The dynamics of the epileptic brain reveal long memory processes

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 manmade 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 8 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 5 out of the 6 subjects whose data was sufficiently stationary for analysis, we found evidence of long memory between epileptic events. This memory spans time scales from 30 minutes to 40 days. The estimated Hurst exponents range from 0.51-0.77±0.01. This finding may provide evidence of phasetransitions underlying the dynamics of epilepsy.