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Pavlov AN, Pavlova ON, Semyachkina-Glushkovskaya OV, Kurths J. Enhanced multiresolution wavelet analysis of complex dynamics in nonlinear systems. Chaos 2021; 31:043110. [PMID: 34251250 DOI: 10.1063/5.0045859] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/29/2021] [Accepted: 03/23/2021] [Indexed: 06/13/2023]
Abstract
Multiresolution wavelet analysis (MWA) is a powerful data processing tool that provides a characterization of complex signals over multiple time scales. Typically, the standard deviations of wavelet coefficients are computed depending on the resolution level and such quantities are used as measures for diagnosing different types of system behavior. To enhance the capabilities of this tool, we propose a combination of MWA with detrended fluctuation analysis (DFA) of detail wavelet coefficients. We find that such an MWA&DFA approach is capable of revealing the correlation features of wavelet coefficients in independent ranges of scales, which provide more information about the complex organization of datasets compared to variances or similar statistical measures of the standard MWA. Using this approach, we consider changes in the dynamics of coupled chaotic systems caused by transitions between different types of complex oscillations. We also demonstrate the potential of the MWA&DFA method for characterizing different physiological conditions by analyzing the electrical brain activity in mice.
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Affiliation(s)
- A N Pavlov
- Institute of Physics, Saratov State University, Astrakhanskaya Str. 83, 410012 Saratov, Russia
| | - O N Pavlova
- Institute of Physics, Saratov State University, Astrakhanskaya Str. 83, 410012 Saratov, Russia
| | | | - J Kurths
- Biology Department, Saratov State University, Astrakhanskaya Str. 83, 410012 Saratov, Russia
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2
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Pavlov AN, Dubrovsky AI, Koronovskii AA, Pavlova ON, Semyachkina-Glushkovskaya OV, Kurths J. Extended detrended fluctuation analysis of electroencephalograms signals during sleep and the opening of the blood-brain barrier. Chaos 2020; 30:073138. [PMID: 32752608 DOI: 10.1063/5.0011823] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/24/2020] [Accepted: 07/07/2020] [Indexed: 06/11/2023]
Abstract
Detrended fluctuation analysis (DFA) is widely used to characterize long-range power-law correlations in complex signals. However, it has restrictions when nonstationarity is not limited only to slow variations in the mean value. To improve the characterization of inhomogeneous datasets, we have proposed the extended DFA (EDFA), which is a modification of the conventional method that evaluates an additional scaling exponent to take into account the features of time-varying nonstationary behavior. Based on EDFA, here, we analyze rat electroencephalograms to identify specific changes in the slow-wave dynamics of brain electrical activity associated with two different conditions, such as the opening of the blood-brain barrier and sleep, which are both characterized by the activation of the brain drainage function. We show that these conditions cause a similar reduction in the scaling exponents of EDFA. Such a similarity may represent an informative marker of fluid homeostasis of the central nervous system.
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Affiliation(s)
- A N Pavlov
- Department of Nonlinear Processes, Saratov State University, Astrakhanskaya Str. 83, 410012 Saratov, Russia
| | - A I Dubrovsky
- Department of Physics, Saratov State University, Astrakhanskaya Str. 83, 410012 Saratov, Russia
| | - A A Koronovskii
- Department of Nonlinear Processes, Saratov State University, Astrakhanskaya Str. 83, 410012 Saratov, Russia
| | - O N Pavlova
- Department of Physics, Saratov State University, Astrakhanskaya Str. 83, 410012 Saratov, Russia
| | | | - J Kurths
- Deparatment of Biology, Saratov State University, Astrakhanskaya Str. 83, 410012 Saratov, Russia
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Pavlov AN, Pavlova ON, Abdurashitov AS, Sindeeva OA, Semyachkina-Glushkovskaya OV, Kurths J. Characterizing scaling properties of complex signals with missed data segments using the multifractal analysis. Chaos 2018; 28:013124. [PMID: 29390623 DOI: 10.1063/1.5009438] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
The scaling properties of complex processes may be highly influenced by the presence of various artifacts in experimental recordings. Their removal produces changes in the singularity spectra and the Hölder exponents as compared with the original artifacts-free data, and these changes are significantly different for positively correlated and anti-correlated signals. While signals with power-law correlations are nearly insensitive to the loss of significant parts of data, the removal of fragments of anti-correlated signals is more crucial for further data analysis. In this work, we study the ability of characterizing scaling features of chaotic and stochastic processes with distinct correlation properties using a wavelet-based multifractal analysis, and discuss differences between the effect of missed data for synchronous and asynchronous oscillatory regimes. We show that even an extreme data loss allows characterizing physiological processes such as the cerebral blood flow dynamics.
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Affiliation(s)
- A N Pavlov
- Yuri Gagarin State Technical University of Saratov, Politehnicheskaya Str. 77, 410054 Saratov, Russia
| | - O N Pavlova
- Department of Physics, Saratov State University, Astrakhanskaya Str. 83, 410012 Saratov, Russia
| | - A S Abdurashitov
- Department of Physics, Saratov State University, Astrakhanskaya Str. 83, 410012 Saratov, Russia
| | - O A Sindeeva
- Department of Biology, Saratov State University, Astrakhanskaya Str. 83, 410012 Saratov, Russia
| | | | - J Kurths
- Potsdam Institute for Climate Impact Research, Telegraphenberg A 31, 14473 Potsdam, Germany
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Anishchenko VS, Igosheva NB, Pavlov AN, Khovanov IA, Yakusheva TA. Cardiovascular System's States under Stress: Reviews of Methods. Crit Rev Biomed Eng 2017; 45:119-138. [PMID: 29953376 DOI: 10.1615/critrevbiomedeng.v45.i1-6.60] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/13/2022]
Abstract
A comparative analysis is made of various methods for processing electrocardiograms and RR-interval sequences. This analysis was carried out by using standard nonlinear-dynamics algorithms and methods. Apart from that, we assessed the expediency of using a number of characteristics to classify the cardiovascular system's state under stress.
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Affiliation(s)
- V S Anishchenko
- Radiophysics and Nonlinear Dynamics Department, Saratov State University, Saratov, Russia
| | - N B Igosheva
- Human and Animal Physiology Department, Saratov State University, Saratov, Russia
| | - A N Pavlov
- Radiophysics and Nonlinear Dynamics Department, Saratov State University, Saratov, Russia
| | - I A Khovanov
- Radiophysics and Nonlinear Dynamics Department, Saratov State University, Saratov, Russia
| | - T A Yakusheva
- Human and Animal Physiology Department, Saratov State University, Saratov, Russia
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Pavlov AN, Pavlova ON, Mohammad YK, Kurths J. Characterization of the chaos-hyperchaos transition based on return times. Phys Rev E Stat Nonlin Soft Matter Phys 2015; 91:022921. [PMID: 25768583 DOI: 10.1103/physreve.91.022921] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/30/2014] [Indexed: 06/04/2023]
Abstract
We discuss the problem of the detection of hyperchaotic oscillations in coupled nonlinear systems when the available information about this complex dynamical regime is very limited. We demonstrate the ability of diagnosing the chaos-hyperchaos transition from return times into a Poincaré section and show that an appropriate selection of the secant plane allows a correct estimation of two positive Lyapunov exponents (LEs) from even a single sequence of return times. We propose a generalized approach for extracting dynamics from point processes that allows avoiding spurious identification of the dynamical regime caused by artifacts. The estimated LEs are nearly close to their expected values if the second positive LE is essentially different from the largest one. If both exponents become nearly close, an underestimation of the second LE may be obtained. Nevertheless, distinctions between chaotic and hyperchaotic regimes are clearly possible.
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Affiliation(s)
- A N Pavlov
- Department of Physics, Saratov State University, Astrakhanskaya Str. 83, 410012, Saratov, Russia
- Saratov State Technical University, Politehnicheskaya Str. 77, 410054, Saratov, Russia
| | - O N Pavlova
- Department of Physics, Saratov State University, Astrakhanskaya Str. 83, 410012, Saratov, Russia
| | - Y K Mohammad
- Department of Physics, Saratov State University, Astrakhanskaya Str. 83, 410012, Saratov, Russia
- Tikrit University Salahudin, Tikrit Qadisiyah, University Str., PO Box 42, Tikrit, Iraq
| | - J Kurths
- Potsdam Institute for Climate Impact Research, Telegraphenberg A 31, 14473 Potsdam, Germany
- Institute of Physics, Humboldt University Berlin, 12489 Berlin, Germany
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Pavlov AN, Pavlova ON, Mohammad YK, Kurths J. Quantifying chaotic dynamics from integrate-and-fire processes. Chaos 2015; 25:013118. [PMID: 25637929 DOI: 10.1063/1.4907175] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
Characterizing chaotic dynamics from integrate-and-fire (IF) interspike intervals (ISIs) is relatively easy performed at high firing rates. When the firing rate is low, a correct estimation of Lyapunov exponents (LEs) describing dynamical features of complex oscillations reflected in the IF ISI sequences becomes more complicated. In this work we discuss peculiarities and limitations of quantifying chaotic dynamics from IF point processes. We consider main factors leading to underestimated LEs and demonstrate a way of improving numerical determining of LEs from IF ISI sequences. We show that estimations of the two largest LEs can be performed using around 400 mean periods of chaotic oscillations in the regime of phase-coherent chaos. Application to real data is discussed.
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Affiliation(s)
- A N Pavlov
- Department of Physics, Saratov State University, Astrakhanskaya Str. 83, 410012 Saratov, Russia
| | - O N Pavlova
- Department of Physics, Saratov State University, Astrakhanskaya Str. 83, 410012 Saratov, Russia
| | - Y K Mohammad
- Department of Physics, Saratov State University, Astrakhanskaya Str. 83, 410012 Saratov, Russia
| | - J Kurths
- Potsdam Institute for Climate Impact Research, Telegraphenberg A 31, 14473 Potsdam, Germany
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Pavlov AN, Semyachkina-Glushkovskaya OV, Zhang Y, Bibikova OA, Pavlova ON, Huang Q, Zhu D, Li P, Tuchin VV, Luo Q. Multiresolution analysis of pathological changes in cerebral venous dynamics in newborn mice with intracranial hemorrhage: adrenorelated vasorelaxation. Physiol Meas 2014; 35:1983-99. [PMID: 25238178 DOI: 10.1088/0967-3334/35/10/1983] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/27/2022]
Abstract
Intracranial hemorrhage (ICH) is the major problem of modern neonatal intensive care. Abnormalities of cerebral venous blood flow (CVBF) can play a crucial role in the development of ICH in infants. The mechanisms underlying these pathological processes remain unclear; however it has been established that the activation of the adrenorelated vasorelaxation can be an important reason. Aiming to reach a better understanding of how the adrenodependent relaxation of cerebral veins contributes to the development of ICH in newborns, we study here the effects of pharmacological stimulation of adrenorelated dilation of the sagittal sinus by isoproterenol on the cerebral venous hemodynamics. Our study is performed in newborn mice at different stages of ICH using the laser speckle contrast imaging and wavelet analysis of the vascular dynamics of CVBF. We show that the dilation of the sagittal sinus with the decreased velocity of blood flow presides to the stress-induced ICH in newborn mice. These morphofunctional vascular changes are accompanied by an increased variance of the wavelet-coefficients in the areas of endothelial and non-endothelial (KATP-channels activity of vascular muscle) sympathetic components of the CVBF variability. Changes in the cerebral venous hemodynamics at the latent stage of ICH are associated with a high responsiveness of the sagittal sinus to isoproterenol quantifying by wavelet-coefficients related to a very slow region of the frequency domain. The obtained results certify that a high activation of the adrenergic-related vasodilatory responses to severe stress in newborn mice can be one of the important mechanisms underlying the development of ICH. Thus, the venous insufficiency with the decreased blood outflow from the brain associated with changes in the endothelial and the sympathetic components of CVBF-variability can be treated as prognostic criteria for the risk of ICH during the first days after birth.
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Affiliation(s)
- A N Pavlov
- Department of Physics, Saratov State University, Astrakhanskaya Str. 83, Saratov, 410012, Russia. Saratov State Technical University, Politehnicheskaya Str. 77, Saratov, 410054, Russia. Wuhan National Laboratory for Optoelectronics, Britton Chance Center for Biomedical Photonics, Huazhong University of Science and Technology, Wuhan 430074, People's Republic of China
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Pavlov AN, Anisimov AA, Semyachkina-Glushkovskaya OV, Matasova EG, Kurths J. Analysis of blood pressure dynamics in male and female rats using the continuous wavelet transform. Physiol Meas 2009; 30:707-17. [DOI: 10.1088/0967-3334/30/7/013] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
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Pavlov AN, Sosnovtseva OV, Pavlova ON, Mosekilde E, Holstein-Rathlou NH. Characterizing multimode interaction in renal autoregulation. Physiol Meas 2008; 29:945-58. [PMID: 18603665 DOI: 10.1088/0967-3334/29/8/007] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
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Pavlov AN, Tupitsyn AN, Legros A, Beuter A, Mosekilde E. Using wavelet analysis to detect the influence of low frequency magnetic fields on human physiological tremor. Physiol Meas 2007; 28:321-33. [PMID: 17322595 DOI: 10.1088/0967-3334/28/3/007] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
Abstract
The influence of extremely low frequency magnetic fields (ELF-MFs) on human physiological processes and, in particular, on motor activity is still not established with certainty. Using the wavelet-transform approach, changes in the characteristics of human finger micromovement are studied in the presence of a low intensity MF centred at the level of the head. Different approaches to nonstationary signal analysis involving real as well as complex wavelet functions are considered. We find evidence that ELF-MFs lead to more regular postural tremor and more homogeneous energy distribution.
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Affiliation(s)
- A N Pavlov
- Department of Physics, Saratov State University, Astrakhanskaya Str 83, Saratov, Russia.
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11
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Brazhe NA, Brazhe AR, Pavlov AN, Erokhova LA, Yusipovich AI, Maksimov GV, Mosekilde E, Sosnovtseva OV. Unraveling cell processes: interference imaging interwoven with data analysis. J Biol Phys 2006; 32:191-208. [PMID: 19669463 PMCID: PMC2651520 DOI: 10.1007/s10867-006-9012-1] [Citation(s) in RCA: 25] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/10/2006] [Accepted: 03/20/2006] [Indexed: 10/23/2022] Open
Abstract
The paper presents results on the application of interference microscopy and wavelet-analysis for cell visualization and studies of cell dynamics. We demonstrate that interference imaging of erythrocytes can reveal reorganization of the cytoskeleton and inhomogenity in the distribution of hemoglobin, and that interference imaging of neurons can show intracellular compartmentalization and submembrane structures. We investigate temporal and spatial variations of the refractive index for different cell types: isolated neurons, mast cells and erythrocytes. We show that the refractive dynamical properties differ from cell type to cell type and depend on the cellular compartment. Our results suggest that low frequency variations (0.1-0.6 Hz) result from plasma membrane processes and that higher frequency variations (20-26 Hz) are related to the movement of vesicles. Using double-wavelet analysis, we study the modulation of the 1 Hz rhythm in neurons and reveal its changes under depolarization and hyperpolarization of the plasma membrane. We conclude that interference microscopy combined with wavelet analysis is a useful technique for non-invasive cell studies, cell visualization, and investigation of plasma membrane properties.
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Affiliation(s)
- N. A. Brazhe
- Biophysics Department, Biological Faculty, Moscow State University, Vorobievy gory 1, Building 12, 119992 Moscow, Russia
| | - A. R. Brazhe
- Biophysics Department, Biological Faculty, Moscow State University, Vorobievy gory 1, Building 12, 119992 Moscow, Russia
| | - A. N. Pavlov
- Physics Department, Saratov State University, Astrakhanskaya Street 83, 410026 Saratov, Russia
| | - L. A. Erokhova
- Biophysics Department, Biological Faculty, Moscow State University, Vorobievy gory 1, Building 12, 119992 Moscow, Russia
| | - A. I. Yusipovich
- Biophysics Department, Biological Faculty, Moscow State University, Vorobievy gory 1, Building 12, 119992 Moscow, Russia
| | - G. V. Maksimov
- Biophysics Department, Biological Faculty, Moscow State University, Vorobievy gory 1, Building 12, 119992 Moscow, Russia
| | - E. Mosekilde
- Department of Physics, The Technical University of Denmark, 2800 Kongens Lyngby, Denmark
| | - O. V. Sosnovtseva
- Department of Physics, The Technical University of Denmark, 2800 Kongens Lyngby, Denmark
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Sosnovtseva OV, Pavlov AN, Brazhe NA, Brazhe AR, Erokhova LA, Maksimov GV, Mosekilde E. Interference microscopy under double-wavelet analysis: a new approach to studying cell dynamics. Phys Rev Lett 2005; 94:218103. [PMID: 16090354 DOI: 10.1103/physrevlett.94.218103] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/27/2005] [Indexed: 05/03/2023]
Abstract
This Letter combines a novel experimental approach to the study of intracellular processes with a newly developed technique for multimode time-series analysis. Experiments are performed on isolated pond snail (Lymnaea stagnalis) neurons. Local variations in the cellular refractive index as detected by laser interference microscopy are related to the processes in the cell. A wavelet analysis shows the presence of several identifiable modes in the membrane and intracellular dynamics, and a double-wavelet analysis reveals nonlinear interactions between the regulatory processes in the form of mutual frequency and amplitude modulations.
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Affiliation(s)
- O V Sosnovtseva
- Department of Physics, The Technical University of Denmark, 2800 Kongens Lyngby, Denmark
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Sosnovtseva OV, Pavlov AN, Mosekilde E, Holstein-Rathlou NH, Marsh DJ. Double-wavelet approach to studying the modulation properties of nonstationary multimode dynamics. Physiol Meas 2005; 26:351-62. [PMID: 15886431 DOI: 10.1088/0967-3334/26/4/002] [Citation(s) in RCA: 22] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
Abstract
On the basis of double-wavelet analysis, the paper proposes a method to study interactions in the form of frequency and amplitude modulation in nonstationary multimode data series. Special emphasis is given to the problem of quantifying the strength of modulation for a fast signal by a coexisting slower dynamics and to its physiological interpretation. Application of the approach is demonstrated for a number of model systems, including a model that generates chaotic dynamics. The approach is then applied to proximal tubular pressure data from rat nephrons in order to estimate the degree to which the myogenic dynamics of the afferent arteriole is modulated by the slower tubulo-glomerular dynamics. Our analysis reveals a significantly stronger interaction between the two mechanisms in spontaneously hypertensive rats than in normotensive rats.
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Affiliation(s)
- O V Sosnovtseva
- Department of Physics, The Technical University of Denmark, 2800 Kongens Lyngby, Denmark
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Sosnovtseva OV, Pavlov AN, Mosekilde E, Holstein-Rathlou NH, Marsh DJ. Double-wavelet approach to study frequency and amplitude modulation in renal autoregulation. Phys Rev E Stat Nonlin Soft Matter Phys 2004; 70:031915. [PMID: 15524557 DOI: 10.1103/physreve.70.031915] [Citation(s) in RCA: 25] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/10/2004] [Indexed: 05/24/2023]
Abstract
Biological time series often display complex oscillations with several interacting rhythmic components. Renal autoregulation, for instance, involves at least two separate mechanisms both of which can produce oscillatory variations in the pressures and flows of the individual nephrons. Using double-wavelet analysis we propose a method to examine how the instantaneous frequency and amplitude of a fast mode is modulated by the presence of a slower mode. Our method is applied both to experimental data from normotensive and hypertensive rats showing different oscillatory patterns and to simulation results obtained from a physiologically based model of the nephron pressure and flow control. We reveal a nonlinear interaction between the two mechanisms that regulate the renal blood flow in the form of frequency and amplitude modulation of the myogenic oscillations.
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Affiliation(s)
- O V Sosnovtseva
- Department of Physics, The Technical University of Denmark, 2800 Kongens Lyngby, Denmark
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Sosnovtseva OV, Pavlov AN, Mosekilde E, Holstein-Rathlou NH. Bimodal oscillations in nephron autoregulation. Phys Rev E Stat Nonlin Soft Matter Phys 2002; 66:061909. [PMID: 12513320 DOI: 10.1103/physreve.66.061909] [Citation(s) in RCA: 22] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/29/2002] [Indexed: 05/24/2023]
Abstract
The individual functional unit of the kidney (the nephron) displays oscillations in its pressure and flow regulation at two different time scales: fast oscillations associated with a myogenic dynamics of the afferent arteriole, and slower oscillations arising from a delay in the tubuloglomerular feedback. We investigate the intra- and internephron entrainment of the two time scales. In addition to full synchronization, both wavelet analyses of experimental data and numerical simulations reveal a partial entrainment in which neighboring nephrons attain a state of chaotic synchronization with respect to their slow dynamics, but the fast dynamics remain desynchronized.
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Affiliation(s)
- O V Sosnovtseva
- Physics Department, Saratov State University, Astrakhanskaya Street 83, Saratov, 410026, Russia
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Anishchenko VS, Igosheva NB, Pavlov AN, Khovanov A, Yakusheva TA. Comparative analysis of methods for classifying the cardiovascular system's states under stress. Crit Rev Biomed Eng 2002; 29:462-81. [PMID: 11730106 DOI: 10.1615/critrevbiomedeng.v29.i3.100] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/13/2022]
Abstract
A comparative analysis is made of various methods for processing electrocardiograms and RR-interval sequences. This analysis was carried out by using standard nonlinear-dynamics algorithms and methods. Apart from that, we assessed the expediency of using a number of characteristics to classify the cardiovascular system's state under stress.
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Affiliation(s)
- V S Anishchenko
- Radiophysics and Nonlinear Dynamics Department, Saratov State University, Russia.
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17
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Pavlov AN, Sosnovtseva OV, Mosekilde E, Anishchenko VS. Chaotic dynamics from interspike intervals. Phys Rev E Stat Nonlin Soft Matter Phys 2001; 63:036205. [PMID: 11308739 DOI: 10.1103/physreve.63.036205] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/29/2000] [Indexed: 05/23/2023]
Abstract
Considering two different mathematical models describing chaotic spiking phenomena, namely, an integrate-and-fire and a threshold-crossing model, we discuss the problem of extracting dynamics from interspike intervals (ISIs) and show that the possibilities of computing the largest Lyapunov exponent (LE) from point processes differ between the two models. We also consider the problem of estimating the second LE and the possibility to diagnose hyperchaotic behavior by processing spike trains. Since the second exponent is quite sensitive to the structure of the ISI series, we investigate the problem of its computation.
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Affiliation(s)
- A N Pavlov
- Nonlinear Dynamics Laboratory, Department of Physics, Saratov State University, Astrakhanskaya Street 83, 410026, Saratov, Russia
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Pavlov AN, Sosnovtseva OV, Mosekilde E, Anishchenko VS. Extracting dynamics from threshold-crossing interspike intervals: possibilities and limitations. Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics 2000; 61:5033-5044. [PMID: 11031546 DOI: 10.1103/physreve.61.5033] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/26/1999] [Revised: 12/16/1999] [Indexed: 05/23/2023]
Abstract
In this paper we estimate dynamical characteristics of chaotic attractors from sequences of threshold-crossing interspike intervals, and study how the choice of the threshold level (which sets the equation of a secant plane) influences the results of the numerical computations. Under quite general conditions we show that the largest Lyapunov exponent can be estimated from a series of return times to the secant plane, even in the case when some of the loops of the phase space trajectory fail to cross this plane.
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Affiliation(s)
- A N Pavlov
- Department of Physics, Saratov State University, Russia
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Pavlov AN, Grebennikov VN, Nazina LD, Nazin GM, Manelis GB. Thermal decomposition of ammonium dinitramide and mechanism of anomalous decay of dinitramide salts. Russ Chem Bull 1999. [DOI: 10.1007/bf02494399] [Citation(s) in RCA: 19] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
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Charskii VV, Pavlov AN, Nazin GM, Korsunskii BL, Fedorov BS. Mechanism of thermal decomposition of N,N-dinitromethylamine. Russ Chem Bull 1989. [DOI: 10.1007/bf00953276] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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Vedrinskii RV, Prosandeev SA, Krivitskii VV, Pavlov AN. Electronic relaxation and the theory of chemical shifts of X-ray characteristic lines. J STRUCT CHEM+ 1981. [DOI: 10.1007/bf00746374] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
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Vedrinskii RV, Prosandeev SA, Krivitskii VV, Pavlov AN. Electronic relaxation and the theory of chemical shifts of X-ray characteristic lines. J STRUCT CHEM+ 1981. [DOI: 10.1007/bf00746373] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
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Vedrinskii RV, Prosandeev SA, Pavlov AN, Kovtun AP. Self-consistent calculation and analysis of the chemical shifts of the K? x-Ray lines of sulfur in the SF6, SO2, and H2S molecules. THEOR EXP CHEM+ 1980. [DOI: 10.1007/bf00524803] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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