A Biologically Constrained, Mathematical Model of Cortical Wave Propagation Preceding Seizure Termination

Epilepsy—the condition of recurrent, unprovoked seizures—manifests in brain voltage activity with characteristic spatiotemporal patterns. These patterns include stereotyped semi-rhythmic activity produced by aggregate neuronal populations, and organized spatiotemporal phenomena, including waves. To assess these spatiotemporal patterns, we develop a mathematical model consistent with the observed neuronal population activity and determine analytically the parameter configurations that support traveling wave solutions. We then utilize high-density local field potential data recorded in vivo from human cortex preceding seizure termination from three patients to constrain the model parameters, and propose basic mechanisms that contribute to the observed traveling waves. We conclude that a relatively simple and abstract mathematical model consisting of localized interactions between excitatory cells with slow adaptation captures the quantitative features of wave propagation observed in the human local field potential preceding seizure termination.Author Summary: Nearly 50 million people worldwide suffer from epilepsy, a chronic neurological condition characterized by recurrent, unprovoked seizures. Although some clinical and biological principles of seizures are known, many aspects of spontaneous human seizures remain poorly understood. Recordings from electrodes placed directly on and within the brain provide a unique view of seizure activity, and have revealed specific brain voltage patterns associated with this pathological state. In particular, there is evidence that organized waves of activity propagate over the brain during a seizure. However, quantitatively characterizing and understanding the mechanisms that support these waves remains an open challenge. The goal of this work is to address this challenge through a combination of mathematical modeling and clinical recordings. Through this interdisciplinary approach, we seek to understand general features that support the spatiotemporal patterns of seizure termination. We propose that a relatively simple and abstract mathematical model consisting of localized interactions of closely neighboring excitatory cells with slow adaptation can support the propagation of the waves found in clinical recordings. Improved understanding of the mechanisms supporting seizure activity promises novel developments in treatment strategies tailored to the observed activity of individual patients.