Estimating coupling directions in the cardiorespiratory system using recurrence properties

Interpolation and sampling effects on recurrence quantification measures

The recurrence plot and the recurrence quantification analysis (RQA) are well-established methods for the analysis of data from complex systems. They provide important insights into the nature of the dynamics, periodicity, regime changes, and many more. These methods are used in different fields of research, such as finance, engineering, life, and earth science. To use them, the data have usually to be uniformly sampled, posing difficulties in investigations that provide non-uniformly sampled data, as typical in medical data (e.g., heart-beat based measurements), paleoclimate archives (such as sediment cores or stalagmites), or astrophysics (supernova or pulsar observations). One frequently used solution is interpolation to generate uniform time series. However, this preprocessing step can introduce bias to the RQA measures, particularly those that rely on the diagonal or vertical line structure in the recurrence plot. Using prototypical model systems, we systematically analyze differences in the RQA measure average diagonal line length for data with different sampling and interpolation. For real data, we show that the course of this measure strongly depends on the choice of the sampling rate for interpolation. Furthermore, we suggest a correction scheme, which is capable of correcting the bias introduced by the prepossessing step if the interpolation ratio is an integer.

Differentiating patients with obstructive sleep apnea from healthy controls based on heart rate-blood pressure coupling quantified by entropy-based indices

We introduce an entropy-based classification method for pairs of sequences (ECPS) for quantifying mutual dependencies in heart rate and beat-to-beat blood pressure recordings. The purpose of the method is to build a classifier for data in which each item consists of two intertwined data series taken for each subject. The method is based on ordinal patterns and uses entropy-like indices. Machine learning is used to select a subset of indices most suitable for our classification problem in order to build an optimal yet simple model for distinguishing between patients suffering from obstructive sleep apnea and a control group.

I, Hramkov A, Kulminskiy D, Semenova N, Sergeev K, Slepnev A, Yu. SE, Zhuravlev M, Fedosov I, Shirokov A, Blokhina I, Dubrovski A, Terskov A, Khorovodov A, Ageev V, Elovenko D, Evsukova A, Adushkina V, Telnova V, Postnov D, Penzel T, Kurths J. EEG biomarkers of activation of the lymphatic drainage system of the brain during sleep and opening of the blood-brain barrier

The lymphatic drainage system of the brain (LDSB) is the removal of metabolites and wastes from its tissues. A dysfunction of LDSB is an important sign of aging, brain oncology, the Alzheimer's and Parkinson's diseases. The development of new strategies for diagnosis of LDSB injuries can improve prevention of age-related cerebral amyloid angiopathy, neurodegenerative and cerebrovascular diseases. There are two conditions, such as deep sleep and opening of the blood-brain-barrier (OBBB) associated with the LDSB activation. A promising candidate for measurement of LDSB could be electroencephalography (EEG). In this pilot study on rats, we tested the hypothesis, whether deep sleep and OBBB can be an informative platform for an effective extracting of information about the LDSB functions. Using the nonlinear analysis of EEG dynamics and machine learning technology, we discovered that the LDSB activation during OBBB and sleep is associated with similar changes in the EEG θ-activity. The OBBB causes the higher LDSB activation vs. sleep that is accompanied by specific changes in the low frequency EEG activity extracted by the power spectra analysis of the EEG dynamics combined with the coherence function. Thus, our findings demonstrate a link between neural activity associated with the LDSB activation during sleep and OBBB that is an important informative platform for extraction of the EEG-biomarkers of the LDSB activity. These results open new perspectives for the development of technology for the LDSB diagnostics that would open a novel era in the prognosis of brain diseases caused by the LDSB disorders, including OBBB.

Detection of hearing losses (HL) via transient-evoked otoacoustic emissions: towards an automatic classification

Transiently evoked otoacoustic emissions (TEOAEs) are routinely used in the hearing assessment of the auditory periphery. The major contribution of TEOAEs is the early detection of hearing losses in neonates, children, and adults. The evaluation of TEOAE responses by specific signal decomposition techniques offers numerous advantages for current and future research. One methodology, based on recurrence quantification analysis (RQA), can identify adult subjects presenting sensorineural hearing impairments. In two previous papers, the RQA-based approach was succesfully applied in identifying and classifying cases presenting noise and age related hearing losses. The current work investigates further two aspects of the previously proposed RQA-based analysis for hearing loss detection: (i) the reliability of a Training set built from different numbers of ears with normal hearing, and (ii) the threshold set of values of the key hearing loss detecting parameter RAD2D. Results: The Training set built from 158 healthy ears was found to be quite reliable and a similar but slightly minor performance was observed for the training set of 118 normal subjects, used in the past; the proposed ROC-curve method, optimizing the values of RAD2D, shows improved sensibility and specificity in one class discrimination. Conclusions: A complete and simplified procedure, based on the combined use of the traditional TEOAE reproducibility value and on values from the RQA-based RAD2D parameter, is proposed as an improved automatic classifier, in terms of sensitivity and specificity, for different types of hearing losses.

Unsupervised Clustering of Heartbeat Dynamics Allows for Real Time and Personalized Improvement in Cardiovascular Fitness

VO₂max index has a significant impact on overall health. Its estimation through wearables notifies the user of his level of fitness but cannot provide a detailed analysis of the time intervals in which heartbeat dynamics are changed and/or fatigue is emerging. Here, we developed a multiple modality biosignal processing method to investigate running sessions to characterize in real time heartbeat dynamics in response to external energy demand. We isolated dynamic regimes whose fraction increases with the VO₂max and with the emergence of neuromuscular fatigue. This analysis can be extremely valuable by providing personalized feedback about the user’s fitness level improvement that can be realized by developing personalized exercise plans aimed to target a contextual increase in the dynamic regime fraction related to VO₂max increase, at the expense of the dynamic regime fraction related to the emergence of fatigue. These strategies can ultimately result in the reduction in cardiovascular risk.

Recurrence quantification analysis of heart rate variability to detect both ventilatory thresholds

Aims of this study were: to verify if Recurrence Quantification Analysis (RQA) of Heart Rate Variability (HRV) time series could determine both ventilatory thresholds in individuals with different fitness levels, and to assess the validity of RQA method compared to gas-exchange method (GE). The two thresholds were estimated in thirty young individuals during incremental exercise on cycle-ergometer: Heart rate (HR), Oxygen consumption (VO₂) and Workload were measured by the two methods (RQA and GE). Repeated measures ANOVA was used to assess main effects of methods and methods-by-groups interaction effects for HR, VO₂ and Workload at aerobic (AerT) and anaerobic (AnT) thresholds. Validity of RQA at both thresholds was assessed for HR, VO₂ and Workload by Ordinary Least Products (OLP) regression, Typical Percentage Error (TE), Intraclass Correlation Coefficients (ICC) and the Bland Altman plots. No methods-by-groups interaction effects were detected for HR, VO₂ and Workload at AerT and AnT. The OLP analysis showed that at both thresholds RQA and GE methods had very strong correlations (r >0.8) in all variables (HR, VO₂ and Workload). Slope and intercept values always included the 1 and the 0, respectively. At AerT the TE ranged from 4.02% (5.48 bpm) to 10.47% (8.53 Watts) (HR and Workload, respectively) and in all variables ICC values were excellent (≥0.85). At AnT the TE ranged from 2.53% (3.98 bpm) to 6.64% (7.81 Watts) (HR and Workload, respectively) and in all variables ICC values were excellent (≥0.90). Therefore, RQA of HRV time series is a new valid approach to determine both ventilatory thresholds in individuals with different physical fitness levels, it can be used when gas analysis is not possible or not convenient.

Frequency spectrum recurrence analysis

In this paper, we present the new frequency spectrum recurrence analysis technique by means of electro-encephalon signals (EES) analyses. The technique is suitable for time series analysis with noise and disturbances. EES were collected, and alpha waves of the occipital region were analysed by comparing the signals from participants in two states, eyes open and eyes closed. Firstly, EES were characterized and analysed by means of techniques already known to compare with the results of the innovative technique that we present here. We verified that, standard recurrence quantification analysis by means of EES time series cannot statistically distinguish the two states. However, the new frequency spectrum recurrence quantification exhibit quantitatively whether the participants have their eyes open or closed. In sequence, new quantifiers are created for analysing the recurrence concentration on frequency bands. These analyses show that EES with similar frequency spectrum have different recurrence levels revealing different behaviours of the nervous system. The technique can be used to deepen the study on depression, stress, concentration level and other neurological issues and also can be used in any complex system.

Physiological and Behavioral Factors in Musicians' Performance Tempo

Musicians display individual differences in their spontaneous performance rates (tempo) for simple melodies, but the factors responsible are unknown. Previous research suggests that musical tempo modulates listeners' cardiovascular activity. We report an investigation of musicians' melody performances measured over a 12-h day and subsequent changes in the musicians' physiological activity. Skilled pianists completed four testing sessions in a single day as cardiac activity was recorded during an initial 5 min of baseline rest and during performances of familiar and unfamiliar melodies. Results indicated slower tempi for familiar and unfamiliar melodies at early testing times. Performance rates at 09 h were predicted by differences in participants' alertness and musical training; these differences were not explained by sleep patterns, chronotype, or cardiac activity. Individual differences in pianists' performance tempo were consistent across testing sessions: participants with a faster tempo at 09 h maintained a faster tempo at later testing sessions. Cardiac measures at early testing times indicated increased heart rates and more predictable cardiac dynamics during music performance than baseline rest, and during performances of unfamiliar melodies than familiar melodies. These findings provide the first evidence of cardiac dynamics that are unique to music performance contexts.

Recurrence quantification analysis of heart rate variability during continuous incremental exercise test in obese subjects

The present paper concerns a new description of changing in metabolism during incremental exercises test that permit an individually tailored program of exercises for obese subjects. We analyzed heart rate variability from RR interval time series (tachogram) with an alternative approach, the recurrence quantification analysis, that allows a description of a time series in terms of its dynamic structure and is able to identify the phase transitions. A transition in cardiac signal dynamics was detected and it perfectly reflects the aerobic threshold, as identified by gas exchange during an incremental exercise test, revealing the coupling from the respiratory system toward the heart. Moreover, our analysis shows that, in the recurrence plot of RR interval, it is possible to identify a specific pattern that allows to identify phase transitions between different dynamic regimes. The perfect match of the occurrence of the phase transitions with changes observed in the VO₂ consumption, the gold standard approach to estimate thresholds, strongly supports the possibility of using our analysis of RR interval to detect metabolic threshold. In conclusion, we propose a novel nonlinear data analysis method that allows for an easy and personalized detection of thresholds both from professional and even from low-cost wearable devices, without the need of expensive gas analyzers.

Diagnostics of coupling between low-frequency loops in cardiovascular autonomic control in adults, newborns and mathematical model using cross-recurrence analysis

The aim of study is to investigate effectiveness of cross-recurrence analysis for the detection of coupling between the loops of heart rate and vessel tone sympathetic control. The cross-recurrence analysis is applied to the interbeat intervals and photopletysmographic signals from the mathematical model of cardiovascular system and from adults and newborn children. The model is examined under the conditions of the four experiments: with fully operational autonomic control, autonomic control weakened by 40%, autonomic control weakened by 70% and autonomic blockade. The coupling is most pronounced in adult subjects and the model with fully operational autonomic control, while it is absent under the autonomic blockade. Autonomic control is also not fully developed in newborn children. As the result, smaller coupling strength is expected. The results of cross-recurrence analysis of the model and experimental data are compared with the results of coupling detection based on the analysos of phase synchronization. Synchronization index demonstrates good correlation with the coupling strength in the model and weak coupling in newborn children in relation to adult subjects. In both cases, no correlation is observed between the synchronization index and the results of cross-recurrence analysis.

Altered Causal Coupling Pathways within the Central-Autonomic-Network in Patients Suffering from Schizophrenia

The multivariate analysis of coupling pathways within physiological (sub)systems focusing on identifying healthy and diseased conditions. In this study, we investigated a part of the central-autonomic-network (CAN) in 17 patients suffering from schizophrenia (SZO) compared to 17 age–gender matched healthy controls (CON) applying linear and nonlinear causal coupling approaches (normalized short time partial directed coherence, multivariate transfer entropy). Therefore, from all subjects continuous heart rate (successive beat-to-beat intervals, BBI), synchronized maximum successive systolic blood pressure amplitudes (SYS), synchronized calibrated respiratory inductive plethysmography signal (respiratory frequency, RESP), and the power P_EEG of frontal EEG activity were investigated for 15 min under resting conditions. The CAN revealed a bidirectional coupling structure, with central driving towards blood pressure (SYS), and respiratory driving towards P_EEG. The central-cardiac, central-vascular, and central-respiratory couplings are more dominated by linear regulatory mechanisms than nonlinear ones. The CAN showed significantly weaker nonlinear central-cardiovascular and central-cardiorespiratory coupling pathways, and significantly stronger linear central influence on the vascular system, and on the other hand significantly stronger linear respiratory and cardiac influences on central activity in SZO compared to CON, and thus, providing better understanding of the interrelationship of central and autonomic regulatory mechanisms in schizophrenia might be useful as a biomarker of this disease.

Multiscale Information Decomposition Dissects Control Mechanisms of Heart Rate Variability at Rest and During Physiological Stress

Heart rate variability (HRV; variability of the RR interval of the electrocardiogram) results from the activity of several coexisting control mechanisms, which involve the influence of respiration (RESP) and systolic blood pressure (SBP) oscillations operating across multiple temporal scales and changing in different physiological states. In this study, multiscale information decomposition is used to dissect the physiological mechanisms related to the genesis of HRV in 78 young volunteers monitored at rest and during postural and mental stress evoked by head-up tilt (HUT) and mental arithmetics (MA). After representing RR, RESP and SBP at different time scales through a recently proposed method based on multivariate state space models, the joint information transfer TRESP,SBP→RR is decomposed into unique, redundant and synergistic components, describing the strength of baroreflex modulation independent of respiration (USBP→RR), nonbaroreflex (URESP→RR) and baroreflex-mediated (RRESP,SBP→RR) respiratory influences, and simultaneous presence of baroreflex and nonbaroreflex respiratory influences (SRESP,SBP→RR), respectively. We find that fast (short time scale) HRV oscillations—respiratory sinus arrhythmia—originate from the coexistence of baroreflex and nonbaroreflex (central) mechanisms at rest, with a stronger baroreflex involvement during HUT. Focusing on slower HRV oscillations, the baroreflex origin is dominant and MA leads to its higher involvement. Respiration influences independent on baroreflex are present at long time scales, and are enhanced during HUT.

Atmosphere-Land Bridge between the Pacific and Tropical North Atlantic SST's through the Amazon River basin during the 2005 and 2010 droughts

The present work uses a new approach to causal inference between complex systems called the Recurrence Measure of Conditional Dependence (RMCD) based on the recurrence plots theory, in order to study the role of the Amazon River basin (AM) as a land-atmosphere bridge between the Niño 3.0 region in the Pacific Ocean and the Tropical North Atlantic. Two anomalous droughts in the Amazon River basin were selected, one mainly attributed to the warming of the Tropical North Atlantic (2005) and the other to a warm phase of El Niño-Southern Oscillation (2010). The results of the RMCD analysis evidence the distinctive behavior in the causal information transferred between the two oceanic regions during the two extreme droughts, suggesting that the land-atmosphere bridge operating over the AM is an active hydroclimate mechanism at interannual timescales, and that the RMCD analysis may be an ancillary resort to complement early warning systems.

Scaling oscillatory platform frequency reveals recurrence of intermittent postural attractor states

The study of postural control has been dominated by experiments on the maintenance of quiet upright standing balance on flat stationary support surfaces that reveal only limited modes of potential configurations of balance stability/instability. Here we examine the self-organization properties of postural coordination as revealed in a dynamic balance task with a moving platform. We scaled a control parameter (platform frequency) to investigate the evolving nature of the coupled oscillator dynamics between center of mass (CoM) and platform. Recurrent map measures were used to reveal whether episodic postural control strategies exist that can be scaled by systematically changing the magnitude of platform motion. The findings showed that at higher platform frequencies (1.2 Hz), the CoM-Platform coupling was less deterministic than lower platform frequencies and evolved to intermittent postural control strategies that oscillated between periodic-chaotic transitions to maintain upright postural balance. Collectively, the recurrence map measures indicated that quasi-static postural attractor states were progressively emerging to the changing task constraints of platform frequency in the maintenance of postural stability. It appears that several dynamic modes of intermittent coupling in postural control can interchangeably co-exist and are expressed as a function of the control parameter of platform frequency.

Using recurrence plots for the analysis of the nonlinear dynamical response of iron passivation-corrosion processes

Recurrence plots (RPs) and recurrence quantification analysis (RQA) are used in this work to study different nonlinear dynamical regimes emerging in an electrochemical system, namely, the electrodissolution-passivation of iron in chloride-containing sulfuric acid solutions. Current oscillations at different applied potentials and chloride concentrations exhibit bifurcations from periodic to complex (bursting) periodic and aperiodic or chaotic behaviors, associated with different dissolution states of iron. The clarification of these transitions is essential to understand the type of corrosion (uniform or localized) taking place as well as the underlying mechanisms governing the stability of the metal. The RQA reveals that the predictability of the chloride-perturbed Fe|0.75M H₂SO₄ system strongly depends on the chloride concentration and the applied potential. At relatively low chloride concentrations, RQA measures, based on vertical and diagonal structures in RPs, display a decrease upon the breakdown of the passivity on iron and the initiation of localized corrosion (pitting). Phases of pitting corrosion (propagation/growth and unstable pitting) that followed pit initiation are discerned by keen changes of complexity measures upon varying the applied potential. At higher chloride concentrations, the evolution of RQA measures with the potential signifies a transition from the passive-active state dissolution to the polishing state dissolution of iron inside pits. The increase of the applied potential at late stages of pitting corrosion increases the nonlinear correlations and thus the complexity of the system decreases, which corroborates the RQA.

Analysis of diagonals in cross recurrence plots between heart rate and systolic blood pressure during supine position and active standing in healthy adults

The inter beat interval (IBI) duration and systolic blood pressure (SBP) are cardiovascular variables related through several feedback mechanisms. We propose the analysis of diagonal lines in cross recurrence plots (CRPs) from IBI and SBP embedded within the same phase space to identify events where trajectories of both variables concur. The aim of the study was to describe the relationship between IBI and SBP of healthy subjects using CRP and diagonal analysis during baseline condition-supine position (SP)-and how the relationship changes during the physiological stress of active standing (AS). IBI and SBP time series were obtained from continuous blood pressure recordings during SP and AS (15 min each) in 19 young healthy subjects. IBI and SBP time series were embedded within a five-dimensional phase space using an embedding delay estimated from cross correlation between IBI and SBP. During SP, mean CRP showed high determinism (≥85%) and also brief but repeated events where both variables stay within a reduced space. Most quantitative recurrences analysis indexes of CRP increased significantly (p < 0.05) during AS. CRP analysis showed short diagonals indicating a very strong deterministic relationship between IBI and SBP with intermittent unlocking periods. The strength of IBI and SBP relationship increased during the physiological stress of AS. The CRP method allowed a rigorous quantitative description of the deterministic association between these two variables. Diagonal lines were intermittent and not always parallel, showing that there is not a defined and unique rhythm. This suggests the activation of different influences at different times and with different precedence between the heart rate and blood pressure in response to AS.

Cardiorespiratory coupling in young healthy subjects

OBJECTIVE

To quantify the presence of cardiorespiratory interaction in a group of 41 healthy subjects performing a subset of the Ewing test battery.

APPROACH

We measure the empirical distribution of the cardiorespiratory coupling time (RI), defined as the time from inspiration onset to R peaks in the ECG. The study protocol is a subset of the Ewing test battery. The respiratory function was measured with a thoracic belt and heart rate was obtained from a two channel ECG measurement. Both series of fiducial points were determined using custom software. Additionally, we determine the presence of cardiorespiratory coupling (CRC) and cardiorespiratory interaction (CRI) using Shannon entropy, synchrograms and coordigrams.

MAIN RESULTS

We observe that the RI distribution is asymmetric and nonuniform. These features are a manifestation of the causal relation between heart action and respiration. The preceding R peak strongly affects a position of inspiration onset. From the asymmetry of the RI distribution we conclude that this relation is stronger than the relation between inspiration onset and the following R peak. We use a suitable choice of surrogate data to prove that the result cannot be falsified. We observe a dual structure of the RI histograms, which may be related to the respiratory rhythmogenesis. We compare the sensitivity of RI histograms with other measures of CRI and CRC. In 46% of subjects, CRC appears in at least one stage of the examination, most often in resting states. In states of increased stress-orthostasis or physical (exercise)-the strength of coupling is visibly diminished. The nonuniform structure of the RI histogram is more sensitive to the presence of CRI than synchrograms or coordigrams are, as is well visible in the group averages. We also refer to the question of the most proper mathematical description of cardiorespiratory dynamics (phase domain or time domain). Finally, we formulate the hypothesis that the arterial blood pressure is a common driver of cardiac and respiratory rhythms.

SIGNIFICANCE

Analysis of the asymmetry of RI histograms is an interesting and sensitive method to study cardiorespiratory interaction and autonomic balance, in order to assess physical and mental health. The dual structure of the RI histograms which we have observed suggests the possible presence of a twofold mechanism for respiratory rhythmogenesis, as proposed by Galletly and Larsen.

Recurrence analysis of ant activity patterns

In this study, we used recurrence quantification analysis (RQA) and recurrence plots (RPs) to compare the movement activity of individual workers of three ant species, as well as a gregarious beetle species. RQA and RPs quantify the number and duration of recurrences of a dynamical system, including a detailed quantification of signals that could be stochastic, deterministic, or both. First, we found substantial differences between the activity dynamics of beetles and ants, with the results suggesting that the beetles have quasi-periodic dynamics and the ants do not. Second, workers from different ant species varied with respect to their dynamics, presenting degrees of predictability as well as stochastic signals. Finally, differences were found among minor and major caste of the same (dimorphic) ant species. Our results underscore the potential of RQA and RPs in the analysis of complex behavioral patterns, as well as in general inferences on animal behavior and other biological phenomena.