It is thought that the critical brain dynamics in sleep is modulated during frequent periods of wakefulness. This paper utilizes the capacity of EEG based scaling analysis to quantify sleep fragmentation in patients with obstructive sleep apnea. The scale-free (fractal) behavior refers to a state where no characteristic scale dominates the dynamics of the underlying process which is evident as long range correlations in a time series. Here, Multiscaling (multifractal) spectrum is utilized to quantify the disturbed dynamic of an OSA brain with fragmented sleep. The whole night multichannel sleep EEG recordings of 18 subjects were employed to compute and quantify variable power-law long-range correlations and singularity spectra. Based on this characteristic, a new marker for sleep fragmentation named ``scaling based sleep fragmentation'' was introduced. This measure takes into account the sleep run length and stage transition quality within a fuzzy inference system to improve decisions made on sleep fragmentation. The proposed index was implemented, validated with sleepiness parameters and compared to some common indexes including sleep fragmentation index, arousal index, sleep diversity index, and sleep efficiency index. Correlations were almost significant suggesting that the sleep characterizing measure, based on singularity spectra range, could properly detect fragmentations and quantify their rate. This method can be an alternative for quantifying the sleep fragmentation in clinical practice after being approved experimentally. Control of sleep fragmentation and, subsequently, suppression of excessive daytime sleepiness will be a promising outlook of this kind of researches.
Keywords: Multifractality; obstructive sleep apnea; self-organized criticality; sleep fragmentation; wavelet transform modulus maxima.