Simulation on relationship between power/phase stability of low frequency oscillatory potentials and activity of dipole current

Abstract

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. When referring to the solution to the forward problem in electroencephalograph, the brain is regarded as a homogenous 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. 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. 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. The narrow-band phase stability of simulated rhythms could highlight the non-linear phase dynamics. It is hypothesized 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.