1
|
Quiroz-Juárez MA, Rosales-Juárez JA, Jiménez-Ramírez O, Vázquez-Medina R, Aragón JL. ECG Patient Simulator Based on Mathematical Models. SENSORS (BASEL, SWITZERLAND) 2022; 22:5714. [PMID: 35957270 PMCID: PMC9370912 DOI: 10.3390/s22155714] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 06/16/2022] [Revised: 07/25/2022] [Accepted: 07/27/2022] [Indexed: 06/15/2023]
Abstract
In this work, we propose a versatile, low-cost, and tunable electronic device to generate realistic electrocardiogram (ECG) waveforms, capable of simulating ECG of patients within a wide range of possibilities. A visual analysis of the clinical ECG register provides the cardiologist with vital physiological information to determine the patient's heart condition. Because of its clinical significance, there is a strong interest in algorithms and medical ECG measuring devices that acquire, preserve, and process ECG recordings with high fidelity. Bearing this in mind, the proposed electronic device is based on four different mathematical models describing macroscopic heartbeat dynamics with ordinary differential equations. Firstly, we produce full 12-lead ECG profiles by implementing a model comprising a network of heterogeneous oscillators. Then, we implement a discretized reaction-diffusion model in our electronic device to reproduce ECG waveforms from various rhythm disorders. Finally, in order to show the versatility and capabilities of our system, we include two additional models, a ring of three coupled oscillators and a model based on a quasiperiodic motion, which can reproduce a wide range of pathological conditions. With this, the proposed device can reproduce around thirty-two cardiac rhythms with the possibility of exploring different parameter values to simulate new arrhythmias with the same hardware. Our system, which is a hybrid analog-digital circuit, generates realistic ECG signals through digital-to-analog converters whose amplitudes and waveforms are controlled through an interactive and friendly graphic interface. Our ECG patient simulator arises as a promising platform for assessing the performance of electrocardiograph equipment and ECG signal processing software in clinical trials. Additionally the produced 12-lead profiles can be tested in patient monitoring systems.
Collapse
Affiliation(s)
- Mario Alan Quiroz-Juárez
- Centro de Física Aplicada y Tecnología Avanzada, Universidad Nacional Autónoma de México, Boulevard Juriquilla 3001, Queretaro 76230, Mexico;
| | - Juan Alberto Rosales-Juárez
- Instituto Politécnico Nacional, Escuela Superior de Ingeniería Mecánica y Eléctrica, Santa Ana 1000, San Francisco Culhuacán, Mexico City 04430, Mexico; (J.A.R.-J.); (O.J.-R.)
| | - Omar Jiménez-Ramírez
- Instituto Politécnico Nacional, Escuela Superior de Ingeniería Mecánica y Eléctrica, Santa Ana 1000, San Francisco Culhuacán, Mexico City 04430, Mexico; (J.A.R.-J.); (O.J.-R.)
| | - Rubén Vázquez-Medina
- Instituto Politécnico Nacional, Centro de Investigación en Ciencia Aplicada y Tecnología Avanzada, Cerro Blanco 141, Colinas del Cimatario, Queretaro 76090, Mexico;
| | - José Luis Aragón
- Centro de Física Aplicada y Tecnología Avanzada, Universidad Nacional Autónoma de México, Boulevard Juriquilla 3001, Queretaro 76230, Mexico;
| |
Collapse
|
2
|
Abstract
In this paper, a complete non-linear symmetric oscillator model using the Hamiltonian approach has been developed and used to describe the cardiovascular conduction process’s dynamics, as the signal generated from the cardiovascular muscle is non-deterministic and random. Electrocardiogram (ECG) signal is a significant factor in the cardiovascular system as most of the medical diagnoses can be well understood by observing the ECG signal’s amplitude. A non-linear cardiovascular muscle model has been proposed in this study, where a modified vanderPol symmetric oscillator-based equation is used. Gone are the days whena non-linear system had been designed using the describing function technique. It is better to design a non-linear model using the Hamiltonian dynamical equation for its high accuracy and flexibility. Varying a non-linear spring constant using this type of approach is more comfortable than the traditional describing function technique. Not only that but different initial conditions can also be taken for experimental purposes. It never affects the overall modeling. The Hamiltonian approach provides the energy of an asymmetric oscillatory system of that cardiovascular conduction system. A non-linear symmetric oscillator was initially depicted by the non-linear mass-spring (two degrees of freedom) model. The motion of an uncertain non-linear cardiovascular system has been solved considering second-order approximation, which also demonstrates the possibility of introducing spatial dimensions. Finally, the model’s natural frequency expression has also been simulated and is composed of the previously published result.
Collapse
|
3
|
Improvement of the Cardiac Oscillator Based Model for the Simulation of Bundle Branch Blocks. APPLIED SCIENCES-BASEL 2019. [DOI: 10.3390/app9183653] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
In this paper, we propose an improvement of the cardiac conduction system based on three modified Van der Pol oscillators. Each oscillator represents one of the components of the heart conduction system: Sino-Atrial node (SA), Atrio-Ventricular node (AV) and His–Purkinje system (HP). However, while SA and AV nodes can be modelled through a single oscillator, the modelling of HP by using a single oscillator is a rough simplification of the cardiac behaviour. In fact, the HP bundle is composed of Right (RB) and Left Bundle (LB) branches that serve, respectively, the right and left ventricles. In order to describe the behaviour of each bundle branch, we build a phenomenological model based on four oscillators: SA, AV, RB and LB. For the characterization of the atrial and ventricular muscles, we used the modified FitzHugh–Nagumo (FHN) equations. The numerical simulation of the model has been implemented in Simulink. The simulation results show that the new model is able to reproduce the heart dynamics generating, besides the physiological signal, also the pathological rhythm in case of Right Bundle Branch Block (RBBB) and Left Bundle Branch Block (LBBB). In particular, our model is able to describe the communication interruption of the conduction system, when one of the HP bundle branches is damaged.
Collapse
|
4
|
Quiroz-Juarez MA, Jimenez-Ramirez O, Vazquez-Medina R, Ryzhii E, Ryzhii M, Aragon JL. Cardiac Conduction Model for Generating 12 Lead ECG Signals With Realistic Heart Rate Dynamics. IEEE Trans Nanobioscience 2018; 17:525-532. [PMID: 30235141 DOI: 10.1109/tnb.2018.2870331] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/10/2022]
Abstract
We present an extended heterogeneous oscillator model of cardiac conduction system for generation of realistic 12 lead ECG waveforms. The model consists of main natural pacemakers represented by modified van der Pol equations, and atrial and ventricular muscles, in which the depolarization and repolarization processes are described by modified FitzHugh-Nagumo equations. We incorporate an artificial RR-tachogram with the specific statistics of a heart rate, the frequency-domain characteristics of heart rate variability produced by Mayer and respiratory sinus arrhythmia waves, normally distributed additive noise and a baseline wander that couple the respiratory frequency. The standard 12 lead ECG is calculated by means of a weighted linear combination of atria and ventricle signals and thus can be fitted to clinical ECG of real subject. The model is capable to simulate accurately realistic ECG characteristics including local pathological phenomena accounting for biophysical properties of the human heart. All these features provide significant advantages over existing nonlinear cardiac models. The proposed model constitutes a useful tool for medical education and for assessment and testing of ECG signal processing software and hardware systems.
Collapse
|
5
|
Ashwin P, Coombes S, Nicks R. Mathematical Frameworks for Oscillatory Network Dynamics in Neuroscience. JOURNAL OF MATHEMATICAL NEUROSCIENCE 2016; 6:2. [PMID: 26739133 PMCID: PMC4703605 DOI: 10.1186/s13408-015-0033-6] [Citation(s) in RCA: 103] [Impact Index Per Article: 12.9] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/07/2015] [Accepted: 10/30/2015] [Indexed: 05/20/2023]
Abstract
The tools of weakly coupled phase oscillator theory have had a profound impact on the neuroscience community, providing insight into a variety of network behaviours ranging from central pattern generation to synchronisation, as well as predicting novel network states such as chimeras. However, there are many instances where this theory is expected to break down, say in the presence of strong coupling, or must be carefully interpreted, as in the presence of stochastic forcing. There are also surprises in the dynamical complexity of the attractors that can robustly appear-for example, heteroclinic network attractors. In this review we present a set of mathematical tools that are suitable for addressing the dynamics of oscillatory neural networks, broadening from a standard phase oscillator perspective to provide a practical framework for further successful applications of mathematics to understanding network dynamics in neuroscience.
Collapse
Affiliation(s)
- Peter Ashwin
- Centre for Systems Dynamics and Control, College of Engineering, Mathematics and Physical Sciences, University of Exeter, Harrison Building, Exeter, EX4 4QF, UK.
| | - Stephen Coombes
- School of Mathematical Sciences, University of Nottingham, University Park, Nottingham, NG7 2RD, UK.
| | - Rachel Nicks
- School of Mathematics, University of Birmingham, Watson Building, Birmingham, B15 2TT, UK.
| |
Collapse
|
6
|
Ryzhii E, Ryzhii M. Formation of second-degree atrioventricular blocks in the cardiac heterogeneous oscillator model. ANNUAL INTERNATIONAL CONFERENCE OF THE IEEE ENGINEERING IN MEDICINE AND BIOLOGY SOCIETY. IEEE ENGINEERING IN MEDICINE AND BIOLOGY SOCIETY. ANNUAL INTERNATIONAL CONFERENCE 2016; 2015:4491-4. [PMID: 26737292 DOI: 10.1109/embc.2015.7319392] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/10/2022]
Abstract
We study formation of second-degree atrioventricular blocks (Wenckebach and Mobitz types) with reduction of coupling between nodes in the heterogeneous oscillator model of cardiac conduction system. We demonstrate that maximal possible number of physiological mode lock patterns in both cases appears at a particular value of coupling coefficient. For the type II atrioventricular block total conduction ratio at high sinus rates might be represented by a product of conduction ratios of atrioventricular nodal and infrahisian blocks.
Collapse
|
7
|
Modelling cell cycle synchronisation in networks of coupled radial glial cells. J Theor Biol 2015; 377:85-97. [PMID: 25908204 DOI: 10.1016/j.jtbi.2015.04.013] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Key Words] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/10/2014] [Revised: 02/26/2015] [Accepted: 04/08/2015] [Indexed: 12/31/2022]
Abstract
Radial glial cells play a crucial role in the embryonic mammalian brain. Their proliferation is thought to be controlled, in part, by ATP mediated calcium signals. It has been hypothesised that these signals act to locally synchronise cell cycles, so that clusters of cells proliferate together, shedding daughter cells in uniform sheets. In this paper we investigate this cell cycle synchronisation by taking an ordinary differential equation model that couples the dynamics of intracellular calcium and the cell cycle and extend it to populations of cells coupled via extracellular ATP signals. Through bifurcation analysis we show that although ATP mediated calcium release can lead to cell cycle synchronisation, a number of other asynchronous oscillatory solutions including torus solutions dominate the parameter space and cell cycle synchronisation is far from guaranteed. Despite this, numerical results indicate that the transient and not the asymptotic behaviour of the system is important in accounting for cell cycle synchronisation. In particular, quiescent cells can be entrained on to the cell cycle via ATP mediated calcium signals initiated by a driving cell and crucially will cycle in near synchrony with the driving cell for the duration of neurogenesis. This behaviour is highly sensitive to the timing of ATP release, with release at the G1/S phase transition of the cell cycle far more likely to lead to near synchrony than release during mid G1 phase. This result, which suggests that ATP release timing is critical to radial glia cell cycle synchronisation, may help us to understand normal and pathological brain development.
Collapse
|
8
|
Ryzhii E, Ryzhii M. A heterogeneous coupled oscillator model for simulation of ECG signals. COMPUTER METHODS AND PROGRAMS IN BIOMEDICINE 2014; 117:40-49. [PMID: 24821399 DOI: 10.1016/j.cmpb.2014.04.009] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/27/2014] [Revised: 03/25/2014] [Accepted: 04/16/2014] [Indexed: 06/03/2023]
Abstract
We present a novel model of cardiac conduction system including main pacemakers and heart muscles. Sinoatrial node, atrioventricular node and His-Purkinje system are represented by modified van der Pol-type oscillators connected with time-delay velocity coupling. For description of atrial and ventricular muscles, where depolarization and repolarization processes are considered as separate waves, we use modified FitzHugh-Nagumo model. In this work, we obtained synthetic ECG as a combined signal of atrial and ventricular muscles and reproduced several normal and pathological rhythms. Inclusion of cardiac muscle response allows to investigate interactions between pacemakers and resulting global heartbeat dynamics by means of clinically comparable realistic ECG signals. This feature distinguishes our model from existing cardiac oscillator models. To solve the system of differential equations describing the proposed heterogeneous coupled oscillator model we developed a software in MATLAB environment utilizing special DDE23 function.
Collapse
Affiliation(s)
- E Ryzhii
- Complex Systems Modeling Laboratory, University of Aizu, Aizu-Wakamatsu 965-8580, Japan.
| | - M Ryzhii
- Complex Systems Modeling Laboratory, University of Aizu, Aizu-Wakamatsu 965-8580, Japan.
| |
Collapse
|
9
|
Podziemski P, Zebrowski JJ. A simple model of the right atrium of the human heart with the sinoatrial and atrioventricular nodes included. J Clin Monit Comput 2013; 27:481-98. [PMID: 23430363 PMCID: PMC3689917 DOI: 10.1007/s10877-013-9429-6] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/23/2012] [Accepted: 01/09/2013] [Indexed: 11/29/2022]
Abstract
Existing atrial models with detailed anatomical structure and multi-variable cardiac transmembrane current models are too complex to allow to combine an investigation of long time dycal properties of the heart rhythm with the ability to effectively simulate cardiac electrical activity during arrhythmia. Other ways of modeling need to be investigated. Moreover, many state-of-the-art models of the right atrium do not include an atrioventricular node (AVN) and only rarely—the sinoatrial node (SAN). A model of the heart tissue within the right atrium including the SAN and AVN nodes was developed. Looking for a minimal model, currently we are testing our approach on chosen well-known arrhythmias, which were until now obtained only using much more complicated models, or were only observed in a clinical setting. Ultimately, the goal is to obtain a model able to generate sequences of RR intervals specific for the arrhythmias involving the AV junction as well as for other phenomena occurring within the atrium. The model should be fast enough to allow the study of heart rate variability and arrhythmias at a time scale of thousands of heart beats in real-time. In the model of the right atrium proposed here, different kinds of cardiac tissues are described by sets of different equations, with most of them belonging to the class of Liénard nonlinear dynamical systems. We have developed a series of models of the right atrium with differing anatomical simplifications, in the form of a 2D mapping of the atrium or of an idealized cylindrical geometry, including only those anatomical details required to reproduce a given physiological phenomenon. The simulations allowed to reconstruct the phase relations between the sinus rhythm and the location and properties of a parasystolic source together with the effect of this source on the resultant heart rhythm. We model the action potential conduction time alternans through the atrioventricular AVN junction observed in cardiac tissue in electrophysiological studies during the ventricular-triggered atrial tachycardia. A simulation of the atrio-ventricular nodal reentry tachycardia was performed together with an entrainment procedure in which the arrhythmia circuit was located by measuring the post-pacing interval (PPI) at simulated mapping catheters. The generation and interpretation of RR times series is the ultimate goal of our research. However, to reach that goal we need first to (1) somehow verify the validity of the model of the atrium with the nodes included and (2) include in the model the effect of the sympathetic and vagal ANS. The current paper serves as a partial solution of the 1). In particular we show, that measuring the PPI–TCL entrainment response in proximal (possibly-the slow-conducting pathway), the distal and at a mid-distance from CS could help in rapid distinction of AVNRT from other atrial tachycardias. Our simulations support the hypothesis that the alternans of the conduction time between the atria and the ventricles in the AV orthodromic reciprocating tachycardia can occur within a single pathway. In the atrial parasystole simulation, we found a mathematical condition which allows for a rough estimation of the location of the parasystolic source within the atrium, both for simplified (planar) and the cylindrical geometry of the atrium. The planar and the cylindrical geometry yielded practically the same results of simulations.
Collapse
Affiliation(s)
- Piotr Podziemski
- Faculty of Physics, Warsaw University of Technology, Koszykowa 75, 00-662, Warsaw, Poland.
| | | |
Collapse
|
10
|
Potapov I, Volkov E, Kuznetsov A. Dynamics of coupled repressilators: the role of mRNA kinetics and transcription cooperativity. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 83:031901. [PMID: 21517519 DOI: 10.1103/physreve.83.031901] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/07/2010] [Indexed: 05/30/2023]
Abstract
Oscillatory regulatory networks have been discovered in many cellular pathways. An especially challenging area is studying dynamics of cellular oscillators interacting with one another in a population. Synchronization is only one of and the simplest outcome of such interaction. It is suggested that the outcome depends on the structure of the network. Phase-attractive (synchronizing) and phase-repulsive coupling structures were distinguished for regulatory oscillators. In this paper, we question this separation. We study an example of two interacting repressilators (artificial regulatory oscillators based on cyclic repression). We show that changing the cooperativity of transcription repression (Hill coefficient) and reaction timescales dramatically alter synchronization properties. The network becomes birhythmic-it chooses between the in-phase and antiphase synchronization. Thus, the type of synchronization is not characteristic for the network structure. However, we conclude that the specific scenario of emergence and stabilization of synchronous solutions is much more characteristic.
Collapse
Affiliation(s)
- I Potapov
- Department of Theoretical Physics, Lebedev Physical Institute, Leninskii 53, Moscow, Russia
| | | | | |
Collapse
|
11
|
Postnova S, Voigt K, Braun HA. Neural synchronization at tonic-to-bursting transitions. J Biol Phys 2007; 33:129-43. [PMID: 19669545 PMCID: PMC2646392 DOI: 10.1007/s10867-007-9048-x] [Citation(s) in RCA: 45] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/17/2007] [Accepted: 09/11/2007] [Indexed: 11/29/2022] Open
Abstract
We studied the synchronous behavior of two electrically-coupled model neurons as a function of the coupling strength when the individual neurons are tuned to different activity patterns that ranged from tonic firing via chaotic activity to burst discharges. We observe asynchronous and various synchronous states such as out-of-phase, in-phase and almost in-phase chaotic synchronization. The highest variety of synchronous states occurs at the transition from tonic firing to chaos where the highest coupling strength is also needed for in-phase synchronization which is, essentially, facilitated towards the bursting range. This demonstrates that tuning of the neuron's internal dynamics can have significant impact on the synchronous states especially at the physiologically relevant tonic-to-bursting transitions.
Collapse
|
12
|
Zebrowski JJ, Grudziński K, Buchner T, Kuklik P, Gac J, Gielerak G, Sanders P, Baranowski R. Nonlinear oscillator model reproducing various phenomena in the dynamics of the conduction system of the heart. CHAOS (WOODBURY, N.Y.) 2007; 17:015121. [PMID: 17411278 DOI: 10.1063/1.2405128] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/14/2023]
Abstract
A dedicated nonlinear oscillator model able to reproduce the pulse shape, refractory time, and phase sensitivity of the action potential of a natural pacemaker of the heart is developed. The phase space of the oscillator contains a stable node, a hyperbolic saddle, and an unstable focus. The model reproduces several phenomena well known in cardiology, such as certain properties of the sinus rhythm and heart block. In particular, the model reproduces the decrease of heart rate variability with an increase in sympathetic activity. A sinus pause occurs in the model due to a single, well-timed, external pulse just as it occurs in the heart, for example due to a single supraventricular ectopy. Several ways by which the oscillations cease in the system are obtained (models of the asystole). The model simulates properly the way vagal activity modulates the heart rate and reproduces the vagal paradox. Two such oscillators, coupled unidirectionally and asymmetrically, allow us to reproduce the properties of heart rate variability obtained from patients with different kinds of heart block including sino-atrial blocks of different degree and a complete AV block (third degree). Finally, we demonstrate the possibility of introducing into the model a spatial dimension that creates exciting possibilities of simulating in the future the SA the AV nodes and the atrium including their true anatomical structure.
Collapse
Affiliation(s)
- J J Zebrowski
- Physics of Complex Systems Division, Faculty of Physics, Warsaw University of Technology, ul. Koszykowa 75, 00-662 Warszawa, Poland
| | | | | | | | | | | | | | | |
Collapse
|
13
|
Tessone CJ, Ullner E, Zaikin AA, Kurths J, Toral R. Noise-induced inhibitory suppression of frequency-selective stochastic resonance. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2006; 74:046220. [PMID: 17155166 DOI: 10.1103/physreve.74.046220] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/03/2005] [Revised: 05/29/2006] [Indexed: 05/12/2023]
Abstract
We study the control of oscillations in a system of inhibitory coupled noisy excitable and oscillatory units. Using dynamical properties of inhibition, we find regimes when the oscillations can be suppressed but the information signal of a certain frequency can be transmitted through the system. The mechanism of this phenomenon is a resonant interplay of noise and the transmission signal provided by certain value of inhibitory coupling. Analyzing a system of three or four oscillators representing neural clusters, we show that this suppression can be effectively controlled by coupling and noise amplitudes.
Collapse
Affiliation(s)
- C J Tessone
- Institut Mediterrani d'Estudis Avançats (IMEDEA), CSIC-Universitat de les Illes Balears, Ed. Mateu Orfila, Campus UIB, E07122 Palma de Mallorca, Spain
| | | | | | | | | |
Collapse
|
14
|
Grudziński K, Zebrowski JJ, Baranowski R. Model of the sino-atrial and atrio-ventricular nodes of the conduction system of the human heart. BIOMED ENG-BIOMED TE 2006; 51:210-4. [PMID: 17061941 DOI: 10.1515/bmt.2006.039] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
Abstract
The coupled sino-atrial and atrio-ventricular nodes of the heart are discussed using a dedicated non-linear oscillator model. Several modes by which the oscillations cease in the system are obtained (asystole models). The oscillations of the model are compared with heart rate variability in heart block patients.
Collapse
|
15
|
Hwang DU, Lee SG, Han SK, Kook H. Phase-model analysis of coupled neuronal oscillators with multiple connections. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2006; 74:031911. [PMID: 17025671 DOI: 10.1103/physreve.74.031911] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/26/2006] [Revised: 08/26/2006] [Indexed: 05/12/2023]
Abstract
Synchronization of the coupled neuronal oscillators with multiple connections of different coupling nature is analyzed using the phase-model reduction method. Each coupling connection contributes to the dynamic behavior of the system in a complex nonlinear fashion. In the phase-model scheme, the contribution of the individual connections can be separated in terms of the effective coupling functions associated with each connection and a linear superposition of them provides the total effective coupling of the coupled system. The case of multiple connections with various conduction time delays is also examined, which is shown to be capable of promoting synchronization over an ensemble of spatially distributed neuronal oscillators in an efficient way.
Collapse
Affiliation(s)
- Dong-Uk Hwang
- Department of Physics, Chungbuk National University, Cheongju 361-763, Korea
| | | | | | | |
Collapse
|
16
|
Volkov EI, Ullner E, Kurths J. Stochastic multiresonance in the coupled relaxation oscillators. CHAOS (WOODBURY, N.Y.) 2005; 15:23105. [PMID: 16035881 DOI: 10.1063/1.1899287] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/03/2023]
Abstract
We study the noise-dependent dynamics in a chain of four very stiff excitable oscillators of the FitzHugh-Nagumo type locally coupled by inhibitor diffusion. We could demonstrate frequency- and noise-selective signal acceptance which is based on several noise-supported stochastic attractors that arise owing to slow variable diffusion between identical excitable elements. The attractors have different average periods distinct from that of an isolated oscillator and various phase relations between the elements. We explain the correspondence between the noise-supported stochastic attractors and the observed resonance peaks in the curves for the linear response versus signal frequency.
Collapse
Affiliation(s)
- E I Volkov
- Department Theoretical Physics, Lebedev Physical Institute, Leninskii 53, Russia.
| | | | | |
Collapse
|
17
|
Volkov EI, Ullner E, Zaikin AA, Kurths J. Frequency-dependent stochastic resonance in inhibitory coupled excitable systems. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2003; 68:061112. [PMID: 14754185 DOI: 10.1103/physreve.68.061112] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/04/2003] [Indexed: 05/24/2023]
Abstract
We study frequency selectivity in noise-induced subthreshold signal processing in a system with many noise-supported stochastic attractors which are created due to slow variable diffusion between identical excitable elements. Such a coupling provides coexisting of several average periods distinct from that of an isolated oscillator and several phase relations between elements. We show that the response of the coupled elements under different noise levels can be significantly enhanced or reduced by forcing some elements in resonance with these new frequencies which correspond to appropriate phase relations.
Collapse
Affiliation(s)
- E I Volkov
- Department of Theoretical Physics, Lebedev Physical Institute, Leninskii 53, Russia
| | | | | | | |
Collapse
|
18
|
Han SK, Postnov DE. Chaotic bursting as chaotic itinerancy in coupled neural oscillators. CHAOS (WOODBURY, N.Y.) 2003; 13:1105-1109. [PMID: 12946203 DOI: 10.1063/1.1598691] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/24/2023]
Abstract
We show that chaotic bursting activity observed in coupled neural oscillators is a kind of chaotic itinerancy. In neuronal systems with phase deformation along the trajectory, diffusive coupling induces a dephasing effect. Because of this effect, an antiphase synchronized solution is stable for weak coupling, while an in-phase solution is stable for very strong coupling. For intermediate coupling, a chaotic bursting activity is generated. It is a mixture of three different states: an antiphase firing state, an in-phase firing state, and a nonfiring resting state. As we construct numerically the deformed torus manifold underlying the chaotic bursting state, it is shown that the three unstable states are connected to give rise to a global chaotic itinerancy structure. Thus we claim that chaotic itinerancy provides an alternative route to chaos via torus breakdown.
Collapse
Affiliation(s)
- Seung Kee Han
- Department of Physics and BSRC, Chungbuk National University, Cheongju, Chungbuk 361-763, Korea
| | | |
Collapse
|
19
|
Zebrowski JJ, Baranowski R. Direct observation of homoclinic orbits in human heart rate variability. PHYSICAL REVIEW E 2003; 67:056216. [PMID: 12786259 DOI: 10.1103/physreve.67.056216] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/13/2002] [Revised: 02/18/2003] [Indexed: 11/07/2022]
Abstract
Homoclinic trajectories of the interbeat intervals between contractions of ventricles of the human heart are identified. The interbeat intervals are extracted from 24-h Holter ECG recordings. Three such recordings are discussed in detail. Mappings of the measured consecutive interbeat intervals are constructed. In the second and in some cases in the fourth iterate of the map of interbeat intervals homoclinic trajectories associated with a hyperbolic saddle are found. The homoclinic trajectories are often persistent for many interbeat intervals, sometimes spanning many thousands of heartbeats. Several features typical for homoclinic trajectories found in other systems were identified, including a signature of the gluing bifurcation. The homoclinic trajectories are present both in recordings of heart rate variability obtained from patients with an increased number of arrhythmias and in cases in which the sinus rhythm is dominant. The results presented are a strong indication of the importance of deterministic nonlinear instabilities in human heart rate variability.
Collapse
Affiliation(s)
- J J Zebrowski
- Faculty of Physics, Warsaw University of Technology, Warsaw, Poland
| | | |
Collapse
|
20
|
Postnov DE, Sosnovtseva OV, Malova SY, Mosekilde E. Complex phase dynamics in coupled bursters. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2003; 67:016215. [PMID: 12636593 DOI: 10.1103/physreve.67.016215] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/07/2002] [Indexed: 05/24/2023]
Abstract
The phenomenon of phase multistability in the synchronization of two coupled oscillatory systems typically arises when the systems individually display complex wave forms associated, for instance, with the presence of subharmonic components. Alternatively, phase multistability can be caused by variations of the phase velocity along the orbit of the individual oscillator. Focusing on the mechanisms underlying the appearance of phase multistability, the paper examines a variety of phase-locked patterns in the bursting behavior of a model of coupled pancreatic cells. In particular, we show how the number of spikes per train and the proximity of a neighboring equilibrium point can influence the formation of coexisting regimes.
Collapse
Affiliation(s)
- D E Postnov
- Physics Department, Saratov State University, Astrakhanskaya Street 83, Saratov 410026, Russia
| | | | | | | |
Collapse
|
21
|
Sosnovtseva OV, Postnov DE, Nekrasov AM, Mosekilde E, Holstein-Rathlou NH. Phase multistability of self-modulated oscillations. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2002; 66:036224. [PMID: 12366241 DOI: 10.1103/physreve.66.036224] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/27/2002] [Indexed: 05/23/2023]
Abstract
The paper examines the type of multistability that one can observe in the synchronization of two oscillators when the systems individually display self-modulation or other types of multicrest wave forms. The investigation is based on a phase reduction method and on the calculation of phase maps for vanishing and finite coupling strengths, respectively. Various phase-locked patterns are observed. In the presence of a frequency mismatch, the two-parameter bifurcation analysis reveals a set of synchronization regions inserted one into the other. Numerical examples using a generator with inertial nonlinearity and a biologically motivated model of nephron autoregulation are presented.
Collapse
Affiliation(s)
- O V Sosnovtseva
- Physics Department, Saratov State University, Astrakhanskaya Street 83, Russia
| | | | | | | | | |
Collapse
|
22
|
Hu B, Zhou C. Synchronization regimes in coupled noisy excitable systems. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2001; 63:026201. [PMID: 11308552 DOI: 10.1103/physreve.63.026201] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/30/2000] [Indexed: 05/23/2023]
Abstract
We study synchronization regimes in a system of two coupled noisy excitable systems which exhibit excitability close to an Andronov bifurcation. The uncoupled system possesses three fixed points: a node, a saddle, and an unstable focus. We demonstrate that with an increase of coupling strength the system undergoes transitions from a desynchronous state to a train synchronization regime to a phase synchronization regime, and then to a complete synchronization regime. Train synchronization is a consequence of the existence of a saddle in the phase space. The mechanism of transitions in coupled noisy excitable systems is different from that in coupled phase-coherent chaotic systems.
Collapse
Affiliation(s)
- B Hu
- Department of Physics and Center for Nonlinear Studies, Hong Kong Baptist University, Hong Kong, China
| | | |
Collapse
|