As a precursor for cardiac arrhythmias such as atrial and ventricular fibrillations, which could ... more As a precursor for cardiac arrhythmias such as atrial and ventricular fibrillations, which could cause sudden cardiac death (SCD), cardiac alternans is essentially an unstable heart rhythm with alternating long and short action potential durations (APD) of cardiac myocytes that usually occurs under fast pacing conditions. In this paper, the constant TR control method based on global pseudo-electrocardiogram (ECG) is studied and compared with the local constant diastolic interval (DI) control method using a 2-dimensional (2-D) cellular automata model (CAM), aiming at preventing or eliminating cardiac alternans before arrhythmias. The results show that both the constant TR and constant DI control methods are effective in stabling the alternans to a smaller basic cycle length (BCL). Also, the efficacy of the two control approaches depends on the “decrease step” Δ in the downsweep protocol, and a smaller Δ could significantly improve their performance. Besides, in general, constant TR c...
Computational and mathematical methods in medicine, 2016
Myocardial ischemia is associated with pathophysiological conditions such as hyperkalemia, acidos... more Myocardial ischemia is associated with pathophysiological conditions such as hyperkalemia, acidosis, and hypoxia. These physiological disorders may lead to changes on the functions of ionic channels, which in turn form the basis for cardiac alternans. In this paper, we investigated the roles of hyperkalemia and calcium handling components played in the genesis of alternans in ischemia at the cellular level by using computational simulations. The results show that hyperkalemic reduced cell excitability and delayed recovery from inactivation of depolarization currents. The inactivation time constant τf of L-type calcium current (ICaL) increased obviously in hyperkalemia. One cycle length was not enough for ICaL to recover completely. Alternans developed as a result of ICaL responding to stimulation every other beat. Sarcoplasmic reticulum calcium-ATPase (SERCA2a) function decreased in ischemia. This change resulted in intracellular Ca (Ca i ) alternans of small magnitude. A strong Na(...
Sudden cardiac death instigated by ventricular fibrillation (VF) is the largest cause of natural ... more Sudden cardiac death instigated by ventricular fibrillation (VF) is the largest cause of natural death in the USA. Alternans, a beat-to-beat alternation in the action potential duration, has been implicated as being proarrhythmic. The onset of alternans is mediated via a bifurcation, which may occur through either a smooth or a border-collision mechanism. The objective of this study was to characterize the mechanism of bifurcation to alternans based on experiments in isolated whole rabbit hearts. High resolution optical mapping was performed and the electrical activity was recorded from the left ventricle (LV) epicardial surface of the heart. Each heart was paced using an “alternate pacing protocol,” where the basic cycle length (BCL) was alternatively perturbed by ±δ. Local onset of alternans in the heart,BCLstart, was measured in the absence of perturbations (δ=0) and was defined as the BCL at which 10% of LV exhibited alternans. The influences of perturbation size were investigat...
Journal of Computational and Nonlinear Dynamics, 2006
Electrically driven impact microactuators generate nanoscale displacements without large driving ... more Electrically driven impact microactuators generate nanoscale displacements without large driving distances and high voltages. These systems exhibit complex dynamics because of inherent nonlinearities due to impacts, friction, and electric forces. As a result, dramatic changes in system behavior, associated with so-called grazing bifurcations, may occur during the transition between impacting and nonimpacting dynamics, including the presence of robust chaos. For successful open-loop operating conditions, the system design is limited to certain parameter regions, where desired system responses reside. The objective of this paper is to overcome this limitation to allow for a more precise displacement manipulation using impact microactuators. This is achieved through a closed-loop feedback scheme that successfully controls the system dynamics in the near-grazing region.
Journal of Computational and Nonlinear Dynamics, 2005
Tapping-mode atomic force microscopy has wide applications for probing the nanoscale surface and ... more Tapping-mode atomic force microscopy has wide applications for probing the nanoscale surface and subsurface properties of a variety of materials in a variety of environments. Strongly nonlinear effects due to large variations in the force field on the probe tip over very small length scales and the intermittency of contact with the sample, however, result in strong dynamical instabilities. These can result in a sudden loss of stability of low-contact-velocity oscillations of the atomic-force-microscope tip in favor of oscillations with high contact velocity, coexistence of stable oscillatory motions, and destructive, nonrepeatable, and unreliable characterization of the nanostructure. In this paper, dynamical systems tools for piecewise-smooth systems are employed to characterize the loss of stability and associated parameter-hysteresis phenomena.
Volume 2: Biomedical and Biotechnology Engineering, 2007
Predicting cardiac alternans is a crucial step toward detection and prevention of ventricular fib... more 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 tim...
ABSTRACT Cardiac cells respond to an electrical stimulus with an action potential, consisting of ... more ABSTRACT Cardiac cells respond to an electrical stimulus with an action potential, consisting of a rapid depolarization of transmembrane voltage followed by a much slower repolarization process before returning to the resting value, see Figure 1. The time interval when voltage is above the resting value is the duration of an action potential (APD). The time between the end of APD to the arrival of the next stimulus is called diastolic interval (DI). The time interval between two consecutive stimuli is called basic cycle length (BCL). The relation between APD and previous pacing history is known as restitution, which is a key concept in understanding cardiac rhythm instabilities.
As a precursor for cardiac arrhythmias such as atrial and ventricular fibrillations, which could ... more As a precursor for cardiac arrhythmias such as atrial and ventricular fibrillations, which could cause sudden cardiac death (SCD), cardiac alternans is essentially an unstable heart rhythm with alternating long and short action potential durations (APD) of cardiac myocytes that usually occurs under fast pacing conditions. In this paper, the constant TR control method based on global pseudo-electrocardiogram (ECG) is studied and compared with the local constant diastolic interval (DI) control method using a 2-dimensional (2-D) cellular automata model (CAM), aiming at preventing or eliminating cardiac alternans before arrhythmias. The results show that both the constant TR and constant DI control methods are effective in stabling the alternans to a smaller basic cycle length (BCL). Also, the efficacy of the two control approaches depends on the “decrease step” Δ in the downsweep protocol, and a smaller Δ could significantly improve their performance. Besides, in general, constant TR c...
Computational and mathematical methods in medicine, 2016
Myocardial ischemia is associated with pathophysiological conditions such as hyperkalemia, acidos... more Myocardial ischemia is associated with pathophysiological conditions such as hyperkalemia, acidosis, and hypoxia. These physiological disorders may lead to changes on the functions of ionic channels, which in turn form the basis for cardiac alternans. In this paper, we investigated the roles of hyperkalemia and calcium handling components played in the genesis of alternans in ischemia at the cellular level by using computational simulations. The results show that hyperkalemic reduced cell excitability and delayed recovery from inactivation of depolarization currents. The inactivation time constant τf of L-type calcium current (ICaL) increased obviously in hyperkalemia. One cycle length was not enough for ICaL to recover completely. Alternans developed as a result of ICaL responding to stimulation every other beat. Sarcoplasmic reticulum calcium-ATPase (SERCA2a) function decreased in ischemia. This change resulted in intracellular Ca (Ca i ) alternans of small magnitude. A strong Na(...
Sudden cardiac death instigated by ventricular fibrillation (VF) is the largest cause of natural ... more Sudden cardiac death instigated by ventricular fibrillation (VF) is the largest cause of natural death in the USA. Alternans, a beat-to-beat alternation in the action potential duration, has been implicated as being proarrhythmic. The onset of alternans is mediated via a bifurcation, which may occur through either a smooth or a border-collision mechanism. The objective of this study was to characterize the mechanism of bifurcation to alternans based on experiments in isolated whole rabbit hearts. High resolution optical mapping was performed and the electrical activity was recorded from the left ventricle (LV) epicardial surface of the heart. Each heart was paced using an “alternate pacing protocol,” where the basic cycle length (BCL) was alternatively perturbed by ±δ. Local onset of alternans in the heart,BCLstart, was measured in the absence of perturbations (δ=0) and was defined as the BCL at which 10% of LV exhibited alternans. The influences of perturbation size were investigat...
Journal of Computational and Nonlinear Dynamics, 2006
Electrically driven impact microactuators generate nanoscale displacements without large driving ... more Electrically driven impact microactuators generate nanoscale displacements without large driving distances and high voltages. These systems exhibit complex dynamics because of inherent nonlinearities due to impacts, friction, and electric forces. As a result, dramatic changes in system behavior, associated with so-called grazing bifurcations, may occur during the transition between impacting and nonimpacting dynamics, including the presence of robust chaos. For successful open-loop operating conditions, the system design is limited to certain parameter regions, where desired system responses reside. The objective of this paper is to overcome this limitation to allow for a more precise displacement manipulation using impact microactuators. This is achieved through a closed-loop feedback scheme that successfully controls the system dynamics in the near-grazing region.
Journal of Computational and Nonlinear Dynamics, 2005
Tapping-mode atomic force microscopy has wide applications for probing the nanoscale surface and ... more Tapping-mode atomic force microscopy has wide applications for probing the nanoscale surface and subsurface properties of a variety of materials in a variety of environments. Strongly nonlinear effects due to large variations in the force field on the probe tip over very small length scales and the intermittency of contact with the sample, however, result in strong dynamical instabilities. These can result in a sudden loss of stability of low-contact-velocity oscillations of the atomic-force-microscope tip in favor of oscillations with high contact velocity, coexistence of stable oscillatory motions, and destructive, nonrepeatable, and unreliable characterization of the nanostructure. In this paper, dynamical systems tools for piecewise-smooth systems are employed to characterize the loss of stability and associated parameter-hysteresis phenomena.
Volume 2: Biomedical and Biotechnology Engineering, 2007
Predicting cardiac alternans is a crucial step toward detection and prevention of ventricular fib... more 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 tim...
ABSTRACT Cardiac cells respond to an electrical stimulus with an action potential, consisting of ... more ABSTRACT Cardiac cells respond to an electrical stimulus with an action potential, consisting of a rapid depolarization of transmembrane voltage followed by a much slower repolarization process before returning to the resting value, see Figure 1. The time interval when voltage is above the resting value is the duration of an action potential (APD). The time between the end of APD to the arrival of the next stimulus is called diastolic interval (DI). The time interval between two consecutive stimuli is called basic cycle length (BCL). The relation between APD and previous pacing history is known as restitution, which is a key concept in understanding cardiac rhythm instabilities.
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