The main scope of this study is the examination of the brain functions responding to the external stimuli. Adopting both of bottom-up and top-down approach, we investigated the neuron encoding mechanism which is responding to external stimuli and the change of electroencephalogram (EEG) induced by sound and light stimuli. Firstly, the stochastic resonance phenomenon on a single neuron was discussed in numerical and analytical ways. Regarding a neuron as an information processor, we calculate mutual information between the weak input and the output of the Hopfield neuron in noisy environment by using the numerical and the analytical methods. Mutual information shows conventional behavior of stochastic resonance phenomenon regardless of the input being periodic or not, which implies that mutual information can be another measure of stochastic resonance. Furthermore, the analytical investigation shows that the location of the noise strength with the maximum mutual information is not changed with respect to the amplitude of the input signal.
Next, we studied the changes in EEG under the application of external sound and light stimuli. Sound and Light Entrainment Devices (SLEDs) have been developed to entrain brain waves based on the fact that photic and/or auditory stimulation of a certain frequency can make brain wave activity fall in synchronization with the frequency of the stimulation. With application of SLED, we examined the changes of the correlation dimension (D2) of EEG. The twelve subjects (6 females and 6 males; age = 13.8 ± 0.6 years) were administered by photic and auditory stimuli of 10Hz frequency by the SLED which corresponds to the alpha frequency of brain waves. We also estimated the spectral dimension of the EEG, which is the generalization of Ω-dimension, defined as the correlation dimension of the band-pass filtered wave from an original multiscaled signal. The calculation of the spectral dimension gives additional information on the properties of the signal like EEG which consists of several components of time series with different dominant frequencies and different sources. We showed that the D2 of the EEG from some channels ($F_3$, $T_4$, $T_6$, $F_{p1}$, $P_3$, and $P_4$) were decreased after application of the SLED, which means that the complexity of the brain dynamics is lowered by SLED. It is also shown from the estimation of the spectral dimension that the alpha band EEG were decreased in complexity after SLED application at channel $F_3$, $T_4$, $T_6$, and $P_4$. The theta band waves are increased in complexity after SLED application at channel $P_4$ and $F_{p1}$. We concluded carefully from this study that the lowered complexity of the EEG induced by SLED may be mainly caused by the decreased complexity of the alpha-band waves. We suggest that the spectral dimension can be helpful to study the mixed signals of multi-components like EEG.
