Chaos in ocular aberration dynamics of the human eye

Since the characterization of the eye’s monochromatic aberration fluctuations in 2001, the power spectrum has remained the most widely used method for analyzing their dynamics. However, the power spectrum does not capture the complexities of the fluctuations. We measured the monochromatic aberration dynamics of six subjects using a Shack-Hartmann sensor sampling at 21 Hz. We characterized the dynamics using techniques from chaos theory. We found that the attractor embedding dimension for all aberrations, for all subjects, was equal to three. The embedding lag averaged across aberrations and subjects was 0.31 ± 0.07 s. The Lyapunov exponent of the rms wavefront error was positive for each subject, with an average value of 0.44 ± 0.15 µm/s. This indicates that the aberration dynamics are chaotic. Implications for future modeling are discussed

IN VIVO analysis of ocular morphological changes during phakic accommodation

The principal theme of this thesis is the in vivo examination of ocular morphological changes during phakic accommodation, with particular attention paid to the ciliary muscle and crystalline lens. The investigations detailed involved the application of high-resolution imaging techniques to facilitate the acquisition of new data to assist in the clarification of aspects of the accommodative system that were poorly understood. A clinical evaluation of the newly available Grand Seiko Auto Ref/ Keratometer WAM-5500 optometer was undertaken to assess its value in the field of accommodation research. The device was found to be accurate and repeatable compared to subjective refraction, and has the added advantage of allowing dynamic data collection at a frequency of around 5 Hz. All of the subsequent investigations applied the WAM-5500 for determination of refractive error and objective accommodative responses. Anterior segment optical coherence tomography (AS-OCT) based studies examined the morphology and contractile response of youthful and ageing ciliary muscle. Nasal versus temporal asymmetry was identified, with the temporal aspect being both thicker and demonstrating a greater contractile response. The ciliary muscle was longer in terms of both its anterior (r = 0.49, P <0.001) and overall length (r = 0.45, P = 0.02) characteristics, in myopes. The myopic ciliary muscle does not appear to be merely stretched during axial elongation, as no significant relationship between thickness and refractive error was identified. The main contractile responses observed were a thickening of the anterior region and a shortening of the muscle, particularly anteriorly. Similar patterns of response were observed in subjects aged up to 70 years, supporting a lensocentric theory of presbyopia development. Following the discovery of nasal/ temporal asymmetry in ciliary muscle morphology and response, an investigation was conducted to explore whether the regional variations in muscle contractility impacted on lens stability during accommodation. A bespoke programme was developed to analyse AS-OCT images and determine whether lens tilt and decentration varied between the relaxed and accommodated states. No significant accommodative difference in these parameters was identified, implying that any changes in lens stability with accommodation are very slight, as a possible consequence of vitreous support. Novel three-dimensional magnetic resonance imaging (MRI) and analysis techniques were used to investigate changes in lens morphology and ocular conformation during accommodation. An accommodative reduction in lens equatorial diameter provides further evidence to support the Helmholtzian mechanism of accommodation, whilst the observed increase in lens volume challenges the widespread assertion that this structure is incompressible due to its high water content. Wholeeye MRI indicated that the volume of the vitreous chamber remains constant during accommodation. No significant changes in ocular conformation were detected using MRI. The investigations detailed provide further insight into the mechanisms of accommodation and presbyopia, and represent a platform for future work in this field

Microfluctuations of Wavefront Aberrations of the Eye

The human eye suffers various optical aberrations that degrade the retinal image. These aberrations include defocus and astigmatism, as well as the higher order aberrations that also play an important role in our vision. The optics of the eye are not static, but are continuously fluctuating. The work reported in this thesis has studied the nature of the microfluctuations of the wavefront aberrations of the eye and has investigated factors that influence the microfluctuations. The fluctuations in the ocular surface of the eye were investigated using high speed videokeratoscopy which measures the dynamics of the ocular surface topography. Ocular surface height difference maps were computed to illustrate the changes in the tear film in the inter-blink interval. The videokeratoscopy data was used to derive the ocular surface wavefront aberrations up to the 4th radial order of the Zernike polynomial expension. We examined the ocular surface dynamics and temporal changes in the ocular surface wavefront aberrations in the inter-blink interval. During the first 0.5 sec following a blink, the tear thickness at the upper edge of the topography map appeared to thicken by about 2 microns. The influence of pulse and instantaneous pulse rate on the microfluctuations in the corneal wavefront aberrations was also investigated. The fluctuations in ocular surface wavefront aberrations were found to be uncorrelated with the pulse and instantaneous heart rates. In the clinical measurement of the ocular surface topography using videokeratoscopy, capturing images 2 to 3 seconds after a blink will result in more consistent results. To investigate fluctuations in the wavefront aberrations of the eye and their relation to pulse and respiration frequencies we used a wavefront sensor to measure the dynamics of the aberrations up to the Zernike polynomial 4th radial order. Simultaneously, the subject's pulse rate was measured, from which the instantaneous heart rate was derived. An auto-regressive process was used to derive the power spectra of the Zernike aberration signals, as well as pulse and instantaneous heart rate signals. Linear regression analysis was performed between the frequency components of Zernike aberrations and the pulse and instantaneous heart rate frequencies. Cross spectrum density and coherence analyses were also applied to investigate the relation between fluctuations of wavefront aberrations and pulse and instantaneous heart rate. The correlations between fluctuations of individual Zernike aberrations were also determined. A frequency component of all Zernike aberrations up to the 4th radial order was found to be significantly correlated with the pulse frequency (all > 2R0.51, p2R0.46, p<0.05). The major correlations among Zernike aberrations occurred between second order and fourth order aberrations with the same angular frequencies. Higher order aberrations appear to be related to the cardiopulmonary system in a similar way to that reported for the accommodation signal and pupil fluctuations. A wavefront sensor and high speed videokeratoscopy were used to investigate the contribution of the ocular surface, the effect of stimulus vergence, and refractive error on the microfluctuations of the wavefront aberrations of the eye. The fluctuations of the Zernike wavefront aberrations were quantified by their variations around the mean and using power spectrum analysis. Integrated power was determined in two regions: 0.1 Hz ─ 0.7 Hz (low frequencies) and 0.8 Hz ─ 1.8 Hz (high frequencies). Changes in the ocular surface topography were measured using high speed videokeratoscopy and variations in the ocular wavefront aberrations were calculated. The microfluctuations of wavefront aberrations in the ocular surface were found to be small compared with the microfluctuations of the wavefront aberrations in the total eye. The variations in defocus while viewing a closer target at 2 D and 4 D stimulus vergence were found to be significantly greater than variations in defocus when viewing a far target. This increase in defocus fluctuations occurred in both the low and high frequency regions (all p<0.001) of the power spectra. The microfluctuations in astigmatism and most of the 3rd order and 4th order Zernike wavefront aberrations of the total eye were found to significantly increase with the magnitude of myopia. The experiments reported in this thesis have demonstrated the characteristics of the microfluctuations of the wavefront aberrations of the eye and have shown some of the factors that can influence the fluctuations. Major fluctuation frequencies of the eye's wavefront aberrations were shown to be significantly correlated with the pulse and instantaneous heart rate frequencies. Fluctuations in the ocular surface wavefront aberrations made a small contribution to those of the total eye. Changing stimulus vergence primarily affected the fluctuations of defocus in both low and high frequency components. Variations in astigmatism and most 3rd and 4th order aberrations were associated with refractive error magnitude. These findings will aid our fundamental understanding of the complex visual optics of the human eye and may allow the opportunity for better dynamic correction of the aberrations with adaptive optics