Correlation dimension analysis of heart rate variability in patients with dilated cardiomyopathy

Correlation dimension and entropy in the assessment of sex differences based on human gait data

Introduction

It is proved that there are differences between gait performed by females and males, which appear in movements of selected body parts. Despite numerous state-of-the-art studies related to the discriminative analysis of motion capture data, the question of whether measures of signal complexity and uncertainty can extract valuable features for the problem of sex distinction still remains open. It is the subject of the paper.

Methods

Correlation dimension, as well as approximate and sample entropies, are selected to describe motion data. In the numerical experiments, the collected dataset with 884 samples of 25 females and 30 males was used. The measurements took place in the Human Motion Laboratory (HML), equipped with a highly precise motion capture system. Two variants of data representation were investigated-time series that contain joint rotations of taken skeleton model as well as positions of the markers attached to the human body. Finally, a comparative analysis between the populations of females and males using descriptive statistics, non-parametric estimation, and statistical hypotheses verification was carried out.

Results

There are statistically significant sex differences extracted by the taken measures. In general, the movements of lower limbs result in greater values of correlation dimension and entropies for females, while selected upper body parts play a similar role for males. The dissimilarities are mainly observed in hip, ankle, shoulder, and head movements.

Discussion

Correlation dimension and entropy measures provide robust and explainable features of motion capture data with a valuable description of the human locomotion system. Thus, beyond the importance of discovered differences between females and males, their interpretation and understanding are also known.

Time-specific associations of wearable sensor-based cardiovascular and behavioral readouts with disease phenotypes in the outpatient setting of the Chronic Renal Insufficiency Cohort

Patients with chronic kidney disease are at risk of developing cardiovascular disease. To facilitate out-of-clinic evaluation, we piloted wearable device-based analysis of heart rate variability and behavioral readouts in patients with chronic kidney disease from the Chronic Renal Insufficiency Cohort and controls (n  =  49). Time-specific partitioning of heart rate variability readouts confirm higher parasympathetic nervous activity during the night (mean RR at night 14.4  ±  1.9 ms vs. 12.8  ±  2.1 ms during active hours; n  =  47, analysis of variance (ANOVA) q  =  0.001). The α2 long-term fluctuations in the detrended fluctuation analysis, a parameter predictive of cardiovascular mortality, significantly differentiated between diabetic and nondiabetic patients (prominent at night with 0.58  ±  0.2 vs. 0.45  ±  0.12, respectively, adj. p  =  0.004). Both diabetic and nondiabetic chronic kidney disease patients showed loss of rhythmic organization compared to controls, with diabetic chronic kidney disease patients exhibiting deconsolidation of peak phases between their activity and standard deviation of interbeat intervals rhythms (mean phase difference chronic kidney disease 8.3 h, chronic kidney disease/type 2 diabetes mellitus 4 h, controls 6.8 h). This work provides a roadmap toward deriving actionable clinical insights from the data collected by wearable devices outside of highly controlled clinical environments.

Application of the Variance Delay Fuzzy Approximate Entropy for Autonomic Nervous System Fluctuation Analysis in Obstructive Sleep Apnea Patients

Obstructive sleep apnea (OSA) is a fatal respiratory disease occurring in sleep. OSA can induce declined heart rate variability (HRV) and was reported to have autonomic nerve system (ANS) dysfunction. Variance delay fuzzy approximate entropy (VD_fApEn) was proposed as a nonlinear index to study the fluctuation change of ANS in OSA patients. Sixty electrocardiogram (ECG) recordings of the PhysioNet database (20 normal, 14 mild-moderate OSA, and 26 severe OSA) were intercepted for 6 h and divided into 5-min segments. HRV analysis were adopted in traditional frequency domain, and nonlinear HRV indices were also calculated. Among these indices, VD_fApEn could significantly differentiate among the three groups (p < 0.05) compared with the ratio of low frequency power and high frequency power (LF/HF ratio) and fuzzy approximate entropy (fApEn). Moreover, the VD_fApEn (90%) reached a higher OSA screening accuracy compared with LF/HF ratio (80%) and fApEn (78.3%). Therefore, VD_fApEn provides a potential clinical method for ANS fluctuation analysis in OSA patients and OSA severity analysis.

Nonlinear Methods Most Applied to Heart-Rate Time Series: A Review

The heart-rate dynamics are one of the most analyzed physiological interactions. Many mathematical methods were proposed to evaluate heart-rate variability. These methods have been successfully applied in research to expand knowledge concerning the cardiovascular dynamics in healthy as well as in pathological conditions. Notwithstanding, they are still far from clinical practice. In this paper, we aim to review the nonlinear methods most used to assess heart-rate dynamics. We focused on methods based on concepts of chaos, fractality, and complexity: Poincaré plot, recurrence plot analysis, fractal dimension (and the correlation dimension), detrended fluctuation analysis, Hurst exponent, Lyapunov exponent entropies (Shannon, conditional, approximate, sample entropy, and multiscale entropy), and symbolic dynamics. We present the description of the methods along with their most notable applications.

Heart Rate Variability in Sport Performance: Do Time of Day and Chronotype Play A Role?

A reliable non-invasive method to assess autonomic nervous system activity involves the evaluation of the time course of heart rate variability (HRV). HRV may vary in accordance with the degree and duration of training, and the circadian fluctuation of this variable is crucial for human health since the heart adapts to the needs of different activity levels during sleep phases or in the daytime. In the present review, time-of-day and chronotype effect on HRV in response to acute sessions of physical activity are discussed. Results are sparse and controversial; however, it seems that evening-type subjects have a higher perturbation of the autonomic nervous system (ANS), with slowed vagal reactivation and higher heart rate values in response to morning exercise than morning types. Conversely, both chronotype categories showed similar ANS activity during evening physical tasks, suggesting that this time of day seems to perturb the HRV circadian rhythm to a lesser extent. The control for chronotype and time-of-day effect represents a key strategy for individual training schedules, and, in perspective, for primary injury prevention.

NONLINEAR HEART RATE VARIABILITY-BASED ANALYSIS AND PREDICTION OF PERFORMANCE STATUS IN PULMONARY METASTASES PATIENTS

Cancer causes chronic stress and is associated with impaired autonomic nervous system (ANS). Heart rate variability (HRV) has been suggested to be an important tool in the identification and prediction of performance status (PS) in cancer. Lead II surface electrocardiogram (ECG) was recorded from 24 pulmonary metastases (PM) subjects and 30 healthy controls for nonlinear HRV analysis. Artificial neural network (ANN) and support vector machine (SVM) were applied for the prediction analysis. Analysis of variance (ANOVA) along with post-hoc Tukey’s HSD test was conducted using statistical R, 64-bit, v.3.3.2, at [Formula: see text]. The obtained results suggested lower HRV that increases with cancer severity from the Eastern Cooperative Oncology Group (ECOG)1 PS to ECOG4 PS. ANOVA results stated that approximate entropy (ApEn) ([Formula: see text]-[Formula: see text], [Formula: see text]), detrended fluctuation analysis (DFA) [Formula: see text] ([Formula: see text]-[Formula: see text], [Formula: see text]) and correlation dimension (CD) ([Formula: see text]-[Formula: see text], [Formula: see text]) were significant. The 13 nonlinear features were fed to ANN and SVM to obtain 82.25% and 100% accuracies, respectively. Nonlinear HRV analysis has given promising results in the prediction of diagnosis of PS in PM patients. These inputs would be very useful for clinicians to diagnose PS in their cancer patients and improve their quality of living.

A Review on the Nonlinear Dynamical System Analysis of Electrocardiogram Signal

Electrocardiogram (ECG) signal analysis has received special attention of the researchers in the recent past because of its ability to divulge crucial information about the electrophysiology of the heart and the autonomic nervous system activity in a noninvasive manner. Analysis of the ECG signals has been explored using both linear and nonlinear methods. However, the nonlinear methods of ECG signal analysis are gaining popularity because of their robustness in feature extraction and classification. The current study presents a review of the nonlinear signal analysis methods, namely, reconstructed phase space analysis, Lyapunov exponents, correlation dimension, detrended fluctuation analysis (DFA), recurrence plot, Poincaré plot, approximate entropy, and sample entropy along with their recent applications in the ECG signal analysis.

Heart Rate Variability (HRV) Analysis: A Methodology for Organizational Neuroscience

Recently, the application of neuroscience methods and findings to the study of organizational phenomena has gained significant interest and converged in the emerging field of organizational neuroscience. Yet, this body of research has principally focused on the brain, often overlooking fuller analysis of the activities of the human nervous system and associated methods available to assess them. In this article, we aim to narrow this gap by reviewing heart rate variability (HRV) analysis, which is that set of methods assessing beat-to-beat changes in the heart rhythm over time, used to draw inference on the outflow of the autonomic nervous system (ANS). In addition to anatomo-physiological and detailed methodological considerations, we discuss related theoretical, ethical, and practical implications. Overall, we argue that this methodology offers the opportunity not only to inform on a wealth of constructs relevant for management inquiries but also to advance the overarching organizational neuroscience research agenda and its ecological validity.

Wearable technology and ECG processing for fall risk assessment, prevention and detection

Falls represent one of the most common causes of injury-related morbidity and mortality in later life. Subjects with cardiovascular disorders (e.g., related to autonomic dysfunctions and postural hypotension) are at higher risk of falling. Autonomic dysfunctions increasing the risk of falling in the short and mid-term could be assessed by Heart Rate Variability (HRV) extracted by electrocardiograph (ECG). We developed three trials for assessing the usefulness of ECG monitoring using wearable devices for: risk assessment of falling in the next few weeks; prevention of imminent falls due to standing hypotension; and fall detection. Statistical and data-mining methods are adopted to develop classification and regression models, validated with the cross-validation approach. The first classifier based on HRV features enabled to identify future fallers among hypertensive patients with an accuracy of 72% (sensitivity: 51.1%, specificity: 80.2%). The regression model to predict falls due to orthostatic dropdown from HRV recorded before standing achieved an overall accuracy of 80% (sensitivity: 92%, specificity: 90%). Finally, the classifier to detect simulated falls using ECG achieved an accuracy of 77.3% (sensitivity: 81.8%, specificity: 72.7%). The evidence from these three studies showed that ECG monitoring and processing could achieve satisfactory performances compared to other system for risk assessment, fall prevention and detection. This is interesting as differently from other technologies actually employed to prevent falls, ECG is recommended for many other pathologies of later life and is more accepted by senior citizens.

Classification of acute stress using linear and non-linear heart rate variability analysis derived from sternal ECG

Chronic stress detection is an important factor in predicting and reducing the risk of cardiovascular disease. This work is a pilot study with a focus on developing a method for detecting short-term psychophysiological changes through heart rate variability (HRV) features. The purpose of this pilot study is to establish and to gain insight on a set of features that could be used to detect psychophysiological changes that occur during chronic stress. This study elicited four different types of arousal by images, sounds, mental tasks and rest, and classified them using linear and non-linear HRV features from electrocardiograms (ECG) acquired by the wireless wearable ePatch® recorder. The highest recognition rates were acquired for the neutral stage (90%), the acute stress stage (80%) and the baseline stage (80%) by sample entropy, detrended fluctuation analysis and normalized high frequency features. Standardizing non-linear HRV features for each subject was found to be an important factor for the improvement of the classification results.

Adaptive correlation dimension method for analysing heart rate variability during the menstrual cycle

Correlation dimension (CD) is used for analysing the chaotic behaviour of the nonlinear heart rate variability (HRV) time series. In CD, the autocorrelation function is used to calculate the time delay. However, it does not provide optimum values of time delays, which leads to an inaccurate estimation of the HRV between phases of the menstrual cycle. Thus, an adaptive CD method is presented here to calculate the optimum value of the time delay based upon the information content in the HRV signal. In the proposed method, the first step is to divide the HRV signal into overlapping windows. Afterwards, the time delay is calculated for each window based on the features of the signal. This procedure of finding the optimum time delay for each window is known as adaptive autocorrelation. Then, the CD for each window is calculated using optimum time delays. Finally, adaptive CD is calculated by averaging the CD of all windows. The proposed method is applied on two data sets: (i) the standard Physionet dataset and (ii) the dataset acquired using BIOPAC(®)MP150. The results show that the proposed method can accurately differentiate between normal and diseased subjects. Further, the results prove that the proposed method is more accurate in detecting HRV variations during the menstrual cycles of 74 young women in lying and standing postures. Three statistical parameters are used to find the effectiveness of adaptive autocorrelation in calculating time delays. The comparative analysis validates the superiority of the proposed method over detrended fluctuation analyses and conventional CD.

Cloud-Based Smart Health Monitoring System for Automatic Cardiovascular and Fall Risk Assessment in Hypertensive Patients

The aim of this paper is to describe the design and the preliminary validation of a platform developed to collect and automatically analyze biomedical signals for risk assessment of vascular events and falls in hypertensive patients. This m-health platform, based on cloud computing, was designed to be flexible, extensible, and transparent, and to provide proactive remote monitoring via data-mining functionalities. A retrospective study was conducted to train and test the platform. The developed system was able to predict a future vascular event within the next 12 months with an accuracy rate of 84 % and to identify fallers with an accuracy rate of 72 %. In an ongoing prospective trial, almost all the recruited patients accepted favorably the system with a limited rate of inadherences causing data losses (<20 %). The developed platform supported clinical decision by processing tele-monitored data and providing quick and accurate risk assessment of vascular events and falls.

Automatic classifier based on heart rate variability to identify fallers among hypertensive subjects

Accidental falls are a major problem of later life. Different technologies to predict falls have been investigated, but with limited success, mainly because of low specificity due to a high false positive rate. This Letter presents an automatic classifier based on heart rate variability (HRV) analysis with the goal to identify fallers automatically. HRV was used in this study as it is considered a good estimator of autonomic nervous system (ANS) states, which are responsible, among other things, for human balance control. Nominal 24 h electrocardiogram recordings from 168 cardiac patients (age 72 ± 8 years, 60 female), of which 47 were fallers, were investigated. Linear and nonlinear HRV properties were analysed in 30 min excerpts. Different data mining approaches were adopted and their performances were compared with a subject-based receiver operating characteristic analysis. The best performance was achieved by a hybrid algorithm, RUSBoost, integrated with feature selection method based on principal component analysis, which achieved satisfactory specificity and accuracy (80 and 72%, respectively), but low sensitivity (51%). These results suggested that ANS states causing falls could be reliably detected, but also that not all the falls were due to ANS states.

Automatic prediction of cardiovascular and cerebrovascular events using heart rate variability analysis

Background

There is consensus that Heart Rate Variability is associated with the risk of vascular events. However, Heart Rate Variability predictive value for vascular events is not completely clear. The aim of this study is to develop novel predictive models based on data-mining algorithms to provide an automatic risk stratification tool for hypertensive patients.

Methods

A database of 139 Holter recordings with clinical data of hypertensive patients followed up for at least 12 months were collected ad hoc. Subjects who experienced a vascular event (i.e., myocardial infarction, stroke, syncopal event) were considered as high-risk subjects. Several data-mining algorithms (such as support vector machine, tree-based classifier, artificial neural network) were used to develop automatic classifiers and their accuracy was tested by assessing the receiver-operator characteristics curve. Moreover, we tested the echographic parameters, which have been showed as powerful predictors of future vascular events.

Results

The best predictive model was based on random forest and enabled to identify high-risk hypertensive patients with sensitivity and specificity rates of 71.4% and 87.8%, respectively. The Heart Rate Variability based classifier showed higher predictive values than the conventional echographic parameters, which are considered as significant cardiovascular risk factors.

Conclusions

Combination of Heart Rate Variability measures, analyzed with data-mining algorithm, could be a reliable tool for identifying hypertensive patients at high risk to develop future vascular events.

Multifractality in heartbeat dynamics in patients undergoing beating-heart myocardial revascularization

BACKGROUND

The multifractal approach of HRV analysis offers new insight into the mechanisms of autonomic modulation of the diseased hearts and has a potential to depict subtle changes in cardiac autonomic nervous control not revealed by conventional linear and non-linear analyses in various conditions like heart failure or stable angina pectoris. The aim of this study was to employ the multifractality approach in cardiac surgery patients and evaluate the multifractality before and after beating-heart myocardial revascularization (off-pump CABG).

METHODS

Twenty-four hour Holter recordings were performed pre- and postoperatively in 60 patients undergoing off-pump CABG. Selected conventional time- and frequency-domain linear HRV indices were calculated from the 24h and 5 min ECG segments, and preselected multifractal parameters τ(q=2), τ(q=3), h_top and Δh were determined for daytime (12:00-18:00) and nighttime (00:00-06:00) periods of the ECG recordings using Ivanov's method. Mean differences over time were tested using paired-samples t-test and exact Wilcoxon matched-pairs test. The results are reported as mean ± SD and median with interquartile range. A p value of <0.05 was considered statistically significant.

RESULTS

All selected conventional linear HRV parameters decreased significantly after off pump CABG (p from <0.001-0.015). Preoperatively, multifractal parameter τ(q=2) was -0.60 ± 0.12 and -0.54 ± 0.12, τ(q=3) -0.52 ± 0.18 and -0.49 ± 0.17, h_top 0.20 ± 0.07 and 0.15 ± 0.07 and Δh 0.31 ± 0.14 and 0.17 ± 0.14 for daytime and nighttime periods, respectively. Postoperatively, τ(q=2) and τ(q=3) were significantly higher for daytime (-0.49 ± 0.15, p<0.001 and -0.43 ± 0.23, p=0.015), whereas h_top and Δh were significantly higher for both daytime and nighttime (0.25 ± 0.07, p<0.001 and 0.19 ± 0.06, p=0.002 for h_top and 0.41 ± 0.20, p=0.003 and 0.31 ± 0.19, p < 0.001 for Δh, respectively). All pre- and postoperative parameters, except τ(q=2) and τ(q=3) preoperatively, were significantly lower for nighttime as compared to daytime periods.

CONCLUSIONS

A significant breakdown of multifractal complexity and anti-correlation behavior with a significant sympathetic overdrive and a concomitant parasympathetic withdrawal occurs after off-pump CABG. The circadian pattern of multifractality regains its day-night variation in the first week after the surgical procedure.

Circadian variation of motor current observed in fixed rotation speed continuous-flow left ventricular assist device support

The algorithm for the physiological control provided by left ventricular assist devices (LVADs) has been controversial. In particular, little is known about the physiological control algorithm (such as for achieving physiological circadian rhythms) in continuous-flow LVADs. To investigate the existence of circadian variation, we retrospectively evaluated the LVAD flow-correlated motor current of patients supported by continuous-flow LVADs. The motor current and the pump speed were collected from the external controller every 10 min after device implantation, and the data were divided for every 30-day period, which began on midnight on the first post-operative day. The subjects were 18 patients (mean age 37.7, mean body surface area 1.71 m(2) at the time of operation) with dilated cardiomyopathy or dilated phase of hypertrophic cardiomyopathy. As of August 1, 2013, the patients' median support duration was 889 days. The mean calculated dominant period of motor current variation was 24.0 h and the mean amplitude was 11.7 mA for the entire duration. The amplitude of the motor current circadian variation tended to be increased until around the fifth month. The motor current had a tendency to be relatively low during the night time and high during the day time. A significant difference was found between the night-time and day-time mean motor current for the entire duration (p < 0.05). In conclusion, the circadian variation of the motor current could be observed over long term in patients with fixed rotation speed continuous-flow LVAD support.

[Heart rate variability during sleep in children with multiple disabilities]

OBJECTIVES

To study heart rate variability during sleep in children with multiple disabilities in order to observe the behavior of the autonomic nervous system.

METHODS

The R-R interval variability of 4 to 12 years old children was recorded with a heart rate monitor during one night. Children with multiple disabilities (G1) and healthy children (G2) were compared in time, frequency, and non-linear domains.

RESULTS

Temporal (P<0.01), frequency (P<0.05), and non-linear (P<0.01) variables in the G1 were lower than in the G2 group.

DISCUSSION

The time and frequency analysis confirmed the predominance of the sympathetic nervous system during sleep in G1 children. Reduced non-linear variables can explain sleep with less informations (correlation dimension: 2.203 ± 1.239 versus 3.842 ± 0.378; P<0.001), less complex cycles of sleep (approximate entropy: 1.153 ± 0.200 versus 1.365 ± 0.099; P<0.01), and a reduced correlation in short-term variability (SD1: 42.37 ± 19.0 (ms) versus 73.44 ± 25.3; P<0.01). The fractal structure of the recordings was not affected (P>0.05). The diseases encountered are probably the reason for these findings, but the variety of disorders and medications of the children with multiple disabilities needs to be studied with a larger and more varied sample.

CONCLUSION

Sympathetic predominance during sleep in children with multiple disabilities is associated with a decrease in adaptive abilities of these children's autonomic nervous system.

NONLINEAR ANALYSIS OF PHYSIOLOGICAL SIGNALS: A REVIEW

This paper reviews various nonlinear analysis methods for physiological signals. The assessment is based on a discussion of chaos-inspired methods, such as fractal dimension (FD), correlation dimension (D2), largest Lyapunov exponet (LLE), Renyi's entropy (REN), Shannon spectral entropy (SEN), and approximate entropy (ApEn). We document that these methods are used to extract discriminative features from electroencephalograph (EEG) and heart rate variability (HRV) signals by reviewing the relevant scientific literature. EEG features can be used to support the diagnosis of epilepsy and HRV features can be used to support the diagnosis of cardiovascular diseases as well as diabetes. Documenting the widespread use of these and other nonlinear methods supports our thesis that the study of feature extraction methods, based on the chaos theory, is an important subject which has been gaining more and significance in biomedical engineering. We adopt the position that pursuing research in the field of biomedical engineering is ultimately a progmatic activity, where it is necessary to engage in features that work. In this case, the nonlinear features are working well, even if we do not have conclusive evidence that the underlying physiological phenomena are indeed chaotic.

Modified permutation-entropy analysis of heartbeat dynamics

Heart rate variability (HRV) contains important information about the modulation of the cardiovascular system. Various methods of nonlinear dynamics (e.g., estimating Lyapunov exponents) and complexity measures (e.g., correlation dimension or entropies) have been applied to HRV analysis. Permutation entropy, which was proposed recently, has been widely used in many fields due to its conceptual and computational simplicity. It maps a time series onto a symbolic sequence of permutation ranks. The original permutation entropy assumes the time series under study has a continuous distribution, thus equal values are rare and can be ignored by ranking them according to their order of emergence, or broken by adding small random perturbations to ensure every symbol in a sequence is different. However, when the observed time series is digitized with lower resolution leading to a greater number of equal values, or the equalities represent certain characteristic sequential patterns of the system, it may not be rational to simply ignore or break them. In the present paper, a modified permutation entropy is proposed that, by mapping the equal value onto the same symbol (rank), allows for a more accurate characterization of system states. The application of the modified permutation entropy to the analysis of HRV is investigated using clinically collected data. Results show that modified permutation entropy can greatly improve the ability to distinguish the HRV signals under different physiological and pathological conditions. It can characterize the complexity of HRV more effectively than the original permutation entropy.

Nonlinear Heart Rate Variability features for real-life stress detection. Case study: students under stress due to university examination

Background

This study investigates the variations of Heart Rate Variability (HRV) due to a real-life stressor and proposes a classifier based on nonlinear features of HRV for automatic stress detection.

Methods

42 students volunteered to participate to the study about HRV and stress. For each student, two recordings were performed: one during an on-going university examination, assumed as a real-life stressor, and one after holidays. Nonlinear analysis of HRV was performed by using Poincaré Plot, Approximate Entropy, Correlation dimension, Detrended Fluctuation Analysis, Recurrence Plot. For statistical comparison, we adopted the Wilcoxon Signed Rank test and for development of a classifier we adopted the Linear Discriminant Analysis (LDA).

Results

Almost all HRV features measuring heart rate complexity were significantly decreased in the stress session. LDA generated a simple classifier based on the two Poincaré Plot parameters and Approximate Entropy, which enables stress detection with a total classification accuracy, a sensitivity and a specificity rate of 90%, 86%, and 95% respectively.

Conclusions

The results of the current study suggest that nonlinear HRV analysis using short term ECG recording could be effective in automatically detecting real-life stress condition, such as a university examination.

Automatic detection of pathological voices using complexity measures, noise parameters, and mel-cepstral coefficients

This paper proposes a new approach to improve the amount of information extracted from the speech aiming to increase the accuracy of a system developed for the automatic detection of pathological voices. The paper addresses the discrimination capabilities of 11 features extracted using nonlinear analysis of time series. Two of these features are based on conventional nonlinear statistics (largest Lyapunov exponent and correlation dimension), two are based on recurrence and fractal-scaling analysis, and the remaining are based on different estimations of the entropy. Moreover, this paper uses a strategy based on combining classifiers for fusing the nonlinear analysis with the information provided by classic parameterization approaches found in the literature (noise parameters and mel-frequency cepstral coefficients). The classification was carried out in two steps using, first, a generative and, later, a discriminative approach. Combining both classifiers, the best accuracy obtained is 98.23% ± 0.001.

Application of HRV-CD for estimation of life expectancy in various clinical disorders

BACKGROUND

Low heart rate variability (HRV) was found in various medical conditions including heart failure and acute myocardial infarction. Decreased HRV in these conditions predicted poor prognosis.

METHODS

HRV was estimated in 133 unselected inpatients with relevant clinical bedside conditions by non-linear analysis derived from chaos theory, which calculates the correlation dimension (CD) of the cardiac electrophysiologic system (HRV-CD).

RESULTS

Mean HRV-CD in the entire group was 3.75+/-0.45. Heart failure, coronary artery disease, cardiac arrhythmia, low serum potassium, renal dysfunction, and diabetes mellitus were significantly associated with reduced HRV-CD compared to their counterparts [3.6 vs. 3.9 (P<.001), 3.65 vs. 3.87 (P=.005), 3.58 vs. 3.8 (P=.01), 3.38 vs. 3.81 (P=.02), 3.59 vs. 3.8 (P=.04), and 3.66 vs. 3.82 (P=.04), respectively]. Stepwise logistic regression showed heart failure to be the condition most significantly associated with low HRV-CD (odds ratio 4.2, 95% confidence interval 1.90-9.28, P<.001). In the entire group, decreased HRV-CD (< or =3.75 vs. >3.75) was associated with lower survival (P=.01). Mortality of diabetic patients with HRV-CD < or =3.75 exceeded the mortality in patients with HRV-CD >3.75 (P=.02). Heart failure, renal dysfunction or age over 70 combined with HRV-CD < or =3.75 also appeared to be associated with augmented mortality.

CONCLUSIONS

Diminished HRV-CD is associated with heart failure, coronary artery disease, cardiac arrhythmia, renal dysfunction, diabetes mellitus and low serum potassium. Among the latter, heart failure is most significantly associated with decreased HRV-CD. Decreased HRV-CD values, especially in diabetics, are also associated with lower survival.

Heart rate variability analysis based on time-frequency representation and entropies in hypertrophic cardiomyopathy patients

In hypertrophic cardiomyopathy (HCM) patients there is an increased risk of premature death, which can occur with little or no warning. Furthermore, classification for sudden cardiac death on patients with HCM is very difficult. The aim of our study was to improve the prognostic value of heart rate variability (HRV) in HCM patients, giving insight into changes of the autonomic nervous system. In this way, the suitability of linear and nonlinear measures was studied to assess the HRV. These measures were based on time-frequency representation (TFR) and on Shannon and Rényi entropies, and compared with traditional HRV measures. Holter recordings of 64 patients with HCM and 55 healthy subjects were analyzed. The HCM patients consisted of two groups: 13 high risk patients, after aborted sudden cardiac death (SCD); 51 low risk patients, without SCD. Five-hour RR signals, corresponding to the sleep period of the subjects, were considered for the analysis as a comparable standard situation. These RR signals were filtered in the three frequency bands: very low frequency band (VLF, 0-0.04 Hz), low frequency band (LF, 0.04-0.15 Hz) and high frequency band (HF, 0.15-0.45 Hz). TFR variables based on instantaneous frequency and energy functions were able to classify HCM patients and healthy subjects (control group). Results revealed that measures obtained from TFR analysis of the HRV better classified the groups of subjects than traditional HRV parameters. However, results showed that nonlinear measures improved group classification. It was observed that entropies calculated in the HF band showed the highest statistically significant levels comparing the HCM group and the control group, p-value < 0.0005. The values of entropy measures calculated in the HCM group presented lower values, indicating a decreasing of complexity, than those calculated from the control group. Moreover, similar behavior was observed comparing high and low risk of premature death, the values of the entropy being lower in high risk patients, p-value < 0.05, indicating an increase of predictability. Furthermore, measures from information entropy, but not from TFR, seem to be useful for enhanced risk stratification in HCM patients with an increased risk of sudden cardiac death.

Automated detection of anesthetic depth levels using chaotic features with artificial neural networks

Monitoring the depth of anesthesia (DOA) during surgery is very important in order to avoid patients' interoperative awareness. Since the traditional methods of assessing DOA which involve monitoring the heart rate, pupil size, sweating etc, may vary from patient to patient depending on the type of surgery and the type of drug administered, modern methods based on electroencephalogram (EEG) are preferred. EEG being a nonlinear signal, it is appropriate to use nonlinear chaotic parameters to identify the anesthetic depth levels. This paper discusses an automated detection method of anesthetic depth levels based on EEG recordings using non-linear chaotic features and neural network classifiers. Three nonlinear parameters, namely, correlation dimension (CD), Lyapunov exponent (LE) and Hurst exponent (HE) are used as features and two neural network models, namely, multi-layer perceptron network (feed forward model) and Elman network (feedback model) are used for classification. The neural network models are trained and tested with single and multiple features derived from chaotic parameters and the performances are evaluated in terms of sensitivity, specificity and overall accuracy. It is found from the experimental results that the Lyapunov exponent feature with Elman network yields an overall accuracy of 99% in detecting the anesthetic depth levels.

A new heart rate variability analysis method by means of quantifying the variation of nonlinear dynamic patterns

A new heart rate variability (HRV) analysis method, quantifying the variation of nonlinear dynamic pattern (VNDP) in heart rate series, is proposed and validated against the age stratified Fantasia database. The method is based on three processes: (1) a recurrence quantification analysis (RQA) to quantify the dynamic patterns, (2) the use of mutual information (MI) and the entropy (EN) to characterize the VNDP, and 3) linear discriminant analysis to exploit the associations within MI and EN measures. Practically, the VNDP method overcomes the nonstationarity problem and exploits the nonstationary properties in HRV analyses. Physiologically, the VNDP reflects the properties of the fundamental short-term HRV dynamic system and the external associations of the system within the autonomous nervous system (ANS). The characteristic probability density peaks portrayed by VNDP plots indicate the quantum-like heart dynamics, which may provide valuable insights into the control of the ANS. The discrimination results of the reduced pattern dynamic range due to aging, from a new perspective, display the reduction in HRV. The significantly improved discriminatory power, compared to conventional RQA analyses, shows that the VNDP analysis can practically quantify the nonstationary nonlinear dynamics for ANS assessments.

Nonlinear analysis of heart rate dynamics in hyperthyroidism

Studies on the physiology of the cardiovascular system suggested that the generation of the heart rate signal is governed by nonlinear chaotic dynamics. No study investigated the nonlinear dynamics of heart rate in hyperthyroidism. We examined whether the heart rate dynamics of hyperthyroid patients is different from normal controls by the nonlinear analysis of heart rate variability (HRV) with correlation dimension (CD). Thirty-three hyperthyroid Graves' disease patients (30 females and 3 males; age 31 +/- 1 years, means +/- SE) and 33 sex-, age-, and body mass index-matched normal controls were recruited to receive one-channel electrocardiogram recording for 30 min. The CD, an index of complexity, was computed from the sequence of normal R-R intervals by the Grassberger and Procaccia algorithm. Compared to the normal controls, the hyperthyroid patients showed significant reductions (P < 0.001) in the mean R-R interval (hyperthyroid 616 +/- 15 versus control 868 +/- 16 ms), the standard deviation of R-R intervals (25 +/- 2 versus 54 +/- 4 ms) and CD (5.02 +/- 0.11 versus 6.42 +/- 0.16). Our study demonstrated for the first time that hyperthyroid patients and normal controls could be distinguished by CD analysis of HRV. In addition, the decreased CD in hyperthyroid patients implies reduced complexity and impaired tolerance to cardiovascular stresses in hyperthyroidism. This finding helps to explain exercise intolerance and irritability manifested by the hyperthyroid patients.

Large-scale dimension densities for heart rate variability analysis

In this work, we reanalyze the heart rate variability (HRV) data from the 2002 Computers in Cardiology (CiC) Challenge using the concept of large-scale dimension densities and additionally apply this technique to data of healthy persons and of patients with cardiac diseases. The large-scale dimension density (LASDID) is estimated from the time series using a normalized Grassberger-Procaccia algorithm, which leads to a suitable correction of systematic errors produced by boundary effects in the rather large scales of a system. This way, it is possible to analyze rather short, nonstationary, and unfiltered data, such as HRV. Moreover, this method allows us to analyze short parts of the data and to look for differences between day and night. The circadian changes in the dimension density enable us to distinguish almost completely between real data and computer-generated data from the CiC 2002 challenge using only one parameter. In the second part we analyzed the data of 15 patients with atrial fibrillation (AF), 15 patients with congestive heart failure (CHF), 15 elderly healthy subjects (EH), as well as 18 young and healthy persons (YH). With our method we are able to separate completely the AF (rho (mu/ls) = 0.97 +/- 0.02) group from the others and, especially during daytime, the CHF patients show significant differences from the young and elderly healthy volunteers (CHF, 0.65 +/- 0.13; EH, 0.54 +/- 0.05; YH, 0.57 +/- 0.05; p < 0.05 for both comparisons). Moreover, for the CHF patients we find no circadian changes in rho (mu/ls) (day, 0.65 +/- 0.13; night, 0.66 +/- 0.12; n.s.) in contrast to healthy controls (day, 0.54 +/- 0.05; night, 0.61 +/- 0.05; p=0.002). Correlation analysis showed no statistical significant relation between standard HRV and circadian LASDID, demonstrating a possibly independent application of our method for clinical risk stratification.