Stochastic dynamics of conduction failure of action potential along nerve fiber with Hopf bifurcation  

作　　者：ZHANG XinJing GU HuaGuang GUAN LiNan 

机构地区：[1]School of Aerospace Engineering and Applied Mechanics, Tongji University

出　　处：《Science China(Technological Sciences)》2019年第9期1502-1511,共10页中国科学（技术科学英文版）

基　　金：supported by the National Natural Science Foundation of China(Grant Nos.11872276,11572225)

摘　　要：Action potentials can be induced by external electronic impulsive stimulations applied at one end of the unmyelinated fibers(C-fibers), while some action potentials fail to conduct to the other end of the fiber when the stimulation frequency becomes high. Such a phenomenon is called as conduction failure, which was observed in the biological experiments and related to the painful diabetic neuropathy, inflammation, and trauma in the previous studies. On-off firing pattern was recorded from the fiber when conduction failure happened. In the present study, the diffusion Hodgkin-Huxley(HH) model with resting state near a Hopf bifurcation is adopted to simulate the experimental observations. When the periodic electrical pulses with high frequency are applied to one end of the fiber described by the deterministic HH model, conduction failure and the corresponding firing patterns different from the on-off firing pattern are simulated. When noise is introduced to form the stochastic HH model, the firing pattern corresponding to conduction failure becomes the on-off firing pattern, which is characterised by transition behaviors between on-phase(continuous action potentials) and off-phase(a long quiescent state) and large variations in the durations of both phases. Furthermore, the increase of potassium conductance can enhance the conduction failure degree, which closely matches those observed in the experiment and is suggested to be related to the reduction of pain signals. The results show that noise is an important factor to evoke the on-off firing pattern, reveal the functional capability in the pain signals propagation along C-fiber,and present a possible measure for the treatment of chronic pain.Action potentials can be induced by external electronic impulsive stimulations applied at one end of the unmyelinated fibers(C-fibers), while some action potentials fail to conduct to the other end of the fiber when the stimulation frequency becomes high. Such a phenomenon is called as conduction failure, which was observed in the biological experiments and related to the painful diabetic neuropathy, inflammation, and trauma in the previous studies. On-off firing pattern was recorded from the fiber when conduction failure happened. In the present study, the diffusion Hodgkin-Huxley(HH) model with resting state near a Hopf bifurcation is adopted to simulate the experimental observations. When the periodic electrical pulses with high frequency are applied to one end of the fiber described by the deterministic HH model, conduction failure and the corresponding firing patterns different from the on-off firing pattern are simulated. When noise is introduced to form the stochastic HH model, the firing pattern corresponding to conduction failure becomes the on-off firing pattern, which is characterised by transition behaviors between on-phase(continuous action potentials) and off-phase(a long quiescent state) and large variations in the durations of both phases. Furthermore, the increase of potassium conductance can enhance the conduction failure degree, which closely matches those observed in the experiment and is suggested to be related to the reduction of pain signals. The results show that noise is an important factor to evoke the on-off firing pattern, reveal the functional capability in the pain signals propagation along C-fiber,and present a possible measure for the treatment of chronic pain.

关 键 词：neural FIRING conduction FAILURE HOPF bifurcation periodic pulse STIMULUS C-FIBER 

分 类 号：TH[机械工程]