Spatio-temporal analysis of monofractal and multifractal properties of the human sleep EEG.

Fractality is a common property in nature. It can also be observed in time series representing dynamics of complex processes. Therefore fractal analysis could be a useful tool to describe the dynamics of brain electrical activities in physiological and pathological conditions. In this study, we carried out a spatio-temporal analysis of monofractal and multifractal properties of whole-night sleep EEG recordings. We estimated the Hurst exponent (H) and the range of fractal spectra (dD) in 10 healthy subjects. We found higher H values during NREM4 compared to NREM2 and REM in all electrodes. Measure dD showed an opposite trend. Differences of H and dD between NREM2 and REM reached significancy at circumscribed regions only. Our results contribute to a deeper understanding of the fractal nature of brain electrical activities and may have implications for automatic classification of sleep stages.

The use of the SPSA method in ECG analysis.

The classification, monitoring, and compression of electrocardiogram (ECG) signals recorded of a single patient over a relatively long period of time is considered. The particular application we have in mind is high-resolution ECG analysis, such as late potential analysis, morphology changes in QRS during arrythmias, T-wave alternants, or the study of drug effects on ventricular activation. We propose to apply a modification of a classical method of cluster analysis or vector quantization. The novelty of our approach is that we use a new distortion measure to quantify the distance of two ECG cycles, and the class-distortion measure is defined using a min-max criterion. The new class-distortion-measure is much more sensitive to outliers than the usual distortion measures using average-distance. The price of this practical advantage is that computational complexity is significantly increased. The resulting nonsmooth optimization problem is solved by an adapted version of the simultaneous perturbation stochastic approximation (SPSA) method of. The main idea is to generate a smooth approximation by a randomization procedure. The viability of the method is demonstrated on both simulated and real data. An experimental comparison with the widely used correlation method is given on real data.