Faculty of Biology, Medicine and Health, University of Manchester, Manchester, M13 9PT, UK.
College of Engineering, Mathematics and Physical Sciences, University of Exeter, Exeter, UK.
Sci Rep. 2021 May 7;11(1):9761. doi: 10.1038/s41598-021-89094-7.
We present a new computational approach to analyse nystagmus waveforms. Our framework is designed to fully characterise the state of the nystagmus, aid clinical diagnosis and to quantify the dynamical changes in the oscillations over time. Both linear and nonlinear analyses of time series were used to determine the regularity and complexity of a specific homogenous phenotype of nystagmus. Two-dimensional binocular eye movement recordings were carried out on 5 adult subjects who exhibited a unilateral, uniplanar, vertical nystagmus secondary to a monocular late-onset severe visual loss in the oscillating eye (the Heimann-Bielschowsky Phenomenon). The non-affected eye held a central gaze in both horizontal and vertical planes (± 10 min. of arc). All affected eyes exhibited vertical oscillations, with mean amplitudes and frequencies ranging from 2.0°-4.0° to 0.25-1.5 Hz, respectively. Unstable periodic orbit analysis revealed only 1 subject exhibited a periodic oscillation. The remaining subjects were found to display quasiperiodic (n = 1) and nonperiodic (n = 3) oscillations. Phase space reconstruction allowed attractor identification and the computation of a time series complexity measure-the permutation entropy. The entropy measure was found to be able to distinguish between a periodic oscillation associated with a limit cycle attractor, a quasiperiodic oscillation associated with a torus attractor and nonperiodic oscillations associated with higher-dimensional attractors. Importantly, the permutation entropy was able to rank the oscillations, thereby providing an objective index of nystagmus complexity (range 0.15-0.21) that could not be obtained via unstable periodic orbit analysis or attractor identification alone. These results suggest that our framework provides a comprehensive methodology for characterising nystagmus, aiding differential diagnosis and also permitting investigation of the waveforms over time, thereby facilitating the quantification of future therapeutic managements. In addition, permutation entropy could provide an additional tool for future oculomotor modelling.
我们提出了一种新的计算方法来分析眼球震颤波形。我们的框架旨在全面描述眼球震颤的状态，辅助临床诊断，并量化随时间变化的振荡的动态变化。使用线性和非线性时间序列分析来确定特定同质性眼球震颤表型的规则性和复杂性。对 5 名成年受试者进行了二维双眼眼球运动记录，这些受试者的摆动眼（Heimann-Bielschowsky 现象）单眼出现晚期严重视力丧失后出现单侧、单平面、垂直眼球震颤。未受影响的眼睛在水平和垂直平面上保持中心注视（± 10 分钟弧）。所有受影响的眼睛均表现出垂直摆动，平均幅度和频率分别为 2.0°-4.0°至 0.25-1.5 Hz。不稳定周期轨道分析显示只有 1 名受试者表现出周期性摆动。其余受试者被发现表现出准周期性（n=1）和非周期性（n=3）摆动。相空间重建允许识别吸引子并计算时间序列复杂度度量-置换熵。熵度量能够区分与极限环吸引子相关的周期性摆动、与环面吸引子相关的准周期性摆动以及与高维吸引子相关的非周期性摆动。重要的是，置换熵能够对摆动进行排序，从而提供眼球震颤复杂性的客观指标（范围 0.15-0.21），这是无法通过不稳定周期轨道分析或吸引子识别单独获得的。这些结果表明，我们的框架为描述眼球震颤、辅助鉴别诊断以及研究随时间变化的波形提供了一种全面的方法，从而有助于未来治疗管理的量化。此外，置换熵可以为未来的眼球运动建模提供额外的工具。
