Nonlinear dynamic properties of low calcium-induced epileptiform activity

The analysis of the dynamic properties of epileptiform activity in vitro has led to a better understanding of the time course of neural synchronization and seizure states. Nonlinear analysis is thus potentially useful for the prediction of seizure onset. We have used nonlinear analysis methods to investigate the development of activity in the low calcium model of epilepsy in brain slices. This model is particularly interesting since neurons synchronize in the absence of synaptic transmission. The dynamic properties calculated from extracellular recordings of activity were used to analyze the transition to synchronous firing and their relation to neuronal excitability. The global embedding dimension, local dimension and the Lyapunov exponent were calculated from time segments corresponding to the onset, transition and fully developed stages of activity. The analysis was repeated for recordings made in the presence of various levels of DC electric fields to modulate neuronal excitability. The global and local dimensions did not change once activity was first initiated, even in the presence of the electric field. The maximum Lyapunov exponents increased during the onset of activity but decreased when the applied hyperpolarizing electric field was large enough to partially suppress the activity. These findings establish a relationship between neuronal excitability and the maximum Lyapunov exponent, and suggest that the Lyapunov exponent may be used to distinguish between various states of the neural network and might be important in seizure prediction and control.