Linear and nonlinear measures and seizure anticipation in temporal lobe epilepsy

In a recent paper, we showed that the value of a nonlinear quantity computed from scalp electrode data was correlated with the time to a seizure in patients with temporal lobe epilepsy. In this paper we study the relationship between the linear and nonlinear content and analyses of the scalp data. We do this in two ways. First, using surrogate data methods, we show that there is important nonlinear structure in the scalp electrode data to which our methods are sensitive. Second, we study the behavior of some simple linear metrics on the same set of scalp data to see whether the nonlinear metrics contain additional information not carried by the linear measures. We find that, while the nonlinear measures are correlated with time to seizure, the linear measures are not, over the time scales we have defined. The linear and nonlinear measures are themselves apparently linearly correlated, but that correlation can be ascribed to the influence of a small set of outliers, associated with muscle artifact. A remaining, more subtle relation between the variance of the values of a nonlinear measure and the expectation value of a linear measure persists. Implications of our observations are discussed.