Sampling frequency of the RR interval time series for spectral analysis of heart rate variability

Spectral analysis of heart rate variability (HRV) is an accepted method for assessment of cardiac autonomic function and its relationship to numerous disorders and diseases. Various non-parametric methods for HRV estimation have been developed and extensive literature on their respective properties is available. The RR interval time series can be seen as a series of non-uniformly spaced samples. To analyse the power spectra of this series using the discrete Fourier transform (DFT), we need to interpolate the series for obtaining uniformly spaced intervals. The selection of sampling period plays a critical role in obtaining the power spectra in terms of computational efficiency and accuracy. In this paper, we shall analyse the RR interval time series from selected subjects for different sampling frequencies to compare the error introduced in selected frequency-domain measures of HRV at a constant frequency resolution for a specific duration of electrocardiogram (ECG) data. It should be pointed out that, although many other error causes are possible in the frequency-domain measures, our attention will be confined only to the performance comparison due to the different sampling frequencies. While the choice of RR interval sampling frequency (f(s)) is arbitrary, the sampling rate of RR interval series must be selected with due consideration to mean and minimum RR interval; f(s = )4 Hz was proposed for a majority of cases. This is an appropriate sampling rate for the study of autonomic regulation, since it enables us to compute reliable spectral estimates between dc and 1 Hz, which represents the frequency band within which the autonomic nervous system has significant response. Furthermore, resampled RR intervals are evenly spaced in time and are synchronized with the samples of the other physiologic signals, enabling cross-spectral estimates with these signals.     

Power spectral analysis of heart rate variability in psychiatry

Power spectrum analysis of heart rate variability (PSA of HRV) is a promising method, which can be used as an index of cardiac autonomic balance. PSA of HRV is a noninvasive technique, based on ECG sampling of RR interval variation, thus providing a dynamic assessment of sympathetic and parasympathetic tone, reflecting the interactions between the two. It has been shown to have potential value in various laboratory and clinical conditions. It is influenced by many factors such as age, sex, position, breathing, smoking, hour of the day and medications. Different methods of data processing by various authors have often elicited conflicting results. Standard values are not yet available to be used or compared in different settings. From the interest it has raised, it may be expected that this method will be in widespread use in clinical practice in the future, providing a useful tool, both for diagnostic and prognostic purposes, as well as serving as a further aid towards monitoring therapeutic interventions. This review highlights techniques of dynamic assessment of HRV and studies of its clinical applications in psychiatry in particular. It raises the potentially important prognostic implications of protracted autonomic dysfunction in psychiatric patient populations, especially for cardiovascular morbidity and mortality.     

Wide-band spectral analysis of blood pressure and RR interval variability in borderline and mild hypertension.

The aim of this study was firstly to investigate whether indices of wide-band spectral analysis in borderline hypertensive (BHT) or mildly hypertensive (HT) subjects differ from those in normotensive (NT) subjects, and secondly to assess the predictive value of these indices for future hypertension. Electrocardiogram and intra-arterial 24 h ambulatory blood pressure (BP) were recorded in 32 NT, 29 BHT and 30 HT middle-aged men. From the recordings, a 16 h period was extracted for wide-band spectral analysis. A single spectrum of BP and RR interval (RRI) variability was computed for each period by the fast Fourier transform method. The slopes of the spectra were assessed on a log-log scale by linear fitting of the spectral values. Power spectral densities were calculated over regions of 0-0.003, 0.003-0.04, 0.04-0.15, 0.15-0.40 and 0-0.4 Hz. No between-group differences were found in the slopes of BP and RRI spectra. The between-group differences in spectral powers for BP variability were almost invariably significant. The spectral powers for RRI variability did not show between-group differences. Five years later, 22 NT, 22 BHT and 18 HT subjects were re-assessed using casual BP measurements. In a logistic regression model for the combined group of NT and BHT subjects who became HT (22 of 44) during the five-year period, none of the parameters of wide-band spectrum predicted the development of hypertension. In conclusion, parameters of wide-band spectral analysis may not be useful in predicting future hypertension in NT and BHT subjects. Because the BP level is a major factor influencing BP variability, the between-group differences in wide-band spectral powers in BP may be due to differences in BP level rather than differences in cardiovascular regulatory mechanisms.     

Application of time series spectral analysis theory: analysis of cardiovascular variability signals

The paper focuses on the most important application problems commonly encountered in spectral analysis of short-term (less than 10 min) recordings of cardiovascular variability signals (CVSs), critically analysing the different approaches to these problems presented in the literature and suggesting practical solutions based on sound theoretical and empirical considerations. The Blackman-Tukey (BT) and Burg methods have been selected as the most representative of classical and AR spectral estimators, respectively. For realistic simulations, ‘synthetic’ CVSs are generated as AR processes whose parameters are estimated on corresponding time series of normal, post-myocardial infarction and congestive heart failure subjects. The problem of resolution of spectral estimates is addressed, and an empirical method is proposed for model order selection in AR estimation. The issue of the understandability and interpretability of spectral shapes is discussed. The problem of non-stationarity and removing trends is dealt with. The important issue of identification and estimation of spectral components is discussed, and the main advantages and drawbacks of spectral decomposition algorithms are critically evaluated.     

Automatic identification of fetal breathing movements in fetal RR interval time series

Fetal breathing movements are associated with respiratory sinus arrhythmia (RSA). We present an algorithm which processes RR interval time series in the time and frequency domain, identifying spectral peaks with characteristics consistent with fetal RSA. Tested on 50 data sets from the second and third trimester, the algorithm had a sensitivity of 96.1%, false positive rate 35.7%, false negative rate 3.9%. The characteristics of automatically and visually identified episodes were very similar and corresponded the expected changes over gestation. The method is suited for easy and reliable identification of fetal breathing movements.     

Breathing frequency bias in fractal analysis of heart rate variability

Detrended Fluctuation Analysis (DFA) is an algorithm widely used to determine fractal long-range correlations in physiological signals. Its application to heart rate variability (HRV) has proven useful in distinguishing healthy subjects from patients with cardiovascular disease. In this study we examined the effect of respiratory sinus arrhythmia (RSA) on the performance of DFA applied to HRV. Predictions based on a mathematical model were compared with those obtained from a sample of 14 normal subjects at three breathing frequencies: 0.1 Hz, 0.2 Hz and 0.25 Hz. Results revealed that: (1) the periodical properties of RSA produce a change of the correlation exponent in HRV at a scale corresponding to the respiratory period, (2) the short-term DFA exponent is significantly reduced when breathing frequency rises from 0.1 Hz to 0.2 Hz. These findings raise important methodological questions regarding the application of fractal measures to short-term HRV.     

Short and long term non-linear analysis of RR variability series

The complexity of RR variability is approached in the short and in the long term by means of black-box data analysis. Short term series of a few hundred beats are explored by means of informational entropy and predictability indexes. A correction to biases toward false determinism is performed assuming maximum uncertainty, whenever data do not furnish sufficient recurrences. Non-randomness and non-linearity are tested by means of surrogate data provided by random shuffling and phase randomization respectively. In the long term of the 24-h or of several hours, similar tests based on mutual information are applied and validated by means of surrogate series. In addition the state space reconstruction is carried out by means of state space non-linear filtering addressing directly the reconstructed trajectories. In this condition, parameters characterizing the hypothetical attractor, mainly the maximum Lyapunov exponent, can be reliably identified.     

Recording of ECG signals on a portable MiniDisc recorder for time and frequency domain heart rate variability analysis

Analysis of heart rate variability (HRV) is a non-invasive technique useful for investigating autonomic function in both humans and animals. It has been used for research into both behaviour and physiology. Commercial systems for human HRV analysis are expensive and may not have sufficient flexibility for appropriate analysis in animals. Some heart rate monitors have the facility to provide inter-beat interval (IBI), but verification following collection is not possible as only IBIs are recorded, and not the raw electrocardiogram (ECG) signal. Computer-based data acquisition and analysis systems such as Po-Ne-Mah and Biopac offer greater flexibility and control but have limited portability. Many laboratories and veterinary surgeons have access to ECG machines but do not have equipment to record ECG signals for further analysis. The aim of the present study was to determine whether suitable HRV data could be obtained from ECG signals recorded onto a MiniDisc (MD) and subsequently digitised and analysed using a commercial data acquisition and analysis package. ECG signals were obtained from six Thoroughbred horses by telemetry. A split BNC connecter was used to allow simultaneous digitisation of analogue output from the ECG receiver unit by a computerised data acquisition system (Po-Ne-Mah) and MiniDisc player (MZ-N710, Sony). Following recording, data were played back from the MiniDisc into the same input channel of the data acquisition system as previously used to record the direct ECG. All data were digitised at a sampling rate of 500 Hz. IBI data were analysed in both time and frequency domains and comparisons between direct recorded and MiniDisc data were made using Bland-Altman analysis. Despite some changes in ECG morphology due to loss of low frequency content (primarily below 5 Hz) following MiniDisc recording, there was minimal difference in IBI or time or frequency domain analysis between the two recording methods. The MiniDisc offers a cost-effective approach to intermediate recording of ECG signals for subsequent HRV analysis and also provides greater flexibility than use of human Holter systems.     

Comparison and clinical application of frequency domain methods in analysis of neonatal heart rate time series

The frequency content of the heart rate (HR) series contains information regarding the state of the autonomic nervous system. Of particular importance is respiratory sinus arrhythmia (RSA), the high-frequency fluctuation in HR attributable to respiration. The unevenly sampled nature of heart rate data, however, presents a problem for the discrete Fourier transform. Interpolation of the HR series allows even sampling, but filters high-frequency content. The Lomb periodogram (LP) is a regression-based method that addresses these issues. To evaluate the efficacy of the LP and Fourier techniques in detecting RSA, we compared the spectrum of intervals, the spectrum of HR samples, and the LP of simulated and clinical neonatal time series. We found the LP was superior to the spectrum of intervals and the spectrum of HR samples in analysis near the critical frequency of one half the average sampling rate. Applying the LP to clinical data, we found (1) evidence of stochastic resonance, an enhancement of periodicity with the addition of small amounts of noise, and (2) reduced power at all frequencies prior to clinical diagnosis of neonatal sepsis. © 2001 Biomedical Engineering Society. PAC01: 8719Hh, 8719La, 0260Ed, 0230Lt, 0545Tp, 0250-r, 0230Nw, 0230Uu     

A new view of a stationarity of the RR series for sinusal variability analysis

The influence of ANS in sinusal variability is studied through analysis of RR series, and particularly RR interval variations during time. Different kinds of RR series signal analysis are applied to clinical situations found in cardiology. However, some of the RR series may be stationary as well as non-stationary. Statistical tests applied to the RR series will establish determinism and stationarity of these signals. The aim of this article is to characterize the statistical behaviour pattern of RR series in order to identify precautions that should be observed when time-frequency transform techniques are used in sinusal clinical investigations. Eight kinds of RR series concerning sinusal variability were submitted to the statistical tests. The results showed the uncertain character of the RR series and their non-stationarity. This result is consequently a warning against using several techniques of time-frequency transform for sinusal variability analysis. Some of the techniques studied are adapted to non-stationary signals under some conditions.     

Evaluation of frequency and time-frequency spectral analysis of heart rate variability as a diagnostic marker of the sleep apnoea syndrome

The sleep apnoea/hypopnoea syndrome (SAHS) elicits a unique heart rate rhythm that may provide the basis for an effective screening tool. The study uses the receiver operator characteristic (ROC) to assess the diagnostic potential of spectral analysis of heart rate variability (HRV) using two methods, the discrete Fourier transform (DFT) and the discrete harmonic wavelet transform (DHWT). These two methods are compared over different sleep stages and spectral frequency bands. The HRV results are subsequently compared with those of the current screening method of oximetry. For both the DFT and the DHWT, the most diagnostically accurate frequency range for HRV spectral power calculations is found to be 0.019-0.036 Hz (denoted by AB2). Using AB2, 15 min sections of non-REM sleep data in 40 subjects produce ROC areas, for the DFT, DHWT and oximetry, of 0.94, 0.97 and 0.67, respectively. In REM sleep, ROC areas are 0.78, 0.79 and 0.71, respectively. In non-REM sleep, spectral analysis of HRV appears to be a significantly better indicator of the SAHS than the current screening method of oximetry, and, in REM sleep, it is comparable with oximetry. The advantage of the DHWT over the DFT is that it produces a greater time resolution and is computationally more efficient. The DHWT does not require the precondition of stationarity or interpolation of raw HRV data.     

Evaluation of frequency and time-frequency spectral analysis of heart rate variability as a diagnostic marker of the sleep apnoea syndrome

The sleep apnoea/hypopnoea syndrome (SAHS) elicits a unique heart rate rhythm that may provide the basis for an effective screening tool. The study uses the receiver operator characteristic (ROC) to assess the diagnostic potential of spectral analysis of heart rate variability (HRV) using two methods, the discrete Fourier transform (DFT) and the discrete harmonic wavelet transform (DHWT). These two methods are compared over different sleep stages and spectral frequency bands. The HRV results are subsequently compared with those of the current screening method of oximetry. For both the DFT and the DHWT, the most diagnostically accurate frequency range for HRV spectral power calculations is found to be 0.019–0.036 Hz (denoted by AB₂). Using AB₂, 15 min sections of non-REM sleep data in 40 subjects produce ROC areas, for the DFT, DHWT and oximetry, of 0.94, 0.97 and 0.67, respectively. In REM sleep, ROC areas are 0.78, 0.79 and 0.71, respectively. In non-REM sleep, spectral analysis of HRV appears to be a significantly better indicator of the SAHS than the current screening method of oximetry, and, in REM sleep, it is comparable with oximetry. The advantage of the DHWT over the DFT is that it produces a greater time resolution and is computationally more efficient. The DHWT does not require the precondition of stationarity or interpolation of raw HRV data.     

Statistical analysis of RR series variability in spinal cord injured persons

Disabled persons with spinal cord injury are prone to cardiovascular dysfunction and an increased risk of cardiovascular disease. Rehabilitation of the disabled person is a critical task as it involves multiple therapies. Physical exercise is an important component of rehabilitation, and depends on cardiovascular health. Reduced RR variability is a marker of poor cardiac health. Time domain RR variability analysis of 38 normal healthy subjects and 20 spinal cord injured subjects has been carried out and compared. In this study, RR intervals were recorded in three different modes or positions: supine, sitting and five-second rhythm respiration. At a time of 150 s RR interval data were acquired in each mode and analysed. Statistical parameters (mean, HR, STD, NN50 and pNN50) were calculated. It was observed that most of the indices were significantly and substantially altered in spinal cord injured persons.     

A robust algorithm for heart rate variability time series artefact correction using novel beat classification

Abstract

Purpose: Heart rate variability is a commonly used measurement to evaluate functioning of autonomic nervous system, psychophysiological stress, and exercise intensity and recovery. HRV measurements contain artefacts such as extra, missed or misaligned beat detections, which can produce significant distortion on HRV parameters. In this paper, a robust automatic method for artefact detection from HRV time series is proposed.

Methods: The proposed detection method is based on time-varying thresholds estimated from distribution of successive RR-interval differences combined with a novel beat classification scheme. The method is validated using simulated extra, missed and misaligned beat detections as well as real artefacts such as atrial and ventricular ectopic beats.

Results: The sensitivity of the algorithm to detect simulated missed/extra beats was 100%. The sensitivity to detect real atrial and ventricular ectopic beats was 96.96%, the corresponding specificity being 99.94%. The mean error in HRV parameters after correction was <2% for missed and extra beats as well as for misaligned beats generated with large displacement factors. Misaligned beats with smallest displacement factor were the most difficult to detect and resulted in largest HRV parameter errors after correction, largest errors being <8%.

Conclusions: The HRV artefact correction algorithm presented in this study provided comparable specificity and better sensitivity to detect ectopic beats as compared to state-of-the-art algorithms. The proposed algorithm detects abnormal beats with high accuracy, is relatively easy to implement, and secures reliable HRV analysis by reducing the effect of possible artefacts to tolerable level.     

Approximate minimum bias multichannel spectral estimation for heart rate variability

Spectral decomposition of variations in heart rate permits noninvasive measurement of autonomic nervous activity in humans and animals. Autonomic metrics based on spectral analysis are useful in monitoring clinical conditions such as diabetic neuropathy and reinnervation in heart transplant patients. A persistent problem in deriving such autonomic measures is the prerequisite of an accurate and unbiased power spectrum of heart rate variability (HRV). Numerous parametric and nonparametric power spectrum estimators have been introduced, each with its own advantages and drawbacks. Estimator bias has received little attention, despite the fact that at least one common HRV spectrum estimator, the autoregressive method, is known to exhibit bias even in idealized circumstances. We introduce an approximately minimum bias, nonparametric, multichannel spectrum estimation procedure for HRV and contemporaneous signals. The procedure, which is designed specifically for irregular sampling, does not require data segmentation and provides statistically consistent, low variance multichannel spectrum estimates. Estimator performance on simulated and clinical data is presented and compared with results from autoregressive models and Welch periodograms with and without compensation for irregular sampling. Results indicate that the proposed method exhibits advantages over conventional HRV spectrum estimators. Relative computational complexity of the proposed method is also considered.     

Statistical analysis of RR series variability in spinal cord injured persons

Disabled persons with spinal cord injury are prone to cardiovascular dysfunction and an increased risk of cardiovascular disease. Rehabilitation of the disabled person is a critical task as it involves multiple therapies. Physical exercise is an important component of rehabilitation, and depends on cardiovascular health. Reduced RR variability is a marker of poor cardiac health. Time domain RR variability analysis of 38 normal healthy subjects and 20 spinal cord injured subjects has been carried out and compared. In this study, RR intervals were recorded in three different modes or positions: supine, sitting and five-second rhythm respiration. At a time of 150 s RR interval data were acquired in each mode and analysed. Statistical parameters (mean, HR, STD, NN50 and pNN50) were calculated. It was observed that most of the indices were significantly and substantially altered in spinal cord injured persons.     

Spectral analysis of heart rate variability using the integral pulse frequency modulation model

Spectral analysis of heart rate variability (HRV) is a widely accepted approach for assessment of cardiac autonomic function and its relationship to numerous disorders and diseases. As a rule, the non-parametric methods for HRV spectral analysis are tested using the integral pulse frequency modulation (IPFM) model. However, published results with simulated HRV signals show differences requiring further development of the existing methods. With the aim of improving estimation accuracy, an entirely IPFM-based method for HRV analysis is investigated. According to this method, the spectra are computed by finding the least squares solution of two matrix equations that are derived using the IPFM model and involve irregular samples of a signal representing the HRV. The method is validated with various synthesised signals (in all tests, the relative errors of the power estimates at the modulating frequencies are within 3%, and the relative power of the spurious terms is less than 0.8% only) and is furthermore applied to the spectral analysis of RR interval series obtained from diabetic children. The results, with simulated and real HRV signals, show that the developed method yields very accurate estimations of the spectral region below half the mean heart rate. Moreover, it allows the detection and assessment of certain genuine modulating components beyond the traditional frequency limit of the HRV spectra.     

Sympathetic nervous system representation in time and frequency domain indices of heart rate variability

This study evaluated the contributions of sympathetic and parasympathetic modulation to heart rate variability during situations in which vagal and sympathetic tone predominated. In a placebo-controlled, randomized, double blind blockade study, six young healthy male individuals received propranolol (0.2?mg?·?kg^?1), atropine (0.04?mg?·?kg^?1), propranolol plus atropine, or placebo infusions over 4 days. Time-domain indices were calculated during 40?min of rest and 20?min of exercise at 70% of maximal exercise intensity. Spectrum analysis, using fast Fourier transformation, was also performed at rest and during the exercise. The time-domain indices standard deviation of R-R intervals, mean of the standard deviations of all R-R intervals for all 5-min segments, percentage of number of pairs of adjacent R-R intervals differing by more than 50?ms, and square root of the mean of the sum of squares of differences between adjacent R-R intervals were reduced after atropine and propranolol plus atropine. Propranolol alone caused no appreciable change in any of the time-domain indices. At rest, all spectrum components were similar after placebo and propranolol infusions, but following parasympathetic and double autonomic blockade there was a reduction in all components of the spectrum analysis, except for the low:high ratio. During exercise, partial and double blockade did not change significantly any of the spectrum components. Thus, time and frequency-domain indices of heart rate variability were able to detect vagal activity, but could not detect sympathetic activity. During exercise, spectrum analysis is not capable of evaluating autonomic modulation of heart rate.     

Cyclic alternating pattern and spectral analysis of heart rate variability during normal sleep

The natural arousal rhythm of non-rapid eye movement (NREM) sleep is known as the cyclic alternating pattern (CAP), which consists of arousal-related phasic events (Phase A) that periodically interrupt the tonic theta/delta activities of NREM sleep (Phase B). The complementary condition, i.e. non-CAP (NCAP), consists of a rhythmic electroencephalogram background with few, randomly distributed arousal-related phasic events. Recently, some relation between CAP and autonomic function has been preliminarily reported during sleep in young adults by means of spectral analysis of heart rate variability (HRV). The present study was aimed at analysing the effects of CAP on HRV in a group of normal children and adolescents. Six normal children and adolescents (age range 10.0-17.5 y) were included in this study. All-night polygraphic recordings were performed after adaptation to the sleep laboratory. Six 5-min epochs were selected from sleep Stage 2 and six from Stages 3 and 4 (slow-wave sleep), both in CAP and NCAP conditions. From such epochs, a series of parameters describing HRV was then calculated, in both time and frequency domains, on the electrocardiographic R-R intervals. Statistical comparison between CAP and NCAP epochs revealed a significant difference for most of the frequency domain parameters (increase of the low-frequency band, increase of the low-frequency/high-frequency ratio and decrease in the high-frequency band during CAP) both in Stage 2 and in slow-wave sleep. Our results demonstrate that the physiological fluctuations of arousal during sleep described as CAP are accompanied by subtle, but significant, changes in balance between the sympathetic and vagal components of the autonomic system.