Mathematical model of heart rate variability

The study presents a mathematical model of non-linear dynamics of the heart rate variability (HRV). The model is based on quantitative characteristics of pulse conduction in the heart conducting system: the delays of sinoatrial (SA) and atrioventricular (AV) pulse conduction and refractors periods of the SA and AV nodes. The model predicts heart rate disturbances in fast electric activity of the atria, increase in the delay of the AV conduction, the critical value of atrial period where transition to non-linear dynamics of the heart rate variability starts. The correlation between indexes of HRV and period of stimulation of atria for 1-contour cardiac control model has been demonstrated.     

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.     

Gaussian mixture model of heart rate variability

Heart rate variability (HRV) is an important measure of sympathetic and parasympathetic functions of the autonomic nervous system and a key indicator of cardiovascular condition. This paper proposes a novel method to investigate HRV, namely by modelling it as a linear combination of Gaussians. Results show that three Gaussians are enough to describe the stationary statistics of heart variability and to provide a straightforward interpretation of the HRV power spectrum. Comparisons have been made also with synthetic data generated from different physiologically based models showing the plausibility of the Gaussian mixture parameters.     

Realtion of heart rate control to heartbeat perception

The relation of heartbeat perception to voluntary control of heart rate (HR) and to learning of enhanced HR control during feedback was studied in three experiments. In Experiment I heartbeat perception was unrelated to voluntary control of HR but was negatively correlated with HR learning. Experiments II and III showed that heartbeat perception was unrelated to either initial voluntary control or learning and suggested that sampling error accounted for the negative correlation in Experiment I. Experiment I also demonstrated that learned increases in HR are retained for at least 10 weeks following feedback training. Autonomic Perception Questionnaire scores were not predictive of voluntary HR control or learning.     

Relation of heart rate control to heartbeat perception

The relation of heartbeat perception to voluntary control of heart rate (HR) and to learning of enhanced HR control during feedback was studied in three experiments. In Experiment I heartbeat perception was unrelated to voluntary control of HR but was negatively correlated with HR learning. Experiments II and III showed that heartbeat perception was unrelated to either initial voluntary control or learning and suggested that sampling error accounted for the negative correlation in Experiment I. Experiment I also demonstrated that learned increases in HR are retained for at least 10 weeks following feedback training. Autonomic Perception Questionnaire scores were not predictive of voluntary HR control or learning.     

Statistical coding and decoding of heartbeat intervals

The heart integrates neuroregulatory messages into specific bands of frequency, such that the overall amplitude spectrum of the cardiac output reflects the variations of the autonomic nervous system. This modulatory mechanism seems to be well adjusted to the unpredictability of the cardiac demand, maintaining a proper cardiac regulation. A longstanding theory holds that biological organisms facing an ever-changing environment are likely to evolve adaptive mechanisms to extract essential features in order to adjust their behavior. The key question, however, has been to understand how the neural circuitry self-organizes these feature detectors to select behaviorally relevant information. Previous studies in computational perception suggest that a neural population enhances information that is important for survival by minimizing the statistical redundancy of the stimuli. Herein we investigate whether the cardiac system makes use of a redundancy reduction strategy to regulate the cardiac rhythm. Based on a network of neural filters optimized to code heartbeat intervals, we learn a population code that maximizes the information across the neural ensemble. The emerging population code displays filter tuning proprieties whose characteristics explain diverse aspects of the autonomic cardiac regulation, such as the compromise between fast and slow cardiac responses. We show that the filters yield responses that are quantitatively similar to observed heart rate responses during direct sympathetic or parasympathetic nerve stimulation. Our findings suggest that the heart decodes autonomic stimuli according to information theory principles analogous to how perceptual cues are encoded by sensory systems.     

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.     

A new method for analysis of heart rate variability: counting statistics of 1/f fluctuations

1/f fluctuations in heart rate are usually measured by spectral analysis using Fast Fourier Transform. Here, we introduce a new method based on counting the number of QRS complexes in time intervals t of various length. For a 1/f ^b spectrum the variance of counts in t follows a power-law as gDt ^1+b. This method is applied to analyze long term fluctuations in heart rate variability in 10 healthy men. The results show periods of 1/f fluctuations with interpolated periods of white noise during night hours.     

Decreased fractal component of human heart rate variability during non-REM sleep

The physiological significance of the fractal component of short-term, spontaneous heart rate variability (HRV) in humans remains unclear. The aim of the present study was to gain further information about the respective fractal components by extracting them from HRV, blood pressure variability (BPV), and instantaneous lung volume (ILV) time series via coarse graining spectral analysis in nine healthy subjects during waking and sleep states. The results show that the contribution made by the fractal component to the total variance in the beat-to-beat R-R interval declined significantly as the depth of non-rapid eye movement (non-REM) sleep increased, that the ILV time series was largely periodic (i.e., nonfractal), and that BPV was unaffected by sleep stage. Finally, the fractal component of HRV during REM sleep was found to be quite similar to that seen during waking. These results suggest that mechanisms involving electroencephalographic desynchronization and/or conscious states of the brain are reflected in the fractal component of HRV.     

The effects of specific respiratory rates on heart rate and heart rate variability

In this study respiratory rates of 3, 4, 6, 8, 10, 12, and 14 breaths per minute were employed to investigate the effects of these rates on heart rate variability (HRV). Data were collected 16 times at each respiratory rate on 3 female volunteers, and 12 times on 2 female volunteers. Although mean heart rates did not differ among these respiratory rates, respiratory-induced trough heart rates at 4 and 6 breaths per minute were significantly lower than those at 14 breaths per minute. Slower respiratory rates usually produced higher amplitudes of HRV than did faster respiratory rates. However, the highest amplitudes were at 4 breaths per minute. HRV amplitude decreased at 3 breaths per minute. The results are interpreted as reflecting the possible effects of the slow rate of acetylcholine metabolism and the effect of negative resonance at 3 cycles per minute.     

A mathematical model of human heart including the effects of heart contractility varying with heart rate changes

Incorporating the intrinsic variability of heart contractility varying with heart rate into the mathematical model of human heart would be useful for addressing the dynamical behaviors of human cardiovascular system, but models with such features were rarely reported. This study focused on the development and evaluation of a mathematical model of the whole heart, including the effects of heart contractility varying with heart rate changes. This model was developed based on a paradigm and model presented by Ottesen and Densielsen, which was used to model ventricular contraction. A piece-wise function together with expressions for time-related parameters were constructed for modeling atrial contraction. Atrial and ventricular parts of the whole heart model were evaluated by comparing with models from literature, and then the whole heart model were assessed through coupling with a simple model of the systemic circulation system and the pulmonary circulation system. The results indicated that both atrial and ventricular parts of the whole heart model could reasonably reflect their contractility varying with heart rate changes, and the whole heart model could exhibit major features of human heart. Results of the parameters variation studies revealed the correlations between the parameters in the whole heart model and performances (including the maximum pressure and the stroke volume) of every chamber. These results would be useful for helping users to adjust parameters in special applications.     

Influence of 50 Hz magnetic field on human heart rate variability: linear and nonlinear analysis

This study investigated the problem of the influence of 50 Hz magnetic field (MF) on human heart rate variability (HRV). The exposure system was a commercial device for magnetotherapy, generating field of the strength of 500 microT at the center of the coil, 150-200 microT at the position of human subjects' heart and 20-30 microT at the position of subjects' head. The exposure protocols, applied randomly, were either "half hour MF-off/half hour MF-on" or "half hour MF-off/half hour MF-off." The phonocardiographic (PhCG) signal of 15 volunteers were obtained during exposure and used for calculation of time-domain HRV parameters (mean time between heart beats (N-N), standard deviation of time between heart beats (SDNN), and the number of differences of successive beat-to-beat intervals greater than 50 ms, divided by the total number of beat-to-beat intervals (pNN50)) and nonlinear HRV measures (approximate entropy (ApEn), detrended fluctuation scaling exponents). The protocol MF-off/MF-on was applied in nine subjects. Repeated measures ANOVA (RMANOVA) performed for Mf-off/MF-off protocol indicated no statistical difference among four 15 min intervals of HRV data (P value >20% for all parameters except for N-N, where P = 3.7%). RMANOVA followed by the post hoc Tukey test performed for Mf-off/MF-on protocol indicated a statistically significant difference during MF on for N-N (8% increase, P <.1%), SDNN (40% increase, P = 1.1%), and pNN50 (110% increase, P <.1%). The results of the analysis indicate that the changes of these parameters could be associated with the influence of MF.     

The genetic contribution to heart rate and heart rate variability in quiescent mice

Recent studies have suggested a genetic component to heart rate (HR) and HR variability (HRV). However, a systematic examination of the genetic contribution to the variation in HR and HRV has not been performed. This study investigated the genetic contribution to HR and HRV using a wide range of inbred and recombinant inbred (RI) mouse strains. Electrocardiogram data were recorded from 30 strains of inbred mice and 29 RI strains. Significant differences in mean HR and total power (TP) HRV were identified between inbred strains and RI strains. Multiple significant differences within the strain sets in mean low-frequency (LF) and high-frequency (HF) power were also found. No statistically significant concordance was found between strain distribution patterns for HR and HRV phenotypes. Genomewide interval mapping identified a significant quantitative trait locus (QTL) for HR [LOD (likelihood of the odds) score = 3.763] on chromosome 6 [peak at 53.69 megabases (Mb); designated HR 1 (Hr1)]. Suggestive QTLs for TP were found on chromosomes 2, 4, 5, 6, and 14. A suggestive QTL for LF was found on chromosome 16; for HF, we found one significant QTL on chromosome 5 (LOD score = 3.107) [peak at 53.56 Mb; designated HRV-high-frequency 1 (Hrvhf1)] and three suggestive QTLs on chromosomes 2, 11 and 15. In conclusion, the results demonstrate a strong genetic component in the regulation of resting HR and HRV evidenced by the significant differences between strains. A lack of correlation between HR and HRV phenotypes in some inbred strains suggests that different sets of genes control the phenotypes. Furthermore, QTLs were found that will provide important insight to the genetic regulation of HR and HRV at rest.     

Resting heart rate,heart rate variability and functional decline in old age

Background:

Heart rate and heart rate variability, markers of cardiac autonomic function, have been linked with cardiovascular disease. We investigated whether heart rate and heart rate variability are associated with functional status in older adults, independent of cardiovascular disease.

Methods:

We obtained data from the Prospective Study of Pravastatin in the Elderly at Risk (PROSPER). A total of 5042 participants were included in the present study, and mean follow-up was 3.2 years. Heart rate and heart rate variability were derived from baseline 10-second electrocardiograms. Heart rate variability was defined as the standard deviation of normal-to-normal RR intervals (SDNN). Functional status in basic (ADL) and instrumental (IADL) activities of daily living was measured using Barthel and Lawton scales, at baseline and during follow-up.

Results:

The mean age of the study population was 75.3 years. At baseline, higher heart rate was associated with worse ADL and IADL, and lower SDNN was related to worse IADL (all p values < 0.05). Participants in the highest tertile of heart rate (range 71–117 beats/min) had a 1.79-fold (95% confidence interval [CI] 1.45–2.22) and 1.35-fold (95% CI 1.12–1.63) higher risk of decline in ADL and IADL, respectively (p for trend < 0.001 and 0.001, respectively). Participants in the lowest tertile of SDNN (range 1.70–13.30 ms) had 1.21-fold (95% CI 1.00–1.46) and 1.25-fold (95% CI 1.05–1.48) higher risk of decline in ADL and IADL, respectively (both p for trends < 0.05). All associations were independent of sex, medications, cardiovascular risk factors and comorbidities.

Interpretation:

Higher resting heart rate and lower heart rate variability were associated with worse functional status and with higher risk of future functional decline in older adults, independent of cardiovascular disease. This study provides insight into the role of cardiac autonomic function in the development of functional decline.Elevated heart rate and reduced heart rate variability — the beat-to-beat variation in heart rate intervals — both reflect an altered balance of the autonomic nervous system tone characterized by increased sympathetic and/or decreased parasympathetic activity.^1–3 Sympathetic overactivity has been linked to a procoagulant state and also to risk factors for atherosclerosis, including metabolic syndrome, obesity and subclinical inflammation.^2–4 Moreover, increased heart rate is related to atherosclerosis, not only as an epiphenomenon of sympathetic overactivity, but also through hemodynamic mechanisms, such as high pulsatile shear stress, which leads to endothelial dysfunction.⁵Atherosclerosis has been linked to increased risk of functional decline in older people via cardiovascular events.⁶ As the world population is aging, the burden of functional disability is expected to increase.⁶ It has been hypothesized that heart rate and heart rate variability are markers of frailty, an increased vulnerability to stressors and functional decline.⁷ However, the direct link between these 2 parameters and risk of functional decline has not been fully established, and it is uncertain whether this association is independent of cardiovascular comorbidities.In this study, we examined whether heart rate and heart rate variability were cross-sectionally and longitudinally associated with functional status in older adults at high risk of cardiovascular disease, independent of cardiovascular risk factors and comorbidities.     

A terminal dynamics model of the heartbeat

 It is widely assumed that heartbeat dynamics are chaotic, although there has been no evidence confirming such an opinion, and some evidence to the contrary. Additionally, the deterministic assumptions of such dynamics cannot be demonstrated. An alternative model is presented based upon the notion of terminal dynamics, which can more faithfully represent key features of the heartbeat: namely, piecewise determinism, and singular points between beats, which allow for adaptability while maintaining stability. Received: 2 February 1996/Accepted in revised form: 20 May 1996     

The circadian rhythm of heart rate variability

Purpose: In recent years, the measurement of heart rate variability (HRV) has gained ground even outside research settings in everyday clinical and outpatient practice and in health promotion. Methods: Using the search terms “heart rate variability”, “hrv” and “circadian”, a systematic review was carried out in the PubMed database to find original work that analysed the course of HRV parameters over a 24-h period. Results: A total of 26 original studies were found. Almost all the studies detected a circadian rhythm for the HRV parameters analysed. HRV increased during the night in particular and a nighttime peak during the second half of the night was identified. Conclusions: HRV follows a circadian rhythm. But until today, there isn′t any possibility to make quantitative statements about changes over the course of the day for planning short-term measurements. More qualitative studies must be carried in order to close this knowledge gaps.     

Inheritance of heart rate variability: the kibbutzim family study

Heart rate variability (HRV) measures are associated with coronary heart disease incidence and mortality. Therefore insight into the genetic and environmental determinants of these measures may have clinical relevance. We assessed the role of genetic and environmental factors of time domain and frequency domain HRV indices. Participants were 451 kibbutz members, aged 15 and up, belonging to 80 families. HRV indices were calculated from Holter recordings measured over 5 min. Our data indicate that for the two time- and four frequency domain indices, a mixture of two normal distributions fit the data significantly better than a single normal distribution (P<0.05). We used complex segregation analysis to infer the modes of inheritance of these HRV measures. We found evidence for possible involvement of a recessive major gene in the inheritance of the root mean square of successive differences in RR intervals (RMSSD), which is predominantly vagally mediated. A putative major gene explains 28%-34% of the adjusted inter-individual variability. The SD, determined by a mixture of mechanisms, is influenced by environmental and polygenic effects, but not by a major gene. The findings regarding the heritability of the frequency domain indices were not conclusive. However, the involvement of genetic factors was not rejected. Additional studies in extended families are needed to confirm the involvement of major genes in the determination of the autonomic activity.     

Initial heart rate variability and radiosensitivity in rabbits

The goal of the work was to investigate the rabbits' radiosensitivity dependence on the initial functional state of the autonomous nervous system (ANS), as assessed by time-frequency parameters of the heart rate variability (HRV). Survival rate and rhythm-cardiologic correlates of the pathological processes following total X-irradiation, at doses of 2 and 12 Gy, were studied with an aid of modern computer technologies of measurement and data analysis. It has been found that the animals with initial prevailing of adrenergic influences on the HRV ("sympathicotonics") are significantly more sensitive to irradiation than those in which the parasympathetic prevalence was evident ("vagotonics"). The most characteristic and determining difference between these two groups of animals is initial level of the sum regulatory influences on the heart rhythm, which is manifested in value of total power of spectral density (TP) of HRV. In the sympathicotonics the TP is significantly lower than in the vagotonics. The primary HRV response to irradiation practically does not differ according to the dose and manifests in sharp suppression of the TP in both groups of the animals. At 12 Gy this process is irreversible. In the sympathicotonics it develops earlier and terminates with death much sooner than in the vagotonics. An average life-span of the rabbits, at this dose, is 18.8 +/- 2.6 days in vagotonics, and 10.3 +/- 1.3 days in sympathicotonics (p < 0.02). At 2 Gy initial sharp decrease of the TP in the vagotonics lasts one week only. Then the sum regulatory influence of the ANS on the heart rate increases (rebound) and this condition, which probably points at general resistance of the organism, could be seen within two months; at the end of third month it stabilizes at the initial level. In the sympathycotonics initial sharp decrease of the TP also occurred, however no rebound was observed. The results obtained show that low initial level of the TP of HRV is sufficiently correct marker for higher radiosensitivity in the sympathotonic rabbits against the vagotonic ones.