Circadian component of actigraphy data.

<p>Shown for the control (upper panel) and the acute insomnia subject (bottom panel) of <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0181762#pone.0181762.g001" target="_blank">Fig 1</a>. The circadian rhythm has been fitted using the model-based cosinor method according to <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0181762#pone.0181762.e002" target="_blank">Eq (2)</a> (dashed curve) and the data-adaptive SSA method using the periodic components <i>g</i>₂(<i>n</i>) and <i>g</i>₃(<i>n</i>) of <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0181762#pone.0181762.e010" target="_blank">Eq (7)</a> (full curve). Vertical gridlines at midnight.</p

Acrophase <i>ϕ</i>₀(<i>t</i>) as a function of time.

<p>Results for the subjects of <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0181762#pone.0181762.g001" target="_blank">Fig 1</a>. Within the cosinor approach (dashed lines), the deviation from the ideal 24h circadian cycle is small for the control subject, Δ<i>T</i> = +3min, such that <i>ϕ</i>₀(<i>t</i>) is rather constant (blue dashed line), whereas for the subject with acute insomnia the circadian deviation is larger, Δ<i>T</i> = −24min, and <i>ϕ</i>₀(<i>t</i>) is a downsloping linear function (red dashed line). SSA (continuous lines) allows to calculate the day-to-day variability of acrophase <i>ϕ</i>₀(<i>t</i>), and are found to fluctuate around the average behaviour obtained within the cosinor approach.</p

Fractal scaling parameters according to SSA analysis.

<p>Box-whisker plots of the scaling exponent of the power law <i>λ</i>_<i>k</i> ∝ 1/<i>k</i>^<i>γ</i> at larger scales (exponent <i>γ</i>₁) and at smaller scales (exponent <i>γ</i>₂) before and after log₁₀ <i>k</i> = 1.5, shown for the control subjects which follow a single power law (blue) and subjects with acute insomnia which exhibit a crossover (red).</p

Day-to-day variability of circadian parameters according to SSA analysis.

<p>Histogram of acrophase <i>ϕ</i>₀, box-whisker plots of standard deviation (SD) and kurtosis (Kurt) of acrophase <i>ϕ</i>₀ (with Kurt = 3 for a gaussian distribution as a reference), and coefficient of variation CV = SD/mean of amplitude <i>A</i>, for the controls (blue) and the acute insomnia subjects (red).</p

SSA scree diagram of ordered fractional partial variances.

<p>Fractional partial variances <i>λ</i>_<i>k</i>/<i>λ</i>_tot ordered from the most dominant <i>λ</i>₁/<i>λ</i>_tot corresponding to the non-oscillating trend or mesor, and (<i>λ</i>₂ + <i>λ</i>₃)/<i>λ</i>_tot corresponding to the periodic circadian cycle, down to higher-order <i>λ</i>_<i>k</i>/<i>λ</i>_tot with <i>k</i> ≥ 4 corresponding to ultradian fluctuations. In the case of the control subjects (blue), fractional partial variances follow a power law <i>λ</i>_<i>k</i>/<i>λ</i>_tot ∝ 1/<i>k</i>^<i>γ</i> with power-law exponent <i>γ</i> ≈ 1 (negative of the slope of the scree diagram in log-log scale), whereas in the case of the acute insomnia subjects (red) this power law is broken because of an increased variability around 〈<i>f</i>〉 = 1/90min, these differences are statistically significant in the range 1.4 ≤ log₁₀ <i>k</i> ≤ 1.6 (shaded region).</p

1-week continuous actigraphy time series.

<p>Shown for a specific control subject (female, 24yo, left-hand panels) and a subject with acute insomnia (male, 22yo, right-hand panels). Shown for 7 successive days (24h per panel), from midnight till midnight, with vertical gridlines at 6h intervals at 00:00, 06:00, 12:00, 18:00 and 24:00 hours. Vertical scale is identical for both subjects, from 0 to 3000 movement counts per minute.</p

Parameter values of the circadian and ultradian rhythms according SSA analysis.

<p>Parameter values of the circadian and ultradian rhythms according SSA analysis.</p

Circadian parameters according to cosinor analysis.

<p>Box-whisker plots for period <i>T</i> with respect to the ideal period of <i>T</i>₀ = 24h = 1440min (dashed horizontal line), and 7-day average acrophase <i>ϕ</i>₀ (°).</p

Mean 24h profile of actigraphy time series.

<p>Averaged over 7 days and over all control subjects (blue curve) and over all subjects with acute insomnia (red curve). Vertical gridlines at 6h intervals. Significant (<i>p</i> < 0.05) minute-to-minute differences are observed between the 2 groups for rest-to-wake (07:22–09:01) and wake-to-rest (23:01–24:00) transitions (orange shading).</p

Intradaily variability <i>IV</i>(<i>P</i>) as a function of sample interval.

<p>Calculated according to <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0181762#pone.0181762.e009" target="_blank">Eq (6)</a>. Shown for the population of asymptomatic controls (blue) and acute insomnia subjects (red). Vertical gridline at traditional sample interval <i>P</i> = 60min.</p