Sleep- spindle frequency: Overnight dynamics, afternoon nap effects, and possible circadian modulation

day-


Summary
Homeostatic and circadian processes play a pivotal role in determining sleep structure, timing, and quality. In sharp contrast with the wide accessibility of the electroencephalogram (EEG) index of sleep homeostasis, an electrophysiological measure of the circadian modulation of sleep is still unavailable. Evidence suggests that sleepspindle frequencies decelerate during biological night. In order to test the feasibility of measuring this marker in common polysomnographic protocols, the Budapest-Munich database of sleep records (N = 251 healthy subjects, 122 females, age range: 4-69 years), as well as an afternoon nap sleep record database (N = 112 healthy subjects, 30 females, age range: 18-30 years) were analysed by the individual adjustment method of sleep-spindle analysis. Slow and fast sleep-spindle frequencies were characterised by U-shaped overnight dynamics, with highest values in the first and the fourth-to-fifth sleep cycle and the lowest values in the middle of the sleeping period (cycles two to three). Age-related attenuation of sleep-spindle deceleration was evident. Estimated phases of the nadirs in sleep-spindle frequencies were advanced in children as compared to other age groups. Additionally, nap sleep spindles were faster than night sleep spindles (0.57 and 0.39 Hz difference for slow and fast types, respectively). The fine frequency resolution analysis of sleep spindles is a feasible method of measuring the assumed circadian modulation of sleep. Moreover, age-related attenuation of circadian sleep modulation might be measurable by assessing the overnight dynamics in sleep-spindle frequency. Phase of the minimal sleep-spindle frequency is a putative biomarker of chronotype.

K E Y W O R D S
biological night, nap sleep, non-rapid eye movement (NREM) sleep, sleep cycle effect, thalamocortical oscillations, time-of-day-effects

| INTRODUC TI ON
Easily accessible and reliable biomarkers of sleep regulatory processes are of utmost importance in the objective measurement of sleep quality and rest-activity rhythms. The two-process model is one of the most influential and substantive theories of sleep regulation, proposing a linear interaction between sleep homeostasis (process S) and the circadian rhythm (process C) in humans (Borbély, 1982). Although the basic tenets and the main predictions of the model are widely accepted and empirically supported (Borbély, Daan, Wirz-Justice, & Deboer, 2016), investigators conducting common polysomnography (PSG) studies are often challenged by the task of depicting and characterising the two sleep regulatory processes. Thanks to widely available digital electroencephalogram (EEG) recording and analysis tools, sleep homeostasis is easily measurable by quantifying EEG slow-wave activity (SWA: spectral power in the 0.75-4.5 Hz range; Achermann, 2009). In contrast, the circadian modulation of sleep EEG is either assumed and hypothetically included in the model, without considering the individual differences in phase (Achermann & Borbély, 2003;Borbély, 1982) or measured in particularly complex chronobiology study settings, like constant routine (Knoblauch et al., 2005) or forced desynchrony protocols (Wei, Riel, Czeisler, & Dijk, 1999), which are not easy to implement in common clinical and research sleep studies and require notoriously large time and labour investments.
Another objective method that is instrumental in the assessment of the circadian modulation of sleep consists of long-term physiological measurements of core body temperature and/or specific endocrine factors, like melatonin or cortisol release (Oster et al., 2017;Reid, 2019). Although these more direct ways of assessing the circadian component of sleep regulation seem promising, they are generally inconvenient and expensive, thus rarely included in the routine PSG-examination protocols. Omitting these measurements leads to a permanent lack of information on the individual differences in chronotype, the latter being defined as the phase of entrainment of the circadian rhythm and the zeitgebers/local time (Roenneberg, 2012). Standard PSG examinations disregard the fact that subjects with earlier or later chronotypes are characterised by different levels of circadian modulation of their sleep during the same period of recording. Known age effects of chronotype include a progressive phase delay from childhood till the end of adolescence, followed by a slow gradual phase advancement during ageing (Roenneberg et al., 2004). As a consequence, a widely accessible EEG index of the circadian processes could significantly improve the insight into sleep regulation and complete our understanding of sleep and chronotype.
Given the intermingling of sleep homeostasis and circadian modulation in natural, night-time sleep, specific EEG measures of the circadian process would be advantageous. Results of studies implementing forced desynchrony, constant routine, sleep displacement or overnight PSG protocols suggest that various aspects of sleep spindles reflect the circadian modulation of sleep or timeof-day (Aeschbach, Dijk, & Borbély, 1997;Knoblauch et al., 2005;Purcell et al., 2017;Wei et al., 1999). Sleep spindles are known as trains of distinct sinusoidal EEG waves with a frequency of 11-16 Hz (most frequently 12-14 Hz) lasting ≥0.5 s and emerging in non-rapid eye movement (NREM) sleep stages N2 and N3 (Berry, Albertario, Harding, 2018). These oscillatory events were shown to arise from the hyperpolarisation-rebound sequences of widely synchronised thalamocortical neurones. The thalamic reticular nucleus is hypothesised to be the main source of hyperpolarisation, whereas the T-type Ca 2+ -channels are sources of the rhythmic recurrence of firing (Fernandez & Lüthi, 2020). Based on topography and dominant frequency, two types of sleep spindles are distinguishable. The anterior (frontal) slow spindles are known to consist of waves of roughly 12 Hz (<12.5 Hz), whereas the posterior (centroparietal) fast sleep spindles are oscillations with a typical frequency of 14 Hz (>12.5 Hz) (Gibbs & Gibbs, 1951). Thorough analyses of sleep spindles indicate considerable individual differences (Bódizs, Körmendi, Rigó, & Lázár, 2009;Cox, Schapiro, Manoach, & Stickgold, 2017), as well as age and sex effects. The latter two consists of unusually low-frequency sleep spindles in prepubertal (and pre-schooler) ages (Ujma, Sándor, Szakadát, Gombos, & Bódizs, 2016), as well as a slightly (0.5 Hz) increased sleep-spindle frequency (SSF) and variability in pubertal girls and adult women as compared to boys and men (Bódizs et al., 2021;Ujma et al., 2014). SSF increases with remarkable linearity across the age range of 6-18 years (Zhang, Campbell, Dhayagude, Espino, & Feinberg, 2021), reaching a plateau in adulthood (Purcell et al., 2017), which was hypothesised to reflect the maturation of thalamocortical circuits via myelination (Zhang et al., 2021). Increased variability of sleep spindles in women is known to reflect the neural effects of hormonal variation during menstrual cycles (Ishizuka et al., 1994). That is, the differentiation of slow and fast sleep spindles and the individual adjustment of SSFs is a basic requirement in conducting studies in the field. Furthermore, sleep spindles were shown to contribute to sleep maintenance, and memory consolidation, as well as to correlate with psychometric measures of intelligence (Fernandez & Lüthi, 2020;Ujma, Bódizs, & Dresler, 2020), but none of these findings were shown to be tightly associated with the small differences in oscillatory wave frequencies.
Circadian modulation of SSF was evidenced in a forced desynchrony study, which is instrumental in differentiating sleep homeostatic and circadian effects by invoking the non-24-hr (usually 28 hr)-day approach. The SSF was lowest at the nadir of the core body temperature rhythm and peaked at the acrophase of the body temperature rhythm. In addition, circadian modulation of SSF, that is the decrease in oscillatory frequency during the biological night, was attenuated in aged subjects as compared to young ones (Wei et al., 1999). These findings cohere with outcomes of nap studies performed in constant routine conditions.
The nadir in SSF (NSSF) was shown to coincide with the acrophase of salivary melatonin levels in humans in this report (Knoblauch et al., 2005). In addition, experimental manipulation of sleep timing indicates prominent time of day effects in SSF activities, suggesting a frequency-specific circadian modulation: lower bins (12.25-13 Hz) of the SSF spectral power peak during the middle of the night sleep period (between 2:00 and 5:00 a.m.), when the highest bins (14.25-15 Hz) reach their nadir (Aeschbach et al., 1997). In addition, daytime recovery sleep after 25 hr of wakefulness was shown to be characterised by increased SSF compared to baseline night sleep records (Rosinvil et al., 2015). This latter effect was more pronounced in young as compared to middle-aged participants. That is sleep spindles are slower in the middle of the habitual sleep periods, characterised by high melatonin and low core body temperature levels. It has to be noted that brain temperature per se is a direct modulator of SSF: higher temperatures imply faster spindles (Csernai et al., 2019).
The above studies were not designed to differentiate between slow and fast sleep spindles, thus the authors could not deduce whether the reported post-midnight deceleration of the SSF reflects a frequency decrease or a change in the relative predominance of slow over fast sleep spindles (Aeschbach et al., 1997;Wei et al., 1999). Moreover, there is no direct evidence for the detectability of the above-described frequency evolution of sleep spindles during habitual (non-displaced) sleep periods. A study examining the overnight evolution of SSFs, but without differentiating slow and fast sleep spindle events, revealed a sleep timedependent increase in SSF (Himanen, Virkkala, Huhtala, & Hasan, 2002). This pattern evidently contrasts the convergent findings The aim of the present study was to test the feasibility of measuring the circadian modulation of SSFs in 1-night records of habitually timed sleep periods in different age groups by analysing its overnight dynamics (change over consecutive sleep cycles) and by comparing night-time SSF with afternoon nap SSF. We also aimed to provide a differential analysis of slow and fast sleep spindles and depict the potential difference between oscillatory deceleration of slow and/or fast sleep spindles and alternatively, the change in the relative predominance of slow over fast sleep spindle events.
To achieve these goals, we used an already established procedure of individualising slow and fast SSFs with high-frequency resolution (Bódizs et al., 2009). Given the already evidenced circadian modulation and the reported melatonin and/or temperature dependence of SSF, we hypothesise that: 1. Overnight dynamics in SSF is characterised by a U-shaped distribution (sleep spindles are slower in the middle of the habitual sleep period, as compared to the first and the last sleep cycles).
2. Middle night slowing of SSF is reduced in aged subjects as compared to young participants.
3. Estimated phase of the NSSF is delayed in teenagers and young adults, as compared to children and middle-aged adults.
4. Night sleep spindles are slower than nap sleep spindles.

| Subjects and databases
Multiple, published databases are used in this study. The Munich-Budapest database of sleep records consists of 251 night-timed PSG registrations (Bódizs et al., 2017). The mean (range) age of the subjects was 25.73 (4-69) years (122 females). Participants of the night sleep record dataset slept at their habitual sleeping time in the laboratory (N = 208) or in their homes (recorded by ambulatory PSG, N = 43) on 2 consecutive nights. In order to attenuate the first-night effect (Agnew, Webb, Williams, & Miller, 1966), only the second night data were used. Caffeine containing, but not alcoholic beverages were allowed in the morning hours in our adult subjects (maximum of two cups of coffee/subject before noon), whereas some of the participants who were light smokers (N = 8) were allowed to smoke during the day. The nap sleep records (N = 112) stem from studies on the effects of napping on memory consolidation (Genzel et al., 2012, as well as from a study analysing the relationship between nap sleep spindles and intelligence (Ujma et al., 2015), but only baseline and not post-learning records are analysed in the present investigation. The mean (range) age of the napping subjects was 23.72 (18-30) years. Women involved in the nap sleep studies (N = 30) were recorded twice: afternoon naps took place during the first and the third week of their menstrual cycle (early-follicular and mid-luteal phases, respectively, with hormonal blood tests confirming this assumption). Data of the two nap records of these subjects were averaged before statistical analyses. All subjects were healthy and free of any medications, except contraceptives in some of the women in the reproductive age group. Details of the recording procedures are reported in Table 1

| EEG processing
Records were scored according to standard criteria of sleep-wake states (Berry et al., 2018), followed by artefact removal on a 4-s basis. Sleep-cycle segmentation was based on reported criteria (Aeschbach & Borbély, 1993). EEG signals (mathematically linked mastoid reference) of the non-artefactual N2 and N3 sleep periods were subjected to the individual adjustment method (IAM) of sleep spindle analysis (Bódizs et al., 2009)   Fast sleep spindle spectral peaks were defined if: 1. there was a negative peak in the averaged second derivative (positive peaks are reverted and negative in the second order derivatives) at the corresponding frequencies.
2. the peak was of highest frequency (there is no spectral peak with higher frequency in the spindle range).
3. the amplitude spectra at the assumed peak frequencies was higher in centroparietal as compared to frontal recording locations ( Figure 1).
Frontal recording locations were defined as all available scalp contacts whose symbol begins with F or AF. In turn, centroparietal region was defined by all available contacts labelled with C or P. Fast SSFs were unambiguously detected in all subjects and sleep cycles.
In contrast, slow sleep spindle spectral peaks were defined if: 1. there was a negative peak in the averaged second derivative at the corresponding frequencies.
2. the peak was of lower frequency (there was at least one peak with higher frequency in the spindle range).
3. the relative difference in centroparietal and frontal amplitude spectra at the assumed peak frequencies was (relatively) lower as compared to this difference seen at the fast SSFs.
In cases in which more than two peaks were present, we based our selection on frontal and centroparietal dominances of the respective frequencies, relying on the amplitude spectra. That is, the peak with most pronounced frontal and centroparietal dominance in amplitude spectra, were considered as slow and fast SSFs, respectively. Lack of a definitive slow spindle peak was handled by searching the relative maxima of the frontal minus centroparietal amplitude spectral values, the slow spindle spectral peaks being defined at the edges of the associated bulge of second-order derivatives (which latter approach but do not reach zero in these cases; see Figure S1; Ujma et al., 2016). Last, but not least the spectral peaks of slow and fast sleep spindles could partially overlap in some cases. In such cases, the intersection of slow and fast sleep spindle-related spectral peaks was considered as a border frequency.
Slow and fast SSFs were defined as the middle of the respective frequency bands (arithmetic mean of lower and upper frequency boundaries).
The estimated phases of the nadirs of slow and fast SSFs was assessed as follows: 1. finding the sleep cycle characterised by the individual minima in SSF.

| Statistical analyses
Subjects of the night sleep study were classified according to the following age ranges (Bódizs et al., 2017): children (4 years ≤ age < 10 years; Besides our main focus (the nap versus night between subject factor), sex (between-subject), and spindle type (slow/fast, within-subject) were included in the GLM. Despite the homogenous age of the subjects of the nap versus night sleep study, the age factor was included in an additional statistical model as a continuous predictor.

| Overnight dynamics in SSF
Sleep architecture data indicated typical sleep composition (   Figure S2; Table S2).  Figure 4, it is evident, that the hypothesised age effects are best approximated by slow SSFs:

| The phase of the NSSF
phase of the NSSF is seen ~1 hr after midnight in children, whereas it reaches 3 hr in teenagers, followed by a slow decrease to 2.5 hr in older age groups. Post hoc Fisher LSD tests revealed a significantly earlier phase of the NSSF (slow spindles) in children as compared to all other age groups. Nominal differences among teenagers and adults (young and middle aged) did not result in significant post hoc effects.
To test the potential dependence of NSSF on bedtimes, which would clearly confuse the interpretation of our findings, a Pearson correlation coefficient was calculated. The latter indicated no relationship between bedtime and NSSF (r = 0.02; p = 0.68), suggesting that later bedtimes do not lead to later NSSF.

F I G U R E 2
The U-shaped dynamics in the overnight evolution of sleep-spindle frequencies. Slow and fast sleep spindles (broken and continuous black lines, respectively) decelerate in sleep cycles two and three, whereas cycles one and four are characterised by higher values. This effect is evident for both females (♀) and males (♂), despite the overall higher oscillatory frequencies of sleep spindles in females. The U-shaped overnight dynamics of the oscillatory frequency of sleep spindles in successive sleep cycles, clearly differs from the exponential decay of slow-wave activity (SWA; shaded area, grey, dotted lines). The latter is known as the most reliable indicator of sleep homeostasis
Although this effect is evident for both spindle types ( Figure 5 (Table S4).

| DISCUSS ION
Our present findings indicate that sleep spindles decelerate in the  (Wei et al., 1999), constant routine (Knoblauch et al., 2005) and sleep displacement (Aeschbach et al., 1997) studies suggest the involvement of circadian regulation in modulating SSF in humans. Former studies analysing the overnight dynamics of SSF in habitually timed PSG records, did not deliberately discern slow and fast sleep spindles (Himanen et al., 2002), thus could at least partially reflect the changing dominance of slow over fast sleep spindles. The latter was reported in former studies, suggesting that both the incidence and the amplitude of slow spindles decreased over successive sleep cycles, whereas an opposite trend was observable for fast sleep spindles (Bódizs et al., 2009;Purcell et al., 2017). Overnight changes in slow and fast sleep spindle incidence might explain the roughly 2-Hz acceleration of sleep spindles reported by Himanen et al. (2002).
Frontal and centroparietal regions are the main sources of slow and fast sleep spindles, respectively. This topographical feature was used as a priori criteria of defining slow and fast SSFs in our present study ( Figure 1), but not investigated as a dependent variable. That is, we assumed that a slow or a fast SSF is individual-but not region-specific.
Given the fact that topographical differences in oscillatory frequencies within the individual-specific slow or fast sleep spindle domain cannot be ruled out, this issue merits further attention in later studies.
The deceleration of slow and fast sleep spindles we report in our present study could be a result of the increased melatonin levels and the associated decrease in core body temperature in the middle F I G U R E 4 Phase of the nadir in sleepspindle frequency (NSSF) as expressed in fraction of hours relative to midnight. Vertical bars denote 95% confidence intervals of the habitual sleep period. The acrophase of the human plasma melatonin rhythm is known to emerge between 2:00 and 5:00 a.m. (Voultsios, Kennaway, & Dawson, 1997). In addition, melatonin receptors are expressed in the reticular thalamic nucleus (Ng, Leong, Liang, & Paxinos, 2017), which is a critical neuroanatomical structure in the process of sleep spindle generation (Fan, Liao, & Wang, 2017). Thus, both the timing and one of the target organs of melatonin release are ideally suited to support the involvement of the pineal hormone in shaping the evolution of SSF during the night. Last, but not least, SSF varies as a function of locally manipulated brain temperature (Csernai et al., 2019), whereas melatonin is known for its hypothermic effect (Marrin, Drust, Gregson, & Atkinson, 2013).
As a consequence, the hypothermia induced by increased melatonin levels in the middle of the sleeping period is potentially involved in the deceleration process of sleep spindling revealed in the present study. This assumption is further supported by differences in SSF activity during and outside melatonin secretory phase (Knoblauch et al., 2005), as well as by the findings indicating that SSF reaches its nadir at the trough of the body temperature cycle (Wei et al., 1999).
The age-dependent attenuation of sleep spindle deceleration in the middle of the habitual sleep period reported in the present study is reminiscent of the age-related decline in the amplitude of the circadian rhythm (Hood & Amir, 2017), the flattening of the body temperature rhythm in the aged (Weitzman, Moline, Czeisler, & Zimmerman, 1982), as well as the associated decline in melatonin release (Waldhauser et al., 1988). Decreased circadian modulation and melatonin production might fail to induce an efficient reduction in core body temperature and consequently a suboptimal modulation of SSF. Our present findings cohere with the forced desynchrony study reporting that older subjects express notably smaller circadian variation of SSF than young subjects (Wei et al., 1999). However, the reason for a lack of the above detailed U-shaped distribution in the frequency of slow sleep spindles in young girls do not cohere with the above reasoning.
Sleep spindles speed up in the fourth sleep cycle and continue to accelerate on the rising limb of the circadian cycle up to the fifth sleep cycle in the subset of subjects having five complete NREM-REM periods in our present dataset. Thus, we assume that sleep spindles are even faster during daytime as compared to night-time sleep. This coheres with our present findings reported in the nap study. That is, in addition to the reported deceleration of spindle oscillations in the middle of the habitual night sleep period, we report accelerated SSF during afternoon naps as compared to nocturnal averages (cycles one to four). The finding that the oscillatory frequency of nap sleep spindles exceeds that of night spindles further strengthens our assumption that the above discussed sleep cycle effects might reflect circadian modulation and/or melatonin release. Core body temperature is known to be higher during afternoon hours as compared to late night periods (Baehr, Revelle, & Eastman, 2000), whereas melatonin release is evidently at its lowest level during these daytime hours (Aulinas, 2000). Thus, the acceleration of sleep spindles in afternoon naps coheres with our assumption regarding the circadian regulation of the duration of thalamocortical hyperpolarisation-rebound sequences. To the best of our knowledge the present study is the first explicitly reporting a nap versus night sleep difference in SSFs.
F I G U R E 5 Nap sleep spindles are higher than night sleep spindles. Individual-specific slow and fast sleep spindles are compared in two groups of age-and sex-matched subjects sleeping during the afternoon and during the night, respectively We hypothesised that the phase of the middle night drop in SSF could serve as an EEG marker of the circadian phase in humans.
Available data in the present set is only suitable for an indirect test of this assumption. That is, NSSFs were found to be independent from bedtimes, which might suggest a time-of-day rather than a sleepdependent effect. Moreover, we tested the known age effects in circadian phase by comparing the different age groups. Our present findings partially support the hypothesis: children were characterised by earlier phases than teenagers or adults. Although, this latter finding coheres with known age differences in circadian phase, additional age effects, namely the phase advancement in middle-aged adults was not unequivocally supported by our present findings. This could reflect the lack of aged subjects in our sample or the insufficient precision of measuring the phase of the NSSF (in the middle of the sleep cycle characterised by lowest SSF). Later studies could invoke a more instantaneous phase measure, providing investigators with increased temporal resolution. Given the partial statistical support, we consider our measure as a potentially suitable EEG index of circadian phase, which might bridge the methodological and conceptual gap between chronobiology and somnology in future investigations.
Besides of the U-shaped overnight dynamics and afternoon nap effect, formerly reported sex-differences, and age effects in SSFs were also supported by our present analyses. That is, sleep spindles were of higher frequency in females as compared to males, an effect that has already been reported by different research groups (Markovic, Kaess, & Tarokh, 2020;Ujma et al., 2014). Moreover, SSFs were significantly lower in prepubertal ages (aged <10 years) as compared to teenagers and adults. This effect was also reported by our own former study (Ujma et al., 2016), as well as by others analysing sleep spindles in children (Campbell & Feinberg, 2016). The convergence of these findings with the available published reports strengthens the validity of our present approach and provides further empirical support for the recent hypothesis on the neurodevelopmental relevance of SSF (Zhang et al., 2021).
Given the fact that individual-specific slow and fast sleep spindle bands are roughly 1 Hz wide each (Bódizs et al., 2009) The strength of our present study is the high number of subjects and wide age range, whereas limitations are the lack of repeated day versus night sleep measurements in the same groups of subjects, the lack of controlling several variables related to menstrual cycles (cycle phase, contraceptive use), as well as the lack of valid circadian measures (body temperature, melatonin release) against which we could perform tests of convergent validity. Although some of the subsamples we use are of lower sampling rate as compared to the current standards of the American Academy of Sleep Medicine (500 Hz), in the present study we only focus on relatively lower frequency oscillations (at least 15-times lower as compared to our lowest sampling rate), which (together with the anti-aliasing hardware filters) provide sufficient technical support for our conclusions. We consider our present findings as a first step in defining an EEG index of the circadian modulation of sleep, which could efficiently complete the already available and widely used measure of sleep homeostasis. We hypothesise that the reliable measurement of the overnight dynamics of slow and fast SSFs might convey information about the amplitude and perhaps the phase of the circadian rhythm in future translational and clinical studies, including investigations on patients with circadian rhythm sleep disorders. to publish, or preparation of the manuscript. Authors wish to thank Dorina Ali and Dávid Rottmayer for their assistance in data analysis.

CO N FLI C T O F I NTE R E S T
No conflicts of interest declared.

AUTH O R CO NTR I B UTI O N S
RB conceived the study; RB, PS, IK, LG, and MD contributed to data collection; RB, CGH, PPU, PS, and FG contributed to data analysis; all authors drafted the manuscript, critically revised the major intellectual content and approved the final version of the paper.

DATA AVA I L A B I L I T Y S TAT E M E N T
Data available on request from the authors.