  Epilepsy is a chronic neurological disorder affecting more than 50 million
people globally. An epileptic seizure acts like a temporary shock to the
neuronal system, disrupting normal electrical activity in the brain. Epilepsy
is frequently diagnosed with electroencephalograms (EEGs). Current methods
study the time-varying spectra and coherence but do not directly model changes
in extreme behavior. Thus, we propose a new approach to characterize brain
connectivity based on the joint tail behavior of the EEGs. Our proposed method,
the conditional extremal dependence for brain connectivity (Conex-Connect), is
a pioneering approach that links the association between extreme values of
higher oscillations at a reference channel with the other brain network
channels. Using the Conex-Connect method, we discover changes in the extremal
dependence driven by the activity at the foci of the epileptic seizure. Our
model-based approach reveals that, pre-seizure, the dependence is notably
stable for all channels when conditioning on extreme values of the focal
seizure area. Post-seizure, by contrast, the dependence between channels is
weaker, and dependence patterns are more "chaotic". Moreover, in terms of
spectral decomposition, we find that high values of the high-frequency
Gamma-band are the most relevant features to explain the conditional extremal
dependence of brain connectivity.
