Center for Aerosol Science and Engineering, Department of Energy, Environmental and Chemical Engineering, Washington University in St Louis, St Louis, MO 63110, USA.
Computational and Systems Biology Program, Division of Biology and Biomedical Sciences, Washington University in St Louis, St Louis, MO 63110, USA.
J R Soc Interface. 2022 Feb;19(187):20210742. doi: 10.1098/rsif.2021.0742. Epub 2022 Feb 23.
Tics manifest as brief, purposeless and unintentional movements or noises that, for many individuals, can be suppressed temporarily with effort. Previous work has hypothesized that the chaotic temporal nature of tics could possess an inherent fractality, that is, have neighbour-to-neighbour correlation at all levels of timescale. However, demonstrating this phenomenon has eluded researchers for more than two decades, primarily because of the challenges associated with estimating the scale-invariant, power law exponent-called the fractal dimension -from fractional Brownian noise. Here, we confirm this hypothesis and establish the fractality of tics by examining two tic time series datasets collected 6-12 months apart in children with tics, using random walk models and directional statistics. We find that is correlated with tic severity as measured by the YGTTS total tic score, and that is a sensitive parameter in examining the effect of several tic suppression conditions on the tic time series. Our findings pave the way for using the fractal nature of tics as a robust quantitative tool for estimating tic severity and treatment effectiveness, as well as a possible marker for differentiating typical from functional tics.
抽动表现为短暂、无目的和无意识的运动或声音，对于许多人来说，可以通过努力暂时抑制。以前的工作假设抽动的混沌时间性质可能具有内在的分形性，即在所有时间尺度上都具有邻居到邻居的相关性。然而，由于与估计具有尺度不变性的分数布朗噪声相关的挑战，这种现象已经困扰了研究人员超过二十年。分数布朗噪声的幂律指数 - 称为分形维数。在这里，我们通过使用随机游走模型和方向统计学，检查了在抽动儿童中相隔 6-12 个月收集的两个抽动时间序列数据集，证实了这一假设并确定了抽动的分形性。我们发现与 YGTTS 总抽动评分测量的抽动严重程度相关，并且在检查几种抽动抑制条件对抽动时间序列的影响时，是一个敏感的参数。我们的发现为使用抽动的分形性质作为估计抽动严重程度和治疗效果的稳健定量工具铺平了道路，并且可能是区分典型抽动和功能性抽动的标志物。
