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. 2018 Mar;35(3):368-377.
doi: 10.1080/07420528.2017.1407779. Epub 2017 Nov 28.

Decrease in Scale Invariance of Activity Fluctuations With Aging and in Patients With Suprasellar Tumors

Free PMC article

Decrease in Scale Invariance of Activity Fluctuations With Aging and in Patients With Suprasellar Tumors

S D Joustra et al. Chronobiol Int. .
Free PMC article


Motor activity in healthy young humans displays intrinsic fluctuations that are scale-invariant over a wide range of time scales (from minutes to hours). Human postmortem and animal lesion studies showed that the intact function of the suprachiasmatic nucleus (SCN) is required to maintain such scale-invariant patterns. We therefore hypothesized that scale invariance is degraded in patients treated for suprasellar tumors that compress the SCN. To test the hypothesis, we investigated 68 patients with nonfunctioning pituitary macroadenoma and 22 patients with craniopharyngioma, as well as 72 age-matched healthy controls (age range 21.0-70.6 years). Spontaneous wrist locomotor activity was measured for 7 days with actigraphy, and detrended fluctuation analysis was applied to assess correlations over a range of time scales from minutes to 24 h. For all the subjects, complex scale-invariant correlations were only present for time scales smaller than 1.5 h, and became more random at time scales 1.5-10 h. Patients with suprasellar tumors showed a larger decrease in correlations at 1.5-10 h as compared to healthy controls. Within healthy subject, gender and age >33 year were associated with attenuated scale invariance. Conversely, activity patterns at time scales between 10 and 24 h were significantly more regular than all other time scales, and this was mostly associated with age. In conclusion, scale invariance is degraded in healthy subjects at the ages of >33 year as characterized by attenuation of correlations at time scales 1.5-10 h. In addition, scale invariance was more degraded in patients with suprasellar tumors as compared to healthy subjects.

Keywords: Circadian rhythmicity; craniopharyngioma; detrended fluctuation analysis; nonfunctioning pituitary macroadenoma; scale invariance; suprachiasmatic nucleus.

Conflict of interest statement

Declaration of interest

The authors report no conflicts of interest. The authors alone are responsible for the content and writing of this article.


Figure 1
Figure 1
Average detrended fluctuation functions F(n) from locomotor activity data of 72 healthy controls, 68 NFMA patients and 22 craniopharyngioma patients. Data are shown on log-log plots and curves are vertically shifted in [A] for better visualization of differences between groups (vertical offset does not alter the slope). The scaling behavior can be separated in three time scale regions based on two breakpoints at ~1.5 h and ~10 h. The break points can be seen more clearly when F(n) is divided by time scale n in [B], indicating the change in F(n) per time unit n. The straight lines represent perfect scale-invariance α = 1.00 [A] or α′ = 0.00 [B].
Figure 2
Figure 2
Scaling exponent α in 72 healthy controls, 68 NFMA patients and 22 craniopharyngioma patients (CP), obtained from detrended fluctuation analysis, separated in three time scale (n) regions of the 24-h analysis period. The dotted lines represent too much randomness or white noise at α = 0.5, too much regularity or red noise at α = 1.5, and the delicate balance between the two in healthy systems known as complex scale invariance or pink noise at α = 1.0. Bars represent mean ± SD.
Figure 3
Figure 3
Scaling exponent α2 (times scales 1.5–10 h) in 72 healthy subjects and 90 patients (NFMA and craniopharyngioma). Data are separated by gender and in four age groups. In healthy subjects, group size for each age group in men is 3, 8, 11 and 16, and for women 3, 7, 19 and 5. For patients, group size for each age group in men is 3, 9, 25 and 13, and for women 4, 6, 21 and 9. The dotted line represents complex scale invariance with α = 1.0. Boxes display the 25th, 50th and 75th percentile, bars the 10th and 90th percentile and dots the outliers.

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