Mode-locking dynamics of corticothalamic system responses to periodic external stimuli

Abstract

A physiologically based continuum model of the corticothalamic system is applied to explore mode-locking dynamics of ongoing cortical activity subject to periodic drive. The ongoing cortical activity is poised near a Hopf bifurcation. Time-dependent center manifold reduction shows that the nonlinear dynamics of driven corticothalamic system with delays can be described by an inhomogeneous low-dimensional equation near the critical point of the Hopf bifurcation. This driven normal form captures the main features of experimentally observed nonlinear interactions between brain activity and periodic stimuli. The effects of underlying physiological parameters on the type of Hopf bifurcation and onset dynamics are then studied, which allows the determination of phase-locked structures for various regions in the parameter space of the drive. It is shown that the system can adjust its oscillation regime to the frequency content of stimuli. The key features of entrainment of the alpha rhythm to periodic stimuli, including harmonic and subharmonic generation, are also explored. The theoretical predictions of these nonlinear responses are confirmed by numerical simulations. Further, photosensitive seizures are predicted for physiologically based model parameters arising from mode locking to the frequency of periodic stimulus, and their harmonics due to higher order synchronization states. These results indicate that the approach used here provides a powerful framework for the study of nonlinear interactions between brain activity and flicker by incorporating periodic driving into the corticothalamic system.