Synchronization in the human cardiorespiratory system

Experimental study of the irrational phase synchronization of coupled nonidentical mechanical metronomes

It has recently been observed in numerical simulations that the phases of two coupled nonlinear oscillators can become locked into an irrational ratio, exhibiting the phenomenon of irrational phase synchronization (IPS) [Phys. Rev. E 69, 056228 (2004)]. Here, using two coupled nonidentical periodic mechanical metronomes, we revisit this interesting phenomenon through experimental studies. It is demonstrated that under suitable couplings, the phases of the metronomes indeed can become locked into irrational ratios. Numerical simulations confirm the experimental observations and also reveal that in the IPS state, the system dynamics are chaotic. Our studies provide a solid step toward further studies of IPS.

Synchronization in an optomechanical cavity

We study self-excited oscillations (SEO) in an on-fiber optomechanical cavity. Synchronization is observed when the optical power that is injected into the cavity is periodically modulated. A theoretical analysis based on the Fokker-Planck equation evaluates the expected phase space distribution (PSD) of the self-oscillating mechanical resonator. A tomography technique is employed for extracting PSD from the measured reflected optical power. Time-resolved state tomography measurements are performed to study phase diffusion and phase locking of the SEO. The detuning region inside which synchronization occurs is experimentally determined and the results are compared with the theoretical prediction.

Joint symbolic dynamics for the assessment of cardiovascular and cardiorespiratory interactions

Beat-to-beat variations in heart period provide information on cardiovascular control and are closely linked to variations in arterial pressure and respiration. Joint symbolic analysis of heart period, systolic arterial pressure and respiration allows for a simple description of their shared short-term dynamics that are governed by cardiac baroreflex control and cardiorespiratory coupling. In this review, we discuss methodology and research applications. Studies suggest that analysis of joint symbolic dynamics provides a powerful tool for identifying physiological and pathophysiological changes in cardiovascular and cardiorespiratory control.

The discrete complex wavelet approach to phase assignment and a new test bed for related methods

A new approach based on the dual-tree complex wavelet transform is introduced for phase assignment to non-linear oscillators, namely, the Discrete Complex Wavelet Approach-DCWA. This methodology is able to measure phase difference with enough accuracy to track fine variations, even in the presence of Gaussian observational noise and when only a single scalar measure of the oscillator is available. So, it can be an especially interesting tool to deal with experimental data. In order to compare it with other phase detection techniques, a testbed is introduced. This testbed provides time series from dynamics similar to non-linear oscillators, such that a theoretical phase choice is known in advance. Moreover, it allows to tune different types of phase synchronization to test phase detection methods under a variety of scenarios. Through numerical benchmarks, we report that the proposed approach is a reliable alternative and that it is particularly effective compared with other methodologies in the presence of moderate to large noises.

Extraction of response waveforms of heartbeat and blood pressure to swallowing. Using mixed signal processing of time domain and respiratory phase domain

BACKGROUND

Evaluating the accurate responses of the cardiovascular system to external stimuli is important for a deeper understanding of cardiovascular homeostasis. However, the responses should be distorted by the conventional time domain analysis when a frequency of the effect of external stimuli matches that of intrinsic fluctuations.

OBJECTIVES

The purpose of this study is to propose a mixed signal processing of time domain and respiratory phase domain to extract the response waveforms of heartbeat and blood pressure (BP) to external stimuli and to clarify the physiological mechanisms of swallowing effects on the cardiovascular system.

METHODS

Measurements were conducted on 12 healthy humans in the sitting and standing positions, with each subject requested to swallow every 30 s between expiration and inspiration. Waveforms of respiratory sinus arrhythmia (RSA) and respiratory-related BP variations were extracted as functions of the respiratory phase. Then, respiratory effects were subtracted from response waveforms with reference to the respiratory phase in the time domain.

RESULTS

As a result, swallowing induced tachycardia, which peaked within 3 s and recovered within 8 s. Tachycardia was greater in the sitting position than during standing. Furthermore, systolic BP and pulse pressure immediately decreased and diastolic BP increased coincident with the occurrence of tachycardia. Subsequently, systolic BP and pulse pressure recovered faster than the R-R interval.

CONCLUSIONS

We conclude that swallowing-induced tachycardia arises largely from the decrease of vagal activity and the baroreflex would yield fast oscillatory responses in recovery.

Sound synchronization of bubble trains in a viscous fluid: experiment and modeling

We investigate the dynamics of formation of air bubbles expelled from a nozzle immersed in a viscous fluid under the influence of sound waves. We have obtained bifurcation diagrams by measuring the time between successive bubbles, having the air flow (Q) as a parameter control for many values of the sound wave amplitude (A), the height (H) of the solution above the top of the nozzle, and three values of the sound frequency (fs). Our parameter spaces (Q,A) revealed a scenario for the onset of synchronization dominated by Arnold tongues (frequency locking) which gives place to chaotic phase synchronization for sufficiently large A. The experimental results were accurately reproduced by numerical simulations of a model combining a simple bubble growth model for the bubble train and a coupling term with the sound wave added to the equilibrium pressure.

Effects of acute hypoxia on heart rate variability, sample entropy and cardiorespiratory phase synchronization

BACKGROUND

Investigating the responses of autonomic nervous system (ANS) in hypoxia may provide some knowledge about the mechanism of neural control and rhythmic adjustment. The integrated cardiac and respiratory system display complicated dynamics that are affected by intrinsic feedback mechanisms controlling their interaction. To probe how the cardiac and respiratory system adjust their rhythms in different simulated altitudes, we studied heart rate variability (HRV) in frequency domain, the complexity of heartbeat series and cardiorespiratory phase synchronization (CRPS) between heartbeat intervals and respiratory cycles.

METHODS

In this study, twelve male subjects were exposed to simulated altitude of sea level, 3000 m and 4000 m in a hypobaric chamber. HRV was assessed by power spectral analysis. The complexity of heartbeat series was quantified by sample entropy (SampEn). CRPS was determined by cardiorespiratory synchrogram.

RESULTS

The power spectral HRV indices at all frequency bands depressed according to the increase of altitude. The SampEn of heartbeat series increased significantly with the altitude (P < 0.01). The duration of CRPS epochs at 3000 m was not significantly different from that at sea level. However, it was significantly longer at 4000 m (P < 0.01).

CONCLUSIONS

Our results suggest the phenomenon of CRPS exists in normal subjects when they expose to acute hypoxia. Further, the autonomic regulation has a significantly stronger influence on CRPS in acute hypoxia. The changes of CRPS and HRV parameters revealed the different regulatory mechanisms of the cardiac and respiratory system at high altitude.

How much time has passed? Ask your heart

Internal signals like one's heartbeats are centrally processed via specific pathways and both their neural representations as well as their conscious perception (interoception) provide key information for many cognitive processes. Recent empirical findings propose that neural processes in the insular cortex, which are related to bodily signals, might constitute a neurophysiological mechanism for the encoding of duration. Nevertheless, the exact nature of such a proposed relationship remains unclear. We aimed to address this question by searching for the effects of cardiac rhythm on time perception by the use of a duration reproduction paradigm. Time intervals used were of 0.5, 2, 3, 7, 10, 14, 25, and 40 s length. In a framework of synchronization hypothesis, measures of phase locking between the cardiac cycle and start/stop signals of the reproduction task were calculated to quantify this relationship. The main result is that marginally significant synchronization indices (SIs) between the heart cycle and the time reproduction responses for the time intervals of 2, 3, 10, 14, and 25 s length were obtained, while results were not significant for durations of 0.5, 7, and 40 s length. On the single participant level, several subjects exhibited some synchrony between the heart cycle and the time reproduction responses, most pronounced for the time interval of 25 s (8 out of 23 participants for 20% quantile). Better time reproduction accuracy was not related with larger degree of phase locking, but with greater vagal control of the heart. A higher interoceptive sensitivity (IS) was associated with a higher synchronization index (SI) for the 2 s time interval only. We conclude that information obtained from the cardiac cycle is relevant for the encoding and reproduction of time in the time span of 2-25 s. Sympathovagal tone as well as interoceptive processes mediate the accuracy of time estimation.

Effects of long-term dharma-chan meditation on cardiorespiratory synchronization and heart rate variability behavior

Remarkable changes in cardiorespiratory interactions are frequently experienced by Chan meditation practitioners following years of practice. This study compares the results of our study on cardiorespiratory interactions for novice (control group) and experienced (experimental group) Chan meditation practitioners. The effectual co-action between the cardiac and respiratory systems was evaluated by the degree of cardiorespiratory phase synchronization (CRPS). In addition, an adaptive-frequency-range (AFR) scheme to reliably quantify heart rate variability (HRV) was developed for assessing the regulation of sympathetic-parasympathetic activity and the efficiency of pulmonary gas exchange. The enhanced HRV method, named HRVAFR, can resolve the issue of overestimating HRV under the condition of slow respiration rates, which is frequently encountered in studies on Chan meditation practitioners. In the comparison of the three data sets collected from the two groups, our findings resulted in innovative hypotheses to interpret the extraordinary process of the rejuvenation of cardiorespiratory functions through long-term Dharma-Chan meditation practice. Particularly, advanced practitioners exhibit a continuously high degree of cardiorespiratory phase synchronization, even during rapid breathing. Based on our post-experimental interview with advanced practitioners, the activation of inner Chakra energy, during the course of Chan-detachment practice, frequently induces perceptible physiological-mental reformation, including an efficient mechanism for regulating cardiorespiratory interactions.

Impact of colored light on cardiorespiratory coordination

Background. Light exposure to the eye can influence different physiological functions, for example, the suprachiasmatic nucleus (SCN). By affecting the autonomic nervous system, the SCN may influence the heart rate variability (HRV). Standardized colored light exposure alters HRV but the results are inconsistent. In this study we investigated the effects of nonstandardized red light (approx. 640 nm) and blue (approx. 480 nm) light (approx. 50 lx) on cardiorespiratory coordination and HRV. Methods. 17 healthy subjects (7 males, age: 26.5 ± 6.2 years) were exposed to the following sequence (10 minutes each): daylight-red light-daylight-blue light-daylight. Red and blue lights were created by daylight passing through colored glass panes. Spectral measures of HRV (LF: low frequency, HF: high frequency oscillations, and sympathovagal balance LF/HF) and measures of cardiorespiratory coordination (HRR: heart respiration ratio, PCR: phase coordination ratio) were analyzed. Results. The LF component increased and the HF component decreased after red light. Consequently, LF/HF increased after red light. Furthermore, during red light HRR and PCR confined to 4 : 1, that is, 4 heartbeats during one respiratory cycle. Conclusion. Nonstandardized red and blue lights are able to alter the autonomic control reflected by HRV as well as cardiorespiratory coordination.

Disruption of phase synchronization between blood pressure and muscle sympathetic nerve activity in postural vasovagal syncope

Withdrawal of muscle sympathetic nerve activity (MSNA) may not be necessary for the precipitous fall of peripheral arterial resistance and arterial pressure (AP) during vasovagal syncope (VVS). We tested the hypothesis that the MSNA-AP baroreflex entrainment is disrupted before VVS regardless of MSNA withdrawal using the phase synchronization between blood pressure and MSNA during head-up tilt (HUT) to measure reflex coupling. We studied eight VVS subjects and eight healthy control subjects. Heart rate, AP, and MSNA were measured during supine baseline and at early, mid, late, and syncope stages of HUT. Phase synchronization indexes, measuring time-dependent differences between MSNA and AP phases, were computed. Directionality indexes, indicating the influence of AP on MSNA (neural arc) and MSNA on AP (peripheral arc), were computed. Heart rate was greater in VVS compared with control subjects during early, mid, and late stages of HUT and significantly declined at syncope (P = 0.04). AP significantly decreased during mid, late, and syncope stages of tilt in VVS subjects only (P = 0.001). MSNA was not significantly different between groups during HUT (P = 0.700). However, the phase synchronization index significantly decreased during mid and late stages in VVS subjects but not in control subjects (P < .001). In addition, the neural arc was significantly affected more than the peripheral arc before syncope. In conclusion, VVS is accompanied by a loss of the synchronous AP-MSNA relationship with or without a loss in MSNA at faint. This provides insight into the mechanisms behind the loss of vasoconstriction and drop in AP independent of MSNA at the time of vasovagal faint.

Phase synchronization of hemodynamic variables at rest and after deep breathing measured during the course of pregnancy

Background

The autonomic nervous system plays a central role in the functioning of systems critical for the homeostasis maintenance. However, its role in the cardiovascular adaptation to pregnancy-related demands is poorly understood. We explored the maternal cardiovascular systems throughout pregnancy to quantify pregnancy-related autonomic nervous system adaptations.

Methodology

Continuous monitoring of heart rate (R-R interval; derived from the 3-lead electrocardiography), blood pressure, and thoracic impedance was carried out in thirty-six women at six time-points throughout pregnancy. In order to quantify in addition to the longitudinal effects on baseline levels throughout gestation the immediate adaptive heart rate and blood pressure changes at each time point, a simple reflex test, deep breathing, was applied. Consequently, heart rate variability and blood pressure variability in the low (LF) and high (HF) frequency range, respiration and baroreceptor sensitivity were analyzed in resting conditions and after deep breathing. The adjustment of the rhythms of the R-R interval, blood pressure and respiration partitioned for the sympathetic and the parasympathetic branch of the autonomic nervous system were quantified by the phase synchronization index γ, which has been adopted from the analysis of weakly coupled chaotic oscillators.

Results

Heart rate and LF/HF ratio increased throughout pregnancy and these effects were accompanied by a continuous loss of baroreceptor sensitivity. The increases in heart rate and LF/HF ratio levels were associated with an increasing decline in the ability to flexibly respond to additional demands (i.e., diminished adaptive responses to deep breathing). The phase synchronization index γ showed that the observed effects could be explained by a decreased coupling of respiration and the cardiovascular system (HF components of heart rate and blood pressure).

Conclusions/Significance

The findings suggest that during the course of pregnancy the individual systems become increasingly independent to meet the increasing demands placed on the maternal cardiovascular and respiratory system.

Improving emotion recognition systems by embedding cardiorespiratory coupling

This work aims at showing improved performances of an emotion recognition system embedding information gathered from cardiorespiratory (CR) coupling. Here, we propose a novel methodology able to robustly identify up to 25 regions of a two-dimensional space model, namely the well-known circumplex model of affect (CMA). The novelty of embedding CR coupling information in an autonomic nervous system-based feature space better reveals the sympathetic activations upon emotional stimuli. A CR synchrogram analysis was used to quantify such a coupling in terms of number of heartbeats per respiratory period. Physiological data were gathered from 35 healthy subjects emotionally elicited by means of affective pictures of the international affective picture system database. In this study, we finely detected five levels of arousal and five levels of valence as well as the neutral state, whose combinations were used for identifying 25 different affective states in the CMA plane. We show that the inclusion of the bivariate CR measures in a previously developed system based only on monovariate measures of heart rate variability, respiration dynamics and electrodermal response dramatically increases the recognition accuracy of a quadratic discriminant classifier, obtaining more than 90% of correct classification per class. Finally, we propose a comprehensive description of the CR coupling during sympathetic elicitation adapting an existing theoretical nonlinear model with external driving. The theoretical idea behind this model is that the CR system is comprised of weakly coupled self-sustained oscillators that, when exposed to an external perturbation (i.e. sympathetic activity), becomes synchronized and less sensible to input variations. Given the demonstrated role of the CR coupling, this model can constitute a general tool which is easily embedded in other model-based emotion recognition systems.

Limit-cycle-based control of the myogenic wingbeat rhythm in the fruit fly Drosophila

In many animals, rhythmic motor activity is governed by neural limit cycle oscillations under the control of sensory feedback. In the fruit fly Drosophila melanogaster, the wingbeat rhythm is generated myogenically by stretch-activated muscles and hence independently from direct neural input. In this study, we explored if generation and cycle-by-cycle control of Drosophila's wingbeat are functionally separated, or if the steering muscles instead couple into the myogenic rhythm as a weak forcing of a limit cycle oscillator. We behaviourally tested tethered flying flies for characteristic properties of limit cycle oscillators. To this end, we mechanically stimulated the fly's 'gyroscopic' organs, the halteres, and determined the phase relationship between the wing motion and stimulus. The flies synchronized with the stimulus for specific ranges of stimulus amplitude and frequency, revealing the characteristic Arnol'd tongues of a forced limit cycle oscillator. Rapid periodic modulation of the wingbeat frequency prior to locking demonstrates the involvement of the fast steering muscles in the observed control of the wingbeat frequency. We propose that the mechanical forcing of a myogenic limit cycle oscillator permits flies to avoid the comparatively slow control based on a neural central pattern generator.

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

Interactions between oscillators can be investigated with standard tools of time series analysis. However, these methods are insensitive to the directionality of the coupling, i.e., the asymmetry of the interactions. An elegant alternative was proposed by Rosenblum and collaborators [M. G. Rosenblum, L. Cimponeriu, A. Bezerianos, A. Patzak, and R. Mrowka, Phys. Rev. E 65, 041909 (2002); M. G. Rosenblum and A. S. Pikovsky, Phys. Rev. E 64, 045202 (2001)] which consists in fitting the empirical phases to a generic model of two weakly coupled phase oscillators. This allows one to obtain the interaction functions defining the coupling and its directionality. A limitation of this approach is that a solution always exists in the least-squares sense, even in the absence of coupling. To preclude spurious results, we propose a three-step protocol: (1) Determine if a statistical dependency exists in the data by evaluating the mutual information of the phases; (2) if so, compute the interaction functions of the oscillators; and (3) validate the empirical oscillator model by comparing the joint probability of the phases obtained from simulating the model with that of the empirical phases. We apply this protocol to a model of two coupled Stuart-Landau oscillators and show that it reliably detects genuine coupling. We also apply this protocol to investigate cardiorespiratory coupling in anesthetized rats. We observe reciprocal coupling between respiration and heartbeat and that the influence of respiration on the heartbeat is generally much stronger than vice versa. In addition, we find that the vagus nerve mediates coupling in both directions.

Joint symbolic dynamics as a model-free approach to study interdependence in cardio-respiratory time series

Heart rate and respiration display fluctuations that are interlinked by central regulatory mechanisms of the autonomic nervous system (ANS). Joint assessment of respiratory time series along with heart rate variability (HRV) may therefore provide information on ANS dysfunction. The aim of this study was to investigate cardio-respiratory interaction in patients with Parkinson's disease (PD), a neurodegenerative disorder that is associated with progressive ANS dysfunction. Short-term ECG and respiration were recorded in 25 PD patients and 28 healthy controls during rest. To assess ANS dysfunction we analyzed joint symbolic dynamics of heart rate and respiration, cardio-respiratory synchrograms along with heart rate variability. Neither HRV nor cardio-respiratory synchrograms were significantly altered in PD patients. Symbolic analysis, however, identified a significant reduction in cardio-respiratory interactions in PD patients compared to healthy controls (16 ± 3.6 % vs. 20 ± 6.1 %; p= 0.02). In conclusion, joint symbolic analysis of cardio-respiratory dynamics provides a powerful tool to detect early signs of autonomic nervous system dysfunction in Parkinson's disease patients at an early stage of the disease.

Synchronization of two bubble trains in a viscous fluid: experiment and numerical simulation

We investigate the interactions of two trains of bubbles, ejected by nozzles immersed in a viscous fluid, due only to the solution's circulation. The air fluxes (Q(1),Q(2)) are controlled independently, and we constructed parameter spaces of the periodicity of the attractors. We have observed complex behavior and many modes of phase synchronization that depend on these airflows as well as on the height (H) of the solution above the tops of the nozzles. Such synchronizations are shown in details in the parameter space (Q(1),Q(2)) and also in the (Q(1),H) space. We also observed that the coupling strength between the two trains of bubbles increases when the solution height increases. The experimental results were reasonably explained by numerical simulations of a model combining a simple bubble growth model for each bubble train and a coupling term between them, which was assumed symmetrical and proportional to the growth velocities.

A robust EC-PC spike detection method for extracellular neural recording

This paper models signals and noise for extracellular neural recording. Although recorded data approximately follow Gaussian distribution, there are slight deviations that are critical for signal detection: a statistical examination of neural data in Hilbert space shows that noise forms an exponential term while signals form a polynomial term. These two terms can be used to estimate a spiking probability map that indicates spike presence. Both synthesized data and animal data are used for the detection performance evaluation and comparison against other popular detectors. Experimental results suggest that the predicted spiking probability map is consistent with the benchmark and work robustly with different recording preparations.

The effect of sigh on cardiorespiratory synchronization in healthy sleeping infants

STUDY OBJECTIVES

Sighs are thought to have a role in regulating breathing control. They may preceed a central apnea (sigh-CA) or a pause (sigh-P), particularly in quiet sleep. Recent techniques characterizing cardiorespiratory synchronization (CRS) provide sensitive measures of cardiorespiratory coupling, which is an important factor in breathing control. We speculated that the strength of CRS and direction of cardiorespiratory coupling (DC), would differ between sigh-P and sigh-CA; before and after a sigh; and with maturation.

DESIGN

Prospective study. CRS and DC were calculated from the respiratory signal and heart rate before and after sighs recorded during overnight polysomnography.

SETTING

Sleep laboratory.

PARTICIPANTS

The data were selected from 15 subjects of a prospective cohort of 34 healthy infants at ages 2 weeks, 3 months and 6 months.

INTERVENTIONS

N/A.

MEASUREMENTS AND RESULTS

Both CRS and respiratory modulation on heart rate (RMH) (negative DC index) were decreased around sigh-CA compared with sigh-P at all ages. Short-term CRS decreased after both sigh-P and sigh-CA in infants aged 2 weeks and 3 months. Long term CRS did not change before and after sigh-P or sigh-CA. CRS and RMH were increased at 3 months and 6 months compared to 2 weeks.

CONCLUSIONS

A sigh was not found to be associated with apparent resetting of breathing control in healthy infants less than 6 months of age. Cardiorespiratory coupling appears to be a leading marker of changes in breathing control, preceding central apnea associated with a sigh.

CITATION

Nguyen CD; Dakin C; Yuill M; Crozier S; Wilson S. The effect of sigh on cardiorespiratory synchronization in healthy sleeping infants. SLEEP 2012;35(12):1643-1650.

Oscillations of heart rate and respiration synchronize during affective visual stimulation

The objective of this study is to investigate the synchronization between breathing patterns and heart rate during emotional visual elicitation, that is, using sets of images gathered from the international affective picture system having five levels of arousal and five levels of valence, including a neutral reference level. Thirty-five healthy volunteers were emotionally elicited in agreement with a bidimensional spatial localization of affective states, i.e., arousal/valence plane, while two peripheral physiological signals, ECG and Respiration activity, were acquired simultaneously. The synchronization was then quantified by applying the concept of phase synchronization of chaotic oscillators, i.e., the cardio-respiratory synchrogram. This technique allowed us to estimate the synchronization ratio m:n as the attendance of n heartbeats in each m respiratory cycle, even for noisy and nonstationary data. We found a stronger evidence of cardiorespiratory synchronization during arousal than during neutral states.

Testing for time-localized coherence in bivariate data

We present a method for the testing of significance when evaluating the coherence of two oscillatory time series that may have variable amplitude and frequency. It is based on evaluating the self-correlations of the time series. We demonstrate our approach by the application of wavelet-based coherence measures to artificial and physiological examples. Because coherence measures of this kind are strongly biased by the spectral characteristics of the time series, we evaluate significance by estimation of the characteristics of the distribution of values that may occur due to chance associations in the data. The expectation value and standard deviation of this distribution are shown to depend on the autocorrelations and higher order statistics of the data. Where the coherence value falls outside this distribution, we may conclude that there is a causal relationship between the signals regardless of their spectral similarities or differences.

Quantification of cardio-respiratory interactions in healthy children during night-time sleep using joint symbolic dynamics

The aim of this paper was to study interactions between R-R intervals and respiratory phases in healthy children during night-time sleep using a novel technique based on joint symbolic dynamics. We investigated overnight polysomnography data of 40 healthy children. The R-R time series were extracted from electrocardiograms (ECG) and respiratory phases were obtained from abdominal sensors using the Hilbert transform. Both the series were transformed into ternary symbol vectors based on the changes between two successive R-R intervals or respiratory phases, respectively. Subsequently, words of length '2' were formed and the correspondence between words of the two series for each sleep stage was determined to quantify cardio-respiratory interaction. We found a significantly higher percentage of similarity in the joint symbolic dynamics of R-R intervals and respiratory phases during slow-wave (SW) sleep compared to any other sleep stage. There was, however, no significant effect of age, gender or BMI on cardio-respiratory interaction. In conclusion, joint symbolic dynamics provides a novel efficient technique for the analysis of cardio-respiratory interaction.

Preventing drowsiness by heartbeat-synchronized vibration

The purpose of this study is to develop a stimulation, which has an active physiological influence to prevent severe driver drowsiness while driving. This paper presents a heartbeat-synchronized vibration, which is the rhythmic pulsation of a motor with each beat of the heart, as an effective means to ease drivers' slight deprivation of oxygen with the appearance of cardiorespiratory coordination. The effects of this stimulation were confirmed by the results of an experiment done in cooperation with 15 subjects. The results showed that cardiorespiratory coordination appeared under the stimulation and it played an active influence on the oxygen supply to the body. We conclude that the vibratory stimulation has an active influence to prevent drowsiness. It might be effective to prevent severe drowsiness while driving.

Automated quantification of the synchrogram by recurrence plot analysis

Recently, the concept of phase synchronization of two weakly coupled oscillators has raised a great research interest and has been applied to characterize synchronization phenomenon in physiological data. Phase synchronization of cardiorespiratory coupling is often studied by a synchrogram analysis, a graphical tool investigating the relationship between instantaneous phases of two signals. Although several techniques have been proposed to automatically quantify the synchrogram, most of them require a preselection of a phase-locking ratio by trial and error. One technique does not require this information; however, it is based on the power spectrum of phase's distribution in the synchrogram, which is vulnerable to noise. This study aims to introduce a new technique to automatically quantify the synchrogram by studying its dynamic structure. Our technique exploits recurrence plot analysis, which is a well-established tool for characterizing recurring patterns and nonstationarities in experiments. We applied our technique to detect synchronization in simulated and measured infants' cardiorespiratory data. Our results suggest that the proposed technique is able to systematically detect synchronization in noisy and chaotic data without preselecting the phase-locking ratio. By embedding phase information of the synchrogram into phase space, the phase-locking ratio is automatically unveiled as the number of attractors.

Computational models for the study of heart-lung interactions in mammals

The operation and regulation of the lungs and the heart are closely related. This is evident when examining the anatomy within the thorax cavity, in the brainstem and in the aortic and carotid arteries where chemoreceptors and baroreceptors, which provide feedback affecting the regulation of both organs, are concentrated. This is also evident in phenomena such as respiratory sinus arrhythmia where the heart rate increases during inspiration and decreases during expiration, in other types of synchronization between the heart and the lungs known as cardioventilatory coupling and in the association between heart failure and sleep apnea where breathing is interrupted periodically by periods of no-breathing. The full implication and physiological significance of the cardiorespiratory coupling under normal, pathological, or extreme physiological conditions are still unknown and are subject to ongoing investigation both experimentally and theoretically using mathematical models. This article reviews mathematical models that take heart-lung interactions into account. The main ideas behind low dimensional, phenomenological models for the study of the heart-lung synchronization and sleep apnea are described first. Higher dimensions, physiology-based models are described next. These models can vary widely in detail and scope and are characterized by the way the heart-lung interaction is taken into account: via gas exchange, via the central nervous system, via the mechanical interactions, and via time delays. The article emphasizes the need for the integration of the different sources of heart-lung coupling as well as the different mathematical approaches.

Time delay correction of the synchrogram for optimized detection of cardiorespiratory coordination

The cardiorespiratory synchrogram, a graphical tool based on the stroboscopic technique, is an established method for evaluating phase-locking between cardiac and respiratory oscillators. In the original method, the phase of the respiratory oscillator is observed at the instants of time when the phase of the cardiac oscillator attains a certain value. In this article, we introduced an additional adaptive delay in the cardiac oscillator based on the maximisation of the cross-correlation or symbolic coupling traces between the phases of respiration and the delayed R-R intervals. We then investigated phase coordination in thirteen normal subjects (five males, eight females; age: 19-24 years) for different body postures. Cardiorespiratory coordination was observed to be significantly reduced in the upright position (supine vs. upright: 11.9 ± 5.1 vs. 6.9 ± 3.6, P < 0.05). Compared to the original algorithm we observed an increase in the detection of average cardiorespiratory coordination (supine original vs. delay: 11.9 vs. 18.9%), together with a decrease in standard deviation of the percentage of coordination in all the subjects, after introducing the heart rate delay (supine original vs. delay: 5.1 vs. 4.4%). In conclusion, the performance of the synchrogram technique was improved by including an adaptive delay in the cardiac oscillator.

Phase synchronization of hemodynamic variables and respiration during mental challenge

We studied the synchronization of heart rate, blood pressure and respiration in the sympathetic and parasympathetic branches of the autonomic nervous system during a cancellation test of attention and during mental arithmetic tasks. The synchronization was quantified by the index γ, which has been adopted from the analysis of weakly coupled chaotic oscillators. We analyzed in twenty healthy women the continuous signals partitioned in low (LF, 0.04-0.15 Hz) and high (HF, 0.15-0.40 Hz) frequencies to investigate whether or not respiration is a main determinant of cardiovascular synchronization. We used surrogate data analysis to distinguish between causal relationships from those that occur by chance. The LF-components of R-R interval and blood pressure showed no synchronization with respiration, whereas synchronization between blood pressure and R-R interval exceeded that occurring by chance (p < .001). Although heart rate, blood pressure and respiratory frequency increased from rest to mental challenge, no effect of mental challenge on the synchronization of the LF-components was seen. The HF-components showed significant synchronization for all variables (p < .001). During mental challenge, synchronization between respiration and R-R interval, respiration and systolic blood pressure (SBP), as well as R-R interval and SBP decreased (p < .01), whereas under resting conditions, respiration was one of the dominant mechanisms determining heart rate variability and systolic blood pressure fluctuations. We conclude that the observed decrease of synchronization during mental challenge is not only driven by the increase in respiratory frequency but that 'top down' intervention by the control system at higher levels may play an additional role.

Global analysis of phase locking in gene expression during cell cycle: the potential in network modeling

Background

In nonlinear dynamic systems, synchrony through oscillation and frequency modulation is a general control strategy to coordinate multiple modules in response to external signals. Conversely, the synchrony information can be utilized to infer interaction. Increasing evidence suggests that frequency modulation is also common in transcription regulation.

Results

In this study, we investigate the potential of phase locking analysis, a technique to study the synchrony patterns, in the transcription network modeling of time course gene expression data. Using the yeast cell cycle data, we show that significant phase locking exists between transcription factors and their targets, between gene pairs with prior evidence of physical or genetic interactions, and among cell cycle genes. When compared with simple correlation we found that the phase locking metric can identify gene pairs that interact with each other more efficiently. In addition, it can automatically address issues of arbitrary time lags or different dynamic time scales in different genes, without the need for alignment. Interestingly, many of the phase locked gene pairs exhibit higher order than 1:1 locking, and significant phase lags with respect to each other. Based on these findings we propose a new phase locking metric for network reconstruction using time course gene expression data. We show that it is efficient at identifying network modules of focused biological themes that are important to cell cycle regulation.

Conclusions

Our result demonstrates the potential of phase locking analysis in transcription network modeling. It also suggests the importance of understanding the dynamics underlying the gene expression patterns.

When does noise destroy or enhance synchronous behavior in two mutually coupled light-controlled oscillators?

We study the influence of white gaussian noise in a system of two mutually coupled light-controlled oscillators (LCOs). We show that under certain noise intensity conditions, noise can destroy or enhance synchronization. We build some Arnold tonguelike structures in order to explain the effects due to noise. It is remarkable that noise-enhanced synchronization is possible only when the variances of the noise acting on each of the LCOs are different.

Potassium diffusive coupling in neural networks

Conventional neural networks are characterized by many neurons coupled together through synapses. The activity, synchronization, plasticity and excitability of the network are then controlled by its synaptic connectivity. Neurons are surrounded by an extracellular space whereby fluctuations in specific ionic concentration can modulate neuronal excitability. Extracellular concentrations of potassium ([K(+)](o)) can generate neuronal hyperexcitability. Yet, after many years of research, it is still unknown whether an elevation of potassium is the cause or the result of the generation, propagation and synchronization of epileptiform activity. An elevation of potassium in neural tissue can be characterized by dispersion (global elevation of potassium) and lateral diffusion (local spatial gradients). Both experimental and computational studies have shown that lateral diffusion is involved in the generation and the propagation of neural activity in diffusively coupled networks. Therefore, diffusion-based coupling by potassium can play an important role in neural networks and it is reviewed in four sections. Section 2 shows that potassium diffusion is responsible for the synchronization of activity across a mechanical cut in the tissue. A computer model of diffusive coupling shows that potassium diffusion can mediate communication between cells and generate abnormal and/or periodic activity in small (section sign 3) and in large networks of cells (section sign 4). Finally, in section sign 5, a study of the role of extracellular potassium in the propagation of axonal signals shows that elevated potassium concentration can block the propagation of neural activity in axonal pathways. Taken together, these results indicate that potassium accumulation and diffusion can interfere with normal activity and generate abnormal activity in neural networks.

Time-frequency characterization of electrocorticographic recordings of epileptic patients using frequency-entropy similarity: a comparison to other bi-variate measures

Expert evaluation of electrocorticographic (ECoG) recordings forms the linchpin of seizure onset zone localization in the evaluation of epileptic patients for surgical resection. Numerous methods have been developed to analyze these complex recordings, including uni-variate (characterizing single channels), bi-variate (comparing channel pairs) and multivariate measures. Developing reliable algorithms may be helpful in clinical tasks such as localization of epileptogenic zones and seizure anticipation, as well as enabling better understanding of neuronal function and dynamics. Recently we have developed the frequency-entropy (F-E) similarity measure, and have tested its capability in mapping the epileptogenic zones. The F-E similarity measure compares time-frequency characterizations of two recordings. In this study, we examine the method's principles and utility and compare it to previously described bi-variate correspondence measures such as correlation, coherence, mean phase coherence and spectral comparison methods. Specially designed synthetic signals were used for illuminating theoretical differences between the measures. Intracranial recordings of four epileptic patients were then used for the measures' comparative analysis by creating a mean inter-electrode matrix for each of the correspondence measures and comparing the structure of these matrices during the inter-ictal and ictal periods. We found that the F-E similarity measure is able to discover spectral and temporal features in data which are hidden for the other measures and are important for foci localization.

Changes of heart and respiratory rate dynamics during weaning from mechanical ventilation: a study of physiologic complexity in surgical critically ill patients

PURPOSE

The aim of the study was to investigate heart rate (HR) and respiratory rate (RR) complexity in patients with weaning failure or success, using both linear and nonlinear techniques.

MATERIALS AND METHODS

Forty-two surgical patients were enrolled in the study. There were 24 who passed and 18 who failed a weaning trial. Signals were analyzed for 10 minutes during 2 phases: (1) pressure support (PS) ventilation (15-20 cm H(2)O) and (2) weaning trials with PS (5 cm H(2)O). Low- and high-frequency (LF, HF) components of HR signals, HR multiscale entropy (MSE), RR sample entropy, cross-sample entropy between cardiorespiratory signals, Poincaré plots, and α1 exponent were computed in all patients and during the 2 phases of PS.

RESULTS

Weaning failure patients exhibited significantly decreased RR sample entropy, LF, HF, and α1 exponent, compared with weaning success subjects (P < .001). Their changes were opposite between the 2 phases, except for MSE that increased between and within groups (P < .001). A new model including rapid shallow breathing index (RSBI), α1 exponent, RR, and cross-sample entropies predicted better weaning outcome compared with RSBI, airway occlusion pressure at 0.1 second (P(0.1)), and RSBI × P(0.1) (conventional model, R(2) = 0.887 vs 0.463; P < .001). Areas under the curve were 0.92 vs 0.86, respectively (P < .005).

CONCLUSIONS

We suggest that nonlinear analysis of cardiorespiratory dynamics has increased prognostic impact upon weaning outcome in surgical patients.

Cardiorespiratory phase-coupling is reduced in patients with obstructive sleep apnea

Cardiac and respiratory rhythms reveal transient phases of phase-locking which were proposed to be an important aspect of cardiorespiratory interaction. The aim of this study was to quantify cardio-respiratory phase-locking in obstructive sleep apnea (OSA). We investigated overnight polysomnography data of 248 subjects with suspected OSA. Cardiorespiratory phase-coupling was computed from the R-R intervals of body surface ECG and respiratory rate, calculated from abdominal and thoracic sensors, using Hilbert transform. A significant reduction in phase-coupling was observed in patients with severe OSA compared to patients with no or mild OSA. Cardiorespiratory phase-coupling was also associated with sleep stages and was significantly reduced during rapid-eye-movement (REM) sleep compared to slow-wave (SW) sleep. There was, however, no effect of age and BMI on phase coupling. Our study suggests that the assessment of cardiorespiratory phase coupling may be used as an ECG based screening tool for determining the severity of OSA.

Nonlinear dynamics of cardiovascular ageing

The application of methods drawn from nonlinear and stochastic dynamics to the analysis of cardiovascular time series is reviewed, with particular reference to the identification of changes associated with ageing. The natural variability of the heart rate (HRV) is considered in detail, including the respiratory sinus arrhythmia (RSA) corresponding to modulation of the instantaneous cardiac frequency by the rhythm of respiration. HRV has been intensively studied using traditional spectral analyses, e.g. by Fourier transform or autoregressive methods, and, because of its complexity, has been used as a paradigm for testing several proposed new methods of complexity analysis. These methods are reviewed. The application of time-frequency methods to HRV is considered, including in particular the wavelet transform which can resolve the time-dependent spectral content of HRV. Attention is focused on the cardio-respiratory interaction by introduction of the respiratory frequency variability signal (RFV), which can be acquired simultaneously with HRV by use of a respiratory effort transducer. Current methods for the analysis of interacting oscillators are reviewed and applied to cardio-respiratory data, including those for the quantification of synchronization and direction of coupling. These reveal the effect of ageing on the cardio-respiratory interaction through changes in the mutual modulation of the instantaneous cardiac and respiratory frequencies. Analyses of blood flow signals recorded with laser Doppler flowmetry are reviewed and related to the current understanding of how endothelial-dependent oscillations evolve with age: the inner lining of the vessels (the endothelium) is shown to be of crucial importance to the emerging picture. It is concluded that analyses of the complex and nonlinear dynamics of the cardiovascular system can illuminate the mechanisms of blood circulation, and that the heart, the lungs and the vascular system function as a single entity in dynamical terms. Clear evidence is found for dynamical ageing.

Quasiperiodic forcing of coupled chaotic systems

We study the manner in which the effect of quasiperiodic modulation is transmitted in a coupled nonlinear dynamical system. A system of Rössler oscillators is considered, one of which is subject to driving, and the dynamics of other oscillators which are, in effect, indirectly forced is observed. Strange nonchaotic dynamics is known to arise only in quasiperiodically driven systems, and thus the transmitted effect is apparent when such motion is seen in subsystems that are not directly modulated. We also find instances of imperfect phase synchronization with forcing, where the system transits from one phase synchronized state to another, with arbitrary phase slips. The stability of phase synchrony for arbitrary initial conditions with identical forcing is observed as a general property of strange nonchaotic motion.

Effects of mental tasks on the cardiorespiratory synchronization

The cardiovascular and respiratory systems are functionally related to each other, but it is unclear if the cerebral cortex can affect their interaction. The effect of a mental task on the synchronization between cardiovascular and respiratory systems was investigated in the article. Electroencephalogram (EEG), electrocardiogram (ECG) and respiratory signal (RES) were collected from 29 healthy male subjects during the mental arithmetic (MA) task and the synchrogram was used to estimate the strength of cardiorespiratory synchronization. Our results showed that MA task significantly increased the breath rate, the heart rate and the EEG power spectral energy in theta band at FC3, FC4 and C4 electrodes (p<0.01), decreased the duration of cardiorespiratory synchronization epochs (p<0.05). Moreover the duration of cardiorespiratory synchronization epochs during MA task was negatively correlated with the EEG power spectral energy in theta band at FC3, FC4 and C4 electrodes and the sympathetic activity (p<0.05). The results demonstrated that ANS and cerebral cortex are implicated in the changes of cardiorespiratory synchronization during MA task.

Increased phase synchronization and decreased cerebral autoregulation during fainting in the young

Vasovagal syncope may be due to a transient cerebral hypoperfusion that accompanies frequency entrainment between arterial pressure (AP) and cerebral blood flow velocity (CBFV). We hypothesized that cerebral autoregulation fails during fainting; a phase synchronization index (PhSI) between AP and CBFV was used as a nonlinear, nonstationary, time-dependent measurement of cerebral autoregulation. Twelve healthy control subjects and twelve subjects with a history of vasovagal syncope underwent 10-min tilt table testing with the continuous measurement of AP, CBFV, heart rate (HR), end-tidal CO2 (ETCO2), and respiratory frequency. Time intervals were defined to compare physiologically equivalent periods in fainters and control subjects. A PhSI value of 0 corresponds to an absence of phase synchronization and efficient cerebral autoregulation, whereas a PhSI value of 1 corresponds to complete phase synchronization and inefficient cerebral autoregulation. During supine baseline conditions, both control and syncope groups demonstrated similar oscillatory changes in phase, with mean PhSI values of 0.58+/-0.04 and 0.54+/-0.02, respectively. Throughout tilt, control subjects demonstrated similar PhSI values compared with supine conditions. Approximately 2 min before fainting, syncopal subjects demonstrated a sharp decrease in PhSI (0.23+/-0.06), representing efficient cerebral autoregulation. Immediately after this period, PhSI increased sharply, suggesting inefficient cerebral autoregulation, and remained elevated at the time of faint (0.92+/-0.02) and during the early recovery period (0.79+/-0.04) immediately after the return to the supine position. Our data demonstrate rapid, biphasic changes in cerebral autoregulation, which are temporally related to vasovagal syncope. Thus, a sudden period of highly efficient cerebral autoregulation precedes the virtual loss of autoregulation, which continued during and after the faint.

Experimental results on synchronization times and stable states in locally coupled light-controlled oscillators

Recently, a new kind of optically coupled oscillators that behave as relaxation oscillators has been studied experimentally in the case of local coupling. Even though numerical results exist, there are no references about experimental studies concerning the synchronization times with local coupling. In this paper, we study both experimentally and numerically a system of coupled oscillators in different configurations, including local coupling. Synchronization times are quantified as a function of the initial conditions and the coupling strength. For each configuration, the number of stable states is determined varying the different parameters that characterize each oscillator. Experimental results are compared with numerical simulations.

Phase synchronization analysis by assessment of the phase difference gradient

Phase synchronization is an important phenomenon of nonlinear dynamics and has recently received much scientific attention. In this work a method for identifying phase synchronization epochs is described which focuses on estimating the gradient of segments of the generalized phase differences between phase slips in an experimental time series. In phase synchronized systems, there should be a zero gradient of the generalized phase differences even if the systems are contaminated by noise. A method which tests if the gradient of the generalized phase difference is statistically different from zero is reported. The method has been validated by numerical studies on model systems and by comparing the results to those published previously. The method is applied to cardiorespiratory time series from a human volunteer measured in clinical settings and compared to synchrogram analysis for the same data. Potential problems with synchrogram analysis of experimental data are discussed.

Automated synchrogram analysis applied to heartbeat and reconstructed respiration

Phase synchronization between two weakly coupled oscillators has been studied in chaotic systems for a long time. However, it is difficult to unambiguously detect such synchronization in experimental data from complex physiological systems. In this paper we review our study of phase synchronization between heartbeat and respiration in 150 healthy subjects during sleep using an automated procedure for screening the synchrograms. We found that this synchronization is significantly enhanced during non-rapid-eye-movement (non-REM) sleep (deep sleep and light sleep) and is reduced during REM sleep. In addition, we show that the respiration signal can be reconstructed from the heartbeat recordings in many subjects. Our reconstruction procedure, which works particularly well during non-REM sleep, allows the detection of cardiorespiratory synchronization even if only heartbeat intervals were recorded.

Diverse routes to oscillation death in a coupled oscillator system

We study oscillation death (OD) in a well-known coupled-oscillator system that has been used to model cardiovascular phenomena. We derive exact analytic conditions that allow the prediction of OD through the two known bifurcation routes, in the same model, and for different numbers of coupled oscillators. Our exact analytic results enable us to generalize OD as a multiparameter-sensitive phenomenon. It can be induced, not only by changes in couplings, but also by changes in the oscillator frequencies or amplitudes. We observe synchronization transitions as a function of coupling and confirm the robustness of the phenomena in the presence of noise. Numerical and analogue simulations are in good agreement with the theory.

Chaotic dynamics of cardioventilatory coupling in humans: effects of ventilatory modes

Cardioventilatory coupling (CVC), a transient temporal alignment between the heartbeat and inspiratory activity, has been studied in animals and humans mainly during anesthesia. The origin of the coupling remains uncertain, whether or not ventilation is a main determinant in the CVC process and whether the coupling exhibits chaotic behavior. In this frame, we studied sedative-free, mechanically ventilated patients experiencing rapid sequential changes in breathing control during ventilator weaning during a switch from a machine-controlled assistance mode [assist-controlled ventilation (ACV)] to a patient-driven mode [inspiratory pressure support (IPS) and unsupported spontaneous breathing (USB)]. Time series were computed as R to start inspiration (RI) and R to the start of expiration (RE). Chaos was characterized with the noise titration method (noise limit), largest Lyapunov exponent (LLE) and correlation dimension (CD). All the RI and RE time series exhibit chaotic behavior. Specific coupling patterns were displayed in each ventilatory mode, and these patterns exhibited different linear and chaotic dynamics. When switching from ACV to IPS, partial inspiratory loading decreases the noise limit value, the LLE, and the correlation dimension of the RI and RE time series in parallel, whereas decreasing intrathoracic pressure from IPS to USB has the opposite effect. Coupling with expiration exhibits higher complexity than coupling with inspiration during mechanical ventilation either during ACV or IPS, probably due to active expiration. Only 33% of the cardiac time series (RR interval) exhibit complexity either during ACV, IPS, or USB making the contribution of the cardiac signal to the chaotic feature of the coupling minimal. We conclude that 1) CVC in unsedated humans exhibits a complex dynamic that can be chaotic, and 2) ventilatory mode has major effects on the linear and chaotic features of the coupling. Taken together these findings reinforce the role of ventilation in the CVC process.

Time-varying surrogate data to assess nonlinearity in nonstationary time series: application to heart rate variability

We propose a method to extend to time-varying (TV) systems the procedure for generating typical surrogate time series, in order to test the presence of nonlinear dynamics in potentially nonstationary signals. The method is based on fitting a TV autoregressive (AR) model to the original series and then regressing the model coefficients with random replacements of the model residuals to generate TV AR surrogate series. The proposed surrogate series were used in combination with a TV sample entropy (SE) discriminating statistic to assess nonlinearity in both simulated and experimental time series, in comparison with traditional time-invariant (TIV) surrogates combined with the TIV SE discriminating statistic. Analysis of simulated time series showed that using TIV surrogates, linear nonstationary time series may be erroneously regarded as nonlinear and weak TV nonlinearities may remain unrevealed, while the use of TV AR surrogates markedly increases the probability of a correct interpretation. Application to short (500 beats) heart rate variability (HRV) time series recorded at rest (R), after head-up tilt (T), and during paced breathing (PB) showed: 1) modifications of the SE statistic that were well interpretable with the known cardiovascular physiology; 2) significant contribution of nonlinear dynamics to HRV in all conditions, with significant increase during PB at 0.2 Hz respiration rate; and 3) a disagreement between TV AR surrogates and TIV surrogates in about a quarter of the series, suggesting that nonstationarity may affect HRV recordings and bias the outcome of the traditional surrogate-based nonlinearity test.

Day-to-night time differences in the relationship between cardiorespiratory coordination and heart rate variability

Heart rate variability (HRV) and cardiorespiratory coordination, i.e. the temporal interplay between oscillations of heartbeat and respiration, reflect information related to the cardiovascular and autonomic nervous system. The purpose of this study was to investigate the relationship between spectral measures of HRV and measures of cardiorespiratory coordination. In 127 subjects from a normal population a 24 h Holter ECG was recorded. Average heart rate (HR) and the following HRV parameters were calculated: very low (VLF), low (LF) and high frequency (HF) oscillations and LF/HF. Cardiorespiratory coordination was quantified using average respiratory rate (RespR), the ratio of heart rate and respiratory rate (HRR), the phase coordination ratio (PCR) and the extent of cardiorespiratory coordination (PP). Pearson's correlation coefficient r was used to quantify the relationship between each pair of the variables across all subjects. HR and HRR correlated strongest during daytime (r = 0.89). LF/HF and PP showed a negative correlation to a reasonable degree (r = -0.69). During nighttime sleep these correlations decreased whereas the correlation between HRR and RespR (r = -0.47) as well as between HRR and PCR (r = 0.73) increased substantially. In conclusion, HRR and PCR deliver considerably different information compared to HRV measures whereas PP is partially linked reciprocally to LF/HF.