Fractal cycles of sleep: a new aperiodic activity-based definition of sleep cycles
Authors: Rosenblum Yevgenia , Esfahani Mahdad Jafarzadeh , Adelhöfer Nico , Zerr Paul , Furrer Melanie , Huber Reto , Roest Famke F. , Steiger Axel , Zeising Marcel , Horváth Csenge G. , Schneider Bence , Bódizs Róbert , Dresler Martin 
Published: July 2023

AbstractNocturnal 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. Based on the observed pattern of fractal fluctuations, we introduced a new concept of fractal activity-based cycles of sleep or “fractal cycles” for short, 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. Next, 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 expected to appear except that it does not, being replaced by lightening of sleep.Regarding the sample, we examined fractal cycles in healthy adults (age range: 18 – 75 years, n = 205) as well as 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. Further, we studied fractal cycles in major depressive disorder (n = 111), the condition characterized by altered REM sleep (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 91 – 98% of 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 cycles. They are useful in healthy adult and pediatric populations as well as in patients with major depressive disorder. Fractal cycles should be extensively studied to advance theoretical research on sleep structure.Highlights-Fractal activity-based cycles of sleep or “fractal cycles” for short is a new concept based on cyclic changes in fractal (aperiodic) neural activity during sleep.-Durations of fractal and classical cycles correlate, and both show an inverted U-shape when seen from early to late cycles.-The fractal cycle algorithm is effective in detecting cycles with skipped REM sleep.-Older healthy adults shower shorter fractal – but not classical – cycle durations.-Fractal cycle duration is shorter in children and adolescents compared to young adults.-In major depressive disorder, antidepressant medication is associated with longer fractal cycles.