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.

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.

A Reduced Order Model for Spatiotemporal Dynamics and Control of Cardiac Alternans

2018 ◽  
Author(s):  
Xiaopeng Zhao ◽  
Elena G. Tolkacheva
Keyword(s):  
Cardiac Arrest ◽  
Sudden Cardiac Arrest ◽  
Cellular Level ◽  
Reduced Order Model ◽  
Western World ◽  
Order Model ◽  
Reduced Order ◽  
Dynamics And Control ◽  
Cardiac Alternans ◽  
And Control

Sudden cardiac arrest, caused primarily by ventricular fibrillation, is one of the leading causes of mortality in the Western world. There is a compelling need for risk stratification to identify patients at risk for sudden cardiac arrest. Cardiac alternans, a recognized harbinger of sudden cardiac arrest, manifests as a beat-to-beat alternation in action potential duration (cellular level) or in electrocardiogram morphology (whole heart level). Although much progress has been made to understand the mechanisms of alternans, predicting and control of alternans, especially at the heart level, remain great challenges. Current approaches to predict cardiac alternans based on restitution properties of the heart are either too simple to be valid or too complex to be useful. In this work, we developed a reduced order model from the amplitude equation to investigate dynamics and control of alternans in cardiac fiber, i.e. beyond single cell level. Detailed bifurcation and stability analyses were carried out to illustrate complex spatiotemporal patterns of alternans and the limitations in feedback control due to spatial effect.

A Cellular Automata Model for Dynamics and Control of Cardiac Arrhythmias

2020 ◽  
Author(s):  
Danny Gallenberger ◽  
Min Xiong ◽  
Tony Z. Zhuang ◽  
Kai Sun ◽  
Elena G. Tolkacheva ◽  
...  
Keyword(s):  
Cellular Automata ◽  
Cardiac Arrhythmias ◽  
Control Method ◽  
Sudden Cardiac Arrest ◽  
Significant Proportion ◽  
The United States ◽  
Effective Control ◽  
Dynamics And Control ◽  
Ca Model ◽  
And Control

Abstract As a leading cause of death in 325,000 adults per year in the United States, a significant proportion of sudden cardiac arrest (SCA) result from arrhythmias. To better understand the onset of arrhythmias and its potential treatment with more rapid and effective control approaches, a two-dimensional 50 × 50 cellular automata (CA) model is used in this study to illustrate the propagation of electrical waves across its tissue, and a constant diastolic interval (DI) control mechanism is adopted to help stabilize and prevent cardiac arrhythmias. Simulations of various scenarios including normal conduction and spiral waves in the presence of scar, normal conduction and alternans under control conditions are shown. The results validate that the CA model and constant DI control method are very efficient and effective in the study of dynamics and control of cardiac arrhythmias.

When Temporal Orbits Collide: Embodied Trans Temporalities in U.S. Prisons

Somatechnics ◽  
2017 ◽  
Vol 7 (1) ◽  
pp. 74-94 ◽  
Author(s):  
Rae Rosenberg
Keyword(s):  
United States ◽  
Case Studies ◽  
The United States ◽  
Industrial Complex ◽  
Prison Industrial Complex ◽  
Trans Women ◽  
And Control

This paper explores trans temporalities through the experiences of incarcerated trans feminine persons in the United States. The Prison Industrial Complex (PIC) has received increased attention for its disproportionate containment of trans feminine persons, notably trans women of colour. As a system of domination and control, the PIC uses disciplinary and heteronormative time to dominate the bodies and identities of transgender prisoners by limiting the ways in which they can express and experience their identified and embodied genders. By analyzing three case studies from my research with incarcerated trans feminine persons, this paper illustrates how temporality is complexly woven through trans feminine prisoners' experiences of transitioning in the PIC. For incarcerated trans feminine persons, the interruption, refusal, or permission of transitioning in the PIC invites several gendered pasts into a body's present and places these temporalities in conversation with varying futures as the body's potential. Analyzing trans temporalities reveals time as layered through gender, inviting multiple pasts and futures to circulate around and through the body's present in ways that can be both harmful to, and necessary for, the assertion and survival of trans feminine identities in the PIC.

A STRATEGY FOR MONITORING THE IMPACTS OF COMBINED SEWER OVERFLOWS ON THE OHIO RIVER

1994 ◽  
Vol 30 (1) ◽  
pp. 167-175
Author(s):  
Alan H. Vicory ◽  
Peter A. Tennant
Keyword(s):  
National Policy ◽  
The United States ◽  
Ohio River ◽  
Combined Sewer Overflows ◽  
Treatment Technology ◽  
Design Storm ◽  
Combined Sewer ◽  
Sewer Overflows ◽  
Definition Of ◽  
And Control

With the attainment of secondary treatment by virtually all municipal discharges in the United States, control of water pollution from combined sewer overflows (CSOs) has assumed a high priority. Accordingly, a national strategy was issued in 1989 which, in 1993, was expanded into a national policy on CSO control. The national policy establishes as an objective the attainment of receiving water quality standards, rather than a design storm/treatment technology based approach. A significant percentage of the CSOs in the U.S. are located along the Ohio River. The states along the Ohio have decided to coordinate their CSO control efforts through the Ohio River Valley Water Sanitation Commission (ORSANCO). With the Commission assigned the responsibility of developing a monitoring approach which would allow the definition of CSO impacts on the Ohio, research by the Commission found that very little information existed on the monitoring and assessment of large rivers for the determination of CSO impacts. It was therefore necessary to develop a strategy for coordinated efforts by the states, the CSO dischargers, and ORSANCO to identify and apply appropriate monitoring approaches. A workshop was held in June 1993 to receive input from a variety of experts. Taking into account this input, a strategy has been developed which sets forth certain approaches and concepts to be considered in assessing CSO impacts. In addition, the strategy calls for frequent sharing of findings in order that the data collection efforts by the several agencies can be mutually supportive and lead to technically sound answers regarding CSO impacts and control needs.

THE DEVELOPMENT OF ACCOUNTING AND INTERNAL CONTROL FOR THE NATIONAL LAND SYSTEM OF THE USA

1994 ◽  
Vol 21 (1) ◽  
pp. 189-213
Author(s):  
Michael P. Schoderbek
Keyword(s):  
United States ◽  
Internal Control ◽  
The United States ◽  
Record Keeping ◽  
Governmental Accounting ◽  
Land System ◽  
The Usa ◽  
And Control

This paper examines the early accounting practices that were used to administer the United States' national land system. These practices are of significance because they provide insights on early governmental accounting and they facilitated an orderly settlement of the western territories. The analysis focuses on the record-keeping and control practices that were developed to meet the provisions of the Land Act of 1800 and to account for land office transactions. These accounting procedures were extracted from the correspondence between the Department of the Treasury and the various land officers.

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