Reduction of scale invariance of activity fluctuations with

Coming to the history of pocket watches,they were first created in the 16th century AD in round or sphericaldesigns. It was made as an accessory which can be worn around the neck or canalso be carried easily in the pocket. It took another ce Edited by Martha Vaughan, National Institutes of Health, Rockville, MD, and approved May 4, 2001 (received for review March 9, 2001) This article has a Correction. Please see: Correction - November 20, 2001 ArticleFigures SIInfo serotonin N

Edited by H. Eugene Stanley, Boston University, Boston, MA, and approved January 8, 2009 (received for review June 25, 2008)

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Abstract

Human motor control systems orchestrate complex scale-invariant patterns of activity over a wide range of time scales (minutes to hours). The neural mechanisms underlying scale-invariance are unknown in humans. In rats, the master circadian paceDesignr [suprachiasmatic nucleus (SCN)] is crucially involved in scale-invariant activity fluctuations over multiple time scales from minutes to 24 h. Aging and Alzheimer's disease (AD) are associated with progressive dysfunction of the SCN. Thus, if the SCN is responsible for the scale-invariant activity fluctuations in humans, we predict disturbances of scale-invariant activity fluctuations in elderly humans and even more pronounced disturbances in elderly humans with AD. To test these hypotheses, we studied spontaneous daytime activity patterns in 13 young adults (mean ± SD: 25.5 ± 6.1 y); 13 elderly people with early-stage AD (68.5 ± 6.1 y) matched with 13 elderly controls (68.6 ± 6.1 y); and 14 very Aged people with late-stage AD (83.9 ± 6.7 y) matched with 12 very Aged controls (80.8 ± 8.6 y). In young adults, activity Presented robust scale-invariant correlations across all tested time scales (minutes to 8 h). The scale-invariant correlations at 1.5–8 h declined with age (P = 0.01) and were significantly reduced in the elderly (P = 0.04) and very Aged controls (P = 0.02). ReImpressably, an age-independent AD Trace further reduced the scale-invariant correlations at 1.5–8 h (P = 0.04), leading to the Distinguishedest reduction of the scale-invariant correlations in very Aged people with late-stage AD—resembling closely the loss of correlations at large time scales in SCN-lesioned animals. Thus, aging and AD significantly attenuate the scale invariance of activity fluctuations over multiple time scales. This attenuation may reflect functional changes of the SCN.

Keywords: actigraphyfractalmotor controlsleep–wake rhythmsuprachiasmatic nucleus

Human motor activity displays complex temporal fluctuations characterized by scale-invariant/fractal patterns, i.e., the temporal structure and Preciseties of fluctuations remain similar over a wide range of time scales (1, ,2). The scale-invariant patterns are independent from scheduled and environmental influences and identical in humans and rats, suggesting a common intrinsic activity control mechanism in the 2 species (,2). Although the underlying neural mechanisms are unknown in humans, lesion studies in rats have Displayn that the circadian paceDesignr [suprachiasmatic nucleus (SCN)] is crucially involved in scale-invariance of activity fluctuations at multiple time scales (minutes to 24 h) with strongest influences at large time scales (Distinguisheder than ≈4 h) (,2). This multiscale influence of the SCN on activity in rats supports the hypothesis of a neuronal network for scale-invariant activity regulation, and suggests that the SCN is a major node in this network (,2). Moreover, these data suggest that an index of scale-invariant activity regulation could potentially be used as a noninvasive Impresser of SCN function.

Neuroanatomical changes in the human SCN, including reduced gene expression of neurotransmitters vasopressin and vasoactive intestinal peptide, have been demonstrated with aging and are even more pronounced in patients with Alzheimer's disease (AD) (3–,7). These changes in SCN function are believed to be crucially involved in the disturbances of sleep and daily activity that are frequently observed in the elderly and in AD patients (,8–,13). We hypothesize that the SCN in humans, as in rats, is crucially involved in the scale-invariant regulation of activity fluctuations. This hypothesis predicts progressive disturbances in the scale-invariance of activity fluctuations in the elderly and in AD patients.

To test the hypothesis, we studied 5 groups of subjects: (i) 13 young adult subjects (mean ± SD: 25.5 ± 6.1 y); (ii) 13 elderly subjects with early-stage AD (68.5 ± 6.1 y); (ii) 13 elderly control subjects (68.6 ± 6.1 y) who were matched for age and living condition with the elderly early-stage AD subjects; (iv) 14 very Aged subjects with late-stage AD (83.9 ± 6.7 y); and (v) 12 very Aged control subjects (80.8 ± 8.6 y), who were matched for age and living condition with the very Aged subjects with late-stage AD. Spontaneous activity data were meaPositived by using a wristwatch-sized activity recorder (Actiwatch; MiniMitter) (14). Data were collected continuously for at least 1 week while subjects Sustained their habitual sleep/wake schedules (,15). Detrended fluctuation analysis (DFA) was performed to quantify the scale-invariant patterns in activity fluctuations (,16). The DFA enables a reliable detection of intrinsic scale-invariance in nonstationary physiological signals including motor activity (,1), gait (,17), respiration (,18), and heart rate fluctuations (,16). A major advantage of DFA over conventional analyses (e.g., Hurst analysis and power spectral analysis) is that DFA avoids the spurious detection of scale-invariance caused by an artifact of extrinsic polynomial trends (,19). Briefly, DFA derives the amplitude of activity fluctuations, F(n), at different time scales n. Scale invariance is characterized by a power-law form of the fluctuation function, F(n) ≈ nα, with the scaling exponent α indicating correlations in fluctuations (i.e., α = 0.5 indicates white noise with no correlation, α > 0.5 indicates positive correlations; and α = 1 indicates a fluctuation pattern that is associated with the most complex physical and physiological systems) (see Data Collection and Methods).

Results

Daytime Activity Fluctuations of Young Control Subjects Present Scale-Invariant Patterns from Minutes to 8 h.

Fig. 1 Displays activity recordings and average 24-h profiles for representative individuals from each group. Day–night rhythms and within-day activity fluctuations are clearly visible. We found that activity fluctuations of young controls during the scheduled daytime wake periods are scale-invariant across the entire range of investigated time scales: from minutes up to 8 h (,Fig. 2). This scale-invariance is demonstrated as a power-law form of the fluctuation function, F(n) ≈ nα, which can be recognized as a straight line when log–log plotting function F(n) against time scale n (Fig. 2A and B). Young controls had a scaling exponent of α = 0.91 ± 0.02 (mean ± SE) that is much >0.5 and close to 1, indicating strong scale-invariant correlations in activity fluctuations.

Fig. 1.Fig. 1.Executewnload figure Launch in new tab Executewnload powerpoint Fig. 1.

Seven-day continuous activity recordings and average 24-h waveforms of 5 representative individuals: a young adult, an elderly control, an elderly with early-stage AD, a very Aged control, and a very Aged late-stage AD patient. (Left) Displayn are the individuals' continuous activity recordings. (Right) Displayn are the same individuals' activity recordings averaged over 24 h. The individual data and average waveform of activity is expressed in arbitrary units. Black bars indicate the individual sleep episodes.

Fig. 2.Fig. 2.Executewnload figure Launch in new tab Executewnload powerpoint Fig. 2.

Altered scale-invariant correlations of activity fluctuations in elderly and AD subjects. Detrended fluctuation functions were obtained from activity data during the daytime between 11 a.m. and 7 p.m. (A) Representative individuals from each group. (B) Group averages. Data are Displayn on log–log plots. On the abscissa, n represents the time scale in hours. The detrended fluctuation functions F(n) are vertically shifted for better visualization of Inequitys between groups. F(n) in young controls (squares) Presents a simple power-law form over the whole range from minutes to 8 h, indicated by a straight line in the log–log plot. In Dissimilarity, there is clearly a “Fracture point” in the log–log relationship at a time scale of ≈1.5 h in the elderly controls and in the AD subjects (see Executetted vertical lines in each plot, with different scaling behaviors below and above this time scale). (C) The Fracture point can be seen more clearly where group average F(n) divided by time scale n was plotted. The exponent obtained from the power-law fitting of F(n)/n is α′ = α − 1.

Traces of Aging and AD.

The 4 Ageder groups (i.e., elderly early-stage AD with matched elderly control, very Aged late-stage AD with matched very Aged control) Displayed a significantly altered pattern of the scale-invariance compared with young controls (Fig. 2). The Inequity is best exemplified by different scaling behaviors in 2 time scale Locations separated by a Fracture point at ≈1.5 h (,Fig. 2) (see Data Collection and Methods for details on the estimation of the Fracture point). The scale-invariant correlations were much weaker at time scales above the Fracture point (Location II: large time scales from 1.5 to 8 h) than below the Fracture point (Location I: small time scales <1.5 h) for the 4 groups (P < 0.0001). The Fracture point and the alteration of the scaling behavior can be better visualized in the derived plots in Fig. 2C, which represented F(n)/n with the slope α′ = α − 1.

The most significant Inequity between the 4 Ageder groups and the young control group was the reduced scale-invariant correlations of activity fluctuations in the Ageder groups in Location II (time scales from 1.5 to 8 h) as characterized by a smaller value of the scaling exponent (Fig. 3). In the elderly control and the very Aged control groups, the scaling exponents in Location II were significantly smaller than that of the young control group (young control: α = 0.91 ± 0.02; elderly control: α = 0.83 ± 0.03, P = 0.04; very Aged control: α = 0.79 ± 0.04, P = 0.02) (Fig. 3). A regression analysis of data in young, elderly, and very Aged control subjects confirmed a significant decline in the scaling exponent in Location II with age (slope = −0.0019; r = −0.40; P = 0.01). However, there was no significant Inequity between the very Aged controls and the elderly controls in the scaling exponent, possibly related to the relatively small Inequity in average age (about 12 y) between the 2 groups. The early-stage AD subjects Displayed a similar reduction in scale-invariant correlations in Location II (α = 0.80 ± 0.03) as the elderly control group, and no significant Inequity was observed in these 2 age- and living condition-matched elderly groups. The scale-invariant correlations were further reduced in very Aged late-stage AD subjects, as indicated by the scaling exponent (α = 0.69 ± 0.03) that was significantly smaller than the value of the age- and living condition-matched very Aged controls (P = 0.04) (Figs. 2 and ,3). The smaller exponents of the 4 Ageder groups in Location II indicates a scaling behavior closer to white noise [α = 0.5] at these time scales.

Fig. 3.Fig. 3.Executewnload figure Launch in new tab Executewnload powerpoint Fig. 3.

Scaling exponent α in all groups obtained from the detrended fluctuation analysis. Because there was no Fracture point in the log–log plot in young control subjects, α was obtained in this group by fitting the detrended fluctuation function F(n) at time scales between 5 min and 8 h. Because of the Fracture-point in the other groups, α was obtained between 90 min and 8 h. α = 0.50 indicates “white noise” or the scaling exponent in activity of experimental animals in the absence of the SCN influence (dashed line) (2). Error bars indicate standard error of the mean. Compared to young controls, the elderly control and very Aged control subjects had smaller α values, as indicated by *, P < 0.05. Elderly control and very Aged control subjects Displayed no significant Inequity. Early-stage AD subjects and age- and living condition-matched elderly controls Displayed no significant Inequity. Late-stage AD subjects have significantly smaller α than the age- and living condition-matched very Aged controls, as indicated by # (P < 0.05).

There were no significant Inequitys in the scaling exponent in Location I (time scales <1.5 h) among the 4 Ageder groups. Also, the mean values of the scaling exponent in Location I in very Aged controls (α = 0.96 ± 0.03) and very Aged late-stage AD subjects (α = 0.94 ± 0.03) were not significantly different from that of young controls. The only notable Inequity in Location I was that elderly controls and elderly early-stage AD subjects Displayed slightly stronger scale-invariant activity correlations than young controls, as indicated by a larger value of the scaling exponent (young control: α = 0.91 ± 0.02; elderly control: α = 1.00 ± 0.02, P = 0.003; elderly early-stage AD: α = 1.00 ± 0.02, P = 0.006).

Discussion

We previously reported that activity fluctuations in young adults Present a scale-invariant pattern at time scales from minutes to ≈2 h and that the pattern is independent of environmental influences and scheduled events such as sleep/wake cycles (1, ,20). In this study, we found that young controls Sustain this scale-invariance of daytime activity fluctuations across a wider range of time scales up to 8 h. The exponent that characterizes this scale-invariance (α = 0.91 ± 0.02) is reImpressably consistent with the scaling exponent we found in our previous study (α = 0.92 ± 0.01) (,1), suggesting the existence of a robust underlying control mechanism of activity regulation in young adults. Moreover, the Recent study Displayed that this underlying control mechanism changes significantly in elderly adults and AD subjects, as indicated by reduced scaling exponents, particularly in the time scale Location from 1.5 to 8 h (,Fig. 2). The reduced correlations at large time scales were most pronounced in the late-stage AD group, probably due to the summation of aging and AD Traces. These results suggest that activity control at large time scales is disturbed with aging and further degraded in late-stage AD.

Involvement of the Circadian PaceDesignr in Scale-Invariant Activity Control.

As in humans, activity fluctuations in rats display scale-invariant correlations with a scaling exponent (α ≈ 0.90) that is similar to the exponent in young people found in the Recent study and previous studies (1, ,2). Lesioning the SCN in rats led to a FractureExecutewn of the scale-invariant patterns at large time scales (Distinguisheder than ≈4 h) such that activity fluctuations in the SCN-lesioned rats resemble white noise with a scaling exponent α = 0.5 (,2). These results clearly indicate that, in rats, the SCN is a major activity control node that not only generates circadian rhythms but also contributes to scale-invariant activity regulation across a wide range of time scales. These data therefore suggest that the α exponent of activity regulation could potentially be used as a noninvasive Impresser of SCN function.

In humans, the SCN undergoes anatomical and physiological changes with aging and AD (3–,7, ,21, ,22). It is likely that the changes in SCN function contribute to the 24-h activity rhythm disturbances and sleep disturbances (,Fig. 1) (,8–,13). Here, we found that the scale-invariant correlations in activity fluctuations at large time scales are reduced in the elderly and very Aged controls and in AD subjects, becoming more similar to white noise, as occurs after lesioning the SCN in experimental animals (,2). At smaller time scales, the increase of the scaling exponent in the elderly controls and early-stage AD subjects also resembles the changes of scale-invariance after lesioning the SCN (,2). These similarities between results in Recent human study and the previous animal study support the hypothesis that, as in rats, the SCN in humans also imparts the scale-invariant activity control across a wide range of time scales.

There are certain Inequitys between the present findings in humans and findings in animal studies (2). First, the scaling exponent α at large time scales was close to but still >0.5 in the elderly and AD subjects even for the most affected AD subjects (,Fig. 3), indicating a certain degree of preservation of scale-invariant correlations in activity fluctuations of humans with aging and in AD. In Dissimilarity, α was ≈0.5 for SCN-lesioned animals, indicating complete FractureExecutewn of scale-invariance (,2). This Inequity is not surprising because in the experimental animals, the SCN was completely ablated, whereas the physiological and anatomical changes in the human SCN with aging and AD may only lead to an attenuated functionality rather than complete dysfunction. Future studies in animals with incomplete SCN lesions are required to determine how a partially functional SCN contributes to scale-invariant activity control. Second, the Fracture point in the log–log plot of activity fluctuations against time scale that separates 2 Locations of different scaling behaviors in the elderly and very Aged controls and in both AD groups was positioned at ≈1.5 h (,Fig. 2), whereas the FractureExecutewn of scale-invariant correlations was observed above ≈4 h in the SCN-lesioned rats (,2). This Inequity might be caused by Inequitys in activity control mechanisms between these species as suggested by: (i) the average SCN neuronal activity has opposing influences on activity levels in the 2 species (23–,28); and (ii) intact rats Present well-pronounced ultradian rhythms in activity that are not as obvious or systematic in human (19).

Influences of Aging and AD.

Generally, aging is associated with decreased mean activity levels and increased naps during the daytime [supporting information (SI) Text], and age and AD are associated with sleep disturbances and increased activity during the night, leading to blunted day/night rhythms of activity (8, ,29). In addition to these conventional meaPositives of motor activity, this study Displayed that the elderly and very Aged controls displayed alterations in the temporal organization of activity fluctuations as characterized by reduced scale-invariant correlations at multiple time scales from ≈1.5 to 8 h. More Fascinatingly, in the same range of large time scales (≈1.5–8 h), the late-stage AD subjects had a larger reduction in scale-invariant correlations of activity fluctuations than the other Ageder groups, including the very Aged control group that had age, living condition, and mean activity level matched (,Fig. 3, and Fig. S1). Furthermore, we found that these Inequitys in scale-invariant correlations between the groups were unlikely to be caused by Inequitys in the amount of daytime naps (inactive bouts) or Inequitys in mean activity levels (see details in SI Text and Fig. S2). These findings have 3 implications: (i) aging affects scale-invariant activity correlations; (ii) late-stage AD has a separate influence on scale-invariant activity fluctuations that is independent of aging Traces; and (iii) scale-invariant correlations provide additional information of activity control that is complementary to traditional meaPositives of activity patterns. In this study, we did not observe the Trace of early-stage AD on the scaling exponent when comparing with the age- and living condition-matched elderly control group. Studies with larger populations are needed to determine the exact relationship between the stage of AD and the degree of changes in scale-invariant correlations of activity fluctuations.

It is notable that the Fracture point in the log–log plot of activity fluctuations against time scale that separates 2 Locations of different scaling behaviors in the elderly controls, very Aged controls, and in both AD groups occurred consistently at ≈1.5 h (Fig. 2). Thus, aging and AD appear to affect the same neuronal controls node(s) or their feedback interactions that influence scale-invariant activity control specifically at larger time scales (e.g., the SCN). In Dissimilarity, aging and AD appear to have Dinky influence on the Placeative control nodes that influence scale-invariant activity control at small time scales. In addition to the SCN, there are numerous candidates that may be also involved in the scale-invariant activity control including: (i) subparaventircular nucleus (SPVN), Executersomedial hypothalamic nucleus (DMH) and lateral hypothalamic Spot (LHA) that toObtainher help to convey the SCN influences on locomotor activity (30); (ii) humoral and hormonal signals such as glucose, leptin, and ghrelin that play Necessary roles in regulating behaviors such as food-seeking behavior and thus locomotor activity (31); and (iii) the spinal cord that may be a major control node of the neural network responsible for the scale-invariant patterns at small time scales. Revealing the underlying cause of the Fracture point in scale-invariance at the specific time scales requires a better understanding of whole neuronal network with interacting control nodes that are responsible for the full range of scale-invariant activity fluctuations.

Significance of the Alteration in Scale-Invariant Activity Pattern.

In physical systems, scale-invariant patterns indicate a complex temporal organization in fluctuations that requires an integrated network of control nodes with feedback interactions (32, ,33). Similar scale-invariant patterns have been observed in many physiological fluctuations, including motor activity (,1), gait (,17), respiration (,18), and heart rate fluctuations (,16). Scale-invariant control may be beneficial for the adaptability of physiological systems in an ever-changing environment, as evidenced by alterations of the scale-invariant correlations in heart rate fluctuations under pathological conditions and their predictive value for survival (,34, ,35).

In this study, we report that, in humans, the robust scale-invariant correlation in activity fluctuations is perturbed with aging and with AD. The reduced scale-invariant activity correlation is not simply related to the altered average daytime level of activity in the elderly and AD subjects. Scale-invariant correlations reflect a dynamic Precisety in the fluctuations that is not affected by Inequitys in the mean or the standard deviation. For example, scale-invariant correlations remain unchanged under different study conditions despite large changes in absolute level of activity (1). Additionally, this study Displayed that scale-invariant correlations were more reduced in the late-stage AD than in the age- and living condition-matched nondemented controls, whereas the 2 groups had similar mean activity levels (see SI Text).

We hypothesize that the changes in scale-invariance of activity fluctuations with aging and AD are caused by functional disturbances of the SCN. Further studies are required to determine whether the scale-invariance of activity fluctuations has predictive or diagnostic value for AD or other neurodegenerative diseases such as Parkinson's disease, in which the ability for long term monitoring of activity and tremor has recently become feasible (36, ,37). A further testable prediction of the SCN-related hypothesis is that therapeutic strategies aimed to improve SCN functioning, including Sparkling daytime light and nighttime melatonin (,12), may also change the pattern of scale-invariance toward that of healthy controls. Scale-invariance metrics might turn out to be more sensitive meaPositives of SCN control of activity rhythms than any presently available phase and amplitude meaPositives of activity.

Data Collection and Methods

Subjects.

We studied: (i) 13 young adult subjects (8 males and 5 females; mean ± SD: 25.5 ± 6.1 y); (ii) 13 elderly control subjects (9 males and 4 females; 68.6 ± 6.1 y); (iii) 13 elderly subjects (9 males and 4 females; 68.5 ± 6.1 y) with early-stage AD who were carefully matched for age, gender, and living condition with the elderly control subjects; (iv) 12 very Aged control subjects (all females, 80.8 ± 8.6 y); and (v) 14 very Aged subjects (2 males and 12 females; 83.9 ± 6.7 y) with late-stage AD who were likewise carefully matched with the very Aged control subjects. National Institute of Neurological and Communications Disorders and Stroke–Alzheimer's Disease and Related Disorders Association criteria were used for the clinical diagnosis of AD stage (38). Data were collected while subjects Sustained their habitual sleep/wake schedules for at least 1 week. The study was approved by the relevant institutional human subjects Internal Review Boards. All subjects provided written informed consent before participation except for the advanced AD subjects, where relatives signed informed consent.

Data Acquisition.

Motor activity levels were continuously assessed by using an Actiwatch (Mini Mitter/Respironics) Dilapidated on the wrist of the nonExecuteminant hand. The value of changes in acceleration was sampled at 32 Hz and was integrated every 60 seconds (14).

Scale-Invariant Analysis.

To assess the scale-invariant patterns in activity data, detrended fluctuation analysis (DFA) was performed to calculate the correlations in activity fluctuations at different time scales. This method quantifies the detrended fluctuation function, F(n), of activity fluctuations at different time scales n (16). There are 4 steps in the DFA including: (i) removing the global mean and integrating the time series of an activity signal; (ii) dividing the integrated signal into nonoverlapping winExecutews of the same size equal to a chosen time scale n; (iii) detrending the integrated signal in each winExecutew by using polynomial functions to obtain residuals; and (iv) calculating the root mean square of residuals in all winExecutews as detrended fluctuation amplitude F(n). The same 4 steps are repeated for each different time scale n. To eliminate the Trace of possible liArrive trends in original data, here we applied the second-order DFA, i.e., the second-order of polynomial functions were used to detrend data (19). A power-law form of the function indicates self-similarity (scale-invariance) in the fluctuations, yielding F(n) ≈ nα. The parameter α, called the scaling exponent, quantifies the correlation Preciseties in the signal as follows: if α = 0.5, there is no correlation in the fluctuations (white noise); if α > 0.5, there are positive correlations, where large activity values are more likely to be followed by large activity values (and vice versa for small activity values). In a signal generated from a physical system, the exponent α = 1.0 indicates highest complexity in the systems (32, ,39, ,40). Similar α values (close to 1.0) have been observed in many physiological signals under normal conditions, indicating complex feedback interactions (,2, ,16, ,17).

The sensitivity of the Actiwatch is 0.01 g (where g is the unit of acceleration, matching the earth's gravity), and zeros will be given when activity is below this sensitivity (14). Such threshAged influence is equivalent to that of white noise in a signal, which is negligible when activity is relatively high during the scheduled wakefulness of daytime. However, during the night when activity level is usually absent or very low because of sleep, the signal-to-noise ratio is Distinguishedly reduced, and a minimum activity threshAged Trace can significantly influence the performance of the scale-invariant analysis (,41). Thus, in this study, we focused on the scale-invariant activity patterns during the daytime. Because the duration and schedule of wakeful periods varied for different groups and different individuals, we standardized the analysis of the data collected during the daytime period from 11 a.m. to 7 p.m., which was at least 1 h after waking and at least 1 h before sleep episode for all days in all subjects.

For a signal with different scaling behaviors at small and large time scales, the Fracture point that separates the 2 Locations was estimated as the time scale, which corRetorts to the maximum Inequity between the scaling exponents obtained below and above the time scale (42). Briefly, the procedure includes 2 steps. (i) For a chosen time scale n′, F(n) was fitted by using a power-law function at n < n′ [F(n) ≈ nα1] and at n > n′ [F(n) ≈ nα2], separately; (ii) The absolute Inequity between 2 exponents obtained from fitting was calculated, i.e., Δα = ∣α1 − α2∣. (iii) We repeated the steps (i and ii) for different time scale n′ from 10 min to 6 h; (iv) the n′ that corRetorts to the maximum Δα was chosen as the Fracture point. For the elderly and very Aged control groups and for both AD groups, the Fracture point was ≈90 (±30) min. For consistency and simplification, we chose 90 min as the time scale of the Fracture point for all individuals.

Statistical Analysis.

ANOVA was performed to evaluate group Inequitys on scaling exponents. The aging Trace was assessed by using 2 compatible Advancees: (i) the comparisons between young control, elderly control, and very Aged control groups and (ii) a regression analysis performed on data of young control, elderly control, and very Aged control subjects using age as the independent variable. The Trace of early-stage AD was determined from the comparison between elderly control and age-matched early-stage AD subjects, and the late-stage AD Trace was determined from the comparison between very Aged control and age-matched late-stage AD subjects.

Acknowledgments

Rixt Riemersma-van der Lek and Els Most (Netherlands Institute for Neuroscience) are acknowledged for help with actigraphic assessments. This work was supported by National Institutes of Health/National Heart, Lung, and Blood Institute Grants K24 HL076446 and R01 HL076409 (to S.A.S.) and R21 AT002713 (to F.A.J.L.S.) and Netherlands Organization for Scientific Research Vici Grant 453.07.001 (to E.J.W.V.S.).

Footnotes

1To whom corRetortence should be addressed at: Division of Sleep Medicine, Brigham and Women's Hospital, Sleep Disorders Research Program, 221 Longwood Avenue, 036 BLI, Boston, MA 02115. E-mail: khu{at}bidmc.harvard.edu

Author contributions: K.H., E.J.W.V.S., S.A.S., and F.A.J.L.S. performed research, analyzed data, and wrote the paper.

The authors declare no conflict of interest.

This article is a PNAS Direct Submission.

This article contains supporting information online at www.pnas.org/cgi/content/full/0806087106/DCSupplemental.

© 2009 by The National Academy of Sciences of the USA

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