Superimposed spindles

In some cases a structure marked by expert as one sleep spindle can have a frequency signature varying with time. Hao et al [Hao et al., 1992] proposed interpretation of such cases as a superposition of two different spindles. They applied complex demodulation to the structures marked especially for this purpose by an electroencephalographer.

Figure 4: Time-frequency energy distribution (equation 12) of 20 seconds of sleep EEG; structures corresponding to sleep spindles are marked by letters A-F. Structures C and D , as well as E and F, were classified as one spindle, i.e. their centers fell within a time section marked by expert as one spindle's occurrence.

Figure 4 presents a time-frequency energy distribution of 20 seconds of sleep EEG, where structures conforming to spindle's criteria are marked by letters A-F. Structures C and D, as well as E and F, were classified as one spindle, i.e. their centers fell within a time section marked by expert as one spindle's occurrence. Results of MP decomposition of these spindles can be interpreted in two possible ways: either we deal with different phenomena appearing closely in time, or the frequency changes within the structure's duration. The structure of changing frequency would be represented as few separate atoms, because in the applied dictionary there are only structures of constant frequency (compare Figure 10).

Figure 5: Spindles F (upper plot) and E (lower plot) from Figure 4 across channels. In each box: frequency [Hz], amplitude [$\mu$V], relative position in time [s], phase. Shades of gray proportional to the amplitude. Front of head towards top of page.

Additional information can be provided by tracing the spatial distribution of these structures. Figure 5 presents distribution of energy of spindles E and F across the electrodes. Each box corresponds to one recorded channel and contains (from the top): frequency [Hz], amplitude [$\mu$V], relative position in time [bottom left, ms] and time width [bottom right, ms] for a spindle possibly detected in related position. Boxes are positioned topographically as in Figures 2-3, shading of each box is proportional to amplitude. We notice that higher-frequency spindle E is stronger in occipital electrodes, while amplitudes of lower-frequency spindle F are higher in frontal electrodes, although in some of them this spindle is missing. These distributions suggest that we deal with two different phenomena rather than one structure of changing frequency.

In the presented framework, separation of superimposed structures with varying time-frequency signatures is straightforward. They can be automatically detected for the purpose of further investigations, based e.g. upon proximity in time. In the work of Hao et al [Hao et al., 1992] each case of superimposed spindles was identified visually, which limits the accuracy of the procedure and possibility to process larger amount of data.