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

Autonomic Function and Baroreflex Control in COVID-19 Patients Admitted to the Intensive Care Unit

Background: Autonomic function and baroreflex control might influence the survival rate of coronavirus disease 2019 (COVID-19) patients admitted to the intensive care unit (ICU) compared to respiratory failure patients without COVID-19 (non-COVID-19). This study describes physiological control mechanisms in critically ill COVID-19 patients admitted to the ICU in comparison to non-COVID-19 individuals with the aim of improving stratification of mortality risk. Methods: We evaluated autonomic and baroreflex control markers extracted from heart period (HP) and systolic arterial pressure (SAP) variability acquired at rest in the supine position (REST) and during a modified head-up tilt (MHUT) in 17 COVID-19 patients (age: 63 ± 10 years, 14 men) and 33 non-COVID-19 patients (age: 60 ± 12 years, 23 men) during their ICU stays. Patients were categorized as survivors (SURVs) or non-survivors (non-SURVs). Results: We found that COVID-19 and non-COVID-19 populations exhibited similar vagal and sympathetic control markers; however, non-COVID-19 individuals featured a smaller baroreflex sensitivity and an unexpected reduction in the HP-SAP association during the MHUT compared to the COVID-19 group. Nevertheless, none of the markers of the autonomic and baroreflex functions could distinguish SURVs from non-SURVs in either population. Conclusions: We concluded that COVID-19 patients exhibited a more preserved baroreflex control compared to non-COVID-19 individuals, even though this information is ineffective in stratifying mortality risk.

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

BACKGROUND AND OBJECTIVE

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

METHODS

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

RESULTS

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

CONCLUSIONS

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

Heart rhythm complexity analysis in patients with inferior ST-elevation myocardial infarction

Heart rhythm complexity (HRC), a subtype of heart rate variability (HRV), is an important tool to investigate cardiovascular disease. In this study, we aimed to analyze serial changes in HRV and HRC metrics in patients with inferior ST-elevation myocardial infarction (STEMI) within 1 year postinfarct and explore the association between HRC and postinfarct left ventricular (LV) systolic impairment. We prospectively enrolled 33 inferior STEMI patients and 74 control subjects and analyzed traditional linear HRV and HRC metrics in both groups, including detrended fluctuation analysis (DFA) and multiscale entropy (MSE). We also analyzed follow-up postinfarct echocardiography for 1 year. The STEMI group had significantly lower standard deviation of RR interval (SDNN), and DFAα2 within 7 days postinfarct (acute stage) comparing to control subjects. LF power was consistently higher in STEMI group during follow up. The MSE scale 5 was higher at acute stage comparing to control subjects and had a trend of decrease during 1-year postinfarct. The MSE area under scale 1-5 showed persistently lower than control subjects and progressively decreased during 1-year postinfarct. To predict long-term postinfarct LV systolic impairment, the slope between MSE scale 1 to 5 (slope 1-5) had the best predictive value. MSE slope 1-5 also increased the predictive ability of the linear HRV metrics in both the net reclassification index and integrated discrimination index models. In conclusion, HRC and LV contractility decreased 1 year postinfarct in inferior STEMI patients, and MSE slope 1-5 was a good predictor of postinfarct LV systolic impairment.

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

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

Heart rate variability in different sleep stages is associated with metabolic function and glycemic control in type 2 diabetes mellitus

Introduction: Autonomic nervous system (ANS) plays an important role in the exchange of metabolic information between organs and regulation on peripheral metabolism with obvious circadian rhythm in a healthy state. Sleep, a vital brain phenomenon, significantly affects both ANS and metabolic function. Objectives: This study investigated the relationships among sleep, ANS and metabolic function in type 2 diabetes mellitus (T2DM), to support the evaluation of ANS function through heart rate variability (HRV) metrics, and the determination of the correlated underlying autonomic pathways, and help optimize the early prevention, post-diagnosis and management of T2DM and its complications. Materials and methods: A total of 64 volunteered inpatients with T2DM took part in this study. 24-h electrocardiogram (ECG), clinical indicators of metabolic function, sleep quality and sleep staging results of T2DM patients were monitored. Results: The associations between sleep quality, 24-h/awake/sleep/sleep staging HRV and clinical indicators of metabolic function were analyzed. Significant correlations were found between sleep quality and metabolic function (|r| = 0.386 ± 0.062, p < 0.05); HRV derived ANS function showed strengthened correlations with metabolic function during sleep period (|r| = 0.474 ± 0.100, p < 0.05); HRV metrics during sleep stages coupled more tightly with clinical indicators of metabolic function [in unstable sleep: |r| = 0.453 ± 0.095, p < 0.05; in stable sleep: |r| = 0.463 ± 0.100, p < 0.05; in rapid eye movement (REM) sleep: |r| = 0.453 ± 0.082, p < 0.05], and showed significant associations with glycemic control in non-linear analysis [fasting blood glucose within 24 h of admission (admission FBG), |r| = 0.420 ± 0.064, p < 0.05; glycated hemoglobin (HbA1c), |r| = 0.417 ± 0.016, p < 0.05]. Conclusions: HRV metrics during sleep period play more distinct role than during awake period in investigating ANS dysfunction and metabolism in T2DM patients, and sleep rhythm based HRV analysis should perform better in ANS and metabolic function assessment, especially for glycemic control in non-linear analysis among T2DM patients.

An Entropy-Based Architecture for Detection of Sepsis in Newborn Cry Diagnostic Systems

The acoustic characteristics of cries are an exhibition of an infant's health condition and these characteristics have been acknowledged as indicators for various pathologies. This study focused on the detection of infants suffering from sepsis by developing a simplified design using acoustic features and conventional classifiers. The features for the proposed framework were Mel-frequency Cepstral Coefficients (MFCC), Spectral Entropy Cepstral Coefficients (SENCC) and Spectral Centroid Cepstral Coefficients (SCCC), which were classified through K-nearest Neighborhood (KNN) and Support Vector Machine (SVM) classification methods. The performance of the different combinations of the feature sets was also evaluated based on several measures such as accuracy, F1-score and Matthews Correlation Coefficient (MCC). Bayesian Hyperparameter Optimization (BHPO) was employed to tailor the classifiers uniquely to fit each experiment. The proposed methodology was tested on two datasets of expiratory cries (EXP) and voiced inspiratory cries (INSV). The highest accuracy and F-score were 89.99% and 89.70%, respectively. This framework also implemented a novel feature selection method based on Fuzzy Entropy (FE) as a final experiment. By employing FE, the number of features was reduced by more than 40%, whereas the evaluation measures were not hindered for the EXP dataset and were even enhanced for the INSV dataset. Therefore, it was deduced through these experiments that an entropy-based framework is successful for identifying sepsis in neonates and has the advantage of achieving high performance with conventional machine learning (ML) approaches, which makes it a reliable means for the early diagnosis of sepsis in deprived areas of the world.

Heart rate variability as a biomarker in patients with Chronic Chagas Cardiomyopathy with or without concomitant digestive involvement and its relationship with the Rassi score

Background

Dysautonomia plays an ancillary role in the pathogenesis of Chronic Chagas Cardiomyopathy (CCC), but is the key factor causing digestive organic involvement. We investigated the ability of heart rate variability (HRV) for death risk stratification in CCC and compared alterations of HRV in patients with isolated CCC and in those with the mixed form (CCC + digestive involvement). Thirty-one patients with CCC were classified into three risk groups (low, intermediate and high) according to their Rassi score. A single-lead ECG was recorded for a period of 10–20 min, RR series were generated and 31 HRV indices were calculated. The HRV was compared among the three risk groups and regarding the associated digestive involvement. Four machine learning models were created to predict the risk class of patients.

Results

Phase entropy is decreased and the percentage of inflection points is increased in patients from the high-, compared to the low-risk group. Fourteen patients had the mixed form, showing decreased triangular interpolation of the RR histogram and absolute power at the low-frequency band. The best predictive risk model was obtained by the support vector machine algorithm (overall F1-score of 0.61).

Conclusions

The mixed form of Chagas' disease showed a decrease in the slow HRV components. The worst prognosis in CCC is associated with increased heart rate fragmentation. The combination of HRV indices enhanced the accuracy of risk stratification. In patients with the mixed form of Chagas disease, a higher degree of sympathetic autonomic denervation may be associated with parasympathetic impairment.

The autonomic balance of heart rhythm complexity after renal artery denervation: insight from entropy of entropy and average entropy analysis

Background

The current method to evaluate the autonomic balance after renal denervation (RDN) relies on heart rate variability (HRV). However, parameters of HRV were not always predictive of response to RDN. Therefore, the complexity and disorder of heart rhythm, measured by entropy of entropy (EoE) and average entropy (AE), have been used to analyze autonomic dysfunction. This study evaluated the dynamic changes in autonomic status after RDN via EoE and AE analysis.

Methods

Five patients were prospectively enrolled in the Global SYMPLICITY Registry from 2020 to 2021. 24-h Holter and ambulatory blood pressure monitoring (ABPM) was performed at baseline and 3 months after RDN procedures. The autonomic status was analyzed using the entropy-based AE and EoE analysis and the conventional HRV-based low frequency (LF), high frequency (HF), and LF/HF.

Results

After RDN, the ABPM of all patients showed a significant reduction in blood pressure (BP) and heart rate. Only AE and HF values of all patients had consistent changes after RDN (p < 0.05). The spearman rank-order correlation coefficient of AE vs. HF was 0.86, but AE had a lower coefficient of variation than HF.

Conclusions

Monitoring the AE and EoE analysis could be an alternative to interpreting autonomic status. In addition, a relative change of autonomic tone, especially an increasing parasympathetic activity, could restore autonomic balance after RDN.

Supplementary Information

The online version contains supplementary material available at 10.1186/s12938-022-00999-4.

Fifty years of Shannon information theory in assessing the accuracy and agreement of diagnostic tests

Since 1948, Shannon theoretic methods for modeling information have found a wide range of applications in several areas where information plays a key role, which goes well beyond the original scopes for which they have been conceived, namely data compression and error correction over a noisy channel. Among other uses, these methods have been applied in the broad field of medical diagnostics since the 1970s, to quantify diagnostic information, to evaluate diagnostic test performance, but also to be used as technical tools in image processing and registration. This review illustrates the main contributions in assessing the accuracy of diagnostic tests and the agreement between raters, focusing on diagnostic test performance measurements and paired agreement evaluation. This work also presents a recent unified, coherent, and hopefully, final information-theoretical approach to deal with the flows of information involved among the patient, the diagnostic test performed to appraise the state of disease, and the raters who are checking the test results. The approach is assessed by considering two case studies: the first one is related to evaluating extra-prostatic cancers; the second concerns the quality of rapid tests for COVID-19 detection.

Adaptive Capacities and Complexity of Heart Rate Variability in Patients With Chronic Obstructive Pulmonary Disease Throughout Pulmonary Rehabilitation

Introduction

The complexity of bio-signals, like R-R intervals, is considered a reflection of the organism's capacity to adapt. However, this association still remains to be consolidated. We investigated whether the complexity of R-R intervals at rest and during perturbation [6-minute walking test (6MWT)], yielded information regarding adaptive capacities in Chronic Obstructive Pulmonary Disease (COPD) patients during pulmonary rehabilitation (PR).

Methods

In total, 23 COPD patients (64 ± 8 years, with forced expiratory volume in 1 s of 55 ± 19% predicted) were tested three times at the start (T1), middle (T2), and end (T3) of 4 weeks PR. Each time, R-R intervals were measured at rest and during 6MWT. The complexity of R-R intervals was assessed by evenly spaced Detrended Fluctuations Analysis and evaluated by the fractal exponent α and deviation from maximal complexity |1-α|.

Results

The 6MWT distance was significantly increased at T2 and T3 compared to T1. Neither α nor |1-α| at rest and during perturbation significantly changed throughout PR, nor were they consistently associated with 6MWT distances at each time. Throughout the PR program, complexity during the 6MWT was significantly lower compared to the rest. The level of α during 6MWT at T1 was positively correlated with the improvement of the 6MWT distance throughout the PR program.

Discussion

Reduced complexity in COPD patients during acute perturbation at the beginning of PR supports a decreased improvement of the 6MWT distance throughout PR. This result seems consistent with the notion that the complexity reflects the patients' adaptive capacities and could therefore become a clinical indicator in an applied perspective.

The Value of Heart Rhythm Complexity in Identifying High-Risk Pulmonary Hypertension Patients

Pulmonary hypertension (PH) is a fatal disease—even with state-of-the-art medical treatment. Non-invasive clinical tools for risk stratification are still lacking. The aim of this study was to investigate the clinical utility of heart rhythm complexity in risk stratification for PH patients. We prospectively enrolled 54 PH patients, including 20 high-risk patients (group A; defined as WHO functional class IV or class III with severely compromised hemodynamics), and 34 low-risk patients (group B). Both linear and non-linear heart rate variability (HRV) variables, including detrended fluctuation analysis (DFA) and multiscale entropy (MSE), were analyzed. In linear and non-linear HRV analysis, low frequency and high frequency ratio, DFAα1, MSE slope 5, scale 5, and area 6–20 were significantly lower in group A. Among all HRV variables, MSE scale 5 (AUC: 0.758) had the best predictive power to discriminate the two groups. In multivariable analysis, MSE scale 5 (p = 0.010) was the only significantly predictor of severe PH in all HRV variables. In conclusion, the patients with severe PH had worse heart rhythm complexity. MSE parameters, especially scale 5, can help to identify high-risk PH patients.

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.

Short-Term Effect of Percutaneous Coronary Intervention on Heart Rate Variability in Patients with Coronary Artery Disease

Myocardial ischemia in patients with coronary artery disease (CAD) leads to imbalanced autonomic control that increases the risk of morbidity and mortality. To systematically examine how autonomic function responds to percutaneous coronary intervention (PCI) treatment, we analyzed data of 27 CAD patients who had admitted for PCI in this pilot study. For each patient, five-minute resting electrocardiogram (ECG) signals were collected before and after the PCI procedure. The time intervals between ECG collection and PCI were both within 24 h. To assess autonomic function, normal sinus RR intervals were extracted and were analyzed quantitatively using traditional linear time- and frequency-domain measures [i.e., standard deviation of the normal-normal intervals (SDNN), the root mean square of successive differences (RMSSD), powers of low frequency (LF) and high frequency (HF) components, LF/HF] and nonlinear entropy measures [i.e., sample entropy (SampEn), distribution entropy (DistEn), and conditional entropy (CE)], as well as graphical metrics derived from Poincaré plot [i.e., Porta’s index (PI), Guzik’s index (GI), slope index (SI) and area index (AI)]. Results showed that after PCI, AI and PI decreased significantly (p < 0.002 and 0.015, respectively) with effect sizes of 0.88 and 0.70 as measured by Cohen’s d static. These changes were independent of sex. The results suggest that graphical AI and PI metrics derived from Poincaré plot of short-term ECG may be potential for sensing the beneficial effect of PCI on cardiovascular autonomic control. Further studies with bigger sample sizes are warranted to verify these observations.

Maturation of the Autonomic Nervous System in Premature Infants: Estimating Development Based on Heart-Rate Variability Analysis

This study aims at investigating the development of premature infants' autonomic nervous system (ANS) based on a quantitative analysis of the heart-rate variability (HRV) with a variety of novel features. Additionally, the role of heart-rate drops, known as bradycardias, has been studied in relation to both clinical and novel sympathovagal indices. ECG data were measured for at least 3 h in 25 preterm infants (gestational age ≤32 weeks) for a total number of 74 recordings. The post-menstrual age (PMA) of each patient was estimated from the RR interval time-series by means of multivariate linear-mixed effects regression. The tachograms were segmented based on bradycardias in periods after, between and during bradycardias. For each of those epochs, a set of temporal, spectral and fractal indices were included in the regression model. The best performing model has R 2 = 0.75 and mean absolute error MAE = 1.56 weeks. Three main novelties can be reported. First, the obtained maturation models based on HRV have comparable performance to other development models. Second, the selected features for age estimation show a predominance of power and fractal features in the very-low- and low-frequency bands in explaining the infants' sympathovagal development from 27 PMA weeks until 40 PMA weeks. Third, bradycardias might disrupt the relationship between common temporal indices of the tachogram and the age of the infant and the interpretation of sympathovagal indices. This approach might provide a novel overview of post-natal autonomic maturation and an alternative development index to other electrophysiological data analysis.

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.

A validity and reliability study of Conditional Entropy Measures of Pulse Rate Variability

In this work, we present the feasibility to use a simpler methodological approach for the assessment of the short-term complexity of Heart Rate Variability (HRV). Specifically, we propose to exploit Pulse Rate Variability (PRV) recorded through photoplethysmography in place of HRV measured from the ECG, and to compute complexity via a linear Gaussian approximation in place of the standard model-free methods (e.g., nearest neighbor entropy estimates) usually applied to HRV. Linear PRV-based and model-free HRV-based complexity measures were compared via statistical tests, correlation analysis and Bland-Altman plots, demonstrating an overall good agreement. These results support the applicability of the simpler proposed approach, which is faster and easier-to-implement, making our approach eligible for portable/wearable devices and thus broadening the out-of-lab accessibility of autonomic indexes.

Early Detection of Sudden Cardiac Death by Using Ensemble Empirical Mode Decomposition-Based Entropy and Classical Linear Features From Heart Rate Variability Signals

Sudden cardiac death (SCD), which can deprive a person of life within minutes, is a destructive heart abnormality. Thus, providing early warning information for patients at risk of SCD, especially those outside hospitals, is essential. In this study, we investigated the performances of ensemble empirical mode decomposition (EEMD)-based entropy features on SCD identification. EEMD-based entropy features were obtained by using the following technology: (1) EEMD was performed on HRV beats to decompose them into intrinsic mode functions (IMFs), (2) five entropy parameters, namely Rényi entropy (RenEn), fuzzy entropy (FuEn), dispersion Entropy (DisEn), improved multiscale permutation entropy (IMPE), and Renyi distribution entropy(RdisEn), were computed from the first four IMFs obtained, which were named EEMD-based entropy features. Additionally, an automated scheme combining EEMD-based entropy and classical linear (time and frequency domains) features was proposed with the intention of detecting SCD early by analyzing 14 min (at seven successive intervals of 2 min) heart rate variability (HRV) in signals from a normal population and subjects at risk of SCD. Firstly, EEMD-based entropy and classical linear measurements were extracted from HRV beats, and then the integrated measurements were ranked by various methodologies, i.e., t-test, entropy, receiver-operating characteristics (ROC), Wilcoxon, and Bhattacharyya. Finally, these ranked features were fed into a k-Nearest Neighbor algorithm for classification. Compared with several state-of-the-art methods, the proposed scheme firstly predicted subjects at risk of SCD up to 14 min earlier with an accuracy of 96.1%, a sensitivity of 97.5%, and a specificity of 94.4% 14 min before SCD onset. The simulation results exhibited that EEMD-based entropy estimators showed significant difference between SCD patients and normal individuals and outperformed the classical linear estimators in SCD detection, the EEMD-based FuEn and IMPE indexes were particularly useful assessments for identification of patients at risk of SCD and can be used as novel indices to reveal the disorders of rhythm variations of the autonomic nervous system when affected by SCD.

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.

Effects of inspiratory muscle-training intensity on cardiovascular control in amateur cyclists

Chronic effects of inspiratory muscle training (IMT) on autonomic function and baroreflex regulation are poorly studied. This study aims at evaluating chronic effects of different IMT intensities on cardiovascular control in amateur cyclists. A longitudinal, randomized, controlled blind study was performed on 30 recreational male cyclists undergoing IMT for 11 wk. Participants were randomly allocated into sham-trained group (SHAM, n = 9), trained group at 60% of the maximal inspiratory pressure (MIP60, n = 10), and trained group at critical inspiratory pressure (CIP, n = 11). Electrocardiogram, finger arterial pressure, and respiratory movements were recorded before (PRE) and after (POST) training at rest in supine position (REST) and during active standing (STAND). From the beat-to-beat series of heart period (HP) and systolic arterial pressure (SAP), we computed time domain markers, frequency domain indexes in the low frequency (0.04-0.15 Hz) and high frequency (HF, 0.15-0.4 Hz) bands, an entropy-based complexity index (CI), and baroreflex markers estimated from spontaneous HP-SAP sequences. Compared with SHAM, the positive effect of MIP60 over the HP series led to the HF power increase during REST (PRE: 521.2 ± 447.5 ms²; POST: 1,161 ± 878.9 ms²) and the CI rise during STAND (PRE: 0.82 ± 0.18; POST: 0.97 ± 0.13). Conversely, the negative effect of CIP took the form of the decreased HP mean during STAND (PRE: 791 ± 71 ms; POST: 737 ± 95 ms). No effect of IMT was visible over SAP and baroreflex markers. These findings suggest that moderate-intensity IMT might be beneficial when the goal is to limit cardiac sympathetic hyperactivity at REST and/or in response to STAND.

Time, frequency and information domain analysis of short-term heart rate variability before and after focal and generalized seizures in epileptic children

OBJECTIVE

In this work we explore the potential of combining standard time and frequency domain indexes with novel information measures, to characterize pre- and post-ictal heart rate variability (HRV) in epileptic children, with the aim of differentiating focal and generalized epilepsy regarding the autonomic control mechanisms.

APPROACH

We analyze short-term HRV in 37 children suffering from generalized or focal epilepsy, monitored 10 s, 300 s, 600 s and 1800 s both before and after seizure episodes. Nine indexes are computed in time (mean, standard deviation of normal-to-normal intervals, root mean square of the successive differences (RMSSD)), frequency (low-to-high frequency power ratio LF/HF, normalized LF and HF power) and information (entropy, conditional entropy and self-entropy) domains. Focal and generalized epilepsy are compared through statistical analysis of the indexes and using linear discriminant analysis (LDA).

MAIN RESULTS

In children with focal epilepsy, early post-ictal phase is characterized by significant tachycardia, depressed HRV, increased LF power and LF/HF, and decreased complexity, progressively recovered across time windows after the episodes. Children with generalized seizures instead show significant tachycardia, lower RMSSD, higher LF power and LF/HF ratio before the seizure. These different behaviors are exploited by LDA analysis to separate focal and generalized epilepsy up to an accuracy of 75%. Results suggest a shift of the sympatho-vagal balance towards sympathetic dominance and vagal withdrawal, noticeable just after the termination of seizure episodes and then reverted in focal epilepsy, and persistent during inter-ictal and pre-ictal periods in generalized epilepsy.

SIGNIFICANCE

Our analysis helps in elucidating the pathophysiology of inter-ictal HRV autonomic control and the differential diagnosis of generalized and focal epilepsy. These findings may have clinical relevance since altered sympatho-vagal control can be related to a higher danger of morbidity and mortality, may reduce thresholds for life-threatening arrhythmias, and could be a biomarker of risk for sudden unexpected death in epilepsy.

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.

Comparison of short-term heart rate variability indexes evaluated through electrocardiographic and continuous blood pressure monitoring

Heart rate variability (HRV) analysis represents an important tool for the characterization of complex cardiovascular control. HRV indexes are usually calculated from electrocardiographic (ECG) recordings after measuring the time duration between consecutive R peaks, and this is considered the gold standard. An alternative method consists of assessing the pulse rate variability (PRV) from signals acquired through photoplethysmography, a technique also employed for the continuous noninvasive monitoring of blood pressure. In this work, we carry out a thorough analysis and comparison of short-term variability indexes computed from HRV time series obtained from the ECG and from PRV time series obtained from continuous blood pressure (CBP) signals, in order to evaluate the reliability of using CBP-based recordings in place of standard ECG tracks. The analysis has been carried out on short time series (300 beats) of HRV and PRV in 76 subjects studied in different conditions: resting in the supine position, postural stress during 45° head-up tilt, and mental stress during computation of arithmetic test. Nine different indexes have been taken into account, computed in the time domain (mean, variance, root mean square of the successive differences), frequency domain (low-to-high frequency power ratio LF/HF, HF spectral power, and central frequency), and information domain (entropy, conditional entropy, self entropy). Thorough validation has been performed using comparison of the HRV and PRV distributions, robust linear regression, and Bland-Altman plots. Results demonstrate the feasibility of extracting HRV indexes from CBP-based data, showing an overall relatively good agreement of time-, frequency-, and information-domain measures. The agreement decreased during postural and mental arithmetic stress, especially with regard to band-power ratio, conditional, and self-entropy. This finding suggests to use caution in adopting PRV as a surrogate of HRV during stress conditions.

Towards understanding the complexity of cardiovascular oscillations: Insights from information theory

Cardiovascular complexity is a feature of healthy physiological regulation, which stems from the simultaneous activity of several cardiovascular reflexes and other non-reflex physiological mechanisms. It is manifested in the rich dynamics characterizing the spontaneous heart rate and blood pressure variability (HRV and BPV). The present study faces the challenge of disclosing the origin of short-term HRV and BPV from the statistical perspective offered by information theory. To dissect the physiological mechanisms giving rise to cardiovascular complexity in different conditions, measures of predictive information, information storage, information transfer and information modification were applied to the beat-to-beat variability of heart period (HP), systolic arterial pressure (SAP) and respiratory volume signal recorded non-invasively in 61 healthy young subjects at supine rest and during head-up tilt (HUT) and mental arithmetics (MA). Information decomposition enabled to assess simultaneously several expected and newly inferred physiological phenomena, including: (i) the decreased complexity of HP during HUT and the increased complexity of SAP during MA; (ii) the suppressed cardiorespiratory information transfer, related to weakened respiratory sinus arrhythmia, under both challenges; (iii) the altered balance of the information transferred along the two arms of the cardiovascular loop during HUT, with larger baroreflex involvement and smaller feedforward mechanical effects; and (iv) an increased importance of direct respiratory effects on SAP during HUT, and on both HP and SAP during MA. We demonstrate that a decomposition of the information contained in cardiovascular oscillations can reveal subtle changes in system dynamics and improve our understanding of the complexity changes during physiological challenges.

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.

Fuzzy Entropy Analysis of the Electroencephalogram in Patients with Alzheimer's Disease: Is the Method Superior to Sample Entropy?

Alzheimer’s disease (AD) is the most prevalent form of dementia in the world, which is characterised by the loss of neurones and the build-up of plaques in the brain, causing progressive symptoms of memory loss and confusion. Although definite diagnosis is only possible by necropsy, differential diagnosis with other types of dementia is still needed. An electroencephalogram (EEG) is a cheap, portable, non-invasive method to record brain signals. Previous studies with non-linear signal processing methods have shown changes in the EEG due to AD, which is characterised reduced complexity and increased regularity. EEGs from 11 AD patients and 11 age-matched control subjects were analysed with Fuzzy Entropy (FuzzyEn), a non-linear method that was introduced as an improvement over the frequently used Approximate Entropy (ApEn) and Sample Entropy (SampEn) algorithms. AD patients had significantly lower FuzzyEn values than control subjects (p < 0.01) at electrodes T6, P3, P4, O1, and O2. Furthermore, when diagnostic accuracy was calculated using Receiver Operating Characteristic (ROC) curves, FuzzyEn outperformed both ApEn and SampEn, reaching a maximum accuracy of 86.36%. These results suggest that FuzzyEn could increase the insight into brain dysfunction in AD, providing potentially useful diagnostic information. However, results depend heavily on the input parameters that are used to compute FuzzyEn.

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.

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

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