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.     

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.     

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.     

Respiratory-related heart rate variability in progressive experimental heart failure

Heart failure is associated with autonomic imbalance, and this can be evaluated by a spectral analysis of heart rate variability. However, the time course of low-frequency (LF) and high-frequency (HF) heart rate variability changes, and their functional correlates during progression of the disease are not exactly known. Progressive heart failure was induced in 16 beagle dogs over a 7-wk period by rapid ventricular pacing. Spectral analysis of heart rate variability and respiration, echocardiography, hemodynamic measurements, plasma atrial natriuretic factor, and norepinephrine was obtained at baseline and every week, 30 min after pacing interruption. Progressive heart failure increased heart rate (from 91 +/- 4 to 136 +/- 5 beats/min; P < 0.001) and decreased absolute and normalized (percentage of total power) HF variability from week 1 and 2, respectively (P < 0.01). Absolute LF variability did not change during the study until it disappeared in two dogs at week 7 (P < 0.05). Normalized LF variability increased in moderate heart failure (P < 0.01), leading to an increased LF-to-HF ratio (P < 0.05), but decreased in severe heart failure (P < 0.044; week 7 vs. week 5). Stepwise regression analysis revealed that among heart rate variables, absolute HF variability was closely associated with wedge pressure, right atrial and pulmonary arterial pressure, left ventricular ejection fraction and volume, ratio of maximal velocity of early (E) and atrial (A) mitral flow waves, left atrial diameter, plasma norepinephrine, and atrial natriuretic peptide (0.45 < r < 0.65, all P < 0.001). In tachycardia-induced heart failure, absolute HF heart rate variability is a more reliable indicator of cardiac dysfunction and neurohumoral activation than LF heart rate variability.     

A latent-class mixture model for incomplete longitudinal Gaussian data

Summary .   In the analyses of incomplete longitudinal clinical trial data, there has been a shift, away from simple methods that are valid only if the data are missing completely at random, to more principled ignorable analyses, which are valid under the less restrictive missing at random assumption. The availability of the necessary standard statistical software nowadays allows for such analyses in practice. While the possibility of data missing not at random (MNAR) cannot be ruled out, it is argued that analyses valid under MNAR are not well suited for the primary analysis in clinical trials. Rather than either forgetting about or blindly shifting to an MNAR framework, the optimal place for MNAR analyses is within a sensitivity-analysis context. One such route for sensitivity analysis is to consider, next to selection models, pattern-mixture models or shared-parameter models. The latter can also be extended to a latent-class mixture model, the approach taken in this article. The performance of the so-obtained flexible model is assessed through simulations and the model is applied to data from a depression trial.     

Dimensional analysis of heart rate variability in heart transplant recipients

Periodicities in the heart rate have been known for some time. We discuss these periodicities in normal and transplanted hearts. We then consider the possibility of dimensional analysis of these periodicities in transplanted hearts and problems associated with the record.     

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.     

Sample entropy analysis of neonatal heart rate variability

Abnormal heart rate characteristics of reduced variability and transient decelerations are present early in the course of neonatal sepsis. To investigate the dynamics, we calculated sample entropy, a similar but less biased measure than the popular approximate entropy. Both calculate the probability that epochs of window length m that are similar within a tolerance r remain similar at the next point. We studied 89 consecutive admissions to a tertiary care neonatal intensive care unit, among whom there were 21 episodes of sepsis, and we performed numerical simulations. We addressed the fundamental issues of optimal selection of m and r and the impact of missing data. The major findings are that entropy falls before clinical signs of neonatal sepsis and that missing points are well tolerated. The major mechanism, surprisingly, is unrelated to the regularity of the data: entropy estimates inevitably fall in any record with spikes. We propose more informed selection of parameters and reexamination of studies where approximate entropy was interpreted solely as a regularity measure.     

电刺激迷走神经对蟾蜍心率和心率变异的影响

目的:观察不同频率迷走神经刺激对蟾蜍离体心脏的心率及心率变异的影响。方法:将蟾蜍心脏和右侧迷走交感干离体后,以不同频率电刺激神经,记录心电图曲线并作心率变异性(HRV)分析。结果:交感神经阻断后,电刺激迷走交感干,心率(HR)显著下降(P0.01),全部正常心动周期的标准差(SDNN)和相邻正常心动周期差值的均方根(RMSSD)显著升高(P0.01),不同频率刺激组之间没有明显差异;与对照组相比,各指标变化较大;给药组0.2Hz时高频(HF)显著升高(P0.01),低频/高频比值(LF/HF)明显降低(P0.05),0.8Hz时HF和LF/HF接近刺激前水平。结论:一定范围内增加刺激频率,迷走神经降低心率的作用增强;没有交感神经调节条件下的迷走神经对心率和心率变异的调节可能存在不同的机制。     

Determination of heart rate and heart rate variability in the equine fetus by fetomaternal electrocardiography

Heart rate is an important parameter of fetal well-being. We have analyzed fetal heart rate (HR) and heart rate variability (HRV) by fetomaternal electrocardiography (ECG) in the horse (Equus caballus) from midpregnancy to foaling. It was the aim of the study to detect changes in the regulation of fetal cardiac activity over time and to establish normal values in undisturbed pregnancies. A total of 22 mares were available for the study. Fetomaternal electrocardiography was a reliable technique to detect cardiac signals in fetuses between Day 173 of gestation and foaling. Fetal HR decreased from 115 ± 4 beats/min (Days 170 to 240 of gestation) to 83 ± 3 beats/min (Day 320) to 79 ± 1 beats/min (1 d before foaling; P < 0.001). Mean beat to beat (RR) interval and standard deviation of the RR interval (SDRR) increased (P < 0.001). Gestational age thus affects RR interval and HR in the equine fetus. From Days 270 to 340 of gestation, SDRR increased from 11.4 ± 1.3 msec on Day 270 to 27.8 ± 3.6 msec on Day 340 (P < 0.05), and the root mean square of successive RR differences (RMSSD) tended to increase (P = 0.07), indicating maturation of the fetal autonomous nervous system. For the last 10 d before foaling, fetal HR and HRV remained constant and did not allow predicting the onset of parturition in the horse. Only during the last 30 min before the foal was born, in 4 of 5 fetuses, HR decreased and RR interval increased. Accelerations and decelerations in HR were detectable at all times, but neither their number nor duration changed over time.     

Autonomic control of heart rate during exercise studied by heart rate variability spectral analysis.

Spectral analysis of heart rate variability (HRV) might provide an index of relative sympathetic (SNS) and parasympathetic nervous system (PNS) activity during exercise. Eight subjects completed six 17-min submaximal exercise tests and one resting measurement in the upright sitting position. During submaximal tests, work rate (WR) was increased for the initial 3 min in a ramp fashion until it reached constant WRs of 20 W, or 30, 60, 90, 100, and 110% of the predetermined ventilatory threshold (Tvent). Ventilatory profile and alveolar gas exchange were monitored breath by breath, and beat-to-beat HRV was measured as R-R intervals of an electrocardiogram. Spectral analysis was applied to the HRV from 7 to 17 min. Low-frequency (0-0.15 Hz) and high-frequency (0.15-1.0 Hz) areas under power spectra (LO and HI, respectively) were calculated. The indicator of PNS activity (HI) decreased dramatically (P less than 0.05) when the subjects exercised compared with rest and continued to decrease until the intensity reached 60% Tvent. The indicator of SNS activity (LO/HI) remained unchanged up to 100% Tvent, whereas it increased abruptly (P less than 0.05) at 110% Tvent. The results suggested that (cardiac) PNS activity decreased progressively from rest to a WR equivalent to 60% Tvent, and SNS activity increased only when exercise intensity exceeded Tvent.     

Unsupervised assessment of microarray data quality using a Gaussian mixture model

Background  

Quality assessment of microarray data is an important and often challenging aspect of gene expression analysis. This task frequently involves the examination of a variety of summary statistics and diagnostic plots. The interpretation of these diagnostics is often subjective, and generally requires careful expert scrutiny.     

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.     

The influence of short-term sedentary behavior on circadian rhythm of heart rate and heart rate variability

The notion that sedentary behavior is harmful to human health is widespread. Little is known about the short term influence of sedentary behavior on heart rate (HR) and heart rate variability (HRV) circadian rhythms. Therefore the purpose of the present study was to examine the influence of short term sedentary behavior on the circadian rhythms of HR and HRV using cosine periodic regression analysis. Sixteen healthy young students were included in a randomized crossover study. All subjects underwent 24-h ECG Holter monitoring in two different states of physical activity, an active condition (more than 15,000 steps per day) and a sedentary condition (less than 1,000 steps per day). Hourly mean values were calculated for HR and HRV, and then were evaluated using cosine periodic regression analysis. The circadian rhythm parameters, amplitude, mesor, and acrophase for HR and HRV variables were obtained. As a result, the significance of the circadian rhythm was confirmed for all variables in each condition. The measure of fit R2 value was decreased in sedentary condition. The amplitude of the sedentary condition was significantly smaller than that of the active condition with respect to HR (7.94 ± 1.91 bpm vs. 15.4 ± 3.93 bpm, p < 0.001), natural log of the high frequency measurement (lnHF) (0.38 ± 0.21 ms2 vs. 0.80 ± 0.28 ms2, p < 0.001), and low frequency/high frequency ratio (LF/HF) (0.75 ± 0.54 vs. 1.24 ± 0.69, p = 0.008). We found that sedentary behavior not only significantly lowered the amplitude of HR and HRV variables, but also might have led to weakness of the circadian rhythm of the HR and HRV variables.     

Association between level of intelligence and heart rate variability

Earlier we discovered that heart rate variability was associated with the level of intelligence. The purpose of this study is to confirm this association using more reliable method and to define more precisely the frequency band within which the amplitude of the heart rate modulations is related to intelligence. 13 males (aged 14 to 17) were the study subjects. The total score of the computer game Tetris was taken as a general measure of the intelligence level. Heart rate was recorded electrocardiographically both at rest and during playing Tetris. Frequency analysis of heart rate was carried out with digital Fourier transformation. Correlation analysis showed that there was positive association between the level of intelligence and the amplitude of heart rate modulation at the frequencies 0.30 and 0.15 modulations per RR interval. This association is closer for the heart rate at rest than for the heart rate during mental work and for the frequency 0.30 than for the 0.15 modulations per RR interval.     

Association of heart rate variability and frontal cortex activation

Literature data and results of our own research suggest that amplitude of periodic modulations of heart rate may be related to the cerebral cortex activity. Verification of this assumption was accomplished by searching for correlation between the heart rate periodogram (as a measure of amplitude of periodic modulations of heart rate at different frequencies), and electroencephalographic evaluation of the level of different cortical areas activation. Positive association between levels of activation of the frontal cortex and amplitude of heart rate modulation with the period of 3 modulations per heart rate interval was discovered.     

Influence of sound and light on heart rate variability

The effects of acoustic and visual stimuli and their synergistic effects on heart rate variability including gender differences were investigated. Of particular interest was the influence of visual stimulus on heart rate variability during listening to simple sounds of different characters. Twelve male and 12 female university students were selected as subjects. The subjects listened at rest to 7 different figures of sound at loudness levels averaging 60 dB. Beat-to-beat R-R intervals were continuously recorded under the closed-eye condition (CEC) and the open-eye condition (OEC) prior to, during, and immediately after the exposure to acoustic stimuli. Low frequency (LF) power was defined over 0.04-0.15 Hz and high frequency (HF) power over 0.15-0.40 Hz. Cardiac autonomic function was estimated by plotting LF/HF in standard measure against HF in standard measure and by plotting LF/HF (%) against HF (%), accompanied by a demarcated central area. Values of LF/HF tended to be smaller under CEC than under OEC. Values of HF while listening to a 110 Hz sine wave under CEC were significantly greater than values for 880 Hz and 3520 Hz sine waves, or for 110 Hz or 880 Hz sawtooth waves, under OEC. Under CEC, values of HF for 7 figures of sound were greater in females than in males. The value of HF of sine wave for 110 Hz under CEC and OEC was significantly greater than that for white noise under the OEC. The results suggest that the cardiac parasympathetic nervous activity during auditory excitation increases with elimination of visual stimuli and tends to be greater in females than in males.