Origin of arrhythmias in a heart model |
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| Authors: | Hiba Sheheitli Richard Rand |
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| Institution: | 1. Key Laboratory of Magnetic Resonance in Biological Systems and State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, Wuhan 430071, China;2. Wuhan National Laboratory for Optoelectronics, Wuhan 430074, China;3. University of Chinese Academy of Sciences, Beijing 100049, China;1. Institute for Disorders of Impulse & Attention, Developmental Brain-Behaviour Laboratory, School of Psychology, University of Southampton, UK;2. School of Psychology and Ψ-P3, Centre for Psychophysics, Psychophysiology and Psychopharmacology, University of Wollongong, Australia;3. Department of Experimental Clinical & Health Psychology, Ghent University, Belgium;1. Hebei Province Key Laboratory of Sustained Utilization & Development of Water Recourse, Hebei Province Collaborative Innovation Center for Sustainable Utilization of Water Resources and Optimization of Industrial Structure, Department of Water Resource and Environment, Hebei Geo University, No. 136 Huai''an Road, Shijiazhuang, 050031, Hebei, PR China;2. School of Energy and Power Engineering, Jiangsu University of Science and Technology, Zhenjiang, 212003, Jiangsu, PR China;3. Key Laboratory of Subsurface Hydrology and Ecological Effects in Arid Region, Ministry of Education, School of Environmental Science and Engineering, Chang''an University, Xi''an, 710064, Shaanxi, PR China;1. Department of Psychology/York Neuroimaging Centre, University of York, Heslington, York, United Kingdom;2. Unit for Visually Impaired People, Istituto Italiano di Tecnologia, Genova, Italy;3. Max Planck Research Group: Neuroanatomy & Connectivity, Max Planck Institute for Human Cognitive and Brain Sciences, Leipzig, Germany |
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| Abstract: | An investigation of the nonlinear dynamics of a heart model is presented. The model compartmentalizes the heart into one part that beats autonomously (the x oscillator), representing the pacemaker or SA node, and a second part that beats only if excited by a signal originating outside itself (the y oscillator), representing typical cardiac tissue. Both oscillators are modeled by piecewise linear differential equations representing relaxation oscillators in which the fast time portion of the cycle is modeled by a jump. The model assumes that the x oscillator drives the y oscillator with coupling constant . As decreases, the regular behavior of y oscillator deteriorates, and is found to go through a series of bifurcations. The irregular behavior is characterized as involving a large amplitude cycle followed by a number n of small amplitude cycles. We compute critical bifurcation values of the coupling constant, , using both numerical methods as well as perturbations. |
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