Criticality in probabilistic models of spreading dynamics in brain networks: Epileptic seizures
Fig 4
Temporal evolution of average spread size and fraction of active (seizing) nodes: Example for patient-specific network P1, EZ = 61.
Each curve contains data from 20 different stochastic realizations. The right vertical axis (red) shows the mean normalized spread size ψ = 〈s/N〉, where s is the number of nodes in the surround to which a seizure has spread to. The left panel corresponds to simulations of the patient-specific epileptor network model. The middle panel relates to the simulations of the proposed probabilistic model with the temporal Gillespie algorithm. The right panel shows simulations based on a derived mean-field dynamics (see below and Materials and methods, Mean-field dynamics). In this mean-field approximation, derived under the assumption of Erdős-Rényi random network connectivity, we used an average connectivity weight and an average interaction delay. For this figure, both were computed from the corresponding patient-specific network.