A model based investigation of the period doubling behavior in human steady-state visual evoked potentials

Abstract

Objective.This study aims at investigating the potential mechanism of period doubling (PD) (subharmonic generation)in human steady-state visual evoked potentials(SSVEPs) by using a mathematical model.Approach.Robinson’s Corticothalamic Model, which includes three main neuronal populations(cortical, thalamic reticular, and thalamic relay neurons)was employed. SSVEP experiments were simulated using this model and dependence of PD behavior in relation to the values of model parameters was investigated. The feedback loop in the model that is responsible for the generation of subharmonic components was thus identified, and this loop was isolatedfrom the rest of the model and analyzed with a describingfunction approach.Main Results.It has beenfound in general, for a wide range of parameter values, that if the excitationfrequency or half of it is close to the native oscillation frequency of the system, the native oscillation ceases to exist and oscillations at either the excitation frequency or half of it are observed. This observation is in line with the experimental findings exceptfor some discrepancies which are also discussed. The intrathalamic feedback loop is identified to be the potential source of subharmonic oscillations.When isolatedfrom the rest of the model and simulated 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 based on the necessary conditionsfor a resonance phenomenon, a semi-analytical method was developed by which one can predict the existence of subharmonic generationfor a given set of parameters and stimulusfrequency. Significance. This study is the first model-based investigation of the mechanism of subharmonic oscillations. The proposed semianalytical method can replace extensive time and memory consuming parameter sweep studies.