The Dynamics of the Epileptic Brain Reveal Long-Memory Processes

Mark J. Cook, Andrea Varsavsky, David Himes, Kent Leyde, Samuel Frank Berkovic, Terence O’Brien, Iven Mareels

The pattern of epileptic seizures is often considered unpredictable and the interval between events without correlation. A number of studies have examined the possibility that seizure activity respects a power-law relationship, both in terms of event magnitude and inter-event intervals. Such relationships are found in a variety of natural and man-made systems, such as earthquakes or Internet traffic, and describe the relationship between the magnitude of an event and the number of events. We postulated that human inter-seizure intervals would follow a power-law relationship, and furthermore that evidence for the existence of a long-memory process could be established in this relationship. We performed a post hoc analysis, studying eight patients who had long-term (up to 2 years) ambulatory intracranial EEG data recorded as part of the assessment of a novel seizure prediction device. We demonstrated that a power-law relationship could be established in these patients (β = - 1.5). In five out of the six subjects whose data were sufficiently stationary for analysis, we found evidence of long memory between epileptic events. This memory spans time scales from 30 min to 40 days. The estimated Hurst exponents range from 0.51 to 0.77 ± 0.01. This finding may provide evidence of phase-transitions underlying the dynamics of epilepsy.