Biomaterial Database

Chaotic activity in a mathematical model of the vagally driven sinoatrial node. 1989

D C Michaels, and D R Chialvo, and E P Matyas, and J Jalife

Department of Pharmacology, State University of New York Health Science Center, Syracuse 13210.

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.

UI	MeSH Term	Description	Entries
D008955	Models, Cardiovascular	Theoretical representations that simulate the behavior or activity of the cardiovascular system, processes, or phenomena; includes the use of mathematical equations, computers and other electronic equipment.	Cardiovascular Model,Cardiovascular Models,Model, Cardiovascular
D010507	Periodicity	The tendency of a phenomenon to recur at regular intervals; in biological systems, the recurrence of certain activities (including hormonal, cellular, neural) may be annual, seasonal, monthly, daily, or more frequently (ultradian).	Cyclicity,Rhythmicity,Biological Rhythms,Bioperiodicity,Biorhythms,Biological Rhythm,Bioperiodicities,Biorhythm,Cyclicities,Periodicities,Rhythm, Biological,Rhythmicities,Rhythms, Biological
D002450	Cell Communication	Any of several ways in which living cells of an organism communicate with one another, whether by direct contact between cells or by means of chemical signals carried by neurotransmitter substances, hormones, and cyclic AMP.	Cell Interaction,Cell-to-Cell Interaction,Cell Communications,Cell Interactions,Cell to Cell Interaction,Cell-to-Cell Interactions,Communication, Cell,Communications, Cell,Interaction, Cell,Interaction, Cell-to-Cell,Interactions, Cell,Interactions, Cell-to-Cell
D006801	Humans	Members of the species Homo sapiens.	Homo sapiens,Man (Taxonomy),Human,Man, Modern,Modern Man
D000109	Acetylcholine	A neurotransmitter found at neuromuscular junctions, autonomic ganglia, parasympathetic effector junctions, a subset of sympathetic effector junctions, and at many sites in the central nervous system.	2-(Acetyloxy)-N,N,N-trimethylethanaminium,Acetilcolina Cusi,Acetylcholine Bromide,Acetylcholine Chloride,Acetylcholine Fluoride,Acetylcholine Hydroxide,Acetylcholine Iodide,Acetylcholine L-Tartrate,Acetylcholine Perchlorate,Acetylcholine Picrate,Acetylcholine Picrate (1:1),Acetylcholine Sulfate (1:1),Bromoacetylcholine,Chloroacetylcholine,Miochol,Acetylcholine L Tartrate,Bromide, Acetylcholine,Cusi, Acetilcolina,Fluoride, Acetylcholine,Hydroxide, Acetylcholine,Iodide, Acetylcholine,L-Tartrate, Acetylcholine,Perchlorate, Acetylcholine
D000818	Animals	Unicellular or multicellular, heterotrophic organisms, that have sensation and the power of voluntary movement. Under the older five kingdom paradigm, Animalia was one of the kingdoms. Under the modern three domain model, Animalia represents one of the many groups in the domain EUKARYOTA.	Animal,Metazoa,Animalia
D012849	Sinoatrial Node	The small mass of modified cardiac muscle fibers located at the junction of the superior vena cava (VENA CAVA, SUPERIOR) and right atrium. Contraction impulses probably start in this node, spread over the atrium (HEART ATRIUM) and are then transmitted by the atrioventricular bundle (BUNDLE OF HIS) to the ventricle (HEART VENTRICLE).	Sinuatrial Node,Sinus Node,Sino-Atrial Node,Sinu-Atrial Node,Node, Sino-Atrial,Node, Sinoatrial,Node, Sinu-Atrial,Node, Sinuatrial,Node, Sinus,Nodes, Sino-Atrial,Nodes, Sinoatrial,Nodes, Sinu-Atrial,Nodes, Sinuatrial,Nodes, Sinus,Sino Atrial Node,Sino-Atrial Nodes,Sinoatrial Nodes,Sinu Atrial Node,Sinu-Atrial Nodes,Sinuatrial Nodes,Sinus Nodes
D013268	Stimulation, Chemical	The increase in a measurable parameter of a PHYSIOLOGICAL PROCESS, including cellular, microbial, and plant; immunological, cardiovascular, respiratory, reproductive, urinary, digestive, neural, musculoskeletal, ocular, and skin physiological processes; or METABOLIC PROCESS, including enzymatic and other pharmacological processes, by a drug or other chemical.	Chemical Stimulation,Chemical Stimulations,Stimulations, Chemical
D014630	Vagus Nerve	The 10th cranial nerve. The vagus is a mixed nerve which contains somatic afferents (from skin in back of the ear and the external auditory meatus), visceral afferents (from the pharynx, larynx, thorax, and abdomen), parasympathetic efferents (to the thorax and abdomen), and efferents to striated muscle (of the larynx and pharynx).	Cranial Nerve X,Pneumogastric Nerve,Tenth Cranial Nerve,Nerve X,Nervus Vagus,Cranial Nerve, Tenth,Cranial Nerves, Tenth,Nerve X, Cranial,Nerve Xs,Nerve, Pneumogastric,Nerve, Tenth Cranial,Nerve, Vagus,Nerves, Pneumogastric,Nerves, Tenth Cranial,Nerves, Vagus,Pneumogastric Nerves,Tenth Cranial Nerves,Vagus Nerves,Vagus, Nervus