Sapir Nir, Karasik Roman, Havlin Shlomo, Simon Ely, Hausdorff Jeffrey M
Department of Physics and Gonda-Goldschmied Medical Diagnostic Research Center, Bar-Ilan University, Ramat-Gan 52900, Israel.
Phys Rev E Stat Nonlin Soft Matter Phys. 2003 Mar;67(3 Pt 1):031903. doi: 10.1103/PhysRevE.67.031903. Epub 2003 Mar 11.
Patients with Parkinson's disease exhibit tremor, involuntary movement of the limbs. The frequency spectrum of tremor typically has broad peaks at "harmonic" frequencies, much like that seen in other physical processes. In general, this type of harmonic structure in the frequency domain may be due to two possible mechanisms: a nonlinear oscillation or a superposition of (multiple) independent modes of oscillation. A broad peak spectrum generally indicates that a signal is semiperiodic with a fluctuating period. These fluctuations may posses intrinsic order that can be quantified using scaling analysis. We propose a method to extract the correlation (scaling) properties in the period dynamics of multimodal oscillations, in order to distinguish between a nonlinear oscillation and a superposition of individual modes of oscillation. The method is based on our finding that the information content of the temporal correlations in a fluctuating period of a single oscillator is contained in a finite frequency band in the power spectrum, allowing for decomposition of modes by bandpass filtering. Our simulations for a nonlinear oscillation show that harmonic modes possess the same scaling properties. In contrast, when the method is applied to tremor records from patients with Parkinson's disease, the first two modes of oscillations yield different scaling patterns, suggesting that these modes may not be simple harmonics, as might be initially assumed.
帕金森病患者会出现震颤，即肢体的不自主运动。震颤的频谱通常在“谐波”频率处有宽峰，这与在其他物理过程中看到的情况非常相似。一般来说，频域中的这种谐波结构可能归因于两种可能的机制：非线性振荡或（多个）独立振荡模式的叠加。宽峰频谱通常表明信号是具有波动周期的半周期信号。这些波动可能具有可以使用标度分析来量化的内在秩序。我们提出了一种方法来提取多模态振荡周期动态中的相关性（标度）特性，以便区分非线性振荡和单个振荡模式的叠加。该方法基于我们的发现，即单个振荡器波动周期中的时间相关性的信息内容包含在功率谱的有限频带中，从而允许通过带通滤波来分解模式。我们对非线性振荡的模拟表明，谐波模式具有相同的标度特性。相比之下，当将该方法应用于帕金森病患者的震颤记录时，前两种振荡模式产生不同的标度模式，这表明这些模式可能不像最初假设的那样是简单的谐波。
