Characterizing nonlinearity in invasive EEG recordings from temporal lobe epilepsy M.C. Casdagli a , L.D. Iasemidis c.e.f.g , J.C. Sackellares c.f.g , S.N. Roper d.g , R.L. Gilmore cf , R.S. Savit a.b a Harrison Randall Laboratory of Physics, University of Michigan. Ann Arbor, M1 48109-1120. USA b Program for the Study of Complex Systems. University of Michigan. Ann Arbor, MI 48109-1120. USA c Department of Neurology, University of Florida. Tampa, FL, USA d Department of Neurosurgery, University of Florida. Tampa, FL, USA e Department of Electrical Engineering, University of Florida, Tampa, FL USA f Department of Neuroscience. University of Florida. Tampa, FL, USA 9 Gainesville VA. Medical Center. Gainesville, FL 32608-1197. USA Received 25 January 1996: accepted 15 May 1996 Communicated by A.M. Albano Abstract Invasive electroencephalographic (EEG) recordings from depth and subdural electrodes, performed in eight patients with temporal lobe epilepsy, are analyzed using a variety of nonlinear techniques. A surrogate data technique is used to find strong evidence for nonlinearities in epileptogenic regions of the brain. Most of these nonlinearities are characterized as "spiking"' by a wavelet analysis. A small fraction of the nonlinearities are characterized as “recurrent” by a nonlinear prediction algorithm. Recurrent activity is found to occur in spatio-temporal patterns related to the location of the epileptogenic focus. Residual delay maps, used to characterize “lag-one nonlinearity”, are remarkably stationary for a given electrode, and exhibit striking variations among electrodes. The clinical and theoretical implications of these results are discussed. Keywords: Epileptogenic focus, Invasive EEG; Nonlinear prediction; Surrogate data; Wavelets 1. Introduction Invasive electroencephalographic (EEG) recordings play a crucial role in the medical diagnosis and treatment of patients with temporal lobe epilepsy (TLE) [8]. TLE is characterized by seizures that are thought to originate from a localized region of the brain (the epileptogenic focus) and rapidly propagate to more normal regions of the brain. Many patients with TLE respond well to drugs; the remainder are candidates for surgical resection of the epileptogenic portion of the brain. Noninvasive techniques such as MRI (Magnetic Resonance Imaging) scans and scalp EEG often fail to unambiguously identify the location of the epileptogenic focus. These cases necessitate EEG recordings with surgically implanted electrodes (invasive EEG recordings), which have much better spatial resolution, and are relatively free of electromyogenic (muscle) artifact, compared to scalp EEG recordings. Recording sessions, during which a patient is hospitalized, may last for several days, the objective being to record several typical seizures. In order to locate the epileptogenic focus, electroencephalographers visually inspect a few minutes of the EEG recordings selected to encompass the seizures [17]. An adequate region around the epileptogenic focus is then surgically resected, its extent defined by stimulus studies in order for the extracted region not to impair basic brain functions. The dynamical mechanisms responsible for the generation of seizures in TLE are not well understood. Mathematical models exhibiting transitions to seizure-like activity in relatively small networks of neurons have been constructed by Freeman for the olfactory system in rabbits [11], and by Traub et al. for rat hippocampi [35]. The degree to which these models apply to TLE remains to be determined, but there is little doubt that the dynamical mechanisms underlying TLE are highly nonlinear. The development of techniques for the nonlinear analysis of time series data [34,36] has made, it possible to investigate nonlinear dynamical mechanisms underlying epilepsy using statistical methods. Evidence for low-dimensional chaos has been reported in scalp EEG recordings of a petit mal seizure by Babloyantz and Destexhe [1], and in scalp EEG recordings of generalized seizures by Frank et al. [10]. Also, the nature of the transition to seizures in invasive EEG recordings from patients with TLE has been investigated using methods of nonlinear dynamics by Iasemidis et al. [14-16], and by Lerner [37]. We recently reported that nonlinearities exist in an invasive EEG recording from a patient with TLE in well-defined regions of the brain, including the epileptogenic focus [4]. A “surrogate data” technique was used to compare correlation integrals of the EEG recording to phase randomized time series with the same power spectrum [31]. This technique has the advantage of being sensitive to a wide range of nonlinearities, and is applicable to both high- and low-dimensional chaotic systems. However, the technique has the limitation that little insight is gained into the nature of the nonlinearities identified. The principal objective of the present paper is to present a detailed characterization of the nonlinearities identified in our earlier paper. We also attempt to relate these characterizations of nonlinearity to the clinical status of the patient. Such relationships are of potential medical value, particularly since linear signal