中国物理B ›› 2018, Vol. 27 ›› Issue (4): 48701-048701.doi: 10.1088/1674-1056/27/4/048701
• INTERDISCIPLINARY PHYSICS AND RELATED AREAS OF SCIENCE AND TECHNOLOGY • 上一篇
Analytically determining frequency and amplitude of spontaneous alpha oscillation in Jansen's neural mass model using the describing function method
Yao Xu(徐瑶), Chun-Hui Zhang(张春会), Ernst Niebur, Jun-Song Wang(王俊松)
- 1. School of Biomedical Engineering, Tianjin Medical University, Tianjin 300070, China;
2. Qingdao Stomatological Hospital, Department of Medical Technology Equipment, Qingdao 266001, China;
3. Zanvyl Krieger Mind/Brain Institute and Solomon Snyder Department of Neuroscience, Johns Hopkins University, Baltimore 21218, MD, USA
Analytically determining frequency and amplitude of spontaneous alpha oscillation in Jansen's neural mass model using the describing function method
Yao Xu(徐瑶)1,2, Chun-Hui Zhang(张春会)1, Ernst Niebur3, Jun-Song Wang(王俊松)1
- 1. School of Biomedical Engineering, Tianjin Medical University, Tianjin 300070, China;
2. Qingdao Stomatological Hospital, Department of Medical Technology Equipment, Qingdao 266001, China;
3. Zanvyl Krieger Mind/Brain Institute and Solomon Snyder Department of Neuroscience, Johns Hopkins University, Baltimore 21218, MD, USA
摘要：
Spontaneous alpha oscillations are a ubiquitous phenomenon in the brain and play a key role in neural information processing and various cognitive functions. Jansen's neural mass model (NMM) was initially proposed to study the origin of alpha oscillations. Most of previous studies of the spontaneous alpha oscillations in the NMM were conducted using numerical methods. In this study, we aim to propose an analytical approach using the describing function method to elucidate the spontaneous alpha oscillation mechanism in the NMM. First, the sigmoid nonlinear function in the NMM is approximated by its describing function, allowing us to reformulate the NMM and derive its standard form composed of one nonlinear part and one linear part. Second, by conducting a theoretical analysis, we can assess whether or not the spontaneous alpha oscillation would occur in the NMM and, furthermore, accurately determine its amplitude and frequency. The results reveal analytically that the interaction between linearity and nonlinearity of the NMM plays a key role in generating the spontaneous alpha oscillations. Furthermore, strong nonlinearity and large linear strength are required to generate the spontaneous alpha oscillations.
中图分类号: (General theory and mathematical aspects)
- 87.10.-e