Cardiac Alternans Arising From an Unfolded Border-Collision Bifurcation

2007 ◽  
Author(s):  
Xiaopeng Zhao ◽  
David G. Schaeffer ◽  
Carolyn M. Berger ◽  
Wanda Krassowska ◽  
Daniel J. Gauthier
Keyword(s):  
Action Potential ◽  
Cardiac Tissue ◽  
Medical Literature ◽  
Period Doubling ◽  
Electrical Stimulus ◽  
Period Doubling Bifurcation ◽  
Small Interval ◽  
Border Collision Bifurcation ◽  
Transmembrane Voltage ◽  
Cardiac Alternans

Following an electrical stimulus, the transmembrane voltage of cardiac tissue rises rapidly and remains at a constant value before returning to the resting value, a phenomenon known as an action potential. When the pacing rate of a periodic train of stimuli is increased above a critical value, the action potential undergoes a period-doubling bifurcation, where the resulting alternation of the action potential duration is known as alternans in the medical literature. In principle, a period-doubling bifurcation may occur through either a smooth or a nonsmooth mechanism. Previous experiments reveal that the bifurcation to alternans exhibits hybrid smooth/nonsmooth behaviors, which is due to large variations in the system’s properties over a small interval of bifurcation parameter. To reproduce the experimentally observed hybrid behaviors, we have developed a model of alternans that exhibits an unfolded border-collision bifurcation. Excellent agreement between simulation of the model and experimental data suggests that features of the unfolded border-collision model should be included in modeling cardiac alternans.

Bifurcation of Spatiotemporal Cardiac Alternans

2008 ◽  
Author(s):  
Xiaopeng Zhao
Keyword(s):  
Action Potential ◽  
Cardiac Tissue ◽  
Period Doubling ◽  
Heart Rhythm ◽  
The Us ◽  
Coupled Cells ◽  
Cardiac Alternans ◽  
Rhythm Disorder ◽  
Bifurcation Structures ◽  
And Control

Cardiac alternans is an initiator of ventricular fibrillation, a fatal heart rhythm disorder that kills hundreds of thousands people in the US each year. Alternans manifests as a pattern with beat-to-beat long-short variations in action potential duration. In an isolated cardiac cell, alternans arises as a supercritical period-doubling bifurcation. In cardiac tissue (coupled cells), propagation effect leads to more complicated bifurcation structures. Specifically, there may coexist multiple spatiotemporal patterns of alternans in tissue due to the interaction between electrotonic coupling and intrinsic instability in the dynamics of action potential. In this work, we carry out a detailed bifurcation analysis to illustrate the mechanism that leads to this phenomenon. The results on this analysis may shed light on the onset and control of the dreadful instability of cardiac alternans.

scholarly journals BORDER COLLISION BIFURCATION CONTROL OF CARDIAC ALTERNANS

2004 ◽  
Vol 14 (09) ◽  
pp. 3303-3315 ◽  
Author(s):  
MUNTHER A. HASSOUNEH ◽  
EYAD H. ABED
Keyword(s):  
Period Doubling ◽  
Region Of Interest ◽  
Period Doubling Bifurcation ◽  
Cardiac Conduction ◽  
Parameter Region ◽  
Conduction Model ◽  
Control Laws ◽  
Border Collision Bifurcation ◽  
Cardiac Alternans ◽  
Smooth System

The quenching of alternans is considered using a nonlinear cardiac conduction model. The model consists of a nonlinear discrete-time piecewise smooth system. Several authors have hypothesized that alternans arise in the model through a period-doubling bifurcation. In this work, it is first shown that the alternans exhibited by the model actually arise through a period-doubling border collision bifurcation. No smooth period-doubling bifurcation occurs in the parameter region of interest. Next, recent results of the authors on feedback control of border collision bifurcation are applied to the model, resulting in control laws that quench the bifurcation, and hence result in alternan suppression.

scholarly journals Period-Doubling Bifurcation to Alternans in Paced Cardiac Tissue: Crossover from Smooth to Border-Collision Characteristics

2007 ◽  
Vol 99 (5) ◽  
Author(s):  
Carolyn M. Berger ◽  
Xiaopeng Zhao ◽  
David G. Schaeffer ◽  
Hana M. Dobrovolny ◽  
Wanda Krassowska ◽  
...  
Keyword(s):  
Cardiac Tissue ◽  
Period Doubling ◽  
Period Doubling Bifurcation

scholarly journals Optimisation of a Generic Ionic Model of Cardiac Myocyte Electrical Activity

2013 ◽  
Vol 2013 ◽  
pp. 1-20 ◽  
Author(s):  
Tianruo Guo ◽  
Amr Al Abed ◽  
Nigel H. Lovell ◽  
Socrates Dokos
Keyword(s):  
Action Potential ◽  
Time Course ◽  
Cardiac Myocyte ◽  
Cardiac Tissue ◽  
Ionic Currents ◽  
Experimental Information ◽  
Electrical Stimulus ◽  
Right Atrial ◽  
Ionic Model ◽  
Multiple Datasets

A generic cardiomyocyte ionic model, whose complexity lies between a simple phenomenological formulation and a biophysically detailed ionic membrane current description, is presented. The model provides a user-defined number of ionic currents, employing two-gate Hodgkin-Huxley type kinetics. Its generic nature allows accurate reconstruction of action potential waveforms recorded experimentally from a range of cardiac myocytes. Using a multiobjective optimisation approach, the generic ionic model was optimised to accurately reproduce multiple action potential waveforms recorded from central and peripheral sinoatrial nodes and right atrial and left atrial myocytes from rabbit cardiac tissue preparations, under different electrical stimulus protocols and pharmacological conditions. When fitted simultaneously to multiple datasets, the time course of several physiologically realistic ionic currents could be reconstructed. Model behaviours tend to be well identified when extra experimental information is incorporated into the optimisation.

scholarly journals Cardiac alternans induced by fibroblast-myocyte coupling: mechanistic insights from computational models

2009 ◽  
Vol 297 (2) ◽  
pp. H775-H784 ◽  
Author(s):  
Yuanfang Xie ◽  
Alan Garfinkel ◽  
James N. Weiss ◽  
Zhilin Qu
Keyword(s):  
Action Potential ◽  
Computational Models ◽  
Cardiac Tissue ◽  
Experimental Studies ◽  
Outward Current ◽  
Transient Outward Current ◽  
Two Dimensional ◽  
Background Current ◽  
Cardiac Alternans ◽  
Main Components

Recent experimental studies have shown that fibroblasts can electrotonically couple to myocytes via gap junctions. In this study, we investigated how this coupling affects action potential and intracellular calcium (Cai) cycling dynamics in simulated fibroblast-myocyte pairs and in two-dimensional tissue with random fibroblast insertions. We show that a fibroblast coupled with a myocyte generates a gap junction current flowing to the myocyte with two main components: an early pulse of transient outward current, similar to the fast transient outward current, and a later background current during the repolarizing phase. Depending on the relative prominence of the two components, fibroblast-myoycte coupling can 1) prolong or shorten action potential duration (APD), 2) promote or suppress APD alternans due to steep APD restitution (voltage driven) and also result in a novel mechanism of APD alternans at slow heart rates, 3) promote Cai-driven alternans and electromechanically discordant alternans, and 4) promote spatially discordant alternans by two mechanisms: by altering conduction velocity restitution and by heterogeneous fibroblast distribution causing electromechanically concordant and discordant alternans in different regions of the tissue. Thus, through their coupling with myocytes, fibroblasts alter repolarization and Cai cycling alternans at both the cellular and tissue scales, which may play important roles in arrhythmogenesis in diseased cardiac tissue with fibrosis.

A Model-Independent Technique for Eigenvalue Identification and Its Application in Predicting Cardiac Alternans

2007 ◽  
Author(s):  
Xiaopeng Zhao ◽  
David G. Schaeffer ◽  
Wanda Krassowska ◽  
Daniel J. Gauthier
Keyword(s):  
Period Doubling ◽  
Time History ◽  
Heart Rhythm ◽  
Promising Tool ◽  
Transmembrane Voltage ◽  
Cardiac Model ◽  
History Of ◽  
Cardiac Alternans ◽  
Independent Technique ◽  
Model Independent

Predicting cardiac alternans is a crucial step toward detection and prevention of ventricular fibrillation, a heart rhythm disorder that kills hundreds of thousands of people in the US each year. According to the theory of dynamical systems, cardiac alternans is mediated by a period-doubling bifurcation, which is associated with variations in a characteristic eigenvalue. Thus, knowing the eigenvalues would allow one to predict the onset of alternans. The existing criteria for alternans either adopt unrealistically simple assumptions and thus produce erroneous predictions or rely on complicated intrinsic functions, which are not possible to measure experimentally. In this work, we present a model-independent technique to estimate a system’s eigenvalues without requirements on the knowledge of the underlying dynamic model. The method is based on principal components analysis of a pseudo-state space; therefore, it allows one to compute the dominant eigenvalues of a system using the time history of a single measurable variable, e.g. the transmembrane voltage or the intracellular calcium concentration in cardiac experiments. Numerical examples based on a cardiac model verify the accuracy of the method. Thus, the technique provides a promising tool for predicting alternans in real-time experiments.

Bifurcation and Control of Cardiac Alternans

2010 ◽  
Author(s):  
Henian Xia ◽  
Xiaopeng Zhao
Keyword(s):  
Feedback Control ◽  
Cardiac Tissue ◽  
Sudden Cardiac Arrest ◽  
Period Doubling ◽  
The United States ◽  
Amplitude Equation ◽  
Cardiac Alternans ◽  
Numerical Bifurcation ◽  
Secondary Bifurcations ◽  
And Control

Cardiac alternans is a marker of sudden cardiac arrest, the leading cause of death in the United States that kills hundreds of thousands of Americans each year. In the language of nonlinear dynamics, the onset of cardiac alternans is induced by a period-doubling bifurcation. In this work, we explore the bifurcation and control of cardiac alternans in a fiber based on numerical analyses of the seminal amplitude equation derived by Echebarria and Karma. First, we seek the solution of the amplitude equation using a series expansion. Then, detailed numerical bifurcation analyses are carried out to illustrate the spatiotemporal patterns of cardiac alternans. We demonstrate that secondary bifurcations lead to multiple unstable patterns, which impose difficulties in feedback control of alternans. Effects and limitations of feedback control algorithms are explored. The theoretical analyses here help to improve the understanding of the mechanisms of alternans in cardiac tissue.

scholarly journals Period-doubling bifurcation analysis and chaos control for load torque using FLC

2021 ◽  
Author(s):  
Eman Moustafa ◽  
Abdel-Azem Sobaih ◽  
Belal Abozalam ◽  
Amged Sayed A. Mahmoud
Keyword(s):  
Floquet Theory ◽  
Chaos Control ◽  
Fuzzy Logic Controller ◽  
Chaotic Behavior ◽  
Period Doubling ◽  
Parameter Variation ◽  
Period Doubling Bifurcation ◽  
Load Torque ◽  
Nonlinear Behaviors ◽  
Scientific Fields

AbstractChaotic phenomena are observed in several practical and scientific fields; however, the chaos is harmful to systems as they can lead them to be unstable. Consequently, the purpose of this study is to analyze the bifurcation of permanent magnet direct current (PMDC) motor and develop a controller that can suppress chaotic behavior resulted from parameter variation such as the loading effect. The nonlinear behaviors of PMDC motors were investigated by time-domain waveform, phase portrait, and Floquet theory. By varying the load torque, a period-doubling bifurcation appeared which in turn led to chaotic behavior in the system. So, a fuzzy logic controller and developing the Floquet theory techniques are applied to eliminate the bifurcation and the chaos effects. The controller is used to enhance the performance of the system by getting a faster response without overshoot or oscillation, moreover, tends to reduce the steady-state error while maintaining its stability. The simulation results emphasize that fuzzy control provides better performance than that obtained from the other controller.

scholarly journals Complex dynamics and coexistence of period-doubling and period-halving bifurcations in an integrated pest management model with nonlinear impulsive control

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Changtong Li ◽  
Sanyi Tang ◽  
Robert A. Cheke
Keyword(s):  
Periodic Solution ◽  
Integrated Pest Management ◽  
Pest Management ◽  
Pest Control ◽  
Impulsive Control ◽  
Period Doubling ◽  
Dynamical Behaviour ◽  
Period Doubling Bifurcation ◽  
Predator Prey ◽  
Predator Prey Model

Abstract An expectation for optimal integrated pest management is that the instantaneous numbers of natural enemies released should depend on the densities of both pest and natural enemy in the field. For this, a generalised predator–prey model with nonlinear impulsive control tactics is proposed and its dynamics is investigated. The threshold conditions for the global stability of the pest-free periodic solution are obtained based on the Floquet theorem and analytic methods. Also, the sufficient conditions for permanence are given. Additionally, the problem of finding a nontrivial periodic solution is confirmed by showing the existence of a nontrivial fixed point of the model’s stroboscopic map determined by a time snapshot equal to the common impulsive period. In order to address the effects of nonlinear pulse control on the dynamics and success of pest control, a predator–prey model incorporating the Holling type II functional response function as an example is investigated. Finally, numerical simulations show that the proposed model has very complex dynamical behaviour, including period-doubling bifurcation, chaotic solutions, chaos crisis, period-halving bifurcations and periodic windows. Moreover, there exists an interesting phenomenon whereby period-doubling bifurcation and period-halving bifurcation always coexist when nonlinear impulsive controls are adopted, which makes the dynamical behaviour of the model more complicated, resulting in difficulties when designing successful pest control strategies.

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