Hampson Karen M, Cufflin Matthew P, Mallen Edward A H
School of Optometry and Vision Science, University of Bradford, Bradford, BD7 1DP, UK.
Bull Math Biol. 2017 Aug;79(8):1870-1887. doi: 10.1007/s11538-017-0310-5. Epub 2017 Jun 21.
When fixating on a stationary object, the power of the eye's lens fluctuates. Studies have suggested that changes in these so-called microfluctuations in accommodation may be a factor in the onset and progression of short-sightedness. Like many physiological signals, the fluctuations in the power of the lens exhibit chaotic behaviour. A breakdown or reduction in chaos in physiological systems indicates stress to the system or pathology. The purpose of this study was to determine whether the chaos in fluctuations of the power of the lens changes with refractive error, i.e. how short-sighted a subject is, and/or accommodative demand, i.e. the effective distance of the object that is being viewed. Six emmetropes (EMMs, non-short-sighted), six early-onset myopes (EOMs, onset of short-sightedness before the age of 15), and six late-onset myopes (LOMs, onset of short-sightedness after the age of 15) took part in the study. Accommodative microfluctuations were measured at 22 Hz using an SRW-5000 autorefractor at accommodative demands of 1 D (dioptres), 2 D, and 3 D. Chaos theory analysis was used to determine the embedding lag, embedding dimension, limit of predictability, and Lyapunov exponent. Topological transitivity was also tested for. For comparison, the power spectrum and standard deviation were calculated for each time record. The EMMs had a statistically significant higher Lyapunov exponent than the LOMs ([Formula: see text] vs. [Formula: see text]) and a lower embedding dimension than the LOMs ([Formula: see text] vs. [Formula: see text]). There was insufficient evidence (non-significant p value) of a difference between EOMs and EMMs or EOMs and LOMs. The majority of time records were topologically transitive. There was insufficient evidence of accommodative demand having an effect. Power spectrum analysis and assessment of the standard deviation of the fluctuations failed to discern differences based on refractive error. Chaos differences in accommodation microfluctuations indicate that the control system for LOMs is under stress in comparison to EMMs. Chaos theory analysis is a more sensitive marker of changes in accommodation microfluctuations than traditional analysis methods.
当注视静止物体时，眼睛晶状体的屈光力会发生波动。研究表明，这些所谓的调节微波动的变化可能是近视发生和发展的一个因素。与许多生理信号一样，晶状体屈光力的波动呈现出混沌行为。生理系统中混沌的破坏或减少表明系统受到压力或存在病变。本研究的目的是确定晶状体屈光力波动的混沌是否随屈光不正（即受试者近视程度）和/或调节需求（即所观察物体的有效距离）而变化。六名正视眼者（EMM，非近视）、六名早发性近视者（EOM，15岁前开始近视）和六名晚发性近视者（LOM，15岁后开始近视）参与了该研究。使用SRW - 5000自动验光仪在1屈光度（D）、2 D和3 D的调节需求下以22赫兹的频率测量调节微波动。采用混沌理论分析来确定嵌入延迟、嵌入维数、可预测性极限和李雅普诺夫指数。还测试了拓扑传递性。为作比较，计算了每次记录的功率谱和标准差。正视眼者的李雅普诺夫指数在统计学上显著高于晚发性近视者（[公式：见原文] 对 [公式：见原文]），且嵌入维数低于晚发性近视者（[公式：见原文] 对 [公式：见原文]）。没有足够证据（p值不显著）表明早发性近视者与正视眼者或早发性近视者与晚发性近视者之间存在差异。大多数时间记录是拓扑传递的。没有足够证据表明调节需求有影响。功率谱分析和波动标准差评估未能辨别出基于屈光不正的差异。调节微波动的混沌差异表明，与正视眼者相比，晚发性近视者的控制系统处于压力之下。混沌理论分析是比传统分析方法更敏感的调节微波动变化指标。
