A theory of neocortical seizure spread: Insights from statistical physics
Authors: Giller Cole A. 
Published: July 2019

The conception of seizures as abnormal synchronies of large neuronal populations has been confirmed by numerous electrophysiological studies, including recent imaging of travelling seizure waves across the neocortex. This traditional viewpoint has been challenged by the finding that during some seizures, neurons with high firing rates are remarkably rare and sparsely distributed into clusters. Reconciliation of these seemingly contradictory descriptions has attracted much attention, raising questions such as how (or if) macroscopic seizure waves arise from these microscope neuronal clusters, and more generally, how other features of macroscopic, clinical seizures arise from microscopic dynamics. Answers to these questions are crucial to the understanding of epilepsy, and could guide development of drugs and other interventions that act at the microscopic level to effect macroscopic improvement.

Relationships between microscopic and macroscopic processes are addressed by the field of statistical physics, offering explanations for how macroscopic quantities such as pressure and temperature arise from microscopic interactions between molecules. Here we hypothesize that these methods could also provide insight between the macroscopic and microscopic dynamics of seizure behavior. We constructed a model of the neocortex composed of small domains, each representing a cluster of neurons. Models with and without refractory periods were studied. Allowing seizures to spread among the clusters in a probabilistic fashion produced a “cellular automaton” amenable to the methods of statistical physics. We thereby showed that the model harbors a continuous phase transition allowing possible explanations for the emergence of seizure waves from microscopic neuronal clusters, and for a surprisingly wide variety of seizure properties. Moreover, the model is easy to use because it requires only a small number of intuitively understood rules and is computationally efficient. We hope that these insights from statistical physics will contribute to the understanding of epilepsy and to the identification of new therapeutic measures.

Author summary

Epilepsy is a common neurological disease characterized by devastating, unpredictable seizures. Extensive research is aimed at improving the treatment of epilepsy through better understanding of how seizures start and spread, but basic questions remain unanswered. Do seizures start as waves of overactive neuronal activity, or as small clusters of activity as suggested by recent data? How do clinical properties of seizures emerge from interactions between small groups of neurons? And would understanding this emergence lead to better treatment?

We address these questions with a mathematical model of seizure spread, using methods of physics designed to explain how quantities such as pressure and temperature emerge from interactions between molecules. The model produced small clusters of activity as observed in recent data, and the methods allowed us to show how these clusters react to increases in neuronal excitation to produce seizure waves and other clinical seizure behavior. The model thus provided possible answers to the questions above, based on new insights from the field of physics. If the model indeed represents a common pathway evoked by many pathological changes, it may inform the development of therapeutic measures such as antiepileptic drugs that act at the microscopic level to improve macroscopic behavior.