Michaels D C, Chialvo D R, Matyas E P, Jalife J
Department of Pharmacology, State University of New York Health Science Center, Syracuse 13210.
Circ Res. 1989 Nov;65(5):1350-60. doi: 10.1161/01.res.65.5.1350.
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.
