Critical dynamics in the spread of focal epileptic seizures: Network connectivity, neural excitability and phase transitions.

Focal epileptic seizures can remain localized or, alternatively, spread across brain areas, often resulting in impairment of cognitive function and loss of consciousness. Understanding the factors that promote spread is important for developing better therapeutic approaches. Here, we show that: (1) seizure spread undergoes "critical" phase transitions in models (epileptor-networks) that capture the neural dynamics of spontaneous seizures while incorporating patient-specific brain network connectivity, axonal delays and identified epileptogenic zones (EZs). We define a collective variable for the spreading dynamics as the spread size, i.e. the number of areas or nodes in the network to which a seizure has spread. Global connectivity strength and excitability in the surrounding non-epileptic areas work as phase-transition control parameters for this collective variable. (2) Phase diagrams are predicted by stability analysis of the network dynamics. (3) In addition, the components of the Jacobian's leading eigenvector, which tend to reflect the connectivity strength and path lengths from the EZ to surrounding areas, predict the temporal order of network-node recruitment into seizure. (4) However, stochastic fluctuations in spread size in a near-criticality region make predictability more challenging. Overall, our findings support the view that within-patient seizure-spread variability can be characterized by phase-transition dynamics under transient variations in network connectivity strength and excitability across brain areas. Furthermore, they point to the potential use and limitations of model-based prediction of seizure spread in closed-loop interventions for seizure control.