Epilepsy
The electroencephalogram (EEG) is a time-varying signal which measures electrical activity in the brain. EEG signals are extremely irregular and are invariably contaminated by measurement errors and artefacts. Although nonlinear methods may offer an explanation for irregular behaviour in biomedical systems which are not well described by traditional linear stochastic models, carefully constructed statistical tests are required to demonstrate that these methods are of clinical utility.
Intracranial EEG
The performance of traditional linear (variance based) methods for the identification and prediction of epileptic seizures are contrasted with nonlinear methods. We note several flaws of design in demonstrations claiming to establish the efficacy of nonlinear techniques; in particular, we examine published evidence for precursor identification. Null hypothesis tests using relevant surrogate data demonstrate that decreases in the correlation density prior to and during seizure may simply reflect increases in the variance [1,2].
Scalp EEG
If it were possible to develop reliable and robust indicators of a seizure ahead of its onset, this would have considerable impact on the quality of life of a very large number of sufferers. It would also alleviate the work of EEG technicians who continue to score multi-channel records manually as automated seizure detection methods remain too inaccurate.
Multi-Dimensional Probability Evolution (MDPE)
Multi-dimensional probability evolution (MDPE) is a conceptually intuitive nonlinear technique. It is based on the time evolution of the probability density function within a multi-dimensional state space. A synthetic recording is employed to illustrate why MDPE is capable of detecting changes in the underlying dynamics which are invisible to linear statistics. If a nonlinear statistic cannot outperform a simple linear statistic such as variance, then there is no reason to advocate its use. Both variance and MDPE were able to detect the seizure in each of the ten scalp EEG recordings investigated. Although MDPE produced fewer false positives, there is no firm evidence to suggest that MDPE or any other nonlinear statistic considered, outperforms variance-based methods at identifying seizures [3].
Detecting Dynamical Transitions
Signal quality is extremely important when attempting to detect transitions. An analysis of the effect of the signal to noise ratio and duration of the recording was performed for the MDPE technique [4]. This suggests that while nonlinear dynamics may underly the mechanisms that generate epileptic seizures, a nonlinear analysis will only be fruitful if the signal available is of sufficient quality (high signal to noise ratio and long stationary periods). MDPE has also shown promise for detecting partial epileptic seizures based on an analysis of the time series reflecting the subject's cardiac rhythm [4].
[1] P.E. McSharry, L.A. Smith, L. Tarassenko (2003), Prediction of epileptic seizures: are nonlinear methods relevant?. Nature Medicine, 9(3): pp. 241-242.
[2] P.E. McSharry, L.A. Smith, L. Tarassenko (2003), Comparison of predictability of epileptic seizures by a linear and a nonlinear method. IEEE Transactions on Biomedical Engineering, 50(5): pp. 628-633.
[3] P.E. McSharry, T. He, L.A. Smith, L. Tarassenko (2002), Linear and non-linear methods for automatic seizure detection in scalp electro-encephalogram recordings. Medical & Biological Engineering & Computing, 40(4): pp. 447-461.
[4] P.E. McSharry (2004), Detection of dynamical transitions in biomedical signals using nonlinear methods in Knowledge-Based Intelligent Information and Engineering Systems, Pt 3, Proceedings, M.G. Negoita, R.J. Howlett, and L.C. Jain, Editors, Springer-Verlag Berlin: Berlin. pp. 483-490.