K-nearest-neighbor conditional entropy approach for the assessment of the short-term complexity of cardiovascular control

Review of calibration strategies for discrete element model in quasi-static elastic deformation

This study first reviewed theories of the mechanical response of structures under loading, and the discrete element method provides a route for studying mechanical response including elastic deformation and structure failure. However, the direct acquisition of the microscopic parameters from the governing equations of the discrete element method via experiments encounters challenges. One possible strategy to obtain these microscopic parameters is parameter calibration that are widely used by researchers. Secondly, the governing equations and failure criterion of the discrete element method are summarized, and the microscopic parameters that would be calibrated are pinpointed. Next, the principles of classical calibration methods of discrete element method are explicated in detail, alongside the validation and discussion of their properties. Lastly, this study examined the applicability of calibrated parameters and points out that the size ratio, porosity, maximum radius, and minimum radius of particles should be identical in both the geometric calibration model and that for applications.

On the Different Abilities of Cross-Sample Entropy and K-Nearest-Neighbor Cross-Unpredictability in Assessing Dynamic Cardiorespiratory and Cerebrovascular Interactions

Nonlinear markers of coupling strength are often utilized to typify cardiorespiratory and cerebrovascular regulations. The computation of these indices requires techniques describing nonlinear interactions between respiration (R) and heart period (HP) and between mean arterial pressure (MAP) and mean cerebral blood velocity (MCBv). We compared two model-free methods for the assessment of dynamic HP-R and MCBv-MAP interactions, namely the cross-sample entropy (CSampEn) and k-nearest-neighbor cross-unpredictability (KNNCUP). Comparison was carried out first over simulations generated by linear and nonlinear unidirectional causal, bidirectional linear causal, and lag-zero linear noncausal models, and then over experimental data acquired from 19 subjects at supine rest during spontaneous breathing and controlled respiration at 10, 15, and 20 breaths·minute-1 as well as from 13 subjects at supine rest and during 60° head-up tilt. Linear markers were computed for comparison. We found that: (i) over simulations, CSampEn and KNNCUP exhibit different abilities in evaluating coupling strength; (ii) KNNCUP is more reliable than CSampEn when interactions occur according to a causal structure, while performances are similar in noncausal models; (iii) in healthy subjects, KNNCUP is more powerful in characterizing cardiorespiratory and cerebrovascular variability interactions than CSampEn and linear markers. We recommend KNNCUP for quantifying cardiorespiratory and cerebrovascular coupling.

Feasibility of Ultra-Short-Term Analysis of Heart Rate and Systolic Arterial Pressure Variability at Rest and during Stress via Time-Domain and Entropy-Based Measures

Heart Rate Variability (HRV) and Blood Pressure Variability (BPV) are widely employed tools for characterizing the complex behavior of cardiovascular dynamics. Usually, HRV and BPV analyses are carried out through short-term (ST) measurements, which exploit ~five-minute-long recordings. Recent research efforts are focused on reducing the time series length, assessing whether and to what extent Ultra-Short-Term (UST) analysis is capable of extracting information about cardiovascular variability from very short recordings. In this work, we compare ST and UST measures computed on electrocardiographic R-R intervals and systolic arterial pressure time series obtained at rest and during both postural and mental stress. Standard time-domain indices are computed, together with entropy-based measures able to assess the regularity and complexity of cardiovascular dynamics, on time series lasting down to 60 samples, employing either a faster linear parametric estimator or a more reliable but time-consuming model-free method based on nearest neighbor estimates. Our results are evidence that shorter time series down to 120 samples still exhibit an acceptable agreement with the ST reference and can also be exploited to discriminate between stress and rest. Moreover, despite neglecting nonlinearities inherent to short-term cardiovascular dynamics, the faster linear estimator is still capable of detecting differences among the conditions, thus resulting in its suitability to be implemented on wearable devices.

Heart Rate Variability for the Early Detection of Cardiac Autonomic Dysfunction in Type 1 Diabetes

Type 1 diabetes mellitus (T1DM) has an important impact on morbidity and mortality because it may start early in life. Therefore, the early detection of cardiovascular autonomic neuropathy (DCAN) in T1DM patients is important to intervene quickly and prevent further deterioration. Traditional autonomic function tests detect abnormalities in severely symptomatic patients but they are difficult to be standardized, require the patient’s active participation and their sensitivity to the early disease is limited. In comparison, heart rate variability (HRV) is easier to be measured and standardized. Therefore, we aim to find the HRV indexes that better identify DCAN at an early stage in T1DM patients, and evaluate if HRV is a valid alternative to traditional tests. For this aim, we administered the SCOPA-AUT questionnaire on symptoms of autonomic dysfunction as well as deep breathing, Valsalva, handgrip, head-up tilt (HUT), and cold-pressor tests, to 52 T1DM patients and 27 controls. We calculated HRV indexes during supine rest (SUP) and HUT, assessing differences between groups and postures by a linear mixed-effect model for repeated measures. Receiver Operating Characteristic (ROC) analysis quantified how each HRV index and autonomic test distinguishes between patients and controls. We found that the SCOPA-AUT score was slightly but significantly (p < 0.05) greater in patients, indicating an early DCAN. T1DM patients preserved the HRV response to changing posture but in SUP they showed significantly lower standard deviation and vagal indexes of HRV than controls. The area under the ROC curve of these HRV indexes was not lower than 0.68. By contrast, traditional autonomic tests did not differ between groups. Therefore, early DCAN initially causes an impairment of the cardiac vagal control manifest in conditions of elevated vagal tone, as in SUP. Compensatory adjustments of the sympathetic control might explain the unaltered response to traditional autonomic tests. In conclusion, vagal HRV indexes in SUP help to identify early DCAN better than traditional tests, potentially allowing rapid interventions.

Improvement of Sympathovagal Balance by Regular Exercise May Counteract the Ageing Process. A Study by the Analysis of QT Variability

QT interval (QT) variability analysis provides pathophysiological and prognostic information utilized in cardiac and non-cardiac diseases, complementary to those obtained from the analysis of heart period (HP) variability. An increased QT variability has been associated to a higher risk for cardiac events and poorest prognosis. Autonomic cardiovascular adaptation to internal and external challenges, such those occurring in athletes exposed to high levels of physical stress and in ageing could also be deepen by analyzing QT variability, searching for early prognostic signatures. The aim of the study was to analyze the QT variability and cardiac control complexity in a group of middle-aged half-marathon runners at baseline (B) and at a 10-year follow-up (FU). We found that the overall QT variability decreased at FU, despite the inescapable increase in age (52.3 ± 8.0 years at FU). This change was accompanied by an increase of the HP variability complexity without changes of the QT variability complexity. Of notice, over the years, the group of athletes maintained their regular physical activity by switching to a moderate intensity rather than strenuous. In conclusion, regular and moderate exercise over the years was beneficial for this group of athletes, as reflected by the decreased overall QT variability that is known to be associated to lower cardiovascular risk. The concomitant enhanced cardiac control complexity also suggests a trend opposite to what usually occurs with ageing, resulting in a more flexible cardiac control, typical of younger people.

Heart Rate Variability from Wearable Photoplethysmography Systems: Implications in Sleep Studies at High Altitude

The interest in photoplethysmography (PPG) for sleep monitoring is increasing because PPG may allow assessing heart rate variability (HRV), which is particularly important in breathing disorders. Thus, we aimed to evaluate how PPG wearable systems measure HRV during sleep at high altitudes, where hypobaric hypoxia induces respiratory disturbances. We considered PPG and electrocardiographic recordings in 21 volunteers sleeping at 4554 m a.s.l. (as a model of sleep breathing disorder), and five alpine guides sleeping at sea level, 6000 m and 6800 m a.s.l. Power spectra, multiscale entropy, and self-similarity were calculated for PPG tachograms and electrocardiography R–R intervals (RRI). Results demonstrated that wearable PPG devices provide HRV measures even at extremely high altitudes. However, the comparison between PPG tachograms and RRI showed discrepancies in the faster spectral components and at the shorter scales of self-similarity and entropy. Furthermore, the changes in sleep HRV from sea level to extremely high altitudes quantified by RRI and PPG tachograms in the five alpine guides tended to be different at the faster frequencies and shorter scales. Discrepancies may be explained by modulations of pulse wave velocity and should be considered to interpret correctly autonomic alterations during sleep from HRV analysis.

Longitudinal Changes and Recovery in Heart Rate Variability of Young Healthy Subjects When Exposure to a Hypobaric Hypoxic Environment

Background: The autonomic nervous system (ANS) is crucial for acclimatization. Investigating the responses of acute exposure to a hypoxic environment may provide some knowledge of the cardiopulmonary system’s adjustment mechanism.

Objective: The present study investigates the longitudinal changes and recovery in heart rate variability (HRV) in a young healthy population when exposed to a simulated plateau environment.

Methods: The study followed a strict experimental paradigm in which physiological signals were collected from 33 healthy college students (26 ± 2 years, 171 cm ± 7 cm, 64 ± 11 kg) using a medical-grade wearable device. The subjects were asked to sit in normoxic (approximately 101 kPa) and hypoxic (4,000 m above sea level, about 62 kPa) environments. The whole experimental process was divided into four stable resting measurement segments in chronological order to analyze the longitudinal changes of physical stress and recovery phases. Seventy-six time-domain, frequency-domain, and non-linear indicators characterizing rhythm variability were analyzed in the four groups.

Results: Compared to normobaric normoxia, participants in hypobaric hypoxia had significantly lower HRV time-domain metrics, such as RMSSD, MeanNN, and MedianNN (p &lt; 0.01), substantially higher frequency domain metrics such as LF/HF ratio (p &lt; 0.05), significantly lower Poincaré plot parameters such as SD1/SD2 ratio and other Poincaré plot parameters are reduced considerably (p &lt; 0.01), and Refined Composite Multi-Scale Entropy (RCMSE) curves are reduced significantly (p &lt; 0.01).

Conclusion: The present study shows that elevated heart rates, sympathetic activation, and reduced overall complexity were observed in healthy subjects exposed to a hypobaric and hypoxic environment. Moreover, the results indicated that Multiscale Entropy (MSE) analysis of RR interval series could characterize the degree of minor physiological changes. This novel index of HRV can better explain changes in the human ANS.

Influence of Ectopic Beats on Heart Rate Variability Analysis

The analysis of heart rate variability (HRV) plays a dominant role in the study of physiological signal variability. HRV reflects the information of the adjustment of sympathetic and parasympathetic nerves on the cardiovascular system and, thus, is widely used to evaluate the functional status of the cardiovascular system. Ectopic beats may affect the analysis of HRV. However, the quantitative relationship between the burden of ectopic beats and HRV indices, including entropy measures, has not yet been investigated in depth. In this work, we analyzed the effects of different numbers of ectopic beats on several widely accepted HRV parameters in time-domain (SDNN), frequency-domain (LF/HF), as well as non-linear features (SampEn and Pt-SampEn (physical threshold-based SampEn)). The results showed that all four indices were influenced by ectopic beats, and the degree of influence was roughly increased with the increase of the number of ectopic beats. Ectopic beats had the greatest impact on the frequency domain index LF/HF, whereas the Pt-SampEn was minimally accepted by ectopic beats. These results also indicated that, compared with the other three indices, Pt-SampEn had better robustness for ectopic beats.

Are Strategies Favoring Pattern Matching a Viable Way to Improve Complexity Estimation Based on Sample Entropy?

It has been suggested that a viable strategy to improve complexity estimation based on the assessment of pattern similarity is to increase the pattern matching rate without enlarging the series length. We tested this hypothesis over short simulations of nonlinear deterministic and linear stochastic dynamics affected by various noise amounts. Several transformations featuring a different ability to increase the pattern matching rate were tested and compared to the usual strategy adopted in sample entropy (SampEn) computation. The approaches were applied to evaluate the complexity of short-term cardiac and vascular controls from the beat-to-beat variability of heart period (HP) and systolic arterial pressure (SAP) in 12 Parkinson disease patients and 12 age- and gender-matched healthy subjects at supine resting and during head-up tilt. Over simulations, the strategies estimated a larger complexity over nonlinear deterministic signals and a greater regularity over linear stochastic series or deterministic dynamics importantly contaminated by noise. Over short HP and SAP series the techniques did not produce any practical advantage, with an unvaried ability to discriminate groups and experimental conditions compared to the traditional SampEn. Procedures designed to artificially increase the number of matches are of no methodological and practical value when applied to assess complexity indexes.

Alterations of Cardiovascular Complexity during Acute Exposure to High Altitude: A Multiscale Entropy Approach

Stays at high altitude induce alterations in cardiovascular control and are a model of specific pathological cardiovascular derangements at sea level. However, high-altitude alterations of the complex cardiovascular dynamics remain an almost unexplored issue. Therefore, our aim is to describe the altered cardiovascular complexity at high altitude with a multiscale entropy (MSE) approach. We recorded the beat-by-beat series of systolic and diastolic blood pressure and heart rate in 20 participants for 15 min twice, at sea level and after arrival at 4554 m a.s.l. We estimated Sample Entropy and MSE at scales of up to 64 beats, deriving average MSE values over the scales corresponding to the high-frequency (MSE_HF) and low-frequency (MSE_LF) bands of heart-rate variability. We found a significant loss of complexity at heart-rate and blood-pressure scales complementary to each other, with the decrease with high altitude being concentrated at Sample Entropy and at MSE_HF for heart rate and at MSE_LF for blood pressure. These changes can be ascribed to the acutely increased chemoreflex sensitivity in hypoxia that causes sympathetic activation and hyperventilation. Considering high altitude as a model of pathological states like heart failure, our results suggest new ways for monitoring treatments and rehabilitation protocols.

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.

Multiscale fractional order generalized information of financial time series based on similarity distribution entropy

This paper addresses a novel multiscale fractional order distribution entropy based on a similarity matrix (MFS-DistEn) approach to quantify the information of time series on multiple time scales. It improves the metric method of distance matrix in the original DistEn algorithm and further defines the similarity degree between each vector so that we could measure the probability density distribution more accurately. Besides, the multiscale distribution entropy based on similarity matrix combines the advantages of both the multiscale analysis and DistEn and is able to identify dynamical and scale-dependent information. Inspired by the properties of Fractional Calculus, we select the MFS-DistEn notation as the main indicator to present the relevant properties. The characteristics of the generalized MFS-DistEn are tested in both simulated nonlinear signals generated by the autoregressive fractionally integrated moving-average process, logistic map, and real world data series. The results demonstrate the superior performance of the new algorithm and reveal that tuning the fractional order allows a high sensitivity to the signal evolution, which is useful in describing the dynamics of complex systems. The improved similarity DistEn still has relatively lower sensitivity to the predetermined parameters and decreases with an increase of scale.

Cardiac and gait rhythms in healthy younger and older adults during treadmill walking tasks

BACKGROUND

Aging and pathology result in changes in the dynamics of several physiological subsystems. Often, these changes are concurrent, altering the dynamics between subsystems. Cardiac and gait rhythms are one example in which patterns change during physical activity.

AIMS

The purpose of this research is to simultaneously monitor changes in cardiac and gait rhythms when participants complete various treadmill walking tasks-normal speed, fast speed, and while synchronizing steps with a blinking metronome.

METHODS

The cardiac and gait rhythms of younger and older healthy adults were examined in this study during treadmill walking tasks. Pre-test and post-test walking at a preferred walking speed were compared to fast walking and walking with a gait synchronization test. Cardiac and gait rhythms were observed to calculate the mean, standard deviation, coefficient of variation, detrended fluctuation analysis scaling exponent alpha (DFA α), and sample entropy from each 15-min trial. Separate MANOVAs were used to examine the two experimental conditions for cardiac and gait rhythm variability.

RESULTS

During the gait synchronization experiment, main effects for phase were exhibited for all gait variables, but none were shown during the fast walking task. Meanwhile, the cardiac rhythms demonstrated decreased mean and increased DFA α only during the synchronization condition.

DISCUSSION

Participants, regardless of age, exhibited similar patterns of change in their cardiac and locomotor rhythms during the treadmill walking tasks. Cardiac rhythms were only altered during the gait synchronization task, suggesting it may be possible to simultaneously influence the variability and structure of cardiac and gait rhythms.

Coupling of local muscle deoxygenation and autonomic control depends on exercise intensity-insights from transfer entropy analysis

OBJECTIVE

We analyzed the driving component between the periods of adjacent heartbeats (R-R intervals) and vastus lateralis-deoxygenation (%HHb) during incremental cycling. Considering a tight matching of local metabolism with systemic and local perfusion, a coupling between indices of cardiovascular control (R-R variability) and %HHb is suggested. Further, an intensity-dependent coupling between R-R variability and %HHb was hypothesized, because a multitude of feedback and feedforward mechanisms to autonomic cardiovascular control as well as local vasodilating mechanisms are associated with muscle metabolism and thus exercise intensity.

APPROACH

Ten male triathletes (age: 34  ±  8 years) completed a test, including baseline (BAS, 50 W), a 25 W * min^-1 ramp incremental phase until exhaustion and a recovery period (REC, 50 W). R-R intervals, %HHb and respiratory responses were simultaneously recorded. Five corresponding data segments were selected: BAS, before the first ventilatory threshold (preGET), between GET and the respiratory compensation point (preRCP), above RCP (postRCP), and REC. Bivariate transfer entropy (BTE) was applied to determine the signal coupling between R-R and %HHb.

MAIN RESULTS

During preGET and preRCP, the analysis yielded the dominating direction from %HHb to R-R intervals, while for postRCP the direction was reversed. No significant signal coupling was detectable for the BAS and REC segments.

SIGNIFICANCE

Assuming that %HHb is related to the metabolic state of the working muscle, BTE results support the role of metaboreceptors in the systemic blood flow regulation at lower exercise intensities, while other mechanisms (e.g. baroreceptor and mechanoreceptor feedback, central command) that modulate cardiovascular control may override this coupling at higher intensities.

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.

Application of Permutation Entropy and Permutation Min-Entropy in Multiple Emotional States Analysis of RRI Time Series

This study’s aim was to apply permutation entropy (PE) and permutation min-entropy (PME) over an RR interval time series to quantify the changes in cardiac activity among multiple emotional states. Electrocardiogram (ECG) signals were recorded under six emotional states (neutral, happiness, sadness, anger, fear, and disgust) in 60 healthy subjects at a rate of 1000 Hz. For each emotional state, ECGs were recorded for 5 min and the RR interval time series was extracted from these ECGs. The obtained results confirm that PE and PME increase significantly during the emotional states of happiness, sadness, anger, and disgust. Both symbolic quantifiers also increase but not in a significant way for the emotional state of fear. Moreover, it is found that PME is more sensitive than PE for discriminating non-neutral from neutral emotional states.

Towards the identification of subjects prone to develop atrial fibrillation after coronary artery bypass graft surgery via univariate and multivariate complexity analysis of heart period variability

The assessment of cardiovascular control complexity as derived from spontaneous heart period (HP) fluctuations can be improved by exploiting a multivariate (MV) approach. This work proposes the assessment of a normalized complexity index (NCI) of HP variability according to a k-nearest-neighbor approach based on local predictability performed in a MV nonuniform embedding space. The method allows the selection of the past components of HP, systolic arterial pressure (SAP) and respiration (R) most useful for the prediction of HP fluctuations. The NCI derived from the MV approach (NCIMV) was compared to a NCI computed via the same technique applied in a univariate (UV) embedding space (NCIUV) formed exclusively by HP past samples. Indexes were computed in 130 patients undergoing coronary artery bypass graft (CABG) surgery before and after the induction of general anesthesia. Thirty-eight subjects developed atrial fibrillation (AF) after surgery, while the remaining ones did not (noAF, n=92). Both NCIUV and NCIMV could separate AF from noAF patients and revealed a larger complexity of the AF subjects. However, the statistical power of the NCIMV was superior given that the probability of type I error was smaller than that of NCIUV. The assessment of cardiac control complexity could improve risk stratification of patients at risk of developing AF after CABG surgery.

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.

Binarized cross-approximate entropy in crowdsensing environment

OBJECTIVES

Personalised monitoring in health applications has been recognised as part of the mobile crowdsensing concept, where subjects equipped with sensors extract information and share them for personal or common benefit. Limited transmission resources impose the use of local analyses methodology, but this approach is incompatible with analytical tools that require stationary and artefact-free data. This paper proposes a computationally efficient binarised cross-approximate entropy, referred to as (X)BinEn, for unsupervised cardiovascular signal processing in environments where energy and processor resources are limited.

METHODS

The proposed method is a descendant of the cross-approximate entropy ((X)ApEn). It operates on binary, differentially encoded data series split into m-sized vectors. The Hamming distance is used as a distance measure, while a search for similarities is performed on the vector sets. The procedure is tested on rats under shaker and restraint stress, and compared to the existing (X)ApEn results.

RESULTS

The number of processing operations is reduced. (X)BinEn captures entropy changes in a similar manner to (X)ApEn. The coding coarseness yields an adverse effect of reduced sensitivity, but it attenuates parameter inconsistency and binary bias. A special case of (X)BinEn is equivalent to Shannon's entropy. A binary conditional entropy for m =1 vectors is embedded into the (X)BinEn procedure.

CONCLUSION

(X)BinEn can be applied to a single time series as an auto-entropy method, or to a pair of time series, as a cross-entropy method. Its low processing requirements makes it suitable for mobile, battery operated, self-attached sensing devices, with limited power and processor resources.

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.

Hippotherapy acute impact on heart rate variability non-linear dynamics in neurological disorders

Neurological disorders are associated with autonomic dysfunction. Hippotherapy (HT) is a therapy treatment strategy that utilizes a horse in an interdisciplinary approach for the physical and mental rehabilitation of people with physical, mental and/or psychological disabilities. However, no studies have been carried out which evaluated the effects of HT on the autonomic control in these patients. Therefore, the objective of the present study was to investigate the effects of a single HT session on cardiovascular autonomic control by time domain and non-linear analysis of heart rate variability (HRV). The HRV signal was recorded continuously in twelve children affected by neurological disorders during a HT session, consisting in a 10-minute sitting position rest (P1), a 15-minute preparatory phase sitting on the horse (P2), a 15-minute HT session (P3) and a final 10-minute sitting position recovery (P4). Time domain and non-linear HRV indices, including Sample Entropy (SampEn), Lempel-Ziv Complexity (LZC) and Detrended Fluctuation Analysis (DFA), were calculated for each treatment phase. We observed that SampEn increased during P3 (SampEn=0.56±0.10) with respect to P1 (SampEn=0.40±0.14, p<0.05), while DFA decreased during P3 (DFA=1.10±0.10) with respect to P1 (DFA=1.26±0.14, p<0.05). A significant SDRR increase (p<0.05) was observed during the recovery period P4 (SDRR=50±30ms) with respect to the HT session period P3 (SDRR=30±10ms). Our results suggest that HT might benefit children with disabilities attributable to neurological disorders by eliciting an acute autonomic response during the therapy and during the recovery period.

Muscular contraction mode differently affects autonomic control during heart rate matched exercise

The precise contributions of afferent feedback to cardiovascular and respiratory responses to exercise are still unclear. The aim of this crossover study was to assess whether and how autonomic cardiovascular and respiratory control differed in response to dynamic (DYN) and isometric contractions (ISO) at a similar, low heart rate (HR) level. Therefore, 22 healthy males (26.7 ± 3.6 yrs) performed two kinds of voluntary exercises at similar HR: ISO and DYN of the right quadriceps femoris muscle. Although HR was eqivalent (82 ± 8 bpm for DYN and ISO, respectively), rating of exertion, blood pressures, and rate pressure product were higher, whereas breathing frequency, minute ventilation, oxygen uptake and carbon dioxide output were significantly lower during ISO. Tidal volume, end-tidal partial pressures of O2 and CO2, respiratory exchange ratio and capillary blood lactate concentration were comparable between both contraction modes. Heart rate variability (HRV) indicators, SDNN, HF-Power and LF-Power, representing both vagal and sympathetic influences, were significantly higher during ISO. Sample entropy, a non-linear measure of HRV was also significantly affected by contraction mode. It can be concluded that, despite the same net effect on HR, the quality of cardiovascular control during low intensity exercise is significantly different between DYN and ISO. HRV analysis indicated a sympatho-vagal coactivation during ISO. Whether mechanoreceptor feedback alone, a change in central command, or the interaction of both mechanisms is the main contributor of the distinct autonomic responses to the different exercise modes remains to be elucidated.

Causation entropy from symbolic representations of dynamical systems

Identification of causal structures and quantification of direct information flows in complex systems is a challenging yet important task, with practical applications in many fields. Data generated by dynamical processes or large-scale systems are often symbolized, either because of the finite resolution of the measurement apparatus, or because of the need of statistical estimation. By algorithmic application of causation entropy, we investigated the effects of symbolization on important concepts such as Markov order and causal structure of the tent map. We uncovered that these quantities depend nonmonotonically and, most of all, sensitively on the choice of symbolization. Indeed, we show that Markov order and causal structure do not necessarily converge to their original analog counterparts as the resolution of the partitioning becomes finer.

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.

The effect of endotoxin on heart rate dynamics in diabetic rats

The effect of endotoxin on heart rate variability (HRV) was assessed in diabetic and controls rats using a telemetric system. Endotoxin induced a reduction in sample entropy of cardiac rhythm in control animals. However, this effect was significantly blunted in streptozotocin-induced diabetic rats. Since uncoupling of cardiac pacemaker from cholinergic control is linked to reduced HRV in endotoxemia, chronotropic responsiveness to cholinergic stimulation was assessed in isolated atria. Endotoxemia was associated with impaired responsiveness to carbacholine in control rats. However, endotoxemia did not impair cholinergic responsiveness in diabetic atria. These findings corroborates with development of endotoxin tolerance in diabetic rats.

Effect of age on complexity and causality of the cardiovascular control: comparison between model-based and model-free approaches

The proposed approach evaluates complexity of the cardiovascular control and causality among cardiovascular regulatory mechanisms from spontaneous variability of heart period (HP), systolic arterial pressure (SAP) and respiration (RESP). It relies on construction of a multivariate embedding space, optimization of the embedding dimension and a procedure allowing the selection of the components most suitable to form the multivariate embedding space. Moreover, it allows the comparison between linear model-based (MB) and nonlinear model-free (MF) techniques and between MF approaches exploiting local predictability (LP) and conditional entropy (CE). The framework was applied to study age-related modifications of complexity and causality in healthy humans in supine resting (REST) and during standing (STAND). We found that: 1) MF approaches are more efficient than the MB method when nonlinear components are present, while the reverse situation holds in presence of high dimensional embedding spaces; 2) the CE method is the least powerful in detecting age-related trends; 3) the association of HP complexity on age suggests an impairment of cardiac regulation and response to STAND; 4) the relation of SAP complexity on age indicates a gradual increase of sympathetic activity and a reduced responsiveness of vasomotor control to STAND; 5) the association from SAP to HP on age during STAND reveals a progressive inefficiency of baroreflex; 6) the reduced connection from HP to SAP with age might be linked to the progressive exploitation of Frank-Starling mechanism at REST and to the progressive increase of peripheral resistances during STAND; 7) at REST the diminished association from RESP to HP with age suggests a vagal withdrawal and a gradual uncoupling between respiratory activity and heart; 8) the weakened connection from RESP to SAP with age might be related to the progressive increase of left ventricular thickness and vascular stiffness and to the gradual decrease of respiratory sinus arrhythmia.

Effect of hormone replacement therapy on cardiac autonomic modulation

OBJECTIVE

To investigate the effects of hormone replacement therapy (HRT) on heart rate variability (HRV) in healthy postmenopausal women.

METHODS

Two groups were evaluated: group 1 (G1): 20 women not undergoing HRT (60 ± 5.89 years), group 2 (G2): 20 women undergoing HRT (59 ± 5.70 years). The HRTs involved were either conjugated equine estrogen with or without medroxyprogesterone, synthetic estrogen hormone, estradiol associated with norethisterone acetate or isoflavonoids. Electrocardiogram was recorded in the supine position for 10 min. Spectral analysis included low and high frequencies in absolute (LF and HF) and normalized units (LFnu and HFnu), which are predominantly cardiac sympathetic modulation (CSM) and cardiac vagal modulation (CVM) indicators, respectively. The LF/HF ratio was also calculated. Symbolic analysis involved the following indexes: 0V % (CSM indicator), 1V % (CSM and CVM indicators), 2LV % (predominantly CVM indicator) and 2UV % (CVM indicator). Shannon and conditional entropies were also calculated.

RESULTS

Spectral analysis demonstrated that HRT affected HRV. LF, LFnu and LF/HF ratio were higher (showing increased CSM), while HFnu was lower (representing decreased CVM) in G2 than in G1. Correlations between complexity indices and HFnu were significant and positive only in G1.

INTERPRETATION

Women undergoing HRT presented higher CSM and lower CVM than those who were not. Moreover, the expected positive relationship between CVM and complexity of HRV was found only in control group, thus indicating that CVM in women under therapy drop below a minimal value necessary to the association to become apparent, suggesting an unfavorable cardiac autonomic modulation in spite of HRT.

Entropy-based complexity of the cardiovascular control in Parkinson disease: comparison between binning and k-nearest-neighbor approaches

Entropy-based approaches are frequently used to quantify complexity of short-term cardiovascular control from spontaneous beat-to-beat variability of heart period (HP) and systolic arterial pressure (SAP). Among these tools the ones optimizing a critical parameter such as the pattern length are receiving more and more attention. This study compares two entropy-based techniques for the quantification of complexity making use of completely different strategies to optimize the pattern length. Comparison was carried out over HP and SAP variability series recorded from 12 Parkinson's disease (PD) patients without orthostatic hypotension or symptoms of orthostatic intolerance and 12 age-matched healthy control (HC) subjects. Regardless of the method, complexity of cardiovascular control increased in PD group, thus suggesting the early impairment of cardiovascular function.

Refined multiscale entropy analysis of heart period and QT interval variabilities in long QT syndrome type-1 patients

This study assesses complexity of cardiovascular control in patients affected by type-1 variant of long QT (LQT1) syndrome. Complexity was assessed by refined multiscale entropy of heart period (HP) and QT interval variabilities. HP was taken as the time distance between two consecutive R peaks (RR) and QT interval was approximated as the time distance between the R-peak and T-wave apex (RTa) and between R-peak and T-wave end (RTe). RR, RTa and RTe intervals were automatically extracted from 24h Holter recordings and the daytime period was analyzed (from 02:00 to 06:00 PM). Non mutation carrier (NMC) individuals (n=11), utilized as a control group, were taken from the same family line of the mutation carrier (MC) subjects (n=26). We found that, while NMC and MC groups were indistinguishable based on time domain and complexity analyses of RR dynamics, complexity analysis of RTa and RTe variabilities clearly separates the two populations and suggests an impairment in the cardiac control mechanisms acting on the ventricles.