Multiscale analysis of short term heart beat interval, arterial blood pressure, and instantaneous lung volume time series

A framework based on the information domain to measure coupling changes in electrophysiological signals

Objectives.In this paper, the features of physiological signals of healthy dataset are extracted using the linear and non-linear techniques, and a comparison has been made on healthy young and old subjects to study the aging and gender-related changes in the contribution of Heart Rate (HR), Blood Pressure (BP), and Respiration (RESP).Methods. To quantify the coupling changes in cardiovascular, cardiorespiratory, and vasculorespiratory complexity, an information domain approach based on compensated transfer entropy (cTE) is proposed.Result. The results show that there is a substantial decrease in the flow of information from BP tro the time interval between successive R-peaks (RR) and from RR to BP. There is also a significant decrease in the flow of information from RESP to BP and RESP to RR but there is no significant change in the information flow from BP to RESP and RR to RESP.Conclusion. We have done linear and non-linear analysis on the healthy datasets of young and old subjects. As already existed techniques lacks in studying complex behaviours of electrophysiological signals so to overcome these limitations, we have proposed compensated transfer entropy (cTE). We conducted an investigation to determine the degree to which recordings of RESP, BP, and HR can be utilized to predict changes in the other parameters. Specifically, the proposed analysis examined the relationship between these variables and assessed their consistency across different age groups and genders. By analyzing the data, we aimed to gain insights into the interdependencies and predictive potential of these physiological measures in relation to each other.

The complexity analysis of cerebral oxygen saturation during pneumoperitoneum and Trendelenburg position: a retrospective cohort study

BACKGROUND

The human brain is a highly complex and nonlinear system, nonlinear complexity measures such as approximate entropy (ApEn) and sample entropy (SampEn) can better reveal characteristics of brain dynamics. However, no studies report complexity of perioperative physiological signals to reveal how brain complexity associates with age, varies along with the development of surgery and postoperative neurological complications.

AIM

This study examined the complexity of intraoperative regional cerebral oxygen saturation (rSO₂), aiming to reveal brain dynamics during surgery.

METHODS

This retrospective cohort study enrolled patients who scheduled for robot-assisted urological surgery. Intraoperative rSO₂ was continuously monitored throughout the surgery. Postoperative delirium (POD) was diagnosed by the Confusion Assessment Method. ApEn and SampEn were used to characterize the complexity of rSO₂. Pearson correlation coefficients were used to measure the correlation between complexity of rSO₂ and age. The association between complexity of rSO₂ and POD was examined using T tests.

RESULTS

A total of 68 patients (mean [SD] age, 63.0 (12.0) years; 47 (69.1%) males) were include in this analysis. There was a significant reverse relationship between the complexity of rSO₂ and age (The correlation coefficients range between - 0.32 and - 0.28, all p < 0.05). Patients  ≥ 75 years showed significantly lower complexity of rSO₂ than the other two groups. Older age remained an independent factor influencing complexity of rSO₂ after adjusting for a number of covariates. Six patients (8.8%) developed POD, and POD patients had lower complexity of rSO₂ compared with non-POD patients.

CONCLUSIONS

The complexity of rSO₂ may serve as a new candidate marker of aging and POD prediction.

Longitudinal study on the effect of surgical weight loss on beat-to-beat blood pressure variability in patients undergoing bariatric surgery: a study protocol

INTRODUCTION

Alterations in linear and non-linear parameters of beat-to-beat blood pressure variability (BPV) have been shown to predict disease prognosis and distinguish between risk categories in various pathological conditions, independently of average blood pressure levels. Obesity places subjects at elevated risk of vascular diseases, including hypertension, resulting in serious cardiac, respiratory and cerebral events. However, little is known about the status of vascular dynamics in obese and morbidly obese adults.

METHODS AND ANALYSIS

In this present quasi-experimental longitudinal study, changes in beat-to-beat BPV, using continuous, non-invasive blood pressure monitoring, in obese subjects undergoing bariatric surgery are characterised. The capacity of linear and non-linear measures of BPV to detect differences between hypertensive, prehypertensive and normotensive obese subjects prebariatric and postbariatric surgery are tested. Additionally, potential correlations between beat-to-beat BPV and age, body mass index, gender and comorbidities will be investigated. In parallel, the impact of the unsteady fluctuations of beat-to-beat blood pressure on the dynamic stresses imparted by blood flow on blood vessel walls will be explored. We expect to find altered BPV profiles in hypertensive and prehypertensive subjects as compared with normotensive subjects. We also expect to see differential normalisation in BPV profiles between hypertensive, prehypertensive and normotensive subjects over time.

ETHICS AND DISSEMINATION

The study has been approved by the Institutional Review Board at the American University of Beirut (IRB ID: BIO-2018-0040). Study results will be made available to the public through publications in peer-reviewed journals and conference papers and/or presentations.

Using complexity-entropy planes to detect Parkinson's disease from short segments of haemodynamic signals

Objective. There is emerging evidence that analysing the entropy and complexity of biomedical signals can detect underlying changes in physiology which may be reflective of disease pathology. This approach can be used even when only short recordings of biomedical signals are available. This study aimed to determine whether entropy and complexity measures can detect differences between subjects with Parkinsons disease and healthy controls (HCs).Approach. A method based on a diagram of entropy versus complexity, named complexity-entropy plane, was used to re-analyse a dataset of cerebral haemodynamic signals from subjects with Parkinsons disease and HCs obtained under poikilocapnic conditions. A probability distribution for a set of ordinal patterns, designed to capture regularities in a time series, was computed from each signal under analysis. Four types of entropy and ten types of complexity measures were estimated from these distributions. Mean values of entropy and complexity were compared and their classification power was assessed by evaluating the best linear separator on the corresponding complexity-entropy planes.Main results. Few linear separators obtained significantly better classification, evaluated as the area under the receiver operating characteristic curve, than signal mean values. However, significant differences in both entropy and complexity were detected between the groups of participants.Significance. Measures of entropy and complexity were able to detect differences between healthy volunteers and subjects with Parkinson's disease, in poikilocapnic conditions, even though only short recordings were available for analysis. Further work is needed to refine this promising approach, and to help understand the findings in the context of specific pathophysiological changes.

Age induced interactions between heart rate variability and systolic blood pressure variability using approximate entropy and recurrence quantification analysis: a multiscale cross correlation analysis

The purpose of this study is to study the effect of age on the correlation between heart rate variability (HRV) and blood pressure variability (BPV). To meet this end, multi-scale cross correlation (CC) analysis of HRV and systolic blood pressure variability (SBPV) was performed. The Approximate Entropy (ApEn) and Recurrence Quantification Analysis (RQA) derived indices, calculated from RR interval series (RRi) and systolic blood pressure (SBP) series at multiple temporal scales, are the basis of this CC analysis. For the computation of ApEn and RQA indices, the tolerance threshold (r) is chosen by either: (i) selecting any arbitrary value (0.2) within the recommended range (0.1-0.25) times standard deviation (SD) of time series, and (ii) taking the 'r' (r_opt) corresponding to maximum ApEn (ApEn_max) as tolerance threshold. It is found that (i) at each time scale (τ), a lower SD is observed when indices are computed using r_opt than [Formula: see text] (r_0.2), for RRi as well as SBP series, (ii) descriptive indices of RRi are found significant (p < 0.05) at all scales (τ), however for SBP, these are found insignificant (p > 0.05) at most of the scales, (iii) CC values of descriptive statistics viz., mean and SD are not significant (p > 0.05) irrespective of τ, barring τ = 1, (iv) CC values of ApEn and RQA indices, found using r_opt, are found significant (p < 0.05) and provide enhanced stratification at τ = 1, 2 and 3, whereas this significant correlation and strong classification is missing for indices calculated using r_0.2, and (v) Lastly as τ increases, ApEn and RQA indices, computed with r_opt, reverse their trend but manage to provide significant difference in elder and younger subjects. It is concluded that HRV and SBPV interactions gets altered with age. Descriptive indicators however are not enough to capture these changes. These complex interactions can only be deciphered using complexity-based methods such as approximate entropy and that too at the multiple scale level.

Beat-to-beat blood pressure variability: an early predictor of disease and cardiovascular risk

Blood pressure (BP) varies on the long, short and very-short term. Owing to the hidden physiological and pathological information present in BP time-series, increasing interest has been given to the study of continuous, beat-to-beat BP variability (BPV) using invasive and noninvasive methods. Different linear and nonlinear parameters of variability are employed in the characterization of BP signals in health and disease. Although linear parameters of beat-to-beat BPV are mainly measures of dispersion, such as standard deviation (SD), nonlinear parameters of BPV quantify the degree of complexity/irregularity- using measures of entropy or self-similarity/correlation. In this review, we summarize the value of linear and nonlinear parameters in reflecting different information about the pathophysiology of changes in beat-to-beat BPV independent of or superior to mean BP. We then provide a comparison of the relative power of linear and nonlinear parameters of beat-to-beat BPV in detecting early and subtle differences in various states. The practical advantage and utility of beat-to-beat BPV monitoring support its incorporation into routine clinical practices.

Multiscale Entropy Analysis: Application to Cardio-Respiratory Coupling

It is known that in pathological conditions, physiological systems develop changes in the multiscale properties of physiological signals. However, in real life, little is known about how changes in the function of one of the two coupled physiological systems induce changes in function of the other one, especially on their multiscale behavior. Hence, in this work we aimed to examine the complexity of cardio-respiratory coupled systems control using multiscale entropy (MSE) analysis of cardiac intervals MSE (RR), respiratory time series MSE (Resp), and synchrony of these rhythms by cross multiscale entropy (CMSE) analysis, in the heart failure (HF) patients and healthy subjects. We analyzed 20 min of synchronously recorded RR intervals and respiratory signal during relaxation in the supine position in 42 heart failure patients and 14 control healthy subjects. Heart failure group was divided into three subgroups, according to the RR interval time series characteristics (atrial fibrillation (HFAF), sinus rhythm (HFSin), and sinus rhythm with ventricular extrasystoles (HFVES)). Compared with healthy control subjects, alterations in respiratory signal properties were observed in patients from the HFSin and HFVES groups. Further, mean MSE curves of RR intervals and respiratory signal were not statistically different only in the HFSin group (p = 0.43). The level of synchrony between these time series was significantly higher in HFSin and HFVES patients than in control subjects and HFAF patients (p < 0.01). In conclusion, depending on the specific pathologies, primary alterations in the regularity of cardiac rhythm resulted in changes in the regularity of the respiratory rhythm, as well as in the level of their asynchrony.

MULTISCALE ENTROPY AND MULTISCALE TIME IRREVERSIBILITY ANALYSIS OF RR TIME SERIES DEPENDING ON AMBIENT TEMPERATURE

Purpose: The main aim of this paper is to study the influence of temperature on multiscale entropy (MSE) and multiscale time irreversibility (MTI) through the use of short-term measurements. Methods: A total of 12 physically active, healthy, and nonsmoker individuals ([Formula: see text] years old; [Formula: see text][Formula: see text]cm of height; and [Formula: see text][Formula: see text]kg of body mass) voluntarily participated in this study. Two beat-to-beat recordings of 15[Formula: see text]min length were performed on every participant, one under hot conditions ([Formula: see text]C) and the other assessment under cool conditions ([Formula: see text]C). The order of these two assessments was randomly assigned. Multiscale sample entropy and MTI were assessed in every measurement through 10 scales. Results: Entropy was significantly higher under hot conditions ([Formula: see text]) from the fifth scale compared to cool conditions. On the contrary, MTI values were significantly lower under hotter conditions ([Formula: see text]). Conclusions: The study of MSE and time irreversibility of short RR measurements presents consistent and reliable data. Moreover, exposures to hot conditions provoke an increment of interbeat complexity throughout larger scales and a decrease in the MTI in a healthy population.

Suppressing the Influence of Ectopic Beats by Applying a Physical Threshold-Based Sample Entropy

Sample entropy (SampEn) is widely used for electrocardiogram (ECG) signal analysis to quantify the inherent complexity or regularity of RR interval time series (i.e., heart rate variability (HRV)), with the hypothesis that RR interval time series in pathological conditions output lower SampEn values. However, ectopic beats can significantly influence the entropy values, resulting in difficulty in distinguishing the pathological situation from normal situations. Although a theoretical operation is to exclude the ectopic intervals during HRV analysis, it is not easy to identify all of them in practice, especially for the dynamic ECG signal. Thus, it is important to suppress the influence of ectopic beats on entropy results, i.e., to improve the robustness and stability of entropy measurement for ectopic beats-inserted RR interval time series. In this study, we introduced a physical threshold-based SampEn method, and tested its ability to suppress the influence of ectopic beats for HRV analysis. An experiment on the PhysioNet/MIT RR Interval Databases showed that the SampEn use physical meaning threshold has better performance not only for different data types (normal sinus rhythm (NSR) or congestive heart failure (CHF) recordings), but also for different types of ectopic beat (atrial beats, ventricular beats or both), indicating that using a physical meaning threshold makes SampEn become more consistent and stable.

Autonomic complexity and emotion (dys-)regulation in early childhood across high- and low-risk contexts

Developing the ability to regulate one's emotions in accordance with contextual demands (i.e., emotion regulation) is a central developmental task of early childhood. These processes are supported by the engagement of the autonomic nervous system (ANS), a physiological hub of a vast network tasked with dynamically integrating real-time experiential inputs with internal motivational and goal states. To date, much of what is known about the ANS and emotion regulation has been based on measures of respiratory sinus arrhythmia, a cardiac indicator of parasympathetic activity. In the present study, we draw from dynamical systems models to introduce two nonlinear indices of cardiac complexity (fractality and sample entropy) as potential indicators of these broader ANS dynamics. Using data from a stratified sample of preschoolers living in high- (i.e., emergency homeless shelter) and low-risk contexts (N = 115), we show that, in conjunction with respiratory sinus arrhythmia, these nonlinear indices may help to clarify important differences in the behavioral manifestations of emotion regulation. In particular, our results suggest that cardiac complexity may be especially useful for discerning active, effortful emotion regulation from less effortful regulation and dysregulation.

Information-Domain Analysis of Cardiovascular Complexity: Night and Day Modulations of Entropy and the Effects of Hypertension

Multiscale entropy (MSE) provides information-domain measures of the systems’ complexity. The increasing interest in MSE of the cardiovascular system lies in the possibility of detecting interactions with other regulatory systems, as higher neural networks. However, most of the MSE studies considered the heart-rate (HR) series only and a limited number of scales: actually, an integrated approach investigating HR and blood-pressure (BP) entropies and cross-entropy over the range of scales of traditional spectral analyses is missing. Therefore, we aim to highlight influences of higher brain centers and of the autonomic control on multiscale entropy and cross-entropy of HR and BP over a broad range of scales, by comparing different behavioral states over 24 h and by evaluating the influence of hypertension, which reduces the autonomic control of BP. From 24-h BP recordings in eight normotensive and eight hypertensive participants, we selected subperiods during daytime activities and nighttime sleep. In each subperiod, we derived a series of 16,384 consecutive beats for systolic BP (SBP), diastolic BP (DBP), and pulse interval (PI). We applied a modified MSE method to obtain robust estimates up to time scales of 334 s, covering the traditional frequency bands of spectral analysis, for three embedding dimensions and compared groups (rank-sum test) and conditions (signed-rank test) at each scale. Results demonstrated night-and-day differences at scales associable with modulations in vagal activity, in respiratory mechanics, and in local vascular regulation, and reduced SBP-PI cross-entropy in hypertension, possibly representing a loss of complexity due to an impaired baroreflex sensitivity.

Complexity-Based Measures of Heart Rate Dynamics in Older Adults Following Long- and Short-Term Tai Chi Training: Cross-sectional and Randomized Trial Studies

Measures characterizing the complexity of heart rate (HR) dynamics have been informative in predicting age- and disease-related decline in cardiovascular health, but few studies have evaluated whether mind-body exercise can impact HR complexity. This study evaluated the effects of long-term Tai Chi (TC) practice on the complexity of HR dynamics using an observational comparison of TC experts and age- and gender-matched TC-naïve individuals. Shorter-term effects of TC were assessed by randomly assigning TC-naïve participants to either TC group to receive six months of TC training or to a waitlist control group. 23 TC experts (age = 63.3 ± 8.0 y; 24.6 ± 12.0 y TC experience) and 52 TC-naïve (age = 64.3 ± 7.7 y) were enrolled. In cross-sectional analyses, TC experts had a higher overall complexity index (CI, p = 0.004) and higher entropy at multiple individual time scales (p < 0.05); these findings persisted in models accounting for age, gender, body mass index (BMI), and physical activity levels. Longitudinal changes in complexity index did not differ significantly following random assignment to six months of TC vs. a waitlist control; however, within the TC group, complexity at select time scales showed statistically non-significant trends toward increases. Our study supports that longer-term TC mind-body training may be associated with increased complexity of HR dynamics.

A study for multiscale information transfer measures based on conditional mutual information

As the big data science develops, efficient methods are demanded for various data analysis. Granger causality provides the prime model for quantifying causal interactions. However, this theoretic model does not meet the requirement for real-world data analysis, because real-world time series are diverse whose models are usually unknown. Therefore, model-free measures such as information transfer measures are strongly desired. Here, we propose the multi-scale extension of conditional mutual information measures using MORLET wavelet, which are named the WM and WPM. The proposed measures are computational efficient and interpret information transfer by multi-scales. We use both synthetic data and real-world examples to demonstrate the efficiency of the new methods. The results of the new methods are robust and reliable. Via the simulation studies, we found the new methods outperform the wavelet extension of transfer entropy (WTE) in both computational efficiency and accuracy. The features and properties of the proposed measures are also discussed.

Refined Multiscale Fuzzy Entropy to Analyse Post-Exercise Cardiovascular Response in Older Adults With Orthostatic Intolerance

Orthostatic intolerance syndrome occurs when the autonomic nervous system is incapacitated and fails to respond to the demands associated with the upright position. Assessing this syndrome among the elderly population is important in order to prevent falls. However, this problem is still challenging. The goal of this work was to determine the relationship between orthostatic intolerance (OI) and the cardiovascular response to exercise from the analysis of heart rate and blood pressure. More specifically, the behavior of these cardiovascular variables was evaluated in terms of refined composite multiscale fuzzy entropy (RCMFE), measured at different scales. The dataset was composed by 65 older subjects, 44.6% (n = 29) were OI symptomatic and 55.4% (n = 36) were not. Insignificant differences were found in age and gender between symptomatic and asymptomatic OI participants. When heart rate was evaluated, higher differences between groups were observed during the recovery period immediately after exercise. With respect to the blood pressure and other hemodynamic parameters, most significant results were obtained in the post-exercise stage. In any case, the symptomatic OI group exhibited higher irregularity in the measured parameters, as higher RCMFE levels in all time scales were obtained. This information could be very helpful for a better understanding of cardiovascular instability, as well as to recognize risk factors for falls and impairment of functional status.

Univariate and multivariate conditional entropy measures for the characterization of short-term cardiovascular complexity under physiological stress

OBJECTIVE

A defining feature of physiological systems under the neuroautonomic regulation is their dynamical complexity. The most common approach to assess physiological complexity from short-term recordings, i.e. to compute the rate of entropy generation of an individual system by means of measures of conditional entropy (CE), does not consider that complexity may change when the investigated system is part of a network of physiological interactions. This study aims at extending the concept of short-term complexity towards the perspective of network physiology, defining multivariate CE measures whereby multiple physiological processes are accounted for in the computation of entropy rates.

APPROACH

Univariate and multivariate CE measures are computed using state-of-the-art methods for entropy estimation and applied to time series of heart period (H), systolic (S) and diastolic (D) arterial pressure, and respiration (R) variability measured in healthy subjects monitored in a resting state and during conditions of postural and mental stress.

MAIN RESULTS

Compared with the traditional univariate metric of short-term complexity, multivariate measures provide additional information with plausible physiological interpretation, such as (i) the dampening of respiratory sinus arrhythmia and activation of the baroreflex control during postural stress; (ii) the increased complexity of heart period and blood pressure variability during mental stress, reflecting the effect of respiratory influences and upper cortical centers; (iii) the strong influence of D on S, mediated by left ventricular ejection fraction and vascular properties; (iv) the role of H in reducing the complexity of D, related to cardiac run-off effects; and (v) the unidirectional role of R in influencing cardiovascular variability.

SIGNIFICANCE

Our results document the importance of employing a network perspective in the evaluation of the short-term complexity of cardiovascular and respiratory dynamics across different physiological states.

Multiscale sample entropy of heart rate and blood pressure: Methodological aspects

The entropy of heart rate variability is one of the main features characterizing the complexity of the cardiovascular system. In order to take into account the multiscale nature of cardiovascular regulation, it was proposed to evaluate entropy with a multiscale approach, based on the estimation of Sample Entropy on progressively coarse-grained series (Multiscale Sample Entropy, MSE). Aim of this work is to investigate two methodological aspects related to MSE of cardiovascular signals. The first aspect regards the tolerance below which a couple of points are considered similar in a given embedding dimension, in particular how the way the tolerance is set at each level of coarse graining influences the MSE estimates. The second aspect regards whether heart rate and blood pressure (BP) signals are characterized by different MSE structures.To investigate these aspects, we analyzed 65 continuous BP recordings of more than 90-minute duration in healthy volunteers sitting at rest, and applied MSE estimators to beat-by-beat series of systolic BP, diastolic BP and pulse interval (inverse of heart rate). Results indicate that the way the tolerance is set during coarse graining influences substantially the MSE profile of cardiovascular signals, modifying the relative level of their unpredictability.

Can Tai Chi training impact fractal stride time dynamics, an index of gait health, in older adults? Cross-sectional and randomized trial studies

Purpose

To determine if Tai Chi (TC) has an impact on long-range correlations and fractal-like scaling in gait stride time dynamics, previously shown to be associated with aging, neurodegenerative disease, and fall risk.

Methods

Using Detrended Fluctuation Analysis (DFA), this study evaluated the impact of TC mind-body exercise training on stride time dynamics assessed during 10 minute bouts of overground walking. A hybrid study design investigated long-term effects of TC via a cross-sectional comparison of 27 TC experts (24.5 ± 11.8 yrs experience) and 60 age- and gender matched TC-naïve older adults (50–70 yrs). Shorter-term effects of TC were assessed by randomly allocating TC-naïve participants to either 6 months of TC training or to a waitlist control. The alpha (α) long-range scaling coefficient derived from DFA and gait speed were evaluated as outcomes.

Results

Cross-sectional comparisons using confounder adjusted linear models suggest that TC experts exhibited significantly greater long-range scaling of gait stride time dynamics compared with TC-naïve adults. Longitudinal random-slopes with shared baseline models accounting for multiple confounders suggest that the effects of shorter-term TC training on gait dynamics were not statistically significant, but trended in the same direction as longer-term effects although effect sizes were very small. In contrast, gait speed was unaffected in both cross-sectional and longitudinal comparisons.

Conclusion

These preliminary findings suggest that fractal-like measures of gait health may be sufficiently precise to capture the positive effects of exercise in the form of Tai Chi, thus warranting further investigation. These results motivate larger and longer-duration trials, in both healthy and health-challenged populations, to further evaluate the potential of Tai Chi to restore age-related declines in gait dynamics.

Trial registration

The randomized trial component of this study was registered at ClinicalTrials.gov (NCT01340365).

Complexity of brain signals is associated with outcome in preterm infants

A characteristic feature of complex healthy biological systems is the ability to react and adapt to minute changes in the environment. This 'complexity' manifests itself in highly irregular patterns of various physiological measurements. Here, we apply Multiscale Entropy (MSE) analysis to assess the complexity of systemic and cerebral near-infrared spectroscopy (NIRS) signals in a cohort of 61 critically ill preterm infants born at median (range) gestational age of 26 (23-31) weeks, before 24 h of life. We further correlate the complexity of these parameters with brain injury and mortality. Lower complexity index (CoI) of oxygenated haemoglobin (HbO₂), deoxygenated haemoglobin (Hb) and tissue oxygenation index (TOI) were observed in those infants who developed intraventricular haemorrhage (IVH) compared to those who did not (P = 0.002, P = 0.010 and P = 0.038, respectively). Mean CoI of HbO₂, Hb and total haemoglobin index (THI) were lower in those infants who died compared to those who survived (P = 0.012, P = 0.004 and P = 0.003, respectively). CoI-HbO₂ was an independent predictor of IVH (P = 0.010). Decreased complexity of brain signals was associated with mortality and brain injury. Measurement of brain signal complexity in preterm infants is feasible and could represent a significant advance in the brain-oriented care.

Pattern Analysis of Oxygen Saturation Variability in Healthy Individuals: Entropy of Pulse Oximetry Signals Carries Information about Mean Oxygen Saturation

Pulse oximetry is routinely used for monitoring patients' oxygen saturation levels with little regard to the variability of this physiological variable. There are few published studies on oxygen saturation variability (OSV), with none describing the variability and its pattern in a healthy adult population. The aim of this study was to characterize the pattern of OSV using several parameters; the regularity (sample entropy analysis), the self-similarity [detrended fluctuation analysis (DFA)] and the complexity [multiscale entropy (MSE) analysis]. Secondly, to determine if there were any changes that occur with age. The study population consisted of 36 individuals. The “young” population consisted of 20 individuals [Mean (±1 SD) age = 21.0 (±1.36 years)] and the “old” population consisted of 16 individuals [Mean (±1 SD) age = 50.0 (±10.4 years)]. Through DFA analysis, OSV was shown to exhibit fractal-like patterns. The sample entropy revealed the variability to be more regular than heart rate variability and respiratory rate variability. There was also a significant inverse correlation between mean oxygen saturation and sample entropy in healthy individuals. Additionally, the MSE analysis described a complex fluctuation pattern, which was reduced with age (p < 0.05). These findings suggest partial “uncoupling” of the cardio-respiratory control system that occurs with aging. Overall, this study has characterized OSV using pre-existing tools. We have showed that entropy analysis of pulse oximetry signals carries information about body oxygenation. This may have the potential to be used in clinical practice to detect differences in diseased patient subsets.

Entropy measures, entropy estimators, and their performance in quantifying complex dynamics: Effects of artifacts, nonstationarity, and long-range correlations

Entropy measures are widely applied to quantify the complexity of dynamical systems in diverse fields. However, the practical application of entropy methods is challenging, due to the variety of entropy measures and estimators and the complexity of real-world time series, including nonstationarities and long-range correlations (LRC). We conduct a systematic study on the performance, bias, and limitations of three basic measures (entropy, conditional entropy, information storage) and three traditionally used estimators (linear, kernel, nearest neighbor). We investigate the dependence of entropy measures on estimator- and process-specific parameters, and we show the effects of three types of nonstationarities due to artifacts (trends, spikes, local variance change) in simulations of stochastic autoregressive processes. We also analyze the impact of LRC on the theoretical and estimated values of entropy measures. Finally, we apply entropy methods on heart rate variability data from subjects in different physiological states and clinical conditions. We find that entropy measures can only differentiate changes of specific types in cardiac dynamics and that appropriate preprocessing is vital for correct estimation and interpretation. Demonstrating the limitations of entropy methods and shedding light on how to mitigate bias and provide correct interpretations of results, this work can serve as a comprehensive reference for the application of entropy methods and the evaluation of existing studies.

Refined multiscale fuzzy entropy based on standard deviation for biomedical signal analysis

Multiscale entropy (MSE) has been a prevalent algorithm to quantify the complexity of biomedical time series. Recent developments in the field have tried to alleviate the problem of undefined MSE values for short signals. Moreover, there has been a recent interest in using other statistical moments than the mean, i.e., variance, in the coarse-graining step of the MSE. Building on these trends, here we introduce the so-called refined composite multiscale fuzzy entropy based on the standard deviation (RCMFE_σ) and mean (RCMFE_μ) to quantify the dynamical properties of spread and mean, respectively, over multiple time scales. We demonstrate the dependency of the RCMFE_σ and RCMFE_μ, in comparison with other multiscale approaches, on several straightforward signal processing concepts using a set of synthetic signals. The results evidenced that the RCMFE_σ and RCMFE_μ values are more stable and reliable than the classical multiscale entropy ones. We also inspect the ability of using the standard deviation as well as the mean in the coarse-graining process using magnetoencephalograms in Alzheimer’s disease and publicly available electroencephalograms recorded from focal and non-focal areas in epilepsy. Our results indicated that when the RCMFE_μ cannot distinguish different types of dynamics of a particular time series at some scale factors, the RCMFE_σ may do so, and vice versa. The results showed that RCMFE_σ-based features lead to higher classification accuracies in comparison with the RCMFE_μ-based ones. We also made freely available all the Matlab codes used in this study at 10.7488/ds/1477.

The Analysis of the Influence of Odorant's Complexity on Fractal Dynamics of Human Respiration

One of the major challenges in olfaction research is to relate the structural features of the odorants to different features of olfactory system. However, no relationship has been yet discovered between the structure of the olfactory stimulus, and the structure of respiratory signal. This study reveals the plasticity of human respiratory signal in relation to 'complex' olfactory stimulus (odorant). We demonstrated that fractal temporal structure of respiration dynamics shifts towards the properties of the odorants used. The results show for the first time that more structurally complex a monomolecular odorant will result in less fractal respiratory signal. On the other hand, odorant with higher entropy will result the respiratory signal with lower entropy. The capability observed in this research can be further investigated and applied for treatment of patients with different respiratory diseases.

Optimal Selection of Threshold Value 'r' for Refined Multiscale Entropy

Refined multiscale entropy (RMSE) technique was introduced to evaluate complexity of a time series over multiple scale factors 't'. Here threshold value 'r' is updated as 0.15 times SD of filtered scaled time series. The use of fixed threshold value 'r' in RMSE sometimes assigns very close resembling entropy values to certain time series at certain temporal scale factors and is unable to distinguish different time series optimally. The present study aims to evaluate RMSE technique by varying threshold value 'r' from 0.05 to 0.25 times SD of filtered scaled time series and finding optimal 'r' values for each scale factor at which different time series can be distinguished more effectively. The proposed RMSE was used to evaluate over HRV time series of normal sinus rhythm subjects, patients suffering from sudden cardiac death, congestive heart failure, healthy adult male, healthy adult female and mid-aged female groups as well as over synthetic simulated database for different datalengths 'N' of 3000, 3500 and 4000. The proposed RMSE results in improved discrimination among different time series. To enhance the computational capability, empirical mathematical equations have been formulated for optimal selection of threshold values 'r' as a function of SD of filtered scaled time series and datalength 'N' for each scale factor 't'.

Filter-based multiscale entropy analysis of complex physiological time series

Multiscale entropy (MSE) has been widely and successfully used in analyzing the complexity of physiological time series. We reinterpret the averaging process in MSE as filtering a time series by a filter of a piecewise constant type. From this viewpoint, we introduce filter-based multiscale entropy (FME), which filters a time series to generate multiple frequency components, and then we compute the blockwise entropy of the resulting components. By choosing filters adapted to the feature of a given time series, FME is able to better capture its multiscale information and to provide more flexibility for studying its complexity. Motivated by the heart rate turbulence theory, which suggests that the human heartbeat interval time series can be described in piecewise linear patterns, we propose piecewise linear filter multiscale entropy (PLFME) for the complexity analysis of the time series. Numerical results from PLFME are more robust to data of various lengths than those from MSE. The numerical performance of the adaptive piecewise constant filter multiscale entropy without prior information is comparable to that of PLFME, whose design takes prior information into account.

Physiologic complexity and aging: implications for physical function and rehabilitation

The dynamics of most healthy physiological processes are complex, in that they are comprised of fluctuations with information-rich structure correlated over multiple temporospatial scales. Lipsitz and Goldberger (1992) first proposed that the aging process may be characterized by a progressive loss of physiologic complexity. We contend that this loss of complexity results in functional decline of the organism by diminishing the range of available, adaptive responses to the innumerable stressors of everyday life. From this relationship, it follows that rehabilitative interventions may be optimized by targeting the complex dynamics of human physiology, and by quantifying their effects using tools derived from complex systems theory. Here, we first discuss several caveats that one must consider when examining the functional and rehabilitative implications of physiologic complexity. We then review available evidence regarding the relationship between physiologic complexity and system functionality, as well as the potential for interventions to restore the complex dynamics that characterize healthy physiological function.

Reduced complexity of intracranial pressure observed in short time series of intracranial hypertension following traumatic brain injury in adults

Physiological parameters, such as intracranial pressure (ICP), are regulated by interconnected feedback loops, resulting in a complex time course. According to the decomplexification theory, disease is characterised by a loss of feedback loops resulting in a reduced complexity of the time course of physiological parameters. We hypothesized that complexity of the ICP time series is decreased during periods of intracranial hypertension (IHT) following adult traumatic brain injury. In an observational retrospective cohort study, ICP was continuously monitored using intraparenchymally implanted probes and stored using ICM + -software. Periods of IHT (ICP > 25 mmHg for at least 1,024 s), were compared with preceding periods of intracranial normotension (ICP < 20 mmHg) and analysed at 1 s-intervals. ICP data (length = 1,024 s) were normalised (mean = 0, SD = 1) and complexity was estimated using the scaling exponent α (as derived from detrended fluctuation analysis), sample entropy (SampEn, m = 1, r = 0.2 × SD) and multiscale entropy. 344 episodes were analysed in 22 patients. During IHT (ICP = 31.7 ± 7.8 mmHg, mean ± SD), α was significantly elevated (α = 1.02 ± 0.22, p < 0.001) and SampEn significantly reduced (SampEn = 1.45 ± 0.46, p = 0.004) as compared to before IHT (ICP = 15.7 ± 3.2 mmHg, α = 0.81 ± 0.14, SampEn = 1.81 ± 0.24). In addition, MSE revealed a significantly (p < 0.05) decreased entropy at scaling factors ranging from 1 to 10. Both the increase in α as well as the decrease in SampEn and MSE indicate a loss of ICP complexity. Therefore following traumatic brain injury, periods of IHT seem to be characterised by a decreased complexity of the ICP waveform.

A systems biology approach to studying Tai Chi, physiological complexity and healthy aging: design and rationale of a pragmatic randomized controlled trial

INTRODUCTION

Aging is typically associated with progressive multi-system impairment that leads to decreased physical and cognitive function and reduced adaptability to stress. Due to its capacity to characterize complex dynamics within and between physiological systems, the emerging field of complex systems biology and its array of quantitative tools show great promise for improving our understanding of aging, monitoring senescence, and providing biomarkers for evaluating novel interventions, including promising mind-body exercises, that treat age-related disease and promote healthy aging.

MATERIAL AND METHODS

An ongoing, two-arm randomized clinical trial is evaluating the potential of Tai Chi mind-body exercise to attenuate age-related loss of complexity. A total of 60 Tai Chi-naïve healthy older adults (aged 50-79) are being randomized to either six months of Tai Chi training (n=30), or to a waitlist control receiving unaltered usual medical care (n=30). Our primary outcomes are complexity-based measures of heart rate, standing postural sway and gait stride interval dynamics assessed at 3 and 6months. Multiscale entropy and detrended fluctuation analysis are used as entropy- and fractal-based measures of complexity, respectively. Secondary outcomes include measures of physical and psychological function and tests of physiological adaptability also assessed at 3 and 6months.

DISCUSSION

Results of this study may lead to novel biomarkers that help us monitor and understand the physiological processes of aging and explore the potential benefits of Tai Chi and related mind-body exercises for healthy aging.

Complexity of intracranial pressure correlates with outcome after traumatic brain injury

This study applied multiscale entropy analysis to investigate the correlation between the complexity of intracranial pressure waveform and outcome after traumatic brain injury. Intracranial pressure and arterial blood pressure waveforms were low-pass filtered to remove the respiratory and pulse components and then processed using a multiscale entropy algorithm to produce a complexity index. We identified significant differences across groups classified by the Glasgow Outcome Scale in intracranial pressure, pressure-reactivity index and complexity index of intracranial pressure (P < 0.0001; P = 0.001; P < 0.0001, respectively). Outcome was dichotomized as survival/death and also as favourable/unfavourable. The complexity index of intracranial pressure achieved the strongest statistical significance (F = 28.7; P < 0.0001 and F = 17.21; P < 0.0001, respectively) and was identified as a significant independent predictor of mortality and favourable outcome in a multivariable logistic regression model (P < 0.0001). The results of this study suggest that complexity of intracranial pressure assessed by multiscale entropy was significantly associated with outcome in patients with brain injury.

MULTISCALE ENTROPY ANALYSIS OF EEG RECORDINGS IN EPILEPTIC RATS

In this study, we investigate multiscale entropy (MSE) as a tool to evaluate the dynamic characteristics of electroencephalogram (EEG) during seizure-free, pre-seizure and seizure state, respectively, in epileptic rats. The results show that MSE method is able to reveal that EEG signals are more complex in seizure-free state than in seizure state, and can successfully distinguish among different seizure states. The classification ability of the MSE measures is tested using the linear discriminant analysis (LDA). Test results confirm that the classification accuracy of MSE method is superior to traditional single-scale entropy method. MSE method has potential in classifying the epileptic EEG signals.

Fast computation of sample entropy and approximate entropy in biomedicine

Both sample entropy and approximate entropy are measurements of complexity. The two methods have received a great deal of attention in the last few years, and have been successfully verified and applied to biomedical applications and many others. However, the algorithms proposed in the literature require O(N(2)) execution time, which is not fast enough for online applications and for applications with long data sets. To accelerate computation, the authors of the present paper have developed a new algorithm that reduces the computational time to O(N(3/2))) using O(N) storage. As biomedical data are often measured with integer-type data, the computation time can be further reduced to O(N) using O(N) storage. The execution times of the experimental results with ECG, EEG, RR, and DNA signals show a significant improvement of more than 100 times when compared with the conventional O(N(2)) method for N=80,000 (N=length of the signal). Furthermore, an adaptive version of the new algorithm has been developed to speed up the computation for short data length. Experimental results show an improvement of more than 10 times when compared with the conventional method for N>4000.

The effect of orthostatic stress on multiscale entropy of heart rate and blood pressure

Cardiovascular control acts over multiple time scales, which introduces a significant amount of complexity to heart rate and blood pressure time series. Multiscale entropy (MSE) analysis has been developed to quantify the complexity of a time series over multiple time scales. In previous studies, MSE analyses identified impaired cardiovascular control and increased cardiovascular risk in various pathological conditions. Despite the increasing acceptance of the MSE technique in clinical research, information underpinning the involvement of the autonomic nervous system in the MSE of heart rate and blood pressure is lacking. The objective of this study is to investigate the effect of orthostatic challenge on the MSE of heart rate and blood pressure variability (HRV, BPV) and the correlation between MSE (complexity measures) and traditional linear (time and frequency domain) measures. MSE analysis of HRV and BPV was performed in 28 healthy young subjects on 1000 consecutive heart beats in the supine and standing positions. Sample entropy values were assessed on scales of 1-10. We found that MSE of heart rate and blood pressure signals is sensitive to changes in autonomic balance caused by postural change from the supine to the standing position. The effect of orthostatic challenge on heart rate and blood pressure complexity depended on the time scale under investigation. Entropy values did not correlate with the mean values of heart rate and blood pressure and showed only weak correlations with linear HRV and BPV measures. In conclusion, the MSE analysis of heart rate and blood pressure provides a sensitive tool to detect changes in autonomic balance as induced by postural change.

Acute increase of complexity in the neurocardiovascular dynamics following carotid stenting

OBJECTIVE

Percutaneous carotid angioplasty and stenting (CAS) has been used to improve cerebral circulation and autoregulation. However, whether CAS ameliorates the autonomic regulatory dynamics remains unclear. This prospective study examines the neurocardiovascular dynamics following carotid stenting.

METHODS

Thirty minutes electrocardiograms were recorded at three different time points (pre-operative, 1-h post-operative, 1-day post-operative) on twelve male patients (mean age 70.8 ± 9.6 years) receiving unilateral primary CAS. The HR data were analyzed by the conventional heart rate variability (HRV) and the multiscale entropy (MSE) methods; the former associates with autonomic activities and the latter quantifies the regulatory complexity of heart beat intervals. Loss of complexity at multiple scales has been associated with decoupled regulatory network in vivo.

RESULTS

Conventional HRV indices showed no difference after CAS. Complexity indices increased significantly on scales 2-8 at 1-h and on scales 2-3 1-day post-treatment. The lower scale MSE (1-5) correlated with the frequency components of conventional HRV indices. The increased complexity could imply a restoration of the neurocardiovascular dynamics on the path to a healthier state.

CONCLUSIONS

Primary CAS can induce a recovery in the neurocardiovascular regulatory dynamics in patients with high-grade carotid stenosis.

Electrocardiogram analysis using a combination of statistical, geometric, and nonlinear heart rate variability features

OBJECTIVE

The paper addresses a common and recurring problem of electrocardiogram (ECG) classification based on heart rate variability (HRV) analysis. Current understanding of the limits of HRV analysis in diagnosing different cardiac conditions is not complete. Existing research suggests that a combination of carefully selected linear and nonlinear HRV features should significantly improve the accuracy for both binary and multiclass classification problems. The primary goal of this work is to evaluate a proposed combination of HRV features. Other explored objectives are the comparison of different machine learning algorithms in the HRV analysis and the inspection of the most suitable period T between two consecutively analyzed R-R intervals for nonlinear features.

METHODS AND MATERIAL

We extracted 11 features from 5min of R-R interval recordings: SDNN, RMSSD, pNN20, HRV triangular index (HTI), spatial filling index (SFI), correlation dimension, central tendency measure (CTM), and four approximate entropy features (ApEn1-ApEn4). Analyzed heart conditions included normal heart rhythm, arrhythmia (any), supraventricular arrhythmia, and congestive heart failure. One hundred patient records from six online databases were analyzed, 25 for each condition. Feature vectors were extracted by a platform designed for this purpose, named ECG Chaos Extractor. The vectors were then analyzed by seven clustering and classification algorithms in the Weka system: K-means, expectation maximization (EM), C4.5 decision tree, Bayesian network, artificial neural network (ANN), support vector machines (SVM) and random forest (RF). Four-class and two-class (normal vs. abnormal) classification was performed. Relevance of particular features was evaluated using 1-Rule and C4.5 decision tree in the cases of individual features classification and classification with features' pairs.

RESULTS

Average total classification accuracy obtained for top three classification methods in the two classes' case was: RF 99.7%, ANN 99.1%, SVM 98.9%. In the four classes' case the best results were: RF 99.6%, Bayesian network 99.4%, SVM 98.4%. The best overall method was RF. C4.5 decision tree was successful in the construction of useful classification rules for the two classes' case. EM and K-means showed comparable clustering results: around 50% for the four classes' case and around 75% for the two classes' case. HTI, pNN20, RMSSD, ApEn3, ApEn4 and SFI were shown to be the most relevant features. HTI in particular appears in most of the top-ranked pairs of features and is the best analyzed feature. The choice of the period T for nonlinear features was shown to be arbitrary. However, a combination of five different periods significantly improved classification accuracy, from 70% for a single period up to 99% for five periods.

CONCLUSIONS

Analysis shows that the proposed combination of 11 linear and nonlinear HRV features gives high classification accuracy when nonlinear features are extracted for five periods. The features' combination was thoroughly analyzed using several machine learning algorithms. In particular, RF algorithm proved to be highly efficient and accurate in both binary and multiclass classification of HRV records. Interpretable and useful rules were obtained with C4.5 decision tree. Further work in this area should elucidate which features should be extracted for the best classification results for specific types of cardiac disorders.

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.

Multiscale entropy analysis of EEG for assessment of post-cardiac arrest neurological recovery under hypothermia in rats

Neurological complications after cardiac arrest (CA) can be fatal. Although hypothermia has been shown to be beneficial, understanding the mechanism and establishing neurological outcomes remains challenging because effects of CA and hypothermia are not well characterized. This paper aims to analyze EEG (and the alpha-rhythms) using multiscale entropy (MSE) to demonstrate the ability of MSE in tracking changes due to hypothermia and compare MSE during early recovery with long-term neurological examinations. Ten Wistar rats, upon post-CA resuscitation, were randomly subjected to hypothermia (32 degrees C-34 degrees C, N = 5) or normothermia (36.5 degrees C-37.5 degrees C, N = 5). EEG was recorded and analyzed using MSE during seven recovery phases for each experiment: baseline, CA, and five early recovery phases (R1-R5). Postresuscitation neurological examination was performed at 6, 24, 48, and 72 h to obtain neurological deficit scores (NDSs). Results showed MSE to be a sensitive marker of changes in alpha-rhythms. Significant difference (p < 0.05) was found between the MSE for two groups during recovery, suggesting that MSE can successfully reflect temperature modulation. A comparison of short-term MSE and long-term NDS suggested that MSE could be used for predicting favorability of long-term outcome. These experiments point to the role of cortical rhythms in reporting early neurological response to ischemia and therapeutic hypothermia.