Understanding epileptiform after-discharges as self-terminating transients

Introduction: Electro-cortical activity in patients with epilepsy may show abnormal rhythmic transients of different waveforms in response to stimulation. These transients have long been considered important for the mapping of the excitability levels in the epileptic brain but their dynamic mechanism is still not well-understood. Methods: To understand the occurrence of abnormal transients dynamically, we use a thalamo-cortical neural population model of epileptic spike-wave activity and study the interaction between slow and fast subsystems. Results: In a reduced version of the thalamo-cortical model, slow wave oscillations arise from a fold of cycles (FoC) bifurcation. This marks the onset of a region of bistability between a high amplitude oscillatory rhythm and the background state. In vicinity of the bistability in parameter space, the model has excitable dynamics, showing prolonged rhythmic transients in response to suprathreshold pulse stimulation. We analyse the state space geometry of the bistable and the excitable state, and find that the rhythmic transient arises when the impending FoC bifurcation deforms the state space and creates an area of locally reduced attraction to the fixed point. This area essentially allows trajectories to dwell in it for before escaping to the stable steady state, thus creating rhythmic transients. In the full thalamo-cortical model, we find a similar FoC bifurcation structure. In addition, the (fast) cortical subsystem can undergo a supercritical Andronov-Hopf bifurcation to fast spiking. Combined with the slow subsystem this results in self-terminating spike-wave or poly-spike-wave oscillations. Discussion: We compare our dynamic mechanism with other mechanisms (such as a slow parameter change) to generate excitable transients and discuss why our mechanism is well-suited to explain stimulation induced epileptiform activity. We also interpret the proposed excitability mechanism in the context of stimulation responses in the epileptic cortex.