Connection of the tangents of the regression slope of the heart rate graph with linear and nonlinear dynamics in stationary short-time series

The connection of the regression slope of heart rate graph (b1) with linear and nonlinear dynamics in stationary short-time series (256 points) was studied. A new index for the estimation of nonlinear dynamics in stationary short-time series was used, which is based on the correlation dimension. The results of the study indicated that the dynamics of heart rate in stationary short-time series can be represented as the sum of linear (periodic) and nonlinear (stochastic) processes. A relation of b1 with both linear and nonlinear dynamics of heart rate was found. The formulas for the calculation of absolute and relative (to the amplitude of periodic fluctuations) noise levels in heart rate dynamics were derived. A comparative analysis of nonlinear dynamics of heart rate in stationary short-time series for different functional states of humans was performed. The increase in the relative noise level in heart rate dynamics with increasing breathing frequency is related not only to a decrease in control breathing amplitude but also to an increase in the noise amplitude. The decrease in the absolute noise level for nervous excitation, fatigue, and mental stress were found. The predominance of nonlinear (stochastic) processes over linear (periodic) processes in the relaxed state was established.     

Nonlinear dynamics of heart rate variability in cocaine-exposed neonates during sleep

The aim of this study was to determine the effects of prenatal cocaine exposure (PCE) on the dynamics of heart rate variability in full-term neonates during sleep. R-R interval (RRI) time series from 9 infants with PCE and 12 controls during periods of stable quiet sleep and active sleep were analyzed using autoregressive modeling and nonlinear dynamics. There were no differences between the two groups in spectral power distribution, approximate entropy, correlation dimension, and nonlinear predictability. However, application of surrogate data analysis to these measures revealed a significant degree of nonlinear RRI dynamics in all subjects. A parametric model, consisting of a nonlinear delayed-feedback system with stochastic noise as the perturbing input, was employed to estimate the relative contributions of linear and nonlinear deterministic dynamics in the data. Both infant groups showed similar proportional contributions in linear, nonlinear, and stochastic dynamics. However, approximate entropy, correlation dimension, and nonlinear prediction error were all decreased in active versus quiet sleep; in addition, the parametric model revealed a doubling of the linear component and a halving of the nonlinear contribution to overall heart rate variability. Spectral analysis indicated a shift in relative power toward lower frequencies. We conclude that 1) RRI dynamics in infants with PCE and normal controls are similar; and 2) in both groups, sympathetic dominance during active sleep produces primarily periodic low-frequency oscillations in RRI, whereas in quiet sleep vagal modulation leads to RRI fluctuations that are broadband and dynamically more complex.     

Changes in nonlinear characteristics of heart rate variability under functional load on the cardiovascular system in healthy subjects and coronary heart disease patients

Some nonlinear characteristics of heart rate variability in the course of functional tests with physical exercise are described. Two groups of volunteers participated in the tests: a control group of 32 healthy subjects (group 1) and a group of 35 coronary heart disease (CHD) patients (group 2). Two series of experiments were performed for each group. An active orthostatic test (AOT) was used in the first series, and a gradually growing physical load on a bicycle ergometer (bicycle ergometer test, BET), in the second series. Along with statistical indices of heart rate (the mean RR interval and standard deviation), nonlinear indices of heart rate were estimated: the correlation dimensionality (D ₂) and approximate entropy (ApEn). Trends of the changes in nonlinear indices of heart rate have been found. The D ₂ and ApEn decreased in both groups of subjects during the AOT and BET under the maximum load. However, the groups of healthy subjects and CHD patients differed in the reactivity of indices, the amplitude of changes in nonlinear indices being narrower in the latter group than in group 1. Differently directed shifts in standard deviation (SDNN) and nonlinear indices have been found. Thus, the data obtained with the use of nonlinear heart rate characteristics show that heart rate under physical load is more multivariate and diverse in healthy subjects at rest and the amplitude of changes during the AOT and BET is greater than in CHD patients, which is a result of the specific autonomic control of heart activity in cardiovascular pathologies.     

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.     

The limitations of heart rate as a predictor of metabolic rate in fish

Although telemetered heart rate (f_H) has been used as a physiological correlate to predict the metabolic rate (as oxygen consumption, V?O₂) of fish in the field, it is our contention that the method has not been validated adequately for fish. If f_H in fish is to be used to estimate V?O₂, a single linear (or log-linear) relationship must be established for each species between the two variables which allows V?O₂ to be predicted accurately under all environmentally relevant conditions. Our analyses of existing data indicate that while a good linear (or log-linear) relationship can be established between f_H and V?O₂, the conditions under which the relationship applies may be quite restricted. Physiological states and environmental factors affect the relationship between f_H and V?O₂ significantly such that several curves can exist for a single species. In addition, there are situations in which f_H and V?O₂ do not covary in a significant manner. In some situations f_H can vary over much of its physiological range while V?O₂ remains constant; in others V?O₂ may vary while f_H is invariate. The theoretical basis for this variability is examined to explain why the use of telemetered f_H in predicting V?O₂ of fish may be limited to certain specified applications.     

糖尿病植物神经病变病人心率变异的非线性定量分析

目的：研究糖尿病人植物神经病变与心率变异的关系。对象：正常对照组和根据临床有无糖尿病神经病变（ＤＡＮ）分组的糖尿病病人,方法：应用２４小时动态心电图对正常和糖尿病人进行心率变异的线性,非线性散点图和非线性定量参数分析,结果：单纯糖尿病组ＳＤＮＮ,ＳＤＡＮＮ和ＰＮＮ５０低于正常组（Ｐ〈０．０５）;糖尿病＋ＤＡＮ组各项线性时域分析指标均低于正常和单纯糖尿病组（Ｐ〈０．０１－０．００１）,散点图分析结果     

An integrated diabetic index using heart rate variability signal features for diagnosis of diabetes

Electrocardiogram (ECG) signals are difficult to interpret, and clinicians must undertake a long training process to learn to diagnose diabetes from subtle abnormalities in these signals. To facilitate these diagnoses, we have developed a technique based on the heart rate variability signal obtained from ECG signals. This technique uses digital signal processing methods and, therefore, automates the detection of diabetes from ECG signals. In this paper, we describe the signal processing techniques that extract features from heart rate (HR) signals and present an analysis procedure that uses these features to diagnose diabetes. Through statistical analysis, we have identified the correlation dimension, Poincaré geometry properties (SD2), and recurrence plot properties (REC, DET, L _mean) as useful features. These features differentiate the HR data of diabetic patients from those of patients who do not have the illness, and have been validated by using the AdaBoost classifier with the perceptron weak learner (yielding a classification accuracy of 86%). We then developed a novel diabetic integrated index (DII) that is a combination of these nonlinear features. The DII indicates whether a particular HR signal was taken from a person with diabetes. This index aids the automatic detection of diabetes, thereby allowing a more objective assessment and freeing medical professionals for other tasks.     

Nonlinear dynamics of heart rate variability during experimental hemorrhage in ketamine-anesthetized rats

Indexes of heart rate variability (HRV) based on linear stochastic models are independent risk factors for arrhythmic death (AD). An index based on a nonlinear deterministic model, a reduction in the point correlation dimension (PD2i), has been shown in both animal and human studies to have a higher sensitivity and specificity for predicting AD. Dimensional reduction subsequent to transient ischemia was examined previously in a simple model system, the intrinsic nervous system of the isolated rabbit heart. The present study presents a new model system in which the higher cerebral centers are blocked chemically (ketamine inhibition of N-methyl-D-aspartate receptors) and the system is perturbed over a longer 15-min interval by continuous hemorrhage. The hypothesis tested was that dimensional reduction would again be evoked, but in association with a more complex relationship between the system variables. The hypothesis was supported, and we interpret the greater response complexity to result from the larger autonomic superstructure attached to the heart. The complexities observed in the nonlinear heartbeat dynamics constitute a new genre of autonomic response, one clearly distinct from a hardwired reflex or a cerebrally determined defensive reaction.     

Modulation of cardiac A1-adenosine receptors in rats following treatment with agents affecting heart rate

Effects of chronic treatment affecting heart rate on A₁ adenosine receptor levels and their functions were studied. Treatment of rats with isoproterenol for 10 days accelerated heart rate and increased the level of adenosine receptors, in both the atria and ventricles. Negative dromotropic response of isolated heart to adenosine was enhanced in isoproterenol-treated rats. Similar results were obtained following treatment with atropine sulfate, or swimming training but not after treatment with thyroxine. On the other hand, treatment with amiodarone, which normally causes a decrease in heart rate, also increased the level of adenosine receptors in both atria and ventricles. The sensitivity of the isolated heart to the negative dromotropic and chronotropic effects of adenosine was not enhanced in the amiodarone treated rats. Similar results were obtained following treatment with propranolol, while treatment with PTU (6-n-propyl-2-thiouracil) increased adenosine sensitivity in the isolated heart. It was concluded that the levels of A₁ adenosine receptors in the heart correspond to heart rate, and to cardiac efficiency. While an increase in heart rate was followed by up-regulation of A₁ adenosine receptors, a decrease in heart rate caused a moderate elevation of these receptors.     

Nonlinear electromagnetic pulse with a superwide frequency bandwidth

A nonlinear equation is derived and its analytic solution describing a soliton-like perturbation propagating at velocity close to the speed of light is found. It is shown that the rate at which the amplitude of a soliton excited by a cold electron beam in a magnetized plasma-filled waveguide grows is proportional to (n _b/n ₀)^1/3, as is the linear growth rate of the beam-plasma instability.     

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.     

Flight modes in migrating European bee-eaters: heart rate may indicate low metabolic rate during soaring and gliding

Background

Many avian species soar and glide over land. Evidence from large birds (m _b>0.9 kg) suggests that soaring-gliding is considerably cheaper in terms of energy than flapping flight, and costs about two to three times the basal metabolic rate (BMR). Yet, soaring-gliding is considered unfavorable for small birds because migration speed in small birds during soaring-gliding is believed to be lower than that of flapping flight. Nevertheless, several small bird species routinely soar and glide.

Methodology/Principal Findings

To estimate the energetic cost of soaring-gliding flight in small birds, we measured heart beat frequencies of free-ranging migrating European bee-eaters (Merops apiaster, m _b∼55 g) using radio telemetry, and established the relationship between heart beat frequency and metabolic rate (by indirect calorimetry) in the laboratory. Heart beat frequency during sustained soaring-gliding was 2.2 to 2.5 times lower than during flapping flight, but similar to, and not significantly different from, that measured in resting birds. We estimated that soaring-gliding metabolic rate of European bee-eaters is about twice their basal metabolic rate (BMR), which is similar to the value estimated in the black-browed albatross Thalassarche (previously Diomedea) melanophrys, m _b∼4 kg). We found that soaring-gliding migration speed is not significantly different from flapping migration speed.

Conclusions/Significance

We found no evidence that soaring-gliding speed is slower than flapping flight in bee-eaters, contradicting earlier estimates that implied a migration speed penalty for using soaring-gliding rather than flapping flight. Moreover, we suggest that small birds soar and glide during migration, breeding, dispersal, and other stages in their annual cycle because it may entail a low energy cost of transport. We propose that the energy cost of soaring-gliding may be proportional to BMR regardless of bird size, as theoretically deduced by earlier studies.     

The use of internal heart rate loggers in determining cardiac breakpoints of fish

As marine environments are influenced by global warming there is a need to thoroughly understand the relationship between physiological limits and temperature in fish. One quick screening method of a physiological thermal tipping point is the temperature at which maximum heart rate (ƒ_Hmax) can no longer scale predictably with warming and is referred to as the Arrhenius break temperature (T_AB). The use of this method has been successful for freshwater fish by using external electrodes to detect an electrocardiogram (ECG), however, the properties of this equipment pose challenges in salt water when evaluating marine fish. To overcome these challenges, this study aimed to explore the potential use of implantable heart rate loggers to quantify the T_AB of Chrysoblephus laticeps, a marine Sparid, following the ECG method protocols where ƒ_Hmax is monitored over an acute warming event and the T_AB is subsequently identified using a piece-wise linear regression model. Of the nine experimental fish, only five (56%) returned accurate ƒ_Hmax data. The T_AB of successful trials was identified each time and ranged from 18.09 to 20.10 °C. This study therefore provides evidence that implantable heart rate loggers can estimate T_AB of fish which can be applied to many marine species.     

Nonlinear heart rate variability measures under electromagnetic fields produced by GSM cellular phones

This study was designed to assess the nonlinear dynamics of heart rate variability (HRV) during exposure to low-intensity EMFs. Twenty-six healthy young volunteers were subjected to a rest-to-stand protocol to evaluate autonomic nervous system in quiet condition (rest, vagal prevalence) and after a sympathetic activation (stand). The procedure was conducted twice in a double-blind design: once with a genuine EMFs exposure (GSM cellular phone at 900 MHz, 2 W) and once with a sham exposure (at least 24 h apart). During each session, three-lead electrocardiograms were recorded and RR series extracted off-line. The RR series were analyzed by nonlinear deterministic techniques in every phase of the protocol and during the different exposures. The analysis of the data shows there was no statistically significant effect due to GSM exposure on the nonlinear dynamics of HRV.     

Properties and regulation of a trans-plasma membrane redox system of perfused rat heart

Ferricyanide was reduced to ferrocyanide by the perfused rat heart at a linear rate of 78 nmol/min per g of heart (non-recirculating mode). Ferricyanide was not taken up by the heart and ferrocyanide oxidation was minimal (3 nmol/min per g of heart). Perfusate samples from hearts perfused without ferricyanide did not reduce ferricyanide. A single high-affinity site (apparent K_m=22 μM) appeared to be responsible for the reduction. Perfusion of the heart with physiological medium containing 0.5 mM ferricyanide did not alter contractility, biochemical parameters or energy status of the heart. Perfusate flow rate and perfusate oxygen concentration exerted opposing effects on the rate of ferricyanide reduction. A net decreased reduction rate resulted from a decreased perfusion flow rate. Thus, the rate of supply of ferricyanide dominated over the stimulatory effect of oxygen restriction; the latter effect only becoming apparent when the oxygen concentration was lowered at a high perfusate flow rate. Whereas glucose (5 mM) increased the rate of ferricyanide reduction, pyruvate (2 mM), acetate (2 mM), lactate (2 mM) and 3-hydroxybutyrate (2 mM) each had no effect. Insulin (3 nM), glucagon (0.5 μM), dibutyryl cyclic AMP (0.1 mM) and the β-adrenergic agonist ritodrine (10 μM) also had no effect, however the α₁-adrenergic agonist, methoxamine (10 μM), produced a net increase in the rate of ferricyanide reduction. It is concluded that a trans-plasma membrane electron efflux occurs in perfused rat heart that is sensitive to oxygen supply, glucose, perfusion flow rate, and the α-adrenergic agonist methoxamine.     

Novel approach for fetal heart rate classification introducing grammatical evolution

Fetal heart rate (FHR) variations reflect the level of oxygenation and blood pressure of the fetus. Electronic Fetal Monitoring (EFM), the continuous monitoring of the FHR, was introduced into clinical practice in the late 1960s and since then it has been considered as an indispensable tool for fetal surveillance. However, EFM evaluation and its merit is still an open field of controversy, mainly because it is not consistently reproducible and effective. In this work, we present a novel method based on grammatical evolution to discriminate acidemic from normal fetuses, utilizing features extracted from the FHR signal during the minutes immediately preceding delivery. The proposed method identifies linear and nonlinear correlations among the originally extracted features and creates/constructs a set of new ones, which, in turn, feed a nonlinear classifier. The classifier, which also uses a hybrid method for training, along with the constructed features was tested using a set of real data achieving an overall performance of 90% (specificity = sensitivity = 90%).     

Respiratory influences on non-linear dynamics of heart rate variability in humans

 The goal of our study was to determine whether evidence for chaos in heart rate variability (HRV) can be observed when the respiratory input to the autonomic controller of heart rate is forced by the deterministic pattern associated with periodic breathing. We simultaneously recorded, in supine healthy volunteers, RR intervals and breathing volumes for 20 to 30 min (1024 data point series) during three protocols: rest (control), fixed breathing (15 breath/min) and voluntary periodic breathing (3 breaths with 2 s inspiration and 2 s expiration followed by an 8 s breath hold). On both the RR interval and breathing volume series we applied the non-linear prediction method (Sugihara and May algorithm) to the original time series and to distribution-conserved isospectral surrogate data. Our results showed that, in contrast to the control test, during both fixed and voluntary periodic breathing the variability of breathing volumes was clearly deterministic non-chaotic. During all the three protocols, the RR-interval series’ non-linear predictability was consistent with one of a chaotic series. However, at rest, no clear difference was observed between the RR-interval series and their surrogates, which means that no clear chaos was observed. During fixed breathing a difference appeared, and this difference seemed clearer during voluntary periodic breathing. We concluded that HRV dynamics were chaotic when respiration was forced with a deterministic non-chaotic pattern and that normal spontaneous respiratory influences might mask the normally chaotic pattern in HRV. Received: 7 August 1995 / Accepted in revised form: 20 March 1997     

Thermal effect on heart rate and hemodynamics in vitelline arteries of stage 18 chicken embryos

We investigated the thermal effects on heart rate, hemodynamics, and response of vitelline arteries of stage-18 chicken embryos. Heart rate was monitored by a high-speed imaging method, while hemodynamic quantities were evaluated using a particle image velocimetry (PIV) technique. Experiments were carried out at seven different temperatures (36–42 °C with 1 °C interval) after 1 h of incubation to stabilize the heart rate. The heart rate increased in a linear manner (r=0.992). Due to the increased cardiac output (or heart rate), the hemodynamic quantities such as mean velocity (U_mean), velocity fluctuation (U_fluc), and peak velocity (U_peak) also increased with respect to the Womersley number (Ω) in the manner r=0.599, 0.693, and 0.725, respectively. This indicates that the mechanical force exerting on the vessel walls increases. However, the active response (or regulation) of the vitelline arteries was not observed in this study.     

Mean and quasideterministic equivalence for linear stochastic dynamics

In linear, stochastic dynamics it is shown that the quasideterministic population size is equivalent to the mean population size. The quasideterministic dynamics are defined by the conditional infinitesimal mean of the process. The stochastic component of the dynamics includes both Gaussian and Poisson white noise, with amplitude coefficients proportional to the population size. Generalizations are given for nonautonomous coefficients and for distributed Poisson jump amplitudes. A counter example--an exactly integrable nonlinear jump model--shows that the equivalence result does not hold for nonlinear stochastic dynamics.