Fractal cycles of sleep: a new aperiodic activity-based definition of sleep cycles

Nocturnal human sleep consists of 4 – 6 ninety-minute cycles defined as episodes of non-rapid eye movement (non-REM) sleep followed by an episode of REM sleep. While sleep cycles are considered fundamental components of sleep, their functional significance largely remains unclear. One of the reasons for a lack of research progress in this field is the absence of a "data-driven" definition of sleep cycles. Here, we proposed to base such a definition on fractal (aperiodic) neural activity, a well-established marker of arousal and sleep stages. We explored temporal dynamics of fractal activity during nocturnal sleep using electroencephalography in 205 healthy adults aged 18 – 75 years. Based on the observed pattern of fractal fluctuations, we introduced a new concept, the "fractal" cycle of sleep, defined as a time interval during which fractal activity descends from its local maximum to its local minimum and then leads back to the next local maximum. Then, we assessed correlations between "fractal" and "classical" (i.e., non-REM – REM) sleep cycle durations. We also studied cycles with skipped REM sleep, i.e., the cycles where the REM phase is replaced by "lightening" of sleep. Finally, we validated the fractal cycle concept in children and adolescents (range: 8 – 17 years, n = 21), the group characterized by deeper sleep and a higher frequency of cycles with skipped REM sleep, as well as in major depressive disorder (n = 111), the condition characterized by altered sleep structure (in addition to its clinical symptoms). We found that "fractal" and "classical" cycle durations (89 ± 34 min vs 90 ± 25 min) correlated positively (r = 0.5, p < 0.001). Cycle-to-cycle overnight dynamics showed an inverted U-shape of both fractal and classical cycle durations and a gradual decrease in absolute amplitudes of the fractal descents and ascents from early to late cycles. In adults, the "fractal" cycle duration and participant's age correlated negatively (r = -0.2, p = 0.006). Children and adolescents had shorter "fractal" cycles compared to young adults (76 ± 34 vs 94 ± 32 min, p < 0.001). The fractal cycle algorithm detected cycles with skipped REM sleep in 53/55 (96%) cases. Medicated patients with depression showed longer "fractal" cycles compared to their own unmedicated state (107 ± 51 min vs 92 ± 38 min, p < 0.001) and age-matched controls (104 ± 49 vs 88 ± 31 min, p < 0.001). In conclusion, "fractal" cycles are an objective, quantifiable, continuous and biologically plausible way to display sleep neural activity and its cycling nature. They are useful in healthy, pediatric and clinical populations and should be extensively studied to advance theoretical research on sleep structure. ### Competing Interest Statement The authors have declared no competing interest.