Applied Mathematics and Mechanics (English Edition) ›› 2022, Vol. 43 ›› Issue (9): 1399-1414.doi: https://doi.org/10.1007/s10483-022-2896-7

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Regulating absence seizures by tri-phase delay stimulation applied to globus pallidus internal

Songan HOU1, Denggui FAN2, Qingyun WANG1,3   

  1. 1. Department of Dynamics and Control, Beihang University, Beijing 100191, China;
    2. School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, China;
    3. Beijing Institute of Brain Disorders, Capital Medical University, Beijing 100069, China
  • Received:2022-05-22 Revised:2022-06-15 Published:2022-08-31
  • Contact: Qingyun WANG, E-mail: nmqingyun@163.com
  • Supported by:
    the National Natural Science Foundation of China (Nos. 11932003, 12072021, and 11672074)

Abstract: In this paper, a reduced globus pallidus internal (GPI)-corticothalamic (GCT) model is developed, and a tri-phase delay stimulation (TPDS) with sequentially applying three pulses on the GPI representing the inputs from the striatal $D_{1}$ neurons, subthalamic nucleus (STN), and globus pallidus external (GPE), respectively, is proposed. The GPI is evidenced to control absence seizures characterized by 2Hz-4,Hz spike and wave discharge (SWD). Hence, based on the basal ganglia-thalamocortical (BGCT) model, we firstly explore the triple effects of $D_{1}$-GPI, GPE-GPI, and STN-GPI pathways on seizure patterns. Then, using the GCT model, we apply the TPDS on the GPI to potentially investigate the alternative and improved approach if these pathways to the GPI are blocked. The results show that the striatum $D_{1}$, GPE, and STN can indeed jointly and significantly affect seizure patterns. In particular, the TPDS can effectively reproduce the seizure pattern if the $D_{1}$-GPI, GPE-GPI, and STN-GPI pathways are cut off. In addition, the seizure abatement can be obtained by well tuning the TPDS stimulation parameters. This implies that the TPDS can play the surrogate role similar to the modulation of basal ganglia, which hopefully can be helpful for the development of the brain-computer interface in the clinical application of epilepsy.

Key words: epileptic absence seizure, spike and wave discharge (SWD), tri-phase delay stimulation (TPDS), mean field model, seizure control

2010 MSC Number: 

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