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.

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 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 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.

scholarly journals Four Weeks of Aerobic Training Affects Cardiac Tissue Matrix Metalloproteinase, Lactate Dehydrogenase and Malate Dehydrogenase Enzymes Activities, and Hepatorenal Biomarkers in Experimental Hyperhomocysteinemia in Rats

2021 ◽  
Vol 22 (13) ◽  
pp. 6792
Author(s):  
Dusan Todorovic ◽  
Marija Stojanovic ◽  
Ana Medic ◽  
Kristina Gopcevic ◽  
Slavica Mutavdzin ◽  
...  
Keyword(s):  
Physical Activity ◽  
Lactate Dehydrogenase ◽  
Malate Dehydrogenase ◽  
Subcutaneous Injection ◽  
Cardiac Tissue ◽  
Albino Rats ◽  
Wistar Albino Rats ◽  
And Control ◽  
Tissue Matrix ◽  
Increased Activity

The aim of this study was to investigate the effect of the application of homocysteine as well as its effect under the condition of aerobic physical activity on the activities of matrix metalloproteinases (MMP), lactate dehydrogenase (LDH) and malate dehydrogenase (MDH) in cardiac tissue and on hepato-renal biochemical parameters in sera of rats. Male Wistar albino rats were divided into four groups (n = 10, per group): C: 0.9% NaCl 0.2 mL/day subcutaneous injection (s.c.); H: homocysteine 0.45 µmol/g b.w./day s.c.; CPA saline (0.9% NaCl 0.2 mL/day s.c.) and a program of physical activity on a treadmill; and HPA homocysteine (0.45 µmol/g b.w./day s.c.) and a program of physical activity on a treadmill. Subcutaneous injection of substances was applied 2 times a day at intervals of 8 h during the first two weeks of experimental protocol. Hcy level in serum was significantly higher in the HPA group compared to the CPA group (p < 0.05). Levels of glucose, proteins, albumin, and hepatorenal biomarkers were higher in active groups compared with the sedentary group. It was demonstrated that the increased activities of LDH (mainly caused by higher activity of isoform LDH2) and mMDH were found under the condition of homocysteine-treated rats plus aerobic physical activity. Independent application of homocysteine did not lead to these changes. Physical activity leads to activation of MMP-2 isoform and to increased activity of MMP-9 isoform in both homocysteine-treated and control rats.

A HIPAA Security and Privacy Compliance Audit and Risk Assessment Mitigation Approach

2021 ◽  
Vol 3 (2) ◽  
pp. 28-45
Author(s):  
Young B. Choi ◽  
Christopher E. Williams
Keyword(s):  
Healthcare System ◽  
Information Assurance ◽  
Healthcare Providers ◽  
Security And Privacy ◽  
Privacy Requirements ◽  
Security Controls ◽  
The Us ◽  
Compliance Audit ◽  
And Control ◽  
Health Laws

Data breaches have a profound effect on businesses associated with industries like the US healthcare system. This task extends more pressure on healthcare providers as they continue to gain unprecedented access to patient data, as the US healthcare system integrates further into the digital realm. Pressure has also led to the creation of the Health Insurance Portability and Accountability Act, Omnibus Rule, and Health Information Technology for Economic and Clinical Health laws. The Defense Information Systems Agency also develops and maintains security technical implementation guides that are consistent with DoD cybersecurity policies, standards, architectures, security controls, and validation procedures. The objective is to design a network (physician's office) in order to meet the complexity standards and unpredictable measures posed by attackers. Additionally, the network must adhere to HIPAA security and privacy requirements required by law. Successful implantation of network design will articulate comprehension requirements of information assurance security and control.

Rate-dependent shortening of action potential duration increases ventricular vulnerability in failing rabbit heart

2011 ◽  
Vol 300 (2) ◽  
pp. H565-H573 ◽  
Author(s):  
Masahide Harada ◽  
Yukiomi Tsuji ◽  
Yuko S. Ishiguro ◽  
Hiroki Takanari ◽  
Yusuke Okuno ◽  
...  
Keyword(s):  
Action Potential ◽  
High Frequency ◽  
Rabbit Heart ◽  
Left Ventricular ◽  
High Frequency Stimulation ◽  
Electrophysiological Properties ◽  
Rate Dependent ◽  
Frequency Stimulation ◽  
And Control

Congestive heart failure (CHF) predisposes to ventricular fibrillation (VF) in association with electrical remodeling of the ventricle. However, much remains unknown about the rate-dependent electrophysiological properties in a failing heart. Action potential properties in the left ventricular subepicardial muscles during dynamic pacing were examined with optical mapping in pacing-induced CHF ( n = 18) and control ( n = 17) rabbit hearts perfused in vitro. Action potential durations (APDs) in CHF were significantly longer than those observed for controls at basic cycle lengths (BCLs) >1,000 ms but significantly shorter at BCLs <400 ms. Spatial APD dispersions were significantly increased in CHF versus control (by 17–81%), and conduction velocity was significantly decreased in CHF (by 6–20%). In both groups, high-frequency stimulation (BCLs <150 ms) always caused spatial APD alternans; spatially concordant alternans and spatially discordant alternans (SDA) were induced at 60% and 40% in control, respectively, whereas 18% and 82% in CHF. SDA in CHF caused wavebreaks followed by reentrant excitations, giving rise to VF. Incidence of ventricular tachycardia/VFs elicited by high-frequency dynamic pacing (BCLs <150 ms) was significantly higher in CHF versus control (93% vs. 20%). In CHF, left ventricular subepicardial muscles show significant APD shortenings at short BCLs favoring reentry formations following wavebreaks in association with SDA. High-frequency excitation itself may increase the vulnerability to VF in CHF.

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