• bifurcation analysis;
  • focal epilepsy;
  • mathematical model;
  • neural mass formulation;
  • numerical continuation;
  • seizure evolution


Focal-onset seizures have traditionally been conceptualised as having a highly circumscribed onset in an ‘abnormal’ brain region, with evolution of the seizure requiring recruitment of adjacent or connected ‘normal’ brain regions. Complementing this concept of the spatial evolution of seizures, the purpose of our present paper is to explore the evidence for the dynamic evolution of focal epilepsy using bifurcation analysis of a neural mass model, and subsequently relating these bifurcations to specific features of clinical data recordings in the time domain. Our study was motivated by recent research in idiopathic generalised epilepsies which has suggested that the temporal evolution of seizures may arise out of gradual changes in underlying physiological mechanisms. We found that spikes in the considered model arose out of so-called ‘false’ bifurcations, a finding consistent with other neural models with two timescales of inhibitory processes. We compared these results with previous studies of the model before extending them to characterise other more complex model behaviours. We then explored the relationship between model dynamics and clinical recordings from patients with focal epilepsies. Here we used an algorithm to subdivide each recording into time windows for which the data is approximately stationary. We then used our bifurcation findings to map out the evolution of seizures based on features of the clinical data from each of the epochs identified by our algorithm. We finally explored the similarity of the seizure evolution within patients, using random surrogates to test for statistical significance.