1
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Ramírez-Ávila GM, Kapitaniak T, Gonze D. Dynamical analysis of a periodically forced chaotic chemical oscillator. CHAOS (WOODBURY, N.Y.) 2024; 34:073154. [PMID: 39047162 DOI: 10.1063/5.0213913] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/14/2024] [Accepted: 07/11/2024] [Indexed: 07/27/2024]
Abstract
We present a comprehensive dynamical analysis of a chaotic chemical model referred to as the autocatalator, when subject to a periodic administration of one substrate. Our investigation encompasses the dynamical characterization of both unforced and forced systems utilizing isospikes and largest Lyapunov exponents-based parameter planes, bifurcation diagrams, and analysis of complex oscillations. Additionally, we present a phase diagram showing the effect of the period and amplitude of the forcing signal on the system's behavior. Furthermore, we show how the landscapes of parameter planes are altered in response to forcing application. This analysis contributes to a deeper understanding of the intricate dynamics induced by the periodic forcing of a chaotic system.
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Affiliation(s)
- Gonzalo Marcelo Ramírez-Ávila
- Namur Institute for Complex Systems (naXys), Université de Namur, Rue de Bruxelles 61, B-5000 Namur, Belgium
- Division of Dynamics, Lodz University of Technology, Stefanowskiego 1/15, 90-924 Lodz, Poland
- Instituto de Investigaciones Físicas, and Planetario Max Schreier, Universidad Mayor de San Andrés, Campus Universitario, C. 27 s/n Cota-Cota, 0000 La Paz, Bolivia
- Unit of Theoretical Chronobiology, Université Libre de Bruxelles, CP231, Boulevard du Triomphe, 1050 Brussels, Belgium
| | - Tomasz Kapitaniak
- Division of Dynamics, Lodz University of Technology, Stefanowskiego 1/15, 90-924 Lodz, Poland
| | - Didier Gonze
- Unit of Theoretical Chronobiology, Université Libre de Bruxelles, CP231, Boulevard du Triomphe, 1050 Brussels, Belgium
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2
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Mitsuyama S, Sakamoto T, Nagasawa T, Kario K, Ozawa S. A pilot study to assess the origin of the spectral power increases of heart rate variability associated with transient changes in the R-R interval. Physiol Rep 2024; 12:e15907. [PMID: 38226411 PMCID: PMC10790152 DOI: 10.14814/phy2.15907] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/07/2023] [Revised: 12/14/2023] [Accepted: 12/15/2023] [Indexed: 01/17/2024] Open
Abstract
Spectral analysis of heart rate variability (HRV) is used to assess cardiovascular autonomic function. In the power density spectrum calculated from a time series of the R-R interval (RRI), three main components are distinguished: very-low-frequency (VLF; 0.003-0.04 Hz), low-frequency (LF; 0.04-0.15 Hz), and high-frequency (HF; 0.15-0.4 Hz) components. However, the physiological correlates of these frequency components have yet to be determined. In this study, we conducted spectral analysis of data segments of various lengths (5, 30, 100, and 200 s) of the RRI time series during active standing. Because of the trade-off relationship between time and frequency resolution, the analysis of the RRI data segment shorter than 30 s was needed to identify the temporal relationships between individual transient increases in RRI and the resulting spectral power changes. In contrast, the segment of 200 s was needed to properly evaluate the magnitude of the increase in the VLF power. The results showed that a transient increase in the RRI was tightly associated with simultaneous increases in the powers of the VLF, LF, and HF components. We further found that the simultaneous power increases in these three components were caused by the arterial baroreceptor reflex responding to rapid blood pressure rise.
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Affiliation(s)
- Satoshi Mitsuyama
- Department of Healthcare InformaticsTakasaki University of Health and WelfareTakasakiGunmaJapan
| | - Teruhiko Sakamoto
- Department of Healthcare InformaticsTakasaki University of Health and WelfareTakasakiGunmaJapan
| | - Toru Nagasawa
- Department of Healthcare InformaticsTakasaki University of Health and WelfareTakasakiGunmaJapan
| | - Kazuomi Kario
- Division of Cardiovascular Medicine, Department of MedicineJichi Medical University School of MedicineTochigiJapan
| | - Seiji Ozawa
- Department of Healthcare InformaticsTakasaki University of Health and WelfareTakasakiGunmaJapan
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3
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Li K, Cardoso C, Moctezuma-Ramirez A, Elgalad A, Perin E. Heart Rate Variability Measurement through a Smart Wearable Device: Another Breakthrough for Personal Health Monitoring? INTERNATIONAL JOURNAL OF ENVIRONMENTAL RESEARCH AND PUBLIC HEALTH 2023; 20:7146. [PMID: 38131698 PMCID: PMC10742885 DOI: 10.3390/ijerph20247146] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/03/2023] [Revised: 11/06/2023] [Accepted: 11/27/2023] [Indexed: 12/23/2023]
Abstract
Heart rate variability (HRV) is a measurement of the fluctuation of time between each heartbeat and reflects the function of the autonomic nervous system. HRV is an important indicator for both physical and mental status and for broad-scope diseases. In this review, we discuss how wearable devices can be used to monitor HRV, and we compare the HRV monitoring function among different devices. In addition, we have reviewed the recent progress in HRV tracking with wearable devices and its value in health monitoring and disease diagnosis. Although many challenges remain, we believe HRV tracking with wearable devices is a promising tool that can be used to improve personal health.
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Affiliation(s)
- Ke Li
- Center for Preclinical Cardiovascular Research, The Texas Heart Institute, Houston, TX 77030, USA
| | - Cristiano Cardoso
- Center for Preclinical Cardiovascular Research, The Texas Heart Institute, Houston, TX 77030, USA
| | - Angel Moctezuma-Ramirez
- Center for Preclinical Cardiovascular Research, The Texas Heart Institute, Houston, TX 77030, USA
| | - Abdelmotagaly Elgalad
- Center for Preclinical Cardiovascular Research, The Texas Heart Institute, Houston, TX 77030, USA
| | - Emerson Perin
- Center for Clinical Research, The Texas Heart Institute, Houston, TX 77030, USA
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4
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Yang PC, Rose A, DeMarco KR, Dawson JRD, Han Y, Jeng MT, Harvey RD, Santana LF, Ripplinger CM, Vorobyov I, Lewis TJ, Clancy CE. A multiscale predictive digital twin for neurocardiac modulation. J Physiol 2023; 601:3789-3812. [PMID: 37528537 PMCID: PMC10528740 DOI: 10.1113/jp284391] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/17/2023] [Accepted: 07/11/2023] [Indexed: 08/03/2023] Open
Abstract
Cardiac function is tightly regulated by the autonomic nervous system (ANS). Activation of the sympathetic nervous system increases cardiac output by increasing heart rate and stroke volume, while parasympathetic nerve stimulation instantly slows heart rate. Importantly, imbalance in autonomic control of the heart has been implicated in the development of arrhythmias and heart failure. Understanding of the mechanisms and effects of autonomic stimulation is a major challenge because synapses in different regions of the heart result in multiple changes to heart function. For example, nerve synapses on the sinoatrial node (SAN) impact pacemaking, while synapses on contractile cells alter contraction and arrhythmia vulnerability. Here, we present a multiscale neurocardiac modelling and simulator tool that predicts the effect of efferent stimulation of the sympathetic and parasympathetic branches of the ANS on the cardiac SAN and ventricular myocardium. The model includes a layered representation of the ANS and reproduces firing properties measured experimentally. Model parameters are derived from experiments and atomistic simulations. The model is a first prototype of a digital twin that is applied to make predictions across all system scales, from subcellular signalling to pacemaker frequency to tissue level responses. We predict conditions under which autonomic imbalance induces proarrhythmia and can be modified to prevent or inhibit arrhythmia. In summary, the multiscale model constitutes a predictive digital twin framework to test and guide high-throughput prediction of novel neuromodulatory therapy. KEY POINTS: A multi-layered model representation of the autonomic nervous system that includes sympathetic and parasympathetic branches, each with sparse random intralayer connectivity, synaptic dynamics and conductance based integrate-and-fire neurons generates firing patterns in close agreement with experiment. A key feature of the neurocardiac computational model is the connection between the autonomic nervous system and both pacemaker and contractile cells, where modification to pacemaker frequency drives initiation of electrical signals in the contractile cells. We utilized atomic-scale molecular dynamics simulations to predict the association and dissociation rates of noradrenaline with the β-adrenergic receptor. Multiscale predictions demonstrate how autonomic imbalance may increase proclivity to arrhythmias or be used to terminate arrhythmias. The model serves as a first step towards a digital twin for predicting neuromodulation to prevent or reduce disease.
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Affiliation(s)
- Pei-Chi Yang
- Department of Physiology and Membrane Biology, University of California Davis, Davis, CA
| | - Adam Rose
- Department of Mathematics, University of California Davis, Davis, CA
| | - Kevin R. DeMarco
- Department of Physiology and Membrane Biology, University of California Davis, Davis, CA
| | - John R. D. Dawson
- Department of Physiology and Membrane Biology, University of California Davis, Davis, CA
| | - Yanxiao Han
- Department of Physiology and Membrane Biology, University of California Davis, Davis, CA
| | - Mao-Tsuen Jeng
- Department of Physiology and Membrane Biology, University of California Davis, Davis, CA
| | | | - L. Fernando Santana
- Department of Physiology and Membrane Biology, University of California Davis, Davis, CA
| | | | - Igor Vorobyov
- Department of Physiology and Membrane Biology, University of California Davis, Davis, CA
| | - Timothy J. Lewis
- Department of Mathematics, University of California Davis, Davis, CA
| | - Colleen E. Clancy
- Department of Physiology and Membrane Biology, University of California Davis, Davis, CA
- Center for Precision Medicine and Data Science, University of California Davis, Sacramento, CA
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5
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Quasinormal Forms for Chains of Coupled Logistic Equations with Delay. MATHEMATICS 2022. [DOI: 10.3390/math10152648] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 02/05/2023]
Abstract
In this paper, chains of coupled logistic equations with delay are considered, and the local dynamics of these chains is investigated. A basic assumption is that the number of elements in the chain is large enough. This implies that the study of the original systems can be reduced to the study of a distributed integro–differential boundary value problem that is continuous with respect to the spatial variable. Three types of couplings of greatest interest are considered: diffusion, unidirectional, and fully connected. It is shown that the critical cases in the stability of the equilibrium state have an infinite dimension: infinitely many roots of the characteristic equation tend to the imaginary axis as the small parameter tends to zero, which characterizes the inverse of the number of elements of the chain. In the study of local dynamics in cases close to critical, analogues of normal forms are constructed, namely quasinormal forms, which are boundary value problems of Ginzburg–Landau type or, as in the case of fully connected systems, special nonlinear integro–differential equations. It is shown that the nonlocal solutions of the obtained quasinormal forms determine the principal terms of the asymptotics of solutions to the original problem from a small neighborhood of the equilibrium state.
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Contribution of Cardiorespiratory Coupling to the Irregular Dynamics of the Human Cardiovascular System. MATHEMATICS 2022. [DOI: 10.3390/math10071088] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 02/01/2023]
Abstract
Irregularity is an important aspect of the cardiovascular system dynamics. Numerical indices of irregularity, such as the largest Lyapunov exponent and the correlation dimension estimated from interbeat interval time series, are early markers of cardiovascular diseases. However, there is no consensus on the origin of irregularity in the cardiovascular system. A common hypothesis suggests the importance of nonlinear bidirectional coupling between the cardiovascular system and the respiratory system for irregularity. Experimental investigations of this theory are severely limited by the capabilities of modern medical equipment and the nonstationarity of real biological systems. Therefore, we studied this problem using a mathematical model of the coupled cardiovascular system and respiratory system. We estimated and compared the numerical indices of complexity for a model simulating the cardiovascular dynamics in healthy subjects and a model with blocked regulation of the respiratory frequency and amplitude, which disturbs the coupling between the studied systems.
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7
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Karavaev AS, Skazkina VV, Borovkova EI, Prokhorov MD, Hramkov AN, Ponomarenko VI, Runnova AE, Gridnev VI, Kiselev AR, Kuznetsov NV, Chechurin LS, Penzel T. Synchronization of the Processes of Autonomic Control of Blood Circulation in Humans Is Different in the Awake State and in Sleep Stages. Front Neurosci 2022; 15:791510. [PMID: 35095399 PMCID: PMC8789746 DOI: 10.3389/fnins.2021.791510] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/08/2021] [Accepted: 12/09/2021] [Indexed: 01/09/2023] Open
Abstract
The influence of higher nervous activity on the processes of autonomic control of the cardiovascular system and baroreflex regulation is of considerable interest, both for understanding the fundamental laws of the functioning of the human body and for developing methods for diagnostics and treatment of pathologies. The complexity of the analyzed systems limits the possibilities of research in this area and requires the development of new tools. Earlier we propose a method for studying the collective dynamics of the processes of autonomic control of blood circulation in the awake state and in different stages of sleep. The method is based on estimating a quantitative measure representing the total percentage of phase synchronization between the low-frequency oscillations in heart rate and blood pressure. Analysis of electrocardiogram and invasive blood pressure signals in apnea patients in the awake state and in different sleep stages showed a high sensitivity of the proposed measure. It is shown that in slow-wave sleep the degree of synchronization of the studied rhythms is higher than in the awake state and lower than in sleep with rapid eye movement. The results reflect the modulation of the processes of autonomic control of blood circulation by higher nervous activity and can be used for the quantitative assessment of this modulation.
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Affiliation(s)
- Anatoly S. Karavaev
- Department of Basic Research in Neurocardiology, Institute of Cardiological Research, Saratov State Medical University, Saratov, Russia
- Smart Sleep Laboratory, Saratov State University, Saratov, Russia
- Laboratory of Nonlinear Dynamics Modeling, Saratov Branch of the Institute of Radio Engineering and Electronics of Russian Academy of Sciences, Saratov, Russia
| | - Viktoriia V. Skazkina
- Smart Sleep Laboratory, Saratov State University, Saratov, Russia
- LUT School of Engineering Science, LUT University, Lappeenranta, Finland
| | - Ekaterina I. Borovkova
- Department of Basic Research in Neurocardiology, Institute of Cardiological Research, Saratov State Medical University, Saratov, Russia
- Smart Sleep Laboratory, Saratov State University, Saratov, Russia
- Laboratory of Nonlinear Dynamics Modeling, Saratov Branch of the Institute of Radio Engineering and Electronics of Russian Academy of Sciences, Saratov, Russia
| | - Mikhail D. Prokhorov
- Smart Sleep Laboratory, Saratov State University, Saratov, Russia
- Laboratory of Nonlinear Dynamics Modeling, Saratov Branch of the Institute of Radio Engineering and Electronics of Russian Academy of Sciences, Saratov, Russia
| | | | - Vladimir I. Ponomarenko
- Laboratory of Nonlinear Dynamics Modeling, Saratov Branch of the Institute of Radio Engineering and Electronics of Russian Academy of Sciences, Saratov, Russia
| | - Anastasiya E. Runnova
- Department of Basic Research in Neurocardiology, Institute of Cardiological Research, Saratov State Medical University, Saratov, Russia
- Smart Sleep Laboratory, Saratov State University, Saratov, Russia
| | - Vladimir I. Gridnev
- Department of Basic Research in Neurocardiology, Institute of Cardiological Research, Saratov State Medical University, Saratov, Russia
| | - Anton R. Kiselev
- Department of Basic Research in Neurocardiology, Institute of Cardiological Research, Saratov State Medical University, Saratov, Russia
- Smart Sleep Laboratory, Saratov State University, Saratov, Russia
- Coordinating Center for Fundamental Research, National Medical Research Center for Therapy and Preventive Medicine, Moscow, Russia
| | - Nikolay V. Kuznetsov
- LUT School of Engineering Science, LUT University, Lappeenranta, Finland
- Faculty of Mathematics and Mechanics, St. Petersburg State University, St. Petersburg, Russia
- Institute for Problems in Mechanical Engineering RAS, St. Petersburg, Russia
| | - Leonid S. Chechurin
- LUT School of Engineering Science, LUT University, Lappeenranta, Finland
- Faculty of Mathematics and Mechanics, St. Petersburg State University, St. Petersburg, Russia
| | - Thomas Penzel
- Smart Sleep Laboratory, Saratov State University, Saratov, Russia
- Interdisciplinary Sleep Medicine Center, Charité - Universitätsmedizin Berlin, Berlin, Germany
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8
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Borovkova EI, Prokhorov MD, Kiselev AR, Hramkov AN, Mironov SA, Agaltsov MV, Ponomarenko VI, Karavaev AS, Drapkina OM, Penzel T. Directional couplings between the respiration and parasympathetic control of the heart rate during sleep and wakefulness in healthy subjects at different ages. FRONTIERS IN NETWORK PHYSIOLOGY 2022; 2:942700. [PMID: 36926072 PMCID: PMC10013057 DOI: 10.3389/fnetp.2022.942700] [Citation(s) in RCA: 7] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/12/2022] [Accepted: 08/15/2022] [Indexed: 11/13/2022]
Abstract
Cardiorespiratory interactions are important, both for understanding the fundamental processes of functioning of the human body and for development of methods for diagnostics of various pathologies. The properties of cardiorespiratory interaction are determined by the processes of autonomic control of blood circulation, which are modulated by the higher nervous activity. We study the directional couplings between the respiration and the process of parasympathetic control of the heart rate in the awake state and different stages of sleep in 96 healthy subjects from different age groups. The detection of directional couplings is carried out using the method of phase dynamics modeling applied to experimental RR-intervals and the signal of respiration. We reveal the presence of bidirectional couplings between the studied processes in all age groups. Our results show that the coupling from respiration to the process of parasympathetic control of the heart rate is stronger than the coupling in the opposite direction. The difference in the strength of bidirectional couplings between the considered processes is most pronounced in deep sleep.
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Affiliation(s)
- Ekaterina I Borovkova
- National Medical Research Center for Therapy and Preventive Medicine, Moscow, Russia
| | - Mikhail D Prokhorov
- Smart Sleep Laboratory, Saratov State University, Saratov, Russia.,Laboratory of Nonlinear Dynamics Modeling, Saratov Branch of Kotelnikov Institute of Radio Engineering and Electronics of Russian Academy of Sciences, Saratov, Russia
| | - Anton R Kiselev
- National Medical Research Center for Therapy and Preventive Medicine, Moscow, Russia.,Institute of Cardiological Research, Saratov State Medical University, Saratov, Russia
| | | | - Sergey A Mironov
- National Medical Research Center for Therapy and Preventive Medicine, Moscow, Russia
| | - Mikhail V Agaltsov
- National Medical Research Center for Therapy and Preventive Medicine, Moscow, Russia
| | - Vladimir I Ponomarenko
- Smart Sleep Laboratory, Saratov State University, Saratov, Russia.,Laboratory of Nonlinear Dynamics Modeling, Saratov Branch of Kotelnikov Institute of Radio Engineering and Electronics of Russian Academy of Sciences, Saratov, Russia
| | - Anatoly S Karavaev
- Smart Sleep Laboratory, Saratov State University, Saratov, Russia.,Laboratory of Nonlinear Dynamics Modeling, Saratov Branch of Kotelnikov Institute of Radio Engineering and Electronics of Russian Academy of Sciences, Saratov, Russia.,Institute of Cardiological Research, Saratov State Medical University, Saratov, Russia
| | - Oksana M Drapkina
- National Medical Research Center for Therapy and Preventive Medicine, Moscow, Russia
| | - Thomas Penzel
- Smart Sleep Laboratory, Saratov State University, Saratov, Russia.,Interdisciplinary Sleep Medicine Center, Charité-Universitätsmedizin Berlin, Berlin, Germany
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9
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Investigation on the Prediction of Cardiovascular Events Based on Multi-Scale Time Irreversibility Analysis. Symmetry (Basel) 2021. [DOI: 10.3390/sym13122424] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022] Open
Abstract
Investigation of the risk factors associated with cardiovascular disease (CVD) plays an important part in the prevention and treatment of CVD. This study investigated whether alteration in the multi-scale time irreversibility of sleeping heart rate variability (HRV) was a risk factor for cardiovascular events. The D-value, based on analysis of multi-scale increments in HRV series, was used as the measurement of time irreversibility. Eighty-four subjects from an open-access database (i.e., the Sleep Heart Health Study) were included in this study. None of them had any CVD history at baseline; 42 subjects had cardiovascular events within 1 year after baseline polysomnography and were classed as the CVD group, and the other 42 subjects in the non-CVD group were age matched with those in the CVD group and had no cardiovascular events during the 15-year follow-up period. We compared D-values of sleeping HRV between the CVD and non-CVD groups and found that the D-values of the CVD group were significantly lower than those of the non-CVD group on all 10 scales, even after adjusting for gender and body mass index. Moreover, we investigated the performance of a machine learning model to classify CVD and non-CVD subjects. The model, which was fed with a feature space based on the D-values on 10 scales and trained by a random forest algorithm, achieved an accuracy of 80.8% and a positive prediction rate of 86.7%. These results suggest that the decreased time irreversibility of sleeping HRV is an independent predictor of cardiovascular events that could be used to assist the intelligent prediction of cardiovascular events.
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10
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Ponomarenko VI, Karavaev AS, Borovkova EI, Hramkov AN, Kiselev AR, Prokhorov MD, Penzel T. Decrease of coherence between the respiration and parasympathetic control of the heart rate with aging. CHAOS (WOODBURY, N.Y.) 2021; 31:073105. [PMID: 34340353 DOI: 10.1063/5.0056624] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/12/2021] [Accepted: 06/16/2021] [Indexed: 06/13/2023]
Abstract
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.
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Affiliation(s)
- V I Ponomarenko
- Kotelnikov Institute of Radioengineering and Electronics of Russian Academy of Sciences, Saratov Branch, Zelyonaya Street, 38, Saratov 410019, Russia
| | - A S Karavaev
- Kotelnikov Institute of Radioengineering and Electronics of Russian Academy of Sciences, Saratov Branch, Zelyonaya Street, 38, Saratov 410019, Russia
| | - E I Borovkova
- Institute of Physics, Saratov State University, Astrakhanskaya Street, 83, Saratov 410012, Russia
| | - A N Hramkov
- Institute of Physics, Saratov State University, Astrakhanskaya Street, 83, Saratov 410012, Russia
| | - A R Kiselev
- Institute of Cardiological Research, Saratov State Medical University, B. Kazachaya Street, 112, Saratov 410012, Russia
| | - M D Prokhorov
- Kotelnikov Institute of Radioengineering and Electronics of Russian Academy of Sciences, Saratov Branch, Zelyonaya Street, 38, Saratov 410019, Russia
| | - T Penzel
- Institute of Physics, Saratov State University, Astrakhanskaya Street, 83, Saratov 410012, Russia
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11
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Mizeva I, Potapova E, Dremin V, Kozlov I, Dunaev A. Spatial heterogeneity of cutaneous blood flow respiratory-related oscillations quantified via laser speckle contrast imaging. PLoS One 2021; 16:e0252296. [PMID: 34043720 PMCID: PMC8158914 DOI: 10.1371/journal.pone.0252296] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/03/2020] [Accepted: 01/21/2021] [Indexed: 11/18/2022] Open
Abstract
LSCI technique provides experimental data which can be considered in the context of spatial blood flow coherency. Analysis of vascular tone oscillations gives additional information to ensure a better understanding of the mechanisms affecting microvascular physiology. The oscillations with different frequencies are due to different physiological mechanisms. The reasons for the generation of peripheral blood flow oscillations in the 0.14-0.6 Hz frequency band are as follows: cardio-respiratory interactions, pressure variations in the venous part of the circulatory system, and the effect of the sympathetic nervous system on the vascular tone. Earlier, we described the spatial heterogeneity of around 0.3 Hz oscillations and this motivated us to continue the research to find the conditions for the occurrence of spatial phase synchronization. For this purpose, a number of physiological tests (controlled respiration, breath holder, and venous occlusion tests) which influence the blood flow oscillations of 0.14-0.6 Hz were considered, an appropriate measurement system and the required data processing algorithms were developed. At spontaneous respiration, the oscillations with frequencies around 0.3 Hz were stochastic, whereas all the performed tests induced an increase in spatial coherence. The protocols and methods proposed here can help to clarify whether the heterogeneity of respiratory-related blood flow oscillations exists on the skin surface.
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Affiliation(s)
- Irina Mizeva
- Institute of Continuous Media Mechanics UrB RAS, Perm, Russia
- Research & Development Center of Biomedical Photonics, Orel State University, Orel, Russia
- * E-mail:
| | - Elena Potapova
- Research & Development Center of Biomedical Photonics, Orel State University, Orel, Russia
| | - Viktor Dremin
- Research & Development Center of Biomedical Photonics, Orel State University, Orel, Russia
- College of Engineering and Physical Sciences, Aston University, Birmingham, United Kingdom
| | - Igor Kozlov
- Research & Development Center of Biomedical Photonics, Orel State University, Orel, Russia
| | - Andrey Dunaev
- Research & Development Center of Biomedical Photonics, Orel State University, Orel, Russia
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12
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Karavaev AS, Ishbulatov YM, Prokhorov MD, Ponomarenko VI, Kiselev AR, Runnova AE, Hramkov AN, Semyachkina-Glushkovskaya OV, Kurths J, Penzel T. Simulating Dynamics of Circulation in the Awake State and Different Stages of Sleep Using Non-autonomous Mathematical Model With Time Delay. Front Physiol 2021; 11:612787. [PMID: 33519518 PMCID: PMC7838681 DOI: 10.3389/fphys.2020.612787] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/30/2020] [Accepted: 11/25/2020] [Indexed: 11/13/2022] Open
Abstract
We propose a mathematical model of the human cardiovascular system. The model allows one to simulate the main heart rate, its variability under the influence of the autonomic nervous system, breathing process, and oscillations of blood pressure. For the first time, the model takes into account the activity of the cerebral cortex structures that modulate the autonomic control loops of blood circulation in the awake state and in various stages of sleep. The adequacy of the model is demonstrated by comparing its time series with experimental records of healthy subjects in the SIESTA database. The proposed model can become a useful tool for studying the characteristics of the cardiovascular system dynamics during sleep.
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Affiliation(s)
- Anatoly S. Karavaev
- Saratov Branch of the Institute of Radio Engineering and Electronics of Russian Academy of Sciences, Saratov, Russia
- Smart Sleep Laboratory, Saratov State University, Saratov, Russia
- Department of Innovative Cardiological Information Technology, Saratov State Medical University, Saratov, Russia
| | - Yurii M. Ishbulatov
- Saratov Branch of the Institute of Radio Engineering and Electronics of Russian Academy of Sciences, Saratov, Russia
- Smart Sleep Laboratory, Saratov State University, Saratov, Russia
- Department of Innovative Cardiological Information Technology, Saratov State Medical University, Saratov, Russia
| | - Mikhail D. Prokhorov
- Saratov Branch of the Institute of Radio Engineering and Electronics of Russian Academy of Sciences, Saratov, Russia
- Smart Sleep Laboratory, Saratov State University, Saratov, Russia
| | - Vladimir I. Ponomarenko
- Saratov Branch of the Institute of Radio Engineering and Electronics of Russian Academy of Sciences, Saratov, Russia
| | - Anton R. Kiselev
- Department of Innovative Cardiological Information Technology, Saratov State Medical University, Saratov, Russia
| | - Anastasiia E. Runnova
- Smart Sleep Laboratory, Saratov State University, Saratov, Russia
- Department of Innovative Cardiological Information Technology, Saratov State Medical University, Saratov, Russia
| | | | | | - Jürgen Kurths
- Smart Sleep Laboratory, Saratov State University, Saratov, Russia
- Physics Department, Humboldt University of Berlin, Berlin, Germany
- Research Department Complexity Science, Potsdam Institute for Climate Impact Research (PIK), Potsdam, Germany
| | - Thomas Penzel
- Smart Sleep Laboratory, Saratov State University, Saratov, Russia
- Interdisciplinary Sleep Medicine Center, Charité – Universitätsmedizin Berlin, Berlin, Germany
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13
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Ishbulatov YM, Karavaev AS, Kiselev AR, Simonyan MA, Prokhorov MD, Ponomarenko VI, Mironov SA, Gridnev VI, Bezruchko BP, Shvartz VA. Mathematical modeling of the cardiovascular autonomic control in healthy subjects during a passive head-up tilt test. Sci Rep 2020; 10:16525. [PMID: 33020530 PMCID: PMC7536219 DOI: 10.1038/s41598-020-71532-7] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/08/2020] [Accepted: 08/18/2020] [Indexed: 01/10/2023] Open
Abstract
A mathematical model is proposed for the autonomic control of cardiovascular system, which takes into account two separated self-exciting sympathetic control loops of heart rate and peripheral vascular tone. The control loops are represented by self-exciting time-delay systems and their tone depends on activity of the aortic, carotid, and lower-body baroreceptors. The model is used to study the dynamics of the adaptive processes that manifest in a healthy cardiovascular system during the passive head-up tilt test. Computer simulation provides continuous observation of the dynamics of the indexes and variables that cannot be measured in the direct experiment, including the noradrenaline concentration in vessel wall and heart muscle, tone of the sympathetic and parasympathetic control, peripheral vascular resistance, and blood pressure. In the supine and upright positions, we estimated the spectral characteristics of the model variables, especially in the low-frequency band, and the original index of total percent of phase synchronization between the low-frequency oscillations in heart rate and blood pressure signals. The model demonstrates good quantitative agreement with the dynamics of the experimentally observed indexes of cardiovascular system that were averaged for 50 healthy subjects.
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Affiliation(s)
- Yurii M Ishbulatov
- Department of Innovative Cardiological Information Technology, Institute of Cardiological Research, Saratov State Medical University, Saratov, Russia.,Department of Surgical Treatment for Interactive Pathology, Bakulev Scientific Center for Cardiovascular Surgery, Moscow, Russia
| | - Anatoly S Karavaev
- Department of Innovative Cardiological Information Technology, Institute of Cardiological Research, Saratov State Medical University, Saratov, Russia.,Laboratory of Nonlinear Dynamics Modeling, Saratov Branch of the Institute of Radio Engineering and Electronics of Russian Academy of Sciences, Saratov, Russia.,Department of Dynamic Modeling and Biomedical Engineering, Saratov State University, Saratov, Russia
| | - Anton R Kiselev
- Department of Innovative Cardiological Information Technology, Institute of Cardiological Research, Saratov State Medical University, Saratov, Russia. .,Department of Surgical Treatment for Interactive Pathology, Bakulev Scientific Center for Cardiovascular Surgery, Moscow, Russia. .,Department of Dynamic Modeling and Biomedical Engineering, Saratov State University, Saratov, Russia.
| | - Margarita A Simonyan
- Department of Atherocslerosis and Chronic Ischemic Heart Disease, Institute of Cardiological Research, Saratov, Russia
| | - Mikhail D Prokhorov
- Laboratory of Nonlinear Dynamics Modeling, Saratov Branch of the Institute of Radio Engineering and Electronics of Russian Academy of Sciences, Saratov, Russia
| | - Vladimir I Ponomarenko
- Laboratory of Nonlinear Dynamics Modeling, Saratov Branch of the Institute of Radio Engineering and Electronics of Russian Academy of Sciences, Saratov, Russia.,Department of Dynamic Modeling and Biomedical Engineering, Saratov State University, Saratov, Russia
| | - Sergey A Mironov
- Department of Innovative Cardiological Information Technology, Institute of Cardiological Research, Saratov State Medical University, Saratov, Russia
| | - Vladimir I Gridnev
- Department of Innovative Cardiological Information Technology, Institute of Cardiological Research, Saratov State Medical University, Saratov, Russia.,Department of Dynamic Modeling and Biomedical Engineering, Saratov State University, Saratov, Russia
| | - Boris P Bezruchko
- Laboratory of Nonlinear Dynamics Modeling, Saratov Branch of the Institute of Radio Engineering and Electronics of Russian Academy of Sciences, Saratov, Russia.,Department of Dynamic Modeling and Biomedical Engineering, Saratov State University, Saratov, Russia
| | - Vladimir A Shvartz
- Department of Surgical Treatment for Interactive Pathology, Bakulev Scientific Center for Cardiovascular Surgery, Moscow, Russia
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14
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Understanding the interplay between baroreflex gain, low frequency oscillations, and pulsatility in the neural baroreflex. Biocybern Biomed Eng 2020. [DOI: 10.1016/j.bbe.2020.07.008] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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15
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Ricci L, Perinelli A, Franchi M. Asymptotic behavior of the time-dependent divergence exponent. Phys Rev E 2020; 101:042211. [PMID: 32422770 DOI: 10.1103/physreve.101.042211] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/11/2020] [Accepted: 04/03/2020] [Indexed: 06/11/2023]
Abstract
The divergence rate method, which is used to determine the maximum Lyapunov exponent out of time series, is based on the evaluation of the time-dependent divergence exponent. For chaotic systems and in the small time regime, this exponent grows linearly in time. The asymptotic regime is instead characterized by a time-independent behavior due to the system eventually losing its memory of the starting conditions. The amplitude of this "plateau"-like divergence exponent depends both on the choice of the embedding dimension and lag and on the maximum distance of nearby starting trajectories in a way that is characteristic of the underlying dynamical system. In this paper, upon introducing the basic mathematical tools, we address the plateau evaluation for two classes of time series, those generated by a white noise source and those generated by a finite-dimensional chaotic system. The different behavior provides a novel tool to distinguish purely stochastic sources from deterministic ones, as well as to provide a precise estimate of the correlation dimension in the latter case. The method is also sensitive to correlated noise sources.
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Affiliation(s)
- Leonardo Ricci
- Department of Physics, University of Trento, 38123 Trento, Italy
| | | | - Matteo Franchi
- Department of Physics, University of Trento, 38123 Trento, Italy
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