Pierre Champetier

Claire André

Frederik D Weber

Stéphane Rehel

Valentin Ourry

Alice Laniepce

Antoine Lutz

Françoise Bertran

Nicolas Cabé

Anne-Lise Pitel

Géraldine Poisnel

Vincent De La Sayette

Denis Vivien

Gaël Chételat

PhD Géraldine Rauchs
email: geraldine.rauchs@inserm.fr

Age-related changes in fast spindle clustering during non-rapid eye movement sleep and their relevance for memory consolidation

Keywords: Sleep, sleep spindles, ageing, memory consolidation, sleep fragmentation, non-rapid eye movement sleep Clinical Trial Information

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Introduction

Maintaining optimal sleep quality is essential for health and well-being. During sleep, the brain fulfils major functions such as memory consolidation (see [1] for review). However, it still has to monitor the surroundings to wake up if necessary. Evolutionary mechanisms shaped our sleep through these opposite selective pressures [START_REF] Samson | Sleep intensity and the evolution of human cognition: Sleep Intensity and the Evolution of Human Cognition[END_REF]. A balance between off-line processes and alertness towards the environment is therefore crucial. Recent evidence on animal and young adults suggests a key role of sigma power fluctuation and non-homogeneous sleep spindle distribution in this equilibrium [START_REF] Lecci | Coordinated infraslow neural and cardiac oscillations mark fragility and offline periods in mammalian sleep[END_REF].

Sleep spindles are transient (0.5-2 s) thalamo-cortical oscillations in the sigma frequency band (~ 11-15 Hz) typically observed in scalp-EEG of polysomnography. These discrete events are generated by the thalamic reticular nucleus (TRN) and are a hallmark of NREM sleep (see [START_REF] Fernandez | Sleep Spindles: Mechanisms and Functions[END_REF] for review). Several spindle parameters (e.g. number, density, activity) increase overnight after learning a new task and have been associated with consolidation in declarative [START_REF] Gais | Learning-Dependent Increases in Sleep Spindle Density[END_REF][6][START_REF] Schabus | Sleep Spindles and Their Significance for Declarative Memory Consolidation[END_REF][START_REF] Lafortune | Sleep spindles and rapid eye movement sleep as predictors of next morning cognitive performance in healthy middle-aged and older participants[END_REF] and procedural [START_REF] Fogel | Learning-dependent changes in sleep spindles and Stage 2 sleep[END_REF]10] memory. Sleep spindles may promote the reactivation of memories [START_REF] Cairney | Memory Consolidation Is Linked to Spindle-Mediated Information Processing during Sleep[END_REF][START_REF] Antony | Sleep Spindle Refractoriness Segregates Periods of Memory Reactivation[END_REF] and the reorganization of memory traces within neural networks [START_REF] Andrade | Sleep Spindles and Hippocampal Functional Connectivity in Human NREM Sleep[END_REF][START_REF] Bergmann | Sleep spindle-related reactivation of category-specific cortical regions after learning face-scene associations[END_REF]. Besides, sleep spindles are also thought to be an index of sleep stability by modulating the effect of external stimuli on brain activity and the propensity to arouse [START_REF] Lecci | Coordinated infraslow neural and cardiac oscillations mark fragility and offline periods in mammalian sleep[END_REF][START_REF] Elton | Event-related potentials to tones in the absence and presence of sleep spindles[END_REF][START_REF] Dang-Vu | Spontaneous brain rhythms predict sleep stability in the face of noise[END_REF][START_REF] Schabus | The Fate of Incoming Stimuli during NREM Sleep is Determined by Spindles and the Phase of the Slow Oscillation[END_REF][START_REF] Wimmer | Sustaining Sleep Spindles through Enhanced SK2-Channel Activity Consolidates Sleep and Elevates Arousal Threshold[END_REF].

Two subtypes of sleep spindles, namely slow (< 13 Hz) and fast (> 13 Hz) spindles, have been described [START_REF] Werth | Spindle frequency activity in the sleep EEG: individual differences and topographic distribution[END_REF][START_REF] Schabus | Hemodynamic cerebral correlates of sleep spindles during human non-rapid eye movement sleep[END_REF][START_REF] Andrillon | Sleep Spindles in Humans: Insights from Intracranial EEG and Unit Recordings[END_REF]. Fast spindles, mainly recorded over centro-parietal regions [START_REF] Dehghani | Topographical frequency dynamics within EEG and MEG sleep spindles[END_REF][START_REF] Cox | Individual Differences in Frequency and Topography of Slow and Fast Sleep Spindles[END_REF][START_REF] Zeitlhofer | Topographic distribution of sleep spindles in young healthy subjects[END_REF] , are assumed to be particularly involved in sleep-dependent memory consolidation [START_REF] Cairney | Memory Consolidation Is Linked to Spindle-Mediated Information Processing during Sleep[END_REF][START_REF] Andrade | Sleep Spindles and Hippocampal Functional Connectivity in Human NREM Sleep[END_REF][START_REF] Schabus | Hemodynamic cerebral correlates of sleep spindles during human non-rapid eye movement sleep[END_REF][START_REF] Mölle | Fast and Slow Spindles during the Sleep Slow Oscillation: Disparate Coalescence and Engagement in Memory Processing[END_REF][START_REF] Cowan | Sleep Spindles Promote the Restructuring of Memory Representations in Ventromedial Prefrontal Cortex through Enhanced Hippocampal-Cortical Functional Connectivity[END_REF]. Some recent studies have focused on the non-homogenous distribution of spindles during NREM sleep and on the fluctuation of spindle frequency power (sigma) [START_REF] Lecci | Coordinated infraslow neural and cardiac oscillations mark fragility and offline periods in mammalian sleep[END_REF]10,[START_REF] Lázár | Infraslow oscillations in human sleep spindle activity[END_REF][START_REF] Weber | Coupling of gamma band activity to sleep spindle oscillations -a combined EEG/MEG study[END_REF]. Lecci et al. [START_REF] Lecci | Coordinated infraslow neural and cardiac oscillations mark fragility and offline periods in mammalian sleep[END_REF] reported that sigma power (and more specifically power in the fast spindle frequency band) fluctuates throughout NREM sleep at an infraslow scale of around 0.02 Hz (i.e., periodicity of about 50 s) in both mice and young adults. This means that during NREM sleep, periods of low sigma power of about 25 seconds are repeatedly followed by equivalent periods (~25-s) of high sigma power. This fluctuation results from a periodic clustering of fast spindle activity. Spindles tend to be separated by 3 to 6 seconds, suggesting a refractory period following a spindle and a rhythmicity gathering spindles into clusters [START_REF] Antony | Sleep Spindle Refractoriness Segregates Periods of Memory Reactivation[END_REF]. Based on these observations, Boutin and Doyon [START_REF] Boutin | A sleep spindle framework for motor memory consolidation[END_REF] proposed the concept of "spindle trains" (or clusters) defined as a group of at least 2 temporally clustered spindles interspaced by less than 6 seconds. These clusters occur in periods of high sigma power, while periods of low sigma power mainly contain sparse isolated spindles. Importantly, this 0.02-Hz infraslow oscillation in sigma power has been associated with behavioral arousability change in mice and with episodic memory consolidation in humans. Auditory stimuli have a higher propensity to wake up the animal when they occur in a period of declining sigma power [START_REF] Lecci | Coordinated infraslow neural and cardiac oscillations mark fragility and offline periods in mammalian sleep[END_REF]. Besides, higher strength of 0.02-Hz sigma oscillation was associated with better overnight memory consolidation [START_REF] Lecci | Coordinated infraslow neural and cardiac oscillations mark fragility and offline periods in mammalian sleep[END_REF]. Moreover, the proportion of clustered spindles appears to increase overnight in the hemisphere that was activated while performing a motor task [START_REF] Solano | Visuomotor Adaptation Modulates the Clustering of Sleep Spindles Into Trains[END_REF], suggesting that learning specifically promotes spindle clustering in the network recruited during encoding. Finally, several spindle cluster parameters (such as the mean number of spindle per cluster or the inter-hemispheric difference in the proportion of clustered spindles the night following a one-handed motor task) have been associated with procedural memory consolidation [START_REF] Boutin | A sleep spindle framework for motor memory consolidation[END_REF][START_REF] Solano | Visuomotor Adaptation Modulates the Clustering of Sleep Spindles Into Trains[END_REF]. This 0.02-Hz infraslow oscillation may allow the brain to switch every ~25 s between an environment monitoring state (with scarce fast spindles) and an off-line state dedicated to internal processes like memory consolidation (with high fast spindle density). Any impairment of this switching may hinder sleep-dependent memory consolidation and increase sleep fragility.

Interestingly, sleep fragmentation increases with age and many studies report that sleep-dependent memory consolidation is less efficient in ageing (see [START_REF] Scullin | Sleep, Cognition, and Normal Aging: Integrating a Half Century of Multidisciplinary Research[END_REF][START_REF] Muehlroth | Episodic memory consolidation during sleep in healthy aging[END_REF] for reviews). However, the debate is still open as other studies reported that this process is preserved in older adults [START_REF] Aly | The effects of sleep on episodic memory in older and younger adults[END_REF][START_REF] Wilson | Sleep modulates word-pair learning but not motor sequence learning in healthy older adults[END_REF].

Although it is well-established that sleep spindle density, amplitude and duration decrease with age [START_REF] Nicolas | Sleep spindle characteristics in healthy subjects of different age groups[END_REF][START_REF] Martin | Topography of age-related changes in sleep spindles[END_REF][START_REF] Purcell | Characterizing sleep spindles in 11,630 individuals from the National Sleep Research Resource[END_REF], the dynamic aspects of fast spindles (i.e., temporal clustering) and of their related power (fluctuation at a 0.02-Hz infraslow scale) have never been investigated in older adults. This may be particularly relevant as we know that subtle changes in spindle dynamic occur with age. While spindle density and duration increase across sleep cycles in young adults, older adults do not appear to exhibit such a temporal pattern [START_REF] Purcell | Characterizing sleep spindles in 11,630 individuals from the National Sleep Research Resource[END_REF][START_REF] Guazzelli | Sleep spindles in normal elderly: comparison with young adult patterns and relation to nocturnal awakening, cognitive function and brain atrophy[END_REF]. Besides, the U-shaped dynamics of spindle frequency overnight recently observed in young adults (with highest values in the first and last sleep cycles and lowest values in the middle ones) is attenuated in older adults [START_REF] Bódizs | Sleep-spindle frequency: Overnight dynamics, afternoon nap effects, and possible circadian modulation[END_REF].

In this context, our first aim was to determine whether power in the fast spindle band fluctuates in older adults at a 0.02-Hz infraslow scale. Second, to better understand the spindle clustering phenomenon, we compared the amplitude, duration and frequency of clustered and isolated fast spindles. Third, we investigated the impact of age on fast spindle clustering and its dynamics across the night. Finally, we also assessed the links between fast spindle clustering, episodic memory consolidation and NREM sleep fragmentation. [START_REF] Martin | Topography of age-related changes in sleep spindles[END_REF]. The other participants (14 young-middle aged and 13 older adults) were included as healthy volunteers in a third study investigating sleep changes in ageing and Alzheimer's disease and their impact on memory performance (CPP Caen, 2001-46). All participants presented no evidence of major neurological, vascular or psychiatric disorders. Sleep medication use was an exclusion criteria.

Methods

None of the older participants had a Mini-Mental State Examination [START_REF] Folstein | Mini-mental state[END_REF] score below 26. These different protocols were approved by ethics committees and participants gave their written consent prior to the examinations after detailed information was provided to them. The use of data from these two latter protocols was approved by the ethics committee (Comité Local d'Ethique de la Recherche en Santé) of Caen University Hospital and University of Caen (approval n° 3381 -05/16/2022). In accordance with this authorization, we ensured that participants did not object to the analysis of their data for a purpose other than the original study in which they were included.

Sleep recording and analysis

Sleep was monitored with polysomnography (PSG). For 152 participants (134 older and 18 youngmiddle aged adults), PSG was performed at home using a portable recording device (Siesta®, Compumedics, Australia). Among them, 90 older participants underwent two recordings but only the second one was included in the analyses. Twenty EEG electrodes were placed over the scalp (Fp1, Fp2, F3, F4, F7, F8, FZ, C3, C4, CZ, T3, T4, P3, P4, PZ, O1, O2, vertex ground and a bi-mastoid reference) according to the international 10-20 system, with impedances kept below 5 kΩ.

Respiratory movements, airflow, and oxygen saturation were recorded respectively with thoracic and abdominal belts, nasal and oral thermistors, and a finger pulse oximeter. The EEG signal was digitalized at a sampling rate of 256 Hz. For the 27 remaining participants (13 older and 14 youngmiddle aged adults), PSG data were acquired in the sleep department of Caen University Hospital using the Nicolet Acquisition System. They underwent two polysomnography nights, the first one being an adaptation night. Eight EEG electrodes were placed over the scalp (C3, C4, T3, T4, O1, O2, vertex ground and a bi-mastoid reference) according to the international 10-20 system, with impedances kept below 10 kΩ. The EEG signal was digitalized at a sampling rate of 125 Hz. For all participants, high-pass and low-pass filters were applied, respectively at 0.3 Hz and 35 Hz.

All recordings were visually scored in 30-second epochs following the recommended standard criteria of the American Academy of Sleep Medicine [START_REF] Berry | AASM Scoring Manual Updates for 2017 (Version 2.4)[END_REF] [START_REF] Oostenveld | FieldTrip: Open Source Software for Advanced Analysis of MEG, EEG, and Invasive Electrophysiological Data[END_REF]. All epochs were visually inspected. An independent component analysis (ICA) was performed for 2 subjects to remove the ECG artifacts on EEG signals. The EEG data of these 2 subjects were visually checked after the procedure. The data were then epoched into 5-s bins. The 5-s epochs containing manually identified EEG artifacts or movement arousals were rejected. Channels with artifacts affecting a majority of the recording were removed. In line with the latest sleep research recommendations in older adults (see [START_REF] Muehlroth | Understanding the interplay of sleep and aging: Methodological challenges[END_REF] for review), we considered N2 and N3 sleep stages as a continuum and performed our analyses on all artifactfree N2 and N3 sleep epochs.

One hundred and thirty four older adults and 18 young-middle aged adults also filled sleep questionnaires (Pittsburgh Sleep Quality Index (PSQI [START_REF] Buysse | The Pittsburgh sleep quality index: A new instrument for psychiatric practice and research[END_REF]) and Insomnia Severity Index (ISI [START_REF] Bastien | Validation of the Insomnia Severity Index as an outcome measure for insomnia research[END_REF])) and rated their sleep quality and depth during the polysomnography night using the Saint Mary's Hospital questionnaire [START_REF] Ellis | The St. Mary's Hospital Sleep Questionnaire: A Study of Reliability[END_REF].

Half of the night, sleep cycles and pre-REM periods identification

We also investigated the dynamics of fast spindle clustering across the night. First, the half of the night was defined as the epoch equally distant from the first and last epochs of sleep for each participant. Second, sleep cycles were automatically identified using SleepTrip and then manually checked. As 81 subjects did not exhibit 5 or more sleep cycles, we only considered the first four sleep cycles. A similar procedure has already been applied in studies analyzing spindle dynamics across NREM sleep cycles [START_REF] Alfonsi | Spatiotemporal Dynamics of Sleep Spindle Sources Across NREM Sleep Cycles[END_REF]. To exclude sleep cycles that have just started, we removed from the analysis sleep cycles with less than 10 min of N2-N3 (13 sleep cycles among 704). Third, we defined the pre-REM periods as the last five minutes of N2-N3 epochs before each transition to REM sleep. The rest of N2-N3 epochs was classified as non pre-REM periods. Three older adults had less than 10 minutes of pre-REM periods over the whole night (due to incomplete sleep cycles caused by sleep fragmentation) and were excluded from this analysis.

Fast spindle detection and cluster identification

For each participant, fast spindles were automatically detected in artifact-free N2 and N3 sleep segments using a validated algorithm used in previous publications [START_REF] Klinzing | Spindle activity phase-locked to sleep slow oscillations[END_REF][START_REF] Pereira | Tactile stimulation during sleep alters slow oscillation and spindle densities but not motor skill[END_REF][START_REF] Rudzik | Sleep spindle characteristics and arousability from nighttime transportation noise exposure in healthy young and older individuals[END_REF] and based on the study by Mölle et al. [START_REF] Mölle | Grouping of Spindle Activity during Slow Oscillations in Human Non-Rapid Eye Movement Sleep[END_REF]. As spindle frequency can differ between participants [START_REF] Werth | Spindle frequency activity in the sleep EEG: individual differences and topographic distribution[END_REF][START_REF] Cox | Individual Differences in Frequency and Topography of Slow and Fast Sleep Spindles[END_REF][START_REF] Buckelmüller | Trait-like individual differences in the human sleep electroencephalogram[END_REF], we used a subject-specific frequency band. NREM sleep power spectra were calculated for all the electrodes of each subject. The individual peak frequency in fast spindle range was visually identified on centroparietal channels (mean ± SD: 13.66 ± 0.5 Hz) and taken as the fast spindle center frequency (Figure 1). Fast spindle peaks were clearly identifiable, except for 3 older adults which were removed from the analyses. The analysis of slow spindles raised several methodological issues. As described above, 14 among the 32 participants of the young-middle aged group and 13 older adults had no frontal EEG channel. Besides, no clear power peak of slow spindles could be identified in a substantial part of the remaining participants with frontal EEG channels. Previous studies using subject-specific frequency band for spindle detection reported similar issues and focused their analyses on fast spindles [START_REF] Pereira | Tactile stimulation during sleep alters slow oscillation and spindle densities but not motor skill[END_REF][START_REF] Thürer | Variable training but not sleep improves consolidation of motor adaptation[END_REF].

We decided to also limit our analyses to fast spindles. For each participant, the EEG signal was filtered with a band-pass width of 2 Hz centered on the fast spindle center frequency (two-pass FIR filter). The root mean square (RMS) signal was calculated using 0.2-s windows for the entire recording and smoothed by a moving average (0.2-s window). A fast spindle was detected if the smoothed RMS signal exceeded an individual amplitude threshold (1.5 times the standard deviation of the filtered signal) for 0.5-2 s. Fast spindles with an amplitude higher than 120 µV were excluded.

A visual inspection was performed in a subgroup of participants to check the validity of fast spindle detection. Fast spindle mean peak-to-trough amplitude, duration, average oscillatory frequency, and density (number of spindles per artifact-free N2 and N3 sleep minute) were calculated for each participant and channel.

Fast spindle clustering (reoccurring spindles within the same channel) was investigated using the criteria proposed by Boutin and Doyon [START_REF] Boutin | A sleep spindle framework for motor memory consolidation[END_REF]. We considered fast spindles as clustered (i.e., temporally clustered into trains) if they were interspaced by less than 6 s. The size of each cluster was defined as the number of fast spindles clustered. A clustering level was associated to each fast spindle. The clustering level corresponded to the number of fast spindles in the potential cluster associated (1 for isolated spindles, ≥ 2 for clustered spindles). Then, for clustered fast spindles, the clustering level corresponded to the size of the cluster to which they belong. To test the effect of fast spindle clustering on their characteristics, we computed the percent difference in amplitude, duration and frequency of clustered fast spindles relative to that of isolated fast spindles. This was performed for each clustering level on all channels of all participants. It allowed us to take into account the interchannel and inter-individual variability of fast spindle characteristics. As some subjects did not have fast spindles in every clustering levels ≥ 6, we gathered all fast spindles with a clustering level ≥ 5.

As fast spindles mainly occur in the centro-parietal region [START_REF] Dehghani | Topographical frequency dynamics within EEG and MEG sleep spindles[END_REF][START_REF] Cox | Individual Differences in Frequency and Topography of Slow and Fast Sleep Spindles[END_REF][START_REF] Zeitlhofer | Topographic distribution of sleep spindles in young healthy subjects[END_REF], we focused our analyses on the channels covering this area. Fast spindle measures were calculated separately on the 2 centroparietal channels available for all participants (i.e., C3 and C4) and were then averaged. For the memory consolidation analysis specifically, the same procedure was applied on C3, CZ, C4, P3, PZ and P4 as all these centro-parietal channels were available for all subjects who performed the memory task.

0.02-Hz infraslow oscillation analyses

The procedure of Lecci et al. [START_REF] Lecci | Coordinated infraslow neural and cardiac oscillations mark fragility and offline periods in mammalian sleep[END_REF] was applied to study fast spindle band power fluctuations. Briefly, all consecutive 120-s periods of artifact-free N2 and N3 sleep were selected for each participant. Here again, a subject-specific frequency band (2 Hz width and centered on individual fast spindle peak frequency) was used to calculate the time-frequency power. The latter was computed for consecutive 100-ms bins in steps of 0.2 Hz with a continuous wavelet transform using Morlet wavelets (4 cycle length). The resulting power time courses were then smoothed (using a symmetric moving average in a 4-s window) and normalized (to the average absolute power in the subject specific fast spindle frequency band across all NREM sleep epochs). Another Morlet wavelet analysis was performed to calculate the spectral profile of the fast spindle band power time courses at a frequency resolution of 0.001 Hz in the 0.001-0.12 Hz range. The resulting signal was averaged across all N2 and N3 sleep epochs of the participant, weighted by their duration. The spectral profile obtained for each subject was normalized to its own mean. Finally, the grand average across subjects was calculated. Individual and group frequency peaks were determined after applying a Gaussian fit (three terms) on each subject and grand average spectra. As the 0.02-Hz sigma oscillation has been reported to be maximal on centro-parietal channels [START_REF] Lecci | Coordinated infraslow neural and cardiac oscillations mark fragility and offline periods in mammalian sleep[END_REF][START_REF] Lázár | Infraslow oscillations in human sleep spindle activity[END_REF], we focused our analyses on C3 and C4 electrodes that were available for all subjects.

Memory task

A subgroup of 77 older participants performed a computerized two-dimensional visuospatial objectlocation task. This task, developed by Rasch et al. [START_REF] Rasch | Odor Cues During Slow-Wave Sleep Prompt Declarative Memory Consolidation[END_REF], is known to be hippocampus-dependent and reinforced by sleep [START_REF] Rasch | Odor Cues During Slow-Wave Sleep Prompt Declarative Memory Consolidation[END_REF], and was successfully used in older adults [START_REF] Cherdieu | Does age worsen sleep-dependent memory consolidation?[END_REF]. Throughout the task, all 24 possible spatial locations were shown as grey squares on the computer screen and corresponded to "the back of the cards". The locations were displayed in a 6 × 4 matrix. During the learning phase, performed at the end of the afternoon before the polysomnography night, the first card of each pair was presented alone for one second, followed by the presentation of both cards for three seconds.

After an inter-stimulus interval of three seconds, the next pair of cards was presented in the same way. The 12 card-pairs were presented twice in the same order. Immediately after these two runs, recall of the spatial locations was tested using a cued recall procedure. The first card of a pair was displayed and the participant had to indicate, using the computer mouse, the location of the second card. A visual feedback was given in each case by presenting the second card at the correct location for two seconds, regardless of whether the response was correct or not. After the 12 pairs of cards were tested, the percentage of correct answers in the trial was displayed. The cued recall procedure was repeated until the participant reached a criterion of 66.7 % correct responses in a trial (i.e., 8 card-pairs correctly located). The learning score was defined as the score at the last trial of the learning phase (first trial with a score ≥ 8/12).

The next morning, after removing electrodes, memory performance was probed in a single trial using the same cued recall procedure as during the learning phase. We evaluated memory consolidation by calculating an overnight change in memory performance as follows: 100 x (recall score -learning score) / learning score. Of note, 11 participants did not reach the learning criterion and were removed from analyses. To allow a minimum level of practice and repetition during the learning phase, the 6 participants who reached the learning criterion in less than 4 trials were also removed.

Finally, after removing 3 participants who did not exhibited a clear fast spindle power peak, the data of 57 older subjects were analyzed.

Statistical analyses

All statistical analyses were performed using R (version 4.1.0; R Project for Statistical Computing; http://www.r-project.org). The threshold for statistical significance was set at p < 0.05 and was twotailed. Group comparisons for demographic variables were assessed using a Chi 2 test for sex (categorical variable) and a non-parametric Wilcoxon signed-rank test for age (continuous variable with non-normal distribution revealed using Shapiro-Wilk test). Between group differences for sleep architecture and fast spindle characteristics were tested using two-way type-II ANOVAs to account for sex ratio disparity.

Linear mixed models were used to assess the effect of clustering level on fast spindle characteristics, the effect of age group on these latter and on fast spindle proportion for each clustering level. The dynamics of fast spindle clustering across the night (effects of the half of the night, sleep cycles and pre-REM periods) were also tested using linear mixed models. Models were fitted to the data with restricted maximum likelihood using the lme4 package. The significance of fixed effects was assessed with type III F-tests with Satterthwaite's method. Clustering level was considered as a categorical variable in the models as fast spindles with a clustering level ≥ 5 were gathered. To further investigate the interaction between age group and fast spindle proportion in the different clustering levels, post-hoc pairwise Wilcoxon tests with Bonferroni correction were used to assess betweengroup differences. A Bonferroni correction was also applied in the analyses investigating the different fast spindle characteristics (amplitude, duration and frequency), setting the significance level at 0.05/3 = 0.016. Linear and non-linear (2 nd order polynomial) regression models were used to evaluate the relationship between age, the proportion of clustered fast spindles and the mean cluster size. Linear and non-linear models were compared using several methods: ANOVA, likelihood ratio test (LRT), Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC). In the 2 nd order polynomial models, the overall significance of age was assessed using type II F-test, and the overall variance proportion of spindle clustering explained by age was calculated by subtracting the R 2 of the complete model to the R 2 of the model with only sex as covariate. The variances of clustered fast spindle proportion in young-middle aged and older adults were compared using a Fisher test. Linear regressions were also used to test the associations between fast spindles, overnight change in memory performance and NREM sleep fragmentation (i.e., density of micro-arousals during NREM sleep). All analyses were controlled for age (except for group comparisons) and sex. Association between fast spindle clustering and subjective sleep reports were tested using non parametric Spearman's rank correlations.

Mediation analyses were performed to test the direct and indirect effects of age on the proportion of clustered fast spindles and on the mean cluster size using nonparametric bootstrapping based on 5,000 bootstrap samples. These analyses were controlled for sex.

Results

Participant characteristics

Demographic data, sleep architecture and spindle parameters of participants are summarized in Table 1. Sex ratio was statistically different between both groups (p = 0.0047) with a higher proportion of men in the young-middle aged group and a higher proportion of women in the older group. Sleep architecture and fast spindle characteristics differed between groups. Thus, compared to young-middle aged individuals, older adults had lower total sleep time (p < 0.001), lighter and more fragmented sleep with an increase in %N1, wake after sleep onset (WASO) and in NREM sleep micro-arousal density (all p-values < 0.001). Older adults also exhibited a decrease in %N3 (p = 0.022) and in sleep efficiency (p < 0.001). Concerning specifically sleep spindles, fast spindle density, amplitude and duration were reduced in older adults (all p-values < 0.001), whereas there was no effect of age on fast spindle frequency (p = 0.49).

Fast spindle band power fluctuation in young-middle aged and older adults Fast spindle band power fluctuated in older adults at an infraslow scale close to 0.02 Hz. The averaged fast Fourier transform (FFT) of fast spindle band power peaked around 0.02 Hz in both young-middle aged and older groups (Figure 2A). After applying a Gaussian fit on grand average spectra, the peaks were respectively at 0.021 Hz for young-middle aged adults and 0.022 Hz for older adults. The individual FFT peaks did not differ between groups (F(1,175) = 0.164, p = 0.69; Figure 2B).

To relate the frequency of the infraslow oscillation to fast spindle clustering, we calculated the mean cluster size (mean number of fast spindles per cluster). A slower infraslow oscillation was associated with a higher number of fast spindles per cluster with or without controlling for age and sex (p < 0.001, β = -0.37; Figure 3). The frequency of the infraslow oscillation was also negatively associated with the proportion of clustered fast spindles with or without controlling for sex (p < 0.001, β = -0.35).

Fast spindles characteristics are modulated by their clustering level

To better understand the phenomenon of fast spindle clustering, we analyzed fast spindle characteristics (i.e., amplitude, duration, frequency) for each clustering level, using the data of both young-middle aged and older adults. The clustering level of fast spindles modulated their characteristics (Figure 4). Fast spindle amplitude (F(4,712) = 190.4, p < 0.001) and duration (F(4,712) = 710.0, p < 0.001) increased with their clustering level while, to a lesser extent, their frequency (F(4,712) = 9.6, p < 0.001) decreased. Fast spindles in clusters of at least 5 spindles showed a 6% increase in amplitude and a 14% increase in duration compared to isolated fast spindles. In contrast, their frequency decreased by 0.2%.

We also investigated whether ageing impacted the effect of clustering level on fast spindle characteristics. After correction for multiple comparisons, a significant interaction between age group and clustering level was observed only for the relative difference in duration (p = 0.012), but not for amplitude (p > 0.49) and frequency (p > 0.21) of fast spindles. Thus, a greater increase in fast spindle duration was observed in young-middle aged compared to old participants, even after considering sex as a confounder (Figure 4).

Age reduces fast spindle clustering

We next investigated the impact of age on fast spindle clustering. Compared to young-middle aged participants, the proportion of clustered fast spindles was reduced in older adults (Table 1) (p < 0.001). Both linear and non-linear (2 nd order polynomial) adjustments significantly predicted the relationship between the proportion of clustered fast spindles and age, even after controlling for sex (all p-values p < 0.001). However, all approaches used to compare the two models (ANOVA, LRT, AIC and BIC) confirmed that the 2 nd order polynomial model fitted better our data. This non-linear relationship between age and the proportion of clustered fast spindles showed that this proportion remained relatively stable from 20 to about 50 years but decreased drastically at older ages (Figure 5A). Accordingly, a linear relationship between age and the proportion of clustered fast spindles was found in the older group (p < 0.001) while no relationship was found in the young-middle aged group (p = 0.47). Of note, greater inter-individual variability in the proportion of clustered fast spindles was observed in older adults compared to young-middle aged ones (p = 0.023). To better characterize the impact of age on fast spindle clustering, we compared the proportion of fast spindles between young-middle aged and older adults for each clustering level (Figure 5B). Age affected the clustering level (F(4,884) = 52.3, p < 0.001). Post-hoc tests revealed that older adults had mostly less clustered fast spindles compared to young-middle aged participants, that is more isolated (p < 0.001) or short clusters of 2 fast spindles (p < 0.001) but fewer long clusters of 4 (p < 0.05) or of more than 5 spindles (p < 0.001). To ensure that this result was not due to the unbalanced sex-ratio of our groups, we replicated our analyses using a subset of the older participants sex-balanced with the young-middle aged participants and obtained similar results to those with the entire cohort.

As sleep fragmentation increases with age, mediation analyses were performed to assess whether the negative association between age and the proportion of clustered fast spindles was mediated by NREM sleep fragmentation (number of micro-arousals per hour of NREM sleep). This relationship was not mediated by NREM sleep fragmentation, age had only a direct effect on the proportion of clustered fast spindles (Figure 6, model 1). Besides, the non-linear association between the proportion of clustered fast spindles and age remained significant after adding NREM sleep fragmentation to the covariates (p < 0.001). Linear and non-linear analyses were also performed with the mean cluster size. A similar non-linear association between age and the mean cluster size was found (p < 0.001). However, the relationship between age and the mean cluster size was fully mediated by fast spindle density (Figure 6, model 2), the proportion of clustered fast spindles (Figure 6, model 3) and partially mediated by NREM sleep fragmentation (Figure 6, model 4). Direct and indirect effects of these models are reported in Table 2.

Dynamics of fast spindle clustering across the night

We examined the dynamics of fast spindle clustering across the night. We first compared the proportion of clustered fast spindles in the first and last half of the night in young-middle aged and older adults (Figure 7A). We found a significant effect of age group (F(1,173) = 41.1, p < 0.001) and of the half of the night (F(1,174) = 15.8, p = 0.001). Moreover, we found a significant age group x half of the night interaction (F(1,174) = 21.9, p < 0.001), such that the proportion of clustered fast spindles increased in the last half of the night compared to the first one in young-middle aged adults, while it remained constant in older adults. Similar results were found when considering the different sleep cycles (Figure 7B), with significant main effects of age group (F(1,172) = 33.6, p < 0.001) and of sleep cycle number (F(3,501) = 12.2, p < 0.001), and a significant age group x sleep cycle number interaction (F(3,501) = 12.7, p < 0.001).

We also analyzed the effect of transitions from NREM sleep to REM in both groups (Figure 7C). We compared fast spindle clustering in the last five minutes of N2-N3 before each transition to REM sleep (pre-REM periods) to the rest of N2-N3 (non pre-REM periods). We found no significant effect of the pre-REM period (F(1,171) = 0.11, p = 0.74) and no significant age group x pre-REM period interaction (F(1,171) = 0.04, p = 0.84).

Association between size of fast spindle clusters and memory consolidation

We investigated the link between fast spindle clustering and the overnight change in memory performance. Memory performance is summarised in Table 3. We focused our analyses on the mean cluster size and the three parameters that mediate the effects of age on the mean cluster size (fast spindle density, proportion of clustered fast spindles and NREM sleep fragmentation). Overnight change in memory performance was not associated with fast spindle density (p = 0.24), proportion of clustered fast spindles (p = 0.13) or NREM sleep fragmentation (p = 0.84). However, better overnight consolidation was associated with a higher number of fast spindles per cluster (β = 0.29, p = 0.036; Figure 8). Importantly, this correlation remained significant after controlling for age and sex. To ensure the robustness of the results, we performed sensitivity analyses with different minimal number of fast spindles to define spindle clusters. The association remained significant for all the size of spindle clusters tested (Table 4). Of note, when considering the first and last half of the night, the association was only significant for the last half of the night (β = 0.33, p = 0.017).

Association between size of fast spindle clusters and NREM sleep stability

As sleep spindles are also an index of sleep stability, we assessed the link between fast spindle clustering and NREM sleep fragmentation, estimated by the number of micro-arousals per hour of NREM sleep. Following the procedure used for the memory analysis, we focused our analyses on fast spindle density, proportion of clustered fast spindles and the mean cluster size. NREM sleep fragmentation was not associated with fast spindle density (p = 0.21) or the proportion of clustered fast spindles (p = 0.36) after controlling for age and sex. However, we found that greater NREM sleep fragmentation was significantly associated with fewer fast spindles per cluster (β = -0.16, p = 0.033; Figure 9). Importantly, this result remained significant after controlling for age and sex and was independent of the number of spindles considered to define the clusters (Table 4).

Besides, we also tested the association between subjective sleep quality variables (PSQI, ISI and subjective sleep quality and depth during the polysomnography night) and fast spindle clustering parameters (proportion of clustered fast spindles and mean cluster size). We found no association between subjective reports of sleep quality and fast spindle clustering (all p-values > 0.05).

Discussion

Recent findings in rodents and young adults have brought to light a fluctuation of the fast spindle band power at an infraslow scale of ~0.02 Hz during NREM sleep, due to periodic alternation between high sigma power periods (dense in spindles) and low sigma power periods (with scarce spindles). In the present study, we replicated these findings in young-middle aged adults and expanded them to cognitively normal older adults. We also provided the first evidence of a nonlinear decrease of the proportion of clustered fast spindles with age. Our data suggest that this proportion remains stable from 20 to approximately 50 years, before dropping at more advanced ages. Importantly, this effect of age on the proportion of clustered fast spindles was not mediated by NREM sleep fragmentation. Interestingly, young-middle aged adults exhibited an increase of the proportion of clustered fast spindles across the night, but this temporal dynamics was not present in older adults. Besides, fast spindle characteristics were modulated by their clustering level, such that isolated fast spindles exhibited the lowest duration and amplitude while those organized in clusters of at least 5 fast spindles had the highest duration and amplitude. This modulation of fast spindle duration appeared to be slightly attenuated in older adults. Finally, we found that the mean number of fast spindles within a cluster was positively associated with overnight change in memory performance and negatively associated with NREM sleep fragmentation.

Fast spindle clusters, windows for stable sleep and efficient memory consolidation

We found a positive association between the mean cluster size and the overnight change in visuospatial memory performance, while fast spindle density and the proportion of clustered fast spindles were not significantly correlated with memory performance. This result suggests that spindle quantity and clustering (i.e., their temporal organization) may together constitute key factors for memory consolidation. According to the active system consolidation view [START_REF] Buzsáki | The Hippocampo-Neocortical Dialogue[END_REF], reactivations of recent, labile memory traces during hippocampal ripples, coordinated with sleep spindles, play a key role in sleep memory consolidation [1]. Indeed, ripples coincide with memory trace reactivations and allow the reorganization of brain regions subserving memory retrieval, with a greater involvement of neocortical areas over time [1]. Besides, hippocampo-neocortical functional connectivity increases during sleep spindles in humans [START_REF] Andrade | Sleep Spindles and Hippocampal Functional Connectivity in Human NREM Sleep[END_REF] and some cortical regions activated during declarative learning are reactivated during spindles, especially during fast spindles [START_REF] Jegou | Cortical reactivations during sleep spindles following declarative learning[END_REF]. Sleep spindles are thought to promote synaptic plasticity [START_REF] Fernandez | Sleep Spindles: Mechanisms and Functions[END_REF], potentially through changes in calcium activity [START_REF] Watson | Cognitive and Physiologic Impacts of the Infraslow Oscillation[END_REF]. Interestingly, it has been shown that calcium activity in dendrites [START_REF] Seibt | Cortical dendritic activity correlates with spindle-rich oscillations during sleep in rodents[END_REF] and the occurrence of hippocampal ripples [START_REF] Lecci | Coordinated infraslow neural and cardiac oscillations mark fragility and offline periods in mammalian sleep[END_REF] also fluctuate during sleep in rodents, all these events occurring in synchrony with spindle band power variations. Moreover, according to the sequential hypothesis, the succession of NREM and REM sleep would be essential for memory consolidation ( [START_REF] Giuditta | The sequential hypothesis of the function of sleep[END_REF], see [START_REF] Giuditta | Sleep memory processing: the sequential hypothesis[END_REF] for review). As the cycling organization of sleep stages is considered to optimize information and memory processing [START_REF] Watson | Sleep, Memory & Brain Rhythms[END_REF][START_REF] Navarro-Lobato | The up and down of sleep: From molecules to electrophysiology[END_REF], repetitive and synchronized fluctuations of spindles-ripples-calcium activity may structure and optimize neuronal plasticity and memory consolidation. In a consistent manner, it has been shown that the effect of NREM sleep disruptions on memory consolidation depends on the periodicity of the disruptions. Using optogenetics to activate arousal-related nuclei, Rolls et al. [START_REF] Rolls | Optogenetic disruption of sleep continuity impairs memory consolidation[END_REF] were able to fragment mice sleep every 60s, 120s or 240s without affecting its overall quantity and quality. Only disruptions every 60s (i.e., approximately at the infraslow time scale) appear to reduce sleep benefit on memory consolidation [START_REF] Rolls | Optogenetic disruption of sleep continuity impairs memory consolidation[END_REF]. Such disruptions would systematically interrupt periods with high spindle power, impairing memory consolidation, while sleep disruptions at longer intervals would still leave some high spindle power periods undisturbed. In this perspective, the correlation observed between mean spindle cluster size and the overnight change in memory performance suggests that the efficiency of memory consolidation requires sufficiently spindle-dense uninterrupted periods. By periodically offering ideal neural conditions for synaptic plasticity, the organization of sleep spindles into clusters would be a major component of the memory consolidation process.

Modulation of fast spindle characteristics contributes to the 0.02-Hz infraslow oscillation We also found that the clustering of fast spindles (inter-spindle parameter) is associated with fine modulations of intra-spindle characteristics (amplitude, duration and frequency). The greater the temporary spindle density (i.e., high clustering level), the higher the amplitude and duration of each fast spindles within this cluster. Similar results were reported in a recent study conducted in a small sample of 10 young adults [START_REF] Solano | Visuomotor Adaptation Modulates the Clustering of Sleep Spindles Into Trains[END_REF]. Despite a slight attenuation of fast spindle duration in older adults, this modulation was present in both young-middle aged and older adults in our study and adds a new degree of complexity to the model proposed by Lecci et al. [START_REF] Lecci | Coordinated infraslow neural and cardiac oscillations mark fragility and offline periods in mammalian sleep[END_REF]. First, NREM sleep periods with high fast spindle band power would constitute a local increase of fast spindle density (inter-spindle modulation). Second, the clustered fast spindles in these periods would have a greater amplitude and longer duration (intra-spindle modulation). These two levels (inter and intra-spindle parameters) may both participate to a clear distinction between environment monitoring and off-line processing periods that would alternate during NREM sleep.

Fast spindle declustering in ageing

Our results showed a decrease in the proportion of clustered fast spindles with age. As sleep fragmentation increases with age, it could be argued that more fragmented sleep would necessarily lead to reduced proportion of clustered spindles in older adults. However, mediation analyses revealed that age had a direct effect on the proportion of clustered fast spindles: NREM sleep fragmentation did not mediate the relationship between these two variables (model 1). Spindle cluster size integrates several aspects as it depends on spindle density (more spindles during the night favor longer spindle clusters), proportion of clustered spindles (a reduced proportion of isolated spindles favors longer clusters at a fixed spindle density) and NREM sleep fragmentation (microarousals could interrupt and shorten spindle clusters). Mediation analyses revealed that these 3 parameters mediated the effects of age on mean cluster size (models 2 to 4). Fast spindle clusters become shorter with age because older adults have less fast spindles, their spindles are more often isolated and they have more micro-arousals that can potentially interrupt the ongoing spindle activity. This age-related reduction of fast spindle cluster size could shorten the windows allowing efficient memory consolidation in older adults. However, it may be less relevant to explain the decrease in subjective sleep quality during ageing as no association was found with sleep questionnaires.

Besides, while the proportion of clustered fast spindles was high for almost all young-middle aged adults, substantial inter-individual variability in older adults was observed. This suggests that brain ageing may affect the clustering of fast spindles with a different magnitude for each participant. This result also raises the question of the neural underpinnings of fast spindle declustering. Fast sleep spindles are known to be generated by the thalamic reticular nucleus (TRN) (see [START_REF] Fernandez | Sleep Spindles: Mechanisms and Functions[END_REF] for review).

Recent data suggest that their clustering may be orchestrated by the locus coeruleus (LC) [START_REF] Osorio-Forero | Noradrenergic circuit control of non-REM sleep substates[END_REF]. The LC is a small nucleus located in the brainstem and a key structure of the noradrenergic system (see [START_REF] Van Egroo | Importance of the locus coeruleusnorepinephrine system in sleep-wake regulation: Implications for aging and Alzheimer's disease[END_REF] for review). Osorio-Forero et al. [START_REF] Osorio-Forero | Noradrenergic circuit control of non-REM sleep substates[END_REF] found that thalamic norepinephrine (NE) level during NREM sleep in mice fluctuates in an anticorrelated manner with spindle clustering, at a periodicity of about 50 s (i.e., at a 0.02-Hz infraslow scale). Using an optogenetic modulation of LC activity, they could inhibit or favor spindle clustering and causally demonstrated a role of noradrenergic thalamic modulation by LC in spindle clustering. Furthermore, it has been shown that micro-arousals also follow NE oscillations, and are more frequent during the peaks of LC activity [START_REF] Kjaerby | Memory-enhancing properties of sleep depend on the oscillatory amplitude of norepinephrine[END_REF]. Then, LC periodic activity appears to be crucial for shaping sleep micro-architecture, with spindle-enriched sleep periods when LC is silent and spindle-scarce sleep periods more prone to micro-arousals when LC releases NE.

Interestingly, MRI studies in humans have shown that LC integrity decreases in ageing [START_REF] Betts | In vivo MRI assessment of the human locus coeruleus along its rostrocaudal extent in young and older adults[END_REF][START_REF] Liu | In vivo visualization of age-related differences in the locus coeruleus[END_REF].Lower LC integrity has been associated with a higher number of self-reported nocturnal awakenings in cognitively unimpaired older adults [START_REF] Van Egroo | Associations between locus coeruleus integrity and nocturnal awakenings in the context of Alzheimer's disease plasma biomarkers: a 7T MRI study[END_REF]. Therefore, age-related atrophy of the LC may explain the spindle declustering observed in older adults and result in greater sleep fragmentation and poorer memory consolidation, but this hypothesis requires further investigation.

It is noteworthy that LC alterations (neuronal loss, neurofibrillary tangles) (see [START_REF] Satoh | Roles of tau pathology in the locus coeruleus (LC) in age-associated pathophysiology and Alzheimer's disease pathogenesis: Potential strategies to protect the LC against aging[END_REF] for review) and spindle changes (density, amplitude and duration reduction) [START_REF] Gorgoni | Parietal Fast Sleep Spindle Density Decrease in Alzheimer's Disease and Amnesic Mild Cognitive Impairment[END_REF][START_REF] Rauchs | Is there a link between sleep changes and memory in Alzheimer's disease?[END_REF] have also been described in some neurodegenerative pathologies such as Alzheimer's disease. Further research focusing on spindle dynamics is needed to better characterize the specific spindle alterations in these disorders and understand their impact on memory.

Dynamics of fast spindle clustering across the night

Previous studies have reported an increase in spindle activity throughout sleep cycles which appears to be attenuated with age [START_REF] Purcell | Characterizing sleep spindles in 11,630 individuals from the National Sleep Research Resource[END_REF][START_REF] Guazzelli | Sleep spindles in normal elderly: comparison with young adult patterns and relation to nocturnal awakening, cognitive function and brain atrophy[END_REF][START_REF] Landolt | Effect of age on the sleep EEG: slow-wave activity and spindle frequency activity in young and middle-aged men[END_REF][START_REF] Carrier | The effects of age and gender on sleep EEG power spectral density in the middle years of life (ages 20-60 years old)[END_REF]. More specifically, Purcell et al. [START_REF] Purcell | Characterizing sleep spindles in 11,630 individuals from the National Sleep Research Resource[END_REF] found, in a large cohort of 11,630 individuals, that fast spindle density increases throughout the night in adults under 40 years old while it remains constant in adults above 40 years. We provide evidence that fast spindle clustering follows similar dynamics across the night. The proportion of clustered fast spindles increases across the night in young-middle aged adults but remains quite stable in older adults.

Interestingly, the link between memory consolidation and fast spindle cluster size was driven by clusters occurring in the last half of the night. Then, the increase of fast spindle clustering across the night may be relevant for memory consolidation but is impaired with age.

Besides, previous studies had also reported an increase in spindle density in the last minutes of NREM sleep before the transitions to REM sleep in both animals [START_REF] Vyazovskiy | The dynamics of spindles and EEG slow-wave activity in NREM sleep in mice[END_REF][START_REF] Bandarabadi | A role for spindles in the onset of rapid eye movement sleep[END_REF] and humans [START_REF] Purcell | Characterizing sleep spindles in 11,630 individuals from the National Sleep Research Resource[END_REF]. More precisely, fast spindle density appears to increase in the last five minutes before the NREM-REM transition in humans [START_REF] Purcell | Characterizing sleep spindles in 11,630 individuals from the National Sleep Research Resource[END_REF]. Our results suggest that fast spindle clustering may not be affected by these transitions as the proportion of clustered fast spindles remained stable in the last five minutes before transitions to REM sleep in both age groups.

Strengths and limitations

To the best of our knowledge, this study is the first to investigate infraslow oscillation in fast spindle band and fast spindle clustering in older adults. One of the strengths of this work is the wide age range of participants, allowing to assess age-related changes in spindle clustering during most of the adult lifespan, i.e. from 20 to more than 80 years old. Another asset of the study is the homogeneity of the manual artifact rejection which was performed by a single sleep specialist for all participants.

However, some limitations must be acknowledged. First, as we used polysomnography data collected in different cohorts, acquisition parameters were not strictly the same for all participants (acquisition device, presence or not of an adaptation night and of sleep questionnaires, number of EEG electrodes, sampling rate). Although all the centro-parietal region was well-covered in the memory consolidation analysis (C3, C4, CZ, P3, P4, PZ), we had to restrict the analyses of age-related changes to C3 and C4 channels. Besides, we had to limit our analyses to fast spindles as almost half of the young-middle aged adults did not have frontal EEG channels and slow spindle power peak was not clearly visible in the remaining participants. The sample size of the young-middle aged group was also moderate. Further studies are needed to replicate our findings and to investigate age-related changes in slow spindle clustering. Moreover, the lack of participants between 52 and 65 years old limits investigations in the first decade following the start of the decrease in fast spindle clustering.

However, the large size of the group of older adults allowed us to confirm the negative association between age and the proportion of clustered fast spindle in the 65-83 years old range. Finally, sex ratio was different between the groups of young-middle aged and older adults. Given the evidence for sex differences in spindle characteristics (see [START_REF] Fernandez | Sleep Spindles: Mechanisms and Functions[END_REF] for review) and although we have statistically addressed this issue, we cannot rule out residual influences on group differences arising from theses biases. However, we replicated our results about age-related changes in fast spindle clustering in sexbalanced subgroups. Besides, given that women tend to show higher spindle density and EEG power, and that the proportion of women was higher in the older adults group, sex bias seems an unlikely explanation for the effects of age on spindle characteristics and clustering reported here.

Conclusion

Overall, our results support the idea that fast spindle organization at an infraslow scale may be a mechanism allowing to maintain a balance between environment monitoring and off-line processing states during NREM sleep. This balance appears to be impaired in older adults, although the switching state periodicity is preserved. Age-related reduction of fast spindle clustering was associated with NREM sleep fragmentation and may affect sleep-dependent memory consolidation.

Further studies are needed to better understand the dynamic aspects of sleep stages, their importance for sleep functions and potential dysregulation in ageing and in various pathological conditions such as neurodegenerative diseases.

  ParticipantsThirty-two young-middle aged adults (age range:[20-52 years], mean ± SD: 34.5 ± 10.9 years, 10 women) and 147 older adults cognitively unimpaired ([65-83 years], 69.3 ± 4.1 years, 89 women) were included. To do so, the data of three cohorts were gathered. Data of 134 older adults were acquired during the baseline visit of the Age-Well randomized clinical trial (RCT) of the Medit-Ageing European project sponsored by the French National Institute of Health and Medical Research ("Institut National de la Santé et de la Recherche Médicale", Inserm)[START_REF] Poisnel | The Age-Well randomized controlled trial of the Medit-Ageing European project: Effect of meditation or foreign language training on brain and mental health in older adults[END_REF]. All participants gave their written informed consent prior to the examinations, and the Age-Well RCT was approved by the ethics committee (CPP Nord-Ouest III; trial registration number: EudraCT: 2016-002441-36; IDRCB: 2016-A01767-44; ClinicalTrials.gov Identifier: NCT02977819). Eighteen participants of the young-middle aged group were included as healthy controls in a study investigating the effects of alcohol use disorder on sleep, cognitive and brain alterations (CPP Nord Ouest III, no. IDRCB: 2011-A00495-

Table 3 . Learning and recall performance at the memory task. Older adults (n = 77)

 3 Data are presented as mean ± SD. The task was performed by a subgroup of 77 older adults (see Material and methods section). The overnight change in performance was calculated as follows: 100 x (recall score -learning score) / learning score.

	Number of subjects achieving the learning criterion	66
	Number of trials needed to reach the learning criterion	7.6 ± 2.8
	Learning score (% correct answers)	71.8 ± 7.3
	Recall score (% correct answers)	52.5 ± 13.6
	Overnight change in performance (%)	-26.3 ± 20.7

Acknowledgements

We are grateful to Dr Alison Mary, Sebastien Polvent, Nicolas Oulhaj and Franck Doidy for their help with data acquisition and analysis. We acknowledge all the participants and the members of the Medit-Ageing Research Group (Alexandre Bejanin 1 , Léa Chauveau 1 , Anne Chocat 1 , Fabienne Collette 2,3,4 , Sophie Dautricourt 1 , Robin De Flores 1 , Marion Delarue 1 , Harriet Demnitz-King 5 , Hélène Espérou 6 , Séverine Fauvel 1 , Francesca Felisatti 1 , Eglantine Ferrand Devouge 1,7,8 , Eric Frison 9,10 , Julie Gonneaud 1 , Sacha Haudry 1 , Oriane Hébert 1 , Olga Klimecki 11,12 , Elizabeth Kuhn 1 , Brigitte Landeau 1 , Valérie Lefranc 1 , Natalie Marchant 5 , Florence Mezenge 1 , Cassandre Palix 1 , Anne Quillard 1 , Florence Requier 2 , Eric Salmon 13 , Edelweiss Touron 1 , Anne-Laure Turpin 1 , Patrik Vuilleumier 14 , Tim Whitfield 5 , Miranka Wirth 15,16 ).

Spindle cluster sizes


Parsa Ghasemi

Reza Noruzi

Keywords: The Čāhārbāzār site, Bačun, city, garden, Sasanian period, Farāšband, Iran

As a result of field survey and remote sensing of aerial photo and satellite imagery, a large archaeological site, probably belonging to the Sasanian period, was identified in Farāšband. This site covers an area of 14.4 square kilometers, very regular and walled, implanted on virgin land. The initial survey shows that it was probably a large geometric city consists of six large almost rectangular shape sections. Based on the archaeological evidence, this site has never been completed nor filled with population and had some gardens.

Introduction

The archaeological site of Čāhārbāzār is located about 11 km east and northeast of Farāšband, 28 km from the ancient city of Gōr (Ardašīr-Xwarrah, commonly known as Firuzābād), in the Bani-Qatār plain of Bačun. The highest level  ORCID iD 0000-0003-0010-9615. parsa.ghassemi@gmail.com; Ph.D. Candidate in Archaeology.  Iranian Center for Archaeological Research. rnoruzi@yahoo.com  Ministry of Cultural Heritage, Tourism and Handicrafts. razizallah@gmail.com  Iranian Center for Archaeological Research. amiri_m27@yahoo.com  Iranian Center for Archaeological Research. of this site is in the northern part and is about 1118m a.s.l. Nārak village is located 2.7 km east of this site and Bačun village is located about 3 km north of it. The area is in the southern Zagros mountain range, which has a semi-arid climate with hot summers and cold rainy winters. The average annual rainfall in this area is 280 mm. The highest peak of the region is located in the north of Bačun with 2600m a.s.l. [Fig. 1]. Because the Farāšband region is located in the heart of Fars, many archeological sites have been identified so far, the most important of which are the structures known as čahār-ṭāq ('four arches') 1 . Thus, the plain is in the heart of the Sasanian Empire, in the region of Ardašīr-Xwarrah province where Ardašīr I (?-242 CE.), the founder of the Sasanian empire, built the city of Gōr along with a palace after he defeated the last Parthian king. It seems that the close proximity of this plain to Gōr city (about 28 km) and its more suitable climate, compared to that of surrounding plains, had been attractive to Sasanians from the beginning of the period. The site had already been marked as a castle on the topographical maps of Iran that were generated in 1955 with a scale of 1/100,000. The last decades have seen many visitors to the site, but they have reported only a few visible buildings, such as a quadrangular building which was reported as a caravanserai, and the central building (kušk). Surprisingly, they saw only a small part of this site2 , because they couldn't see the full site, and they thought it was just the area of pavilion, which will be mentioned below. These incomplete reports show that the site was completely underestimated and misunderstood until now.

The Remains of the Čāhārbāzār Site on the Bani-Qatār Plain, Bačun

Our initial ground survey of the site took place in December 2018, and then by remote sensing. Aerial photos and satellite images show that the Čāhārbāzār site is rectangular in plan with an area of 14.4 square kilometers, about 4 km long in the north-south direction, and 3.6 km wide in the east-west direction. The site was constructed on a gentle slope that allows water to reach all of its area [Figs. 2,3,4]. It is enclosed by a wall, that has four entrances, one at each of the directions. The inner part of the site is in the shape of a cross-axes, the four main streets of which, 50 meters wide, intersect in the southern one-third of the site. In addition to the main streets, there were probably two other side streets, between the northern sections (E, F; C and D) that are much less wide; evidence of this is now visible in aerial photographs as a southeast-northwest longitudinal line, which could be also interpreted as a wall. These main streets and the secondary limit formed six large rectangular sections within the enclosing wall.

All major architectural structures on the site are situated at the intersection of the four southern sections. This includes an internal fortification with a square courtyard, and the main building larger than a pavilion (kušk) cross-shaped in the plan. This main complex of the site is within a square fortification wall with dimensions of about 550 by 550 meters, its general form of fortification looks similar to the wall of the temple complex at Takht-e Soleymān, although it is four times the size of the Takht-e Soleymān temple's wall complex3 . The fortification wall has four entrances of the same width as the entrance to the main streets; based on Google Earth images, it has many (14 semi-circular and 4 two-third circular) towers on its exterior face but most of them destroyed by modern earthmoving. The outer wall of this fortification is made of cobblestone and gypsum mortar and is 2 meters thick. On one side of all entrances to this fortification are the remains of a rectangular room/structure measuring 30 by 15 meters; they were probably the forecourt or a guardroom and seems to have been symmetrical on the one side of the other four entrances of this central fortification. however, the forecourt or guard room at the eastern entrance appears to be larger (44 by 38 meters). In the four L-Shape quarters of the interior yard, the Persian garden model (čahārbāḡ or 'four gardens', a rectangular garden divided by paths or waterways into four smaller symmetrical sections) is seen symmetrically; only the southeastern one is well preserved, the rest having been destroyed by modern agricultural activity, but their remains were visible on old aerial images [Figs. 2,5,6]. In the center of this fortification, or at the intersection of the main streets, is a square, measuring 300 by 300 meters, in which the four main streets meet. In the center of this square is the main building (pavilion/kušk), which has a square plan with the interior cross-shaped, measuring 132 by 132 meters. This kušk has four equal arms or side corridors (probably barrel-vaulted corridors or ayvāns), each measuring 50 by 30 meters, and are situated symmetrically in the direction of the four main streets. Four square rooms/court (?), each measuring 50 by 50 meters (less likely vaulted), are built around the side corridors.

Apart from the main complex within the central fortification, the remains of residential structures, terraces, regular geometric plots with pools, and regular irrigation canals are visible in the other parts of the six sections along pathways [Fig. 4]. In addition to the central fortification, about 100 meters east of it, there is a rectangular piece of land enclosed by a wall (?) that measures about 250 by 100 meters, (Figs. 5 and6, n.1). On the northeastern side of the interior, the remains of a ruined building measuring 127 by 120 meters with a large courtyard can be made out [Fig. 6,n. 3]. The building has a circular pool of approximately 24 meters in diameter. According to the construction material and architectural evidence, the building is one of the first buildings in this site. In the middle of its courtyard is, a quadrangular building very looks like a residence building, measuring 25.50 by 25.50 meters. it was built in the Islamic period with materials from Sasanian-period buildings and gypsum mortar [Figs. 2,5,6]. Construction of a building in front of a pool or pond occurs at many Sasanian period sites, the nearest example to Čāhārbāzār being is the palace of Ardašīr in near Firuzābād. Additionally, outside the outer enclosure, another irregular-rectangular enclosed (?) field (section G) is visible on a CORONA satellite imagery (taken 25 May 1970) and Google Earth 2015. Interestingly the eastern street or pathways continues until the middle of this walled (?) field (probably extending to the end of the field but destroyed by modern agricultural activities and road construction). Approximately in the center of this field, where the street disappears or is cut off by the modern road, is the remains of a rectangular building built of stone and gypsum mortar. This building was destroyed by the landowner who has cultivated its center; based on surface finds of potsherds, it dates to the late Sasanian period. If the foundation of the wall (?) around section G belongs to the Sasanian period, then it might be assumed that this building in the middle of this land was constructed at the same time [Fig. 4].

Water Resources

The Bani-Qatār plain has one of the richest aquifers thanks to its alluvial fans in the north of the plain. The Barm-e Farhād, and Bačun springs, seem to have been the most important source for the site's permanent water supply. Many open surface canals brought the water to the site from the northern side of the plain. The site is built on a fertile plain that is rich in surface and aquifer water; this is likely the reason why no qanats were dug at the site, in contrast to the surrounding plains' extensive use of the qanat system to supply the water for residents and agriculture. (The only qanat near the site has been dug in its western corner at a lower level; this directs the water to the outer lands west of the site and probably dates to Islamic times). A large number of circular pools, with an average diameter of 20 meters, has been built with cobblestone and sarooj mortar (sarooj is a local water-resistant mortar used in water-related structures such as pool, cistern, dam, etc.) in different sectors to conserve water.

The Site Function

Having described this large regularly-planned site in detail, we now must explore its purpose. Was it to accommodate a large population, either one from the region or some forced transfer of people from some captured region? Since it seems to have included several gardens, might the entire site have been a large royal or aristocratic estate with palatial buildings among trees and farmlands? Based on the available dataalbeit before future excavation and field surveyswe may consider this hypothesis:

The site was a large-scale walled city, built on an axial geometric plan. In the center of the south of the city, inside a fortification, at the intersection of the main streets, was built a large pavilion surrounded by a Persian garden. The lack of much evidence for structures and building construction material on the surface, as well as scarcity of surface evidence of material culture within the six rectangular sections may be explained if part of the planned construction did not occur, and most parts of the city were never built. After the site was abandoned, in some later periods such as in the middle Islamic period, the courtyard of the abandoned Sasanian building was used to build a quadrangular building.

An alternative hypothesis to the aborted project of construction of a city that would have been several times larger than Bīšāpūr (about 1.5 square kilometer) or the city of Gōr (about 3.14 square kilometers) is to consider that it might have had some large sections for agriculture; or less likely it has been used as a large garden with few palaces probably in the same period or the later, due to the abundance of water and fertile land.

It is worth mentioning that in some Sasanian cities, such as Bīšāpūr, Gōr, and Ayvān-e Karḵa, the interior spaces have not been completely filled with structures, which probably were empty spaces devoted to gardens. In Čāhārbāzār, the six sections are mostly empty of structures, and the dearth of potsherds and other material culture remains. The built area is only inside the central fortification (that is, the kušk). A surrounding ditch, which was an important means of protection for most cities of this period is absent: the location of the site on a plain enclosed by mountains and near the alluvial fans might strengthen the hypothesis that it was an unfinished city and had gardens designed for agriculture as well as arboriculture, used for royal entertainment such as hunting and the enjoyment of various indigenous trees.

Therefore, the site of Čāhārbāzār with this unusual size and careful geometric plan might have been intended for other purposes than only resettling a population. Section G, was probably used as a garden area, outside the main wall [Fig. 2].

According to the historian al-Ṭabarī (839-923 CE), Mehr-Narseh (the great vizier of several 5th-century Sasanian kings) established in his birthplace (Abrovān village) in the Dašt-e Bārin and Jereh -the region in which Čāhārbāzār is locatedvillages, fire temples, and three large gardens (twelve thousand palms, twelve thousand olive trees, and twelve thousand cedars)4 . This is the only historical evidence that shows that there were many large-scale agriculture fields and settlements in this region which were built by aristocrats; further information must come from archaeological surveys.

The presence of a central kušk and the axial pathways leading to it, as well as the four gardens around it, of course, recalls the only previously known Persian garden (čahārbāḡ), at Pasargadae in the Achaemenid period5 . The existence of this example indicates the continuation of the čahārbāḡ palatial garden tradition from the Achaemenid period into Islamic times6 .

Chronology

In what period was this site established? Sasanian, Post-Sasanian, or early Islamic?

Our initial field survey based on the surface pottery and construction techniques show that a Sasanian building was constructed within a large rectangular space west of the central fortification [Figs. 5 and 6,n. 3]. Although this building is not located inside the main central fortification, its presence beside the central fortification is important. As already noted, potsherds are rare on the surface of this huge site; however, those that have been found belong to the Sasanian period. The rectangular plan with regularly laid-out streets and interior geometric divisions shows that this large-scale site was probably built by the Sasanians. This type of plan was first used in the Sasanian period by Šāpur I (239-270 CE) in Bīšāpūr (around 266 CE)7 . There is however no textual or other evidence to show that here in Čāhārbāzār it was designed and executed by Šāpur I or one of his successors. Its dating to the Sasanian period at this stage thus remains conjectural.

However, there is also no reliable evidence to indicate that it was designed in the post-Sasanian or early Islamic period. The only evidence for an Islamic date is the quadrangular building, n. 2], which, due to its resemblance to other the quadrangular building in this region, can be dated between the 11th and 15th centuries.

Thus, there is not enough evidence to prove that the main site was planned during the Sasanian or early Islamic period. But certainly, if implemented in Sasanian times, this geometric plan cannot date earlier than Šāpur I. The city or garden areas, if built during the Sasanian period, must have belonged to a king or a leading noble who wanted to create a masterful rectangular city according to Roman models mixed with Persian elements, such as the Achaemenid four-garden design, near the circular city of Gōr.

Conclusion

Only with further study of this large site will we be able to understand its main function and its date of establishment. Whether it was created to resettle other populations or it was a sizable agriculture/arboriculture estate, it was a large-scale imperial project that at that time would have been an ambitious and costly undertaking. The creation of a large site, with wide streets, the construction of external and internal fortifications, required precise engineering, skilled design, and a large labor force. Thus, it is logical that this site was built by the Sasanians. Their skill in managing and implementing large urban and engineering projects helped their empire flourish.

Future study of the site should yield a detailed picture of its function, date, and site pattern. It is necessary to mention that most of our current knowledge is based on remote sensing of aerial images carried out by the first author (Parsa Ghasemi); to expand this knowledge it will be necessary to conduct systematic archaeological ground surveys and excavation.

Fig. 1 .

 1 Fig. 1. Location of Čāhārbāzār site, northeast, and east of Farāšband city, southwestern Fars, Iran. For comparison of the site with other ancient as well as new settlements, all are shown according to their actual size. Drawing by Parsa Ghasemi using ArcGIS (SRTM 90m resolution, data available from the U.S. Geological Survey)

Fig. 2 .

 2 Fig. 2. The oldest satellite image of the site in a Corona declassified archive taken 25 May 1970. Due to modern agriculture and road construction, some of the features seen in this photo no longer exist. This image shows the location of sections and streets and other important structures. Modified by Parsa Ghasemi (data available from the U.S. Geological Survey).

Fig. 3 .

 3 Fig. 3. Photographs of different areas of the site, including the foundation wall around the main streets or sections (1, 2, and 4), and the remains of the central part or the pavilion (3). Figs by Reza Noruzi and Aziz Rezaei

Fig. 4 .

 4 Fig. 4. Location of Čāhārbāzār site, on Bani-Qatār plain, southwest and west of Bačun village. Drawing by Parsa Ghasemi using ArcGIS (background Google Earth 2016)

Fig. 5 .

 5 Fig. 5. Plan of the central fortification and the remains of the main streets (on Google Earth 2015 image) which form the main square of the site and are surrounded by the remains of terraces and four gardens. In the center is the pavilion (kušk) (n. 4). The location of the oldest part of the building (no. 3), and the quadrangular building of the Islamic period (no. 2), are shown. Drawing by Parsa Ghasemi using ArcGIS.

Fig. 6 .

 6 Fig. 6. Plan of the central fortification and the remains of the main streets, which form the main square of the site and are surrounded by the remains of terraces and four gardens. In the center is the pavilion (kušk) (no. 4). The location of the oldest part of the building and the quadrangular building of the Islamic period, are indicated by (no. 2) are shown. Drawing by Parsa Ghasemi using ArcGIS.

AMIRI 2003: 235;[START_REF] Rajaei | The First season of Archaeological Survey of Farāšband County[END_REF] NIKNAMI and FAZEL 2016: 129.

[START_REF] Huff | Recherches archéologiques à Takht-i Suleiman (Iran), centre religieux royal sassanide[END_REF]

Ṭabarī 2004: 626 and 280.

[START_REF] Stronach | Čahārbāḡ[END_REF]

For more information about Islamic Garden, see GOLOMBEK 2012.

[START_REF] Ghirshman R | Bichâpour I, Fouilles de Châpour[END_REF]

Acknowledgment

I would like to thank Dr. Remy Boucharlat, Dr. Judith Lerner, Dr. Francois Villeneuve, and Dr. Alastair Northedge for their advice, helpful and critical comments, and corrections on the draft version. All errors are, of course, those of the principal author, Parsa Ghasemi.