above criticality, forgetfulness can occur due to neuronal noise with ionic-current fluctuations, yielding a plateau, representing memory with very slow decay, and eventually a fast memory decay. Our results could have implications for developing new medications, targeted against memory impairments, through modifying neuronal noise.

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.

Central Sleep Apnea Alters Neuronal Excitability and Increases the Randomness in Sleep-Wake Transitions.

OBJECTIVE: While most studies on Central Sleep Apnea (CSA) have focused on breathing and metabolic disorders, the neuronal dysfunction that causes CSA remains largely unknown. Here, we investigate the underlying neuronal mechanism of CSA by studying the sleep-wake dynamics as derived from hypnograms. METHODS: We analyze sleep data of seven groups of subjects: healthy adults (n = 48), adults with obstructive sleep apnea (OSA) (n = 29), adults with CSA (n = 25), healthy children (n = 40), children with OSA (n = 18), children with CSA (n = 73) and CSA children treated with CPAP (n = 10). We calculate sleep-wake parameters based on the probability distributions of wake-bout durations and sleep-bout durations. We compare these parameters with results obtained from a neuronal model that simulates the interplay between sleep- and wake-promoting neurons. RESULTS: We find that sleep arousals of CSA patients show a characteristic time scale (i.e., exponential distribution) in contrast to the scale-invariant (i.e., power-law) distribution that has been reported for arousals in healthy sleep. Furthermore, we show that this change in arousal statistics is caused by triggering more arousals of similar durations, which through our model can be related to a higher excitability threshold in sleep-promoting neurons in CSA patients. CONCLUSIONS: We propose a neuronal mechanism to shed light on CSA pathophysiology and a method to discriminate between CSA and OSA. We show that higher neuronal excitability thresholds can lead to complex reorganization of sleep-wake dynamics. SIGNIFICANCE: The derived sleep parameters enable a more specific evaluation of CSA severity and can be used for CSA diagnosis and monitor CSA treatment.

Neuronal noise as an origin of sleep arousals and its role in sudden infant death syndrome.

In addition to regular sleep/wake cycles, humans and animals exhibit brief arousals from sleep. Although much is known about consolidated sleep and wakefulness, the mechanism that triggers arousals remains enigmatic. Here, we argue that arousals are caused by the intrinsic neuronal noise of wake-promoting neurons. We propose a model that simulates the superposition of the noise from a group of neurons, and show that, occasionally, the superposed noise exceeds the excitability threshold and provokes an arousal. Because neuronal noise decreases with increasing temperature, our model predicts arousal frequency to decrease as well. To test this prediction, we perform experiments on the sleep/wake behavior of zebrafish larvae and find that increasing water temperatures lead to fewer and shorter arousals, as predicted by our analytic derivations and model simulations. Our findings indicate a previously unrecognized neurophysiological mechanism that links sleep arousals with temperature regulation, and may explain the origin of the clinically observed higher risk for sudden infant death syndrome with increased ambient temperature.

Stochastic pacing effect on cardiac alternans--simulation study of a 2D human ventricular tissue.

The physiological heart rate is not deterministic but rather varies in time; those variations are termed heart rate variability (HRV). It is well known that low HRV is often seen in patients prone to arrhythmias. The ability of HRV to predict arrhythmia events is traditionally attributed to an impaired balance between the autonomic sympathetic and parasympathetic tone. However, there is no concrete model that directly relates low HRV to the electrical conduction in the cardiac tissue and to arrhythmogenic dynamic properties. We simulated stochastic cardiac pacing with Gaussian distribution using 2D human ventricular tissue model. Conduction stabilization was obtained with stochastic pacing owing to reduced propensity of the appearance of action potential duration (APD) discordant alternans and reduced APD spatial heterogeneity.

A novel heart rate control model provides insights linking LF-HRV behavior to the open-loop gain.

BACKGROUND: Low-frequency heart rate variability (LF-HRV) at rest has already been successfully modeled as self-sustained oscillations in a nonlinear control loop, but these models fail to simulate LF-HRV decreases either during aerobic exercise or in heart failure patients. Following control engineering practices, we assume the existence of a biological excitation (dither) within the heart rate control loop that softens the nonlinearity and studied LF-HRV behavior in a dither-embedded model. METHODS: We adopted the Ottesen model with some revisions and induced a dither of high-frequency stochastic perturbations. We simulated scenarios of a healthy subject at rest and during aerobic exercise (by decreasing peripheral vascular resistance) and a heart failure patient (by decreasing stroke volume). RESULTS: The simulations resembled physiological LF-HRV behavior, i.e., LF-HRV decreased during aerobic exercise and in the heart failure patient. The simulations exhibited LF-HRV dependency on the open-loop gain, which is related to the product of the feedback gain and the feed forward gain. CONCLUSIONS: We are the first to demonstrate that LF-HRV may be dependent on the open-loop gain. Accordingly, reduced open-loop gain results in decreased LF-HRV, and vice versa. Our findings explain a well-known but unexplained observed phenomenon of reduced LF-HRV both in heart failure patients and in healthy subjects performing aerobic exercise. These findings have implications on how changes in LF-HRV can be interpreted physiologically, a necessary step towards the clinical utilization of LF-HRV.

Heart rate variability effect on the myocyte action potential duration restitution: insights from switched systems theory.

The physiological heart rate presents a stochastic behavior known as heart rate variability (HRV). In this framework the influence of HRV on the action potential duration (APD) of the atrial myocyte is analyzed in a computer model. We have found that introducing HRV into the myocyte action potential model decreases the APD of the extra beat S2 in an S1-S2 protocol compared to constant heart rate. A possible theoretical explanation for this is also presented and is derived from switched systems theory. It is suggested to consider the myocyte action potential phase 4 and phase 2 as two operation modes of a switching system and analyze the stability of switching between them. Since random switching is known to have a stabilization effect on a switching system, this might explain why HRV has a stabilization effect on the myocyte APD restitution. Implications of this finding include reduced system stability for conditions with low HRV. A possible application for this phenomenon regards artificial pacemakers, where a preset added HRV is predicted to reduce susceptibility to arrhythmias.