Design Principle for a Population-Based Model of Epileptic Dynamics

Epilepsy is defined as the brain’s susceptibility to recurrent, hypersynchronous discharges that disrupt normal neuronal function. Over the last decades, progress has been made in using dynamical systems theory and computational analyses to characterise the nature of seizure-like activity. Using simplified models of population dynamics, macroscale features of epileptic seizures can be described as expressions of model interactions. There is a trade-off between complexity of these models and their explanatory power: Models that represent biophysical components of the brain often contain many degrees of freedom and nonlinearities, which can make them challenging to interpret and often means that different model parameterisations can produce similar results. Simple models, on the other hand, do not usually have a direct correlate in brain anatomy or physiology, but rather capture more abstract quantities in the brain. However, the effects of individual parameters are easier to interpret. Here we suggest a design principle to generate the complex rhythmic evolution of tonic-clonic epileptic seizures in a neural population approach. Starting from a simple neuronal oscillator with a single nonlinearity, we show in a step-by-step analysis how complex neuronal dynamics derived from patient observations can be reconstructed.