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耦合神经元模型中簇放电的动力学分析
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Abstract:
呼吸系统是人和动物重要的生理器官之一，位于新生和成年哺乳动物延髓腹外侧区的pre-B？tzinger复合体被认为是呼吸节律产生的中枢，对于研究呼吸系统起着很重要的作用，正常状态和病理状态下呼吸节律有所不同。本文基于pre-B？tzinger复合体耦合神经元模型，利用相平面分析、分岔分析和快慢动力学分析等方法，研究了耦合pre-B？tzinger复合体的簇放电模式及其转迁机制。结果表明钠电导(gNa)对耦合pre-B？tzinger复合体中兴奋性神经元的簇放电节律有重要的影响。
Respiratory system is one of the important physiological organs of human and animal. The pre- B？tzinger complex (pre-B？tC) is located at a ventrolateral medulla of humans and other mammals, which is considered to be the center for the generation of respiratory rhythms. Respiratory rhythm differs between normal and pathological states, which plays an important role in studying the respiratory system. In this paper, we investigate the bursting and their dynamic mechanisms by phase plane analysis, fast-slow decomposition and bifurcation analysis in coupled-neuron model of the pre-B？tC. The results indicate that the Na conductance (gNa) has an important effect on the excitatory neural bursting patterns in the pre-Botzinger complex.
| [1] | Zhen, B. and Xu, J. (2010) Fold-Hopf Bifurcation Analysis for a Coupled FitzHugh-Nagumo Neural System with Time Delay. International Journal of Bifurcation and Chaos, 20, 3919-3934. https://doi.org/10.1142/S0218127410028112 |
| [2] | Izhikevich, E.M. (2000) Neural Excitability, Spiking and Bursting. International Journal of Bifurcation & Chaos in Applied Sciences & Engineering, 10, 1171-1266. https://doi.org/10.1142/S0218127400000840 |
| [3] | Duan, L., Zhai, D. and Tang, X. (2012) Bursting Induced by Excitatory Synaptic Coupling in the Pre-B？tzinger Complex. International Journal of Bifurcation and Chaos, 22, Article ID: 1250114.
https://doi.org/10.1142/S0218127412501143 |
| [4] | Lü, Z.S., Chen, L.N. and Duan, L.X. (2019) Bifurcation Analysis of Mixed Bursting in the Pre-B？tzinger Complex. Applied Mathematical Modelling, 67, 234-251. https://doi.org/10.1016/j.apm.2018.10.031 |
| [5] | Duan, L., Yuan, D., Chen, X., et al. (2015) Transition Mechanisms of Bursting in a Two-Cell Network Model of the Pre-B？tzinger Complex. International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, 25, Article ID: 1550069. https://doi.org/10.1142/S0218127415500698 |
| [6] | Smith, J.C., Ellenberger, H.H., Ballanyi, K. and Feldman, J.L. (1991) Pre-B？tzinger Complex: A Brainstem Region that May Generate Respiratory Rhythm in Mammals. Science, 254, 726-729. https://doi.org/10.1126/science.1683005 |
| [7] | Ramirez, J.M. and Richter, D.W. (1996) The Neuronal Mechanisms of Respiratory Rhythm Generation. Current Opinion in Neurobiology, 6, 817-825. https://doi.org/10.1016/S0959-4388(96)80033-X |
| [8] | Rekling, J.C. and Feldman, J.L. (1998) Pre-B？tzinger Complex and Pacemaker Neurons: Hypothesized Site and Kernel for Respiratory Rhythm Generation. Annual Review of Physiology, 60, 385-405.
https://doi.org/10.1146/annurev.physiol.60.1.385 |
| [9] | Wei, X.Y., Zhao, Y., Wong-Riley, M.T., Ju, G. and Liu, Y.Y. (2012) Synaptic Relationship between Somatostatin- and Neurokinin-1 Receptor-Immunoreactive Neurons in the Pre-B？tzinger Complex of Rats. Journal of Neurochemistry, 122, 923-933. https://doi.org/10.1111/j.1471-4159.2012.07862.x |
| [10] | Hodgkin, A.L. and Huxley, A.F. (1952) A Quantitative Description of Membrane Current and Its Application to Conduction and Excitation in Nerve. The Journal of Physiology, 117, 500-544.
https://doi.org/10.1113/jphysiol.1952.sp004764 |
| [11] | Butera, R.J., Rinzel, J. and Smith, J.C. (1999) Models of Respiratory Rhythm Generation in the Pre-B？tzinger Complex. I. Bursting Pacemaker Neurons. Journal of Neurophysiology, 82, 382-397.
https://doi.org/10.1152/jn.1999.82.1.382 |
| [12] | Butera, R.J., Rinzel, J. and Smith, J.C. (1999) Models of Respiratory Rhythm Generation in the Pre-B？tzinger Complex. II. Populations of Coupled Pacemaker Neurons. Journal of Neurophysiology, 82, 398-415.
https://doi.org/10.1152/jn.1999.82.1.398 |
| [13] | Toporikova, N. and Butera, R.J. (2011) Two Types of Independent Bursting Mechanisms in Inspiratory Neurons: An Integrative Model. Journal of Computational Neuroscience, 30, 515-528. https://doi.org/10.1007/s10827-010-0274-z |
| [14] | Park, C. and Rubin, J.E. (2013) Cooperation of Intrinsic Bursting and Calcium Oscillations Underlying Activity Patterns of Model Pre-B？tzinger Complex Neurons. Journal of Computational Neuroscience, 34, 345-366.
https://doi.org/10.1007/s10827-012-0425-5 |
| [15] | Rinzel, J. (1985) Bursting Oscillations in an Excitable Membrane Model. Ordinary and Partial Differential Equations Proceedings of the 8th Conference, Dundee, 25-29 June 1984, 304-316. https://doi.org/10.1007/BFb0074739 |
| [16] | Dunmyre, J.R., Del Negro, C.A. and Rubin, J.E. (2011) Interactions of Persistent Sodium and Calcium-Activated Nonspecific Cationic Currents Yield Dynamically Distinct Bursting Regimes in a Model of Respiratory Neurons. Journal of Computational Neuroscience, 31, 305-328. https://doi.org/10.1007/s10827-010-0311-y |
| [17] | Gu, H.G. (2013) Different Bifurcation Scenarios of Neural Firing Patterns Observed in the Biological Experiment on Identical Pacemakers. International Journal of Bifurcation and Chaos, 23, Article ID: 1350195.
https://doi.org/10.1142/S0218127413501952 |
| [18] | Wang, Y.Y. and Rubin, J.E. (2016) Multiple Timescale Mixed Bursting Dynamics in a Respiratory Neuron Model. Journal of Computational Neuroscience, 41, 245-268. https://doi.org/10.1007/s10827-016-0616-6 |
| [19] | Bertram, R. and Rubin, J.E. (2017) Multi-Timescale Systems and Fast-Slow Analysis. Mathematical Biosciences, 287, 105-121. https://doi.org/10.1016/j.mbs.2016.07.003 |
| [20] | Wang, Z.J., Duan, L.X. and Cao, Q.Y. (2018) Multi-Stability Involved Mixed Bursting within the Coupled Pre-B？tzinger Complex Neurons. Chinese Physics B, 27, Article ID: 070502.
https://doi.org/10.1088/1674-1056/27/7/070502 |
| [21] | Li, X. and Hou, J. (2016) Bursting Phenomenon in a Piecewise Mechanical System with Parameter Perturbation in Stiffness. International Journal of Non-Linear Mechanics, 81, 165-176.
https://doi.org/10.1016/j.ijnonlinmec.2016.01.014 https://www.nstl.gov.cn/paper_detail.html?id=d62118e9afa263bcb87987dbe7d7d718 |
| [22] | 凯歌. 若干经济系统的Hopf分叉和非线性动力学研究[D]: [博士学位论文]. 北京: 北京工业大学, 2018. |
| [23] | Yu, Y., Zhang, Z., Bi, Q. and Gao, Y. (2016) Bifurcation Analysis on Delay-Induced Bursting in a Shape Memory Alloy Oscillator with Time Delay Feedback. Applied Mathematical Modelling, 40, 1816-1824.
https://doi.org/10.1016/j.apm.2015.09.010 |
