Decrease of coherence between the respiration and parasympathetic control of the heart rate with aging.

The study of coordinated behavior between different systems of the human body provides useful information on the functioning of the body. The peculiarities of interaction and coordinated dynamics of the heart rate and respiration are of particular interest. We investigated the coherence of the processes of respiration and autonomic control of the heart rate for people of different ages in the awake state, in sleep with rapid eye movement, and in deep sleep. Our analysis revealed a monotonic decrease in the coherence of these processes with increasing age. This can be explained by age-related changes in the system of autonomic control of circulation. For all age groups, we found a qualitatively similar dynamics of the coherence between the studied processes during a transition from the awake state to sleep.

Autonomic control is a source of dynamical chaos in the cardiovascular system.

The origin of complex irregular dynamics in a cardiovascular system is still being actively debated. Some hypotheses suggest the crucial role of stochastic modulation of cardiovascular parameters, while others argue for the importance of cardiac pacemakers' chaotic deterministic dynamics. In the present study, we estimate the largest Lyapunov exponent and the correlation dimension for the 4-h experimental interbeat intervals and the chaotic signals generated by the mathematical model of the cardiovascular system. We study the complexity of the mathematical model for such cases as the autonomic blockade, the exclusion of all the stochastic components, and the absence of variability of respiration. The obtained results suggest that the complexity of the heart rate variability is largely due to the chaotic dynamics in the loops of autonomic control of circulation.

Synchronization of infra-slow oscillations of brain potentials with respiration.

We study the synchronization of infra-slow oscillations in human scalp electroencephalogram signal with the respiratory signal. For the cases of paced respiration with a fixed frequency and linearly increasing frequency, we reveal the phase and frequency locking of infra-slow oscillations of brain potentials by respiration. It is shown that for different brain areas, the infra-slow oscillations and respiration can exhibit synchronous regimes of different orders.

Model of Human Cardiovascular System Containing a Loop for the Autonomic Control of Mean Arterial Pressure.

We proposed a model of human cardiovascular system that describes the cardiac cycle, the autonomic regulation of heart and vessels, the baroreflex, and the formation of arterial pressure. The model also makes allowance for the influence of respiration on these processes. It was found that an allowance for nonlinearity and insertion of a loop for the autonomic control of mean arterial pressure (having the form of self oscillating time-delay system) enables to obtain model signals with statistical and spectral characteristics that are qualitatively and quantitatively similar to.those for experimental signals. The model reproduces the phenomenon of synchronization of the loop for mean arterial pressure regulation with a basic frequency of approximately 10 s by the signal of respiration.

[Phase and frequency locking of 0.1 Hz oscillations in heart rhythm and baroreflex control of arterial pressure by respiration with linearly varying frequency in healthy subjects].

We studied the features of functional interaction between the subsystems of autonomic control of heart rate (HR) and arterial pressure (AP) giving rise to 0.1 Hz oscillations in R-R intervals (RRI) and photoplethysmogram (PPG). The study included 25 healthy subjects (6 women and 19 men) aged between 18 and 32 years. The signals of RRI, PPG and respiration were simultaneously recorded under breathing with a frequency linearly increasing from 0.05 Hz to 0.25 Hz within 25 minutes in a sitting position of a subject. The possibility of phase and frequency locking of 0.1 Hz oscillations in RRI and PPG by respiration is shown. We revealed that theses oscillations have different width and location of the intervals of phase and frequency locking by respiration. This distinction points to the functional independence between the mechanisms of autonomic control of 0.1 Hz oscillations in RRI and PPG.

[Investigation of biophysical features of interaction between 0.1 Hz oscillations in heart rate variability and distal blood flow variability].

We studied biophysical features of interaction between 0.1 Hz oscillations in heart rate variability (HRV) and distal blood flow (DBF) variability in healthy subjects and patients after acute myocardial infarction (MI). 125 patients after acute MI (72 male and 53 female) aged between 30 and 83 years and 33 healthy subjects (23 male and 10 female) aged between 20 and 46 years were included in the study. The duration of prospective study of MI patients was one year. We estimated the delay in coupling between 0.1 Hz oscillations in H RV and DBF variability. It is found out that in healthy subjects the delay in coupling from heart rate to DBF is less than delay in coupling from DBF to heart rate. Acute MI results mainly in disruption of coupling from heart rate to DBF. This coupling is partially restored in one year after acute MI, but the delay in coupling remains significantly smaller than in healthy subjects. The features of coupling from DBF to heart rate are restored in MI patients within three weeks after infarction. After this period the delay in this coupling in MI patients is approximately the same as it is in healthy subjects.

Interbeat interval variability versus frequency modulation of heart rate.

The heart rate in humans is regulated by the autonomic nervous system, which modulates the frequency of heart contractions, resulting in heart rate variability (HRV). Therefore, to assess the activity of the autonomic nervous system, which contains important information for medical diagnostics, methods based on the analysis of interbeat interval variability are often used. This approach does not require the use of invasive methods for measuring the signals of the autonomic nervous system, but its accuracy is an open question. Using mathematical modeling, we investigate the possibility of extracting the signal of frequency modulation of the heartbeats from the electrocardiogram (ECG) signal and conduct a detailed comparison of the extracted signal with the real modulating signal. Since the quality of extraction of the signal of frequency modulation from the ECG depends on the method of demodulation, we compare two different approaches. One is based on the detection of the main oscillation rhythm and its bandpass filtering, and the other on the heterodyning technique. It is shown that low-frequency (LF) and high-frequency (HF) oscillations in HRV associated, respectively, with sympathetic and parasympathetic modulation by the autonomic nervous system, in the general case, significantly differ from the signals of frequency modulation of the heart rate in shape, but have close similarity with them in the frequency domain. We find that in model systems, the similarity of the LF component of HRV with sympathetic modulation of the heart rate is higher than the similarity of the HF component of HRV with parasympathetic modulation.

Reconstruction of parameters and unobserved variables of a semiconductor laser with optical feedback from intensity time series.

We propose a method for the reconstruction of time-delayed feedback systems having unobserved variables from scalar time series. The method is based on the modified initial condition approach, which allows one to significantly reduce the number of starting guesses for an unobserved variable with a time delay. The proposed method is applied to the reconstruction of the Lang-Kobayashi equations, which describe the dynamics of a single-mode semiconductor laser with external optical feedback. We consider the case where only the time series of laser intensity is observable and the other two variables of the model are hidden. The dependence of the quality of the system reconstruction on the accuracy of assignment of starting guesses for unobserved variables and unknown laser parameters is studied. The method could be used for testing the security of information transmission in laser-based chaotic communication systems.

A comparison of statistical methods for assessing winter wheat grain yield stability.

The multitude of existing methods for assessing the phenotypic stability of plants makes breeders be faced with the problem of choosing an appropriate variant. The purpose of this study was to compare different methods of analyzing the genotype × environment interaction and, on their basis, assess the stability of the yield of 7 varieties of winter wheat. The article compares 17 stability statistics by applying them to data obtained from agrotechnical experiments carried in 2009-2011 for evaluating the grain yield of 7 varieties of winter common wheat of Siberian selection (Novosibirskaya 32, Novosibirskaya 40, Novosibirskaya 51, Novosibirskaya 3, Novosibirskaya 2, Obskaya winter, Omskaya 6). Analysis of variance revealed a significant ( p < 0.001) genotype × environment interaction in the experiments, which indicates a different reaction of genotypes to changes in environmental conditions. Genotypes were ranked according to the level of stability. Based on the analysis of the rank correlation matrix, the stability statistics were categorized in five groups. Recommendations were made on which group of methods to use depending on the objectives of the study. In the case when the goal of breeding research is the selection of the most biologically stable varieties with the minimum variance across a range of environments, one should use the methods of the static concept. If it is necessary to choose a genotype with a predictable reaction to changes of environmental conditions, corresponding to the calculated level or forecast, the regression approach is the most appropriate. The stability statistics generally identified Novosibirskaya 32 as the most stable variety from a biological point of view. The regression approach showed that Novosibirskaya 3 was the genotype with the smallest deviation from mean yield in all environments, while methods accessing the contribution of each genotype to the genotype × environment interaction defined Novosibirskaya 51 as the most stable variety.

Synchronization of low-frequency oscillations in the human cardiovascular system.

We investigate synchronization between the low-frequency oscillations of heart rate and blood pressure having in humans a basic frequency close to 0.1 Hz. A method is proposed for quantitative estimation of synchronization between these oscillating processes based on calculation of relative time of phase synchronization of oscillations. It is shown that healthy subjects exhibit on average substantially longer epochs of internal synchronization between the low-frequency oscillations in heart rate and blood pressure than patients after acute myocardial infarction.

Recovery of systems with a linear filter and nonlinear delay feedback in periodic regimes.

We propose a set of methods for the estimation of the parameters of time-delay systems with a linear filter and nonlinear delay feedback performing periodic oscillations. The methods are based on an analysis of the system response to regular external perturbations and are valid only for systems whose dynamics can be perturbed. The efficiency of the methods is illustrated using both numerical and experimental data.

[Assessment of dynamics of the autonomic cardiovascular system regulation based on low-frequency rhythm synchronization in patients with ischemic heart diseases complicated by myocardial infarction treated with metoprolol].

AIM: To develop a procedure for assessing the adequacy of metoprolol use in patients with coronary heart disease (CHD) on the basis of synchronization of 0.1-Hz rhythms in cardiac rhythm variability (CRV) and vascular blood filling in the microcirculatory bed (MCB). Materials and methods. 43 patients with CHD (age 63 +/- 8 years), who had sustained myocardial infarction about 6 months before, were examined. Synchronous registration of ECG and a pulsogram were made during an orthostatic test before and after therapy with metoprolol in the maximum tolerable doses during 3 months. The presence of synchronization of 0.1-Hz rhythms identified from a series of R-R intervals and the pulsogram was determined from the difference of phases; the total percent of synchronization (S) was estimated. RESULTS: The authors identified 2 groups of CHD patients: those with positive (n=21) and negative (n=16) orthostatic S, trends during treatment. The groups were matched by major clinical characteristics. There was an inverse relationship between the values of S, in the lying and standing position prior to or following treatment. It is suggested that there is the optimum range of 0.1-Hz rhythm synchronization values in the cardiovascular system during beta-blocker therapy in patients with CHD. CONCLUSION: There is a possibility applying an objective approach to assessing the adequacy of metoprolol treatment in CHD patients on the basis of synchronization of 0.1-Hz fluctuations in variations CR V and vascular blood filling in MCB.

Chimeralike states in networks of bistable time-delayed feedback oscillators coupled via the mean field.

We study the collective dynamics of oscillators in a network of identical bistable time-delayed feedback systems globally coupled via the mean field. The influence of delay and inertial properties of the mean field on the collective behavior of globally coupled oscillators is investigated. A variety of oscillation regimes in the network results from the presence of bistable states with substantially different frequencies in coupled oscillators. In the physical experiment and numerical simulation we demonstrate the existence of chimeralike states, in which some of the oscillators in the network exhibit synchronous oscillations, while all other oscillators remain asynchronous.

Recovery of couplings and parameters of elements in networks of time-delay systems from time series.

We propose a method for the recovery of coupling architecture and the parameters of elements in networks consisting of coupled oscillators described by delay-differential equations. For each oscillator in the network, we introduce an objective function characterizing the distance between the points of the reconstructed nonlinear function. The proposed method is based on the minimization of this objective function and the separation of the recovered coupling coefficients into significant and insignificant coefficients. The efficiency of the method is shown for chaotic time series generated by model equations of diffusively coupled time-delay systems and for experimental chaotic time series gained from coupled electronic oscillators with time-delayed feedback.

Correlations Between Cardiovascular Autonomic Control Indices During the Two-hour Immobilization Test in Healthy Subjects.

OBJECTIVE: The aim of the present study was to assess the features of dynamics of cardiovascular autonomic indices and correlations between them during the two-hour immobilization test in healthy subjects. METHODS: Photoplethysmogram (PPG) and electrocardiogram were recorded simultaneously during the two-hour immobilization test in 14 healthy subjects (5 men and 9 women) aged 29±5 years (mean±SD). Dynamics of heart rate variability (HRV) power spectrum in high-frequency and low-frequency ranges (in ms2 and percents of total spectral power), mean heart rate (HR), and index S of synchronization between 0.1-Hz rhythms in PPG and HR were analyzed. RESULTS: Individual dynamics of all studied cardiovascular autonomic indices during the two-hour immobilization test was unique in each healthy subject. Two groups of healthy subjects were identified basing on individual features of autonomic control. The group with initial low level of index S maintained the low level of S during the two-hour immobilization test. The group with initial high index S maintained the high level of S only during the first 100 minutes of test. During the last 20 minutes of test, index S was similar in both groups. Many cardiovascular autonomic indices correlate between themselves for an individual subject, but they do not correlate between the subjects. Multiple regression analysis in each subject has shown a high correlation between mean HR and all other studied autonomic parameters in 57% of subjects (multiple R>0.9, P<0.05). For 204 records analyzed without taking into account the individual features of subjects, the above mentioned correlation was smaller (multiple R=0.45, P<0.001). Index S was found out to be the most independent one among the autonomic indices. CONCLUSION: Cardiovascular autonomic control is characterized by a pronounced variability among healthy subjects and stability in time in each subject. We have not found any regularity in variation of cardiovascular autonomic indices, which is common for the entire group of healthy subjects during the two-hour immobilization test. Mean HR is a summary index of efficiency of heart autonomic control. Index S is the most independent cardiovascular autonomic parameter.

A comprehensive assessment of cardiovascular autonomic control using photoplethysmograms recorded from the earlobe and fingers.

We compare the spectral indices of photoplethysmogram variability (PPGV) estimated using photoplethysmograms recorded from the earlobe and the middle fingers of the right and left hand and analyze their correlation with similar indices of heart rate variability (HRV) in 30 healthy subjects (26 men) aged 27 (25, 29) years (median with inter-quartile ranges) at rest and under the head-up tilt test. The following spectral indices of PPGV and HRV were compared: mean heart rate (HR), total spectral power (TP), high-frequency (HF) and low-frequency (LF) ranges of TP in percents (HF% and LF%), LF/HF ratio, and spectral coherence. We assess also the index S of synchronization between the LF oscillations in HRV and PPGV. The constancy of blood pressure (BP) and moderate increase of HR under the tilt test indicate the presence of fast processes of cardiovascular adaptation with the increase of the sympathetic activity in studied healthy subjects. The impact of respiration on the PPGV spectrum (accessed by HF%) is less than on the HRV spectrum. It is shown that the proportion of sympathetic vascular activity (accessed by LF%) is constant in the PPGV of three analyzed PPGs during the tilt test. The PPGV for the ear PPG was less vulnerable to breathing influence accessed by HF% (independently from body position) than for PPGs from fingers. We reveal the increase of index S under the tilt test indicating the activation of interaction between the heart and distal vessels. The PPGV spectra for finger PPGs from different hands are highly coherent, but differ substantially from the PPGV spectrum for the ear PPG. We conclude that joint analysis of frequency components of PPGV (for the earlobe and finger PPGs of both hands) and HRV and assessment of their synchronization provide additional information about cardiovascular autonomic control.

Estimation of coupling between time-delay systems from time series.

We propose a method for estimation of coupling between the systems governed by scalar time-delay differential equations of the Mackey-Glass type from the observed time series data. The method allows one to detect the presence of certain types of linear coupling between two time-delay systems, to define the type, strength, and direction of coupling, and to recover the model equations of coupled time-delay systems from chaotic time series corrupted by noise. We verify our method using both numerical and experimental data.

[The investigation of the synchronization between rhythms in the human cardiovascular system from time series of R-R-intervals].

We demonstrated that, from the sequence of R-R intervals, it is possible to calculate the instantaneous phases and instantaneous frequencies of the main rhythmic processes governing the cardiovascular dynamics in humans, namely, the main heart rhythm, respiration, and the process of slow regulation of blood pressure with basic frequency close to 0.1 Hz. For the cases of spontaneous respiration and paced respiration with a fixed frequency, the synchronization between the rhythms of the cardiovascular system was investigated based on the analysis of only the time series of R-R intervals. It is shown that the main heart rhythm and the rhythm of low-frequency regulation of blood pressure can be synchronized with respiration.

Extracting information masked by the chaotic signal of a time-delay system.

We further develop the method proposed by Bezruchko et al. [Phys. Rev. E 64, 056216 (2001)] for the estimation of the parameters of time-delay systems from time series. Using this method we demonstrate a possibility of message extraction for a communication system with nonlinear mixing of information signal and chaotic signal of the time-delay system. The message extraction procedure is illustrated using both numerical and experimental data and different kinds of information signals.

Mandelbrot set in coupled logistic maps and in an electronic experiment.

We suggest an approach to constructing physical systems with dynamical characteristics of the complex analytic iterative maps. The idea follows from a simple notion that the complex quadratic map by a variable change may be transformed into a set of two identical real one-dimensional quadratic maps with a particular coupling. Hence, dynamical behavior of similar nature may occur in coupled dissipative nonlinear systems, which relate to the Feigenbaum universality class. To substantiate the feasibility of this concept, we consider an electronic system, which exhibits dynamical phenomena intrinsic to complex analytic maps. Experimental results are presented, providing the Mandelbrot set in the parameter plane of this physical system.