A mathematical model of automaticity in the sinus node and AV junction based on weakly coupled relaxation oscillators

A heterogeneous coupled oscillator model for simulation of ECG signals

Mutual entrainment of two pacemaker cells. A study with an electronic parallel conductance model

Recent clinical reports have suggested that conduction disturbances of the Wenckebach type occur below the atrioventricular junction. The purpose of this study was to demonstrate this type of conduction delay within the canine specialized Purkinje fiber system and human ventricular tissue. Conventional microelectrode techniques were utilized in these experiments. Wenckebach periods with 4:3 conduction occurred within the His bundle in response to hyperkalemic (10.8 mEq/liter) Tyrode infusion. Impalement into the false tendons of the right and left bundle demonstrated typical 5:4 and 3:2 interelectrode Wenckebach periods after administration of nicotine. Similar studies were performed in the distal specialized conducting system where microelectrodes were impaled in a terminal Purkinje cell and ventricular cell. With the administration of acetylstrophanthidin and subsequent development of automaticity, beats conducted in orthograde fashion demonstrated typical 3:2 Wenckebach conduction while maintaining 1:1 stimulated retrograde conduction. When human ventricular tissue was exposed to Tyrode solution containing 4 × normal potassium (10.8 mEq/liter), conduction times from the stimulating to recording electrodes demonstrated 4:3; 3:2 and, finally, 2:1 Wenckebach conduction. These experiments demonstrated the electrophysiologic evidence for Wenckebach structures at all levels of the canine His-Purkinje system and human ventricular muscle.

Electrophysiologic studies on Wenckebach structures below the atrioventricular junction.

Electrophysiologic mechanisms responsible for Wenckebach periodicity produced experimentally in a segment of blocked canine Purkinje fibers were investigated with multiple microelectrode recordings. Transmission through the zone of block was electrotonic. The Wenckebach mechanism was related to a progressive decrease in the efficacy of the transmitted electrotonic potential as a stimulus for the regenerative response at the distal block boundary with successive impulses of the cycle. This was manifested in the transmembrane potentials as a progressive decrease in upstroke velocity and a voltage change that caused the electrotonic potential to become progressively removed from the threshold for stimulation. The immediate cause of this phenomenon was a progressive increase in the voltage level (more negative) from which the electrotonic potential originated and a resulting change in voltage-dependent membrane resistance that further attenuated the signal with successive impulses of the cycle. Two main mechanisms appeared to be responsible for these phenomena: (1) a progressive increase in maximal repolarization voltage (more negative) of the transmembrane potential, and (2) a progressive decrease in the diastolic interval that, in the presence of enhanced phase 4 diastolic depolarization, caused the voltage level from which the electrotonic potential originated to become further removed from the stimulation threshold with successive impulses of the cycle.

Microelectrode study of Wenckebach periodicity in canine Purkinje fibers

A cardiac pacemaker model is described based on a close approximation of the properties of cardiac pacemaker cells. It is a minimum-parameter model which has a simple relaxation oscillator circuit as its main element. The pacemaker model is analyzed in detail in order to show that its behaviour is similar to that of cardiac pacemaker cells. The main feature of the model is the possibility of controlling the time course of phase 4 depolarization, the threshold level and the maximum level of repolarization. Emphasis is placed on phenomena of acceleration and deceleration of the pacemaker model by pulsatile stimulation, and on synchronization and frequency entrainment. Finally it is noted that this particular pacemaker model is very useful for the study of interactions between cardiac pacemakers and the description of the mechanism of arrhythmias.

A cardiac pacemaker model

This paper describes an electronic model of the conduction system of the heart, in the form of a simulation unit for cardiac arrhythmias. The basic assumptions made are the existence of two distinct cardiac pacemaking centres, and the possibility of reciprocal interaction between them. Details concerning the construction of the simulation unit are given, and its operation is illustrated by means of a few simple examples of cardiac arrhythmias. The advantages presented by this device for teaching and demonstration of various cardiac arrhythmic patterns are also emphasized.

F. A. Roberge

Papers

A cardiac pacemaker model

A simulation unit for cardiac arrhythmias.

The mechanism of the Wenckebach phenomenon.