Chaos in ocular aberration dynamics of the human eye

The effect of image resolution of display types on accommodative microfluctuations

PURPOSE

To determine whether accommodative microfluctuations (AMFs) are affected by the image resolution of the display type being observed. The effect of refractive error is also examined.

METHODS

Twenty participants, (10 myopes and 10 emmetropes) observed a target on four different displays: paper, smartphone, e-reader and visual display unit screen (VDU), whilst their accommodative responses were measured using a continuous recording infrared autorefractor. The accommodative response and AMF measures comprising low frequency components (LFC), high frequency components (HFC) and the root mean square (RMS) of the AMFs were analysed.

RESULTS

A significant increase in LFC power was observed for the paper stimulus when compared to the VDU and smartphone conditions. Myopes demonstrated a significantly higher LFC and mean accommodative response compared to emmetropes across the four displays. A significant difference in the mean AR between the displays with the lowest and highest resolution was found. A higher mean AR was found with higher resolution of the image. The HFC and RMS accommodation were not affected by display type.

CONCLUSION

The mean accommodative response and the mean LFC power appear to respond differently depending on the type of display in use. Higher resolution devices showed a reduced lag of accommodation to the accommodative demand; however, this may cause a lead of accommodation in myopes for higher resolution display types.

The random walk of accommodation fluctuations

The focusing distance of the eye fluctuates during accommodation. However, the visual role of these accommodation fluctuations is not yet fully understood. The fluctuation complexity is one of the obstacles to this long standing challenge in visual science. In this work we seek to develop a statistical approach that i) accurately describes experimental measurements and ii) directly generates randomized and realistic simulations of accommodation fluctuations for use in future experiments. To do so we use the random walk approach, which is usually appropriate to describe the dynamics of systems that combine both randomness and memory.

Adaptive optics imaging of the human retina

Adaptive Optics (AO) retinal imaging has provided revolutionary tools to scientists and clinicians for studying retinal structure and function in the living eye. From animal models to clinical patients, AO imaging is changing the way scientists are approaching the study of the retina. By providing cellular and subcellular details without the need for histology, it is now possible to perform large scale studies as well as to understand how an individual retina changes over time. Because AO retinal imaging is non-invasive and when performed with near-IR wavelengths both safe and easily tolerated by patients, it holds promise for being incorporated into clinical trials providing cell specific approaches to monitoring diseases and therapeutic interventions. AO is being used to enhance the ability of OCT, fluorescence imaging, and reflectance imaging. By incorporating imaging that is sensitive to differences in the scattering properties of retinal tissue, it is especially sensitive to disease, which can drastically impact retinal tissue properties. This review examines human AO retinal imaging with a concentration on the use of the Adaptive Optics Scanning Laser Ophthalmoscope (AOSLO). It first covers the background and the overall approaches to human AO retinal imaging, and the technology involved, and then concentrates on using AO retinal imaging to study the structure and function of the retina.

Cognitive Demand and Accommodative Microfluctuations

Previous studies have shown cognition to have an influence on accommodation. Temporal variation in the accommodative response occurs during the fixation on a stationary target. This constantly shifting response has been called accommodative micro-fluctuations (AMFs). The aim of this study is to determine the effects of increasing task cognitive demand on the ocular accommodation response. AMFs for 12 myopes and 12 emmetropes were measured under three conditions of varying cognitive demand and comprising reading of numbers (Num), simple arithmetic (SA), and complex arithmetic (CA). Fast Fourier transforms were used to analyze the different frequency band components of the AMFs. Other aspects of AMFs including root mean square accommodation values and chaos analysis was applied. A repeated measures ANOVA revealed a significant main effect of cognition in the mean power of the high frequency component (HFC) (F_2,44 = 10.03, p < 0.005). Pairwise analyses revealed that these differences exist between SA and CA tasks (p < 0.005) and the Num and CA (p < 0.005) tasks with the HFC power being the highest for the CA condition. It appears that the difficulty of a task does affect active accommodation but to a lesser extent than other factors affecting accommodation.

Sensitivity of Chaos Measures in Detecting Stress in the Focusing Control Mechanism of the Short-Sighted Eye

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 (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$0.64\pm 0.33$$\end{document}0.64±0.33 vs. \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$0.39\pm 0.20~\hbox {D}/\hbox {s}$$\end{document}0.39±0.20D/s) and a lower embedding dimension than the LOMs (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$3.28\pm 0.46$$\end{document}3.28±0.46 vs. \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$3.67\pm 0.49$$\end{document}3.67±0.49). 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.

Significance of using a nonlinear analysis technique, the Lyapunov exponent, on the understanding of the dynamics of the cardiorespiratory system in rats

BACKGROUND/AIM

Pneumocardiography (PNCG) is the recording method of cardiac-induced tracheal air flow and pressure pulsations in the respiratory airways. PNCG signals reflect both the lung and heart actions and could be accurately recorded in spontaneously breathing anesthetized rats. Nonlinear analysis methods, including the Lyapunov exponent, can be used to explain the biological dynamics of systems such as the cardiorespiratory system.

MATERIALS AND METHODS

In this study, we recorded tracheal air flow signals, including PNCG signals, from 3 representative anesthetized rats and analyzed the nonlinear behavior of these complex signals using Lyapunov exponents.

RESULTS

Lyapunov exponents may also be used to determine the normal and pathological structure of biological systems. If the signals have at least one positive Lyapunov exponent, the signals reflect chaotic activity, as seen in PNCG signals in rats; the largest Lyapunov exponents of the signals of the healthy rats were greater than zero in this study.

CONCLUSION

A method was proposed to determine the diagnostic and prognostic values of the cardiorespiratory system of rats using the arrangement of the PNCG and Lyapunov exponents, which may be monitored as vitality indicators.

Are the fluctuations in dynamic anterior surface aberrations of the human eye chaotic?

The purpose of the study is to measure chaos in dynamic anterior surface aberrations and examine how it varies between the eyes of an individual. Noninvasive tear breakup time and dynamic corneal surface aberrations were measured for two open-eye intervals of 15 s. The maximal Lyapunov exponent (MLE) was calculated to test the nature of the fluctuations of the dynamic anterior surface aberrations. The average MLE for total higher-order aberration (HOA) was found to be small (+0.0102±0.0072) μm/s. No significant difference in MLE was found between the eyes for HOA (t-test; p=0.131). Data analysis was carried out for individual Zernike coefficients, including vertical prism as it gives a direct measure of the thickness of the tear film over time. The results show that the amount of chaos was small for each Zernike coefficient and not significantly correlated between the eyes.

Effect of correction of aberration dynamics on chaos in human ocular accommodation

We used adaptive optics to determine the effect of monochromatic aberration dynamics on the level of chaos in the accommodation control system. Four participants viewed a stationary target while the dynamics of their aberrations were either left uncorrected, defocus was corrected, or all aberrations except defocus were corrected. Chaos theory analysis was used to discern changes in the accommodative microfluctuations. We found a statistically significant reduction in the chaotic nature of the accommodation microfluctuations during correction of defocus, but not when all aberrations except defocus were corrected. The Lyapunov exponent decreased from 0.71 ± 0.07 D/s (baseline) to 0.55 ± 0.03 D/s (correction of defocus fluctuations). As the reduction of chaos in physiological signals is indicative of stress to the system, the results indicate that for the participants included in this study, fluctuations in defocus have a more profound effect than those of the other aberrations. There were no changes in the power spectrum between experimental conditions. Hence chaos theory analysis is a more subtle marker of changes in the accommodation control system and will be of value in the study of myopia onset and progression.

Correspondence of chaos in binocular aberration dynamics

We used a binocular Shack-Hartmann sensor to measure the aberration dynamics of six participants at a rate of 21 Hz. Chaos theory analysis was used to determine the Lyapunov exponent for the time evolution of the rms wavefront error, accommodation, and each individual Zernike coefficient up to and including the fifth radial order. In all cases there was no statistically significant difference between the Lyapunov exponents between the two eyes, suggesting that the level of chaos is common between them. The mean Lyapunov exponent averaged across both eyes of all participants was 0.42±0.14 μm/s for the rms wavefront error, 0.37±0.06 D/s for accommodation, and 0.32±0.09 μm/s averaged across Zernike coefficients. We found no statistically significant correlation per se between the eyes, except for horizontal coma. The correlation may be masked by the impact of differing tear film dynamics. Understanding the nature of aberration dynamics has utility in optimizing the performance of adaptive optics systems for the human eye.