Evaluation of heart rhythm variability by heart rate or heart period: differences, pitfalls and help from logarithms

Functional brain-heart interplay extends to the multifractal domain

The study of functional brain-heart interplay has provided meaningful insights in cardiology and neuroscience. Regarding biosignal processing, this interplay involves predominantly neural and heartbeat linear dynamics expressed via time and frequency domain-related features. However, the dynamics of central and autonomous nervous systems show nonlinear and multifractal behaviours, and the extent to which this behaviour influences brain-heart interactions is currently unknown. Here, we report a novel signal processing framework aimed at quantifying nonlinear functional brain-heart interplay in the non-Gaussian and multifractal domains that combines electroencephalography (EEG) and heart rate variability series. This framework relies on a maximal information coefficient analysis between nonlinear multiscale features derived from EEG spectra and from an inhomogeneous point-process model for heartbeat dynamics. Experimental results were gathered from 24 healthy volunteers during a resting state and a cold pressor test, revealing that synchronous changes between brain and heartbeat multifractal spectra occur at higher EEG frequency bands and through nonlinear/complex cardiovascular control. We conclude that significant bodily, sympathovagal changes such as those elicited by cold-pressure stimuli affect the functional brain-heart interplay beyond second-order statistics, thus extending it to multifractal dynamics. These results provide a platform to define novel nervous-system-targeted biomarkers. This article is part of the theme issue 'Advanced computation in cardiovascular physiology: new challenges and opportunities'.

The integral pulse frequency modulation model with time-varying threshold: application to heart rate variability analysis during exercise stress testing

In this paper, an approach for heart rate variability analysis during exercise stress testing is proposed based on the integral pulse frequency modulation (IPFM) model, where a time-varying threshold is included to account for the nonstationary mean heart rate. The proposed technique allows the estimation of the autonomic nervous system (ANS) modulating signal using the methods derived for the IPFM model with constant threshold plus a correction, which is shown to be needed to take into account the time-varying mean heart rate. On simulations, this technique allows the estimation of the ANS modulation on the heart from the beat occurrence time series with lower errors than the IPFM model with constant threshold (1.1% ± 1.3% versus 15.0% ± 14.9%). On an exercise stress testing database, the ANS modulation estimated by the proposed technique is closer to physiology than that obtained from the IPFM model with constant threshold, which tends to overestimate the ANS modulation during the recovery and underestimate it during the initial rest.

Predicting clinical physiology: a Markov chain model of heart rate recovery after spontaneous breathing trials in mechanically ventilated patients

Analysis of heart rate (HR) dynamics before, during, and after a physiologic stress has clinical importance. For example, the celerity of heart rate recovery (HRR) after a cardiac stress test (eg, treadmill exercise test) has been shown to be an independent predictor of all-cause mortality. Heart rate dynamics are modulated, in part, by the autonomic nervous system. These dynamics are commonly abstracted using metrics of heart rate variability (HRV), which are known to be sensitive to the influence of the autonomic nervous system on HR. The patient-specific modulators of HR should be reflected both in the response to stress as well as in the recovery from stress. We therefore hypothesized that the patient-specific HR response to stress could be used to predict the HRR after the stress. We devised a Markov chain model to predict the poststress HRR dynamics using the parameters (transition matrix) calculated from HR data during the stress. The model correctly predicts the exponential shape of poststress HRR. This model features a simple analytical relationship linking poststress HRR time constant (T(off)) with a standard measure of HRV, namely the correlation coefficient of the Poincaré plot (first return map) of the HR recorded during the stress. A corresponding relationship exists between the time constant (T(on)) of R-R interval decrease at the onset of stress and the correlation coefficient of the Poincaré plot of prestress R-R intervals. Consequently, the model can be used for the prediction of poststress HRR using the HRV measured during the stress. This direct relationship between the event-to-event microscopic fluctuations (HRV) during the stress and the macroscopic response (HRR) after the stress terminates can be interpreted as an instance of a fluctuation-dissipation relationship. We have thus applied the fluctuation-dissipation theorem to the analysis of heart rate dynamics. The approach is specific neither to cardiac physiology nor to transitions between mechanical and free ventilation as a specific stress. It may therefore have wider applicability to physiologic systems subject to modest stresses.

Analysis of heart rate variability in the presence of ectopic beats using the heart timing signal

The time-domain signals representing the heart rate variability (HRV) in the presence of an ectopic beat exhibit a sharp transient at the position of the ectopic beat, which corrupts the signal, particularly the power spectral density (PSD) of the HRV. Consequently, there is a need for correction of this type of beat prior to any HRV analysis. This paper deals with the PSD estimation of the HRV by means of the heart timing (HT) signal when ectopic beats are present. These beat occurrence times are modeled from a generalized, continuous time integral pulse frequency modulation model and, from this point of view, a specific method for minimizing the effect of the presence of ectopic beats is presented to work together with the HT signal. By using both, a white noise driven autoregressive model of the HRV signal with artificially introduced ectopic beats and actual heart rate series including ectopic beats, the more usual methods of HRV spectral estimation are compared. Results of the PSD estimation error function of the number of ectopic beats are presented. These results demonstrate that the proposed method has one order of magnitude lower error than usual ectopic beats removal strategies in preserving PSD, thus, this strategy better recovers the original clinical indexes of interest.

Instant centre frequency at anaesthetic induction--a new way to analyse sympathovagal balance

The instant centre frequency (ICF) of RR interval has been proposed as a global index to analyse the sympathovagal interaction in the heart. The aim of this study was to assess the ICF during anaesthesia to test if it can reliably capture the neural control of the cardiovascular system. Twenty-four ASA II or III patients scheduled for cardiac surgery were included in the study. They were allocated in two groups: control, no treatment (group 1, n = 12), and beta-adrenergic blockade by atenolol (group 2, n = 12). Spectra of pulse interval series were computed with a time-frequency method and they were divided into: very low frequency (VLF, 0.000-0.040 Hz), low frequency (LF, 0.050-0.150 Hz) and high frequency (HF, 0.160-0.500 Hz). Normalized power was obtained by dividing the cumulative power within each frequency band (LF or HF) by the sum of LF and HF; the ratio of LF/HF was also calculated. Instant centre frequency is a time-varying parameter that the evolution along time of the gravity centrum of a local spectrum. All spectral indexes were recorded at the following time points: before induction, after induction and before intubation, during intubation, and after intubation. The atenolol group had lower normalized LF and the LF/HF ratio (P < 0.05) higher HF before induction; and lower LF/HF ratio after induction and before intubation (P < 0.05). The ICF was higher in atenolol group at all times. The ICF shifted towards HF frequency after induction and before intubation and shifted towards LF during intubation in both groups. The autonomic nervous system control on the heart through the interaction of sympathetic and parasympathetic reflex mechanisms could be studied by the ICF. The ICF may assess the autonomic cardiac modulation and may provide useful information for anaesthetic management.

Effects of drugs on the autonomic control of short-term heart rate variability

The autonomic nervous system links the brain and the heart. Efferent links in the neural control of the heart consist of sympathetic and parasympathetic (vagal) fibers innervating the sinus node. Because sympathetic and vagal firing alter spontaneous sinus node depolarization, cardiac rate and rhythm convey information about autonomic influences on the heart. The easy availability of ECG rendered possible the assessment of sinus rhythm as an index of autonomic outflow. The frequency-domain approach uses non-invasive recordings and appears to provide a quantitative evaluation of the autonomic modulation of cardiovascular function. Spectral profiles resulting from vagal or sympathetic blockades at the cardiac (or vascular) level might be used as references to unravel the mechanism of action of the drug under examination. A more comprehensive assessment will be obtained if spectral analysis is used as a complement to existing techniques applied for describing the neurohumoral status of patients (microneurographic recordings, norepinephrine spillover). This review also reports some pitfalls encountered in variability studies.

Improved heart rate variability signal analysis from the beat occurrence times according to the IPFM model

The heart rate variability (HRV) is an extended tool to analyze the mechanisms controlling the cardiovascular system. In this paper, the integral pulse frequency modulation model (IPFM) is assumed. It generates the beat occurrence times from a modulating signal. This signal is thought to represent the autonomic nervous system action, mostly studied in its frequency components. Different spectral estimation methods try to infer the modulating signal characteristics from the available beat timing on the electrocardiogram signal. These methods estimate the spectrum through the heart period (HP) or the heart rate (HR) signal. We introduce a new time domain HRV signal, the Heart Timing (HT) signal. We demonstrate that this HT signal, in contrast with the HR or HP, makes it possible to recover an unbiased estimation of the modulating signal spectra. In this estimation we avoid the spurious components and the low-pass filtering effect generated when analyzing HR or HP.

Frequency domain analysis of heart rate variability in horses at rest and during exercise

The pattern of variation in heart rate on a beat-to-beat basis contains information concerning sympathetic (SNS) and parasympathetic (PNS) contributions to autonomic nervous system (ANS) modulation of heart rate (HR). In the present study, heart period (RR interval) time series data were collected at rest and during 3 different treadmill exercise protocols from 6 Thoroughbred horses. Frequency and spectral power were determined in 3 frequency bands: very low (VLF) 0-< or = 0.01, low (LO) >0.01-< or = 0.07 and high (HI) >0.07-< or = 0.5 cycles/beat. Indicators of sympathetic (SNSI = LO/HI) and parasympathetic (PNSI = HI/TOTAL) activity were calculated. Power in all bands fell progressively with increasing exercise intensity from rest to trot. At the gallop VLF and LO power continued to fall but HI power rose. SNSI rose from rest to walk, then fell with increasing effort and was lowest at the gallop. PNSI fell from rest to walk, then rose and was highest at the gallop. Normalised HI power exceeded combined VLF and LO power at all gaits, with the ratio HI to LO power being lowest at the walk and highest at the gallop. ANS indicators showed considerable inter-horse variation, and varied less consistently than raw power with increasing physical effort. In the horses studied, the relationship between power and HR changed at exercise intensities associated with heart rates above approximately 120-130 beats/min. At this level, humoral and other non-neural mechanisms may become more important than autonomic modulation in influencing heart rate and heart rate variability (HRV). HRV at intense effort may be influenced by respiratory-gait entrainment, energetics of locomotion and work of breathing. HRV analysis in the frequency domain would appear to be of potential value as a noninvasive means of assessing autonomic modulation of heart rate at low exercise intensities, only. The technique may be a sensitive method for assessing exercise response to experimental manipulations and disease states.

Short-term and long-term blood pressure and heart rate variability in the mouse

Knowledge on murine blood pressure and heart rate control mechanisms is limited. With the use of a tethering system, mean arterial pressure (MAP) and pulse interval (PI) were continuously recorded for periods up to 3 wk in Swiss mice. The day-to-day variation of MAP and PI was stable from 5 days after surgery. Within each mouse (n = 9), MAP and PI varied by 21+/-6 mm Hg and 17+/-4 ms around their respective 24-h averages (97+/-3 mm Hg and 89+/-3 ms). Over 24-h periods, MAP and PI were bimodally distributed and clustered around two preferential states. Short-term variability of MAP and PI was compared between the resting (control) and active states using spectral analysis. In resting conditions, variability of MAP was mainly confined to frequencies <1 Hz, whereas variability of PI was predominantly linked to the respiration cycle (3-6 Hz). In the active state, MAP power increased in the 0.08- to 3-Hz range, whereas PI power fell in the 0.08- to 0.4-Hz range. In both conditions, coherence between MAP and PI was high at 0.4 Hz with MAP leading the PI fluctuations by 0.3-0.4 s, suggesting that reflex coupling between MAP and PI occurred at the same frequency range as in rats. Short-term variability of MAP and PI was studied after intravenous injection of autonomic blockers. Compared with the resting control state, MAP fell and PI increased after ganglionic blockade with hexamethonium. Comparable responses of MAP were obtained with the alpha-blocker prazosin, whereas the beta-blocker metoprolol increased PI similarly. Muscarinic blockade with atropine did not significantly alter steady-state levels of MAP and PI. Both hexamethonium and prazosin decreased MAP variability in the 0.08- to 1-Hz range. In contrast, after hexamethonium and metoprolol, PI variability increased in the 0.4- to 3-Hz range. Atropine had no effect on MAP fluctuations but decreased those of PI in the 0.08- to 1-Hz range. These data indicate that, in mice, blood pressure and its variability are predominantly under sympathetic control, whereas both vagal and sympathetic nerves control PI variability. Blockade of endogenous nitric oxide formation by N(G)-nitro-L-arginine methyl ester increased MAP variability specifically in the 0.08- to 0.4-Hz range, suggesting a role of nitric oxide in buffering blood pressure fluctuations.

The trigonometric regressive spectral analysis--a method for mapping of beat-to-beat recorded cardiovascular parameters on to frequency domain in comparison with Fourier transformation

Heart rate and peripheral blood pressure as physiological recorded vegetative parameters are very often rhythmically investigated with the Fourier Transformation (FT). In contrast to the original use of FT these parameters are still stochastic with overlaying rhythmical structures. The R-R intervals as independent variables of time are not equidistant. The mathematical structure for the spectral decomposition is critically analysed. The purpose of this article is the presentation of a mathematical method, considering both the statistical and rhythmical features of such time series. On the basis of trigonometric regressions, this method is presented to eliminate the equidistance problems, arising with the usage of FT, by a new mathematical approach. This method computes more precisely the spectral power especially in the VLF range (0.003-0.04 Hz) than FT, because this method of trigonometric regression does not perform a frequency quantization. This method has been used and successfully tested for the analysis of peripheral blood pressure and R-R intervals including an effective reduction of input data.

Acute effects of bisoprolol on respiratory sinus arrhythmia

Respiratory sinus arrhythmia (RSA) is often quantified by computing the spectra of heart period (HP) or of its reciprocal heart rate (HR) at the respiratory frequency. This study was undertaken to describe the effect of an acute beta-blockade achieved with bisoprolol on RSA, obtained during a calibrated breathing (breathing frequency 0.25 Hz, tidal volume VT 500 or 700 mL) in 15 normal volunteers, using a double-blind, placebo-controlled, cross-over method. The two heart signals were computed and the RSA values were compared to the individual estimates of vagal tone obtained using an additional atropine injection. The difference between the HP (or HR) value obtained after beta-blockade and the HP (or HR) value observed following the double blockade (bisoprolol plus atropine) was taken as an index of cardiac vagal tone. Bisoprolol administration resulted in a significant reduction in HR reaching 60.3 +/- 1.4 bpm at VT of 500 mL (compared to 70.5 +/- 1.8 bpm with placebo, P < 0.001). Changes in HP were also significant with an increase in HP reaching 1004.5 +/- 22.2 msec at this controlled VT (compared to 860.3 +/- 21.5 msec with placebo, P < 0.001). Similar changes were observed at a VT of 700 mL. The relationship between RSA in bpm and vagal tone was not significant for HR while a significant positive relationship was observed between RSA in msec and vagal tone for the two respiratory patterns (r = 0.65 for a tidal volume of 500 mL, P < 0.01, and r = 0.62 for 700 mL, P < 0.05). This demonstrates that the detection of the variability effect highly depends upon the unit. The parallelism between vagal tone and RSA supports the view that the HF component of HRV in msec quantifies the vagal tone. The increased RSA during beta-blockade could well reflect this vagotonic effect of this class of drugs.

Power spectral density of unevenly sampled data by least-square analysis: performance and application to heart rate signals

This work studies the frequency behavior of a least-square method to estimate the power spectral density of unevenly sampled signals. When the uneven sampling can be modeled as uniform sampling plus a stationary random deviation, this spectrum results in a periodic repetition of the original continuous time spectrum at the mean Nyquist frequency, with a low-pass effect affecting upper frequency bands that depends on the sampling dispersion. If the dispersion is small compared with the mean sampling period, the estimation at the base band is unbiased with practically no dispersion. When uneven sampling is modeled by a deterministic sinusoidal variation respect to the uniform sampling the obtained results are in agreement with those obtained for small random deviation. This approximation is usually well satisfied in signals like heart rate (HR) series. The theoretically predicted performance has been tested and corroborated with simulated and real HR signals. The Lomb method has been compared with the classical power spectral density (PSD) estimators that include resampling to get uniform sampling. We have found that the Lomb method avoids the major problem of classical methods: the low-pass effect of the resampling. Also only frequencies up to the mean Nyquist frequency should be considered (lower than 0.5 Hz if the HR is lower than 60 bpm). We conclude that for PSD estimation of unevenly sampled signals the Lomb method is more suitable than fast Fourier transform or autoregressive estimate with linear or cubic interpolation. In extreme situations (low-HR or high-frequency components) the Lomb estimate still introduces high-frequency contamination that suggest further studies of superior performance interpolators. In the case of HR signals we have also marked the convenience of selecting a stationary heart rate period to carry out a heart rate variability analysis.

Short-term variability of blood pressure and heart rate in hyperthyroidism

The effect of hyperthyroidism on the short-term memory variability of blood pressure and heart rate was evaluated in 12 untreated hyperthyroid patients during thyrotoxicosis and after a 6 1/2 month treatment designed to achieve a stable euthyroid state. Beat-by-beat finger blood pressure was measured with a Finapres device. The pulse interval, from which pulse rate was derived, was obtained from the blood pressure signal. Due to the significant change in heart rhythm associated with thyrotoxicosis, both pulse interval (taken as a surrogate of heart period) and pulse rate (taken as a surrogate of heart rate) were computed. Power spectral analysis showed a reduction in the overall heart period variability in the supine position in the hyperthyroid compared to the euthyroid state. This effect was observed in the low-frequency (0.005-0.068 Hz), mid-frequency (0.068-0.127 Hz) and high-frequency (respiratory) domains as well, with a significant reduction of the modulus of these bands of 31%, 35% and 47%, respectively. The heart rate spectral modulus also exhibited a reduction of the high-frequency component (31%) in the supine position in the hyperthyroid subjects. These changes in heart rhythmicity corroborate a vagal deficit in hyperthyroidism. In addition, blood pressure spectral power exhibited a significant deficit in the orthostatism-induced mid-frequency systolic blood pressure rise in the hyperthyroid state (64%) compared with the euthyroid state. This observation may reflect a reduced vascular sympathetic activation with standing. The resulting vasodilatation could well contribute to normalize blood pressure in thyrotoxicosis in which cardiac output is increased.

Heart rate variability as an index of cue reactivity in alcoholics

BACKGROUND

Autonomic responses follow exposure to conditioned stimuli such as contextual factors associated with alcohol ingestion. Heart rate variability is under autonomic control and may be a measure of such response.

METHODS

Twenty alcoholics and 23 matched social drinkers (all male) were exposed to a neutral cue and then an alcohol cue in identical settings, during which the electrocardiogram of these subjects was recorded. Time and frequency domain parameters of heart rate variability (HRV) were computed by a blind rater.

RESULTS

Coefficient of variation of R-R intervals and absolute powers of HRV spectrum (in frequency bands 0.05-0.15 Hz and 0.01-0.05 Hz) following alcohol cue were significantly higher in alcoholics than social drinkers. The mean heart rate (MHR) failed to reflect this difference.

CONCLUSIONS

HRV paradigm appears more sensitive than MHR to measure cue reactivity.

A comparative analysis of preprocessing techniques of cardiac event series for the study of heart rhythm variability using simulated signals

In the present study, using noise-free stimulated signals, we performed a comparative examination of several preprocessing techniques that are used to transform the cardiac event series in a regularly sampled time series, appropriate for spectral analysis of heart rhythm variability (HRV). First, a group of noise-free simulated point event series, which represents a time series of heartbeats, was generated by an integral pulse frequency modulation models. In order to evaluate the performance of the preprocessing methods, the differences between the spectra of the preprocessed simulated signals and the true spectrum (spectrum of the model input modulating signals) were surveyed by visual analysis and by contrasting merit indices. It is desired that estimated spectra match the true spectrum as close as possible, showing a minimum of harmonic components and other artifacts. The merit indices proposed to quantify these mismatches were the leakage rate, defined as a measure of leakage components (located outside some narrow windows centered at frequencies of model input modulating signals) with respect to the whole spectral components, and the numbers of leakage components with amplitudes greater than 1%, 5% and 10% of the total spectral components. Our data, obtained from a noise-free simulation, indicate that the utilization of heart rate values instead of heart period values in the derivation of signals representative of heart rhythm results in more accurate spectra. Furthermore, our data support the efficiency of the widely used preprocessing technique based on the convolution of inverse interval function values with a rectangular window, and suggest the preprocessing technique based on a cubic polynomial interpolation of inverse interval function values and succeeding spectral analysis as another efficient and fast method for the analysis of HRV signals.