Suppression of pacemaker activity by rapid repetitive phase delay

What keeps us ticking? Sinoatrial node mechano-sensitivity: the grandfather clock of cardiac rhythm

The rhythmic and spontaneously generated electrical excitation that triggers the heartbeat originates in the sinoatrial node (SAN). SAN automaticity has been thoroughly investigated, which has uncovered fundamental mechanisms involved in cardiac pacemaking that are generally categorised into two interacting and overlapping systems: the 'membrane' and 'Ca²⁺ clock'. The principal focus of research has been on these two systems of oscillators, which have been studied primarily in single cells and isolated tissue, experimental preparations that do not consider mechanical factors present in the whole heart. SAN mechano-sensitivity has long been known to be a contributor to SAN pacemaking-both as a driver and regulator of automaticity-but its essential nature has been underappreciated. In this review, following a description of the traditional 'clocks' of SAN automaticity, we describe mechanisms of SAN mechano-sensitivity and its vital role for SAN function, making the argument that the 'mechanics oscillator' is, in fact, the 'grandfather clock' of cardiac rhythm.

A simulation of the SA node by a phase response curve-based model of a two-dimensional pacemaker cells array

This paper presents a simulation of the sino-atrial (SA) node by a two-dimensional pacemaker cells array model, based on phase response curve (PRC) interaction. This simple model of the cardiac pacemaker cells, involves only the most basic functional properties, which play a direct role in the determination of the SA node rhythm. The two most relevant functional properties of the pacemaker cells are: The intrinsic cycle length, an "internal" feature of each pacemaker cell, and the PRC, an "overall collective" function. The PRC contains the "information" about the type of interactions of each pacemaker cell with the outside world (i.e., interaction with neighboring cells, external stimulus, etc.), and "strength" of the interaction (strong, weak, etc.). We studied the spatial interaction among a large number of pacemaker cells (15 x 15), as a function of the regional variation of cells properties, the "electrical" coupling between cells (the PRC), and the appearance of regions with abnormal cycle lengths. We investigated the influence of those parameters on the mutual interaction between the pacemaker cells, on the activation pattern and conduction time of the array, and on a pseudo-electrocardioigram (ECG) signal. This study demonstrates that by representing the pacemaker cells in the SA node by only two fundamental features, and by applying a simple physical-mathematical model, we can create a global picture of the SA node system. This enables us to explore physiological phenomena related to the genesis and maintenance of the SA node activity, and to gain insight into the conditions which predispose the SA node instability, and conduction disturbances.

Discrete-time stimulation of the oscillatory and excitable forms of a FitzHugh-Nagumo model applied to the pulsatile release of luteinizing hormone releasing hormone

A model for the pulsatile release of luteinizing hormone releasing hormone (LHRH) can be reduced to a FitzHugh-Nagumo model subject to regular and quasiregular (i.e., with slight random variation in the interstimulus interval), discrete-time stimulation. The relationship of output pulse frequency (OPF) to stimulus frequency is compared between the excitable and oscillatory forms of the model and discussed in the context of results from other pulse-driven model systems. Some examples of the changes in OPF caused by quasiregular and purely Poissonian stimuli are given for the excitable case. The unstimulated system frequently interacts with the stimulation in such a complex manner that the OPF bears little resemblance to the frequency of stimulation or of the unstimulated system. Furthermore, the inability of the oscillatory form of the model to allow complete suppression of output pulses for moderate stimulation frequencies suggests that the LHRH system can be more appropriately described by the excitable form of the model. (c) 1995 American Institute of Physics.

Chaotic activity in a mathematical model of the vagally driven sinoatrial node

Phase-locking behavior and irregular dynamics were studied in a mathematical model of the sinus node driven with repetitive vagal input. The central region of the sinus node was simulated as a 15 x 15 array of resistively coupled pacemakers with each cell randomly assigned one of 10 intrinsic cycle lengths (range 290-390 msec). Coupling of the pacemakers resulted in their mutual entrainment to a common frequency and the emergence of a dominant pacemaker region. Repetitive acetylcholine (ACh; vagal) pulses were applied to a randomly selected 60% of the cells. Over a wide range of stimulus intensities and basic cycle lengths, such perturbations resulted in a large variety of stimulus/response patterns, including phase locking (1:1, 3:2, 2:1, etc.) and irregular (i.e., chaotic) dynamics. At a low ACh concentration (1 microM), the patterns followed the typical Farey sequence of phase-locked behavior. At a higher concentration (5 microM), period doubling and aperiodic patterns were found. When a single pacemaker cell was perturbed with repetitive ACh pulses, qualitatively similar results were obtained. In both types of simulation, chaotic behavior was investigated using phase-plane (orbital) plots, Poincaré mapping, and return mapping. Period-doubling bifurcations (2:2, 4:4, and 8:8) were found temporally and spatially within the array. Under certain conditions of stimulation, the attractor in the return map during chaotic activity of the single cell resembled the Lorenz tent map. However, when electrical coupling between cells was allowed, the interactions with neighboring cells exhibiting chaotic dynamics resulted in characteristic alterations of the attractor geometry. Our results suggest that irregular dynamics obeying the rules derived from other chaotic systems are present during vagal stimulation of the sinus node. In addition, application of the same analytical tools to the analysis of simulation of reflex vagal control of sinus rate suggests that chaotic dynamics can be obtained in the physiologically relevant case of the baroreceptor reflex loop. These results may provide insight into the mechanisms of dynamic vagal control of heart rate and may help to provide insights into clinically relevant disturbances of cardiac rate and rhythm.

Synchronization in chains of pacemaker cells by phase resetting action potential effects

Interactions between pacemaker cells in a chain were calculated according to a "phase-reset" model. It is based on effects of action potentials in the cells on the cycle lengths of neighbouring cells. These effects were defined for each cell by a latency-phase curve (LPC), giving the latency time (L) until the onset of the next action potential in that cell, as a function of the phase (phi) at which a neighbour cell fired an action potential. Neighbour cells with simultaneous action potentials did not influence each others cycle length. We investigated how stable synchronization depends on the shape of the LPC's of the pacemaker cells and on chain length. Three types of interactive behaviour were distinguished. First, anti-phase synchrony, in which neighbouring cells fired with large phase differences with respect to the synchronized period Ps. Second, asynchrony, in which the periods of the cells did not become equal and constant. Third, in-phase synchrony, in which the phase differences between the neighbouring cells were zero or much smaller than the synchronized period Ps, depending on the differences between the intrinsic periods. Asynchrony and anti-phase synchrony may be seen as cardiophysiological arrhythmias, while in-phase synchrony represents the physiological type of synchrony in the heart. In-phase synchrony appeared to be strongly favoured by LPC's, which have a no-effect (refractory) part at early phases, a lengthened latency (or phase delay) part at intermediate phases and a shortened latency (or phase advance) part at late phases in the cycle. Such LPC-shapes are commonly found in preparations of cardiac pacemaker cells. When the pacemaker cells were identical, the synchronized period Ps during in-phase synchrony was equal to their intrinsic period P*i. For different intrinsic periods, Ps was equal to the intrinsic period of the fastest cell if the LPC's contained a sufficiently long initial no-effect period at early phases and a shortened latency part at late phases. When, on the other hand, such cell chains had a linear gradient in their intrinsic periods, "action potentials" started from the fast end and traveled along the chain. The propagation of an action potential wave slowed down as it reached the slower cells. When the gradient in the intrinsic periods was too steep, only the intrinsically fast end of the chain developed synchrony.(ABSTRACT TRUNCATED AT 400 WORDS)