The role of the sleep K‐complex on the conversion from mild cognitive impairment to Alzheimer's disease

The present literature points to an alteration of the human K‐complex during non‐rapid eye movement sleep in Alzheimer's disease. Nevertheless, the few findings on the K‐complex changes in mild cognitive impairment and their possible predictive role on the Alzheimer's disease conversion show mixed findings, lack of replication, and a main interest for the frontal region. The aim of the present study was to assess K‐complex measures in amnesic mild cognitive impairment subsequently converted in Alzheimer's disease over different cortical regions, comparing them with healthy controls and stable amnesic mild cognitive impairment. We assessed baseline K‐complex density, amplitude, area under the curve and overnight changes in frontal, central and parietal midline derivations of 12 amnesic mild cognitive impairment subsequently converted in Alzheimer's disease, 12 stable amnesic mild cognitive impairment and 12 healthy controls. We also assessed delta electroencephalogram power, to determine if K‐complex alterations in amnesic mild cognitive impairment occur with modification of the electroencephalogram power in the frequency range of the slow‐wave activity. We found a reduced parietal K‐complex density in amnesic mild cognitive impairment subsequently converted in Alzheimer's disease compared with stable amnesic mild cognitive impairment and healthy controls, without changes in K‐complex morphology and overnight modulation. Both amnesic mild cognitive impairment groups showed decreased slow‐wave sleep percentage compared with healthy controls. No differences between groups were observed in slow‐wave activity power. Our findings suggest that K‐complex alterations in mild cognitive impairment may be observed earlier in parietal regions, likely mirroring the topographical progression of Alzheimer's disease‐related brain pathology, and express a frontal predominance only in a full‐blown phase of Alzheimer's disease. Consistently with previous results, such K‐complex modification occurs in the absence of significant electroencephalogram power changes in the slow oscillations range.


| INTRODUCTION
The present literature points to a mechanistic bidirectional relationship between disruption of non-rapid eye movement (NREM) sleep electroencephalographic (EEG) hallmarks and Alzheimer's disease (AD) pathophysiology (Mander, 2020).In this context, the interest in the role of NREM sleep slow-wave activity (SWA) is growing.
Altered NREM sleep SWA seems associated with cognitive functioning and pathological markers of AD in healthy aging (Mander et al., 2015;Varga et al., 2016).Moreover, the speed of beta-amyloid (Aβ) aggregation/deposition over time, one of the main AD pathological markers, can be selectively predicted by the amount of NREM sleep SWA < 1 Hz and sleep efficiency (Winer et al., 2020).These findings suggest that disrupted SWA may have a role in the development of AD pathology, and point to the importance of its assessment in the transitional stage between healthy aging and AD, represented by mild cognitive impairment (MCI), particularly in its amnesic subtype (aMCI).Nevertheless, the assessment of SWA in aMCI and AD showed mixed findings (D'Atri, Scarpelli et al., 2021;De Gennaro et al., 2017;Lucey et al., 2019;Westerberg et al., 2012), suggesting that AD pathology may have different effects on NREM sleep slow waves according to the specific SWA frequency considered and the disease stage (Mander, 2020).It has been proposed that the assessment of the overall SWA power may not be sensitive enough to discriminate between distinct effects of the AD pathology on NREM slow waves, and the focus should be moved to specific phenomena in the SWA frequency range like K-complexes (KCs), slow oscillations (≤ 1 Hz) and high-frequency SWA (D'Atri, Scarpelli et al., 2021).
The KC can be defined as an isolated downstate during NREM sleep (Cash et al., 2009), with a frontal predominance, duration > 0.5 s and frequency < 1 Hz (Halász, 2005).Present hypotheses on its functional meaning suggest both arousal-related mechanisms and sleepprotecting processes (Halász, 2005).Recently, we described a striking KC density decrease (more than 40% in the frontal derivation) during stage 2 NREM in AD compared with healthy controls (HC), associated with the level of cognitive decline, which allowed a correct classification of 80% (De Gennaro et al., 2017).Other studies confirmed the KC density reduction in AD (Liu, Pan, Tang et al., 2020;Reda et al., 2017).On the other hand, results in MCI are less clear; this uncertainty might be largely explained by the fact that the MCI group is heterogeneous, half of it including patients in a prodromalto-dementia stage, the remaining half represented by subjects who will never become demented on follow-up.In the first study from our group, the absence of difference in frontal KC density between aMCI and HC was found (Reda et al., 2017), suggesting that the KC alterations are not observable in the early stages of the AD pathology.
More recently, Liu and co-workers (2020) replicated this finding on KC density, but they observed that the frontal KC amplitude was progressively lower from HC to aMCI, to AD.The same research group performed a prospective cohort study to describe the changing trend in KC features during the progression of the disease, comparing KC measures between HCs, stable aMCI and progressive aMCI (i.e.converted in AD after 2 years from the baseline evaluation), actually those being in a prodromal-to-dementia stage already at baseline (Liu, Pan, Lei et al., 2020).The authors found a reduction of KC amplitude in the earliest evaluations in aMCI compared with HC, which can distinguish progressive and stable aMCI in follow-up evaluations at 12 and 24 months.On the other hand, they found no difference in KC density between the three groups at baseline and 6 months after the baseline, while HC had greater KC density compared with aMCI groups at 12 and 24 months follow-up evaluations, and stable aMCI exhibited higher KC density compared with progressive aMCI.Finally, in another pathological model represented by isolated rapid eye movement (REM) sleep behaviour disorder, a prodromal condition for alpha-synucleinopathies characterized by mounting evidence of NREM sleep EEG alterations (Gorgoni & Galbiati, 2022), a frontal KC density reduction in patients with MCI compared with those without MCI has been observed, without differences in KC amplitude (Galbiati et al., 2021).
Overall, only a few studies assessed KCs in individuals with MCI, and mainly focused on frontal areas, and replication is substantially lacking.A clear understanding of KC alterations in MCI, their specificity for the AD pathology, and their ability to predict the conversion in AD (orbetterto intercept those in a prodromal-to-AD stage early) is still missing.It is worth noting that the progression of several functional and structural brain alterations in MCI exhibits an early involvement of posterior regions.The posteromedial cortex and the medial temporal lobe appear particularly vulnerable to AD-related pathological changes (Grothe & Teipel, 2016;La Joie et al., 2012).Depth electrode recordings suggest that KCs can be generated throughout the cortex and travel in different directions (Mak-McCully et al., 2015).A recent finding also points to a genetic influence on KC features mainly expressed in central and parietal regions (Gorgoni et al., 2019).In this view, it could be proposed that a hypothetical early alteration of the KC in individuals with MCI, able to predict the conversion in AD, does not necessarily involve the frontal regions (i.e. it could be expressed earlier in other cortical areas and develop a frontal predominance only in full-blown AD).Nevertheless, the present studies on KCs in aMCI are mainly focused on the frontal regions.Starting from these premises, the aim of the present study was to assess baseline spontaneous KC measures in aMCI subsequently converted in AD over frontal, central and parietal regions, comparing them with healthy elderly subjects and stable aMCI.Together with classical measures of KC density and peak-to-peak amplitude, we also assessed for the first time in patients with MCI the area under the curve (AUC), as this measure previously exhibited a strong genetic influence (Gorgoni et al., 2019) and may represent an accurate measure of KC morphology.Also, because SWA exhibits a homeostatic decrease during the night of sleep (Achermann & Borbély, 2017) and the KC mimics this overnight SWA reduction (Curcio et al., 2003;De Gennaro et al., 2000), we compared for the first time in aMCI the KC measures during early and late sleep.
Finally, because we previously found that KC density discriminates patients with AD from HC in the absence of differences in SWA (De Gennaro et al., 2017), we have assessed the delta EEG power with the hypothesis that potential MCI-related changes of KC measures can occur without relevant SWA modifications during Stage 2 NREM sleep.

| Subjects
This is a retrospective analysis performed on data previously collected.From a pool of 50 MCI baseline sleep EEG recordings, we selected for the present study 35 patients for which we had follow-up information.Eight individuals were excluded from this group because they were non-amnesic MCI.Finally, three individuals (< 65 years old) were excluded in order to have two aMCI groups (i.e.stable versus converted in AD) with an equal number of subjects and comparable age.Therefore, the analyses were conducted on 12 individuals with aMCI that converted to AD at a follow-up neuropsychological investigation (aMCI-CO; 7 F, mean age ± SD = 74.58± 4.81 years), and an equal number of aMCI that remained stable at the follow-up evaluation (aMCI-ST; n = 12, 5 F, mean age ± SD = 71.16± 5.44 years).
Individuals met criteria for aMCI single (7 aMCI-ST; 5 aMCI-CO) or multiple (5 aMCI-ST; 7 aMCI-CO) domains according to the Winblad et al. (2004) criteria.Specifically, cut-off scores for each neuropsychological test were set at 1.67 SD below the mean of distribution on normal population (Carlesimo et al., 1996).Twelve healthy elderly individuals (7 F, mean age ± SD = 73.8± 5.94 years) with similar age and gender distribution were selected from our database as the HC group.Table 1 reports  All participants underwent a cognitive screening using the Mini Mental State Examination (MMSE; Folstein et al., 1975).To exclude major psychiatric illness, the Hamilton Depression Rating Scale (HDRS; Hamilton, 1967) and the State Trait Anxiety Index (STAI-Y1 and STAI-Y2; Spielberg, 1989) were administered.
The neuropsychological investigation for aMCI included a structured clinical evaluation, brain neuroimaging (magnetic resonance imaging or computed tomography) and a neuropsychological test battery assessing specific cognitive domains (i.e.memory, attention, executive function, visuo-construction abilities and language).Specifically, memory assessment included Rey's Auditory Verbal Learning Test (RAVLT; Carlesimo et al., 1996), involving immediate recall (RAVLTir), delayed recall (RAVLTdr), delayed recognition (RAVLTrec), delayed recall of the Rey figures (Rey, 1968), delayed recall of a threeword list (Chandler et al., 2004), and delayed recall of a story (Spinnler & Tognoni, 1987).The functional status was assessed by the Activities of Daily Living/Instrumental Activities of Daily Living (ADL/IADL) questionnaire (Lawton & Brodie, 1969).At follow-up, patients were also assessed according to the Clinical Dementia Rating scale (CDR).Individuals with aMCI were enrolled according to guidelines and clinical standards (Petersen et al., 1997;Portet et al., 2006;Zaudig, 1992).Patients were considered converted if they showed an impairment of IADL/ADL below 70%, and they perform CDR 1 and they met criteria for AD (McKhan et al., 2011).
All participants gave their written informed consent.The study was approved by the local Institutional Ethics Committee and was conducted in accordance with the Declaration of Helsinki.

| Study design
In correspondence with the baseline evaluation, participants

| Sleep measures
Because we performed a retrospective analysis of previously collected PSG data already scored using the Rechtschaffen and Kales (1968) standard criteria, and considering that our interest was focused on the KCs and not sleep macrostructure, we decided to maintain this sleep scoring criteria and not adopt the current American Academy of Sleep Medicine (AASM) criteria (Iber et al., 2007).Therefore, sleep stages of the PSG recording were visually scored in 20-s epochs (Rechtschaffen & Kales, 1968), excluding ocular and muscle artefacts.
The following dependent variables were considered:

| Detection and analysis of KCs
Spontaneous KCs during NREM stage 2 in the three groups were visually identified on Fz, Cz and Pz cortical derivations by a blind scorer.We applied the following criteria to score a KC: a nonstationary event with (a) a marked and well-delineated initial negative sharp wave, immediately followed by a positive component; (b) a maximum amplitude at frontocentral derivations; (c) a minimum duration of 0.5 s and a maximum duration of 3 s.Following Crowley and coworkers (2004), no amplitude criterion was applied in the present study due to the age-related KC amplitude decrease (Halász, 2005).If multiple KCs appeared in sequence, only the first one was considered.
For each midline derivation, KC density was computed as the number of KCs divided by NREM stage 2 sleep minutes.For each KC, the peak-to-peak amplitude was calculated as the difference between the large negative peak of the KC and the following (300-400 ms later) prominent positive peak.The mean of the data points around the maximum and minimum values (± 25 ms) was considered as the negative and positive peaks, respectively, to reduce the possible influence of noise in the peak amplitude measures (Gorgoni et al., 2019).
Then, for each participant and separately for each midline derivation, the mean amplitude of the KCs was considered as the individual average peak-to-peak amplitude for subsequent analyses.
To obtain an accurate KC morphological measure, the individual KCs were averaged using the maximum negative peak as point for alignment, considering an interval from 550 ms before to 950 ms after such negative peak.In this way, an individual KC average waveform with a duration of 1500 ms and a negative peak at 550 ms was obtained.The AUC of the KC average waveform (absolute values) was calculated by the trapezoidal rule (TRAPZ function in MATlab) in the given time range (the entire 1500 ms period considered, from 550 ms before to 950 ms after the negative peak).This method approximates the AUC circumscribing the number of trapezoids under a curve.Then, the areas of the trapezoids are summed to obtain the total AUC. Figure 1

| Slow-wave activity
We used a Fast Fourier Transform routine (4 s periodograms) to calcu- for the 1 and 2 half of the sleep period.

| Statistical analysis
Gender distribution was assessed using the Chi-square test.We assessed the KC modification during the night in the three groups performing a 3 Â 2 mixed design ANOVA having Group (HC versus MCI-ST versus MCI-CO) as between-subject factor and Phase (1 half versus 2 half of the night) as within-subject factor on log-transformed KC measures.Partial eta-squared was used to assess the effect size, and post-hoc Tukey tests followed significant interactions.To control for homeostatic modifications during the night in SWA, the same 3 Â 2 ANOVA has been conducted on the delta frequency bins power topography, followed by post hoc comparisons (t-tests).
The alpha level was always set at 0.05, except for the analyses performed on the topographical EEG power: in this case, the alpha level was corrected applying the false discovery rate (FDR; Benjamini & Hochberg, 1995).All statistical analyses were performed using Jamovi v. 2.3.21.0 and Matlab R2011b.The results of the statistical comparisons (one-way ANOVAs and Kruskal-Wallis test) are also reported.The alpha level was set at 0.05.The asterisk indexes a significant difference.The last column on the right reports the effect size of significant findings.ANOVA was used for the between-groups comparison.On a descriptive level, all groups show a predominant fronto-central distribution of delta power, more pronounced in the slowest delta bins.Welch's

| Slow-wave activity
ANOVAs showed the absence of significant differences between groups ( p > 0.06), albeit several frontal derivations exhibit a pattern of progressive power increase in aMCI-ST and aMCI-CO, approaching the statistical significance in the 3-4-Hz bins.
Descriptive values (Figure S1) and results (Figure S2) of the 3 Â 2 mixed design ANOVAs Group (HC versus MCI-ST versus MCI-CO) Â Phase (1 half versus 2 half of the night) performed to assess differences in the homeostatic regulation of the SWA power are reported in the Supporting Information.We found a significant (critic p after FDR correction = 0.0006) effect of Phase in all cortical derivations at each delta frequency bin, pointing to a generalized decrease of delta activity during the second half of the night compared with the first one.The effects of Group and Interaction were not significant.

| DISCUSSION
In the present study, we observed for the first time a selective reduction of parietal KC density in aMCI-CO compared with HC and aMCI-ST during a baseline night of sleep without morphological alterations or changes in overnight homeostatic regulation, suggesting that a posterior KC decrease may be observable at an early stage of the AD neurodegenerative process.Moreover, we found no MCI-related changes in the delta EEG power during Stage 2 NREM sleep, confirming our previous observation that KC alterations in AD pathology may occur in the absence of SWA power changes (De Gennaro et al., 2017), and extending this observation to individuals with aMCI.
Previous cross-sectional comparisons suggested a reduction of KC density only in a full-blown phase of AD, without differences between HC and aMCI (Liu, Pan, Tang et al., 2020;Reda et al., 2017).
However, these studies were mainly focused on the frontal regions.
Moreover, MCI represents a heterogeneous condition that only in about 50% to 60% of cases will convert in AD or (better) can be considered in a prodromal-to-AD condition already at baseline, while the others will remain in the MCI condition for all their life or even return to a normal cognitive state.Therefore, the distinction between aMCI-ST and aMCI-CO may be crucial to detect specific AD-related alterations of sleep electrophysiology.Only Liu and co-workers ( 2020  Raw descriptive values are also reported.F-values and p-values are reported for each main factor and interaction.Asterisks index significant differences.The effect size (partial eta-squared) is reported for significant differences.
temporoparietal association neocortex (Fox et al., 1996;Whitwell et al., 2007).Individuals with MCI exhibit a similar (less severe) pattern.In particular, cortical atrophy in MCI appears prevalent in temporal, parietal and occipital areas (Whitwell, 2010).Moreover, cerebral blood flow (CBF) reduction can be observed in elderly individuals with high AD risk (Clark et al., 2017;Ruitenberg et al., 2005).The spatiotemporal pattern of AD-related CBF decline spreads from the precuneus, posterior cingulate cortex and temporo-parietal areas to broader brain regions, accompanying the progression from HC to MCI to fullblown AD (Zhang et al., 2021).Temporal, parietal and hippocampal regions exhibit a rapid decline in the earlier stages of the disease associated with the level of cognitive deterioration (Zhang et al., 2021).
Studies in preclinical AD, MCI and full-blown AD suggest that the posteromedial cortex and the medial temporal lobe appear particularly vulnerable to AD-related pathological changes (Grothe & Teipel, 2016;La Joie et al., 2012).Overall, different functional and structural brain alterations early affect the parietal areas in AD.In this view, the parietal reduction of KC density in aMCI-CO may mirror the underlying level of local AD pathology progression.Therefore, it is possible that the AD-related KC alterations may be observed earlier in the parietal regions than in the anterior ones in individuals with MCI, while it may express a frontal predominance only in a more advanced phase of the pathology (De Gennaro et al., 2017).Another explanation for the selective parietal KC density reduction is based on connectivity measures.Indeed, converging evidence shows that individuals with AD and MCI are characterized by altered functional and effective connectivity (Rossini et al., 2020).The KC is considered an isolated slow wave arising from cortico-cortical connections activity.Findings from intracortical studies point to a widespread cortical involvement in the generation of KCs (Cash et al., 2009;Latreille et al., 2020;Mak-McCully et al., 2015).Mak-McCully and co-workers (2015) found that KCs can spread in variable directions but exhibit a prevalent anterior-to-posterior propagation.In this view, it could be speculated that the reduced parietal KC density may represent a decreased posterior propagation of anteriorly generated KCs.Such hypotheses need to be systematically assessed.
We found no KC amplitude differences between groups.Also, we assessed for the first time KC AUC in healthy and pathological aging, showing no KC morphological differences between MCI-ST, MCI-CO and HC.Overall, we did not replicate findings from Liu and coworkers (Liu, Pan, Lei et al., 2020;Liu, Pan, Tang et al., 2020), which suggested an early alteration of KC amplitude in individuals with MCI.frequency and decreased high-frequency EEG activity) during wakefulness and REM sleep (Babiloni et al., 2006;Brayet et al., 2016;D'Atri, Scarpelli et al., 2021;Hassaina et al., 1997;Jeong, 2004) and an alteration of sleep spindles during NREM sleep (D'Atri, Scarpelli et al., 2021;Gorgoni et al., 2016;Liu, Pan, Tang et al., 2020;Westerberg et al., 2012) in AD/MCI, results about NREM sleep SWA are less clear.Several studies found a reduction of SWA over midline derivations in AD and MCI (Westerberg et al., 2012;Mander et al., 2015;Varga et al., 2016;Lucey et al., 2019).Moreover, reduced SWA in healthy aging is associated with pathological markers of AD (Mander et al., 2015;Varga et al., 2016), and its amount in the < 1-Hz frequency range can predict the speed of Aβ deposition over time (Winer et al., 2020).On the other hand, different findings described the absence of changes in the delta frequency range and SWA ≤ 1 Hz power during NREM sleep in AD/MCI (D'Atri, Scarpelli et al., 2021;De Gennaro et al., 2017) and the absence of a relationship between NREM sleep SWA and cortical thickness in AD (D'Atri, Gorgoni et al., 2021).Crucially, opposite AD-related SWA changes according to the considered frequency range have been highlighted (Bonanni et al., 2012;Mander et al., 2015).It is possible that distinct processes in AD and MCI have opposite frequency-specific influences on NREM, likely with a differential effect according to the stage of the pathology.
Hypothetically, an increase of "pathological" slow waves (i.e.EEG slowing) may coexist with a reduction of "healthy" slow waves (i.e.KCs), and the assessment of the SWA power may not be sensitive enough to discriminate between them.Our observation that aMCI-CO appears characterized by a parietal KC density reduction and absence of changes in SWA power, the latter showing a descriptive (non-significant) enhancement, mainly expressed in the frontal region in the 3-4 Hz-bins, goes in this direction.
Concerning the homeostatic overnight changes, we confirmed also in HC, aMCI-ST and aMCI-CO, the classical reduction of KC density during late sleep compared with early sleep (Curcio et al., 2003;De Gennaro et al., 2000) without differences between the three groups, suggesting that AD pathology, at least in its prodromal stage, does not affect this pattern of overnight regulation of KC density.
Also, SWA confirmed its classical pattern of homeostatic modulation across the night (Achermann & Borbély, 2017), exhibiting a generalized pattern of delta power reduction in all the delta frequency bins in HC, aMCI-ST and aMCI-CO, without differences between groups.In a previous study, we found that the post-sleep reduction of waking delta activity, proposed as an index of sleep-dependent restoring processes efficiency (Corsi-Cabrera et al., 1992), gradually disappeared in

| CONCLUSIONS
The interest in sleep electrophysiology in the field of AD research is growing.In this context, only a few studies focused on the KC, providing relevant but still limited and mixed evidence about their alterations in the presence of neurodegeneration.While the existence of a KC decline has been consistently observed in full-blown AD (De Gennaro et al., 2017;Liu, Pan, Lei et al., 2020;Liu, Pan, Tang et al., 2020;Reda et al., 2017), the nature of this alteration, its functional meaning, relationship with AD neuropathology, and time course are still unclear.
The present findings show a selective KC density reduction in the parietal area specific for individuals with MCI that will convert to AD, suggesting that future research in this field should not be limited to the KC expressed in the anterior brain regions.We underline the need to clarify in future studies the role of the KC in AD, its relationship with well-known AD pathological features, and its possible usefulness as an early biomarker of the disease and potential target of clinical intervention (Cordone et al., 2021).Moreover, further effort is needed to understand the effects of AD on different EEG phenomena in the SWA range in specific stages of the pathology.
the demographic and clinical features of the sample.Individuals with aMCI were selected among the elderly persons referred to the Neuropsychology Unit of the Policlinic A. Gemelli Foundation & Catholic University of Rome.HCs were recruited in clubs for retired people.
of alcoholism or drug abuse.The final enrolment in the study was based on the evaluation of the regular sleep-wake cycle and the absence of self-rated sleep disorders.Polysomnographic (PSG) recordings objectively evaluated the presence of other sleep disorders.Subjects were excluded by subsequent analyses in case of sleep disorders and/or respiratory diseases and obstructive sleep apnea syndrome.Participants were not taking hypnotic drugs that could affect NREM sleep physiology.The Italian version of the Pittsburgh Sleep Quality Index (PSQI;Curcio et al., 2013), the Epworth Sleepiness Scale (ESS;Vignatelli et al., 2003), and the pre-and post-sleep Karolinska Sleepiness Scale (KSS;Akerstedt & Gillberg, 1990) were administered to assess subjective sleep quality and sleepiness.The patients with aMCI repeated the neuropsychological investigation procedure at a follow-up evaluation (at least 6 months after the baseline evaluation).According to the follow-up evaluation results, patients were classified as aMCI-ST or aMCI-CO.The mean duration of the time between baseline and follow-up did not differ between the two groups (aMCI-ST: Mean ± SD = 29.25 ± 20.55 months; aMCI-CO: Mean ± SD = 25.50 ± 18.30 months; t = 0.47; p = 0.64).
underwent a PSG recording of an undisturbed night of sleep.The EEG electrode montage procedure started at 19:00 hours.PSG recording started according to the individual habitual sleep schedule (21:00 hours-23:00 hours) and ended with the spontaneous awakening in the morning.A Micromed system Morpheus digital polygraph was used for the PSG recording.EEG signals were acquired using Ag/AgCl electrodes with a sampling frequency of 256 Hz and band-pass filtered at 0.53-40 Hz.The 19 unipolar EEG derivations of the international 10-20 system (C3, C4, Cz, Fp1, Fp2, F3, F4, F7, F8, Fz, O1, O2, P3, P4, Pz, T3, T4, T5, T6) were recorded from scalp electrodes referenced to the ground electrode at Fpz, and off-line re-referenced to the average of the mastoids (A1-A2).Electro-oculogram was recorded from electrodes placed about 1 cm from the medial and lateral canthi of the dominant eye.Electrocardiogram and submental electromyogram (EMG) were also recorded.Finally, a pulse oximeter was placed on the right index finger to exclude respiratory sleep disorders.Periodic limb movements were not measured by a tibialis EMG recording but excluded on the basis of the PSQI evaluation and their clinical history.Any contamination of EEG recordings by muscle activity was, however, excluded by subsequent analyses.Impedance was kept below 5 kOhm.
depicts the KC average waveforms of a representative HC at Fz, Cz and Pz, and the absolute values on which the trapezoidal rule has been calculated.All KC measures during Stage 2 NREM were collected for the entire night of sleep, and separately for the 1 and 2 half of the sleep period.
late power spectra within the delta range during Stage 2 NREM sleep.Absolute power spectra were averaged over five consecutive 4-s epochs to yield a 20-s spectrum, to match sleep scoring.We computed the EEG power values in the 0.5-4.75-Hzrange.Data were reduced to a 1-Hz bin width by collapsing four adjacent 0.25-Hz bins.The only exception was the 0.5-1.00-Hzbin, for which two adjacent 0.25-Hz bins were collapsed.The bins were referred to and plotted by the centre frequency included in our study (e.g. the 3-Hz bin referred to the averaged values of the following bins: 3.00, 3.25, 3.50, 3.75 Hz).For all the available scalp derivations, values were log-transformed, colour coded, plotted at the corresponding position on the planar projection of the scalp surface, and interpolated (biharmonic spline) between electrodes.SWA power during Stage 2 NREM was computed for the entire night of sleep, and separately Demographic and clinical data, macrostructural sleep variables, KC measures, and delta power of aMCI-ST, aMCI-CO and HC groups were compared by means of one-way analyses of variance (ANOVAs) followed by post hoc Tukey test.Shapiro-Wilk and Levene's tests were used to assess the assumptions of normality and homogeneity of the variances, respectively.When the assumption of normality was not fulfilled, logarithmic transformation was used.When data were not normalized through logarithmic transformation, the Kruskal-Wallis test was performed followed by Mann-Whitney U-test for pairwise comparisons.When the assumption of variance homogeneity was not fulfilled, Welch's ANOVA followed by Games-Howell post hoc comparisons was performed to compare groups.Omega-squared and epsilon-squared were used to assess the effect size for ANOVAs and Kruskal-Wallis test, respectively.As control analyses for the potential influence of the duration of the time between baseline and follow-up, we also performed one-way analyses of covariance (ANCOVAs) on KC measures comparing aMCI-ST and aMCI-CO and using time from the baseline evaluation as covariate.

F
I G U R E 1 Example of K-complex (KC) averaging for the assessment of the area under the curve (AUC).(a) Individual KC average waveform realigned to the negative peak in a representative healthy control (HC) at Fz, Cz and Pz.The single KCs were time-locked to the large negative peak and then averaged considering the interval that goes from 550 ms before to 950 ms after the negative peak, obtaining an individual KC average waveform with a duration of 1500 ms and a negative peak at 550 ms.Data are plotted with upwards negative values on the y-axis.Amplitude is expressed in μV.(b) Absolute values of the KC waveform, on which the trapezoidal rule has been calculated to obtain the AUC.In this representative subject the obtained AUCs were 11950.70 at Fz, 7672.79 at Cz, and 5841.67 at Pz. concerning gender distribution, age and years of education.MMSE scores were heteroscedastic (F 2,33 = 3.76, p = 0.034), as well as HDRS (F 2,33 = 5.64, p = 0.008), and Welch's ANOVA was used for the comparison between groups in these variables.A violation of the assumption of normality was found for ESS (W = 0.94, p = 0.04), KSS collected in the pre-sleep evening (W = 0.93, p = 0.02) and post-sleep morning (W = 0.89, p = 0.002).Therefore, these variables were logtransformed.Results showed a significant difference in MMSE scores (F 2,21 = 16.97,p < 0.001) with a large effect size (ω 2 = 0.47).Games-Howell post hoc comparisons pointed to significantly higher MMSE scores in HC compared with aMCI-ST ( p < 0.001) and aMCI-CO (p = 0.002).Also, ESS showed a significant difference (F 2,33 = 8.84, p < 0.001) with a large effect size (ω 2 = 0.36).Post hoc comparisons point to a significantly lower overall subjective sleepiness in MCI-CO compared with HC ( p = 0.006) and MCI-ST (p = 0.005), without differences between HC and MCI-ST.No difference between groups has been observed in subjective sleepiness assessed with KSS before and after sleep, self-reported sleep quality (PSQI), state and trait anxiety (STAI), and depression (HDRS).

a
Logarithmic transformation.parietalKC density in aMCI-CO compared with HC ( p = 0.02) and aMCI-ST ( p = 0.03), without differences between HC and MCI-ST ( p = 0.41; Figure2).No significant differences between groups were observed for KC amplitude and AUC.The results from the control analyses (ANCOVAs) performed on KC measures comparing aMCI-ST and aMCI-CO using the time between baseline and follow-up evaluation as covariate substantially confirm the results, showing a significant difference between groups only in KC density at Pz (F 1,21 = 6.83, p = 0.02) with a large effect size (ω 2 = 0.20), without changes in other derivations (Fz: F 1,21 = 0.19, p = 0.67; Cz: F 1,21 = 2.18, p = 0.15).No significant difference was observed in KC amplitude (Fz: F 1,21 = 0.26, p = 0.61; Cz: F 1,21 = 0.03, p = 0.85; Pz: F 1,20 = 0.13, p = 0.72) and AUC (Fz: F 1,21 = 0.44, p = 0.51; Cz: F 1,21 = 0.008, p = 0.93; Pz: F 1,20 = 0.12, p = 0.73).Table 4 reports the results of the 3 Â 2 mixed design ANOVAs Group (HC versus MCI-ST versus MCI-CO) Â Phase (1 half versus 2 half of the night) performed on log-transformed KC measures.While the Group factor substantially confirms the findings of the main analysis on KC density, the Phase factor points to a significative reduction of KC density during the 2 half of the night compared with the 1 one, without significant amplitude and AUC differences.Only KC amplitude at Fz exhibited a significant interaction, but post hoc tests did not provide significant differences ( p > 0.22).

Figure 3
Figure 3 depicts the topographic distribution of delta EEG power during Stage 2 NREM sleep in HCs, aMCI-ST and aMCI-CO, and their statistical comparison.The violation of the assumption of variance's homogeneity was found in many derivations, therefore the Welch's were (2, 32), as one participant had no KCs at Pz.F I G U R E 2 K-complex (KC) density of healthy controls (HC), stable amnesic mild cognitive impairment (aMCI-ST), and aMCI converted in Alzheimer's disease (AD) at the follow-up evaluation (aMCI-CO) at Pz cortical derivation.Error bars represent the standard errors.Asterisks (*) indicate statistically significant differences ( p < 0.05) between groups after the Mann-Whitney U-test.
) separately described KC density in aMCI-ST, aMCI-CO and HC, showing no difference between the three groups at baseline and 6 months after the baseline.Only 12 and 24 months after the baseline HC exhibited higher KC density compared with aMCI groups, and aMCI-ST showed greater KC density than aMCI-CO.The present finding integrates the previous observation ofLiu and co-workers (2020), suggesting that early disruption of KC density along the time course of AD pathology (i.e.MCI-CO) may be observed focusing on the parietal region where the specific pathology (density of amyloid plaques, neurofibrillary tangles and atrophy) is mainly concentrated.Patients with AD typically exhibit a pattern of brain atrophy that involves the medial temporal lobe and the posterior cingulate, precuneus, and T A B L E 4 Results of the 3 Â 2 ANOVAs performed on log-transformed KC measures having Group (HC versus MCI-ST versus MCI-CO) as between factor, and Phase (

Further
studies are needed to understand changes in KC morphology in individuals with MCI.Because the MCI condition may have different primary causes, the assessment of the main AD biomarkers (Aβ and tau neurofibrillary tangles) and their relationship with KC measures may help disentangle this issue.While the parietal KC density decrease was observable only in aMCI-CO, we found a SWS reduction in both aMCI-ST and aMCI-CO compared with HC.This finding extends our previous observation of a SWS decrease in MCI(D'Atri, Scarpelli et al., 2021;Reda et al., 2017), and suggests that changes in NREM macrostructure may characterize the MCI condition independently from its specific aetiology, while the alteration of the KC density may represent a more specific early marker of neurodegeneration.The absence of differences in NREM SWA between aMCI and HC is not surprising.While the present literature consistently describes a slowing of the cortical rhythms (i.e.increased low-F I G U R E 3 Topographical scalp maps of delta electroencephalogram (EEG) power in healthy controls (HC), stable amnesic mild cognitive impairment (aMCI-ST) and aMCI converted in Alzheimer's disease (AD) at the follow-up evaluation (aMCI-CO) during Stage 2 non-rapid eye movement (NREM) sleep.The maps are based on the 19 derivations of the 10-20 system (electrode positions indicated by black dots).Values are colour-coded and plotted at the corresponding position on the planar projection of the hemispheric scalp model.Values between electrodes were interpolated (biharmonic spline interpolation).Values are expressed in terms of log values of 0.5, 1, 2, 3 and 4 Hz during Stage 2 NREM sleep of the three groups (a) and F-values of Welch's ANOVAs (b).
MCI and AD compared with HC (D'Atri, Scarpelli et al., 2021).Such a finding suggested that sleep may progressively reduce its restorative function in the AD pathology.Because NREM SWA is considered a reliable marker of sleep pressure and intensity(Achermann & Borbély, 2017), it is possible that AD may be characterized by an alteration of SWA homeostatic modulation, leading to the reduced influence of sleep on waking delta activity previously observed(D'Atri,   Scarpelli et al., 2021).The present findings point to a preserved homeostatic regulation of both KC density and SWA power at least in Stage 2 and in the prodromal stage of AD, but we believe that a deeper and specific investigation of the homeostatic regulation of the slow waves during NREM sleep in AD pathology is needed.The present findings should be cautiously interpreted, and several limitations should be taken into account.First, it is worth noting that the present study is characterized by a low sample size due to the limited number of available individuals with MCI in our database with both sleep EEG recordings and follow-up evaluation.Moreover, although the MCI groups did not differ concerning the mean duration between baseline and follow-up, individuals with MCI did not perform the follow-up evaluation at a fixed time after the baseline, which may represent a relevant source of variability.Also, we did not perform a follow-up cognitive evaluation for HC.Therefore, we do not know if HC developed an MCI/AD condition.It should be considered that the spatial resolution of the KCs detected in our study is limited to the midline derivations, reducing the possibility to observe local KC changes in other cortical areas.Finally, our study does not report data about the relationship between the observed KC density reduction and consolidated AD biomarkers, which could hint at the specific pathophysiological mechanisms underlining the KC alteration.

Table 2
reports the results of the comparisons between HC, aMCI-ST AUC, area under the curve; HC, healthy control; KC, K-complex; MCI-CO, mild cognitive impairment converted in Alzheimer's disease at the follow-up evaluation; MCI-ST, stable mild cognitive impairment.