A new algorithm for wavelet-based heart rate variability analysis

One of the most promising non-invasive markers of the activity of the autonomic nervous system is heart rate variability (HRV). HRV analysis toolkits often provide spectral analysis techniques using the Fourier transform, which assumes that the heart rate series is stationary. To overcome this issue, the Short Time Fourier Transform (STFT) is often used. However, the wavelet transform is thought to be a more suitable tool for analyzing non-stationary signals than the STFT. Given the lack of support for wavelet-based analysis in HRV toolkits, such analysis must be implemented by the researcher. This has made this technique underutilized.This paper presents a new algorithm to perform HRV power spectrum analysis based on the Maximal Overlap Discrete Wavelet Packet Transform (MODWPT). The algorithm calculates the power in any spectral band with a given tolerance for the band's boundaries. The MODWPT decomposition tree is pruned to avoid calculating unnecessary wavelet coefficients, thereby optimizing execution time. The center of energy shift correction is applied to achieve optimum alignment of the wavelet coefficients. This algorithm has been implemented in RHRV, an open-source package for HRV analysis. To the best of our knowledge, RHRV is the first HRV toolkit with support for wavelet-based spectral analysis.     

Cardiovascular variability after arousal from sleep: time-varying spectral analysis.

We performed time-varying spectral analyses of heart rate variability (HRV) and blood pressure variability (BPV) recorded from 16 normal humans during acoustically induced arousals from sleep. Time-varying autoregressive modeling was employed to estimate the time courses of high-frequency HRV power, low-frequency HRV power, the ratio between low-frequency and high-frequency HRV power, and low-frequency power of systolic BPV. To delineate the influence of respiration on HRV, we also computed respiratory airflow high-frequency power, the modified ratio of low-frequency to high-frequency HRV power, and the average transfer gain between respiration and heart rate. During cortical arousal, muscle sympathetic nerve activity and heart rate increased and returned rapidly to baseline, but systolic blood pressure, the ratio between low-frequency and high-frequency HRV power, low-frequency HRV power, the modified ratio of low-frequency to high-frequency HRV power, and low-frequency power of systolic BPV displayed increases that remained above baseline up to 40 s after arousal. High-frequency HRV power and airflow high-frequency power showed concommitant decreases to levels below baseline, whereas the average transfer gain between respiration and heart rate remained unchanged. These findings suggest that 1) arousal-induced changes in parasympathetic activity are strongly coupled to respiratory pattern and 2) the sympathoexcitatory cardiovascular effects of arousal are relatively long lasting and may accumulate if repetitive arousals occur in close succession.     

Coarse-graining spectral analysis: new method for studying heart rate variability.

Heart rate variability (HRV) spectra are typically analyzed for the components related to low- (less than 0.15 Hz) and high- (greater than 0.15 Hz) frequency variations. However, there are very-low-frequency components with periods up to hours in HRV signals, which might smear short-term spectra. We developed a method of spectral analysis suitable for selectively extracting very-low-frequency components, leaving intact the low- and high-frequency components of interest in HRV spectral analysis. Computer simulations showed that those low-frequency components were well characterized by fractional Brownian motions (FBMs). If the scale invariant, or self-similar, property of FBMs is considered a new time series (x') was constructed by sampling only every other point (course graining) of the original time series (x). Evaluation of the cross-power spectra between these two (Sxx') showed that the power of the FBM components was preserved, whereas that of the harmonic components vanished. Subtraction of magnitude of Sxx from the autopower spectra of the original sequence emphasized only the harmonic components. Application of this method to HRV spectral analyses indicated that it might enable one to observe more clearly the low- and high-frequency components characteristic of autonomic control of heart rate.     

Identification of development and autonomic nerve activity from heart rate variability in preterm infants

Heartbeat intervals, which are determined basically by regular excitations of the sinoatrial node, show significant fluctuation referred to as the heart rate variability (HRV). The HRV is mostly due to nerve activities through the sympathetic and parasympathetic branches of the autonomic nervous system (ANS). In recent years, it has been recognized that the HRV shows a greater complexity than ever expected, suggesting that it includes much information about ANS activities. In this study, we investigated relationship between HRV and development in preterm infants. To this end, heartbeat intervals were continuously recorded from 11 preterm infants in NICU. The recording periods were ranging from several days to weeks depending on the individuals. The HRV at various ages was then characterized by several indices. They include power spectrum as well as the mean and standard deviation of the series. For the power spectrum, the low-frequency band power (LF), high-frequency band power (HF), LF/HF (the ratio between LF and HF), beta (scaling exponent of the spectrum) were estimated. The detrended fluctuation analysis (DFA) was also employed to obtain short- and long-range scaling exponents. Each of these indices showed a correlation with the age. We showed that the long-range scaling exponent, derived from the DFA, was most significantly correlated with the age, suggesting that it could be a robust index to characterize the development of preterm infants.     

Comparative Evaluation of Heart Rate Variability Based on the Data of ECG and Blood Pressure Measurements

The development of new approaches to the assessment of heart rate variability (HRV) is an important problem, since HRV reflects the functioning of cardiovascular control and is affected by various diseases. The purpose of this study was to evaluate the informative value of statistical and spectral HRV parameters calculated from pulse interval (PI) data of blood pressure as compared with those calculated from RR-interval data of electrocardiograms (ECG). We recorded ECG in conscious rats using skin adhesive electrodes simultaneously with blood pressure signal obtained through a catheter in the femoral artery. It has been found that the PI sequence can be used to calculate the statistical HRV indices that describe the HRV at time intervals about 1 min or longer, but statistical indices of the PI and RR intervals may differ in the analysis of beat-tobeat variations. The power spectra of the RR intervals and PI coincide in the low-frequency region, including the band of baroreflex cardiac rhythm oscillation. However, they can differ in the high-frequency region (at respiration frequency and above).     

Characteristics of autonomic nervous function in Zucker-fatty rats: investigation by power spectral analysis of heart rate variability.

We investigated the characteristics of autonomic nervous function in Zucker-fatty and Zucker-lean rats. For this purpose, a long-term electrocardiogram (ECG) was recorded from conscious and unrestrained rats using a telemetry system, and the autonomic nervous function was investigated by power spectral analysis of heart rate variability (HRV). Although heart rate (HR) in Zucker-fatty rats was lower than that in Zucker-lean rats throughout 24 h, apparent diurnal variation in HR was observed in both strains and HR during the dark period was significantly higher than that in light period. Diurnal variation in locomotor activity (LA) in Zucker-fatty rats was also observed, but LA was lower than that in Zucker lean rats, especially during the dark period. There were no significant differences, however, in high-frequency (HF) power, low-frequency (LF) power, and the LF/HF ratio between Zucker-fatty and Zucker-lean rats. The circadian rhythm of these parameters was mostly preserved in both strains of rats. Moreover, the effect of autonomic blockades on HRV was nearly the same in Zucker-fatty and Zucker-lean rats. These results suggest that the autonomic nervous function of insulin-resistant Zucker-fatty rats remain normal, from the aspect of power spectral analysis of HRV.     

A modified Zeeman model for producing HRV signals and its application to ECG signal generation

Developing a mathematical model for the artificial generation of electrocardiogram (ECG) signals is a subject that has been widely investigated. One of the challenges is to generate ECG signals with a wide range of waveforms, power spectra and variations in heart rate variability (HRV)--all of which are important indexes of human heart functions. In this paper we present a comprehensive model for generating such artificial ECG signals. We incorporate into our model the effects of respiratory sinus arrhythmia, Mayer waves and the important very low-frequency component in the power spectrum of HRV. We use a new modified Zeeman model for generating the time series for HRV, and a single cycle of ECG is produced by using a simple neural network. The importance of the work is the model's ability to produce artificial ECG signals that resemble experimental recordings under various physiological conditions. As such the model provides a useful tool to simulate and analyse the main characteristics of ECG, such as its power spectrum and HRV under different conditions. Potential applications of this model include using the generated ECG as a flexible signal source to assess the effectiveness of a diagnostic ECG signal-processing device.     

Assessment of Heart Autonomic Control on the Basis of Spectral Analysis of Heart Rate Variability

An orthostatic test with frequency-controlled breathing (with a respiration period of 10 s) or spontaneous breathing was used to analyze frequency estimates of the heart rate variability (HRV) in the low-frequency (LF) and high-frequency (HF) ranges in young men and women. It was demonstrated that the spectral components of HRV bear no signs of sex differentiation, suggesting a uniform structural organization of the system of autonomic nervous control of the heart (SANCH) in humans. The LF component of the HRV spectrum is a marker of the functional state of the SANCH; it should be studied under conditions of controlled breathing at a frequency of 0.1 Hz. The HF and LF components of the HRV characterize the state of the SANCH at a given moment and do not reflect directly its adaptation reserve. The HF component of the HRV is interesting as a parameter that may be used for estimating the changes in the adaptation reserve of heart autonomic control. It is preferable to analyze this component in the absence of external disturbances in the LF range of the spectrum.     

Relationship between cortical electrical and cardiac autonomic activities in the awake lizard, Gallotia galloti

ECG and EEG signals were simultaneously recorded in lizards, Gallotia galloti, both in control conditions and under autonomic nervous system (ANS) blockade, in order to evaluate possible relationships between the ANS control of heart rate and the integrated central nervous system activity in reptiles. The ANS blockers used were prazosin, propranolol, and atropine. Time-domain summary statistics were derived from the series of consecutive R-R intervals (RRI) of the ECG to measure beat-to-beat heart rate variability (HRV), and spectral analysis techniques were applied to the EEG activity to assess its frequency content. Both prazosin and atropine did not alter the power spectral density (PSD) of the EEG low frequency (LF: 0.5-7.5 Hz) and high frequency (HF: 7.6-30 Hz) bands, whereas propranolol decreased the PSD in these bands. These findings suggest that central beta-adrenergic receptor mechanisms could mediate the reptilian waking EEG activity without taking part any alpha(1)-adrenergic and/or cholinergic receptor systems. In 55% of the lizards in control conditions, and in approximately 43% of the lizards under prazosin and atropine, a negative correlation between the coefficient of variation of the series of RRI value (CV(RRI)) and the mean power frequency (MPF) of the EEG spectra was found, but not under propranolol. Consequently, the lizards' HRV-EEG-activity relationship appears to be independent of alpha(1)-adrenergic and cholinergic receptor systems and mediated by beta-adrenergic receptor mechanisms.     

Relationships between the EEG θ- and β-parameters and heart rate variability during human cognitive performance

We studied the dynamics of spectral coherence characteristics of the EEG θ-, β₁-, and β₂-activity and the heart rate variability (HRV) in subjects performing cognitive tests. We found an association between the HRV parameters in the process of cognitive activity and the coherence of potentials in the EEG θ-, β₁-, and β₂-bands. The heart rate parameters in the baseline state and during the test performance best correlated with the levels of the right-hemispheric coherence of potentials in the θ-, β₁-, and β₂-bands of the baseline EEG (eyes closed). The higher coherence levels corresponded to lower values of the mean time of RR intervals (RRNN), coefficient of variation (CV), total power (TP), the power of the high-frequency (HF) and low-frequency (LF) components in the HRV spectrum. During the performance of the test, higher coherence values in the EEG θ-bands with the focus in the right temporal lead corresponded to higher LF/HF values reflecting the predominance of sympathetic effects on heart rate.     

Wavelet analysis of instantaneous heart rate: a study of autonomic control during thrombolysis

Myocardial infarction (MI) is known to elicit activation of the autonomic nervous system. Reperfusion, induced by thrombolysis, is thus expected to bring about a shift in the balance between the sympathetic and vagal systems, according to the infarct location. In this study, we explored the correlation between reperfusion and the spectral components of heart rate (HR) variability (HRV), which are associated with autonomic cardiac control. We analyzed the HR of patients during thrombolysis: nine anterior wall MI (AW-MI) and eight inferoposterior wall MI (IW-MI). Reperfusion was determined from changes in ST levels and reported pain. Reocclusion was detected in four patients. HRV was analyzed using a modified continuous wavelet transform, which provided time-dependent versions of the typically used low-frequency (LF) and high-frequency (HF) peaks and of their ratio, LF/HF. Marked alterations in at least one of the HRV parameters was found in all 18 reperfusion events. Patterns of HRV, compatible with a shift toward relative sympathetic enhancement, were found in all of the nine reperfusion events in IW-MI patients and in three AW-MI patients. Patterns of HRV compatible with relative vagal enhancement were found in six AW-MI patients (P < 0.001). Significant changes in HRV parameters were also found after reocclusion. Time-dependent spectral analysis of HRV using the wavelet transform was found to be valuable for explaining the patterns of cardiac rate control during reperfusion. In addition, examination of the entire record revealed epochs of markedly diminished HRV in two patients, which we attribute to vagal saturation.     

Modern Methods of Functional Studies of the Autonomic Nervous System

Contemporary methods to assess the functional state of the autonomic nervous system are reviewed. This paper discusses different hypotheses on the nature of the low- and very low-frequency waves (LFand VLF, respectively) that are recorded during the spectral analysis of the heart-rate variability (HRV). Analysis of their own data along with data found in literature enabled the authors to propose the possible parasympathetic nature of the LF-wave generators. The application of the established indices of the absolute power of all the components of the HRV spectrum led to the hypothesis that emotional stress is related to the attenuation in the regulatory effects of the higher levels of the central nervous system.     

A comparison of patients’ heart rate variability and blood flow variability during surgery based on the Hilbert–Huang Transform

Previous studies have indicated that heart rate variability (HRV) is considered to be one of the effective parameters for assessing autonomous nervous system activity. Therefore, HRV can be used to detect the state of patients during surgery, even for estimating depth of anaesthesia (DOA). However, the heartbeat can be affected by anaesthesia drugs, breathing rate and electric influence during surgery, which can result in inaccurate information about the patient. To contend with this problem, blood flow variability (BFV) is proposed in this paper as an indicator to monitor the patient's status when HRV is not appropriate. In our experiments, thirty patients undergoing ear, nose, and throat (ENT) surgery with different anaesthetics are used to compare the efficiency and validity between the fast Fourier transform (FFT) and the Hilbert–Huang transform (HHT). Of another thirty patients, twenty patients accepted ENT surgery, of which ten have received Atropine, while the others have not. The other ten patients who have accepted abdominal surgery with an electric knife were compared with the previously mentioned ten patients who did not receive an Atropine injection for ENT surgery. As a result, the FFT that is applied in this study was replaced with the HHT for analysing the data in a particular frequency range of sympathetic and parasympathetic divisions, because of the lesser response of the results that were analysed by FFT for intubation. Also, BFV is proven to be a useful indicator for assisting doctors to assess the state of the patients instead of HRV during the operation in comparison with HRV under drugs (i.e., Atropine and Glycopyrrolate) and diathermy effects (i.e., high frequency interference from electric knife).     

Heart rate variability in weightlifters

On the basis of the literature and original data, heart rate variability (HRV) in weightlifters has been studied. The results showed that the distribution mode (a parameter of mathematical analysis that is equal to the most frequent length of RR intervals) indicates the intensity of physical exercise. Specific changes in the autonomic balance in athletes as dependent on their degree of training and sports qualification are important characteristics of adaptations to physical loads. For example, the degree of training of weightlifters is reflected by the level of the respiratory component as an index of the activity of the parasympathetic nervous system. Adaptation to physical exercise leads to an increase in the power of the spectrum of neurohumoral modulation and to changes in the ratio between the levels of the total spectral power of HRV.     

An empirical link between the spectral colour of climate and the spectral colour of field populations in the context of climate change

1. The spectral colour of population dynamics and its causes have attracted much interest. The spectral colour of a time series can be determined from its power spectrum, which shows what proportion of the total variance in the time series occurs at each frequency. A time series with a red spectrum (a negative spectral exponent) is dominated by low-frequency oscillations, and a time series with a blue spectrum (a positive spectral exponent) is dominated by high-frequency oscillations. 2. Both climate variables and population time series are characterised by red spectra, suggesting that a population's environment might be partly responsible for its spectral colour. Laboratory experiments and models have been used to investigate this potential link. However, no study using field data has directly tested whether populations in redder environments are redder. 3. This study uses the Global Population Dynamics Database together with climate data to test for this effect. We found that the spectral exponent of mean summer temperatures correlates positively and significantly with population spectral exponent. 4. We also found that over the last century, temperature climate variables on most continents have become bluer. 5. Although population time series are not long or abundant enough to judge directly whether their spectral colours are changing, our two results taken together suggest that population spectral colour may be affected by the changing spectral colour of climate variables. Population spectral colour has been linked to extinction; we discuss the potential implications of our results for extinction probability.     

Incoherent oscillations of respiratory sinus arrhythmia during acute mental stress in humans

Respiratory sinus arrhythmia (RSA) has been widely used as a measure of the cardiac vagal control in response to stress. However, RSA seems not to be a generalized indicator because of its dependency on respiratory parameter and individual variations of RSA amplitude (A(RSA)). We hypothesized that phase-lag variations between RSA and respiration may serve as a normalized index of the degree of mental stress. Twenty healthy volunteers performed mental arithmetic task (ART) after 5 min of resting control followed by 5 min of recovery. Breathing pattern, beat-to-beat R-R intervals, and blood pressure (BP) were determined using inductance plethysmography, electrocardiography, and a Finapres device, respectively. The analytic signals of breathing and RSA were obtained by Hilbert transform and the degree of phase synchronization (λ) was quantified. With the use of spectral analysis, heart rate variability (HRV) was estimated for the low-frequency (LF) and high-frequency (HF) bands. A steady-state 3-min resting period (REST), the first 3 min (ART1), and the last 3 min (ART2) of the ART period (ranged from 6- to 19 min) and the last 3 min of the recovery period (RCV) were analyzed separately. Heart rate, systolic BP, and breathing frequency (f(R)) increased and λ, A(RSA), and HF power decreased from REST to ART (P < 0.01). The λ was correlated with normalized A(RSA) and the HF power. The decrease in λ could not be explained solely by the increase in f(R). We conclude that mental stress exerts an influence on RSA oscillations, inducing incoherent phase lag with respect to breathing, in addition to a decrease in RSA.     

Poincaré plot interpretation using a physiological model of HRV based on a network of oscillators

In this paper, we develop a physiological oscillator model of which the output mimics the shape of the R-R interval Poincaré plot. To validate the model, simulations of various nervous conditions are compared with heart rate variability (HRV) data obtained from subjects under each prescribed condition. For a variety of sympathovagal balances, our model generates Poincaré plots that undergo alterations strongly resembling those of actual R-R intervals. By exploiting the oscillator basis of our model, we detail the way that low- and high-frequency modulation of the sinus node translates into R-R interval Poincaré plot shape by way of simulations and analytic results. With the use of our model, we establish that the length and width of a Poincaré plot are a weighted combination of low- and high-frequency power. This provides a theoretical link between frequency-domain spectral analysis techniques and time-domain Poincaré plot analysis. We ascertain the degree to which these principles apply to real R-R intervals by testing the mathematical relationships on a set of data and establish that the principles are clearly evident in actual HRV records.     

Automatic filtering of outliers in RR intervals before analysis of heart rate variability in Holter recordings: a comparison with carefully edited data

Background  

Undetected arrhythmic beats seriously affect the power spectrum of the heart rate variability (HRV). Therefore, the series of RR intervals are normally carefully edited before HRV is analysed, but this is a time consuming procedure when 24-hours recordings are analysed. Alternatively, different methods can be used for automatic removal of arrhythmic beats and artefacts. This study compared common frequency domain indices of HRV when determined from manually edited and automatically filtered RR intervals.     

Sleep-related sympathovagal imbalance in SHR

The role of the autonomic nervous system in spontaneous hypertension during each stage of the sleep-wake cycle remains unclear. The present study attempted to evaluate the differences in cardiac autonomic modulations among spontaneously hypertensive rats (SHR), normotensive Wistar-Kyoto rats (WKY), and Sprague-Dawley rats (SD) across sleep-wake cycles. Continuous power spectral analysis of electroencephalogram, electromyogram, and heart rate variability was performed in unanesthetized free moving rats during daytime sleep. Frequency-domain analysis of the stationary R-R intervals (RR) was performed to quantify the high-frequency power (HF), low-frequency power (LF)-to-HF ratio (LF/HF), and normalized LF (LF%) of heart rate variability. WKY and SD had similar mean arterial pressure, which is significantly lower than that of SHR during active waking, quiet sleep, and paradoxical sleep. Compared with WKY and SD, SHR had lower HF but similar RR, LF/HF, and LF% during active waking. During quiet sleep, SHR developed higher LF/HF and LF% in addition to lower HF. SHR ultimately exhibited significantly lower RR accompanied with higher LF/HF and LF% and lower HF during paradoxical sleep compared with WKY. We concluded that significant cardiac sympathovagal imbalance with an increased sympathetic modulation occurred in SHR during sleep, although it was less evident during waking.     

A pilot investigation of the effect of extremely low frequency pulsed electromagnetic fields on humans' heart rate variability

The question whether pulsed electromagnetic field (PEMF) can affect the heart rhythm is still controversial. This study investigates the effects on the cardiocirculatory system of ELF-PEMFs. It is a follow-up to an investigation made of the possible therapeutic effect ELF-PEMFs, using a commercially available magneto therapeutic unit, had on soft tissue injury repair in humans. Modulation of heart rate (HR) or heart rate variability (HRV) can be detected from changes in periodicity of the R-R interval and/or from changes in the numbers of heart-beat/min (bpm), however, R-R interval analysis gives only a quantitative insight into HRV. A qualitative understanding of HRV can be obtained considering the power spectral density (PSD) of the R-R intervals Fourier transform. In this study PSD is the investigative tool used, more specifically the low frequency (LF) PSD and high frequency (HF) PSD ratio (LF/HF) which is an indicator of sympatho-vagal balance. To obtain the PSD value, variations of the R-R time intervals were evaluated from a continuously recorded ECG. The results show a HR variation in all the subjects when they are exposed to the same ELF-PEMF. This variation can be detected by observing the change in the sympatho-vagal equilibrium, which is an indicator of modulation of heart activity. Variation of the LF/HF PSD ratio mainly occurs at transition times from exposure to nonexposure, or vice versa. Also of interest are the results obtained during the exposure of one subject to a range of different ELF-PEMFs. This pilot study suggests that a full investigation into the effect of ELF-PEMFs on the cardiovascular system is justified.