Human heart rate is moderated by the autonomous nervous system acting predominantly through the sinus node (the main cardiac physiological pacemaker). One of the dominant factors that determine the heart rate in physiological conditions is its coupling with the respiratory rhythm. Using the language of stochastic processes, we analyzed both rhythms simultaneously taking the data from polysomnographic recordings of two healthy individuals. Each rhythm was treated as a sum of a deterministic drift term and a diffusion term (Kramers-Moyal expansion). We found that normal heart rate variability may be considered as the result of a bidirectional coupling of two nonlinear oscillators: the heart itself and the respiratory system. On average, the diffusion (noise) component measured is comparable in magnitude to the oscillatory (deterministic) term for both signals investigated. The application of the Kramers-Moyal expansion may be useful for medical diagnostics providing information on the relation between respiration and heart rate variability. This interaction is mediated by the autonomous nervous system, including the baroreflex, and results in a commonly observed phenomenon--respiratory sinus arrhythmia which is typical for normal subjects and often impaired by pathology.
Modeling of recorded time series may be used as a method of analysis for heart rate variability studies. In particular, the extraction of the first two Kramers-Moyal coefficients has been used in this context. Recently, the method was applied to a wide range of signal analysis: from financial data to physiological and biological time series. Modeling of the signal is important for the prediction and interpretation of the dynamics underlying the process. The method requires the determination of the Markov time. Obtaining the drift and diffusion term of the Kramers-Moyal expansion is crucial for the modeling of the original time series with the Langevin equation. Both Tabar [Comput. Sci. Eng. 8, 54 (2006)] and T. Kuusela [Phys. Rev. E 69, 031916 (2004)] suggested that these terms may be used to distinguish healthy subjects from those with heart failure. The research groups applied a somewhat different methodology and obtained substantially different ranges of the Markov time. We show that the two studies may be considered consistent with each other as Kuusela analyzed 24 h recordings while Tabar analyzed daytime and nighttime recordings, separately. However, both groups suggested using the Langevin equation for modeling of time series which requires the fluctuation force to be a Gaussian. We analyzed heart rate variability recordings for ten young male (age 26-4+3 y ) healthy subjects. 24 h recordings were analyzed and 6-h-long daytime and nighttime fragments were selected. Similar properties of the data were observed in all recordings but all the nighttime data and seven of the ten 24 h series exhibited higher-order, non-negligible Kramers-Moyal coefficients. In such a case, the reconstruction of the time series using the Langevin equation is impossible. The non-negligible higher-order coefficients are due to autocorrelation in the data. This effect may be interpreted as a result of a physiological phenomenon (especially occurring for nighttime data): respiratory sinus arrhythmia (RSA). We detrended the nighttime recordings for the healthy subjects and obtained an asymmetry in the dependence of the diffusion term on the rescaled heart rate. This asymmetry seems to be an effect of different time scales during the inspiration and the expiration phase of breathing. The asymmetry was significantly decreased in the diffusion term found for detrended nighttime recordings obtained from five hypertrophic cardiomyopathy (HCM) patients. We conclude that the effect of RSA is decreased in the heart rate variability of HCM patients-a result which may contribute to a better medical diagnosis by supplying a new quantitative measure of RSA.
Ambulatory blood pressure monitoring provides information about the day-night blood pressure profile, which can be divided into dipping and non-dipping pattern. Non-dipping hypertension is recently thought to have increased cardiovascular risk and outcomes than dipping hypertension. The dipping pattern is explained by physiological changes in circadian rhythm, while the pathomechanism of non-dipping hypertension is not fully understood. Is it considered to be a result of many factors, such as: sympathetic nervous system overactivation, which can be accompanied by impaired parasympathetic nervous system response, obesity, concurrent diabetes mellitus and metabolic syndrome. Moreover abnormalities of hormones levels such as melatonin, catecholamines, thyroid and parathyroid hormones are connected to occurrence of non-dipping hypertension. Other widely discussed problem is obstructive sleep apnoea and its influence on circadian rhythm changes. Also dysfunction in activity of renin-angiotensin-aldosterone axis is thought to cause non-dipping pattern. There are some studies that indicate on role of inappropriate sodium intake in mentioned pathology. The chronic kidney disease and relationship with non-dipping hypertension will be also described. The last considered factor is influence of age on the development of non-dipping hypertension. key words: circadian blood pressure profile, blood pressure regulation, chronobiology, nocturnal hypertension, non-dipping pathomechanism
Due to the prolonged inflammatory process induced by infection of the novel severe acute respiratory syndrome coronavirus-2 (SARS-CoV-2), indices of autonomic nervous system dysfunction may persist long after viral shedding. Previous studies showed significant changes in HRV parameters in severe (including fatal) infection of SARS-CoV-2. However, few studies have comprehensively examined HRV in individuals who previously presented as asymptomatic or mildly symptomatic cases of COVID-19. In this study, we examined HRV in asymptomatic or mildly symptomatic individuals 5–7 weeks following positive confirmation of SARS-CoV-2 infection. Sixty-five ECG Holter recordings from young (mean age 22.6 ± 3.4 years), physically fit male subjects 4–6 weeks after the second negative test (considered to be the start of recovery) and twenty-six control male subjects (mean age 23.2 ± 2.9 years) were considered in the study. Night-time RR time series were extracted from ECG signals. Selected linear as well as nonlinear HRV parameters were calculated. We found significant differences in Porta’s symbolic analysis parameters V0 and V2 (p < 0.001), α2 (p < 0.001), very low-frequency component (VLF; p = 0.022) and respiratory peak (from the PRSA method; p = 0.012). These differences may be caused by the changes of activity of the parasympathetic autonomic nervous system as well as by the coupling of respiratory rhythm with heart rate due to an increase in pulmonary arterial vascular resistance. The results suggest that the differences with the control group in the HRV parameters, that reflect the functional state of the autonomic nervous system, are measurable after a few weeks from the beginning of the recovery even in the post-COVID group—a young and physically active population. We indicate HRV sensitive markers which may be used in long-term monitoring of patients after recovery.
We present a method for the reconstruction of the dynamics of processes with discrete time. The time series from such a system is described by a stochastic recurrence equation, the continuous form of which is known as the Langevin equation. The deterministic f and stochastic g components of the stochastic equation are directly extracted from the measurement data with the assumption that the noise has finite moments and has a zero mean and a unit variance. No other information about the noise distribution is needed. This is contrary to the usual Langevin description, in which the additional assumption that the noise is Gaussian (δ-correlated) distributed as necessary. We test the method using one dimensional deterministic systems (the tent and logistic maps) with Gaussian and with Gumbel noise. In addition, results for human heart rate variability are presented as an example of the application of our method to real data. The differences between cardiological cases can be observed in the properties of the deterministic part f and of the reconstructed noise distribution.
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