Chaotic behavior in two hippocampal models of epilepsy

Understanding the dynamics of electrical behavior in the brain is essential in order to control the bursting that is characteristic of epilepsy. Epileptiform bursting was induced in transverse rat hippocampal slices by bathing them in artificial cerebrospinal fluid (ACSF) containing either a high concentration of potassium ([K⁺ ]₀=10.5 mM) or zero magnesium. Interburst intervals (IBIs) were embedded into phase space using a delay coordinate system. The existence of chaos and determinism was assessed using two different analytical techniques. First, maximal Lyapunov exponents were calculated using a local divergence rate technique that is highly robust to noise. Positive Lyapunov exponents were found in 14 of 17 high-[K⁺] ₀ and 4 of 5 zero-[Mg²⁺]₀ experiments. Surrogate data sets were created by randomizing experimental data and used as controls. A paired comparison of experimental and surrogate data sets showed significant difference (p<0.0001) supporting the hypothesis that bursting behavior is chaotic. Additionally, the presence of determinism on a local scale was assayed by searching for unstable periodic orbits (SPOs) using a recently developed transform technique. The positive findings using both techniques strongly suggest that interictal bursting induced by either depolarization (high-[K⁺]₀) or through activation of NMDA receptor channels (zero-[Mg²⁺]₀) is chaotic in nature. This has implications for controlling epileptiform electrical activity in the brain