Peterson B S, Leckman J F
Yale Child Study Center, Yale University School of Medicine, New Haven, Connecticut, USA.
Biol Psychiatry. 1998 Dec 15;44(12):1337-48. doi: 10.1016/s0006-3223(98)00176-0.
Statistical characterization of tic behavior in Gilles de la Tourette syndrome (GTS) may provide insight into the dynamic functioning of the human central nervous system, as well as improve the quantitative assessment of tic symptom severity.
Twenty-two medication-free GTS subjects underwent videotaping of their tics. The intervals between temporally adjacent tics were measured, and the statistical properties of these intervals were assessed through graphical representation of frequency distributions, autoregressive integrated moving average (ARIMA) modeling, spectral analysis, and construction of first return maps.
The frequency distribution of tic interval durations followed an inverse power law of temporal scaling. Spectral analyses similarly demonstrated that the spectral power density of tic interval duration scales inversely with frequency. ARIMA modeling suggested that the time series for tics are nonstationary as well as moving average processes. The first return maps demonstrated "burstlike" behavior and short-term periodicity in tics, and proved that successive tic intervals are not statistically independent. Graphic display of the time series confirmed shortterm periodicity, and in addition suggested the presence of period doubling.
These findings are suggestive though not conclusive evidence for the presence of a fractal, deterministic, and possibly chaotic process in the tic time series. These analytic methods provide insight into the temporal features of tics that commonly are described clinically (such as short-term bouts or bursting, and longer term waxing and waning), and they reveal certain important temporal features of tics that have not been clinically described. The methods may also prove useful in the improved characterization of tic symptom severity.
抽动秽语综合征（GTS）中抽动行为的统计特征可能有助于深入了解人类中枢神经系统的动态功能，同时改善抽动症状严重程度的定量评估。
22名未服用药物的GTS受试者进行了抽动录像。测量了时间上相邻抽动之间的间隔，并通过频率分布的图形表示、自回归积分移动平均（ARIMA）建模、频谱分析和首次返回映射的构建来评估这些间隔的统计特性。
抽动间隔持续时间的频率分布遵循时间尺度的逆幂律。频谱分析同样表明，抽动间隔持续时间尺度的频谱功率密度与频率成反比。ARIMA建模表明抽动的时间序列是非平稳的以及移动平均过程。首次返回映射显示了抽动中的“爆发样”行为和短期周期性，并证明连续的抽动间隔在统计上不是独立的。时间序列的图形显示证实了短期周期性，此外还表明存在倍周期现象。
这些发现提示了抽动时间序列中存在分形、确定性且可能混沌的过程，但并非确凿证据。这些分析方法有助于深入了解临床上通常描述的抽动的时间特征（如短期发作或爆发，以及长期的波动），并揭示了某些尚未在临床上描述的抽动的重要时间特征。这些方法也可能有助于更好地表征抽动症状的严重程度。
