The Dynamics of the Epileptic Brain Reveal Long-Memory Processes

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Abstract
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, both in terms of event magnitude and inter-event intervals, respect a power-law relationship. 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 studied 8 patients who had long-term ambulatory EEG data recorded as part of the assessment of a novel seizure prediction device, in which data was sufficiently stationary in 6. We demonstrated that a power law relationship could be established in these patients, β=1.5. In 5/6 subjects we found evidence of long memory process, spanning time scales from 30 minutes to 40 days, using a wavelet based analysis technique. The Hurst exponent values ranged from 0.5 to 0.76. We conclude there is evidence of long memory processes in adult human epilepsy, with a heterogeneous range of time scales demonstrated between individuals. This finding may provide evidence of phase-transitions underlying the dynamics of epilepsy.

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