Complexity of Body Movements during Sleep in Children with Autism Spectrum Disorder

Abstract

Recently, measuring the complexity of body movements during sleep has been proven as an objective biomarker of various psychiatric disorders. Although sleep problems are common in children with autism spectrum disorder (ASD) and might exacerbate ASD symptoms, their objectivity as a biomarker remains to be established. Therefore, details of body movement complexity during sleep as estimated by actigraphy were investigated in typically developing (TD) children and in children with ASD. Several complexity analyses were applied to raw and thresholded data of actigraphy from 17 TD children and 17 children with ASD. Determinism, irregularity and unpredictability, and long-range temporal correlation were examined respectively using the false nearest neighbor (FNN) algorithm, information-theoretic analyses, and detrended fluctuation analysis (DFA). Although the FNN algorithm did not reveal determinism in body movements, surrogate analyses identified the influence of nonlinear processes on the irregularity and long-range temporal correlation of body movements. Additionally, the irregularity and unpredictability of body movements measured by expanded sample entropy were significantly lower in ASD than in TD children up to two hours after sleep onset and at approximately six hours after sleep onset. This difference was found especially for the high-irregularity period. Through this study, we characterized details of the complexity of body movements during sleep and demonstrated the group difference of body movement complexity across TD children and children with ASD. Complexity analyses of body movements during sleep have provided valuable insights into sleep profiles. Body movement complexity might be useful as a biomarker for ASD.

Keywords: accelerometer; actigraphy; circadian rhythm disruption; detrended fluctuation analysis (DFA); entropy-based methods; expanded sample entropy (expSampEn); false nearest neighbors (FNN); information theory; insomnia; long-range temporal correlation.

Figure 1

Surrogate data generated by the iterative amplitude-adjusted Fourier transform (IAAFT) algorithm: examples of original time series (left) and its surrogate (middle). The mean power spectral density (PSD) of TD, ASD, and surrogates (right). No significant difference of PSD was found among TD (blue), ASD (orange), and surrogates (gray). TD, typically developing children; ASD, children with autism spectrum disorder.

Figure 2

Thresholds of TD children and children with ASD. The median value of each time series was used as the threshold. No significant difference was found between TD and ASD. Error bars represent the standard deviation of the thresholds.

Figure 3

Time delay and false nearest neighbor (FNN). Upper and lower panels respectively show those of raw data and thresholded data. Left panels—Median values of autocorrelation time were set to the time delay for the FNN method (raw data, 116 s; thresholded data, 347 s). Orange lines, boxes, and whiskers respectively, indicate the median, percentiles 25 and 75, and minimum and maximum of autocorrelation time of all subjects. Right panels—Tests I and II respectively signify FNN for Equations (2) and (3) (see Section 2.4.1). The shaded areas represent the standard deviation of the fraction of FNN. For neither raw nor thresholded data did the fraction of FNN converge to zero.

Figure 4

ApEn and SampEn for raw and thresholded data. Time scales are 30, 100, and 300 s. No significant difference between TD children and children with ASD was found for either raw or thresholded data on any time scale, although significant differences were found between original and surrogate data. ApEn, approximate entropy; SampEn, sample entropy; n.s., not significant (p ≥ 0.05); *, p < 0.001.

Figure 5

expSampEn time series are shown (moving-averaged over 60 min). (A) Typical examples of the expSampEn time series of raw and thresholded data. Both are measured on the same day for the same subject. (B) Left and right panels respectively show expSampEn for raw data and thresholded data. Time scales are 30 (upper panels), 100 (middle panels), and 300 s (lower panels). The solid line and the shaded area respectively show the mean and the standard error. Green shading represents that the expSampEn is significantly lower in ASD than in TD (p < 0.05).

Figure 6

DFA for raw and thresholded data. The log–log plot shows the mean of F(τ). The bar plot shows the mean ± SD of exponent α. Exponent α of surrogates were significantly lower than that of TD and ASD children for thresholded data. n.s., not significant (p ≥ 0.05); * p < 0.001.