Seizure characterisation using frequency-dependent multivariate dynamics

Abstract

The characterisation of epileptic seizures assists in the design of targeted pharmaceutical seizure prevention techniques and pre-surgical evaluations. In this paper, we expand on recent use of multivariate techniques to study the crosscorrelation dynamics between electroencephalographic (EEG) channels. The Maximum Overlap Discrete Wavelet Transform (MODWT) is applied in order to separate the EEG channels into their underlying frequencies. The dynamics of the cross-correlation matrix between channels, at each frequency, are then analysed in terms of the eigenspectrum. By examination of the eigenspectrum, we show that it is possible to identify frequency dependent changes in the correlation structure between channels which may be indicative of seizure activity.The technique is applied to EEG epileptiform data and the results indicate that the correlation dynamics vary over time and frequency, with larger correlations between channels at high frequencies. Additionally, a redistribution of wavelet energy is found, with increased fractional energy demonstrating the relative importance of high frequencies during seizures. Dynamical changes also occur in both correlation and energy at lower frequencies during seizures, suggesting that monitoring frequency dependent correlation structure can characterise changes in EEG signals during these. Future work will involve the study of other large eigenvalues and inter-frequency correlations to determine additional seizure characteristics.

Received Total Wideband Power Data Analysis

“…The wavelet variance 2 ( ) is defined as the expected value of ̃, 2 considering only non-boundary coefficients 2 . The unbiased estimator of the wavelet variance is achieved by omitting the coefficients impacted by boundary conditions and is calculated as follows:…”

“…Again, all wavelet coefficients affected by the boundary are removed [14], and = − + 1. The MODWT estimate of the wavelet correlation between functions ( ) and ( ) is found with the wavelet covariance and square root of the wavelet variance of 2 The MODWT treats the time series as if they are periodic using "circular boundary conditions". There are Lj wavelet and scaling coefficients that are the functions at each scale [14].…”

“…Wavelet techniques have been used extensively in a broad range of research areas e.g. engineering [1], medicine [2], fractals [3] and geophysics [4]. Robertson et al in [1], first used wavelets for power engineering to analyse electromagnetic transients from power system faults and switching.…”

“…Since then there has been a significant increase in the application of wavelet transforms to power systems including power system protection, power quality and load forecasting. Biomedical engineering research has also used wavelet transforms, specifically in seizure prevention techniques and presurgical evaluations [2]. Identifying correlations between nonstationary signals is a common approach particularly in finance in measuring the relationship between two or more signals over time.…”

Modelling DNA Methylation Dynamics

“…Although DWT is not quite often used as fourier, it has also been applied to visualise both frequency and location specific information of the DNA sequence patterns, (Tsonis et al, 1996;Zhao et al, 2001). Elaboration on this family of approaches, is not explicitly dealt in this chapter, hence more details on the method of Maximal Overlap Discrete Wavelet Transformation, (MODWT -extension to DWT), (Conlon et al, 2009), application to study patterns in DNA sequence and results thus obtained, are reported in .…”