Criticality in probabilistic models of spreading dynamics in brain networks: Epileptic seizures

The spread of seizures across brain networks is the main impairing factor, often leading to loss-of-consciousness, in people with epilepsy. Despite advances in recording and modeling brain activity, uncovering the nature of seizure spreading dynamics remains an important challenge to understanding and treating pharmacologically resistant epilepsy. To address this challenge, we introduce a new probabilistic model that captures the spreading dynamics in patient-specific complex networks. Network connectivity and interaction time delays between brain areas were estimated from white-matter tractography. The model’s computational tractability allows it to play an important complementary role to more detailed models of seizure dynamics. We illustrate model fitting and predictive performance in the context of patient-specific Epileptor networks. We derive the phase diagram of spread size (order parameter) as a function of brain excitability and global connectivity strength, for different patient-specific networks. Phase diagrams allow the prediction of whether a seizure will spread depending on excitability and connectivity strength. In addition, model simulations predict the temporal order of seizure spread across network nodes. Furthermore, we show that the order parameter can exhibit both discontinuous and continuous (critical) phase transitions as neural excitability and connectivity strength are varied. Existence of a critical point, where response functions and fluctuations in spread size show power-law divergence with respect to control parameters, is supported by mean-field approximations and finite-size scaling analyses. Notably, the critical point separates two distinct regimes of spreading dynamics characterized by unimodal and bimodal spread-size distributions. Our study sheds new light on the nature of phase transitions and fluctuations in seizure spreading dynamics. We expect it to play an important role in the development of closed-loop stimulation approaches for preventing seizure spread in pharmacologically resistant epilepsy. Our findings may also be of interest to related models of spreading dynamics in epidemiology, biology, finance, and statistical physics.Author summary: We introduce a new probabilistic model for understanding and predicting the spreading dynamics of epileptic seizures in patient-specific brain networks. The model allows the prediction of whether a seizure will spread or not based on derived phase diagrams that take brain excitability and global network connectivity strength as control parameters. In addition, it also predicts the temporal sequence of spreading across different nodes in patient-specific networks. Importantly, the model’s tractability allows mean-field and finite-size scaling analyses to better understand the nature of the seizure spreading dynamics in large networks, revealing the existence of both discontinuous and continuous (critical) phase transitions. In addition to furthering the understanding of spreading dynamics, these findings are fundamental for the development of new closed-loop control approaches for preventing seizure spread, the main impairing factor leading to loss-of-consciousness, in people with pharmacologically resistant epilepsy.