Dynamic Control of Cardiac Alternans

Abstract

A dynamic control technique was used to suppress a cardiac arrhythmia called an alternans rhythm in a piece of dissected rabbit heart. Our control algorithm adapted to drifting system parameters, making it well suited for the control of physiological rhythms. Control of cardiac alternans rhythms may have important clinical implications since they often precede serious cardiac arrhythmias and are a harbinger of sudden cardiac death.[S0031-9007 (97)03337-1] PACS numbers: 87.22. -q, 05.45. + b, 07.05.Dz, 87.10.+e Control techniques from the field of nonlinear dynamics [1] have been used to control both chaotic [2] and nonchaotic [3] dynamical systems. Since these control methods do not require knowledge of the system's governing equations, they are particularly applicable in biology where detailed mathematical models are usually unavailable. Control of biological dynamics is important for medical science since abnormal physiological rhythms can be life threatening [4]. Attempts have already been made to control both experimental [5] and model [6,7] biological systems. However, none of these studies used control algorithms which adapted to evolving system parameters. Since physiological environments typically drift over time, practical biological control schemes must adapt to these changes. Here, we utilize an algorithm which controls an evolving cardiac arrhythmia called an alternans rhythm in the rabbit heart.Cardiac alternans rhythms are characterized by an alternation of the timing or morphology of the heart's electrical activity from one beat to the next. While the clinical importance of cardiac alternans has only recently been recognized [8], their discovery dates back to the earliest recordings of cardiac electrical signals [9]. We generated cardiac alternans by electrically stimulating a piece of dissected rabbit heart [10]. Each stimulus delivered to the upper atrium caused a wave of electrical activity to propagate through the atrium, the atrioventricular (AV) node and out the His bundle which is the output of the AV node [ Fig. 1(a)]. We measured the electrical activity near an atrial input of the AV node and at the His bundle output [ Fig. 1(b)]. X was the time for the impulse to pass through the AV node. The output impulse was reinjected into the atrium after a time delay l. When l was made sufficiently small, the conduction time through the AV node began to alternate [11] [ Fig. 1(b)].The dynamics of AV nodal conduction can be characterized by a one-dimensional mapwhere X n is the AV nodal conduction time following the nth atrial stimulus, l is the time delay from His bundle activation to the next atrial stimulus, and f is a nonlinear, decreasing function of both arguments which relates the successive conduction times [11]. The map is represented as a graph in Fig. 2(a). This map determines the sequence of AV nodal conduction times, X 1 , X 2 , X 3 , . . . , X n given some initial conduction time, X 0 , for fixed l. The intersection of the curve with the line of identity (X n11 X n ) defines the period-...

Control of Electrical Alternans in Canine Cardiac Purkinje Fibers

“…Initial work in that direction showed that closed-loop feedback methods could be used to suppress a type of alternans (known as atrioventricular-nodal conduction alternans) with period-doubling dynamics that are related to those of APD alternans [10][11][12][13]. More recently, it was shown that a related control method could terminate APD alternans in isolated frog hearts [14,15].…”

On the stability of delayed feedback controllers

“…DFC has been successfully applied to many systems, including the stabilization of coherent modes of laser [5,6]; cardiac systems, [7,8], controlling friction, [9]; chaotic electronic oscillators, [10,11]; chemical systems, [12]. To overcome the limitations of DFC, several modifications have been proposed, [13][14][15][16][17].…”

Control of electrical alternans in simulations of paced myocardium using extended time-delay autosynchronization

“…For this reason, we refer to R as the history parameter for the ETDAS method. We remark that variants of the special case of ETDAS in which R = 0 (i.e., A n+1 is directly influenced only by the most recent APD value, A n ) have been used for experimental control of alternans both in vivo [14] and in vitro [7,17,28].…”

“…Notably, by writing the ADIC scheme in an apparently different but equivalent way, one finds that the ADIC scheme is actually a special case of ETDAS and the important advantages of ADIC are shared by all ETDAS schemes. ETDAS has several noteworthy features, such as: (i) the control domain (i.e., the set of all possible parameter choices for which control successfully suppresses alternans) is large; (ii) various special cases of ETDAS have been used to control AV-nodal conduction time alternans in humans in vivo [14] as well as APD alternans in canines [7], frogs [17] and rabbits [28] in vitro; (iii) ETDAS is amenable to experimental setup and has already been used for chaos control in physical systems [24,29]; (iv) it is possible to restrict the ETDAS parameters to achieve control while allowing only shortening of BCL; (v) the additional freedom gained by using ETDAS as opposed to restrictive cases such as ADIC allows the experimenter to choose parameters in such a way that sensitivity to background noise is reduced; and (vi) because ETDAS has been studied for over a decade, one may exploit prior mathematical analysis [23,24] as a guide for choosing system parameters that lead to successful control of alternans.…”