Estimating regularity in epileptic seizure time-series data

Abstract

The authors apply Ziv-Lempel (LZ) complexity and approximate entropy (ApEn) as measures to quantify the regularity in the various epochs of epileptic seizure time series data. They demonstrate the potential of complexity measures such as LZ and ApEn in quantifying the regularity at different epochs of epileptic seizure time-series data. It is clearly shown that these measures have high values at the beginning and the end of the seizure, and that they decrease during mid-seizure. In fact, the authors observe in the histogram plot that the frequency of the complexity measure in mid-seizure is quite prominent. This gives one an idea about the epoch where one can find more regular patterns. These measures can also be used as relative indices (comparing across state), rather than absolute indices, by using a larger number of subjects to obtain statistical validity in comparing across conditions. The analysis of time series obtained from complex systems, such as the brain, by the above measures provides an alternative easy way to quantify the regularity with finite-length segments (of the order of 1000 samples). The same can be inferred by calculating the correlation dimension and Lyapunov exponent, but the algorithms used to estimate these invariants are susceptible to error due to the finite sample size and are also highly sensitive to noise. The computational complexity of these algorithms is also high. The authors have also applied these measures across the various states of epilepsy.