Spectral decomposition of heart rate variability using generalized harmonic analysis

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 R-R 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.

Integral pulse frequency modulation model driven by sympathovagal dynamics: Synthetic vs. real heart rate variability

This paper introduces an efficient algorithm to reconstruct heart rate signal based on an integral pulse frequency modulation (IPFM) model. The heart rate signal was reconstructed by the summation of a set of sinc functions with different weights, whose value could be determined from the IPFM process. Simulation study demonstrated that the signal reconstructed by the proposed method would preserve high frequency component with less distortion than the popular derivative of cubic spline interpolation (DCSI) method. When applied to the spectral analysis of heart rate variability (HRV) of simulated heart rate signal, the proposed method achieved smaller bias than the DCSI method. Therefore, the proposed method would be beneficial for the reconstruction of heart rate signal and the relevant spectral analysis of HRV in the future.

An integral pulse frequency modulation (IPFM) model is a pulse generation mechanism model for the nervous systems and is one of the models which connects heart rate variability to autonomic nervous system activity. There is a refractory period just after a heart beat impulse occurs, in which no heart beat impulses occur at any rate. The IPFM model does not take the refractory period into account. It would be good to consider the refractory periods in order to make the IPFM model realistic. In this paper, we are examining the effects of the absolute refractory period on the spectral distortion properties and the demodulation accuracy. Spurious components, (which are caused by mutual interference among the frequency components), decreased as the absolute refractory period increased, while the side-band distortion around the input frequency components increased. The direct FFT method impairs demodulation accuracy as the absolute refractory period increases. Even the integral function (IF) method without taking the absolute refractory period into account can reduce the distortion that is peculiar to the absolute refractory period. Moreover, the IF method which took the absolute refractory period into account has higher demodulation accuracy in spite of the absolute refractory period.

The analysis and interpretation of heart rate variability (HRV) during exercise is challenging not only because of the nonstationary nature of exercise, the time-varying mean heart rate, and the fact that respiratory frequency exceeds 0.4 Hz, but there are also other factors, such as the component centered at the pedaling frequency observed in maximal cycling tests, which may confuse the interpretation of HRV analysis. The objectives of this study are to test the hypothesis that a component centered at the running stride frequency (SF) appears in the HRV of subjects during maximal treadmill exercise testing, and to study its influence in the interpretation of the low-frequency (LF) and high-frequency (HF) components of HRV during exercise. The HRV of 23 subjects during maximal treadmill exercise testing is analyzed. The instantaneous power of different HRV components is computed from the smoothed pseudo-Wigner-Ville distribution of the modulating signal assumed to carry information from the autonomic nervous system, which is estimated based on the time-varying integral pulse frequency modulation model. Besides the LF and HF components, the appearance is revealed of a component centered at the running SF as well as its aliases. The power associated with the SF component and its aliases represents 22±7% (median±median absolute deviation) of the total HRV power in all the subjects. Normalized LF power decreases as the exercise intensity increases, while normalized HF power increases. The power associated with the SF does not change significantly with exercise intensity. Consideration of the running SF component and its aliases is very important in HRV analysis since stride frequency aliases may overlap with LF and HF components.

The application of the Lomb-Scargle periodogram to heart rate variability (HRV), which makes spectral analysis on unevenly sampled data allowable, is considered. To this end, the Lomb-Scargle periodogram was applied to various cardiac event series from IPFM simulation and real ECG signals. To assess the performance of the Lomb-Scargle periodogram, the resultant power spectrum was compared with that obtained by classical periodogram analysis on the evenly-spaced time series derived from a cardiac event series. In conclusion, it has been shown that the Lomb-Scargle periodogram is very effective in the power spectral analysis of HRV, especially in the presence of arrhythmia and/or dropouts of cardiac events.

The origin of very low frequency (VLF) oscillations in the power spectra of heart rate variability (HRV) is controversial with possible mechanisms involving thermoregulation and/or renin-angiotensin-aldosterone system. Recently, a major contribution from vagal influences has been suggested. The present study investigated the behaviour of VLF (0.004–0.040 Hz) components of HRV power spectra in a group of healthy male volunteers during their exposure to (1) dry, supine, immersion in thermo-neutral water for 6 h (n = 7) and (2) non-hypoxic hypobaria (breathing 40–60% oxygen at 15 000′ simulated in a decompression chamber) for 5 h (n = 15). The two manoeuvres are established to increase vagal outflow. During both the manoeuvres, all the frequency domain indices of HRV exhibited a significant increase. Increase in HRV was much more than that in the R-R interval. At 6 h of immersion, the R-R interval increased by ∼15% but the total power increased ∼fourfold. Similarly, at 5 h of exposure to hypobaria, total power increased ∼twofold with a very modest increase in an R-R of ∼9%. Increase in spectral power was appreciable even after normalization with mean R-R2. Increase in VLF during immersion was more than reported during enalaprilat blockade of angiotensin convertase enzyme. Plasma renin activity did not vary during hypobaria. There was a significant increase in pNN50, an established marker of cardiac vagal activity. Centre frequencies of the spectra and slope (β) of the relation between log(PSD) and log(frequency) did not change. Results were supportive of the notion that the parasympathetic system is pre-potent to influence slower (than respiratory) frequency components in HRV spectrum. Additionally, such an effect was without a change in the time constant of effector responses or pacemaker frequencies of VLF and LF periodicities and HRV was not a simple linear surrogate for cardiac vagal effects. An invariance of spectral exponent (β) ruled out contamination of VLF and LF spectra from fractal power as an alternate explanation.

To apply both autoregressive (AR) and fast Fourier transform (FFT) spectral analysis at rest, during two different dynamic exercise intensities and in recovery from maximal exercise and to compare raw and normalized powers obtained with both methods. Sixteen participants (age 22.3 +/- 4.3 year) performed resting, submaximal and maximal protocols. The submaximal protocol consisted of two 5-min walks at 4 km h(-1) at treadmill grades of 0 and 7.5%. Beat-to-beat R-R series were recorded. FFT and AR analyses were preformed on the same R-R series. Compared to AR, FFT provided higher total power (TP) and raw high-frequency (HF) power at rest and exercise. Furthermore, FFT LF/HF ratio was lower than with the AR, except under resting conditions. Both methods showed reductions in TP, raw HF and LF powers during exercise and recovery. Only the AR revealed a significant reduction for normalized HF power and increase for normalized LF power in transition from rest to exercise conditions. AR and FFT methods are not interchangeable at rest or during dynamic exercise conditions. The AR method is more sensitive to the effects of exercise on the normalized power spectra of heart rate variability (HRV) than FFT. Finally, as both approaches are equally insensitive to the increase of exercise relative intensity, there is no practical advantage of performing HRV spectral analyses by the AR or FFT at higher workloads.

The purpose of the study is on the model of vasorenal hypertension (2 kidney, 1 clamp) to study the dynamics of heart rate variability (HRV) spectrum components depending on stability of hypertension, developed after renal artery clamping. Experiments were put on Wistar male rats. During experiments in awake animals conducted registration systolic blood pressure (SBP), beat-to-beat interval (RR), spectral analysis of HRV. 1-3 weeks after the clipping of the renal artery, an elevation of MAP was observed in 21 of 33 rats. However, by week 8 of observations, the level of SBP was normalized in 11 animals. Analysis of the parameters studied in animals in which, after applying a clamp to the renal artery, an unstable elevation in the SBP was registered, showed a decrease in the high-frequency component (HF) of the HRV spectrum with an increase in the SBP. Normalization of SBP occurred within 1-5 weeks and was accompanied by restoration of HF and an increase in the length of RR. It was concluded that with unilateral ischemia of the kidneys, including mechanisms that positively affect the tone of the vagus, which counteracts the rise in blood pressure and promotes the normalization of its level, are activated.

S134 Spectral analysis of heart rate variability (HRV) and blood pressure variability (BPV) resulted in a characteristic power spectrum with two main regions: a low frequency peak (<0.15Hz) and a high frequency peak centered at the respiratory frequency. The shape of HRV and BPV power spectra may be markedly altered by hypovolemia, since hypovolemia modifies autonomic nervous control of the cardiovascular system. The aim of the present study was to evaluate the effects of hypovolemia on HRV and BPV simultaneously in dogs. METHODS: Seven dogs weighing 13-16kg were anesthetized with thiamylal(10mg/kg), maintained with alpha-chloralose(15mg/kg/hr) and vecuronium(0.1mg/kg/hr) and mechanically ventilated with room air at 14 breaths/min. Catheters were placed in the femoral artery for measurement of arterial blood pressure and in the left femoral artery for removing blood. Splenectomy was done. We induced hypovolemia by removing blood in graded stages (0%, 10%, 20%, 30%, 40% of the estimated blood volume; EBV). After blood pressure was stabilized in each stage, heart rate and mean blood pressure were continuously recorded for 10 min. The areas of the spectral peaks within each measurement were calculated as follows: LF (0.04-0.15 Hz) and HF (0.15-0.4 Hz). The data were analyzed using repeated measurement of ANOVA followed by Fisher PLSD test. P < 0.05 was considered statistically significant. RESULTS: HR did not change during hypovolemia while mean BP decreased significantly after 30% of EBV hemorrhage. LF of HRV significantly increased after 20% of EBV hemorrhage, but HF of HRV did not change. Both LF and HF of BPV increased significantly in proportion to cumulative withdrawal of the blood. DISCUSSION: LF of HRV and BPV during hypovolemia increased and HF of HRV did not changed, indicating the shift of the autonomic balance towards sympathetic dominant. An excellent quantitative correlation between the HF and LF of BPV and the degree of hypovolemia was shown during graded hemorrhage. Even small degree of hypovolemia was detected by changes in LFs of HRV and BPV and HF of BPV. HF of HRV was not useful to detect hypovolemia. Our study suggests that the spectral analysis of HRV and BPV during graded hemorrhage shows different characteristics in the quantitative evaluations of autonomic nervous system during hypovolemia. (Table 1)Table 1: Power spectrum of HRV and BPV during graded hemorrhage

Heart rate variability (HRV) and baroreceptor sensitivity (BRS) quantify autonomic variability in heart pacing and the autonomic response to blood pressure changes respectively. By necessity, the signals used to calculate HRV and BRS (systolic blood pressure (SBP) and RR interval) have one data point every cardiac cycle. Due to inherent variability in heart rate, these are non-uniformly sampled data. A number of calculation methods exist that adjust for non-uniform sampled signals. This study compared frequency domain methods of HRV and BRS calculation to ascertain whether more complex methods resulted in different results to simpler methods. Wistar rats (n=10), and rats with induced diabetes (n=8) were anesthetized and SBP and RR interval measured for a period of approximately 5 minutes. This data were analyzed using the sequence technique (for BRS), fast Fourier transform (FFT), non-uniform discrete Fourier transform (NDFT) and an extended Lomb-Scargle Periodogram (LSP). There were small but significant differences in NDFT from LSP technique for both BRS in the low frequency range (p=0.005) and HRV in the high frequency range (p=0.001). The NDFT technique was also significantly different to FFT technique for BRS in the low frequency range (p=0.023). All other methods were not statistically different. However, all techniques showed the same results comparing diabetic to control rats. This study shows more complex methods that correct for the non-uniformity of the sampling have significant differences but those differences are small to the point of not altering findings associated with HRV or BRS.

Power spectral analysis of fetal heart rate variability has been proposed to provide a non-invasive estimate of autonomic balance. However, there are few systematic data before birth. We therefore examined developmental changes in the frequency power spectrum at very low (0-0.04 Hz), low (0.04-0.15 Hz) and high frequencies (0.15-0.4 Hz), as well as the ratio of low- to high-frequency power (LF/HF), in chronically catheterized, healthy fetal sheep at 0.6 (n = 8), 0.7 (n = 7) and 0.8 gestational age (ga; n = 11). In a second study, 0.8 ga fetuses received either atropine (4.8 mg bolus, then 4.8 mg h(-1) for 30 min, n = 6) or 6-hydroxydopamine (20 mg ml(-1) at 2.5 ml h(-1) for 3 h; n = 9). Data were analysed by sleep state, defined by low-voltage-high-frequency (LV) or high-voltage-low-frequency (HV) EEG. Total spectral power increased with gestational age (P < 0.05), while LF/HF decreased from 0.6 to 0.7 ga. At 0.8 ga, heart rate and LF/HF were significantly higher during HV than LV sleep (P < 0.05). Consistent with this, although total spectral power was not significantly greater during HV sleep, there was a significant interaction between sleep state and frequency band (P = 0.02). Both atropine (P = 0.05) and 6-hydroxydopamine (P < 0.05) were associated with an overall reduction in spectral power but no significant effect on the LF/HF ratio. This study does not support substantial, consistent differences between the frequencies of sympathetic and parasympathetic activity in late-gestation fetal sheep.

Heart rate variability (HRV) is an important non-invasive parameter to assess the cardiac autonomic nervous system. In particular, spectrum matrices of HRV data have been widely used for physical and mental health monitoring. However, measurement uncertainties from data acquisition and physiological factors can easily affect the HRV spectrum and degrade outcomes of health monitoring. In this paper, we propose a new model for incomplete spectrum estimation of the HRV data based on matrix completion (MC). We show that our model performs efficiently when estimating missing entries for HRV spectra. Moreover, a refined model of matrix completion (RMC) is proposed that can be derived from correlation analysis of the HRV spectra. Two benchmark electrocardiography (ECG) datasets are retrieved and used to derive the HRV data, which are employed to evaluate the performance of our RMC method on the estimation of missing entries in the spectra. Furthermore, four different types of deep recurrent neural networks and the traditional MC method are used for a comparison study, and our RMC method obtains the least estimation error with different masking ratios. The experimental studies and comparison results demonstrate the advantages and robustness of our developed method for the estimation of incomplete HRV spectra.

Background. Cardiovascular system recovery after physical activity with explosive exercises is essential for cardiovascular pathology prevention. The efficiency of short-term biofeedback training (BFB training) in such conditions in adolescents have not been studied earlier. Objective. Our aim was to study the effect of BFB training on cardiovascular rehabilitation after speed and power training in adolescents according to general heart rate variability (HRV) spectrum total power parameter. Methods. The research has included healthy eighth-grade students (14–15 years old boys) from regular school. Inclusion in experimental and control groups was regulated by researches. Such indicators as total power (TP) of HRV spectrum, tension index (TI), systolic and diastolic arterial blood pressure (ABP), heart rate (HR) were registered initially, after three standing long jumps with double take-off and after recovery. All members of experimental group performed BFB training in order to increase TP (3 min) during recovery period. Members of control group were resting. Results. Initially all members of experimental (n = 17) and control (n = 10) groups were compared on age, height, weight and TP, TI, ABP and HR indicators. The TP level in boys of experimental group was higher than in control group during recovery period after BFB training: 3.22 (1.96; 6.13) against 1.36 (1.15; 1.84) X 1000 ms2 respectively (р = 0.041). There were no differences in TI, ABP and HR levels between two groups during recovery period. Conclusion. Implementation of short-term BFB training according to general HRV spectrum total power parameter in 14–15 years old boys after speed and power training perpetuates vagal impact on heart rate during recovery period.

The effects of steady state exercise on the power spectrum of heart rate variability were studied in 19 healthy subjects. Continuous ECG signals were recorded during 1) 15 min of rest in the supine state, 2) 10 min of standing, 3) 10 min of steady state exercise at 50% of maximum predicted power output on a cycle ergometer, and 4) 15 min of post-exercise recovery in the supine state. Autoregressive modeling was used to determine the power spectrum of heart rate variability. While orthostatic stress produced a significant 51% increase in the ratio of low to high frequency peak spectral power, steady state exercise caused a significant suppression of both low and high frequency components. The low frequency peak power rose to significantly high levels throughout 15 min of the post-exercise recovery period. There was a significant leftward shift in the frequency of the low frequency peak with exercise and a rightward shift during the recovery supine state. These results suggest that neuroregulatory control of heart rate plays a major role in adaptive responses to orthostatic stress and post-exercise recovery, while humoral factors are probably more important in maintaining heart rate during steady state exercise.