Regulation of epileptiform discharges in thalamocortical model based on preview control theory

Based on the important function of the thalamic reticular nucleus(TRN) in epileptic seizures, we explore how changes in TRN information affect epileptic seizures across the entire brain nervous system by adjusting the excitatory coupling strength of excitatory pyramidal neuron(PY) and specific relay nucleus(SRN) to TRN. Through single-parameter and double-parameter bifurcation analyses, we derive that Hopf bifurcation and limit point cycle bifurcation are the critical elements triggering the system's state transitions, which subsequently gives rise to the tristable region. We design a preview controller to suppress epileptic seizures within the tristable region and investigate the control effect on epileptic seizures under the initial states of SWD and 2-SWD respectively. The results show that only PY has a significant effect when we apply the controller to a single nucleus. Based on this, we choose the controller to act on multiple nuclei containing PY simultaneously. Through numerical analysis, we find that the control effect is optimal when the controller is simultaneously applied to the PY, inhibitory interneuron(IN), and excitatory interneuron(EIN) populations. The preview controller performs better in suppressing seizures and responding to secondary disturbances when applied to multiple populations that include PY, whereas its advantage is not significant for single nucleus control acting solely on non-PY populations. This provides a new theoretical perspective for the design of closed-loop neuromodulation strategies.