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 associatedwithmany neural functions, which were usually evaluated by physical parameters, such as power, frequency, and phase.However, how the parametersmight 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 rhythmswere derived from the oscillatoryfield potentials (FPs) on a homogeneous spheremodel 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 oscillationwith a nonlinear phase course, and the source locationwas changeable. After the instantaneous power and phase of simulated rhythmswere estimated by theHilbert transformation, theNBPSwas calculated and the statistical properties of power andNBPSwere analyzed. It was found that only nonlinear phase dynamics could lower the NBPS.However, power depended onmany factors, such as conducting anisotropy, amplitude and positon of dipole current, andmeshes on the spheremodel.We hypothesized thatNBPSwouldmap the influence of nonlinear phase dynamics on the brain rhythms, but be independent of power. This researchmight highlight the nonlinear phase dynamics of intrinsic low-frequency oscillations in the brain. The resultsmight be beneficial for themeasurement and analysis of spontaneous EEG rhythms.