A step towards complete description of sleep EEG

Reports discussed in previous sections were aimed at a simultaneous presentation of spindles detected in all EEG derivations. Time course of spindle's occurrence in one channel, as presented in Figure 6, relates directly to the classical perception of the sleep process--the ``sleep staircase'' or hypnogram (presented in Figure 6a).

Figure 6: Hypnogram a) and time course--in the same horizontal scale--of: b) frequencies and c) amplitudes of detected spindles, d) spindles density [1/min], e) SWA power, f) and g) frequencies and amplitudes of structures classified as SWA.

In order to provide a more complete picture, the time course of slow wave activity (SWA) is drawn simultaneously. Description of the SWA was traditionally assessed by spectral analysis. In the framework of MP we pick from the decomposition (already performed for the purpose of spindles parametrization) atoms conforming to the following criteria: frequency 0.5-4 Hz, amplitude $>$75 $\mu$V and time span $>$2.35 s.

Figure 6 presents the time course of spindles (b-d) and SWA (e-g) together with hypnogram (a) in the same time scale. Data from the whole overnight recording is presented for the Pz electrode. Plots (b-c) show time distribution of frequencies and amplitudes of spindles, (d) gives a number of spindles detected per minute. Plots (f) and (g) give frequencies and amplitudes of SWA structures, while (e) presents a magnitude corresponding to the spectral power of structures classified as SWA, calculated in each minute. Time course of the spindle's density is quite similar to the time course of amplitudes of detected spindles. That means that in epochs where more spindles are detected, usually also higher-amplitude spindles are present (compare also Figure 3). Time course of spindle activity and SWA in slow-wave sleep episodes [stages 3-4 on hypnogram] conforms to their previously recognized inverse relationship [Aeschbach and Borbély, 1993].

This example demonstrates how easily MP parametrization can be extended to describe any time-frequency phenomena. Description of SWA was achieved by a direct implementation of it's generally acknowledged time-frequency characteristics. Since the MP decomposition is a general procedure, we do not have to repeat this time-consuming step to parametrize each new kind of structures. Construction of filters, choosing from the fitted atoms those corresponding to structures of interest, in many cases can be directly based upon the ``classical'' knowledge of EEG, formulated in terms close to the time-frequency parameters. For a complete concordance with traditional methods, we can compute from MP parametrization e.g. a spectral power density estimate. In comparison to the traditional spectral estimates, this magnitude should reflect the investigated phenomena more accurately, since we take into account only the structures of interest, explicitly avoiding other structures of overlapping spectral characteristics.