Sustainable time and stability of hippocampal and cortical EEG theta waves

Abstract

Sinusoidal wave function is used to quantify brain rhythms characterized by the interaction of frequency, amplitude, and phase angle (FAP). Their combinations have been differentiated in terms of gamma, beta, alpha, theta, and delta waves, in accordance with test data obtained from electroencephalography (EEG) at different locations of the scalp, and hence neurons at the different locations of the brain. The standard wave-type classifications, however, refer to a wide range of situations that are changeable according to variations of the sensory stimuli such that one wave type may switch into another. Even for the same wave type, say theta, a perturbation of frequency and/or amplitude can alter the sustainable time of the wave.The Least Variance Principle (LVP) is applied to determine the stable and reliable state of the “hippocampal” and “cortical” EEG theta waves having the, respective, frequency ranges of 7–9Hz and 4–7Hz. The sustainable time of the hippocampal waves are longer and more stable while those of the cortical waves are shorter and less stable. These findings are in general agreement with the available experimental results obtained from small mammals and humans. Also keep in mind of the difference in the method of recording the EEG waves. Seven different cases are reported from the LVP model. They are characterized by a comparative scheme for testing the sensitivity of the frequency and phase angle changes.Using the average frequencies of 8.0Hz for the hippocampal waves and a higher phase angle and 5.5Hz for the cortical waves and a lower phase angle, the, respective, sustainable times are found to be 2.2s and 0.5s. The hippocampal waves were found to be more stable. These results correspond precisely to test measurements where perturbation of the frequencies and phase angles can correspond to large variations in the sustainable time of the hippocampal and cortical theta waves. In general, larger frequencies and phase angles favor longer sustainable and stable time. That is perturbation of the theta wave frequency and phase angle can result in appreciable change of the sustainable time of the theta wave. These features are exhibited consistently by the results for seven different FAPs. Other situations can be generated to propose additional theta wave oscillation experiments.