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J Theor Biol. 2019 Jun 7;470:1-16. doi: 10.1016/j.jtbi.2019.03.008. Epub 2019 Mar 8.

The onset mechanism of Parkinson's beta oscillations: A theoretical analysis.

Author information

1
Department of Applied Mathematics, Zhejiang University of Technology, Hangzhou 310023, China; Key Laboratory of Systems Biology, Center for Excellence in Molecular Cell Science, Institute of Biochemistry and Cell Biology, Shanghai Institute of Biological Sciences, Chinese Academy of Sciences, Shanghai 200031, China. Electronic address: djhubingst@163.com.
2
Department of Mathematics and Statistics, College of Science, Huazhong Agricultural University, Wuhan 430070, China.
3
Key Laboratory of Systems Biology, Center for Excellence in Molecular Cell Science, Institute of Biochemistry and Cell Biology, Shanghai Institute of Biological Sciences, Chinese Academy of Sciences, Shanghai 200031, China.
4
Key Laboratory of Systems Biology, Center for Excellence in Molecular Cell Science, Institute of Biochemistry and Cell Biology, Shanghai Institute of Biological Sciences, Chinese Academy of Sciences, Shanghai 200031, China; Center for Excellence in Animal Evolution and Genetics, Chinese Academy of Sciences, Kunming 650223, China; School of Life Science and Technology, ShanghaiTech University, Shanghai 200031, China; Shanghai Research Center for Brain Science and Brain-Inspired Intelligence, Shanghai 201210, China. Electronic address: lnchen@sibs.ac.cn.

Abstract

In this paper, we build a basal ganglia-cortex-thalamus model to study the oscillatory mechanisms and boundary conditions of the beta frequency band (13-30 Hz) that appears in the subthalamic nucleus. First, a theoretical oscillatory boundary formula is obtained in a simplified model by using the Laplace transform and linearization process of the system at fixed points. Second, we simulate the oscillatory boundary conditions through numerical calculations, which fit with our theoretical results very well, at least in the changing trend. We find that several critical coupling strengths in the model exert great effects on the oscillations, the mechanisms of which differ but can be explained in detail by our model and the oscillatory boundary formula. Specifically, we note that the relatively small or large sizes of the coupling strength from the fast-spiking interneurons to the medium spiny neurons and from the cortex to the fast-spiking interneurons both have obvious maintenance roles on the states. Similar phenomena have been reported in other neurological diseases, such as absence epilepsy. However, some of those interesting mutual regulation mechanisms in the model have rarely been considered in previous studies. In addition to the coupling weight in the pathway, in this work, we show that the delay is a key parameter that affects oscillations. On the one hand, the system needs a minimum delay to generate oscillations; on the other hand, in the appropriate range, a longer delay leads to a higher activation level of the subthalamic nucleus. In this paper, we study the oscillation activities that appear on the subthalamic nucleus. Moreover, all populations in the model show the dynamic behaviour of a synchronous resonance. Therefore, we infer that the mechanisms obtained can be expanded to explore the state of other populations, and that the model provides a unified framework for studying similar problems in the future. Moreover, the oscillatory boundary curves obtained are all critical conditions between the stable state and beta frequency oscillation. The method is also suitable for depicting other common frequency bands during brain oscillations, such as the alpha band (8-12 Hz), theta band (4-7 Hz) and delta band (1-3 Hz). Thus, the results of this work are expected to help us better understand the onset mechanism of parkinson's oscillations and can inspire related experimental research in this field.

KEYWORDS:

Basal ganglia; Beta oscillation; Mean-field network; Subthalamic nucleus

PMID:
30858065
DOI:
10.1016/j.jtbi.2019.03.008

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