Effects of physiological parameter evolution on the dynamics of tonic-clonic seizures

Abstract The temporal and spectral characteristics of tonic-clonic seizures are investigated using a neural field model of the corticothalamic system in the presence of a temporally varying connection strength between the cerebral cortex and thalamus. Increasing connection strength drives the system into ∼ 10 Hz seizure oscillations once a threshold is passed and a subcritical Hopf bifurcation occurs. In this study, the spectral and temporal characteristics of tonic-clonic seizures are explored as functions of the relevant properties of physiological connection strengths, such as maximum strength, time above threshold, and the ramp rate at which the strength increases or decreases. Analysis shows that the seizure onset time decreases with the maximum connection strength and time above threshold, but increases with the ramp rate. Seizure duration and offset time increase with maximum connection strength, time above threshold, and rate of change. Spectral analysis reveals that the power of nonlinear harmonics and the duration of the oscillations increase as the maximum connection strength and the time above threshold increase. A secondary limit cycle at ∼ 18 Hz, termed a saddle-cycle, is also seen during seizure onset and becomes more prominent and robust with increasing ramp rate. If the time above the threshold is too small, the system does not reach the 10 Hz limit cycle, and only exhibits 18 Hz saddle-cycle oscillations. It is also seen that the times to reach the saturated large amplitude limit-cycle seizure oscillation from both the instability threshold and from the end of the saddle-cycle oscillations are inversely proportional to the square root of the ramp rate. Author Summary Epilepsy, which is characterized by recurrent seizures, affects around 1% of the world population at some point in their lives. Tonic-clonic seizures are the most commonly encountered primary generalized seizures and it is widely considered that they can be induced by an increase in the connection strength between the cerebral cortex and the thalamus. In this paper, we analyze the detailed dynamics of tonic-clonic seizures along with their dependence on the parameters of the changing connection strength. We study the relationship of the seizure onset, offset, oscillation strength, and oscillation frequency to the duration, amplitude, and rate of change of the connection strength. A detailed understanding of the dynamics and their dependence on the physiological parameters of the brain may explain the variability of seizure dynamics among patients. It may also help to constitute successful seizure prediction.