A model of electrically coupled sinus node cells was used to investigate pacemaker coordination and conduction. Individual cells were simulated using differential equations describing transmembrane ionic currents. Intrinsic cycle lengths (periods) were adjusted by applying constant depolarizing or hyperpolarizing bias current, and cells were coupled through ohmic resistances to form two-dimensional arrays. Activation maps of 81-225 coupled cells showed an apparent wavefront conducting from a leading pacemaker region to the rest of the matrix even though the pattern actually resulted from mutual entrainment of all spontaneously beating cells. Apparent conduction time increased with increasing intercellular resistance. Appropriate selection of pacemaker cycle lengths and intercellular resistances permitted the accurate simulation of the activation sequence seen experimentally for the rabbit sinus node. Furthermore, a simulated acetylcholine pulse applied to a randomly selected 20% of the cells in this model produced a pacemaker shift that lasted several beats. These results support the hypothesis that sinus node synchronization occurs through a "democratic" process resulting from the phase-dependent interactions of thousands of pacemakers.

Supernormality, which can be defined as greater than normal excitability during or immediately after action potential repolarization, has been observed in a variety of cardiac preparations. However, as yet, no description of the dynamics of tissue response to repetitive stimulation in the presence of supernormal or relatively supernormal excitability has appeared. Isolated sheep cardiac Purkinje fibers (2-5 mm in length) were superfused with Tyrode's solution and stimulated with depolarizing current pulses through a suction pipette. Recovery of excitability, restitution of the action potential duration, and response patterns were measured in each fiber for a wide range of current amplitudes and stimulation frequencies. When the potassium chloride concentration of the Tyrode's solution was decreased from 7 to 4 mM, the excitability recovery function consistently changed from monophasic ("normal") to triphasic ("supernormal'). During repetitive stimulation at increasing rates, normal preparations responded only with gradual changes in the activation ratio, expressed as periodic phase-locked responses (i.e., Wenckebach-like patterns, etc.). Supernormal preparations showed a nonmonotonic change in the activation ratio, as well as complex aperiodic response patterns. Numerical results from an analytical model gave a quantitative basis for the relation between nonmonotonicity in the excitability function and the development of complex rhythms in cardiac Purkinje fibers. Both our experimental and theoretical results indicate that the presence of supernormality and the slope of the action potential duration restitution curve at short diastolic intervals are responsible for the development of chaotic dynamics. Moreover, our results give an accurate description of the supernormality phenomenon, predict the behavior expected under such conditions, and provide insight about the role of membrane recovery in determining regular and irregular frequency-dependent rhythm and conduction disturbances.

Propagation in cardiac muscle is faster in the longitudinal than in the transverse axis of the cells. Yet, as a result of the larger upstroke velocity of action potentials propagating transversely, it has been suggested that longitudinal propagation is more vulnerable to block. To study the relation between conduction velocity and maximal upstroke velocity (Vmax), as well as the time course of conduction delay and block in the transverse vs. longitudinal direction, thin square pieces of sheep epicardial muscle were superfused with the cellular uncoupler heptanol (1.5 mM). Action potentials were recorded with microelectrodes at opposite corners of the preparation while stimulating alternately in the longitudinal or transverse direction with bipolar electrodes located at contralateral corners. In all cases, block occurred more promptly for transverse than for longitudinal propagation. The decrease in conduction velocity was greater than expected for Vmax decay and, in some cases, Vmax increased while conduction velocity decreased. In the presence of high grade conduction impairment, foot potentials appeared and the upstrokes became "notched." We conclude that when intercellular coupling is impaired, transverse propagation is more vulnerable to block, and need not be dependent on changes in Vmax.

Sustained reentrant excitation may be initiated in small (20 X 20 X <0.6 mm) preparations of normal ventricular muscle. A single appropriately timed premature electrical stimulus applied perpendicularly to the wake of a propagating quasiplanar wavefront gives rise to circulation of self-sustaining excitation waves, which pivot at high fequency (5-7 Hz) around a relatively small "phaseless" region. Such a region develops only very low amplitude depolarizations. Once initiated, most episodes of reentrant activity last indefinitely but can be interrupted by the application of an appropriately timed electrical stimulus. The entire course of the electrical activity is visualized with high temporal and spatial resolution, as well as high signal-to-noise ratio, using voltage-sensitive dyes and optical mapping. Two-and three-dimensional graphics of the fluorescence changes recorded by a 10 X 10 photodiode array from a surface of 12 x 12 mm provide sequential images (every msec) of voltage distribution during a reentrant vortex. The results suggest that two-dimensional vortex-like reentry in cardiac muscle is analogous to spiral waves in other biological and chemical excitable media.Many hypotheses have been postulated to explain reentrant excitation in cardiac muscle. Beginning with the classical studies of Mines (1), in which reentry occurs around an anatomical obstacle, through Allessie's leading circle hypothesis (2), to the more recently postulated anisotropic reentry (3), most mechanisms proposed by experimental electrophysiologists are focused on preexisting functional or anatomical inhomogeneities in the myocardium. On the other hand, theoretical studies based on wave propagation in other types of excitable media such as, for example, the BelousovZhabotinsky reaction (4) suggest that these rotating waves, also known as "spiral waves," "reverberators," and "vortices," may occur even in totally homogeneous and continuous media (4-8). As proposed by Winfree (9) and later shown in the whole heart (10), initiation of reentry depends not only on the properties inherent to the myocardium but also on transient local conditions created by the impulse that triggers the reentry. In fact, reentrant excitation may be initiated in the myocardium at a critical point that results from the interaction of a geometrically graded recovery of excitation (i.e., the "tail" of a planar wavefront) with a geometrically graded transverse premature stimulus (10). Our objective was to utilize these concepts to develop an in vitro model of sustained reentry, in which the electrical activity can be closely monitored. Here we demonstrate that self-sustaining vortex-like reentry can be induced in small two-dimensional pieces of cardiac muscle and that the entire course of the excitation-recovery process during the reentrant cycle can be analyzed in detail through the use of optical mapping and voltage-sensitive dyes. METHODSHearts were dissected from anesthetized sheep (sodium pentobarbital, 35 mg/kg, i.v.). Thin slices of left ventricul...

SUMMARY. Dynamic heart rate control by parasympathetic nervous input involves feedback mechanisms and reflex bursting of efferent cardiac vagal fibers. Periodic vagal bursting induces phasic changes in sinoatrial cycle length and can entrain the pacemaker to beat at periods that may be identical to those of the vagal burst. We investigated the electrophysiological basis of these phenomena in isolated sinus node preparations (rabbit, cat, and sheep). In the presence of propranolol (3.9 X 10~6 M), relatively brief (50-150 msec) trains of stimuli, applied onto the endocardial surface of the preparation, activated postganglionic vagal terminals and induced a brief hyperpolarization of sinoatrial pacemaker cells. This vagally mediated hyperpolarization could alter the pacemaker rhythm by an amount that depended on its duration and its position in the cycle, as well as on the duration of the free-running pacemaker period. When the free-running period was sufficiently long and the hyperpolarization was induced sufficiently early in the spontaneous cycle, a "paradoxical" acceleration of the pacemaker rhythm ensued. Phasic changes were plotted on phase-response curves, constructed by scanning systematically the sinoatrial pacemaker period with single or repetitive vagal trains. These phase-response curves enabled us to predict the entrainment characteristics and the levels of synchronization of the pacemaker to the vagal periodicity. The overall data explain the cellular mechanisms involved in the phasic effects of brief vagal discharges on sinoatrial periodicity, and provide conclusive evidence for the prediction that repetitive vagal input is capable of forcing the cardiac pacemaker to beat at rates that can be faster or slower than the intrinsic pacemaker rate. These data should improve our knowledge of the dynamic control of heart rate by neural reflexes and aid in our understanding of rhythm disturbances generated by the interaction of the cardiac pacemaker with vagal activity. (Circ Res 52: 642-656, 1983)