Quantifying interactions between real oscillators with information theory and phase models: application to cardiorespiratory coupling

Changes in the autonomic cardiorespiratory activity in parturient women with severe and moderate features of preeclampsia

Background

Cardiorespiratory coupling (CRC) is a physiological phenomenon that reflects the mutual interaction between the cardiac and respiratory control systems. It is mainly associated with efferent vagal activity from the central autonomic network. Few studies have explored the autonomic changes of CRC in preeclampsia, a critical obstetric complication related to possible autonomic dysfunctions and inflammatory disturbances. This study examined the autonomic mechanisms of CRC in women with severe and moderate preeclampsia and healthy controls by applying nonlinear methods based on information theory, such as mutual information (MI) and Renyi's mutual information (RMI) and the linear and nonlinear analysis of the Pulse-Respiration Quotient (PRQ).

Methods

We studied three groups of parturient women in the third trimester of pregnancy with a clinical diagnosis of preeclampsia without severe symptoms (P, 38.5 ± 1.4 weeks of pregnancy, n=19), preeclampsia with severe symptoms (SP, 37.5 ± 0.9 weeks of pregnancy, n=22), and normotensive control women (C, 39.1 ± 1.3 weeks of pregnancy, n=20). 10-minutes of abdominal electrocardiograms (ECG) and respiratory signals (RESP) were recorded in all the participants. Subsequently, we obtained the maternal beat-to-beat (RR) and breath-to-breath (BB) time series from ECG and RESP, respectively. The CRC between RR and BB was quantified by nonlinear methods based on information theory, such as MI and RMI, along with the analysis of the novel index of PRQ. Subsequently, we computed the mean PRQ (mPRQ) and the normalized permutation entropy (nPermEn_PRQ) from the PRQ time series generated from BB and RR. In addition, we examined the vagal activity in the three groups by the logarithm of the median of the distribution of the absolute values of successive RR differences (logRSA).

Results

The MI and RMI values were significantly lower (p<0.05) in the preeclamptic groups compared to the control group. However, no significant differences were found between the preeclamptic groups. The logRSA and nPermEn_PRQ indices were significantly lower (p<0.05) in SP compared to C and P.

Conclusion

Our data suggest that parturient women with severe and mild preeclampsia may manifest an altered cardiorespiratory coupling compared with normotensive control women. Disrupted CRC in severe preeclampsia could be associated with vagal withdrawal and less complex cardiorespiratory dynamics. The difference in vagal activity between the preeclamptic groups may suggest a further reduction in vagal activity associated with the severity of the disease.

Cardiorespiratory coupling in mechanically ventilated patients studied via synchrogram analysis

Respiration and cardiac activity are strictly interconnected with reciprocal influences. They act as weakly coupled oscillators showing varying degrees of phase synchronization and their interactions are affected by mechanical ventilation. The study aims at differentiating the impact of three ventilatory modes on the cardiorespiratory phase coupling in critically ill patients. The coupling between respiration and heartbeat was studied through cardiorespiratory phase synchronization analysis carried out via synchrogram during pressure control ventilation (PCV), pressure support ventilation (PSV), and neurally adjusted ventilatory assist (NAVA) in critically ill patients. Twenty patients were studied under all the three ventilatory modes. Cardiorespiratory phase synchronization changed significantly across ventilatory modes. The highest synchronization degree was found during PCV session, while the lowest one with NAVA. The percentage of all epochs featuring synchronization regardless of the phase locking ratio was higher with PCV (median: 33.9%, first-third quartile: 21.3-39.3) than PSV (median: 15.7%; first-third quartile: 10.9-27.8) and NAVA (median: 3.7%; first-third quartile: 3.3-19.2). PCV induces a significant amount of cardiorespiratory phase synchronization in critically ill mechanically ventilated patients. Synchronization induced by patient-driven ventilatory modes was weaker, reaching the minimum with NAVA. Findings can be explained as a result of the more regular and powerful solicitation of the cardiorespiratory system induced by PCV. The degree of phase synchronization between cardiac and respiratory activities in mechanically ventilated humans depends on the ventilatory mode.

Cardiorespiratory alterations following intermittent photostimulation of RVLM C1 neurons: Implications for long-term blood pressure, breathing and sleep regulation in freely moving rats

AIM

Sympathoexcitation and sleep-disordered breathing are common contributors for disease progression. Catecholaminergic neurons from the rostral ventrolateral medulla (RVLM-C1) modulate sympathetic outflow and have anatomical projections to respiratory neurons; however, the contribution of highly selective activation of RVLM-C1 neurons on long-term autonomic and breathing (dys)regulation remains to be understood.

METHODS

To explore this relationship, a lentiviral vector carrying the light-sensitive cation channel channelrhodopsin-2 (LVV-PRSX8-ChR2-YFP) was unilaterally injected into the RVLM of healthy rats. On the contralateral side, LVV-PRSX8-ChR2-YFP was co-injected with a specific immunotoxin (DβH-SAP) targeted to eliminate C1 neurons.

RESULTS

Intermittent photostimulation of RVLM-C1 in vivo, in unrestrained freely moving rats, elicited long-term facilitation of the sympathetic drive, a rise in blood pressure and sympatho-respiratory coupling. In addition, photoactivation of RVLM-C1 induced long-lasting ventilatory instability, characterized by oscillations in tidal volume and increased breathing variability, but only during non-rapid eye movement sleep. These effects were not observed when photostimulation of the RVLM was performed in the presence of DβH-SAP toxin.

CONCLUSIONS

The finding that intermittent activation of RVLM-C1 neurons induces autonomic and breathing dysfunction suggest that episodic stimulation of RVLM-C1 may serve as a pathological substrate for the long-term development of cardiorespiratory disorders.

The Link Between Spinal Cord Stimulation and the Parasympathetic Nervous System in Patients With Failed Back Surgery Syndrome

OBJECTIVES

In patients with chronic pain, a relative lower parasympathetic activity is suggested based on heart rate variability measurements. It is hypothesized that spinal cord stimulation (SCS) is able to influence the autonomic nervous system. The aim of this study is to further explore the influence of SCS on the autonomic nervous system by evaluating whether SCS is able to influence skin conductance, blood volume pulse, heart rate, and respiration rate.

MATERIALS AND METHODS

Twenty-eight patients with Failed Back Surgery Syndrome (FBSS), who are treated with SCS, took part in this multicenter study. Skin conductance and cardiorespiratory parameters (blood volume pulse, heart rate, and respiration rate) were measured during on and off states of SCS. Paired statistics were performed on a 5-min recording segment for all parameters.

RESULTS

SCS significantly decreased back and leg pain intensity scores in patients with FBSS. Skin conductance level and blood volume pulse were not altered between on and off states of SCS. Heart rate and respiration rate significantly decreased when SCS was activated.

CONCLUSIONS

Parameters that are regulated by the sympathetic nervous system were not significantly different between SCS on and off states, leading to the hypothesis that SCS is capable of restoring the dysregulation of the autonomic nervous system by primarily increasing the activity of the parasympathetic system, in patients with FBSS.

Acute effects of high-intensity interval training session and endurance exercise on pulmonary function and cardiorespiratory coupling

The aim of this study was to determine the acute effects of high-intensity interval training (HIIT) exercise and endurance exercise (EE) on pulmonary function, sympathetic/parasympathetic balance, and cardiorespiratory coupling (CRC) in healthy participants. Using a crossover repeated-measurements design, four females and four males were exposed to EE (20 min at 80% maximal heart rate [HR]), HIIT (1 min of exercise at 90% maximal HR per 1 min of rest, 10 times), or control condition (resting). Pulmonary function, HR, CRC, and heart rate variability (HRV) were assessed before and after the interventions. Results revealed no significant effects of EE or HIIT on pulmonary function. The EE, but not HIIT, significantly increased CRC. In contrast, HRV was markedly changed by HIIT, not by EE. Indeed, both the low-frequency (LFHRV ) and high-frequency (HFHRV ) components of HRV were increased and decreased, respectively, after HIIT. The increase in LFHRV was greater after HIIT than after EE. Therefore, a single bout of HIIT or EE has no effects on pulmonary function. Moreover, CRC and cardiac autonomic regulation are targeted differently by the two exercise modalities.

A practical method for estimating coupling functions in complex dynamical systems

A foremost challenge in modern network science is the inverse problem of reconstruction (inference) of coupling equations and network topology from the measurements of the network dynamics. Of particular interest are the methods that can operate on real (empirical) data without interfering with the system. One such earlier attempt (Tokuda et al. 2007 Phys. Rev. Lett. 99, 064101. (doi:10.1103/PhysRevLett.99.064101)) was a method suited for general limit-cycle oscillators, yielding both oscillators' natural frequencies and coupling functions between them (phase equations) from empirically measured time series. The present paper reviews the above method in a way comprehensive to domain-scientists other than physics. It also presents applications of the method to (i) detection of the network connectivity, (ii) inference of the phase sensitivity function, (iii) approximation of the interaction among phase-coherent chaotic oscillators, and (iv) experimental data from a forced Van der Pol electric circuit. This reaffirms the range of applicability of the method for reconstructing coupling functions and makes it accessible to a much wider scientific community. This article is part of the theme issue 'Coupling functions: dynamical interaction mechanisms in the physical, biological and social sciences'.

Increasing Local Excitability of Brainstem Respiratory Nuclei Reveals a Distributed Network Underlying Respiratory Motor Pattern Formation

The core circuit of the respiratory central pattern generator (rCPG) is located in the ventrolateral medulla, especially in the pre-Bötzinger complex (pre-BötC) and the neighboring Bötzinger complex (BötC). To test the hypothesis that this core circuit is embedded within an anatomically distributed pattern-generating network, we investigated whether local disinhibition of the nucleus tractus solitarius (NTS), the Kölliker-Fuse nuclei (KFn), or the midbrain periaqueductal gray area (PAG) can similarly affect the respiratory pattern compared to disinhibition of the pre-BötC/BötC core. In arterially-perfused brainstem preparations of rats, we recorded the three-phase respiratory pattern (inspiration, post-inspiration and late-expiration) from phrenic and vagal nerves before and after bilateral microinjections of the GABA(A)R antagonist bicuculline (50 nl, 10 mM). Local disinhibition of either NTS, pre-BötC/BötC, or KFn, but not PAG, triggered qualitatively similar disruptions of the respiratory pattern resulting in a highly significant increase in the variability of the respiratory cycle length, including inspiratory and expiratory phase durations. To quantitatively analyze these motor pattern perturbations, we measured the strength of phase synchronization between phrenic and vagal motor outputs. This analysis showed that local disinhibition of all brainstem target nuclei, but not the midbrain PAG, significantly decreased the strength of phase synchronization. The convergent perturbations of the respiratory pattern suggest that the rCPG expands rostrally and dorsally from the designated core but does not include higher mid-brain structures. Our data also suggest that excitation-inhibition balance of respiratory network synaptic interactions critically determines the network dynamics that underlie vital respiratory rhythm and pattern formation.

The Role of Failing Autonomic Nervous System on Life-Threatening Idiopathic Systemic Capillary Leak Syndrome

Idiopathic systemic capillary leak syndrome (ISCLS) is a rare disease that involves the endothelium and microcirculation, leading to an abrupt shift of fluids and proteins from the intravascular to the interstitial compartment. The consequence of the capillary leakage is a life-threatening hypovolemic shock that can lead to lethal multiple organ dysfunction. The autonomic nervous system (ANS) is central in regulating the cardiovascular response to hypovolemia, but ANS modulation in ISCLS has not yet been investigated. Here, we report ANS activity during acute phase and recovery from a severe ISCLS shock and speculate on the possibility that autonomic mechanisms underlie the pathogenesis of attacks.

Kölliker-Fuse nuclei regulate respiratory rhythm variability via a gain-control mechanism

Respiration varies from breath to breath. On the millisecond timescale of spiking, neuronal circuits exhibit variability due to the stochastic properties of ion channels and synapses. Does this fast, microscopic source of variability contribute to the slower, macroscopic variability of the respiratory period? To address this question, we modeled a stochastic oscillator with forcing; then, we tested its predictions experimentally for the respiratory rhythm generated by the in situ perfused preparation during vagal nerve stimulation (VNS). Our simulations identified a relationship among the gain of the input, entrainment strength, and rhythm variability. Specifically, at high gain, the periodic input entrained the oscillator and reduced variability, whereas at low gain, the noise interacted with the input, causing events known as "phase slips", which increased variability on a slow timescale. Experimentally, the in situ preparation behaved like the low-gain model: VNS entrained respiration but exhibited phase slips that increased rhythm variability. Next, we used bilateral muscimol microinjections in discrete respiratory compartments to identify areas involved in VNS gain control. Suppression of activity in the nucleus tractus solitarii occluded both entrainment and amplification of rhythm variability by VNS, confirming that these effects were due to the activation of the Hering-Breuer reflex. Suppressing activity of the Kölliker-Fuse nuclei (KFn) enhanced entrainment and reduced rhythm variability during VNS, consistent with the predictions of the high-gain model. Together, the model and experiments suggest that the KFn regulates respiratory rhythm variability via a gain control mechanism.

Heart Rate and Respiratory Rate Influence on Heart Rate Variability Repeatability: Effects of the Correction for the Prevailing Heart Rate

Background: Since heart rate variability (HRV) is associated with average heart rate (HR) and respiratory rate (RespRate), alterations in these parameters may impose changes in HRV. Hence the repeatability of HRV measurements may be affected by differences in HR and RespRate. The study aimed to evaluate HRV repeatability and its association with changes in HR and RespRate.

Methods: Forty healthy volunteers underwent two ECG examinations 7 days apart. Standard HRV indices were calculated from 5-min ECG recordings. The ECG-derived respiration signal was estimated to assess RespRate. To investigate HR impact on HRV, HRV parameters were corrected for prevailing HR.

Results: Differences in HRV parameters between the measurements were associated with the changes in HR and RespRate. However, in multiple regression analysis only HR alteration proved to be independent determinant of the HRV differences—every change in HR by 1 bpm changed HRV values by 16.5% on average. After overall removal of HR impact on HRV, coefficients of variation of the HRV parameters significantly dropped on average by 26.8% (p < 0.001), i.e., by the same extent HRV reproducibility improved. Additionally, the HRV correction for HR decreased association between RespRate and HRV.

Conclusions: In stable conditions, HR but not RespRate is the most powerful factor determining HRV reproducibility and even a minimal change of HR may considerably alter HRV. However, the removal of HR impact may significantly improve HRV repeatability. The association between HRV and RespRate seems to be, at least in part, HR dependent.

Respiratory Changes in Response to Cognitive Load: A Systematic Review

When people focus attention or carry out a demanding task, their breathing changes. But which parameters of respiration vary exactly and can respiration reliably be used as an index of cognitive load? These questions are addressed in the present systematic review of empirical studies investigating respiratory behavior in response to cognitive load. Most reviewed studies were restricted to time and volume parameters while less established, yet meaningful parameters such as respiratory variability have rarely been investigated. The available results show that respiratory behavior generally reflects cognitive processing and that distinct parameters differ in sensitivity: While mentally demanding episodes are clearly marked by faster breathing and higher minute ventilation, respiratory amplitude appears to remain rather stable. The present findings further indicate that total variability in respiratory rate is not systematically affected by cognitive load whereas the correlated fraction decreases. In addition, we found that cognitive load may lead to overbreathing as indicated by decreased end-tidal CO₂ but is also accompanied by elevated oxygen consumption and CO₂ release. However, additional research is needed to validate the findings on respiratory variability and gas exchange measures. We conclude by outlining recommendations for future research to increase the current understanding of respiration under cognitive load.

Phase-dependent modulation as a novel approach for therapeutic brain stimulation

Closed-loop paradigms provide us with the opportunity to optimize stimulation protocols for perturbation of pathological oscillatory activity in brain-related disorders. In this vein, spiking activity of motor cortex neurons and beta activity of local field potentials in the subthalamic nucleus have both been used independently of each other as neuronal signals to trigger deep brain stimulation for alleviating Parkinsonism. These approaches were superior to the standard continuous high-frequency stimulation protocols used in daily practice. However, they achieved their effects by bursts of stimulation that were applied at high-frequency as well, i.e., independent of the phase information in the stimulated region. In this context, we propose that, by timing stimulation pulses relative to the ongoing oscillation, an alternative approach, namely the targeted perturbation of pathological rhythms, could be obtained. In this modeling study, we first captured the underlying dynamics of neuronal oscillations in the human subthalamic nucleus by phased coupled neuronal oscillators. We then quantified the nature of the interaction between these coupled oscillators by obtaining a physiologically informed phase response curve from local field potentials. Reconstruction of the phase response curve predicted the sensitivity of the phase oscillator to external stimuli, revealing phase intervals that optimally maximized the degree of perturbation. We conclude that our specifically timed intervention based on the coupled oscillator concept will enable us to identify personalized ways of delivering stimulation pulses in closed-loop paradigms triggered by the phase of pathological oscillations. This will pave the way for novel physiological insights and substantial clinical benefits. In addition, this precisely phased modulation may be capable of modifying the effective interactions between oscillators in an entirely new manner.

Considerations in the assessment of heart rate variability in biobehavioral research

Heart rate variability (HRV) refers to various methods of assessing the beat-to-beat variation in the heart over time, in order to draw inference on the outflow of the autonomic nervous system. Easy access to measuring HRV has led to a plethora of studies within emotion science and psychology assessing autonomic regulation, but significant caveats exist due to the complicated nature of HRV. Firstly, both breathing and blood pressure regulation have their own relationship to social, emotional, and cognitive experiments – if this is the case are we observing heart rate (HR) changes as a consequence of breathing changes? Secondly, experiments often have poor internal and external controls. In this review we highlight the interrelationships between HR and respiration, as well as presenting recommendations for researchers to use when collecting data for HRV assessment. Namely, we highlight the superior utility of within-subjects designs along with the importance of establishing an appropriate baseline and monitoring respiration.

Fine temporal structure of cardiorespiratory synchronization

Cardiac and respiratory rhythms are known to exhibit a modest degree of phase synchronization, which is affected by age, diseases, and other factors. We study the fine temporal structure of this synchrony in healthy young, healthy elderly, and elderly subjects with coronary artery disease. We employ novel time-series analysis to explore how phases of oscillations go in and out of the phase-locked state at each cycle of oscillations. For the first time we show that cardiorespiratory system is engaged in weakly synchronized dynamics with a very specific temporal pattern of synchrony: the oscillations go out of synchrony frequently, but return to the synchronous state very quickly (usually within just 1 cycle of oscillations). Properties of synchrony depended on the age and disease status. Healthy subjects exhibited more synchrony at the higher (1:4) frequency-locking ratio between respiratory and cardiac rhythms, whereas subjects with coronary artery disease exhibited relatively more 1:2 synchrony. However, multiple short desynchronization episodes prevailed regardless of the age and disease status. The same average synchrony level could be alternatively achieved with few long desynchronizations, but this was not observed in the data. This implies functional importance of short desynchronization dynamics. These dynamics suggest that a synchronous state is easy to create if needed but is also easy to break. Short desynchronization dynamics may facilitate the mutual coordination of cardiac and respiratory rhythms by creating intermittent synchronous episodes. It may be an efficient background dynamics to promote adaptation of cardiorespiratory coordination to various external and internal factors.

Cardiorespiratory coupling: common rhythms in cardiac, sympathetic, and respiratory activities

Cardiorespiratory coupling is an encompassing term describing more than the well-recognized influences of respiration on heart rate and blood pressure. Our data indicate that cardiorespiratory coupling reflects a reciprocal interaction between autonomic and respiratory control systems, and the cardiovascular system modulates the ventilatory pattern as well. For example, cardioventilatory coupling refers to the influence of heart beats and arterial pulse pressure on respiration and is the tendency for the next inspiration to start at a preferred latency after the last heart beat in expiration. Multiple complementary, well-described mechanisms mediate respiration's influence on cardiovascular function, whereas mechanisms mediating the cardiovascular system's influence on respiration may only be through the baroreceptors but are just being identified. Our review will describe a differential effect of conditioning rats with either chronic intermittent or sustained hypoxia on sympathetic nerve activity but also on ventilatory pattern variability. Both intermittent and sustained hypoxia increase sympathetic nerve activity after 2 weeks but affect sympatho-respiratory coupling differentially. Intermittent hypoxia enhances sympatho-respiratory coupling, which is associated with low variability in the ventilatory pattern. In contrast, after constant hypobaric hypoxia, 1-to-1 coupling between bursts of sympathetic and phrenic nerve activity is replaced by 2-to-3 coupling. This change in coupling pattern is associated with increased variability of the ventilatory pattern. After baro-denervating hypobaric hypoxic-conditioned rats, splanchnic sympathetic nerve activity becomes tonic (distinct bursts are absent) with decreases during phrenic nerve bursts and ventilatory pattern becomes regular. Thus, conditioning rats to either intermittent or sustained hypoxia accentuates the reciprocal nature of cardiorespiratory coupling. Finally, identifying a compelling physiologic purpose for cardiorespiratory coupling is the biggest barrier for recognizing its significance. Cardiorespiratory coupling has only a small effect on the efficiency of gas exchange; rather, we propose that cardiorespiratory control system may act as weakly coupled oscillator to maintain rhythms within a bounded variability.

Interaction function of oscillating coupled neurons

Large scale simulations of electrically coupled neuronal oscillators often employ the phase coupled oscillator paradigm to understand and predict network behavior. We study the nature of the interaction between such coupled oscillators using weakly coupled oscillator theory. By employing piecewise linear approximations for phase response curves and voltage time courses and parametrizing their shapes, we compute the interaction function for all such possible shapes and express it in terms of discrete Fourier modes. We find that reasonably good approximation is achieved with four Fourier modes that comprise of both sine and cosine terms.

Decreased Hering-Breuer input-output entrainment in a mouse model of Rett syndrome

Rett syndrome, a severe X-linked neurodevelopmental disorder caused by mutations in the gene encoding methyl-CpG-binding protein 2 (Mecp2), is associated with a highly irregular respiratory pattern including severe upper-airway dysfunction. Recent work suggests that hyperexcitability of the Hering-Breuer reflex (HBR) pathway contributes to respiratory dysrhythmia in Mecp2 mutant mice. To assess how enhanced HBR input impacts respiratory entrainment by sensory afferents in closed-loop in vivo-like conditions, we investigated the input (vagal stimulus trains) - output (phrenic bursting) entrainment via the HBR in wild-type and MeCP2-deficient mice. Using the in situ perfused brainstem preparation, which maintains an intact pontomedullary axis capable of generating an in vivo-like respiratory rhythm in the absence of the HBR, we mimicked the HBR feedback input by stimulating the vagus nerve (at threshold current, 0.5 ms pulse duration, 75 Hz pulse frequency, 100 ms train duration) at an inter-burst frequency matching that of the intrinsic oscillation of the inspiratory motor output of each preparation. Using this approach, we observed significant input-output entrainment in wild-type mice as measured by the maximum of the cross-correlation function, the peak of the instantaneous relative phase distribution, and the mutual information of the instantaneous phases. This entrainment was associated with a reduction in inspiratory duration during feedback stimulation. In contrast, the strength of input-output entrainment was significantly weaker in Mecp2 (-/+) mice. However, Mecp2 (-/+) mice also had a reduced inspiratory duration during stimulation, indicating that reflex behavior in the HBR pathway was intact. Together, these observations suggest that the respiratory network compensates for enhanced sensitivity of HBR inputs by reducing HBR input-output entrainment.