Mutual information and phase dependencies: measures of reduced nonlinear cardiorespiratory interactions after myocardial infarction

NLDyn - An open source MATLAB toolbox for the univariate and multivariate nonlinear dynamical analysis of physiological data

BACKGROUND AND OBJECTIVE

We present NLDyn, an open-source MATLAB toolbox tailored for in-depth analysis of nonlinear dynamics in biomedical signals. Our objective is to offer a user-friendly yet comprehensive platform for researchers to explore the intricacies of time series data.

METHODS

NLDyn integrates approximately 80 distinct methods, encompassing both univariate and multivariate nonlinear dynamics, setting it apart from existing solutions. This toolbox combines state-of-the-art nonlinear dynamical techniques with advanced multivariate entropy methods, providing users with powerful analytical capabilities. NLDyn enables analyses with or without a sliding window, and users can easily access and customize default parameters.

RESULTS

NLDyn generates results that are both exportable and visually informative, facilitating seamless integration into research and presentations. Its ongoing development ensures it remains at the forefront of nonlinear dynamics analysis.

CONCLUSIONS

NLDyn is a valuable resource for researchers in the biomedical field, offering an intuitive interface and a wide array of nonlinear analysis tools. Its integration of advanced techniques empowers users to gain deeper insights from their data. As we continually refine and expand NLDyn's capabilities, we envision it becoming an indispensable tool for the exploration of complex dynamics in biomedical signals.

Bradycardia May Decrease Cardiorespiratory Coupling in Preterm Infants

Bradycardia, frequently observed in preterm infants, presents significant risks due to the immaturity of their autonomic nervous system (ANS) and respiratory systems. These infants may face cardiorespiratory events, leading to severe complications like hypoxemia and neurodevelopmental disorders. Although neonatal care has advanced, the influence of bradycardia on cardiorespiratory coupling (CRC) remains elusive. This exploratory study delves into CRC in preterm infants, emphasizing disparities between events with and without bradycardia. Using the Preterm Infant Cardio-Respiratory Signals (PICS) database, we analyzed interbeat (R-R) and inter-breath intervals (IBI) from 10 preterm infants. The time series were segmented into bradycardic (B) and non-bradycardic (NB) segments. Employing information theory measures, we quantified the irregularity of cardiac and respiratory time series. Notably, B segments had significantly lower entropy values for R-R and IBI than NB segments, while mutual information was higher in NB segments. This could imply a reduction in the complexity of respiratory and cardiac dynamics during bradycardic events, potentially indicating weaker CRC. Building on these insights, this research highlights the distinctive physiological characteristics of preterm infants and underscores the potential of emerging non-invasive diagnostic tools.

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.

Application of Multiscale Sample Entropy in Assessing Effects of Exercise Training on Skin Blood Flow Oscillations in People with Spinal Cord Injury

Spinal cord injury (SCI) causes a disruption of autonomic nervous regulation to the cardiovascular system, leading to various cardiovascular and microvascular diseases. Exercise training is an effective intervention for reducing risk for microvascular diseases in healthy people. However, the effectiveness of exercise training on improving microvascular function in people with SCI is largely unknown. The purpose of this study was to compare blood flow oscillations in people with spinal cord injury and different physical activity levels to determine if such a lifestyle might influence skin blood flow. A total of 37 participants were recruited for this study, including 12 athletes with SCI (ASCI), 9 participants with SCI and a sedentary lifestyle (SSCI), and 16 healthy able-bodied controls (AB). Sacral skin blood flow (SBF) in response to local heating at 42 °C for 50 min was measured using laser Doppler flowmetry. The degree of the regularity of blood flow oscillations (BFOs) was quantified using a multiscale entropy approach. The results showed that BFO was significantly more irregular in ASCI and AB compared to SSCI during the maximal vasodilation period. Our results also demonstrate that the difference in the regularity of BFOs between original SBF signal and phase-randomized surrogate time series was larger in ASCI and AB compared to SSCI. Our findings indicate that SCI causes a loss of complexity of BFOs and exercise training may improve complexity in people with SCI. This study demonstrates that multiscale entropy is a sensitive method for detecting differences between different categories of people with SCI and might be able to detect effects of exercise training related to skin blood flow.

Mindfulness-Based Student Training Improves Vascular Variability Associated With Sustained Reductions in Physiological Stress Response

In today's fast-paced society, chronic stress has become an increasing problem, as it can lead to psycho-physiological health problems. University students are also faced with stress due to the demands of many courses and exams. The positive effects of mindfulness-based stress reduction (MBSR) on stress management and self-regulation have already been studied. We have developed a new mindfulness intervention tailored for students—the Mindfulness-Based Student Training (MBST). In this study, we present longitudinal results of the MBST evaluation. Biosignal analysis methods, including pulse wave variability (PWV), heart rate variability, and respiratory activity, were used to assess participants' state of autonomic regulation during the 12-week intervention and at follow-up. The progress of the intervention group (IGR, N = 31) up to 3 months after the end of MBST was compared with that of a control group (CON, N = 34). In addition, the long-term effect for IGR up to 1 year after intervention was examined. The analysis showed significant positive changes in PWV exclusively for IGR. This positive effect, particularly on vascular function, persists 1 year after the end of MBST. These results suggest a physiologically reduced stress level in MBST participants and a beneficial preventive health care program for University students.

Directional couplings between the respiration and parasympathetic control of the heart rate during sleep and wakefulness in healthy subjects at different ages

Cardiorespiratory interactions are important, both for understanding the fundamental processes of functioning of the human body and for development of methods for diagnostics of various pathologies. The properties of cardiorespiratory interaction are determined by the processes of autonomic control of blood circulation, which are modulated by the higher nervous activity. We study the directional couplings between the respiration and the process of parasympathetic control of the heart rate in the awake state and different stages of sleep in 96 healthy subjects from different age groups. The detection of directional couplings is carried out using the method of phase dynamics modeling applied to experimental RR-intervals and the signal of respiration. We reveal the presence of bidirectional couplings between the studied processes in all age groups. Our results show that the coupling from respiration to the process of parasympathetic control of the heart rate is stronger than the coupling in the opposite direction. The difference in the strength of bidirectional couplings between the considered processes is most pronounced in deep sleep.

Effect of Stress on Cardiorespiratory Synchronization of Ironman Athletes

The aim of this paper is to investigate the cardiorespiratory synchronization in athletes subjected to extreme physical stress combined with a cognitive stress tasks. ECG and respiration were measured in 14 athletes before and after the Ironman competition. Stroop test was applied between the measurements before and after the Ironman competition to induce cognitive stress. Synchrogram and empirical mode decomposition analysis were used for the first time to investigate the effects of physical stress, induced by the Ironman competition, on the phase synchronization of the cardiac and respiratory systems of Ironman athletes before and after the competition. A cognitive stress task (Stroop test) was performed both pre- and post-Ironman event in order to prevent the athletes from cognitively controlling their breathing rates. Our analysis showed that cardiorespiratory synchronization increased post-Ironman race compared to pre-Ironman. The results suggest that the amount of stress the athletes are recovering from post-competition is greater than the effects of the Stroop test. This indicates that the recovery phase after the competition is more important for restoring and maintaining homeostasis, which could be another reason for stronger synchronization.

Spectral Analysis and Mutual Information Estimation of Left and Right Intracardiac Electrograms during Ventricular Fibrillation

Ventricular fibrillation (VF) signals are characterized by highly volatile and erratic electrical impulses, the analysis of which is difficult given the complex behavior of the heart rhythms in the left (LV) and right ventricles (RV), as sometimes shown in intracardiac recorded Electrograms (EGM). However, there are few studies that analyze VF in humans according to the simultaneous behavior of heart signals in the two ventricles. The objective of this work was to perform a spectral and a non-linear analysis of the recordings of 22 patients with Congestive Heart Failure (CHF) and clinical indication for a cardiac resynchronization device, simultaneously obtained in LV and RV during induced VF in patients with a Biventricular Implantable Cardioverter Defibrillator (BICD) Contak Renewal IV^TM (Boston Sci.). The Fourier Transform was used to identify the spectral content of the first six seconds of signals recorded in the RV and LV simultaneously. In addition, measurements that were based on Information Theory were scrutinized, including Entropy and Mutual Information. The results showed that in most patients the spectral envelopes of the EGM sources of RV and LV were complex, different, and with several frequency peaks. In addition, the Dominant Frequency (DF) in the LV was higher than in the RV, while the Organization Index (OI) had the opposite trend. The entropy measurements were more regular in the RV than in the LV, thus supporting the spectral findings. We can conclude that basic stochastic processing techniques should be scrutinized with caution and from basic to elaborated techniques, but they can provide us with useful information on the biosignals from both ventricles during VF.

Mindfulness-Based Student Training Leads to a Reduction in Physiological Evaluated Stress

Background and Objective

In today’s fast-paced modern lifestyle, chronic stress has become a serious issue with potential consequences for our physical and mental health. The concept of mindfulness and its derived Mindfulness-Based Stress Reduction (MBSR) program is considered to be an effective stress management technique for patients as well as for healthy persons. The effects of MBSR interventions on their participants have been subject of previous research, especially with regard to psychological or social science approaches using self-reports and questionnaires. In contrast, medical investigations in this field have been less frequent and often somehow limited, for example, addressing only absolute (discrete) mean values for heart rate or blood pressure.

Methods

In this study, we have evaluated a Mindfulness Based Student Training program (MBST) by applying methods of biosignal analysis to examine its impact on the training participants’ autonomic regulation. This intervention program included classical MBSR elements but was adapted to suit the normal daily needs of university students. We obtained the electrocardiogram, finger-pulse plethysmography, and respiration activity from students participating in either the intervention group (IGR, 38 subjects) or a passive control group (CON, 35 subjects) prior to and after 8 weeks of MBST intervention.

Results

When comparing various indices from heart rate variability, pulse wave variability, and respiration in linear and nonlinear domains, significant changes in the autonomic regulation were observed for the IGR group after 8 weeks of MBST.

Conclusion

The results indicate a reduced stress level exclusively for the intervention participants, and therefore, we assume a health benefit from the MBST program.

Amplitude- and Fluctuation-Based Dispersion Entropy

Dispersion entropy (DispEn) is a recently introduced entropy metric to quantify the uncertainty of time series. It is fast and, so far, it has demonstrated very good performance in the characterisation of time series. It includes a mapping step, but the effect of different mappings has not been studied yet. Here, we investigate the effect of linear and nonlinear mapping approaches in DispEn. We also inspect the sensitivity of different parameters of DispEn to noise. Moreover, we develop fluctuation-based DispEn (FDispEn) as a measure to deal with only the fluctuations of time series. Furthermore, the original and fluctuation-based forbidden dispersion patterns are introduced to discriminate deterministic from stochastic time series. Finally, we compare the performance of DispEn, FDispEn, permutation entropy, sample entropy, and Lempel–Ziv complexity on two physiological datasets. The results show that DispEn is the most consistent technique to distinguish various dynamics of the biomedical signals. Due to their advantages over existing entropy methods, DispEn and FDispEn are expected to be broadly used for the characterization of a wide variety of real-world time series. The MATLAB codes used in this paper are freely available at http://dx.doi.org/10.7488/ds/2326.

Dynamics of the cardiovascular autonomic regulation during orthostatic challenge is more relaxed in women

Linear dynamic analysis of cardiovascular and respiratory time series was performed in healthy subjects with respect to gender by shifted short-term segments throughout a head-up tilt (HUT) test. Beat-to-beat intervals (BBI), systolic (SYS) and diastolic (DIA) blood pressure and respiratory interval (RESP) time series were acquired in 14 men and 15 women. In time domain (TD), the descending slope of the auto-correlation function (ACF) (BBI_a31cor) was more pronounced in women than in men (p<0.05) during the HUT test and considerably steeper (p<0.01) at the end of orthostatic phase (OP). The index SYS_meanNN was slightly but significantly lower (p<0.05) in women during the complete test, while higher respiratory frequency and variability (RESP_sdNN) were found in women (p<0.05), during 10–20 min after tilt-up. In frequency domain (FD), during baseline (BL), BBI-normalized low frequency (BBI_LFN) and BBI_LF/HF were slightly but significantly lower (p<0.05), while normalized high frequency (BBI_HFN) was significantly higher in women. These differences were highly significant from the first 5 min after tilt-up (p<0.01) and highly significant (p<0.001) during 10–14 min of OP. Findings revealed that men showed instantaneously a pronounced and sustained increase in sympathetic activity to compensate orthostatism. In women, sympathetic activity was just increased slightly with delayed onset without considerably affecting sympatho-vagal balance.

Men and women should be separately investigated in studies of orthostatic challenge due to different gender-related dynamics of autonomic response

In studies of autonomic regulation during orthostatic challenges only a few nonlinear methods have been considered without investigating the effect of gender in young controls. Especially, the temporal development of the autonomic regulation has not yet been explicitly analyzed using short-term segments in supine position, transition and orthostatic phase (OP). In this study, nonlinear analysis of cardiovascular and respiratory time series was performed to investigate how nonlinear indices are dynamically changing with respect to gender during orthostatic challenges. The analysis was carried out using shifted short-term segments throughout a head-up tilt test in 24 healthy subjects, 12 men (26  ±  4 years) and 12 age-matched women (26  ±  5 years), at supine position and during OP at 70°. The nonlinear methods demonstrated statistical differences in the autonomic regulation between males and females. Orthostatic stress caused significantly decreased heart rate variability due to increased sympathetic activity mainly in men, already at the beginning and during the complete OP, revealed by (a) increased occurrence of specific word types with constant fluctuations as pW111 from symbolic dynamics, (b) augmented fractal correlation properties by the short-term index alpha1 from detrended fluctuation analysis, (c) increased slope indices (21ati and 31ati) from auto-transinformation and (d) augmented time irreversibility indices demonstrating more temporal asymmetries and nonlinear dynamics in men than in women. After tilt-up, both men and women increased their sympathetic activity but in a different way. Time-dependent gender differences during orthostatic challenge were shown directly between men and women or indirectly comparing baseline and different temporal stages of OP. The proposed dynamical study of autonomic regulation has the advantage of screening the fluctuations of the sympathetic and vagal activities that can be quantified by the temporal behavior of nonlinear indices. The findings in this paper strongly suggest the need for gender separation in studies of the dynamics of autonomic regulation during orthostatic challenge.

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.

Mutual information measures applied to EEG signals for sleepiness characterization

Excessive daytime sleepiness (EDS) is one of the main symptoms of several sleep related disorders with a great impact on the patient lives. While many studies have been carried out in order to assess daytime sleepiness, the automatic EDS detection still remains an open problem. In this work, a novel approach to this issue based on non-linear dynamical analysis of EEG signal was proposed. Multichannel EEG signals were recorded during five maintenance of wakefulness (MWT) and multiple sleep latency (MSLT) tests alternated throughout the day from patients suffering from sleep disordered breathing. A group of 20 patients with excessive daytime sleepiness (EDS) was compared with a group of 20 patients without daytime sleepiness (WDS), by analyzing 60-s EEG windows in waking state. Measures obtained from cross-mutual information function (CMIF) and auto-mutual-information function (AMIF) were calculated in the EEG. These functions permitted a quantification of the complexity properties of the EEG signal and the non-linear couplings between different zones of the scalp. Statistical differences between EDS and WDS groups were found in β band during MSLT events (p-value < 0.0001). WDS group presented more complexity than EDS in the occipital zone, while a stronger nonlinear coupling between occipital and frontal zones was detected in EDS patients than in WDS. The AMIF and CMIF measures yielded sensitivity and specificity above 80% and AUC of ROC above 0.85 in classifying EDS and WDS patients.

Interaction between EEG and drug concentration to predict response to noxious stimulation during sedation-analgesia: effect of the A118G genetic polymorphism

The level of sedation in patients undergoing medical procedures is affected by the interaction between the effect of the anesthetic and analgesic agents and the pain stimuli. The presence of the A118G single nucleotide polymorphism (SNP) in the OPRM1 gene affects the requirements of opioids for patients undergoing sedation-analgesia. The purpose of this work is to evaluate the influence of the SNP A118G in OPRM1 on EEG measures for the prediction of the response to pain stimulation during endoscopy procedure. The proposed measures were based on power spectral density and auto-mutual information function. It was found that the statistical performances of the EEG measures improved when the presence of the SNP was taken into account (prediction probability Pk>0.9).

Effect of resistive inspiratory and expiratory loading on cardio-respiratory interaction in healthy subjects

Resistive loading affects the breathing pattern and causes an increase in negative intrathoracic pressure. The aim of this paper was to study the influence inspiratory and expiratory loading on cardio-respiratory interaction. We recorded electrocardiogram (ECG) and respiratory inductance plethysmogram (RIP) in 11 healthy male subjects under normal and resistive loading conditions. The R-R time series were extracted from the ECG and respiratory phases were calculated from the ribcage and abdominal RIP 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 `3 digits' were formed and the correspondence between words of the two series was determined to quantify cardio-respiratory interaction. Adding inspiratory and expiratory resistive loads resulted in an increase in inspiratory and expiatory time, respectively. Furthermore, we observed a significant increase in cardio-respiratory interaction during inspiratory resistive loading as compared to expiratory resistive loading (ribcage: 22.1±7.2 vs. 12.5±4.3 %, p<;0.0001; abdomen: 18.8±8.5 vs. 12.1±3.1 %, p<;0.05, respectively). Further studies may aid in better understanding the underlying physiological mechanisms and management of patients with breathing disorders.

To control false positives in gene-gene interaction analysis: two novel conditional entropy-based approaches

Genome-wide analysis of gene-gene interactions has been recognized as a powerful avenue to identify the missing genetic components that can not be detected by using current single-point association analysis. Recently, several model-free methods (e.g. the commonly used information based metrics and several logistic regression-based metrics) were developed for detecting non-linear dependence between genetic loci, but they are potentially at the risk of inflated false positive error, in particular when the main effects at one or both loci are salient. In this study, we proposed two conditional entropy-based metrics to challenge this limitation. Extensive simulations demonstrated that the two proposed metrics, provided the disease is rare, could maintain consistently correct false positive rate. In the scenarios for a common disease, our proposed metrics achieved better or comparable control of false positive error, compared to four previously proposed model-free metrics. In terms of power, our methods outperformed several competing metrics in a range of common disease models. Furthermore, in real data analyses, both metrics succeeded in detecting interactions and were competitive with the originally reported results or the logistic regression approaches. In conclusion, the proposed conditional entropy-based metrics are promising as alternatives to current model-based approaches for detecting genuine epistatic effects.

Estimating coupling directions in the cardiorespiratory system using recurrence properties

The asymmetry of coupling between complex systems can be studied by conditional probabilities of recurrence, which can be estimated by joint recurrence plots. This approach is applied for the first time on experimental data: time series of the human cardiorespiratory system in order to investigate the couplings between heart rate, mean arterial blood pressure and respiration. We find that the respiratory system couples towards the heart rate, and the heart rate towards the mean arterial blood pressure. However, our analysis could not detect a clear coupling direction between the mean arterial blood pressure and respiration.

Cardiovascular and cardiorespiratory coupling analyses: a review

Recently, methods have been developed to analyse couplings in dynamic systems. In the field of medical analysis of complex cardiovascular and cardiorespiratory systems, there is growing interest in how insights may be gained into the interaction between regulatory mechanisms in healthy and diseased persons. The couplings within and between these systems can be linear or nonlinear. However, the complex mechanisms involved in cardiovascular and cardiorespiratory regulation very likely interact with each other in a nonlinear way. Recent advances in nonlinear dynamics and information theory have allowed the multivariate study of information transfer between time series. They therefore might be able to provide additional diagnostic and prognostic information in medicine and might, in particular, be able to complement traditional linear coupling analysis techniques. In this review, we describe the approaches (Granger causality, nonlinear prediction, entropy, symbolization, phase synchronization) most commonly applied to detect direct and indirect couplings between time series, especially focusing on nonlinear approaches. We will discuss their capacity to quantify direct and indirect couplings and the direction (driver-response relationship) of the considered interaction between different biological time series. We also give their basic theoretical background, their basic requirements for application, their main features and demonstrate their usefulness in different applications in the field of cardiovascular and cardiorespiratory coupling analyses.

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.

Effect of spontaneous arousals on cardio-respiratory interaction in healthy children

The aim of this paper was to study the effect of spontaneous arousals during night-time sleep on the interactions between R-R intervals and respiratory phases in healthy children. We collected overnight polysomnography data of 40 healthy children and investigated cardio-respiratory interaction before and after spontaneous arousals during stage 2 sleep using joint symbolic dynamics. 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 was determined to quantify cardio-respiratory interaction for pre- and post-spontaneous arousal episodes. We observed a brief but significant shortening in R-R and respiratory intervals after arousal. There was also a significant short-term increase in cardio-respiratory interaction during the first 30-second post-arousal episode as compared to 30-second pre-arousal episode (7.5±3.4 vs. 5.2±3.7%, p&#60;0.0001, respectively). In conclusion, spontaneous arousals in healthy children during night-time sleep are associated with a temporal but significant increase in cardio-respiratory interaction.

NONLINEAR ANALYSIS OF PHYSIOLOGICAL SIGNALS: A REVIEW

This paper reviews various nonlinear analysis methods for physiological signals. The assessment is based on a discussion of chaos-inspired methods, such as fractal dimension (FD), correlation dimension (D2), largest Lyapunov exponet (LLE), Renyi's entropy (REN), Shannon spectral entropy (SEN), and approximate entropy (ApEn). We document that these methods are used to extract discriminative features from electroencephalograph (EEG) and heart rate variability (HRV) signals by reviewing the relevant scientific literature. EEG features can be used to support the diagnosis of epilepsy and HRV features can be used to support the diagnosis of cardiovascular diseases as well as diabetes. Documenting the widespread use of these and other nonlinear methods supports our thesis that the study of feature extraction methods, based on the chaos theory, is an important subject which has been gaining more and significance in biomedical engineering. We adopt the position that pursuing research in the field of biomedical engineering is ultimately a progmatic activity, where it is necessary to engage in features that work. In this case, the nonlinear features are working well, even if we do not have conclusive evidence that the underlying physiological phenomena are indeed chaotic.

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.

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.

Symbolic dynamic analysis of relations between cardiac and breathing cycles in patients on weaning trials

Traditional time-domain techniques of data analysis are often not sufficient to characterize the complex dynamics of the cardiorespiratory interdependencies during the weaning trials. In this paper, the interactions between the heart rate (HR) and the breathing rate (BR) were studied using joint symbolic dynamic analysis. A total of 133 patients on weaning trials from mechanical ventilation were analyzed: 94 patients with successful weaning (group S) and 39 patients that failed to maintain spontaneous breathing (group F). The word distribution matrix enabled a coarse-grained quantitative assessment of short-term nonlinear analysis of the cardiorespiratory interactions. The histogram of the occurrence probability of the cardiorespiratory words presented a higher homogeneity in group F than in group S, measured with a higher number of forbidden words in group S as well as a higher number of words whose probability of occurrence is higher than a probability threshold in group S. The discriminant analysis revealed the best results when applying symbolic dynamic variables. Therefore, we hypothesize that joint symbolic dynamic analysis provides enhanced information about different interactions between HR and BR, when comparing patients with successful weaning and patients that failed to maintain spontaneous breathing in the weaning procedure.

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.

Impact of movement on cardiorespiratory coordination in conscious rats

In this study we assessed the impact of movement on the interaction between the heart rhythm and respiration in rats while they were conscious and freely moving. In eight male adult Sprague-Dawley (SD, n=4) and Hooded Wistar (HW, n=4) rats, we recorded respiratory rate using whole-body plethysmography with a piezoelectric sensor attached to simultaneously monitor body movement. Heart rate was recorded using a radio-telemetry transmitter. For the assessment of cardiorespiratory coordination, we analysed the phase-locking between heart rate and respiration, estimating the instantaneous phases using Hilbert transform. For statistical analysis, the piezoelectric signal was dichotomized into low-intensity (LIm) and high-intensity (HIm) movement. The R-R intervals, respiratory intervals and cardiorespiratory coordination between LIm and HIm of each rat were assessed with Student's t-test. A significant decrease in the mean values for respiratory interval (0.34 ± 0.1 vs. 0.23 ± 0.1 s, p < 0.01 in HW rats) and R-R interval (0.19 ± 0.01 vs. 0.17 ± 0.01 s, p < 0.001 in SD rats) was observed during HIm. The phase-locking between the cardiac and respiratory signals also decreased significantly during HIm (overall coordination during LIm vs. HIm: 89.3 ± 3.3% vs. 8.7 ± 1.7%, p < 0.001). In conclusion the interaction between the cardiac and respiratory oscillators is affected by voluntary movements in rats.

Multiscale, multiorgan and multivariate complexity analyses of cardiovascular regulation

Cardiovascular system complexity is confirmed by both its generally variegated structure of physiological modelling and the richness of information detectable from processing of the signals involved in it, with strong linear and nonlinear interactions with other biological systems. In particular, this behaviour may be accordingly described by means of what we call MMM paradigm (i.e. multiscale, multiorgan and multivariate). Such an approach to the cardiovascular system emphasizes where the genesis of its complexity is potentially allocated and how it is possible to detect information from it. No doubt that processing signals from multi-leads of the same system (multivariate), from the interaction of different physiological systems (multiorgan) and integrating all this information across multiple scales (from genes, to proteins, molecules, cells, up to the whole organ) could really provide us with a more complete look at the overall phenomenon of cardiovascular system complexity, with respect to the one which is obtainable from its single constituent parts. In this paper, some examples of approaches are discussed for investigating the cardiovascular system in different time and spatial scales, in studying a different organ involvement (such as sleep, depression and multiple organ dysfunction) and in using a multivariate approach via various linear and nonlinear methods for cardiovascular risk stratification and pathology assessment.

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.

Interpretation of the auto-mutual information rate of decrease in the context of biomedical signal analysis. Application to electroencephalogram recordings

The mutual information (MI) is a measure of both linear and nonlinear dependences. It can be applied to a time series and a time-delayed version of the same sequence to compute the auto-mutual information function (AMIF). Moreover, the AMIF rate of decrease (AMIFRD) with increasing time delay in a signal is correlated with its entropy and has been used to characterize biomedical data. In this paper, we aimed at gaining insight into the dependence of the AMIFRD on several signal processing concepts and at illustrating its application to biomedical time series analysis. Thus, we have analysed a set of synthetic sequences with the AMIFRD. The results show that the AMIF decreases more quickly as bandwidth increases and that the AMIFRD becomes more negative as there is more white noise contaminating the time series. Additionally, this metric detected changes in the nonlinear dynamics of a signal. Finally, in order to illustrate the analysis of real biomedical signals with the AMIFRD, this metric was applied to electroencephalogram (EEG) signals acquired with eyes open and closed and to ictal and non-ictal intracranial EEG recordings.

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.

Information flow to assess cardiorespiratory interactions in patients on weaning trials

Nonlinear processes of the autonomic nervous system (ANS) can produce breath-to-breath variability in the pattern of breathing. In order to provide assess to these nonlinear processes, nonlinear statistical dependencies between heart rate variability and respiratory pattern variability are analyzed. In this way, auto-mutual information and cross-mutual information concepts are applied. This information flow analysis is presented as a short-term non linear analysis method to investigate the information flow interactions in patients on weaning trials. 78 patients from mechanical ventilation were studied: Group A of 28 patients that failed to maintain spontaneous breathing and were reconnected; Group B of 50 patients with successful trials. The results show lower complexity with an increase of information flow in group A than in group B. Furthermore, a more (weakly) coupled nonlinear oscillator behavior is observed in the series of group A than in B.

On the application of the auto mutual information rate of decrease to biomedical signals

The auto mutual information function (AMIF) evaluates the signal predictability by assessing linear and non-linear dependencies between two measurements taken from a single time series. Furthermore, the AMIF rate of decrease (AMIFRD) is correlated with signal entropy. This metric has been used to analyze biomedical data, including cardiac and brain activity recordings. Hence, the AMIFRD can be a relevant parameter in the context of biomedical signal analysis. Thus, in this pilot study, we have analyzed a synthetic sequence (a Lorenz system) and real biosignals (electroencephalograms recorded with eyes open and closed) with the AMIFRD. We aimed at illustrating the application of this parameter to biomedical time series. Our results show that the AMIFRD can detect changes in the non-linear dynamics of a sequence and that it can distinguish different physiological conditions.

Evaluation of Respiratory Muscles Activity by Means of Cross Mutual Information Function at Different Levels of Ventilatory Effort

Analysis of respiratory muscles activity is an effective technique for the study of pulmonary diseases such as obstructive sleep apnea syndrome (OSAS). Respiratory diseases, especially those associated with changes in the mechanical properties of the respiratory apparatus, are often associated with disruptions of the normally highly coordinated contractions of respiratory muscles. Due to the complexity of the respiratory control, the assessment of OSAS related dysfunctions by linear methods are not sufficient. Therefore, the objective of this study was the detection of diagnostically relevant nonlinear complex respiratory mechanisms. Two aims of this work were: (1) to assess coordination of respiratory muscles contractions through evaluation of interactions between respiratory signals and myographic signals through nonlinear analysis by means of cross mutual information function (CMIF); (2) to differentiate between functioning of respiratory muscles in patients with OSAS and in normal subjects. Electromyographic (EMG) and mechanomyographic (MMG) signals were recorded from three respiratory muscles: genioglossus, sternomastoid and diaphragm. Inspiratory pressure and flow were also acquired. All signals were measured in eight patients with OSAS and eight healthy subjects during an increased respiratory effort while awake. Several variables were defined and calculated from CMIF in order to describe correlation between signals. The results indicate different nonlinear couplings of respiratory muscles in both populations. This effect is progressively more evident at higher levels of respiratory effort.

Autonomic Information Flow during awakeness, sleep, and multiple organ dysfunction syndrome assessed by mutual information function of heart rate fluctuations

The Autonomic Information Flow (AIF) represents the complex communication within the autonomic nervous system (ANS). It can be assessed by the mutual information function (MIF) of heart rate fluctuations (HRF). AIF represented by HRF is based on several interacting physiological mechanisms operating at different time scales. Therefore one prominent time scale for HRF complexity analysis is not given a priori. MIF reflects the information flow at different time scales. This allows a more specific characterization of the complex communication leading to dynamic stability (homeostasis) of the cardiovascular-respiratory system. Three clinically relevant examples of autonomic communication, namely AIF of normals during awake state and deep sleep, and of patients with multiple organ dysfunction syndrome (MODS) were investigated. In these states MIF clearly represents and distinguishes the different communication in dependence on the time scale of information transfer. The results confirm our systems-theoretical concept that AIF, represented by MIF, characterizes the complex communication of the ANS at different time scales.

Changes of autonomic information flow due to idiopathic dilated cardiomyopathy

Risk stratification of patients with idiopathic dilated cardiomyopathy (IDC) is an epidemiologically relevant question. But the results based on conventional heart rate variability (HRV) analysis are still unsatisfactory. The adjustments within the cardiovascular system incorporate nonlinear and complex mechanisms of information exchange which may have additional prognostic value. It is an objective of the present work to evaluate the prognostic value of autonomic information flow (AIF) measures in IDC patients compared to conventional HRV measures in a first explorative study. Holter recordings of 32 patients with idiopathic dilated cardiomyopathy (IDC) and 12 normal subjects (NRM) were analyzed. The IDC patients consisted of two groups: 10 high risk (HR) patients, after aborted sudden cardiac death (SCD); 22 low risk (LR) patients, without SCD. Sensitivity, specificity, positive predictive value, negative predictive value and ROC characteristics of a comprehensive set of AIF measures, organized according to the conventional HRV standards, and conventional HRV measures were investigated. The significant risk predictors were evaluated by Spearman's rank correlation. While the only traditional HRV measure discriminating IDC patients from NRM was ln(LF) most of the AIF measures had a discriminatory value. Concerning the prognosis of the IDC patients by conventional HRV we found that SDNN and all frequency band measures (lnHF, lnLF, lnVLF) significantly discriminated HR from LR. Among the AIF measures the time shift related peak decay (PD(dHF)) reflecting the HF band information flow had a prognostic value. PD(dHF) was identified as a promising candidate which might improve the predictive value of traditional HRV analysis, predominantly represented by SDNN. A subsequent comprehensive clinical study is necessary to validate this hypothesis.

Autonomic organization of respirocardial function in healthy human neonates in quiet and active sleep

BACKGROUND AND AIM

It is not known on which time scales the nonlinear respirocardial interactions occur. This work's aim is to quantitatively assess functional respirocardial organization during quiet and active sleep of healthy full-term neonates by autonomic information flow (AIF) without limitation on specific time scales. Representing respirocardial interactions on a global time scale AIF carries information on a wider scope of interdependencies than known linear and nonlinear measures described. It assesses the complexity of heart rate fluctuations (HRF) and respiratory movements (RM) and their interaction comprising both linear and nonlinear properties. Thus, we hypothesized AIF to characterize novel aspects of sleep state-dependent respirocardial interaction.

METHODS

RM and ECG-derived HRF of six healthy full-term neonates were studied. We analyzed their power spectra, coherence, auto- and cross-correlation and complexity estimated on local ("next sample" prediction) and global time scales (an integral over AIF predicting for all time lags in HRF and RM).

RESULTS

We found the global AIF of HRF and RM to differ significantly between active and quiet sleep in all neonates, whereas on a local time scale this applied to the HRF AIF only. HRF complexity was larger in quiet than in active sleep. Respirocardial interaction was less complex in quiet versus active sleep in the high frequency band only.

CONCLUSION

Complex sleep state-related changes of respirocardial interdependencies cannot be identified completely on the local time scale. Considering the global time scale of respirocardial interactions allows a more complete physiological interpretation with regard to the underlying autonomic dynamics.

Evaluation of different rhythms by hidden Markov models in heart rate variability of hypertrophic cardiomyopathy patients

Synchronization and regularity between different rhythms were evaluated in the HRV using hidden Markov models (HMMs) at very low (VLF), low (LF) and high (HF) frequency bands. Phase synchronization of these rhythms was studied in RR series of hypertrophic cardiomyopathy (HCM) patients during the sleeping period. Two groups of patients were considered in the HCM group: high risk (HR), patients after aborted sudden death (SCD) or that died during follow up, and low risk (LR), patients without SCD. RR time-series were filtered in the following frequency-bands, VLF, LF and HF. The RR phase differences of HF vs. VLF, HF vs. LF and LF vs. VLF were calculated and then the amplitude range partitioned into 8 bins. Finally, these series (O, observations) were modeled using HMM. The models lambda = (A,B,pi) were selected such that P(O/lambda) was locally maximized. Ergodic topology and N = {5,10,15,20} states were considered also for this analysis. Ergodic HMMs with 10 states were found to be sufficient to characterize the HRV rhythms of HR and LR patients. Different synchronization strength was observed studying the phase entropies. However, only the parameters obtained from the HMM were able to differentiate the different groups, with p-value < 0.0005.

Analysis of respiratory and muscle activity by means of cross information function between ventilatory and myographic signals

Analysis of respiratory muscle activity is a promising technique for the study of pulmonary diseases such as obstructive sleep apnea syndrome (OSAS). Evaluation of interactions between muscles is very useful in order to determine the muscular pattern during an exercise. These interactions have already been assessed by means of different linear techniques like cross-spectrum, magnitude squared coherence or cross-correlation. The aim of this work is to evaluate interactions between respiratory and myographic signals through nonlinear analysis by means of cross mutual information function (CMIF), and finding out what information can be extracted from it. Some parameters are defined and calculated from CMIF between ventilatory and myographic signals of three respiratory muscles. Finally, differences in certain parameters were obtained between OSAS patients and healthy subjects indicating different respiratory muscle couplings.

Analysis of the nonlinear autodependencies of respiratory pattern in patients on weaning trials

Traditional time domain techniques of data analysis are often not sufficient to characterize the nonlinear dynamics of respiration. In this study, the respiratory pattern variability was analyzed using auto mutual information measures. These provide access to nonlinear statistical autodependencies of respiratory pattern variability. A group of 20 patients on weaning trials from mechanical ventilation were studied at two different pressure support ventilation levels, in order to obtain respiratory volume signals with different variability. Time series of breathing duration, inspiratory time, fractional inspiratory time, tidal volume and mean inspiratory flow were analyzed. Different measures based on auto-mutual information were studied to characterize the respiratory pattern variability with regard to its complex organization.