The influences of tissue anisotropy and source activity on power and phase stability of low-frequency EEG rhythms: a mathematical observation of the forward problem model

Spontaneous low-frequency brain rhythms could be associated with many neural functions, which were usually evaluated by physical parameters, such as power, frequency, and phase. However, how the parameters might be affected by the electrical features of brain tissue and the electrical activity of the rhythm source is not yet clearly known. To address this issue, the electrical significance of power and narrow-band phase stability (NBPS) was investigated by simulated rhythms. The rhythms were derived from the oscillatory field potentials (FPs) on a homogeneous sphere model of the solution to the electroencephalogram (EEG) forward problem. The sphere's electrical feature was set as isotropic or anisotropic conductivity. The source was set as a quasi-static dipole current, whose activity was representative of a low-frequency sine oscillation with a nonlinear phase course, and the source location was changeable. After the instantaneous power and phase of simulated rhythms were estimated by the Hilbert transformation, the NBPS was calculated and the statistical properties of power and NBPS were analyzed. It was found that only nonlinear phase dynamics could lower the NBPS. However, power depended on many factors, such as conducting anisotropy, amplitude and positon of dipole current, and meshes on the sphere model. Wehypothesized that NBPS would map the influence of nonlinear phase dynamics on the brain rhythms, but be independent of power. This research might highlight the nonlinear phase dynamics of intrinsic low-frequency oscillations in the brain. The results might be beneficial for the measurement and analysis of spontaneous EEG rhythms.