低频振荡电位的能量和相位稳定性与偶极子电流活动相关性的仿真∗

摘要

能量和相位是分析脑节律的重要物理量，虽有许多研究，但其与脑组织电特性和脑节律源的关系尚不完全清楚，弄清这一问题有助于脑电测量及脑功能和疾病的分析。为此，借鉴脑电正问题研究方法，大脑可看作均匀球，脑组织电特性用导体各向同性和各向异性电导率来表示，脑节律源用准静态偶极子电流来模拟，其活动表达为较低频率的正弦振荡，在改变该活动的振幅和相位时程时，用球表面剖分网格的振荡电位仿真脑节律，提取节律的能量和相位，计算源和节律的窄带相位稳定性。结果表明：仿真节律的能量随电导率增大而减小，受网格位置、电导率各向异性、偶极子电流幅值和偏心位置影响较大；但仿真节律的相位稳定性只与自身的相位时程有关。说明能量与相位稳定性电学意义无交集，同时用来分析脑节律可提供更多神经信息；能量的电学意义更复杂，取决于包括测量条件在内的多种因素；相位稳定性的优势在于它仅与脑节律相位时程直接相关，可预测的是脑的非线性导致的相位时程越离散，则相位稳定性越差。%The physical parameters, e.g. power and phase, are usually employed in the neural analysis of brain rhythms, which are important in brain function and disease diagnosis. Though there has been extensive work, how both parameters are related to the electrical properties of brain tissue and the sources of brain rhythms has not been fully understood. To address the issue, a simulation is done based on the theory of dipole current. n When referring to the solution to the forward problem in electroencephalograph, the brain is regarded as a ho-mogenous sphere model, the electrical features of brain tissue are described by an isotropic electrical conductivity. The source of brain rhythms is simulated by the quasi-static dipole current whose activity is described as a sine oscillation at low frequency. The electrical field generated by the dipole current is considered to be quasi-static. By changing the amplitude and the phase time course of oscillatory dipole current, the distribution of potentials produced by the dipole current at a time-point could be calculated by applying the finite element method to the sphere model. Over a time period of sine oscillation, the oscillatory potentials regarded as the brain rhythms could be produced. Instantaneous power and phase of simulated rhythms are estimated by Hilbert transform, and then a method of phase stability in narrow-band is developed for a single oscillator. To highlight this method, three manners are employed to describe it, i.e., mean relative phase value termed phase preserved index, histogram on rose plane, and phase sorting with the help of EEGLAB. Finally the relationship between two physical parameters and the electrical features of brain tissue/the source activity of brain rhythms is investigated under the conditions of (an) isotropy of conductivity, linear or nonlinear phase dynamics and amplitude, eccentricity of dipole current, etc. The statistical methods of t-test and bootstrapping technology are performed respectively to show the significance of power and phase stability. n It is obtained that the power of simulated rhythms decreases with the increase of electrical conductivity, and it is not only proportional to the square of the amplitude of dipole current, but also correlated with the anisotropy of conductivity and the locations of dipole current as well as meshes on the sphere model, however no relevance to other factors. On the contrary, the phase stability of simulated rhythms is correlated only with the non-linear time course of their own phase dynamics. n The results imply that the power of brain rhythms is related to many factors such as brain tissue and amplitude of rhythm generator as well as placements of recording electrodes, but the phase stability is related only to the non-linear phase dynamics of brain rhythms. Thus, the electrical significance of the power is more complicated than that of the phase stability. This work might be helpful for understanding in depth the significance of both physical parameters from the perspective of electricity. n The narrow-band phase stability of simulated rhythms could highlight the non-linear phase dynamics. It is hy-pothesized that the phase stability could not only map the synchrony in the neural activity as a custom means of phase coherence, but also reflect directly the non-linearity in phase dynamics, and the more divergent the phase dynamics, the lower the phase stability is, and vice verse. Therefore it is suggested that the phase stability of brain rhythms could be related closely to the non-linear factors to affect the phase dynamics of brain rhythms, e.g., the non-linear phase dynamics of rhythm generators. It is also suggested that both parameters of power and phase stability would offer more neural information.