Experimental and model based investigation of period doubling phenomenon in human steady state visual evoked potential responses
Objective. Previous human Steady State Visual Evoked Potential (SSVEP) experiments have yielded different results regarding the range of stimulus frequencies in which Period Doubling (PD) behavior is observed. There also is lacking information about the consistency and repeatability of the occurences of subharmonic oscillations. The neural mechanism of such oscillations have also not been explored. To elaborate these rather unknown aspects of the PD behavior in SSVEP responses, an experimental and model based approach has been taken. Approach. The experimental side of the study aims at obtaining experimental and statistical data regarding the frequency range of PD generation and also investigates other characteristics of PD. In two sets of experiments, seven subjects were presented a sinusoidal flickering light stimulus with frequencies varying from 15 Hz to 42 Hz. To observe the short term repeatability in PD generation, another set of 5 successive experiments performed on five subjects with 10-minute breaks in between. To obtain the SSVEP responses, filtering, signal averaging and Power Spectral Density (PSD) estimation were applied to the recorded EEG. From the PSD estimates, Subharmonic Occurrence Rates (SORs) were calculated for each experiment and were used along with ANOVA for interpreting the outcomes of the short term repeatability experiments. The model based side of the study aims at explaining the observed phenomena in mathematical terms. For this purpose, Robinson’s Corticothalamic Model was implemented in both C and Simulink. The experimental procedure was reanimated on the model and the subharmonic generation in the model depending on different values for parameters was observed. The feedback loop that is responsible for the generation of subharmonic components was identified in the model, and this loop was isolated from the rest of the model and further analyzed with a describing function approach. Main Results. The experimental results showed that although fundamental (excitation frequency) and second harmonic components appear in almost all SSVEP spectra, there is considerable inter-subject and intra-subject variability regarding PD occurrence. PD occurs for all stimulus frequencies from 15 Hz to 42 Hz when all subjects are considered together. Furthermore, the statistical analyses of short term repeatability experiments suggest that in the short term, PD generation is consistent when all frequencies are considered together but for a single frequency significant short term differences occur. There also is considerable variation in the ratio of subharmonic amplitude to fundamental amplitude across different frequencies for a given subject. The modelling results showed that the subharmonic oscillations in the model are of resonance nature and that they can be obtained virtually in any frequency interval depending on the values of the parameters in the system. The intra-thalamic feedback loop in the model is identified to be the potential source of subharmonic oscillations in the system output. When isolated from the rest of the model and examined by itself, it has been found that this feedback loop can show a resonance phenomenon at the subharmonic frequency. By deriving a set of equations containing the necessary conditions for this resonance phenomenon, a semi-analytical method by which one can find the existence of these oscillations has been developed. Significance. From the experimental studies, important results and statistical data are obtained regarding PD generation. Our results indicate that modelling studies should attempt to generate PD for a broader range of stimulus frequencies by adjusting the parameter values. It is argued that SSVEP based BCI applications would likely benefit from the utilization of subharmonics in classification. Our modelling study is the first to investigate the source of subharmonic oscillations on a mathematical brain model. An experimental verification of the potential origin of such oscillations, which was identified to be the intra-thalamic loop, would be an important work. The proposed semi-analytical method could potentially be used to speed up a future parameter sweep study. We observed that in the current model alpha oscillation and subharmonic oscillations are in some way interrelated and they can not be generated together for any stimulation frequency. This is referred to as alpha entrainment, and is visible only for some stimulation frequencies in experimental results. Thus, we claim that the model is insufficient in explaining the PD phenomenon in SSVEP responses.