Alternans and period-doubling bifurcations in atrioventricular nodal conduc

Sun, Jiong; Amellal, Farid; Glass, Leon; Billette, Jacques

doi:10.1006/jtbi.1995.0045

Cited by 72 publications

(76 citation statements)

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“…Incorporation of fatigue and facilitation into mathematical models of the AV node can lead to a variety of subtle dynamical effects including changes in ratio of atrial to ventricular beats during stimulation at fixed frequency (Talajic et al, 1991), or alternation of the conduction time through the AV node during atrial stimulation at a fixed delay after ventricular activation (Sun et al, 1995;Amellal et al, 1996). Though inclusion of fatigue and facilitation would have been possible in the current model, the incorporation of extra parameters would have made it much more difficult to scan the parameter space.…”

Section: Discussionmentioning

confidence: 99%

“…Though inclusion of fatigue and facilitation would have been possible in the current model, the incorporation of extra parameters would have made it much more difficult to scan the parameter space. Furthermore, fatigue and facilitation are especially important during rapid activation in which each atrial stimulus is conducted to the ventricles or when a small fraction of atrial activations are blocked in the AV node (Talajic et al, 1991;Sun et al, 1995;Amellal et al, 1996).…”

Section: Discussionmentioning

confidence: 99%

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A Mathematical Model of Human Atrioventricular Nodal Function Incorporating Concealed Conduction

Jørgensen

Schäfer

Guerra

et al. 2002

Bulletin of Mathematical Biology

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This work develops a mathematical model for the atrioventricular (AV) node in the human heart, based on recordings of electrical activity in the atria (the upper chambers of the heart) and the ventricles (the lower chambers of the heart). Intracardiac recordings of the atrial and ventricular activities were recorded from one patient with atrial flutter and one with atrial fibrillation. During these arrhythmias, not all beats in the atria are conducted to the ventricles. Some are blocked (concealed). However, the blocked beats can affect the properties of the AV node. The activation times of the atrial events were regarded as inputs to a mathematical model of conduction in the AV node, including a representation of AV nodal concealment. The model output was compared to the recorded ventricular response to search for and identify the best possible parameter combinations of the model. Good agreement between the distribution of interbeat intervals in the model and data for durations of 5 min was achieved. A model of AV nodal behavior during atrial flutter and atrial fibrillation could potentially help to understand the relative roles of atrial input activity and intrinsic AV nodal properties in determining the ventricular response.

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Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

A Mathematical Model of Human Atrioventricular Nodal Function Incorporating Concealed Conduction

Jørgensen

Schäfer

Guerra

et al. 2002

Bulletin of Mathematical Biology

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“…However, Billette and coworkers (29,30) have demonstrated clearly that alternans can result solely from the conduction properties of a single AV-nodal pathway. In fact, alternans attributed to a single AV-nodal pathway have been observed in humans during AV orthodromic reciprocating tachycardia (ORT; refs.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear-dynamical arrhythmia control in humans

Christini

Steín²,

Markowitz³

et al. 2001

Proc. Natl. Acad. Sci. U.S.A.

114

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Nonlinear-dynamical control techniques, also known as chaos control, have been used with great success to control a wide range of physical systems. Such techniques have been used to control the behavior of in vitro excitable biological tissue, suggesting their potential for clinical utility. However, the feasibility of using such techniques to control physiological processes has not been demonstrated in humans. Here we show that nonlinear-dynamical control can modulate human cardiac electrophysiological dynamics by rapidly stabilizing an unstable target rhythm. Specifically, in 52͞54 control attempts in five patients, we successfully terminated pacing-induced period-2 atrioventricular-nodal conduction alternans by stabilizing the underlying unstable steady-state conduction. This proof-of-concept demonstration shows that nonlinear-dynamical control techniques are clinically feasible and provides a foundation for developing such techniques for more complex forms of clinical arrhythmia.I ncreasingly, it is recognized that many cardiac arrhythmias can be characterized on the basis of the physical principles of nonlinear dynamics (1, 2). A nonlinear-dynamical system is one that changes with time and cannot be broken down into a linear sum of its individual components. For certain nonlinear systems, known as chaotic systems, behavior is aperiodic and long-term prediction is impossible, even though the dynamics are entirely deterministic (i.e., the dynamics of the system are completely determined from known inputs and the previous state of the system, with no influence from random inputs). Importantly, such determinism actually can be exploited to control the dynamics of a chaotic system. To this end, a variety of nonlineardynamical control techniques, also known as chaos control, ‡ have been developed (3, 4) and applied successfully to a wide range of physical systems (5)(6)(7)(8)(9)(10)(11)(12)(13)(14). Such techniques are modelindependent, i.e., they require no a priori knowledge of the underlying equations of a system and are therefore appropriate for systems that are essentially ''black boxes.''The success of nonlinear-dynamical control techniques in stabilizing physical systems, together with the facts that many physiological systems are nonlinear (e.g., the cardiac conduction system, because of its numerous complex nonlinear component interactions) and lack the detailed analytical system models required for model-based control techniques, have fostered widespread interest in applying these model-independent techniques to biological dynamical systems (15)(16)(17)(18)(19)(20)(21)(22)(23)(24)(25)(26). In a pioneering application, Garfinkel et al. (15) stabilized drug-induced irregular cardiac rhythms by means of dynamically timed electrical stimulation in an in vitro rabbit ventricular-tissue preparation. That work was an important demonstration that the physical principles of nonlinear-dynamical control could be extended into the realm of cardiac dynamics. Although extension of that work to the control of fibrill...

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“…These points satisfy (14) It follows from the above equations that (15) where (16) For these calculations to be consistent and for the orbit to be stable, we need the following condition. …”

Section: Analysis Of Period-two Solutions-whenmentioning

confidence: 99%

“…Examples of B/C bifurcations have been observed in various engineering and biological systems [4,13,14,15]. Different phenomena in B/C bifurcations have been classified by a few authors [1,3,4,5,6,7,9].…”

Section: Introductionmentioning

confidence: 99%

Alternate pacing of border-collision period-doubling bifurcations

Zhao

Schaeffer

2007

Nonlinear Dyn

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Unlike classical bifurcations, border-collision bifurcations occur when, for example, a fixed point of a continuous, piecewise map crosses a boundary in state space. Although classical bifurcations have been much studied, border-collision bifurcations are not well understood. This paper considers a particular class of border-collision bifurcations, i.e., border-collision perioddoubling bifurcations. We apply a subharmonic perturbation to the bifurcation parameter, which is also known as alternate pacing, and we investigate the response under such pacing near the original bifurcation point. The resulting behavior is characterized quantitatively by a gain, which is the ratio of the response amplitude to the applied perturbation amplitude. The gain in a bordercollision period-doubling bifurcation has a qualitatively different dependence on parameters from that of a classical period-doubling bifurcation. Perhaps surprisingly, the differences are more readily apparent if the gain is plotted vs. the perturbation amplitude (with the bifurcation parameter fixed) than if plotted vs. the bifurcation parameter (with the perturbation amplitude fixed). When this observation is exploited, the gain under alternate pacing provides a useful experimental tool to identify a border-collision period-doubling bifurcation.

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Alternans and period-doubling bifurcations in atrioventricular nodal conduc

Cited by 72 publications

References 0 publications

A Mathematical Model of Human Atrioventricular Nodal Function Incorporating Concealed Conduction

A Mathematical Model of Human Atrioventricular Nodal Function Incorporating Concealed Conduction

Nonlinear-dynamical arrhythmia control in humans

Alternate pacing of border-collision period-doubling bifurcations

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