中国物理B ›› 2023, Vol. 32 ›› Issue (9): 90502-090502.doi: 10.1088/1674-1056/acd7d3

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Bifurcations for counterintuitive post-inhibitory rebound spike related to absence epilepsy and Parkinson disease

Xian-Jun Wang(王宪军)1, Hua-Guang Gu(古华光)2,†, Yan-Bing Jia(贾雁兵)3, Bo Lu(陆博)1, and Hui Zhou(周辉)1   

  1. 1 School of Mathematics and Science, Henan Institute of Science and Technology, Xinxiang 453003, China;
    2 School of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai 200092, China;
    3 School of Mathematics and Statistics, Henan University of Science and Technology, Luoyang 471000, China
  • 收稿日期:2023-04-01 修回日期:2023-04-25 接受日期:2023-05-23 发布日期:2023-08-23
  • 通讯作者: Hua-Guang Gu E-mail:guhuaguang@tongji.edu.cn
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant Nos. 12072236, 11872276, and 11802086), the Postdoctoral Research Project of Henan Province, China (Grant No. 19030095), and the Science and Technology Development Program of Henan Province, China (Grant No. 212102210543).

Bifurcations for counterintuitive post-inhibitory rebound spike related to absence epilepsy and Parkinson disease

Xian-Jun Wang(王宪军)1, Hua-Guang Gu(古华光)2,†, Yan-Bing Jia(贾雁兵)3, Bo Lu(陆博)1, and Hui Zhou(周辉)1   

  1. 1 School of Mathematics and Science, Henan Institute of Science and Technology, Xinxiang 453003, China;
    2 School of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai 200092, China;
    3 School of Mathematics and Statistics, Henan University of Science and Technology, Luoyang 471000, China
  • Received:2023-04-01 Revised:2023-04-25 Accepted:2023-05-23 Published:2023-08-23
  • Contact: Hua-Guang Gu E-mail:guhuaguang@tongji.edu.cn
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant Nos. 12072236, 11872276, and 11802086), the Postdoctoral Research Project of Henan Province, China (Grant No. 19030095), and the Science and Technology Development Program of Henan Province, China (Grant No. 212102210543).

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摘要： Seizures are caused by increased neuronal firing activity resulting from reduced inhibitory effect and enhancement of inhibitory modulation to suppress this activity is used as a therapeutic tool. However, recent experiments have shown a counterintuitive phenomenon that inhibitory modulation does not suppress but elicit post-inhibitory rebound (PIR) spike along with seizure to challenge the therapeutic tool. The nonlinear mechanism to avoid the PIR spike can present theoretical guidance to seizure treatment. This paper focuses on identifying credible bifurcations that underlie PIR spike by modulating multiple parameters in multiple theoretical models. The study identifies a codimension-2 bifurcation called saddle-node homoclinic orbit (SNHOB), which is an intersection between saddle node bifurcation on invariant cycle (SNIC) and other two bifurcations. PIR spike cannot be evoked for the SNIC far from the SNHOB but induced for the SNIC close to the SNHOB, which extends the bifurcation condition for PIR spike from the well-known Hopf to SNIC. Especially, in a thalamic neuron model, increases of conductance of T-type Ca2+ (TCa) channel induce SNIC bifurcation approaching to the SNHOB to elicit PIR spikes, closely matching experimental results of the absence seizure or Parkinson diseases. Such results imply that, when inhibition is employed to relieve absence seizure and Parkinson diseases related to PIR spike, modulating SNIC to get far from the SNHOB to avoid PIR spike is the principle. The study also addresses the complex roles of TCa current and comprehensive relationships between PIR spike and nonlinear conceptions such as bifurcation types and shapes of threshold curve.

关键词: bifurcation, threshold, post-inhibitory rebound spike, brain disease

Abstract: Seizures are caused by increased neuronal firing activity resulting from reduced inhibitory effect and enhancement of inhibitory modulation to suppress this activity is used as a therapeutic tool. However, recent experiments have shown a counterintuitive phenomenon that inhibitory modulation does not suppress but elicit post-inhibitory rebound (PIR) spike along with seizure to challenge the therapeutic tool. The nonlinear mechanism to avoid the PIR spike can present theoretical guidance to seizure treatment. This paper focuses on identifying credible bifurcations that underlie PIR spike by modulating multiple parameters in multiple theoretical models. The study identifies a codimension-2 bifurcation called saddle-node homoclinic orbit (SNHOB), which is an intersection between saddle node bifurcation on invariant cycle (SNIC) and other two bifurcations. PIR spike cannot be evoked for the SNIC far from the SNHOB but induced for the SNIC close to the SNHOB, which extends the bifurcation condition for PIR spike from the well-known Hopf to SNIC. Especially, in a thalamic neuron model, increases of conductance of T-type Ca2+ (TCa) channel induce SNIC bifurcation approaching to the SNHOB to elicit PIR spikes, closely matching experimental results of the absence seizure or Parkinson diseases. Such results imply that, when inhibition is employed to relieve absence seizure and Parkinson diseases related to PIR spike, modulating SNIC to get far from the SNHOB to avoid PIR spike is the principle. The study also addresses the complex roles of TCa current and comprehensive relationships between PIR spike and nonlinear conceptions such as bifurcation types and shapes of threshold curve.

Key words: bifurcation, threshold, post-inhibitory rebound spike, brain disease

中图分类号:  (Nonlinear dynamics and chaos)

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87.19.lg (Synapses: chemical and electrical (gap junctions))