Correlation properties of spontaneous motor activity in healthy infants: a new computer-assisted method to evaluate neurological maturation

Abstract

Qualitative assessment of spontaneous motor activity in early infancy is widely used in clinical practice. It enables the description of maturational changes of motor behavior in both healthy infants and infants who are at risk for later neurological impairment. These assessments are, however, time-consuming and are dependent upon professional experience. Therefore, a simple physiological method that describes the complex behavior of spontaneous movements (SMs) in infants would be helpful. In this methodological study, we aimed to determine whether time series of motor acceleration measurements at 40–44 weeks and 50–55 weeks gestational age in healthy infants exhibit fractal-like properties and if this self-affinity of the acceleration signal is sensitive to maturation. Healthy motor state was ensured by General Movement assessment. We assessed statistical persistence in the acceleration time series by calculating the scaling exponent α via detrended fluctuation analysis of the time series. In hand trajectories of SMs in infants we found a mean α value of 1.198 (95 % CI 1.167–1.230) at 40–44 weeks. Alpha changed significantly (p = 0.001) at 50–55 weeks to a mean of 1.102 (1.055–1.149). Complementary multilevel regression analysis confirmed a decreasing trend of α with increasing age. Statistical persistence of fluctuation in hand trajectories of SMs is sensitive to neurological maturation and can be characterized by a simple parameter α in an automated and observer-independent fashion. Future studies including children at risk for neurological impairment should evaluate whether this method could be used as an early clinical screening tool for later neurological compromise.

Appendices

Appendix 1: Detrended fluctuation analysis (DFA)

Detrended fluctuation analysis has been introduced in medical research to assess vital signals and biofeedback systems. DFA is an extension of fluctuation analysis of non-stationary time series (a signal whose mean and variance dynamics change over time) of stochastic processes to determine self-affinity of the signal and uncover fractal like properties. DFA was implemented according to Peng et al. (1995) as follows: The time series was first integrated and then divided into non-overlapping windows of size n. For each window, a least square first-order approximation was obtained which represents the “trend” in the signal. This first approximation of the integrated signal was denoted y_n(k). By subtracting y_n(k) from the integrated signal y(k), the detrended signal was obtained. This is the approximation error e _n (k) for which the root mean squared error was obtained and denoted

$$ {F_n = }{\sqrt {{\frac {1} {N}} {\sum_{k=1}^{N} {e_n} {{(k)}^2}}}} $$

where N is the number of intervals in the signal. Fn was obtained for several different window lengths n. With increasing window length, the approximation error increased: Log (n) versus log (Fn) gave a monotonically increasing relation that in the context of physiological signals has been found to be linear with slope alpha. Previous research has provided evidence for fractal characteristics in the signal: Fn and n are related via a power-law, thus the linear characteristic of the log–log relation. This scaling behaviour can then be precisely characterized by the value of alpha.

While Peng et al. (1993) have generally interpreted DFA as a measure of long-range correlations, recently Dingwell et al. (2010) and Maraun et al. (2004) proposed the interpretation of DFA as an indicator of persistence and anti-persistence (see “Introduction”). Herein we have followed their approach, thus, our results are interpretated in terms of persistence and anti-persistence of the acceleration time series.

An accelerometer time series with an α of 0.5 indicates a system that is not deterministic and is prone to instabilities, whereas higher α value implies more deterministic behavior with stronger correlations between an accelerated movement and its preceding accelerated movements (=persistence of an acceleration time series).

Appendix 2: Statistical tests using surrogate time series

Following Dingwell and Cusumano (2010), we generated for each measured time series one thousand randomly shuffled surrogates by independently permuting the order of the values in the time series (Hausdorff et al. 1995; Gates and Dingwell 2007; Theiler et al. 1992). These surrogates were used to test the hypothesis that the participants controlled their movements by sending signals to their muscles that are temporally independent from previous signals. The distribution of alpha values displayed by the surrogate time series clearly allows for a rejection of this hypothesis for each participant at a significance level of α = 0.05 (see Tables 5, 6), after correcting the p values for multiple comparison using Bonferroni’s method.

Table 5 Shuffling surrogate analysis MS I

Table 6 Shuffling surrogate analysis MS II

Dingwell and Cusumano (2010) demonstrated that phase-randomized surrogates of stride-length time series and of stride-time time series obtained from young healthy adults walking on a motorized treadmill cannot be distinguished from the original time series in terms of detrended fluctuation analysis. Thereby, the hypothesis cannot be rejected, that subjects independently choose their stride-time and stride-length as temporally correlated auto-regressive (AR) process (Theiler et al. 1992; Schreiber and Schmitz 2000), or more generally as nearly equivalent auto-regressive moving-average (ARMA) process (Theiler et al., p. 81). We investigated to what extent this result applies to time series of motor acceleration measurements in healthy infants (at 40–44 and 50–55 weeks gestational age). Accordingly, we generated for each measured time series one thousand phase-randomized surrogates. That is, for each time series, we computed the Fourier transform, randomized the phase spectrum, and then computed the inverse Fourier transform (Theiler et al. 1992; Schreiber and Schmitz 2000; Dingwell and Cusumano 2000). These surrogates preserve the power spectra and auto-correlation properties of each original time series, thus preserving their statistical persistence.

Based on our results, for almost all participants, the aforementioned hypothesis, now concerning the subjects’ limb acceleration patterns, cannot be rejected. Tables 7 and 8 list the resulting p values from our statistical analysis using phase-randomized surrogate data for MS I and MS II.

Table 7 Phase-randomized surrogate analysis MS I

Table 8 Phase-randomized surrogate analysis MS II

The present work focuses on statistically significant changes in the alpha value of time series of motor acceleration measurements taken at 40–44 and at 50–55 weeks of gestational age and their potential interpretation as an indicator of maturational changes of motor behavior. However, we considered it pertinent to conduct similar tests as the ones performed in Dingwell and Cusumano (2010) in order to investigate potential analogies in the properties of the time series under consideration.

All calculations were conducted in R (R Core Team 2012).

Appendix 3: Sampling frequency issues during measurements

In order to study potential issues with the method of detrended fluctuation analysis that could arise from a low sampling frequency during the measurement, we conducted a simulation study. We investigated the effect of applying detrended fluctuation analysis to a time series obtained from an “original” time series by sampling the time series with a lower sampling rate. This sampling procedure boils down to leaving out one or more consecutive values from the original time series in a periodic manner.

The “original” time series consisted of pink noise generated via simulation. It can be theoretically shown that the alpha value obtained from such a time series should be approximately equal to 1. We generated one thousand such time series and with each one we conducted the sampling procedure with a fixed sampling rate. Different sampling rates were used in order to assess the strength of the effect as the sampling frequency is lowered. For a given sampling rate, the aforementioned procedure yielded one thousand shorter time series. We then compared the alpha value of the original time series with the alpha value of the series obtained via the sampling procedure. We observed a change of the alpha value, which was consistently in the same direction. The distribution of the differences in the alpha values is displayed in Fig. 4.

Fig. 4

Histograms of absolute errors due to subsampling. The distribution of the differences in the alpha values due to sampling frequency issues. Every panel corresponds to a different sampling frequency. The number of data points left out between recorded values are: Upper row, from left to right 1, 2, 3, 4. Lower Row, from left to right 10, 20, 50, 100

Since the sampling procedure generates shorter time series, we also generated additional one thousand pink noise time series of the same length as the ones resulting from the sampling procedure. We compared the distributions of the alpha values in each of the two groups observing a statistically significant difference (p values ≤1.705e−10, Mann–Whitney test, p values ≤1.866e−8, Kolmogorov–Smirnov test).

The mean strength of the effect varied with the sampling frequency used. The introduced relative error (in percentage) ranges from 4.65 %, when leaving out every other value, to 19.37 %, when only every hundredth value is considered (see Fig. 5).

Fig. 5

Relative error due to subsampling

Fortunately, the effect is consistent in direction, suggesting that the errors in the alpha values caused by a low sampling rate during measurement should not jeopardize the validity of our main results. Of central importance for our study is the change in the alpha values during development. While the interpretation of the actual absolute alpha values might be interesting (and controversial, as pointed out in the literature, see, for instance, Maraun et al. 2004), we focused herein more on the change of this value during development. We believe that, as long as we consistently use the same sampling frequency during all measurements, the reported changes in the value of alpha properly quantify the changes in the statistical persistence and anti-persistence properties of the sampled time series. Consequently, the reported changes in the value of alpha might represent a legitimate way of systematically quantifying neurological maturation.

All calculations were conducted in R (R Core Team 2012).