Sustainable reliability of brain rhythms modeled as sinusoidal waves with frequency–amplitude trade-off

Abstract

Brain activities are quantifiable by wave forms with interactive frequency, amplitude, and phase angle. They have been known as the gamma, beta, alpha, theta, and delta waves, in accordance with the intensity and quality of waveforms measured by electroencephalography (EEG) at different locations of the scalp. However, the established interrelations of these waves associated with different sensory stimuli and setting of various encephalopathies are mostly empirical. Possible redundancies of the classification of these waves can be explored by studying the transitory character of one kind of these waves with another under controlled sensory stimuli. A case in point is the association of the gamma waves having high frequency and low amplitude with alpha waves having lower frequency and higher amplitude. The biological–electrical–chemical process of the neurons further implicates the spatial–temporal scale changes from the nano to the macro via the micro. The characterization of this highly transitory character of the information transmission process can be made by the combined use the transitional function from Ideomechanics (IDM) and the Principle of Least Variance (PLV).Using the wave length as one of the root functions of IDM, the time intervals for sustaining the minima of least variances of the five waves can be determined. The degree of sustainability of the waves is shown to decrease with time as the minima of the least variances increase with time. These trends are consistent with the waveforms observed from electroencephalography (EEG). The combined variations of the frequencies, phase angles, and amplitudes can thus be analyzed quantitatively and qualitatively to define brain waveforms, mitigating the empiricism of observing EGG data alone.Gamma and alpha band response to photic driving stimulus in human and rat hippocampus have been observed via amplitude modulation. An interaction was observed between the gamma and alpha oscillatory activity in the human visual system. The visual stimulus has an onset time range of 75–150ms. These data correspond well with the minima of least variances of 0.11 for gamma and 0.23 for alpha at 22–25ms and 0.19 for gamma and 0.02 for alpha at about 75ms. The analytical switch over from gamma to alpha occurred at about 46ms. The precise numbers can vary with duration of the stimulus. Based on the Principle of Least Variance (PLV), the gamma waves are more sustainable and reliable at 22–25ms, since 0.11<0.23, representing the gamma phase-on, while the alpha phase becomes more sustainable and reliable at about 75ms, since 0.02<0.19. Suggested are the ON and OFF phases of gamma and alpha.The least variances suggest that the apparent waves can further delineate the brain behavior characteristics, notwithstanding the difference of the sub-atomistic character of gamma, alpha and beta entities. The overlapping classification of the apparent waves is likely to be caused by the ambiguities in distinguishing gamma, alpha and beta. The results from IDM and PLV, however, do indicate that the EGG data possess sufficient details for assessing the degree of normality and abnormality of brain waves.