(A) 72-hour activity recording of a representative dementia patient. (B) Detrended fluctuation function F(n) of the activity signal shown in (a). F(n) displayed different power-law behavior with different scaling exponent, α₁ and α₂, at time scales smaller than and larger than ~ 2 hours (indicated by dotted dashed line). For comparison, F(n) of young adults as observed in a previous study was also plotted (dashed black line). (C) Difference between α₁ and α₂ for all subjects (except for 5 individuals with no α₂ due to many missing data points in their recordings). The subject # 13 (filled circle) is the patient whose data are shown in (A) and (B).

(A) Δα = α₁ − α₂ was negatively correlated with the number of vasopressin-positive SCN neurons after adjusting for the effect of the number of neurotensin-positive SCN neurons. (B) Δα was correlated with the number of neurotensin-positive SCN neurons after adjusting for the effect of the number of vasopressin-positive SCN neurons. Results in (A) and (B) were obtained from 13 subjects with dementia (10 with AD) using a regression model in which the two SCN neurotransmitters (vasopressin and neurotensin) were included as two factors (See Model 1 in ). (C) α₁-α₂ was correlated with the number of vasopressin-positive SCN neurons after adjusting for the effect of AD severity as characterized by the plaque density from occipital Bielschowsky stain. (D) α₁-α₂ was correlated with the AD severity after adjusted for the effect of the number of vasopressin-positive SCN neurons. Results in (C) and (D) were obtained from 13 subjects with dementia (9 with AD) using a regression model in which vasopressin neuronal density and plaque density were included as two factors (see Model 2 in ).

Only neurotensin neuronal density (not assessed in 1 AD and 1 frontotemporal dementia patients) was significantly associated with plaque density (R² = 0.35, p = 0.016), i.e., patients with more plaques had fewer neurotensin-positive SCN neurons.

(A) Simulated 72-hour activity recording that possesses fractal correlations but no 24-h rhythm. (B) The same signal as shown in A except for an increased activity level between 9AM and 4PM that was used to simulate the environmental influence due scheduled daily events. (C) Fourier amplitudes of the signals shown in (A) and (B). (D) Detrended fluctuation function F(n) of the signals shown in (A) and (B). Daily events led to a significant 24-hour rhythm (C) but barely affected fractal patterns as revealed by detrended fluctuation analysis (D).