1
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Park P, Wong-Campos D, Itkis DG, Lee BH, Qi Y, Davis H, Antin B, Pasarkar A, Grimm JB, Plutkis SE, Holland KL, Paninski L, Lavis LD, Cohen AE. Dendritic excitations govern back-propagation via a spike-rate accelerometer. BIORXIV : THE PREPRINT SERVER FOR BIOLOGY 2024:2023.06.02.543490. [PMID: 37398232 PMCID: PMC10312650 DOI: 10.1101/2023.06.02.543490] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 07/04/2023]
Abstract
Dendrites on neurons support nonlinear electrical excitations, but the computational significance of these events is not well understood. We developed molecular, optical, and analytical tools to map sub-millisecond voltage dynamics throughout the dendritic trees of CA1 pyramidal neurons under diverse optogenetic and synaptic stimulus patterns, in acute brain slices. We observed history-dependent spike back-propagation in distal dendrites, driven by locally generated Na+ spikes (dSpikes). Dendritic depolarization created a transient window for dSpike propagation, opened by A-type K V channel inactivation, and closed by slow N a V inactivation. Collisions of dSpikes with synaptic inputs triggered calcium channel and N-methyl-D-aspartate receptor (NMDAR)-dependent plateau potentials, with accompanying complex spikes at the soma. This hierarchical ion channel network acts as a spike-rate accelerometer, providing an intuitive picture of how dendritic excitations shape associative plasticity rules.
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Affiliation(s)
- Pojeong Park
- Department of Chemistry and Chemical Biology, Harvard University, Cambridge, MA, USA
| | - David Wong-Campos
- Department of Chemistry and Chemical Biology, Harvard University, Cambridge, MA, USA
| | - Daniel G Itkis
- Department of Chemistry and Chemical Biology, Harvard University, Cambridge, MA, USA
| | - Byung Hun Lee
- Department of Chemistry and Chemical Biology, Harvard University, Cambridge, MA, USA
| | - Yitong Qi
- Department of Chemistry and Chemical Biology, Harvard University, Cambridge, MA, USA
| | - Hunter Davis
- Department of Chemistry and Chemical Biology, Harvard University, Cambridge, MA, USA
| | - Benjamin Antin
- Departments of Statistics and Neuroscience, Columbia University, New York, NY, USA
| | - Amol Pasarkar
- Departments of Statistics and Neuroscience, Columbia University, New York, NY, USA
| | - Jonathan B Grimm
- Janelia Research Campus, Howard Hughes Medical Institute, Ashburn, VA, USA
| | - Sarah E Plutkis
- Janelia Research Campus, Howard Hughes Medical Institute, Ashburn, VA, USA
| | - Katie L Holland
- Janelia Research Campus, Howard Hughes Medical Institute, Ashburn, VA, USA
| | - Liam Paninski
- Departments of Statistics and Neuroscience, Columbia University, New York, NY, USA
| | - Luke D Lavis
- Janelia Research Campus, Howard Hughes Medical Institute, Ashburn, VA, USA
| | - Adam E Cohen
- Department of Chemistry and Chemical Biology, Harvard University, Cambridge, MA, USA
- Department of Physics, Harvard University, Cambridge, MA, USA
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2
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Nolte DD. Coherent light scattering from cellular dynamics in living tissues. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2024; 87:036601. [PMID: 38433567 DOI: 10.1088/1361-6633/ad2229] [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: 11/01/2022] [Accepted: 01/24/2024] [Indexed: 03/05/2024]
Abstract
This review examines the biological physics of intracellular transport probed by the coherent optics of dynamic light scattering from optically thick living tissues. Cells and their constituents are in constant motion, composed of a broad range of speeds spanning many orders of magnitude that reflect the wide array of functions and mechanisms that maintain cellular health. From the organelle scale of tens of nanometers and upward in size, the motion inside living tissue is actively driven rather than thermal, propelled by the hydrolysis of bioenergetic molecules and the forces of molecular motors. Active transport can mimic the random walks of thermal Brownian motion, but mean-squared displacements are far from thermal equilibrium and can display anomalous diffusion through Lévy or fractional Brownian walks. Despite the average isotropic three-dimensional environment of cells and tissues, active cellular or intracellular transport of single light-scattering objects is often pseudo-one-dimensional, for instance as organelle displacement persists along cytoskeletal tracks or as membranes displace along the normal to cell surfaces, albeit isotropically oriented in three dimensions. Coherent light scattering is a natural tool to characterize such tissue dynamics because persistent directed transport induces Doppler shifts in the scattered light. The many frequency-shifted partial waves from the complex and dynamic media interfere to produce dynamic speckle that reveals tissue-scale processes through speckle contrast imaging and fluctuation spectroscopy. Low-coherence interferometry, dynamic optical coherence tomography, diffusing-wave spectroscopy, diffuse-correlation spectroscopy, differential dynamic microscopy and digital holography offer coherent detection methods that shed light on intracellular processes. In health-care applications, altered states of cellular health and disease display altered cellular motions that imprint on the statistical fluctuations of the scattered light. For instance, the efficacy of medical therapeutics can be monitored by measuring the changes they induce in the Doppler spectra of livingex vivocancer biopsies.
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Affiliation(s)
- David D Nolte
- Department of Physics and Astronomy, Purdue University, West Lafayette, IN 47907, United States of America
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3
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Bury TM, Diagne K, Olshan D, Glass L, Shrier A, Lerman BB, Bub G. The inverse problem for cardiac arrhythmias. CHAOS (WOODBURY, N.Y.) 2023; 33:123130. [PMID: 38149994 DOI: 10.1063/5.0161210] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/08/2023] [Accepted: 11/20/2023] [Indexed: 12/28/2023]
Abstract
A cardiac arrhythmia is an abnormality in the rate or rhythm of the heart beat. We study a type of arrhythmia called a premature ventricular complex (PVC), which is typically benign, but in rare cases can lead to more serious arrhythmias or heart failure. There are three known mechanisms for PVCs: reentry, an ectopic focus, and triggered activity. We develop minimal models for each mechanism and attempt the inverse problem of determining which model (and therefore which mechanism) best describes the beat dynamics observed in an ambulatory electrocardiogram. We demonstrate our approach on a patient who exhibits frequent PVCs and find that their PVC dynamics are best described by a model of triggered activity. Better identification of the PVC mechanism from wearable device data could improve risk stratification for the development of more serious arrhythmias.
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Affiliation(s)
- T M Bury
- Department of Physiology, McGill University, 3655 Promenade Sir William Osler, Montreal, Quebec H3G 1Y6, Canada
| | - K Diagne
- Department of Physiology, McGill University, 3655 Promenade Sir William Osler, Montreal, Quebec H3G 1Y6, Canada
| | - D Olshan
- Department of Medicine, Division of Cardiology, Cornell University Medical Center, New York, New York 10065, USA
| | - L Glass
- Department of Physiology, McGill University, 3655 Promenade Sir William Osler, Montreal, Quebec H3G 1Y6, Canada
| | - A Shrier
- Department of Physiology, McGill University, 3655 Promenade Sir William Osler, Montreal, Quebec H3G 1Y6, Canada
| | - B B Lerman
- Department of Medicine, Division of Cardiology, Cornell University Medical Center, New York, New York 10065, USA
| | - G Bub
- Department of Physiology, McGill University, 3655 Promenade Sir William Osler, Montreal, Quebec H3G 1Y6, Canada
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4
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U(1) dynamics in neuronal activities. Sci Rep 2022; 12:17629. [PMID: 36271115 PMCID: PMC9587059 DOI: 10.1038/s41598-022-22526-0] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/17/2022] [Accepted: 10/17/2022] [Indexed: 01/13/2023] Open
Abstract
Neurons convert external stimuli into action potentials, or spikes, and encode the contained information into the biological nervous system. Despite the complexity of neurons and the synaptic interactions in between, rate models are often adapted to describe neural encoding with modest success. However, it is not clear whether the firing rate, the reciprocal of the time interval between spikes, is sufficient to capture the essential features for the neuronal dynamics. Going beyond the usual relaxation dynamics in Ginzburg-Landau theory for statistical systems, we propose that neural activities can be captured by the U(1) dynamics, integrating the action potential and the "phase" of the neuron together. The gain function of the Hodgkin-Huxley neuron and the corresponding dynamical phase transitions can be described within the U(1) neuron framework. In addition, the phase dependence of the synaptic interactions is illustrated and the mapping to the Kinouchi-Copelli neuron is established. It suggests that the U(1) neuron is the minimal model for single-neuron activities and serves as the building block of the neuronal network for information processing.
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5
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Tao P, Cheng J, Chen L. Brain-inspired chaotic backpropagation for MLP. Neural Netw 2022; 155:1-13. [PMID: 36027661 DOI: 10.1016/j.neunet.2022.08.004] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/04/2022] [Revised: 06/14/2022] [Accepted: 08/03/2022] [Indexed: 11/17/2022]
Abstract
Backpropagation (BP) algorithm is one of the most basic learning algorithms in deep learning. Although BP has been widely used, it still suffers from the problem of easily falling into the local minima due to its gradient dynamics. Inspired by the fact that the learning of real brains may exploit chaotic dynamics, we propose the chaotic backpropagation (CBP) algorithm by integrating the intrinsic chaos of real neurons into BP. By validating on multiple datasets (e.g. cifar10), we show that, for multilayer perception (MLP), CBP has significantly better abilities than those of BP and its variants in terms of optimization and generalization from both computational and theoretical viewpoints. Actually, CBP can be regarded as a general form of BP with global searching ability inspired by the chaotic learning process in the brain. Therefore, CBP not only has the potential of complementing or replacing BP in deep learning practice, but also provides a new way for understanding the learning process of the real brain.
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Affiliation(s)
- Peng Tao
- Key Laboratory of Systems Health Science of Zhejiang Province, School of Life Science, Hangzhou Institute for Advanced Study, University of Chinese Academy of Sciences, Chinese Academy of Sciences, Hangzhou 310024, China; Key Laboratory of Systems Biology, Shanghai Institute of Biochemistry and Cell Biology, Center for Excellence in Molecular Cell Science, Chinese Academy of Sciences, Shanghai 200031, China.
| | - Jie Cheng
- Key Laboratory of Systems Biology, Shanghai Institute of Biochemistry and Cell Biology, Center for Excellence in Molecular Cell Science, Chinese Academy of Sciences, Shanghai 200031, China.
| | - Luonan Chen
- Key Laboratory of Systems Health Science of Zhejiang Province, School of Life Science, Hangzhou Institute for Advanced Study, University of Chinese Academy of Sciences, Chinese Academy of Sciences, Hangzhou 310024, China; Key Laboratory of Systems Biology, Shanghai Institute of Biochemistry and Cell Biology, Center for Excellence in Molecular Cell Science, Chinese Academy of Sciences, Shanghai 200031, China; Guangdong Institute of Intelligence Science and Technology, Hengqin, Zhuhai, Guangdong 519031, China.
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6
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Goldbeter A, Yan J. Multi-synchronization and other patterns of multi-rhythmicity in oscillatory biological systems. Interface Focus 2022; 12:20210089. [PMID: 35450278 PMCID: PMC9016794 DOI: 10.1098/rsfs.2021.0089] [Citation(s) in RCA: 6] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/22/2021] [Accepted: 03/09/2022] [Indexed: 12/13/2022] Open
Abstract
While experimental and theoretical studies have established the prevalence of rhythmic behaviour at all levels of biological organization, less common is the coexistence between multiple oscillatory regimes (multi-rhythmicity), which has been predicted by a variety of models for biological oscillators. The phenomenon of multi-rhythmicity involves, most commonly, the coexistence between two (birhythmicity) or three (trirhythmicity) distinct regimes of self-sustained oscillations. Birhythmicity has been observed experimentally in a few chemical reactions and in biological examples pertaining to cardiac cell physiology, neurobiology, human voice patterns and ecology. The present study consists of two parts. We first review the mechanisms underlying multi-rhythmicity in models for biochemical and cellular oscillations in which the phenomenon was investigated over the years. In the second part, we focus on the coupling of the cell cycle and the circadian clock and show how an additional source of multi-rhythmicity arises from the bidirectional coupling of these two cellular oscillators. Upon bidirectional coupling, the two oscillatory networks generally synchronize in a unique manner characterized by a single, common period. In some conditions, however, the two oscillators may synchronize in two or three different ways characterized by distinct waveforms and periods. We refer to this type of multi-rhythmicity as ‘multi-synchronization’.
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Affiliation(s)
- Albert Goldbeter
- Unité de Chronobiologie théorique, Faculté des Sciences, Université Libre de Bruxelles (ULB), 1050 Brussels, Belgium
| | - Jie Yan
- Center for Systems Biology, School of Mathematical Sciences, Soochow University, Suzhou, People's Republic of China
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7
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Jiménez A, Lu Y, Jambhekar A, Lahav G. Principles, mechanisms and functions of entrainment in biological oscillators. Interface Focus 2022; 12:20210088. [PMID: 35450280 PMCID: PMC9010850 DOI: 10.1098/rsfs.2021.0088] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/17/2021] [Accepted: 03/07/2022] [Indexed: 12/12/2022] Open
Abstract
Entrainment is a phenomenon in which two oscillators interact with each other, typically through physical or chemical means, to synchronize their oscillations. This phenomenon occurs in biology to coordinate processes from the molecular to organismal scale. Biological oscillators can be entrained within a single cell, between cells or to an external input. Using six illustrative examples of entrainable biological oscillators, we discuss the distinctions between entrainment and synchrony and explore features that contribute to a system's propensity to entrain. Entrainment can either enhance or reduce the heterogeneity of oscillations within a cell population, and we provide examples and mechanisms of each case. Finally, we discuss the known functions of entrainment and discuss potential functions from an evolutionary perspective.
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Affiliation(s)
- Alba Jiménez
- Department of Systems Biology, Blavatnik Institute at Harvard Medical School, Boston, MA 02115, USA
| | - Ying Lu
- Department of Systems Biology, Blavatnik Institute at Harvard Medical School, Boston, MA 02115, USA
| | - Ashwini Jambhekar
- Department of Systems Biology, Blavatnik Institute at Harvard Medical School, Boston, MA 02115, USA
- Ludwig Center at Harvard, Boston, MA 02115, USA
| | - Galit Lahav
- Department of Systems Biology, Blavatnik Institute at Harvard Medical School, Boston, MA 02115, USA
- Ludwig Center at Harvard, Boston, MA 02115, USA
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8
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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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9
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Tsumoto K, Kurata Y. Bifurcations and Proarrhythmic Behaviors in Cardiac Electrical Excitations. Biomolecules 2022; 12:459. [PMID: 35327651 PMCID: PMC8946197 DOI: 10.3390/biom12030459] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/17/2022] [Revised: 03/09/2022] [Accepted: 03/14/2022] [Indexed: 12/23/2022] Open
Abstract
The heart is a hierarchical dynamic system consisting of molecules, cells, and tissues, and acts as a pump for blood circulation. The pumping function depends critically on the preceding electrical activity, and disturbances in the pattern of excitation propagation lead to cardiac arrhythmia and pump failure. Excitation phenomena in cardiomyocytes have been modeled as a nonlinear dynamical system. Because of the nonlinearity of excitation phenomena, the system dynamics could be complex, and various analyses have been performed to understand the complex dynamics. Understanding the mechanisms underlying proarrhythmic responses in the heart is crucial for developing new ways to prevent and control cardiac arrhythmias and resulting contractile dysfunction. When the heart changes to a pathological state over time, the action potential (AP) in cardiomyocytes may also change to a different state in shape and duration, often undergoing a qualitative change in behavior. Such a dynamic change is called bifurcation. In this review, we first summarize the contribution of ion channels and transporters to AP formation and our knowledge of ion-transport molecules, then briefly describe bifurcation theory for nonlinear dynamical systems, and finally detail its recent progress, focusing on the research that attempts to understand the developing mechanisms of abnormal excitations in cardiomyocytes from the perspective of bifurcation phenomena.
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Affiliation(s)
| | - Yasutaka Kurata
- Department of Physiology II, Kanazawa Medical University, Uchinada 920-0293, Japan;
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10
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Burt P, Grabe S, Madeti C, Upadhyay A, Merrow M, Roenneberg T, Herzel H, Schmal C. Principles underlying the complex dynamics of temperature entrainment by a circadian clock. iScience 2021; 24:103370. [PMID: 34816105 PMCID: PMC8593569 DOI: 10.1016/j.isci.2021.103370] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/30/2021] [Revised: 09/01/2021] [Accepted: 10/25/2021] [Indexed: 01/20/2023] Open
Abstract
Autonomously oscillating circadian clocks resonate with daily environmental (zeitgeber) rhythms to organize physiology around the solar day. Although entrainment properties and mechanisms have been studied widely and in great detail for light-dark cycles, entrainment to daily temperature rhythms remains poorly understood despite that they are potent zeitgebers. Here we investigate the entrainment of the chronobiological model organism Neurospora crassa, subject to thermocycles of different periods and fractions of warm versus cold phases, mimicking seasonal variations. Depending on the properties of these thermocycles, regularly entrained rhythms, period-doubling (frequency demultiplication) but also irregular aperiodic behavior occurs. We demonstrate that the complex nonlinear phenomena of experimentally observed entrainment dynamics can be understood by molecular mathematical modeling.
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Affiliation(s)
- Philipp Burt
- Institute for Theoretical Biology, Faculty of Life Sciences, Humboldt-Universität zu Berlin, Unter den Linden 6, 10117 Berlin, Germany
- Institute for Theoretical Biology, Charité Universitätsmedizin Berlin, Charitéplatz 1, 10117 Berlin, Germany
| | - Saskia Grabe
- Institute for Theoretical Biology, Faculty of Life Sciences, Humboldt-Universität zu Berlin, Unter den Linden 6, 10117 Berlin, Germany
- Institute for Theoretical Biology, Charité Universitätsmedizin Berlin, Charitéplatz 1, 10117 Berlin, Germany
| | - Cornelia Madeti
- Institute of Medical Psychology, Faculty of Medicine, LMU Munich, Goethestrasse 31, 80336 Munich, Germany
| | - Abhishek Upadhyay
- Institute for Theoretical Biology, Faculty of Life Sciences, Humboldt-Universität zu Berlin, Unter den Linden 6, 10117 Berlin, Germany
- Institute for Theoretical Biology, Charité Universitätsmedizin Berlin, Charitéplatz 1, 10117 Berlin, Germany
- Friedrich Miescher Institute for Biomedical Research, Maulbeerstrasse 66, 4058 Basel, Switzerland
| | - Martha Merrow
- Institute of Medical Psychology, Faculty of Medicine, LMU Munich, Goethestrasse 31, 80336 Munich, Germany
| | - Till Roenneberg
- Institute of Medical Psychology, Faculty of Medicine, LMU Munich, Goethestrasse 31, 80336 Munich, Germany
| | - Hanspeter Herzel
- Institute for Theoretical Biology, Faculty of Life Sciences, Humboldt-Universität zu Berlin, Unter den Linden 6, 10117 Berlin, Germany
- Institute for Theoretical Biology, Charité Universitätsmedizin Berlin, Charitéplatz 1, 10117 Berlin, Germany
| | - Christoph Schmal
- Institute for Theoretical Biology, Faculty of Life Sciences, Humboldt-Universität zu Berlin, Unter den Linden 6, 10117 Berlin, Germany
- Institute for Theoretical Biology, Charité Universitätsmedizin Berlin, Charitéplatz 1, 10117 Berlin, Germany
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11
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Nakano K, Nanri N, Tsukamoto Y, Akashi M. Mechanical activities of self-beating cardiomyocyte aggregates under mechanical compression. Sci Rep 2021; 11:15159. [PMID: 34312427 PMCID: PMC8313529 DOI: 10.1038/s41598-021-93657-z] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/06/2021] [Accepted: 06/29/2021] [Indexed: 11/29/2022] Open
Abstract
Since the discovery of synchronous pulsations in cardiomyocytes (CMs), electrical communication between CMs has been emphasized; however, recent studies suggest the possibility of mechanical communication. Here, we demonstrate that spherical self-beating CM aggregates, termed cardiac spheroids (CSs), produce enhanced mechanical energy under mechanical compression and work cooperatively via mechanical communication. For single CSs between parallel plates, compression increased both beating frequency and beating energy. Contact mechanics revealed a scaling law on the beating energy, indicating that the most intensively stressed cells in the compressed CSs predominantly contributed to the performance of mechanical work against mechanical compression. For pairs of CSs between parallel plates, compression immediately caused synchronous beating with mechanical coupling. Compression tended to strengthen and stabilize the synchronous beating, although some irregularity and temporary arrest were observed. These results suggest that mechanical compression is an indispensable control parameter when evaluating the activities of CMs and their aggregates.
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Affiliation(s)
- Ken Nakano
- Yokohama National University, 79-7 Tokiwadai, Hodogaya, Yokohama, Kanagawa, 240-8501, Japan.
| | - Naoya Nanri
- Yokohama National University, 79-7 Tokiwadai, Hodogaya, Yokohama, Kanagawa, 240-8501, Japan
| | | | - Mitsuru Akashi
- Osaka University, 1-3 Yamadaoka, Suita, Osaka, 565-0871, Japan
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12
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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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13
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Novel Approach for EKG Signals Analysis Based on Markovian and Non-Markovian Fractalization Type in Scale Relativity Theory. Symmetry (Basel) 2021. [DOI: 10.3390/sym13030456] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022] Open
Abstract
Two distinct operational procedures are proposed for diagnosis and tracking of heart disease evolution (in particular atrial fibrillations). The first procedure, based on the application of non-linear dynamic methods (strange attractors, skewness, kurtosis, histograms, Lyapunov exponent, etc.) analyzes the electrical activity of the heart (electrocardiogram signals). The second procedure, based on multifractalization through Markovian and non-Markovian-type stochasticizations in the framework of the scale relativity theory, reconstructs any type of EKG signal by means of harmonic mappings from the usual space to the hyperbolic one. These mappings mime various scale transitions by differential geometries, in Riemann spaces with symmetries of SL(2R)-type. Then, the two operational procedures are not mutually exclusive, but rather become complementary, through their finality, which is gaining valuable information concerning fibrillation crises. As such, the author’s proposed method could be used for developing new models for medical diagnosis and evolution tracking of heart diseases (patterns dynamics, signal reconstruction, etc.).
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14
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Biasci V, Sacconi L, Cytrynbaum EN, Pijnappels DA, De Coster T, Shrier A, Glass L, Bub G. Universal mechanisms for self-termination of rapid cardiac rhythm. CHAOS (WOODBURY, N.Y.) 2020; 30:121107. [PMID: 33380016 DOI: 10.1063/5.0033813] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/20/2020] [Accepted: 11/14/2020] [Indexed: 06/12/2023]
Abstract
Excitable media sustain circulating waves. In the heart, sustained circulating waves can lead to serious impairment or even death. To investigate factors affecting the stability of such waves, we have used optogenetic techniques to stimulate a region at the apex of a mouse heart at a fixed delay after the detection of excitation at the base of the heart. For long delays, rapid circulating rhythms can be sustained, whereas for shorter delays, there are paroxysmal bursts of activity that start and stop spontaneously. By considering the dependence of the action potential and conduction velocity on the preceding recovery time using restitution curves, as well as the reduced excitability (fatigue) due to the rapid excitation, we model prominent features of the dynamics including alternation of the duration of the excited phases and conduction times, as well as termination of the bursts for short delays. We propose that this illustrates universal mechanisms that exist in biological systems for the self-termination of such activities.
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Affiliation(s)
- Valentina Biasci
- Division of Physiology, Department of Experimental and Clinical Medicine, University of Florence, 50134 Florence, Italy
| | - Leonardo Sacconi
- National Institute of Optics, National Research Council, 50125 Florence, Italy
| | - Eric N Cytrynbaum
- Department of Mathematics, UBC, Vancouver British Columbia V6T 1Z2, Canada
| | - Daniël A Pijnappels
- Department of Cardiology, Leiden University Medical Center, Albinusdreef 2 2333 ZA Leiden, The Netherlands
| | - Tim De Coster
- Department of Cardiology, Leiden University Medical Center, Albinusdreef 2 2333 ZA Leiden, The Netherlands
| | - Alvin Shrier
- Department of Physiology, McGill University, 3655 Promenade Sir William Osler, Montreal, Quebec H3G 1Y6, Canada
| | - Leon Glass
- Department of Physiology, McGill University, 3655 Promenade Sir William Osler, Montreal, Quebec H3G 1Y6, Canada
| | - Gil Bub
- Department of Physiology, McGill University, 3655 Promenade Sir William Osler, Montreal, Quebec H3G 1Y6, Canada
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15
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Huang K, Sorrentino F, Hossein-Zadeh M. Experimental observations of synchronization between two bidirectionally coupled physically dissimilar oscillators. Phys Rev E 2020; 102:042215. [PMID: 33212708 DOI: 10.1103/physreve.102.042215] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/14/2020] [Accepted: 09/10/2020] [Indexed: 06/11/2023]
Abstract
We experimentally study the complex dynamics of two mutually coupled physically dissimilar oscillators with two different kinds of coupling mechanisms. Specifically, an optoelectronic oscillator is coupled to a Colpitts oscillator via optical power and the Colpitts oscillator is coupled back to the optoelectronic oscillator via electric voltage. We investigate and characterize phase synchronization and generalized chaos synchronization in this coupled system. Phase synchronization is observed when both oscillators are preset to oscillate periodically prior to coupling while generalized chaos synchronization is observed when both oscillators are preset to oscillate chaotically prior to coupling. In the periodical oscillation regime, we observe a linear relationship between the strengths of the two unidirectional coupling factors at which the system transitions to a synchronized state. In the chaotic regime, we observe a transition from hyperchaos to chaos associated with the onset of generalized synchronization.
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Affiliation(s)
- Ke Huang
- Center for High Technology Materials, The University of New Mexico, 1313 Goddard Street SE, Albuquerque, New Mexico 87106, USA
| | - Francesco Sorrentino
- Department of Mechanical Engineering, The University of New Mexico, Albuquerque, New Mexico 87131, USA
| | - Mani Hossein-Zadeh
- Center for High Technology Materials, The University of New Mexico, 1313 Goddard Street SE, Albuquerque, New Mexico 87106, USA
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16
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Chen YF, Lee CC, Hsiao JQ, Huang HY, Tsou CH, Liang HC, Huang KF. Exploiting a monolithic passively Q-switched Nd:YAG laser to mimic a single neuron cell under periodic stimulation. OPTICS LETTERS 2020; 45:4032-4035. [PMID: 32667347 DOI: 10.1364/ol.399253] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/02/2020] [Accepted: 06/20/2020] [Indexed: 06/11/2023]
Abstract
A monolithic passively Q-switched Nd:YAG laser under periodic pulse pumping is originally exploited to emulate the response of a single neuron cell stimulated by periodic pulse inputs. Experimental results reveal that the output characteristics of the monolithic passively Q-switched laser can analogously manifest not only the firing patterns but also the frequency-locked plateaus of the single neuron cell. Moreover, the sine circle map is innovatively used to generate the output pulse sequences that can exactly correspond to experimental firing patterns. The present exploration indicates that a monolithic passively Q-switched solid-state laser is highly feasible to be developed as a compact artificial neuron cell.
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17
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Wang J, Deng B, Gao T, Wang J, Yi G, Wang R. Frequency-dependent response in cortical network with periodic electrical stimulation. CHAOS (WOODBURY, N.Y.) 2020; 30:073130. [PMID: 32752642 DOI: 10.1063/5.0007006] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/09/2020] [Accepted: 06/24/2020] [Indexed: 06/11/2023]
Abstract
Electrical stimulation can shape oscillations in brain activity. However, the mechanism of how periodic electrical stimulation modulates brain oscillations by time-delayed neural networks is poorly understood at present. To address this question, we investigate the effects of periodic stimulations on the oscillations generated via a time-delayed neural network. We specifically study the effect of unipolar and asymmetric bidirectional pulse stimulations by altering amplitude and frequency in a systematic manner. Our findings suggest that electrical stimulations play a central role in altering oscillations in the time-delayed neural network and that these alterations are strongly dependent on the stimulus frequency. We observe that the time-delayed neural network responds differently as the stimulation frequency is altered, as manifested by changes in resonance, entrainment, non-linear oscillation, or oscillation suppression. The results also indicate that the network presents similar response activities with increasing stimulus frequency under different excitation-inhibition ratios. Collectively, our findings pave the way for exploring the potential mechanism underlying the frequency-dependent modulation of network activity via electrical stimulations and provide new insights into possible electrical stimulation therapies to the neurological and psychological disorders in clinical practice.
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Affiliation(s)
- Jixuan Wang
- School of Electrical and Information Engineering, Tianjin University, 300072 Tianjin, China
| | - Bin Deng
- School of Electrical and Information Engineering, Tianjin University, 300072 Tianjin, China
| | - Tianshi Gao
- School of Electrical and Information Engineering, Tianjin University, 300072 Tianjin, China
| | - Jiang Wang
- School of Electrical and Information Engineering, Tianjin University, 300072 Tianjin, China
| | - Guosheng Yi
- School of Electrical and Information Engineering, Tianjin University, 300072 Tianjin, China
| | - Ruofan Wang
- School of Information Technology Engineering, Tianjin University of Technology and Education, 300222 Tianjin, China
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18
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Cusimano N, Gizzi A, Fenton F, Filippi S, Gerardo-Giorda L. Key aspects for effective mathematical modelling of fractional-diffusion in cardiac electrophysiology: a quantitative study. COMMUNICATIONS IN NONLINEAR SCIENCE & NUMERICAL SIMULATION 2020; 84:105152. [PMID: 32863678 PMCID: PMC7453933 DOI: 10.1016/j.cnsns.2019.105152] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
Microscopic structural features of cardiac tissue play a fundamental role in determining complex spatio-temporal excitation dynamics at the macroscopic level. Recent efforts have been devoted to the development of mathematical models accounting for non-local spatio-temporal coupling able to capture these complex dynamics without the need of resolving tissue heterogeneities down to the micro-scale. In this work, we analyse in detail several important aspects affecting the overall predictive power of these modelling tools and provide some guidelines for an effective use of space-fractional models of cardiac electrophysiology in practical applications. Through an extensive computational study in simplified computational domains, we highlight the robustness of models belonging to different categories, i.e., physiological and phenomenological descriptions, against the introduction of non-locality, and lay down the foundations for future research and model validation against experimental data. A modern genetic algorithm framework is used to investigate proper parameterisations of the considered models, and the crucial role played by the boundary assumptions in the considered settings is discussed. Several numerical results are provided to support our claims.
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Affiliation(s)
- N. Cusimano
- Basque Center for Applied Mathematics, Alameda de Mazarredo 14, 48009 Bilbao, Spain
| | - A. Gizzi
- Department of Engineering, University of Rome Campus Bio-Medico, via A. del Portillo 21, 00128 Rome, Italy
| | - F.H. Fenton
- School of Physics, Georgia Insitute of Technology, 837 State Street NW, Atlanta, GA 30332, United States
| | - S. Filippi
- Department of Engineering, University of Rome Campus Bio-Medico, via A. del Portillo 21, 00128 Rome, Italy
| | - L. Gerardo-Giorda
- Basque Center for Applied Mathematics, Alameda de Mazarredo 14, 48009 Bilbao, Spain
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19
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Chou PY, Chiang WY, Chan CK, Lai PY. Dynamics of beating cardiac tissue under slow periodic drives. Phys Rev E 2020; 101:012201. [PMID: 32069621 DOI: 10.1103/physreve.101.012201] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/03/2019] [Indexed: 11/06/2022]
Abstract
Effects of mechanical coupling on cardiac dynamics are studied by monitoring the beating dynamics of a cardiac tissue which is being pulled periodically at a pace slower than its intrinsic beating rate. The tissue is taken from the heart of a bullfrog that includes pacemaker cells. The cardiac tissue beats spontaneously with an almost constant interbeat interval (IBI) when there is no external forcing. On the other hand, the IBI is observed to vary significantly under an external periodic drive. Interestingly, when the period of the external drive is about two times the intrinsic IBI of the tissue without pulling, the IBI as a function of time exhibits a wave packet structure. Our experimental results can be understood theoretically by a phase-coupled model under external driving. In particular, the theoretical prediction of the wave-packet period as a function of the normalized driving period agrees excellently with the observations. Furthermore, the cardiac mechanical coupling constant can be extracted from the experimental data from our model and is found to be insensitive to the external driving period. Implications of our results on cardiac physiology are also discussed.
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Affiliation(s)
- Po-Yu Chou
- Department of Physics, and Center for Complex Systems, National Central University, Chungli District, TaoYuan City 320, Taiwan, Republic of China
| | - Wei-Yin Chiang
- Department of Physics, and Center for Complex Systems, National Central University, Chungli District, TaoYuan City 320, Taiwan, Republic of China
| | - C K Chan
- Institute of Physics, Academia Sinica, Nankang, Taipei 115, Taiwan, Republic of China
| | - Pik-Yin Lai
- Department of Physics, and Center for Complex Systems, National Central University, Chungli District, TaoYuan City 320, Taiwan, Republic of China
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20
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Toker D, Sommer FT, D’Esposito M. A simple method for detecting chaos in nature. Commun Biol 2020; 3:11. [PMID: 31909203 PMCID: PMC6941982 DOI: 10.1038/s42003-019-0715-9] [Citation(s) in RCA: 33] [Impact Index Per Article: 8.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/29/2019] [Accepted: 11/26/2019] [Indexed: 11/18/2022] Open
Abstract
Chaos, or exponential sensitivity to small perturbations, appears everywhere in nature. Moreover, chaos is predicted to play diverse functional roles in living systems. A method for detecting chaos from empirical measurements should therefore be a key component of the biologist's toolkit. But, classic chaos-detection tools are highly sensitive to measurement noise and break down for common edge cases, making it difficult to detect chaos in domains, like biology, where measurements are noisy. However, newer tools promise to overcome these limitations. Here, we combine several such tools into an automated processing pipeline, and show that our pipeline can detect the presence (or absence) of chaos in noisy recordings, even for difficult edge cases. As a first-pass application of our pipeline, we show that heart rate variability is not chaotic as some have proposed, and instead reflects a stochastic process in both health and disease. Our tool is easy-to-use and freely available.
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Affiliation(s)
- Daniel Toker
- Helen Wills Neuroscience Institute, University of California, Berkeley, CA USA
| | - Friedrich T. Sommer
- Helen Wills Neuroscience Institute, University of California, Berkeley, CA USA
| | - Mark D’Esposito
- Helen Wills Neuroscience Institute, University of California, Berkeley, CA USA
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21
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Karavaev AS, Ishbulatov YM, Ponomarenko VI, Bezruchko BP, Kiselev AR, Prokhorov MD. Autonomic control is a source of dynamical chaos in the cardiovascular system. CHAOS (WOODBURY, N.Y.) 2019; 29:121101. [PMID: 31893640 DOI: 10.1063/1.5134833] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/06/2019] [Accepted: 11/22/2019] [Indexed: 06/10/2023]
Abstract
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.
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Affiliation(s)
- A S Karavaev
- Saratov Branch of the Institute of Radio Engineering and Electronics of Russian Academy of Sciences, Zelyonaya Street, 38, Saratov 410019, Russia
| | - Yu M Ishbulatov
- Saratov Branch of the Institute of Radio Engineering and Electronics of Russian Academy of Sciences, Zelyonaya Street, 38, Saratov 410019, Russia
| | - V I Ponomarenko
- Saratov Branch of the Institute of Radio Engineering and Electronics of Russian Academy of Sciences, Zelyonaya Street, 38, Saratov 410019, Russia
| | - B P Bezruchko
- Saratov Branch of the Institute of Radio Engineering and Electronics of Russian Academy of Sciences, Zelyonaya Street, 38, Saratov 410019, Russia
| | - A R Kiselev
- Department of Innovative Cardiological Information Technology, Institute of Cardiological Research, Saratov State Medical University, B. Kazachaya Street, 112, Saratov 410012, Russia
| | - M D Prokhorov
- Saratov Branch of the Institute of Radio Engineering and Electronics of Russian Academy of Sciences, Zelyonaya Street, 38, Saratov 410019, Russia
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22
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Hussain L, Aziz W, Alshdadi AA, Abbasi AA, Majid A, Marchal AR. Multiscale entropy analysis to quantify the dynamics of motor movement signals with fist or feet movement using topographic maps. Technol Health Care 2019; 28:259-273. [PMID: 31594269 DOI: 10.3233/thc-191803] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
Abstract
BACKGROUND Brain neural activity is measured using electroencephalography (EEG) recording from the scalp. The EEG motor/imagery tasks help disabled people to communicate with the external environment. OBJECTIVE In this paper, robust multiscale sample entropy (MSE) and wavelet entropy measures are employed using topographic maps' analysis and tabulated form to quantify the dynamics of EEG motor movements tasks with actual and imagery opening and closing of fist or feet movements. METHODS To distinguish these conditions, we used the topographic maps which visually show the significance level of the brain regions and probes for dominant activities. The paired t-test and Posthoc Tukey test are used to find the significance levels. RESULTS The topographic maps results obtained using MSE reveal that maximum electrodes show the significance in frontpolar, frontal, and few frontal and parietal brain regions at temporal scales 3, 4, 6 and 7. Moreover, it was also observed that the distribution of significance is from frontoparietal brain regions. Using wavelet entropy, the significant results are obtained at frontpolar, frontal, and few electrodes in right hemisphere. The highest significance is obtained at frontpolar electrodes followed by frontal and few central and parietal electrodes.
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Affiliation(s)
- Lal Hussain
- Department of Computer Science and IT, The University of Azad Jammu and Kashmir, City Campus, Muzaffarabad 13100, Pakistan
| | - Wajid Aziz
- Department of Computer Science and IT, The University of Azad Jammu and Kashmir, City Campus, Muzaffarabad 13100, Pakistan.,College of Computer Sciences and Engineering, University of Jeddah, Jeddah 23890, Saudi Arabia
| | - Abdulrahman A Alshdadi
- College of Computer Sciences and Engineering, University of Jeddah, Jeddah 23890, Saudi Arabia
| | - Adeel Ahmed Abbasi
- Department of Computer Science and IT, The University of Azad Jammu and Kashmir, City Campus, Muzaffarabad 13100, Pakistan
| | - Abdul Majid
- Department of Computer Science and IT, The University of Azad Jammu and Kashmir, City Campus, Muzaffarabad 13100, Pakistan
| | - Ali Raza Marchal
- Department of Computer Science and IT, The University of Azad Jammu and Kashmir, City Campus, Muzaffarabad 13100, Pakistan
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23
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Loppini A, Gizzi A, Cherubini C, Cherry EM, Fenton FH, Filippi S. Spatiotemporal correlation uncovers characteristic lengths in cardiac tissue. Phys Rev E 2019; 100:020201. [PMID: 31574686 DOI: 10.1103/physreve.100.020201] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/14/2018] [Indexed: 06/10/2023]
Abstract
Complex spatiotemporal patterns of action potential duration have been shown to occur in many mammalian hearts due to period-doubling bifurcations that develop with increasing frequency of stimulation. Here, through high-resolution optical mapping experiments and mathematical modeling, we introduce a characteristic spatial length of cardiac activity in canine ventricular wedges via a spatiotemporal correlation analysis, at different stimulation frequencies and during fibrillation. We show that the characteristic length ranges from 40 to 20 cm during one-to-one responses and it decreases to a specific value of about 3 cm at the transition from period-doubling bifurcation to fibrillation. We further show that during fibrillation, the characteristic length is about 1 cm. Another significant outcome of our analysis is the finding of a constitutive phenomenological law obtained from a nonlinear fitting of experimental data which relates the conduction velocity restitution curve with the characteristic length of the system. The fractional exponent of 3/2 in our phenomenological law is in agreement with the domain size remapping required to reproduce experimental fibrillation dynamics within a realistic cardiac domain via accurate mathematical models.
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Affiliation(s)
- Alessandro Loppini
- Department of Engineering, Campus Bio-Medico University of Rome, Via A. del Portillo 21, I-00128 Rome, Italy
| | - Alessio Gizzi
- Department of Engineering, Campus Bio-Medico University of Rome, Via A. del Portillo 21, I-00128 Rome, Italy
| | - Christian Cherubini
- Department of Engineering, Campus Bio-Medico University of Rome, Via A. del Portillo 21, I-00128 Rome, Italy
- ICRANet, Piazza delle Repubblica 10, I-65122 Pescara, Italy
| | - Elizabeth M Cherry
- School of Mathematical Sciences, Rochester Institute of Technology, 85 Lomb Memorial Drive, Rochester, New York 14623, USA
| | - Flavio H Fenton
- School of Physics, Georgia Institute of Technology, 837 State Street, Atlanta, Georgia 30332, USA
| | - Simonetta Filippi
- Department of Engineering, Campus Bio-Medico University of Rome, Via A. del Portillo 21, I-00128 Rome, Italy
- ICRANet, Piazza delle Repubblica 10, I-65122 Pescara, Italy
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24
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How to correctly quantify neuronal phase-response curves from noisy recordings. J Comput Neurosci 2019; 47:17-30. [PMID: 31231777 DOI: 10.1007/s10827-019-00719-3] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/14/2019] [Revised: 04/09/2019] [Accepted: 05/07/2019] [Indexed: 10/26/2022]
Abstract
At the level of individual neurons, various coding properties can be inferred from the input-output relationship of a cell. For small inputs, this relation is captured by the phase-response curve (PRC), which measures the effect of a small perturbation on the timing of the subsequent spike. Experimentally, however, an accurate experimental estimation of PRCs is challenging. Despite elaborate measurement efforts, experimental PRC estimates often cannot be related to those from modeling studies. In particular, experimental PRCs rarely resemble the characteristic theoretical PRC expected close to spike initiation, which is indicative of the underlying spike-onset bifurcation. Here, we show for conductance-based model neurons that the correspondence between theoretical and measured phase-response curve is lost when the stimuli used for the estimation are too large. In this case, the derived phase-response curve is distorted beyond recognition and takes on a generic shape that reflects the measurement protocol and masks the spike-onset bifurcation. We discuss how to identify appropriate stimulus strengths for perturbation and noise-stimulation methods, which permit to estimate PRCs that reliably reflect the spike-onset bifurcation - a task that is particularly difficult if a lower bound for the stimulus amplitude is dictated by prominent intrinsic neuronal noise.
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25
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Attuel G, Gerasimova-Chechkina E, Argoul F, Yahia H, Arneodo A. Multifractal Desynchronization of the Cardiac Excitable Cell Network During Atrial Fibrillation. II. Modeling. Front Physiol 2019; 10:480. [PMID: 31105585 PMCID: PMC6492055 DOI: 10.3389/fphys.2019.00480] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/03/2018] [Accepted: 04/05/2019] [Indexed: 11/13/2022] Open
Abstract
In a companion paper (I. Multifractal analysis of clinical data), we used a wavelet-based multiscale analysis to reveal and quantify the multifractal intermittent nature of the cardiac impulse energy in the low frequency range ≲ 2Hz during atrial fibrillation (AF). It demarcated two distinct areas within the coronary sinus (CS) with regionally stable multifractal spectra likely corresponding to different anatomical substrates. The electrical activity also showed no sign of the kind of temporal correlations typical of cascading processes across scales, thereby indicating that the multifractal scaling is carried by variations in the large amplitude oscillations of the recorded bipolar electric potential. In the present study, to account for these observations, we explore the role of the kinetics of gap junction channels (GJCs), in dynamically creating a new kind of imbalance between depolarizing and repolarizing currents. We propose a one-dimensional (1D) spatial model of a denervated myocardium, where the coupling of cardiac cells fails to synchronize the network of cardiac cells because of abnormal transjunctional capacitive charging of GJCs. We show that this non-ohmic nonlinear conduction 1D modeling accounts quantitatively well for the "multifractal random noise" dynamics of the electrical activity experimentally recorded in the left atrial posterior wall area. We further demonstrate that the multifractal properties of the numerical impulse energy are robust to changes in the model parameters.
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Affiliation(s)
- Guillaume Attuel
- Geometry and Statistics in Acquisition Data, Centre de Recherche INRIA, Talence, France
| | | | - Françoise Argoul
- Laboratoire Ondes et Matières d'Aquitaine, Université de Bordeaux, UMR 5798, CNRS, Talence, France
| | - Hussein Yahia
- Geometry and Statistics in Acquisition Data, Centre de Recherche INRIA, Talence, France
| | - Alain Arneodo
- Laboratoire Ondes et Matières d'Aquitaine, Université de Bordeaux, UMR 5798, CNRS, Talence, France
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26
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Kim JC, Large EW. Mode locking in periodically forced gradient frequency neural networks. Phys Rev E 2019; 99:022421. [PMID: 30934299 DOI: 10.1103/physreve.99.022421] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/13/2018] [Indexed: 11/07/2022]
Abstract
We study mode locking in a canonical model of gradient frequency neural networks under periodic forcing. The canonical model is a generic mathematical model for a network of nonlinear oscillators tuned to a range of distinct frequencies. It is mathematically more tractable than biological neuron models and allows close analysis of mode-locking behaviors. Here we analyze individual modes of synchronization for a periodically forced canonical model and present a complete set of driven behaviors for all parameter regimes available in the model. Using a closed-form approximation, we show that the Arnold tongue (i.e., locking region) for k:m synchronization gets narrower as k and m increase. We find that numerical simulations of the canonical model closely follow the analysis of individual modes when forcing is weak, but they deviate at high forcing amplitudes for which oscillator dynamics are simultaneously influenced by multiple modes of synchronization.
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Affiliation(s)
- Ji Chul Kim
- Department of Psychological Sciences and CT Institute for Brain and Cognitive Science, University of Connecticut, Storrs, Connecticut 06269, USA
| | - Edward W Large
- Department of Psychological Sciences and CT Institute for Brain and Cognitive Science, University of Connecticut, Storrs, Connecticut 06269, USA
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27
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Abnormal synchronization patterns in the electrical stimulation-contractile response coupling decrease with noise. Biosystems 2019; 180:63-70. [PMID: 30885687 DOI: 10.1016/j.biosystems.2019.03.004] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/07/2018] [Revised: 03/07/2019] [Accepted: 03/12/2019] [Indexed: 11/24/2022]
Abstract
Synchronization theory predicts that if an oscillator interacts with a rhythmical external force, then it should react to a rhythmical force by adjusting its frequency. Furthermore, noise is present in nature, and it affects the nervous and cardiovascular systems. In this paper, we analyze the heart as an oscillator, where noisy periodic electrical stimulation can be regarded as an external forcing. This study aimed to investigate, from an experimental point of view, whether noise can induce synchronization of higher order in the mechanical heart response. A Langendorff heart preparation was used to obtain two variables of the mechanical response, intensity of contractile force and heart rate. The experiments show frequency locking in the electrical stimulation-contractile response coupling with and without noise induced. The role of noise in the response of effector organs invites further investigation.
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28
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Davison EN, Aminzare Z, Dey B, Ehrich Leonard N. Mixed mode oscillations and phase locking in coupled FitzHugh-Nagumo model neurons. CHAOS (WOODBURY, N.Y.) 2019; 29:033105. [PMID: 30927863 DOI: 10.1063/1.5050178] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/27/2018] [Accepted: 02/08/2019] [Indexed: 06/09/2023]
Abstract
We study the dynamics of a low-dimensional system of coupled model neurons as a step towards understanding the vastly complex network of neurons in the brain. We analyze the bifurcation structure of a system of two model neurons with unidirectional coupling as a function of two physiologically relevant parameters: the external current input only to the first neuron and the strength of the coupling from the first to the second neuron. Leveraging a timescale separation, we prove necessary conditions for multiple timescale phenomena observed in the coupled system, including canard solutions and mixed mode oscillations. For a larger network of model neurons, we present a sufficient condition for phase locking when external inputs are heterogeneous. Finally, we generalize our results to directed trees of model neurons with heterogeneous inputs.
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Affiliation(s)
- Elizabeth N Davison
- Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, New Jersey 08540, USA
| | - Zahra Aminzare
- Department of Mathematics, University of Iowa, Iowa City, Iowa 52242, USA
| | - Biswadip Dey
- Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, New Jersey 08540, USA
| | - Naomi Ehrich Leonard
- Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, New Jersey 08540, USA
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29
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Kesmia M, Boughaba S, Jacquir S. Nonlinear dynamics of two-dimensional cardiac action potential duration mapping model with memory. J Math Biol 2019; 78:1529-1552. [DOI: 10.1007/s00285-018-1318-7] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/26/2018] [Revised: 12/02/2018] [Indexed: 12/27/2022]
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30
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Kembro JM, Cortassa S, Lloyd D, Sollott SJ, Aon MA. Mitochondrial chaotic dynamics: Redox-energetic behavior at the edge of stability. Sci Rep 2018; 8:15422. [PMID: 30337561 PMCID: PMC6194025 DOI: 10.1038/s41598-018-33582-w] [Citation(s) in RCA: 18] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/11/2018] [Accepted: 09/25/2018] [Indexed: 12/14/2022] Open
Abstract
Mitochondria serve multiple key cellular functions, including energy generation, redox balance, and regulation of apoptotic cell death, thus making a major impact on healthy and diseased states. Increasingly recognized is that biological network stability/instability can play critical roles in determining health and disease. We report for the first-time mitochondrial chaotic dynamics, characterizing the conditions leading from stability to chaos in this organelle. Using an experimentally validated computational model of mitochondrial function, we show that complex oscillatory dynamics in key metabolic variables, arising at the “edge” between fully functional and pathological behavior, sets the stage for chaos. Under these conditions, a mild, regular sinusoidal redox forcing perturbation triggers chaotic dynamics with main signature traits such as sensitivity to initial conditions, positive Lyapunov exponents, and strange attractors. At the “edge” mitochondrial chaos is exquisitely sensitive to the antioxidant capacity of matrix Mn superoxide dismutase as well as to the amplitude and frequency of the redox perturbation. These results have potential implications both for mitochondrial signaling determining health maintenance, and pathological transformation, including abnormal cardiac rhythms.
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Affiliation(s)
- Jackelyn M Kembro
- Instituto de Investigaciones Biológicas y Tecnológicas (IIByT-CONICET), and Instituto de Ciencia y Tecnología de los Alimentos, Cátedra de Química Biológica, Facultad de Ciencias Exactas, Físicas y Naturales, Universidad Nacional de Córdoba, Velez Sarsfield 1611, Córdoba, X5000HUA, Cordoba, Argentina
| | - Sonia Cortassa
- Laboratory of Cardiovascular Science, National Institute on Aging, NIH. 251 Bayview Boulevard, Baltimore, 21224, MD, USA
| | - David Lloyd
- School of Biosciences, Cardiff University, Main Building, Museum Avenue, Cardiff, CF10 3AT, Wales, UK
| | - Steven J Sollott
- Laboratory of Cardiovascular Science, National Institute on Aging, NIH. 251 Bayview Boulevard, Baltimore, 21224, MD, USA
| | - Miguel A Aon
- Laboratory of Cardiovascular Science, National Institute on Aging, NIH. 251 Bayview Boulevard, Baltimore, 21224, MD, USA.
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Guan Y, Murugesan M, Li LKB. Strange nonchaotic and chaotic attractors in a self-excited thermoacoustic oscillator subjected to external periodic forcing. CHAOS (WOODBURY, N.Y.) 2018; 28:093109. [PMID: 30278637 DOI: 10.1063/1.5026252] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/17/2018] [Accepted: 08/28/2018] [Indexed: 06/08/2023]
Abstract
We experimentally investigate the synchronization dynamics of a self-excited thermoacoustic system forced beyond its phase-locked state. The system consists of a laminar premixed flame in a tube combustor subjected to periodic acoustic forcing. On increasing the forcing amplitude above that required for phase locking, we find that the system can transition out of phase locking and into chaos, which is consistent with the Afraimovich-Shilnikov theorem for the breakdown of a phase-locked torus. However, we also find some unexpected behavior, most notably the emergence of a strange nonchaotic attractor (SNA) before the onset of chaos. We verify the existence of the SNA and chaotic attractor by examining the correlation dimension, the autocorrelation function, the power-law scaling in the Fourier amplitude spectrum, the permutation entropy in a pseudoperiodic surrogate test, and the permutation spectrum. In summary, this study explores the SNA and chaotic dynamics of a thermoacoustic system forced beyond its phase-locked state, opening up new pathways for the development of alternative strategies to control self-excited thermoacoustic oscillations in combustion devices such as gas turbines and rocket engines.
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Affiliation(s)
- Yu Guan
- Department of Mechanical and Aerospace Engineering, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong
| | - Meenatchidevi Murugesan
- Department of Mechanical and Aerospace Engineering, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong
| | - Larry K B Li
- Department of Mechanical and Aerospace Engineering, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong
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Landaw J, Qu Z. Memory-induced nonlinear dynamics of excitation in cardiac diseases. Phys Rev E 2018; 97:042414. [PMID: 29758700 PMCID: PMC6542282 DOI: 10.1103/physreve.97.042414] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/08/2017] [Indexed: 11/07/2022]
Abstract
Excitable cells, such as cardiac myocytes, exhibit short-term memory, i.e., the state of the cell depends on its history of excitation. Memory can originate from slow recovery of membrane ion channels or from accumulation of intracellular ion concentrations, such as calcium ion or sodium ion concentration accumulation. Here we examine the effects of memory on excitation dynamics in cardiac myocytes under two diseased conditions, early repolarization and reduced repolarization reserve, each with memory from two different sources: slow recovery of a potassium ion channel and slow accumulation of the intracellular calcium ion concentration. We first carry out computer simulations of action potential models described by differential equations to demonstrate complex excitation dynamics, such as chaos. We then develop iterated map models that incorporate memory, which accurately capture the complex excitation dynamics and bifurcations of the action potential models. Finally, we carry out theoretical analyses of the iterated map models to reveal the underlying mechanisms of memory-induced nonlinear dynamics. Our study demonstrates that the memory effect can be unmasked or greatly exacerbated under certain diseased conditions, which promotes complex excitation dynamics, such as chaos. The iterated map models reveal that memory converts a monotonic iterated map function into a nonmonotonic one to promote the bifurcations leading to high periodicity and chaos.
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Affiliation(s)
- Julian Landaw
- Department of Medicine (Cardiology), University of California, Los Angeles, California 90095, USA and Department of Biomathematics, University of California, Los Angeles, California 90095, USA
| | - Zhilin Qu
- Department of Medicine (Cardiology), University of California, Los Angeles, California 90095, USA and Department of Biomathematics, University of California, Los Angeles, California 90095, USA
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Liu W, Kim TY, Huang X, Liu MB, Koren G, Choi BR, Qu Z. Mechanisms linking T-wave alternans to spontaneous initiation of ventricular arrhythmias in rabbit models of long QT syndrome. J Physiol 2018; 596:1341-1355. [PMID: 29377142 DOI: 10.1113/jp275492] [Citation(s) in RCA: 26] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/31/2017] [Accepted: 01/23/2018] [Indexed: 01/23/2023] Open
Abstract
KEY POINTS T-wave alternans (TWA) and T-wave lability (TWL) are precursors of ventricular arrhythmias in long QT syndrome; however, the mechanistic link remains to be clarified. Computer simulations show that action potential duration (APD) prolongation and slowed heart rates promote APD alternans and chaos, manifesting as TWA and TWL, respectively. Regional APD alternans and chaos can exacerbate pre-existing or induce de novo APD dispersion, which combines with enhanced ICa,L to result in premature ventricular complexes (PVCs) originating from the APD gradient region. These PVCs can directly degenerate into re-entrant arrhythmias without the need for an additional tissue substrate or further exacerbate the APD dispersion to cause spontaneous initiation of ventricular arrhythmias. Experiments conducted in transgenic long QT rabbits show that PVC alternans occurs at slow heart rates, preceding spontaneous intuition of ventricular arrhythmias. ABSTRACT T-wave alternans (TWA) and irregular beat-to-beat T-wave variability or T-wave lability (TWL), the ECG manifestations of action potential duration (APD) alternans and variability, are precursors of ventricular arrhythmias in long QT syndromes. TWA and TWL in patients tend to occur at normal heart rates and are usually potentiated by bradycardia. Whether or how TWA and TWL at normal or slow heart rates are causally linked to arrhythmogenesis remains unknown. In the present study, we used computer simulations and experiments of a transgenic rabbit model of long QT syndrome to investigate the underlying mechanisms. Computer simulations showed that APD prolongation and slowed heart rates caused early afterdepolarization-mediated APD alternans and chaos, manifesting as TWA and TWL, respectively. Regional APD alternans and chaos exacerbated pre-existing APD dispersion and, in addition, APD chaos could also induce APD dispersion de novo via chaos desynchronization. Increased APD dispersion, combined with substantially enhanced ICa,L , resulted in a tissue-scale dynamical instability that gave rise to the spontaneous occurrence of unidirectionally propagating premature ventricular complexes (PVCs) originating from the APD gradient region. These PVCs could directly degenerate into re-entrant arrhythmias without the need for an additional tissue substrate or could block the following sinus beat to result in a longer RR interval, which further exacerbated the APD dispersion giving rise to the spontaneous occurrence of ventricular arrhythmias. Slow heart rate-induced PVC alternans was observed in experiments of transgenic LQT2 rabbits under isoproterenol, which was associated with increased APD dispersion and spontaneous occurrence of ventricular arrhythmias, in agreement with the theoretical predictions.
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Affiliation(s)
- Weiqing Liu
- Department of Medicine, University of California, Los Angeles, California, USA.,School of Science, Jiangxi University of Science and Technology, Ganzhou, China
| | - Tae Yun Kim
- Cardiovascular Research Center, Division of Cardiology, Rhode Island Hospital, Warren Alpert Medical School of Brown University, Providence, Rhode Island, USA
| | - Xiaodong Huang
- Department of Medicine, University of California, Los Angeles, California, USA.,Department of Physics, South China University of Technology, Guangzhou, China
| | - Michael B Liu
- Department of Medicine, University of California, Los Angeles, California, USA
| | - Gideon Koren
- Cardiovascular Research Center, Division of Cardiology, Rhode Island Hospital, Warren Alpert Medical School of Brown University, Providence, Rhode Island, USA
| | - Bum-Rak Choi
- Cardiovascular Research Center, Division of Cardiology, Rhode Island Hospital, Warren Alpert Medical School of Brown University, Providence, Rhode Island, USA
| | - Zhilin Qu
- Department of Medicine, University of California, Los Angeles, California, USA.,Department of Biomathematics, University of California, Los Angeles, California, USA
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Yambe T, Abe Y, Yoshizawa M, Imachi K, Tabayashi K, Takayasu H, Takeda H, Gouhara K, Nitta S. Strange Hemodynamic Attractor Parameter with 1/R Total Artificial Heart Automatic Control Algorithm. Int J Artif Organs 2018. [DOI: 10.1177/039139889601900508] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
Abstract
To evaluate the automatic control algorithm of the total artificial heart (TAH) as an entity, and not just as parts, a non-linear mathematical analyzing technique including chaos theory was utilized. Chronic experiments on the biventricular bypass type artificial heart implantation were performed in healthy adult goats after the natural ventricles were removed. Hemodynamic time series data were recorded under the awake standing condition with TAH 1/R and fixed driving. Time series data were recorded on a magnetic tape and analyzed on a personal computer system with an A-D converter. Using the nonlinear mathematical technique, the time series data were embedded into the phase space and the Lyapunov numerical method was carried out for the quantitative evaluation of the sensitive dependence on the initial condition of the reconstructed attractor. Calculation of the largest Lyapunov exponents suggested that the reconstructed attractor of the left pump output during TAH 1/R control was a larger dimensional strange attractor, a characteristic pattern of deterministic chaos. A total system indicating chaotic dynamics was thought to be a flexible and intelligent control system. Thus, our results suggest that 1/R TAH control may be suitable for the biventricular assist type total artificial heart.
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Affiliation(s)
- T. Yambe
- Department of Medical Engineering and Cardiology, Division of Organ Pathophysiology, Institute of Development, Aging and Cancer, Tohoku University, Sendai
| | - Y. Abe
- The Institute of Medical Electronics, Faculty of Medicine, University of Tokyo, Tokyo
| | - M. Yoshizawa
- Graduate School of Information Sciences, Tohoku University, Sendai
| | - K. Imachi
- The Institute of Medical Electronics, Faculty of Medicine, University of Tokyo, Tokyo
| | - K. Tabayashi
- Department of Thoracic and Cardiovascular Surgery, Tohoku University School of Medicine, Sendai
| | - H. Takayasu
- Graduate School of Information Sciences, Tohoku University, Sendai
| | - H. Takeda
- Faculty of Engineering, Tohoku-gakuin University, Sendai
| | - K. Gouhara
- Faculty of Engineering, Hokkado University, Sapporo - Japan
| | - S. Nitta
- Department of Medical Engineering and Cardiology, Division of Organ Pathophysiology, Institute of Development, Aging and Cancer, Tohoku University, Sendai
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Notarnicola S, Iemini F, Rossini D, Fazio R, Silva A, Russomanno A. From localization to anomalous diffusion in the dynamics of coupled kicked rotors. Phys Rev E 2018; 97:022202. [PMID: 29548167 DOI: 10.1103/physreve.97.022202] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/26/2017] [Indexed: 06/08/2023]
Abstract
We study the effect of many-body quantum interference on the dynamics of coupled periodically kicked systems whose classical dynamics is chaotic and shows an unbounded energy increase. We specifically focus on an N-coupled kicked rotors model: We find that the interplay of quantumness and interactions dramatically modifies the system dynamics, inducing a transition between energy saturation and unbounded energy increase. We discuss this phenomenon both numerically and analytically through a mapping onto an N-dimensional Anderson model. The thermodynamic limit N→∞, in particular, always shows unbounded energy growth. This dynamical delocalization is genuinely quantum and very different from the classical one: Using a mean-field approximation, we see that the system self-organizes so that the energy per site increases in time as a power law with exponent smaller than 1. This wealth of phenomena is a genuine effect of quantum interference: The classical system for N≥2 always behaves ergodically with an energy per site linearly increasing in time. Our results show that quantum mechanics can deeply alter the regularity or ergodicity properties of a many-body-driven system.
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Affiliation(s)
| | - Fernando Iemini
- Abdus Salam ICTP, Strada Costiera 11, I-34151 Trieste, Italy
| | - Davide Rossini
- Dipartimento di Fisica, Università di Pisa and INFN, Largo Pontecorvo 3, I-56127 Pisa, Italy
| | - Rosario Fazio
- Abdus Salam ICTP, Strada Costiera 11, I-34151 Trieste, Italy
- NEST, Scuola Normale Superiore & Istituto Nanoscienze-CNR, I-56126 Pisa, Italy
| | | | - Angelo Russomanno
- Abdus Salam ICTP, Strada Costiera 11, I-34151 Trieste, Italy
- NEST, Scuola Normale Superiore & Istituto Nanoscienze-CNR, I-56126 Pisa, Italy
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36
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Li S, Zhang G, Wang J, Deng B. Firing regularity control of single neuron based on closed-loop ISI clamp. Neurocomputing 2018. [DOI: 10.1016/j.neucom.2017.09.008] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
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37
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Kuang D, Yang R, Chen X, Lao G, Wu F, Huang X, Lv R, Zhang L, Song C, Ou S. Depression recognition according to heart rate variability using Bayesian Networks. J Psychiatr Res 2017; 95:282-287. [PMID: 28926794 DOI: 10.1016/j.jpsychires.2017.09.012] [Citation(s) in RCA: 27] [Impact Index Per Article: 3.9] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 06/24/2017] [Revised: 08/20/2017] [Accepted: 09/08/2017] [Indexed: 11/18/2022]
Abstract
BACKGROUND Doctors mainly use scale tests and subjective judgment in the clinical diagnosis of depression. Researches have demonstrated that depression is associated with the dysfunction of the autonomic nervous system (ANS), where its modulation can be evaluated by heart rate variability (HRV). Depression patients have lower HRV than healthy subjects. Therefore, HRV may be used to distinguish depression patients from healthy people. METHODS HRV signals were collected from 76 female subjects composed of 38 depression patients and 38 healthy people. Time domain, frequency domain, and non-linear features were extracted from the HRV signals of these subjects, who were subjected to the Ewing test as an ANS stimulus. Then, these multiple features were input into Bayesian networks, served as a classifier, to distinguish depression patients from healthy people. Hence, accuracy, sensitivity, and specificity were calculated to evaluate the performance of the classifier. RESULTS Recognition results indicate 86.4% accuracy, 89.5% sensitivity, and 84.2% specificity. The individuals subjected to the Ewing test showed better recognition results than those at individual test states (resting state, deep breathing state, Valsalva state, and standing state) of the Ewing test. The root mean square of successive differences (RMSSD) of the HRV exhibits a significant relevance with recognition. CONCLUSION Bayesian networks can be applied to the recognition of depression patients from healthy people and the recognition results demonstrate the significant association between depression and HRV. The Ewing test is a good ANS stimulus for acquiring the difference of HRV between depression patients and healthy people to recognize depression. The RMSSD of the HRV is important in recognition and may be a significant index in distinguishing depression patients from healthy people.
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Affiliation(s)
- Danni Kuang
- Department of Biomedical Engineering, South China University of Technology, Guangzhou, China
| | - Rongqian Yang
- Department of Biomedical Engineering, South China University of Technology, Guangzhou, China.
| | - Xiuwen Chen
- Department of Biomedical Engineering, South China University of Technology, Guangzhou, China
| | - Guohui Lao
- The Affiliated Brain Hospital of Guangzhou Medical University (Guangzhou Huiai Hospital), Guangzhou, China
| | - Fengchun Wu
- The Affiliated Brain Hospital of Guangzhou Medical University (Guangzhou Huiai Hospital), Guangzhou, China
| | - Xiong Huang
- The Affiliated Brain Hospital of Guangzhou Medical University (Guangzhou Huiai Hospital), Guangzhou, China
| | - Ruixue Lv
- Shenzhen Sayes Medical Technology Co., Ltd., Shenzhen, China
| | - Lei Zhang
- Shenzhen Sayes Medical Technology Co., Ltd., Shenzhen, China
| | - Chuanxu Song
- Shenzhen Sayes Medical Technology Co., Ltd., Shenzhen, China
| | - Shanxing Ou
- General Hospital of Guangzhou Military Command of PLA, Guangzhou, China
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38
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Gizzi A, Loppini A, Cherry EM, Cherubini C, Fenton FH, Filippi S. Multi-band decomposition analysis: application to cardiac alternans as a function of temperature. Physiol Meas 2017; 38:833-847. [DOI: 10.1088/1361-6579/aa64af] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
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39
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Period doubling cascades of limit cycles in cardiac action potential models as precursors to chaotic early Afterdepolarizations. BMC SYSTEMS BIOLOGY 2017; 11:42. [PMID: 28376924 PMCID: PMC5379775 DOI: 10.1186/s12918-017-0422-4] [Citation(s) in RCA: 18] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 10/06/2016] [Accepted: 03/24/2017] [Indexed: 12/02/2022]
Abstract
Background Early afterdepolarizations (EADs) are pathological voltage oscillations during the repolarization phase of cardiac action potentials (APs). EADs are caused by drugs, oxidative stress or ion channel disease, and they are considered as potential precursors to cardiac arrhythmias in recent attempts to redefine the cardiac drug safety paradigm. The irregular behaviour of EADs observed in experiments has been previously attributed to chaotic EAD dynamics under periodic pacing, made possible by a homoclinic bifurcation in the fast subsystem of the deterministic AP system of differential equations. Results In this article we demonstrate that a homoclinic bifurcation in the fast subsystem of the action potential model is neither a necessary nor a sufficient condition for the genesis of chaotic EADs. We rather argue that a cascade of period doubling (PD) bifurcations of limit cycles in the full AP system paves the way to chaotic EAD dynamics across a variety of models including a) periodically paced and spontaneously active cardiomyocytes, b) periodically paced and non-active cardiomyocytes as well as c) unpaced and spontaneously active cardiomyocytes. Furthermore, our bifurcation analysis reveals that chaotic EAD dynamics may coexist in a stable manner with fully regular AP dynamics, where only the initial conditions decide which type of dynamics is displayed. Conclusions EADs are a potential source of cardiac arrhythmias and hence are of relevance both from the viewpoint of drug cardiotoxicity testing and the treatment of cardiomyopathies. The model-independent association of chaotic EADs with period doubling cascades of limit cycles introduced in this article opens novel opportunities to study chaotic EADs by means of bifurcation control theory and inverse bifurcation analysis. Furthermore, our results may shed new light on the synchronization and propagation of chaotic EADs in homogeneous and heterogeneous multicellular and cardiac tissue preparations. Electronic supplementary material The online version of this article (doi:10.1186/s12918-017-0422-4) contains supplementary material, which is available to authorized users.
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40
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Landaw J, Garfinkel A, Weiss JN, Qu Z. Memory-Induced Chaos in Cardiac Excitation. PHYSICAL REVIEW LETTERS 2017; 118:138101. [PMID: 28409990 PMCID: PMC5519322 DOI: 10.1103/physrevlett.118.138101] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/08/2016] [Indexed: 05/03/2023]
Abstract
Excitable systems display memory, but how memory affects the excitation dynamics of such systems remains to be elucidated. Here we use computer simulation of cardiac action potential models to demonstrate that memory can cause dynamical instabilities that result in complex excitation dynamics and chaos. We develop an iterated map model that correctly describes these dynamics and show that memory converts a monotonic first return map of action potential duration into a nonmonotonic one, resulting in a period-doubling bifurcation route to chaos.
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Affiliation(s)
- Julian Landaw
- Department of Medicine (Cardiology), University of California, Los Angeles, California 90095, USA
- Department of Biomathematics, University of California, Los Angeles, California 90095, USA
| | - Alan Garfinkel
- Department of Medicine (Cardiology), University of California, Los Angeles, California 90095, USA
- Department of Integrative Biology and Physiology, University of California, Los Angeles, California 90095, USA
| | - James N. Weiss
- Department of Medicine (Cardiology), University of California, Los Angeles, California 90095, USA
- Department of Physiology, University of California, Los Angeles, California 90095, USA
| | - Zhilin Qu
- Department of Medicine (Cardiology), University of California, Los Angeles, California 90095, USA
- Department of Biomathematics, University of California, Los Angeles, California 90095, USA
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41
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Yalcin GC, Velarde C, Robledo A. Entropies for severely contracted configuration space. Heliyon 2016; 1:e00045. [PMID: 27441229 PMCID: PMC4945624 DOI: 10.1016/j.heliyon.2015.e00045] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/09/2015] [Revised: 10/28/2015] [Accepted: 10/29/2015] [Indexed: 11/24/2022] Open
Abstract
We demonstrate that dual entropy expressions of the Tsallis type apply naturally to statistical-mechanical systems that experience an exceptional contraction of their configuration space. The entropic index [Formula: see text] describes the contraction process, while the dual index [Formula: see text] defines the contraction dimension at which extensivity is restored. We study this circumstance along the three routes to chaos in low-dimensional nonlinear maps where the attractors at the transitions, between regular and chaotic behavior, drive phase-space contraction for ensembles of trajectories. We illustrate this circumstance for properties of systems that find descriptions in terms of nonlinear maps. These are size-rank functions, urbanization and similar processes, and settings where frequency locking takes place.
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Affiliation(s)
- G Cigdem Yalcin
- Department of Physics, Istanbul University, 34134, Vezneciler, Istanbul, Turkey
| | - Carlos Velarde
- Instituto de Matemáticas Aplicadas y Sistemas, Universidad Nacional Autónoma de México, Apartado Postal 20-364, México 01000 Distrito Federal, Mexico
| | - Alberto Robledo
- Instituto de Física y Centro de Ciencias de la Complejidad, Universidad Nacional Autónoma de México, Apartado Postal 20-364, México 01000 Distrito Federal, Mexico
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Veber T, Schreiberová L, Schreiber I. Use of Phase Transition Curves for Testing Models of the pH-Oscillatory Hydrogen Peroxide-Thiosulfate-Sulfite Reaction. J Phys Chem B 2016; 120:2929-41. [PMID: 26900770 DOI: 10.1021/acs.jpcb.6b00441] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
The reaction system hydrogen peroxide-thiosulfate-sulfite in diluted sulfuric acid (HPTS) displays strongly nonlinear dynamics when operated in a continuous-flow stirred tank reactor. Due to a crucial role of hydrogen ion during the reaction, this system is a prime example of an inorganic pH-oscillator. Under specific external conditions the system exhibits multiple steady states, periodic oscillations and chaotic behavior. We focus on evaluating alternative kinetic models by exploring phase resetting of the periodic oscillatory regime caused by a single-pulse perturbation with various reacting species. Phase transition curve (PTC), the plot of phase after the resetting against the phase of perturbation, is a convenient characteristic of the oscillatory dynamics adopted as a major tool in this work. Experimental results for hydrogen ions, hydroxide ions, thiosulfate ions, sulfite ions, and hydrogen sulfite ions used as perturbants are systematically compared with calculations under corresponding conditions using two available reaction mechanisms. In addition, we use the stoichiometric network analysis to identify possible core oscillatory subnetworks in the models and choose the one that corresponds best to the measured PTCs.
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Affiliation(s)
- Tomáš Veber
- Department of Chemical Engineering, University of Chemistry and Technology , Prague, Technická 5, 166 28 Prague 6, Czech Republic
| | - Lenka Schreiberová
- Department of Chemical Engineering, University of Chemistry and Technology , Prague, Technická 5, 166 28 Prague 6, Czech Republic
| | - Igor Schreiber
- Department of Chemical Engineering, University of Chemistry and Technology , Prague, Technická 5, 166 28 Prague 6, Czech Republic
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43
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Prudat Y, Madhvani RV, Angelini M, Borgstom NP, Garfinkel A, Karagueuzian HS, Weiss JN, de Lange E, Olcese R, Kucera JP. Stochastic pacing reveals the propensity to cardiac action potential alternans and uncovers its underlying dynamics. J Physiol 2016; 594:2537-53. [PMID: 26563830 DOI: 10.1113/jp271573] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/10/2015] [Accepted: 11/05/2015] [Indexed: 12/30/2022] Open
Abstract
KEY POINTS Beat-to-beat alternation (alternans) of the cardiac action potential duration is known to precipitate life-threatening arrhythmias and can be driven by the kinetics of voltage-gated membrane currents or by instabilities in intracellular calcium fluxes. To prevent alternans and associated arrhythmias, suitable markers must be developed to quantify the susceptibility to alternans; previous theoretical studies showed that the eigenvalue of the alternating eigenmode represents an ideal marker of alternans. Using rabbit ventricular myocytes, we show that this eigenvalue can be estimated in practice by pacing these cells at intervals varying stochastically. We also show that stochastic pacing permits the estimation of further markers distinguishing between voltage-driven and calcium-driven alternans. Our study opens the perspective to use stochastic pacing during clinical investigations and in patients with implanted pacing devices to determine the susceptibility to, and the type of alternans, which are both important to guide preventive or therapeutic measures. ABSTRACT Alternans of the cardiac action potential (AP) duration (APD) is a well-known arrhythmogenic mechanism. APD depends on several preceding diastolic intervals (DIs) and APDs, which complicates the prediction of alternans. Previous theoretical studies pinpointed a marker called λalt that directly quantifies how an alternating perturbation persists over successive APs. When the propensity to alternans increases, λalt decreases from 0 to -1. Our aim was to quantify λalt experimentally using stochastic pacing and to examine whether stochastic pacing allows discriminating between voltage-driven and Ca(2+) -driven alternans. APs were recorded in rabbit ventricular myocytes paced at cycle lengths (CLs) decreasing progressively and incorporating stochastic variations. Fitting APD with a function of two previous APDs and CLs permitted us to estimate λalt along with additional markers characterizing whether the dependence of APD on previous DIs or CLs is strong (typical for voltage-driven alternans) or weak (Ca(2+) -driven alternans). During the recordings, λalt gradually decreased from around 0 towards -1. Intermittent alternans appeared when λalt reached -0.8 and was followed by sustained alternans. The additional markers detected that alternans was Ca(2+) driven in control experiments and voltage driven in the presence of ryanodine. This distinction could be made even before alternans was manifest (specificity/sensitivity >80% for -0.4 > λalt > -0.5). These observations were confirmed in a mathematical model of a rabbit ventricular myocyte. In conclusion, stochastic pacing allows the practical estimation of λalt to reveal the onset of alternans and distinguishes between voltage-driven and Ca(2+) -driven mechanisms, which is important since these two mechanisms may precipitate arrhythmias in different manners.
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Affiliation(s)
- Yann Prudat
- Department of Physiology, University of Bern, Bern, Switzerland
| | - Roshni V Madhvani
- Department of Anesthesiology and Perioperative Medicine, Division of Molecular Medicine, David Geffen School of Medicine, University of California, Los Angeles, CA, USA
| | - Marina Angelini
- Department of Anesthesiology and Perioperative Medicine, Division of Molecular Medicine, David Geffen School of Medicine, University of California, Los Angeles, CA, USA
| | - Nils P Borgstom
- Department of Bioengineering, University of California, Los Angeles, CA, USA
| | - Alan Garfinkel
- Cardiovascular Research Laboratory, David Geffen School of Medicine, University of California, Los Angeles, CA, USA
| | - Hrayr S Karagueuzian
- Cardiovascular Research Laboratory, David Geffen School of Medicine, University of California, Los Angeles, CA, USA
| | - James N Weiss
- Cardiovascular Research Laboratory, David Geffen School of Medicine, University of California, Los Angeles, CA, USA.,Department of Physiology, David Geffen School of Medicine, University of California, Los Angeles, CA, USA.,Department of Medicine (Cardiology), David Geffen School of Medicine, University of California, Los Angeles, CA, USA
| | - Enno de Lange
- Department of Knowledge Engineering, Maastricht University, Maastricht, The Netherlands
| | - Riccardo Olcese
- Department of Anesthesiology and Perioperative Medicine, Division of Molecular Medicine, David Geffen School of Medicine, University of California, Los Angeles, CA, USA.,Cardiovascular Research Laboratory, David Geffen School of Medicine, University of California, Los Angeles, CA, USA.,Department of Physiology, David Geffen School of Medicine, University of California, Los Angeles, CA, USA
| | - Jan P Kucera
- Department of Physiology, University of Bern, Bern, Switzerland
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Pearl Mizrahi S, Sandler O, Lande-Diner L, Balaban NQ, Simon I. Distinguishing between stochasticity and determinism: Examples from cell cycle duration variability. Bioessays 2015; 38:8-13. [PMID: 26628302 DOI: 10.1002/bies.201500113] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/31/2023]
Abstract
We describe a recent approach for distinguishing between stochastic and deterministic sources of variability, focusing on the mammalian cell cycle. Variability between cells is often attributed to stochastic noise, although it may be generated by deterministic components. Interestingly, lineage information can be used to distinguish between variability and determinism. Analysis of correlations within a lineage of the mammalian cell cycle duration revealed its deterministic nature. Here, we discuss the sources of such variability and the possibility that the underlying deterministic process is due to the circadian clock. Finally, we discuss the "kicked cell cycle" model and its implication on the study of the cell cycle in healthy and cancerous tissues.
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Affiliation(s)
- Sivan Pearl Mizrahi
- Racah Institute of Physics, Edmond J. Safra Campus, The Hebrew University, Jerusalem, Israel.,Department of Microbiology and Molecular Genetics, IMRIC, The Hebrew University Hadassah Medical School, Jerusalem, Israel
| | - Oded Sandler
- Department of Molecular Cell Biology, Weizmann Institute of Science, Rehovot, Israel
| | | | - Nathalie Q Balaban
- Racah Institute of Physics, Edmond J. Safra Campus, The Hebrew University, Jerusalem, Israel
| | - Itamar Simon
- Department of Microbiology and Molecular Genetics, IMRIC, The Hebrew University Hadassah Medical School, Jerusalem, Israel
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45
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Ahmed H, Ushirobira R, Efimov D. On robustness of phase resetting to cell division under entrainment. J Theor Biol 2015; 387:206-13. [DOI: 10.1016/j.jtbi.2015.09.033] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/05/2015] [Revised: 09/03/2015] [Accepted: 09/28/2015] [Indexed: 12/01/2022]
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46
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Klinshov V, Lücken L, Shchapin D, Nekorkin V, Yanchuk S. Emergence and combinatorial accumulation of jittering regimes in spiking oscillators with delayed feedback. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 92:042914. [PMID: 26565311 DOI: 10.1103/physreve.92.042914] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/11/2015] [Indexed: 06/05/2023]
Abstract
Interaction via pulses is common in many natural systems, especially neuronal. In this article we study one of the simplest possible systems with pulse interaction: a phase oscillator with delayed pulsatile feedback. When the oscillator reaches a specific state, it emits a pulse, which returns after propagating through a delay line. The impact of an incoming pulse is described by the oscillator's phase reset curve (PRC). In such a system we discover an unexpected phenomenon: for a sufficiently steep slope of the PRC, a periodic regular spiking solution bifurcates with several multipliers crossing the unit circle at the same parameter value. The number of such critical multipliers increases linearly with the delay and thus may be arbitrary large. This bifurcation is accompanied by the emergence of numerous "jittering" regimes with nonequal interspike intervals (ISIs). Each of these regimes corresponds to a periodic solution of the system with a period roughly proportional to the delay. The number of different "jittering" solutions emerging at the bifurcation point increases exponentially with the delay. We describe the combinatorial mechanism that underlies the emergence of such a variety of solutions. In particular, we show how a periodic solution exhibiting several distinct ISIs can imply the existence of multiple other solutions obtained by rearranging of these ISIs. We show that the theoretical results for phase oscillators accurately predict the behavior of an experimentally implemented electronic oscillator with pulsatile feedback.
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Affiliation(s)
- Vladimir Klinshov
- Institute of Applied Physics of the Russian Academy of Sciences, 46 Ul'yanov Street, 603950, Nizhny Novgorod, Russia
| | - Leonhard Lücken
- Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstrasse 39, 10117, Berlin, Germany
| | - Dmitry Shchapin
- Institute of Applied Physics of the Russian Academy of Sciences, 46 Ul'yanov Street, 603950, Nizhny Novgorod, Russia
| | - Vladimir Nekorkin
- Institute of Applied Physics of the Russian Academy of Sciences, 46 Ul'yanov Street, 603950, Nizhny Novgorod, Russia
- University of Nizhny Novgorod, 23 Prospekt Gagarina, 603950, Nizhny Novgorod, Russia
| | - Serhiy Yanchuk
- Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstrasse 39, 10117, Berlin, Germany
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47
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Glass L. Dynamical disease: Challenges for nonlinear dynamics and medicine. CHAOS (WOODBURY, N.Y.) 2015; 25:097603. [PMID: 26428556 DOI: 10.1063/1.4915529] [Citation(s) in RCA: 21] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
Dynamical disease refers to illnesses that are associated with striking changes in the dynamics of some bodily function. There is a large literature in mathematics and physics which proposes mathematical models for the physiological systems and carries out analyses of the properties of these models using nonlinear dynamics concepts involving analyses of the stability and bifurcations of attractors. This paper discusses how these concepts can be applied to medicine.
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Affiliation(s)
- Leon Glass
- Department of Physiology, McGill University, 3655 Promenade Sir William Osler, Montreal, Quebec H3G 1Y6, Canada
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48
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Predicting the onset of period-doubling bifurcations in noisy cardiac systems. Proc Natl Acad Sci U S A 2015; 112:9358-63. [PMID: 26170301 DOI: 10.1073/pnas.1424320112] [Citation(s) in RCA: 39] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
Biological, physical, and social systems often display qualitative changes in dynamics. Developing early warning signals to predict the onset of these transitions is an important goal. The current work is motivated by transitions of cardiac rhythms, where the appearance of alternating features in the timing of cardiac events is often a precursor to the initiation of serious cardiac arrhythmias. We treat embryonic chick cardiac cells with a potassium channel blocker, which leads to the initiation of alternating rhythms. We associate this transition with a mathematical instability, called a period-doubling bifurcation, in a model of the cardiac cells. Period-doubling bifurcations have been linked to the onset of abnormal alternating cardiac rhythms, which have been implicated in cardiac arrhythmias such as T-wave alternans and various tachycardias. Theory predicts that in the neighborhood of the transition, the system's dynamics slow down, leading to noise amplification and the manifestation of oscillations in the autocorrelation function. Examining the aggregates' interbeat intervals, we observe the oscillations in the autocorrelation function and noise amplification preceding the bifurcation. We analyze plots--termed return maps--that relate the current interbeat interval with the following interbeat interval. Based on these plots, we develop a quantitative measure using the slope of the return map to assess how close the system is to the bifurcation. Furthermore, the slope of the return map and the lag-1 autocorrelation coefficient are equal. Our results suggest that the slope and the lag-1 autocorrelation coefficient represent quantitative measures to predict the onset of abnormal alternating cardiac rhythms.
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49
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Huaguang G, Zhiguo Z, Bing J, Shenggen C. Dynamics of on-off neural firing patterns and stochastic effects near a sub-critical Hopf bifurcation. PLoS One 2015; 10:e0121028. [PMID: 25867027 PMCID: PMC4395087 DOI: 10.1371/journal.pone.0121028] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/29/2014] [Accepted: 02/07/2015] [Indexed: 11/18/2022] Open
Abstract
On-off firing patterns, in which repetition of clusters of spikes are interspersed with epochs of subthreshold oscillations or quiescent states, have been observed in various nervous systems, but the dynamics of this event remain unclear. Here, we report that on-off firing patterns observed in three experimental models (rat sciatic nerve subject to chronic constrictive injury, rat CA1 pyramidal neuron, and rabbit blood pressure baroreceptor) appeared as an alternation between quiescent state and burst containing multiple period-1 spikes over time. Burst and quiescent state had various durations. The interspike interval (ISI) series of on-off firing pattern was suggested as stochastic using nonlinear prediction and autocorrelation function. The resting state was changed to a period-1 firing pattern via on-off firing pattern as the potassium concentration, static pressure, or depolarization current was changed. During the changing process, the burst duration of on-off firing pattern increased and the duration of the quiescent state decreased. Bistability of a limit cycle corresponding to period-1 firing and a focus corresponding to resting state was simulated near a sub-critical Hopf bifurcation point in the deterministic Morris-Lecar (ML) model. In the stochastic ML model, noise-induced transitions between the coexisting regimes formed an on-off firing pattern, which closely matched that observed in the experiment. In addition, noise-induced exponential change in the escape rate from the focus, and noise-induced coherence resonance were identified. The distinctions between the on-off firing pattern and stochastic firing patterns generated near three other types of bifurcations of equilibrium points, as well as other viewpoints on the dynamics of on-off firing pattern, are discussed. The results not only identify the on-off firing pattern as noise-induced stochastic firing pattern near a sub-critical Hopf bifurcation point, but also offer practical indicators to discriminate bifurcation types and neural excitability types.
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Affiliation(s)
- Gu Huaguang
- School of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai 200092, China
- * E-mail:
| | - Zhao Zhiguo
- School of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai 200092, China
| | - Jia Bing
- Centre for Computational Systems Biology, Fudan University, Shanghai 200433, China
| | - Chen Shenggen
- School of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai 200092, China
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50
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Huang X, Cui X. The functions of atrial strands interdigitating with and penetrating into sinoatrial node: a theoretical study of the problem. PLoS One 2015; 10:e0118623. [PMID: 25803434 PMCID: PMC4372425 DOI: 10.1371/journal.pone.0118623] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/10/2014] [Accepted: 01/21/2015] [Indexed: 11/18/2022] Open
Abstract
The sinoatrial node (SAN)-atrium system is closely involved with the activity of heart beating. The impulse propagation and phase-locking behaviors of this system are of theoretical interest. Some experiments have revealed that atrial strands (ASs) interdigitate with and penetrate into the SAN, whereby the SAN-atrium system works as a complex network. In this study, the functions of ASs are numerically investigated using realistic cardiac models. The results indicate that the ASs penetrating into the central region of the SAN play a major role in propagating excitation into the atrium. This is because the threshold SAN-AS coupling for an AS to function as an alternative path for propagation is lower at the center than at the periphery. However, ASs penetrating into the peripheral region have a great effect in terms of enlarging the 1:1 entrainment range of the SAN because the automaticity of the SAN is evidently reduced by ASs. Moreover, an analytical formula for approximating the enlargement of the 1:1 range is derived.
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Affiliation(s)
- Xiaodong Huang
- Department of Physics, South China University of Technology, Guangzhou, China
- * E-mail:
| | - Xiaohua Cui
- School of Systems Science, Beijing Normal University, Beijing, China
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