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

Combining blood pressure variability and heart rate variability to analyze the autonomic nervous function of rotenone induced Parkinson's rat model

BACKGROUND

Parkinson's patients have significant autonomic dysfunction, early detect the disorder is a major challenge. To assess the autonomic function in the rat model of rotenone induced Parkinson's disease (PD), Blood pressure and ECG signal acquisition are very important.

NEW METHOD

We used telemetry to record the electrocardiogram and blood pressure signals from awake rats, with linear and nonlinear analysis techniques calculate the heart rate variability (HRV) and blood pressure variability (BPV). we applied nonlinear analysis methods like sample entropy and detrended fluctuation analysis to analyze blood pressure signals. Particularly, this is the first attempt to apply nonlinear analysis to the blood pressure evaluate in rotenone induced PD model rat.

RESULTS

HRV in the time and frequency domains indicated sympathetic-parasympathetic imbalance in PD model rats. Linear BPV analysis didn't reflect changes in vascular function and blood pressure regulation in PD model rats. Nonlinear analysis revealed differences in BPV, with lower sample entropy results and increased detrended fluctuation analysis results in the PD group rats.

COMPARISON WITH EXISTING METHODS AND CONCLUSIONS

our experiments demonstrate the ability to evaluate autonomic dysfunction in models of Parkinson's disease by combining the analysis of BPV with HRV, consistent with autonomic impairment in PD patients. Nonlinear analysis by blood pressure signal may help in early detection of the PD. It indicates that the fluctuation of blood pressure in the rats in the rotenone model group tends to be regular and predictable, contributes to understand the PD pathophysiological mechanisms and to find strategies for early diagnosis.

Synchronization between music dynamics and heart rhythm is modulated by the musician’s emotional involvement: A single case study

In this study we evaluated heart rate variability (HRV) changes in a pianist, playing in a laboratory, to investigate whether HRV changes are guided by music temporal features or by technical difficulty and/or subjective factors (e.g., experienced effort). The pianist was equipped with a wearable telemetry device for ECG recording during the execution of 4 classical and 5 jazz pieces. From ECG we derived the RR intervals series (tachogram), and, for each piece, analyzed HRV in the time (RR, RMSSD, Stress Index) and frequency domains (Total spectral power) and performed non-linear analysis (Multiscale Entropy). We also studied the correlation (Pearson) between the time course of music volume envelope and tachogram. Results showed a general reduction of parasympathetic and an increase of sympathetic activity, with the greatest changes during the classical pieces execution, the pianist appraised as more demanding than the jazz ones. The most marked changes occurred during the most technically/emotionally demanding piece, and correlation analysis revealed a negative association between music volume envelope time course and tachogram only for this piece, suggesting a modulation of the limbic system on the synchronization between heart rhythm and music temporal features. Classical music was also associated with the increase of entropy (1st scale) with respect to rest, indicating its effectiveness in driving flexible, healthy, heart dynamics. In conclusion, HRV seems modulated not only by the music temporal features, but also by the pianist’s emotional involvement, which is greatly influenced, in a non-trivial manner, by the technical demands and musician expertise.

Optimized Multiscale Entropy Model Based on Resting-State fMRI for Appraising Cognitive Performance in Healthy Elderly

Many studies have indicated that an entropy model can capture the dynamic characteristics of resting-state functional magnetic resonance imaging (rfMRI) signals. However, there are problems of subjectivity and lack of uniform standards in the selection of model parameters relying on experience when using the entropy model to analyze rfMRI. To address this issue, an optimized multiscale entropy (MSE) model was proposed to confirm the parameters objectively. All healthy elderly volunteers were divided into two groups, namely, excellent and poor, by the scores estimated through traditional scale tests before the rfMRI scan. The parameters of the MSE model were optimized with the help of sensitivity parameters such as receiver operating characteristic (ROC) and area under the ROC curve (AUC) in a comparison study between the two groups. The brain regions with significant differences in entropy values were considered biomarkers. Their entropy values were regarded as feature vectors to use as input for the probabilistic neural network in the classification of cognitive scores. Classification accuracy of 80.05% was obtained using machine learning. These results show that the optimized MSE model can accurately select the brain regions sensitive to cognitive performance and objectively select fixed parameters for MSE. This work was expected to provide the basis for entropy to test the cognitive scores of the healthy elderly.

A Multiscale Partition-Based Kolmogorov–Sinai Entropy for the Complexity Assessment of Heartbeat Dynamics

Background: Several methods have been proposed to estimate complexity in physiological time series observed at different time scales, with a particular focus on heart rate variability (HRV) series. In this frame, while several complexity quantifiers defined in the multiscale domain have already been investigated, the effectiveness of a multiscale Kolmogorov–Sinai (K-S) entropy has not been evaluated yet for the characterization of heartbeat dynamics. Methods: The use of the algorithmic information content, which is estimated through an effective compression algorithm, is investigated to quantify multiscale partition-based K-S entropy on publicly available experimental HRV series gathered from young and elderly subjects undergoing a visual elicitation task (Fantasia). Moreover, publicly available HRV series gathered from healthy subjects, as well as patients with atrial fibrillation and congestive heart failure in unstructured conditions have been analyzed as well. Results: Elderly people are associated with a lower HRV complexity and a more predictable cardiovascular dynamics, with significantly lower partition-based K-S entropy than the young adults. Major differences between these groups occur at partitions greater than six. In case of partition cardinality greater than 5, patients with congestive heart failure show a minimal predictability, while atrial fibrillation shows a higher variability, and hence complexity, which is actually reduced by the time coarse-graining procedure. Conclusions: The proposed multiscale partition-based K-S entropy is a viable tool to investigate complex cardiovascular dynamics in different physiopathological states.

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.

Associations between Cardiovascular Signal Entropy and Cognitive Performance over Eight Years

In this study, the relationship between non-invasively measured cardiovascular signal entropy and global cognitive performance was explored in a sample of community-dwelling older adults from The Irish Longitudinal Study on Ageing (TILDA), both cross-sectionally at baseline (n = 4525; mean (SD) age: 61.9 (8.4) years; 54.1% female) and longitudinally. We hypothesised that signal disorder in the cardiovascular system, as quantified by short-length signal entropy during rest, could provide a marker for cognitive function. Global cognitive function was assessed via Mini Mental State Examination (MMSE) across five longitudinal waves (8 year period; n = 4316; mean (SD) age: 61.9 (8.4) years; 54.4% female) and the Montreal Cognitive Assessment (MOCA) across two longitudinal waves (4 year period; n = 3600; mean (SD) age: 61.7 (8.2) years; 54.1% female). Blood pressure (BP) was continuously monitored during supine rest at baseline, and sample entropy values were calculated for one-minute and five-minute sections of this data, both for time-series data interpolated at 5 Hz and beat-to-beat data. Results revealed significant associations between BP signal entropy and cognitive performance, both cross-sectionally and longitudinally. Results also suggested that as regards associations with cognitive performance, the entropy analysis approach used herein potentially outperformed more traditional cardiovascular measures such as resting heart rate and heart rate variability. The quantification of entropy in short-length BP signals could provide a clinically useful marker of the cardiovascular dysregulations that potentially underlie cognitive decline.

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.

Associations between Neurocardiovascular Signal Entropy and Physical Frailty

In this cross-sectional study, the relationship between noninvasively measured neurocardiovascular signal entropy and physical frailty was explored in a sample of community-dwelling older adults from The Irish Longitudinal Study on Ageing (TILDA). The hypothesis under investigation was that dysfunction in the neurovascular and cardiovascular systems, as quantified by short-length signal complexity during a lying-to-stand test (active stand), could provide a marker for frailty. Frailty status (i.e., "non-frail", "pre-frail", and "frail") was based on Fried's criteria (i.e., exhaustion, unexplained weight loss, weakness, slowness, and low physical activity). Approximate entropy (ApEn) and sample entropy (SampEn) were calculated during resting (lying down), active standing, and recovery phases. There was continuously measured blood pressure/heart rate data from 2645 individuals (53.0% female) and frontal lobe tissue oxygenation data from 2225 participants (52.3% female); both samples had a mean (SD) age of 64.3 (7.7) years. Results revealed statistically significant associations between neurocardiovascular signal entropy and frailty status. Entropy differences between non-frail and pre-frail/frail were greater during resting state compared with standing and recovery phases. Compared with ApEn, SampEn seemed to have better discriminating power between non-frail and pre-frail/frail individuals. The quantification of entropy in short length neurocardiovascular signals could provide a clinically useful marker of the multiple physiological dysregulations that underlie physical frailty.

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.

Autonomic Control of the Heart and Its Clinical Impact. A Personal Perspective

This essay covers several aspects of the autonomic control of the heart, all relevant to cardiovascular pathophysiology with a direct impact on clinical outcomes. Ischemic heart disease, heart failure, channelopathies, and life-threatening arrhythmias are in the picture. Beginning with an overview on some of the events that marked the oscillations in the medical interest for the autonomic nervous system, our text explores specific areas, including experimental and clinical work focused on understanding the different roles of tonic and reflex sympathetic and vagal activity. The role of the baroreceptors, not just for the direct control of circulation but also because of the clinical value of interpreting alterations (spontaneous or induced) in their function, is discussed. The importance of the autonomic nervous system for gaining insights on risk stratification and for providing specific antiarrhythmic protection is also considered. Examples are the interventions to decrease sympathetic activity and/or to increase vagal activity. The non-invasive analysis of the RR and QT intervals provides additional information. The three of us have collaborated in several studies and each of us contributes with very specific and independent areas of expertise. Here, we have focused on those areas to which we have directly contributed and hence speak with personal experience. This is not an attempt to provide a neutral and general overview on the autonomic nervous system; rather, it represents our effort to share and provide the readers with our own personal views matured after many years of research in this field.

Short-Term Model-Based Multiscale Complexity Analysis of Cardiac Control Provides Complementary Information to Single-Scale Approaches

The study compares a recently proposed shortterm model-based linear multiscale complexity approach to a single-scale application of the same method and to a model-free nonlinear one based on the computation of conditional entropy with the aim at assessing the complementary information. Comparison was carried out over 24 hours Holter recordings of heart period variability during daytime and nighttime in 12 healthy men (age: 34-55 years). Single-scale methods were able to detect the increased complexity of the cardiac control during nighttime. Multiscale complexity analysis showed that this increase was due to an increase of complexity in the low frequency band (from 0.04 to 0.15 Hz), while complexity in the range of frequencies typical of the respiratory rate was unmodified. Regardless of the method (i.e. linear or nonlinear) single-scale complexity indexes were uncorrelated to the multiscale ones. We conclude that short-term model-based linear multiscale complexity approach provides complementary information to single-scale methods in an application devoted to the analysis of cardiac control from 24 hours Holter recordings.

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.

Increased brain entropy of resting-state fMRI mediates the relationship between depression severity and mental health-related quality of life in late-life depressed elderly

BACKGROUND

Entropy analysis is a computational method used to quantify the complexity in a system, and loss of brain complexity is hypothesized to be related to mental disorders. Here, we applied entropy analysis to the resting-state functional magnetic resonance imaging (rs-fMRI) signal in subjects with late-life depression (LLD), an illness combined with emotion dysregulation and aging effect.

METHODS

A total of 35 unremitted depressed elderly and 22 control subjects were recruited. Multiscale entropy (MSE) analysis was performed in the entire brain, 90 automated anatomical labeling-parcellated ROIs, and five resting networks in each study participant.

LIMITATIONS

Due to ethical concerns, all the participants were under medication during the study.

RESULTS

Regionally, subjects with LLD showed decreased entropy only in the right posterior cingulate gyrus but had universally increased entropy in affective processing (putamen and thalamus), sensory, motor, and temporal nodes across different time scales. We also found higher entropy in the left frontoparietal network (FPN), which partially mediated the negative correlation between depression severity and mental components of the quality of life, reflecting the possible neural compensation during depression treatment.

CONCLUSION

MSE provides a novel and complementary approach in rs-fMRI analysis. The temporal-spatial complexity in the resting brain may provide the adaptive variability beneficial for the elderly with depression.

Short-term multiscale complexity analysis of cardiovascular variability improves low cardiac output syndrome risk stratification after coronary artery bypass grafting

BACKGROUND

Low cardiac output syndrome (LCOS) is a myocardial dysfunction leading to systemic hypoperfusion, favored by particular conditions of the autonomic nervous system. LCOS is one of the adverse events that might occur after cardiac surgery.

OBJECTIVE

The aim is to test the hypothesis that short-term multiscale complexity (MSC) analysis of heart period (HP) and systolic arterial pressure (SAP) variability series in the frequency bands typical of cardiovascular control could be fruitfully exploited in identifying subjects at risk of developing LCOS after coronary artery bypass graft (CABG).

APPROACH

HP and SAP beat-to-beat series were derived from electrocardiogram (ECG) and invasive arterial pressure (AP) signal acquired in 128 patients scheduled for CABG before (PRE) and after (POST) the induction of general anesthesia with propofol and remifentanil. Subjects were labeled as LCOS (n  =  14) and noLCOS (n  =  114) according to the LCOS development. MSC markers were calculated as the complement to 1 of the modulus of the average position of the poles dropping in the low-frequency (LF, 0.04-0.15 Hz) and high-frequency (HF, 0.15-0.5 Hz) bands as derived from the autoregressive model of HP and SAP series. Traditional time and frequency domain indexes were also calculated.

MAIN RESULTS

Traditional parameters were able to assess the depression of the cardiovascular regulation induced by general anesthesia, but showed weak performances in differentiating LCOS and noLCOS groups. Conversely, HP complexity in LF band and SAP complexity in HF band assessed during POST remained associated with LCOS even after entering a multivariate logistic regression model adjusted for clinical and demographic factors.

SIGNIFICANCE

The MSC approach can be fruitfully applied to improve risk stratification for LCOS after CABG likely because MSC markers describe the dysfunction of the sympathetic control and the impairment of the mechanical properties of the heart in the LCOS group.

Multiscale information storage of linear long-range correlated stochastic processes

Information storage, reflecting the capability of a dynamical system to keep predictable information during its evolution over time, is a key element of intrinsic distributed computation, useful for the description of the dynamical complexity of several physical and biological processes. Here we introduce a parametric approach which allows one to compute information storage across multiple timescales in stochastic processes displaying both short-term dynamics and long-range correlations (LRC). Our analysis is performed in the popular framework of multiscale entropy, whereby a time series is first "coarse grained" at the chosen timescale through low-pass filtering and downsampling, and then its complexity is evaluated in terms of conditional entropy. Within this framework, our approach makes use of linear fractionally integrated autoregressive (ARFI) models to derive analytical expressions for the information storage computed at multiple timescales. Specifically, we exploit state space models to provide the representation of lowpass filtered and downsampled ARFI processes, from which information storage is computed at any given timescale relating the process variance to the prediction error variance. This enhances the practical usability of multiscale information storage, as it enables a computationally reliable quantification of a complexity measure which incorporates the effects of LRC together with that of short-term dynamics. The proposed measure is first assessed in simulated ARFI processes reproducing different types of autoregressive dynamics and different degrees of LRC, studying both the theoretical values and the finite sample performance. We find that LRC alter substantially the complexity of ARFI processes even at short timescales, and that reliable estimation of complexity can be achieved at longer timescales only when LRC are properly modeled. Then, we assess multiscale information storage in physiological time series measured in humans during resting state and postural stress, revealing unprecedented responses to stress of the complexity of heart period and systolic arterial pressure variability, which are related to the different role played by LRC in the two conditions.

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.

On the Relevance of Computing a Local Version of Sample Entropy in Cardiovascular Control Analysis

OBJECTIVE

Traditional definition of sample entropy (SampEn), here referred to as global SampEn (GSampEn), provides a conditional entropy estimate that blurs the local statistical properties of the time series. We hypothesized that a local version of SampEn (LSampEn) might be more powerful in the presence of determinism than GSampEn.

METHODS

LSampEn was computed by calculating the probability of the current sample conditioned on each reference pattern and averaging it over all reference patterns. The improved ability of LSampEn compared to GSampEn was demonstrated by simulating deterministic periodic, deterministic chaotic, and linear stochastic dynamics corrupted by additive noise and over real cardiovascular variability series recorded from 16 healthy subjects (max-min age range: 22-58 years) during incremental bicycle ergometer exercise.

RESULTS

We found that: i) LSampEn is more robust in describing deterministic periodic or nonlinear features in the presence of additive noise than GSampEn, ii) in association with a surrogate approach, LSampEn is more powerful in detecting nonlinear dynamics than GSampEn, iii) LSampEn and GSampEn are equivalent in the presence of stochastic linear dynamics, and iv) only LSampEn can detect the decrease of complexity of heart period variability during bicycle exercise being a likely hallmark of sympathetic activation.

CONCLUSION

LSampEn preserves the GSampEn capability in characterizing the complexity of short sequences but improves its reliability in the presence of deterministic patterns featuring sharp state transitions and nonlinear dynamics.

SIGNIFICANCE

Variations of complexity can be measured with a greater statistical power over short series using LSampEn, especially when nonlinear features are present.

Chronic vagus nerve stimulation reverses heart rhythm complexity in patients with drug-resistant epilepsy: An assessment with multiscale entropy analysis

OBJECTIVE

Vagus nerve stimulation (VNS) is an adjunctive treatment in drug-resistant epilepsy. The alterations in heart rate dynamics through VNS are not well understood. This study aimed to determine changes in heart rhythm complexity in association with VNS and to relate the findings to the outcome of VNS treatment in patients with drug-resistant epilepsy.

METHODS

We prospectively analyzed 32 patients with drug-resistant epilepsy, who underwent VNS implantation, and 32 age- and sex-matched healthy control subjects. The interictal heartbeat intervals were analyzed using the heart rhythm complexity with multiscale entropy (MSE) and traditional heart rate variability (HRV) analyses based on ambulatory 24-hour electrocardiograms (ECGs).

RESULTS

Patients had significantly decreased complexity indices (Slope 5, Area 1-5, Area 6-15, Area 6-20) on MSE analysis and decreased HRV measurements (standard deviation of the heartbeat interval (SDNN), square root of the mean of sum of squares of the differences between adjacent RR intervals (RMSSD), pNN50, very low frequency (VLF), low frequency (LF), high frequency (HF), total power (TP)) in time and frequency domain analyses. After one year of VNS treatment in patients with drug-resistant epilepsy, there was a trend in an elevated MSE profile with significant higher values between the scales 1 and 9. Vagus nerve stimulation induces a more significant increase of MSE in VNS responders than those in the nonresponders. The conventional HRV measurements did not change.

CONCLUSION

Our results suggest that heart rhythm complexity is impaired in patients with drug-resistant epilepsy, and this is at least partially reversed by VNS treatment. Furthermore, VNS-induced effects on heart rate complexity may be associated with the therapeutic response to VNS in patients with drug-resistant epilepsy.

Association between autonomic control indexes and mortality in subjects admitted to intensive care unit

This study checks whether autonomic markers derived from spontaneous fluctuations of heart period (HP) and systolic arterial pressure (SAP) and from their interactions with spontaneous or mechanical respiration (R) are associated with mortality in patients admitted to intensive care unit (ICU). Three-hundred consecutive HP, SAP and R values were recorded during the first day in ICU in 123 patients. Population was divided into survivors (SURVs, n = 83) and non-survivors (NonSURVs, n = 40) according to the outcome. SURVs and NonSURVs were aged- and gender-matched. All subjects underwent modified head-up tilt (MHUT) by tilting the bed back rest segment to 60°. Autonomic control indexes were computed using time-domain, spectral, cross-spectral, complexity, symbolic and causality techniques via univariate, bivariate and conditional approaches. SAP indexes derived from time-domain, model-free complexity and symbolic approaches were associated with the endpoint, while none of HP variability markers was. The association was more powerful during MHUT. Linear cross-spectral and causality indexes were useless to separate SURVs from NonSURVs, while nonlinear bivariate symbolic markers were successful. When indexes were combined with clinical scores, only SAP variance provided complementary information. Cardiovascular control variability indexes, especially when derived after an autonomic challenge such as MHUT, can improve mortality risk stratification in ICU.

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.

Temporal Analysis of Cardiovascular and Respiratory Complexity by Multiscale Entropy Based on Symbolic Dynamics

The effect of an orthostatic stress on cardiovascular and respiratory complexity was investigated to detect impaired autonomic regulation in patients with vasovagal syncope (VVS). A total of 16 female patients and 12 age-matched healthy female subjects were enrolled in a passive 70° head-up tilt test. Also, 12 age-matched healthy male subjects were enrolled to study gender differences. Analysis was performed dynamically using various short-term (5 min) windows shifted by 1 min as well as by 20 min of orthostatic phase (OP) to evaluate local and global complexity. Complexity was determined over multiple time scales by the established method of refined composite multiscale entropy (RCMSE) and by a new proposed method of multiscale entropy based on symbolic dynamics (MSE-SD). Concerning heart rate variability (HRV) during OP, both methods revealed the highest complexity for female controls followed by lower complexity in male controls (p < 0.01) and by the lowest complexity in female patients (p < 0.01). For blood pressure variability (BPV), no gender differences in controls were shown by any method. However, MSE-SD demonstrated highly significantly increased BPV complexity in patients during OP (p < 0.01 on 4 time-scales after 7 min, p < 0.001 on 5 time-scales after 11 min) while RCMSE did not reveal considerable differences (p < 0.05 on 2 time scales after 7 min). Respiratory complexity was further increased in patients primary shown by MSE-SD. Findings indicated impaired autonomic regulation in VVS patients characterized by predominantly increased BPV complexity accompanied with decreased HRV complexity. In addition, results suggested extending the concept of complexity loss with disease.

Impairment of heart rhythm complexity in patients with drug-resistant epilepsy: An assessment with multiscale entropy analysis

OBJECTIVE

Epilepsy and seizures can have dramatic effects on the cardiac function. The aim of this study was to investigate the heart rhythm complexity in patients with drug-resistant epilepsy (DRE).

METHODS

Ambulatory 24-h electrocardiograms (ECG) from 70 DRE patients and 50 healthy control subjects were analyzed using conventional heart rate variability (HRV) and multiscale entropy (MSE) methods The variation of complexity indices (CI), which was calculated from MSE profile, was determined.

RESULTS

DRE patients had significantly lower time domain (Mean RR, SDNN, RMSSD, pNN50) and frequency domain (VLF, LF, HF, TP) HRV measurements than healthy controls. Of the MSE analysis, MSE profile, CI including Slope 5, Area 1-5, Area 6-15 and Area 6-20 were significantly lower than those in the healthy control group. In receiver operating characteristic (ROC) curve analysis, VLF had the greatest discriminatory power for the two groups. In both net reclassification improvement (NRI) model and integrated discrimination improvement (IDI) models, CI derived from MSE profiles significantly improved the discriminatory power of Mean RR, SDNN, RMSSD, pNN50, VLF, LF, HF and TP.

SIGNIFICANCE

The heart rate complexity is impaired for DRE patients. CI are useful to discriminate DRE patients from subjects with normal cardiac complexity. These findings indicate that MSE method may serve as a complementary approach for characterizing and understanding abnormal heart rate dynamics in epilepsy. Furthermore, the CI may potentially be used as a biomarker in monitoring epilepsy.

Assessing multiscale complexity of short heart rate variability series through a model-based linear approach

We propose a multiscale complexity (MSC) method assessing irregularity in assigned frequency bands and being appropriate for analyzing the short time series. It is grounded on the identification of the coefficients of an autoregressive model, on the computation of the mean position of the poles generating the components of the power spectral density in an assigned frequency band, and on the assessment of its distance from the unit circle in the complex plane. The MSC method was tested on simulations and applied to the short heart period (HP) variability series recorded during graded head-up tilt in 17 subjects (age from 21 to 54 years, median = 28 years, 7 females) and during paced breathing protocols in 19 subjects (age from 27 to 35 years, median = 31 years, 11 females) to assess the contribution of time scales typical of the cardiac autonomic control, namely in low frequency (LF, from 0.04 to 0.15 Hz) and high frequency (HF, from 0.15 to 0.5 Hz) bands to the complexity of the cardiac regulation. The proposed MSC technique was compared to a traditional model-free multiscale method grounded on information theory, i.e., multiscale entropy (MSE). The approach suggests that the reduction of HP variability complexity observed during graded head-up tilt is due to a regularization of the HP fluctuations in LF band via a possible intervention of sympathetic control and the decrement of HP variability complexity observed during slow breathing is the result of the regularization of the HP variations in both LF and HF bands, thus implying the action of physiological mechanisms working at time scales even different from that of respiration. MSE did not distinguish experimental conditions at time scales larger than 1. Over a short time series MSC allows a more insightful association between cardiac control complexity and physiological mechanisms modulating cardiac rhythm compared to a more traditional tool such as MSE.

Vascular aging and subclinical atherosclerosis: why such a "never ending" and challenging story in cardiology?

The true onset of atherosclerosis remains one of the biggest challenges for cardiologists. Is atheroma plaque development considered the earliest step of vascular aging? If so, when it starts? Before or after birth? If it starts before birth or early during childhood, it seems that Thomas Sydenham was right: "A man is as old as his arteries." Except disorganization of elastic fibers, less is known about the morphology of vascular aging and also about the molecular events influencing the age of arteries, arterial stiffness, and their role in the appearance of future complications. Cellular and molecular events responsible for the switch from physiologic to pathologic aging of human arteries are less known. Epigenetic, genetic, and environmental influences at the onset of early vascular aging (EVA) should specifically influence the process. This paper briefly reviews the controversial data regarding vascular aging with an emphasis on the less known facts about the morphology of EVA.

Comparison between K-nearest-neighbor approaches for conditional entropy estimation: Application to the assessment of the cardiac control in amyotrophic lateral sclerosis patients

The study evaluates the k-nearest-neighbor (KNN) strategy for the assessment of complexity of the cardiac neural control from spontaneous fluctuations of heart period (HP). Two different procedures were assessed: i) the KNN estimation of the conditional entropy (CE) proposed by Porta et al; ii) the KNN estimation of mutual information proposed by Kozachenko-Leonenko, refined by Kraskov-Stögbauer-Grassberger and here adapted for the CE estimation. The two procedures were compared over HP variability recordings obtained at rest in supine position and during head-up tilt (HUT) in amyotrophic lateral sclerosis patients and healthy subjects. We found that the indexes derived from the two procedures were significantly correlated and both methods were able to detect the effect of HUT on HP complexity within the same group and distinguish the two populations within the same experimental condition. We recommend the use of the KNN strategy to quantify the dynamical complexity of cardiac neural control in addition to more traditional approaches.

Complexity of cardiovascular rhythms during head-up tilt test by entropy of patterns

OBJECTIVE

The head-up tilt (HUT) test, which provokes transient dynamical alterations in the regulation of cardiovascular system, provides insights into complex organization of this system. Based on signals with heart period intervals (RR-intervals) and/or systolic blood pressure (SBP), differences in the cardiovascular regulation between vasovagal patients (VVS) and the healthy people group (CG) are investigated.

APPROACH

Short-term relations among signal data represented symbolically by three-beat patterns allow to qualify and quantify the complexity of the cardiovascular regulation by Shannon entropy. Four types of patterns: permutation, ordinal, deterministic and dynamical, are used, and different resolutions of signal values in the the symbolization are applied in order to verify how entropy of patterns depends on a way in which values of signals are preprocessed.

MAIN RESULTS

At rest, in the physiologically important signal resolution ranges, independently of the type of patterns used in estimates, the complexity of SBP signals in VVS is different from the complexity found in CG. Entropy of VVS is higher than CG what could be interpreted as substantial presence of noisy ingredients in SBP of VVS. After tilting this relation switches. Entropy of CG occurs significantly higher than VVS for SBP signals. In the case of RR-intervals and large resolutions, the complexity after the tilt becomes reduced when compared to the complexity of RR-intervals at rest for both groups. However, in the case of VVS patients this reduction is significantly stronger than in CG.

SIGNIFICANCE

Our observations about opposite switches in entropy between CG and VVS might support a hypothesis that baroreflex in VVS affects stronger the heart rate because of the inefficient regulation (possibly impaired local vascular tone alternations) of the blood pressure.

The role of sympathetic and vagal cardiac control on complexity of heart rate dynamics

Analysis of heart rate variability (HRV) by nonlinear approaches has been gaining interest due to their ability to extract additional information from heart rate (HR) dynamics that are not detectable by traditional approaches. Nevertheless, the physiological interpretation of nonlinear approaches remains unclear. Therefore, we propose long-term (60 min) protocols involving selective blockade of cardiac autonomic receptors to investigate the contribution of sympathetic and parasympathetic function upon nonlinear dynamics of HRV. Conscious male Wistar rats had their electrocardiogram (ECG) recorded under three distinct conditions: basal, selective (atenolol or atropine), or combined (atenolol plus atropine) pharmacological blockade of autonomic muscarinic or β1-adrenergic receptors. Time series of RR interval were assessed by multiscale entropy (MSE) and detrended fluctuation analysis (DFA). Entropy over short (1 to 5, MSE1–5) and long (6 to 30, MSE6–30) time scales was computed, as well as DFA scaling exponents at short (αshort, 5 ≤ n ≤ 15), mid (αmid, 30 ≤ n ≤ 200), and long (αlong, 200 ≤ n ≤ 1,700) window sizes. The results show that MSE1–5 is reduced under atropine blockade and MSE6–30 is reduced under atropine, atenolol, or combined blockade. In addition, while atropine expressed its maximal effect at scale six, the effect of atenolol on MSE increased with scale. For DFA, αshort decreased during atenolol blockade, while the αmid increased under atropine blockade. Double blockade decreased αshort and increased αlong. Results with surrogate data show that the dynamics during combined blockade is not random. In summary, sympathetic and vagal control differently affect entropy (MSE) and fractal properties (DFA) of HRV. These findings are important to guide future studies.

NEW & NOTEWORTHY Although multiscale entropy (MSE) and detrended fluctuation analysis (DFA) are recognizably useful prognostic/diagnostic methods, their physiological interpretation remains unclear. The present study clarifies the effect of the cardiac autonomic control on MSE and DFA, assessed during long periods (1 h). These findings are important to help the interpretation of future studies.

Assessing the evolution of redundancy/synergy of spontaneous variability regulation with age

OBJECTIVE

We exploited a model-based Wiener-Granger causality method in the information domain for the evaluation of the transfer entropy (TE) and interaction TE (ITE), the latter taken as a measure of the net balance between redundancy and synergy, to describe the interactions between the spontaneous variability of heart period (HP) and systolic arterial pressure (SAP) and the effect of respiration (R) on both variables.

APPROACH

Cardiac control was typified via the genuine TE from SAP to HP, that from R to HP, and the ITE from SAP and R to HP, while vascular control was characterized via the genuine TE from HP to SAP, that from R to SAP, and the ITE from HP and R to SAP. The approach was applied to study age-related modifications of cardiac and vascular controls in a cohort of 100 healthy humans (age from 21 to 70 years, 54 males) recorded at supine rest (REST) and during active standing (STAND). A surrogate approach was exploited to test the significance of the computed quantities.

MAIN RESULTS

Trends of the genuine information transfer with age, already present in literature, were here confirmed. We originally found that: (i) at REST redundancy was predominant over synergy in both vascular and cardiac controls; (ii) the predominance of redundancy of the cardiac control was not affected by postural challenge, while STAND reduced redundancy of vascular control; (iii) the net redundancy of the cardiac control at REST gradually decreased with age, while that of vascular control remained stable; (iv) during STAND net redundancy of both cardiac and vascular controls was stable with age.

SIGNIFICANCE

The study confirms the relevance of computing genuine information transfer in cardiovascular control analysis and stresses the importance of evaluating the ITE to quantify the degree of redundancy of physiological mechanisms operating to maintain cardiovascular homeostasis.

Influence of Heart Rate in Non-linear HRV Indices as a Sampling Rate Effect Evaluated on Supine and Standing

The purpose of this study is to characterize and attenuate the influence of mean heart rate (HR) on nonlinear heart rate variability (HRV) indices (correlation dimension, sample, and approximate entropy) as a consequence of being the HR the intrinsic sampling rate of HRV signal. This influence can notably alter nonlinear HRV indices and lead to biased information regarding autonomic nervous system (ANS) modulation. First, a simulation study was carried out to characterize the dependence of nonlinear HRV indices on HR assuming similar ANS modulation. Second, two HR-correction approaches were proposed: one based on regression formulas and another one based on interpolating RR time series. Finally, standard and HR-corrected HRV indices were studied in a body position change database. The simulation study showed the HR-dependence of non-linear indices as a sampling rate effect, as well as the ability of the proposed HR-corrections to attenuate mean HR influence. Analysis in a body position changes database shows that correlation dimension was reduced around 21% in median values in standing with respect to supine position (p < 0.05), concomitant with a 28% increase in mean HR (p < 0.05). After HR-correction, correlation dimension decreased around 18% in standing with respect to supine position, being the decrease still significant. Sample and approximate entropy showed similar trends. HR-corrected nonlinear HRV indices could represent an improvement in their applicability as markers of ANS modulation when mean HR changes.

Are Nonlinear Model-Free Conditional Entropy Approaches for the Assessment of Cardiac Control Complexity Superior to the Linear Model-Based One?

OBJECTIVE

We test the hypothesis that the linear model-based (MB) approach for the estimation of conditional entropy (CE) can be utilized to assess the complexity of the cardiac control in healthy individuals.

METHODS

An MB estimate of CE was tested in an experimental protocol (i.e., the graded head-up tilt) known to produce a gradual decrease of cardiac control complexity as a result of the progressive vagal withdrawal and concomitant sympathetic activation. The MB approach was compared with traditionally exploited nonlinear model-free (MF) techniques such as corrected approximate entropy, sample entropy, corrected CE, two k -nearest-neighbor CE procedures and permutation CE. Electrocardiogram was recorded in 17 healthy subjects at rest in supine position and during head-up tilt with table angles of 15°, 30°, 45°, 60°, and 75°. Heart period (HP) was derived as the temporal distance between two consecutive R-wave peaks and analysis was carried out over stationary sequences of 256 successive HPs.

RESULTS

The performance of the MB method in following the progressive decrease of HP complexity with tilt table angles was in line with those of MF approaches and the MB index was remarkably correlated with the MF ones.

CONCLUSION

The MB approach can be utilized to monitor the changes of the complexity of the cardiac control, thus speeding up dramatically the CE calculation.

SIGNIFICANCE

The remarkable performance of the MB approach challenges the notion, generally assumed in cardiac control complexity analysis based on CE, about the need of MF techniques and could allow real-time applications.

Traditional Chinese medicine: potential approaches from modern dynamical complexity theories

Despite the widespread use of traditional Chinese medicine (TCM) in clinical settings, proving its effectiveness via scientific trials is still a challenge. TCM views the human body as a complex dynamical system, and focuses on the balance of the human body, both internally and with its external environment. Such fundamental concepts require investigations using system-level quantification approaches, which are beyond conventional reductionism. Only methods that quantify dynamical complexity can bring new insights into the evaluation of TCM. In a previous article, we briefly introduced the potential value of Multiscale Entropy (MSE) analysis in TCM. This article aims to explain the existing challenges in TCM quantification, to introduce the consistency of dynamical complexity theories and TCM theories, and to inspire future system-level research on health and disease.

Multiscale entropic assessment of autonomic dysfunction in patients with obstructive sleep apnea and therapeutic impact of continuous positive airway pressure treatment

OBJECTIVE

Obstructive sleep apnea (OSA) is an independent risk factor for cardiovascular disease because of its associated autonomic nervous and vascular regulatory dysfunctions. We tested the hypothesis that the multiscale entropy (MSE) approach to heart rate variability analysis may be used for evaluating OSA severity through simultaneous assessment of these abnormalities.

METHODS

A total of 147 subjects were divided into four groups according to apnea-hypopnea index (AHI) from polysomnography (PSG): Snoring without OSA (5 > AHI, n = 31), mild (5 ≤ AHI < 15, n = 31), moderate (15 ≤ AHI < 30, n = 41), and severe (AHI ≥ 30, n = 44) OSA. Of the patients, 41 receiving continuous positive airway pressure (CPAP) treatment were included for comparison. For each subject, two segments of electrocardiographic (ECG) signals (both at stage N2) were used for R-R interval (RRI) analysis, including a 10-minute recording 10 minutes after falling asleep (ie, early phase) and another 10-minute segment at 3 hours (ie, late phase). Heart rate variability as reflected in changes in RRI between the two segments was assessed with small-scale multiscale entropy index (MEISS, sum of sample entropy from time scale from 1 to 5) and large-scale multiscale entropy index (MEILS, scale from 6 to 10).

RESULTS

Increase in MEILS in the late phase of sleep was noted in both the normal snoring and CPAP groups (P <0.01). Although the moderate OSA group exhibited MEISS drop in the late phase (P < 0.02), both MEISS and MEILS decreased in the late phase in the severe OSA group (P < 0.001, P < 0.02). However, no differences were noted in mild OSA subjects in both parameters.

CONCLUSION

The results demonstrated significant severity-dependent deterioration in autonomic and vascular regulatory function in patients with OSA as reflected in the reductions in MEISS and MEILS, respectively, and notable improvement after CPAP treatment. The MEI obtainable through PSG may indicate not only OSA severity and physiological status but also therapeutic outcome for OSA patients.

Limits of permutation-based entropies in assessing complexity of short heart period variability

The study compares permutation-based and coarse-grained entropy approaches for the assessment of complexity of short heart period (HP) variability recordings. Shannon permutation entropy (SPE) and conditional permutation entropy (CPE) are computed as examples of permutation-based entropies, while the k-nearest neighbor conditional entropy (KNNCE) is calculated as an example of coarse-grained conditional entropy. SPE, CPE and KNNCE were applied to ad-hoc simulated autoregressive processes corrupted by increasing amounts of broad band noise and to real HP variability series recorded after complete vagal blockade obtained via administration of a high dose of atropine (AT) in nine healthy volunteers and during orthostatic challenge induced by 90° head-up tilt (T90) in 15 healthy individuals. Over the simulated series the performances of SPE and CPE degraded more rapidly with the amplitude of the superimposed broad band noise than those of KNNCE. Over real data KNNCE identified the expected decrease of the HP variability complexity both after AT and during T90. Conversely SPE and CPE detected the decrease of HP variability complexity solely during T90 as a likely result of the more favorable signal-to-noise ratio during T90 than after AT. Results derived from both simulations and real data indicated that permutation-based entropies had a larger susceptibility to broad band noise than KNNCE. We recommend caution in applying permutation-based entropies in presence of short HP variability series characterized by a low signal-to-noise ratio.

Filtering approach based on empirical mode decomposition improves the assessment of short scale complexity in long QT syndrome type 1 population

This study assesses the complexity of heart period (HP) and QT variability series through sample entropy (SampEn) in long QT syndrome type 1 individuals. In order to improve signal-to-noise ratio SampEn was evaluated over the original series (SampEn0) and over the residual computed by subtracting the first oscillatory mode identified by empirical mode decomposition (SampEn(EMD1R)). HP and QT interval were continuously extracted during daytime (2:00-6:00 PM) from 24 hour Holter recordings in 14 non mutation carriers (NMCs) and 34 mutation carriers (MCs) subdivided in 11 asymptomatic (ASYMP) and 23 symptomatic (SYMP). Both NMCs and MCs belonged to the same family line. While SampEn0 did not show differences among the three groups, Samp(EnEMD1R) assessed over the QT series significantly decreased in ASYMP subjects. SampEn(EMD1R) identified a possible factor (i.e. the lower short scale QT complexity) that might contribute to the different risk profile of the ASYMP group.

Heart rate complexity in sinoaortic-denervated mice

NEW FINDINGS

What is the central question of this study? New measurements for cardiovascular complexity, such as detrended fluctuation analysis (DFA) and multiscale entropy (MSE), have been shown to predict cardiovascular outcomes. Given that cardiovascular diseases are accompanied by autonomic imbalance and decreased baroreflex sensitivity, the central question is: do baroreceptors contribute to cardiovascular complexity? What is the main finding and its importance? Sinoaortic denervation altered both DFA scaling exponents and MSE, indicating that both short- and long-term mechanisms of complexity are altered in sinoaortic denervated mice, resulting in a loss of physiological complexity. These results suggest that the baroreflex is a key element in the complex structures involved in heart rate variability regulation. Recently, heart rate (HR) oscillations have been recognized as complex behaviours derived from non-linear processes. Physiological complexity theory is based on the idea that healthy systems present high complexity, i.e. non-linear, fractal variability at multiple scales, with long-range correlations. The loss of complexity in heart rate variability (HRV) has been shown to predict adverse cardiovascular outcomes. Based on the idea that most cardiovascular diseases are accompanied by autonomic imbalance and a decrease in baroreflex sensitivity, we hypothesize that the baroreflex plays an important role in complex cardiovascular behaviour. Mice that had been subjected to sinoaortic denervation (SAD) were implanted with catheters in the femoral artery and jugular vein 5 days prior to the experiment. After recording the baseline arterial pressure (AP), pulse interval time series were generated from the intervals between consecutive values of diastolic pressure. The complexity of the HRV was determined using detrended fluctuation analysis and multiscale entropy. The detrended fluctuation analysis α1 scaling exponent (a short-term index) was remarkably decreased in the SAD mice (0.79 ± 0.06 versus 1.13 ± 0.04 for the control mice), whereas SAD slightly increased the α2 scaling exponent (a long-term index; 1.12 ± 0.03 versus 1.04 ± 0.02 for control mice). In the SAD mice, the total multiscale entropy was decreased (13.2 ± 1.3) compared with the control mice (18.9 ± 1.4). In conclusion, fractal and regularity structures of HRV are altered in SAD mice, affecting both short- and long-term mechanisms of complexity, suggesting that the baroreceptors play a considerable role in the complex structure of HRV.

Applications of dynamical complexity theory in traditional Chinese medicine

Traditional Chinese medicine (TCM) has been gradually accepted by the world. Despite its widespread use in clinical settings, a major challenge in TCM is to study it scientifically. This difficulty arises from the fact that TCM views human body as a complex dynamical system, and focuses on the balance of the human body, both internally and with its external environment. As a result, conventional tools that are based on reductionist approach are not adequate. Methods that can quantify the dynamics of complex integrative systems may bring new insights and utilities about the clinical practice and evaluation of efficacy of TCM. The dynamical complexity theory recently proposed and its computational algorithm, Multiscale Entropy (MSE) analysis, are consistent with TCM concepts. This new system level analysis has been successfully applied to many health and disease related topics in medicine. We believe that there could be many promising applications of this dynamical complexity concept in TCM. In this article, we propose some promising applications and research areas that TCM practitioners and researchers can pursue.

Multiscale complexity analysis of the cardiac control identifies asymptomatic and symptomatic patients in long QT syndrome type 1

The study assesses complexity of the cardiac control directed to the sinus node and to ventricles in long QT syndrome type 1 (LQT1) patients with KCNQ1-A341V mutation. Complexity was assessed via refined multiscale entropy (RMSE) computed over the beat-to-beat variability series of heart period (HP) and QT interval. HP and QT interval were approximated respectively as the temporal distance between two consecutive R-wave peaks and between the R-wave apex and T-wave end. Both measures were automatically taken from 24-hour electrocardiographic Holter traces recorded during daily activities in non mutation carriers (NMCs, n = 14) and mutation carriers (MCs, n = 34) belonging to a South African LQT1 founder population. The MC group was divided into asymptomatic (ASYMP, n = 11) and symptomatic (SYMP, n = 23) patients according to the symptom severity. Analyses were carried out during daytime (DAY, from 2PM to 6PM) and nighttime (NIGHT, from 12PM to 4AM) off and on beta-adrenergic blockade (BBoff and BBon). We found that the complexity of the HP variability at short time scale was under vagal control, being significantly increased during NIGHT and BBon both in ASYMP and SYMP groups, while the complexity of both HP and QT variability at long time scales was under sympathetic control, being smaller during NIGHT and BBon in SYMP subjects. Complexity indexes at long time scales in ASYMP individuals were smaller than those in SYMP ones regardless of therapy (i.e. BBoff or BBon), thus suggesting that a reduced complexity of the sympathetic regulation is protective in ASYMP individuals. RMSE analysis of HP and QT interval variability derived from routine 24-hour electrocardiographic Holter recordings might provide additional insights into the physiology of the cardiac control and might be fruitfully exploited to improve risk stratification in LQT1 population.