Brett A. Davis

Optimal modeling of corneal surfaces with Zernike polynomials

Zernike polynomials are often used as an expansion of corneal height data and for analysis of optical wavefronts. Accurate modeling of corneal surfaces with Zernike polynomials involves selecting the order of the polynomial expansion based on the measured data. The authors have compared the efficacy of various classical model order selection techniques that can be utilized for this purpose, and propose an approach based on the bootstrap. First, it is shown in simulations that the bootstrap method outperforms the classical model order selection techniques. Then, it is proved that the bootstrap technique is the most appropriate method in the context of fitting Zernike polynomials to corneal elevation data, allowing objective selection of the optimal number of Zernike terms. The process of optimal fitting of Zernike polynomials to corneal elevation data is discussed and examples are given for normal corneas and for abnormal corneas with significant distortion. The optimal model order varies as a function of the diameter of the cornea.

The accuracy and precision performance of four videokeratoscopes in measuring test surfaces.

In this study we evaluated the accuracy and precision of three placido-disk videokeratoscopes (the Keratron, Medmont and TMS) and one videokeratoscope that uses the raster-stereogrammetry technique (PAR-CTS) in elevation topography with six test surfaces. The test surfaces were a sphere, an asphere, a multicurve, and three bicurve surfaces. Each instrument performed well on certain test surfaces, but none of the instruments excelled on all of the surfaces. The results showed high accuracy of the Keratron and Medmont instruments in measuring the sphere, asphere, and multicurve surfaces, but not the bicurve surfaces. The precision of the Keratron and Medmont instruments were high. The TMS and PAR-CTS instruments showed poorer accuracy than the Keratron and Medmont instruments for the multicurve test surface but showed better performance for the bicurve surfaces. The PAR-CTS had the poorest performance in precision of the four instruments. The use of the Noryl spherical test surface instead of polymethyl methacrylate (PMMA) resulted in small differences in the accuracy performance of the placido-disk videokeratoscopes only.

Corneal topography with Scheimpflug imaging and videokeratography: Comparative study of normal eyes

PURPOSE: To compare the repeatability within anterior corneal topography measurements and agreement between measurements with the Pentacam HR rotating Scheimpflug camera and with a previously validated Placido disk–based videokeratoscope (Medmont E300). SETTING: Contact Lens and Visual Optics Laboratory, School of Optometry, Queensland University of Technology, Brisbane, Queensland, Australia. METHODS: Normal eyes in 101 young adult subjects had corneal topography measured using the Scheimpflug camera (6 repeated measurements) and videokeratoscope (4 repeated measurements). The best‐fitting axial power corneal spherocylinder was calculated and converted into power vectors. Corneal higher‐order aberrations (HOAs) (up to the 8th Zernike order) were calculated using the corneal elevation data from each instrument. RESULTS: Both instruments showed excellent repeatability for axial power spherocylinder measurements (repeatability coefficients <0.25 diopter; intraclass correlation coefficients >0.9) and good agreement for all power vectors. Agreement between the 2 instruments was closest when the mean of multiple measurements was used in analysis. For corneal HOAs, both instruments showed reasonable repeatability for most aberration terms and good correlation and agreement for many aberrations (eg, spherical aberration, coma, higher‐order root mean square). For other aberrations (eg, trefoil and tetrafoil), the 2 instruments showed relatively poor agreement. CONCLUSIONS: For normal corneas, the Scheimpflug system showed excellent repeatability and reasonable agreement with a previously validated videokeratoscope for the anterior corneal axial curvature best‐fitting spherocylinder and several corneal HOAs. However, for certain aberrations with higher azimuthal frequencies, the Scheimpflug system had poor agreement with the videokeratoscope; thus, caution should be used when interpreting these corneal aberrations with the Scheimpflug system.

Microfluctuations of steady-state accommodation and the cardiopulmonary system.

The relationship between variations in steady-state accommodation (microfluctuations) and rhythmic cycles in cardiopulmonary system was investigated. As previously reported, vascular pulse frequency was consistently correlated with the high frequency component of steady-state accommodation microfluctuations. In a new finding, respiration rate and an associated cycle in the instantaneous pulse rate also showed a correlation with a low frequency component of the accommodation power spectra. This apparent coherence between respiration frequency and an accommodation low frequency component was maintained during rapid breathing and was evident at the expected frequency during regulated breathing patterns. This association may reflect the direct influence of the autonomic nervous system upon the ciliary muscle or may be caused by the modulation of intraocular pulse by the autonomic nervous system.

Modeling of corneal surfaces with radial polynomials

We consider analytical modeling of the anterior corneal surface with a set of orthogonal basis functions that are a product of radial polynomials and angular functions. Several candidate basis functions were chosen from the repertoire of functions that are orthogonal in the unit circle and invariant in form with respect to rotation about the origin. In particular, it is shown that a set of functions that is referred herein as Bhatia-Wolf polynomials, represents a better and more robust alternative for modeling corneal elevation data than traditionally used Zernike polynomials. Examples of modeling corneal elevation are given for normal corneas and for abnormal corneas with significant distortion.

The relation between corneal and total astigmatism

Using computer-assisted videokeratoscopy we measured corneal astigmatism and compared these results over a range of corneal zone diameters with total ocular astigmatism derived by subjective refraction. Videokeratoscopes permit a more detailed analysis of the power distribution within a given corneal surface area, enabling comparison to the total astigmatism for equivalent aperture sizes. Although there were significant individual variations, the group average data supports the traditional view of a linear relation between corneal and total astigmatism. This was true across the range of apertures tested from 2 to 7 mm, with the coordinates of the relation being consistent with that of the modified Javals rule; namely a slope of 1 and an intercept of approximately 0.50 D against-the-rule residual astigmatism.

Eyelid pressure and contact with the ocular surface.

Purpose. To investigate static upper eyelid pressure and contact with the ocular surface in a group of young adult subjects. Methods. Static upper eyelid pressure was measured for 11 subjects using a piezoresistive pressure sensor attached to a rigid contact lens. Measures of eyelid pressure were derived from an active pressure cell (1.14-mm square) beneath the central upper eyelid margin. To investigate the contact region between the upper eyelid and the ocular surface, the authors used pressure-sensitive paper and the lissamine-green staining of Marxs line. These measures, combined with the pressure sensor readings, were used to derive estimates of eyelid pressure. Results. The mean contact width between the eyelids and the ocular surface estimated using pressure-sensitive paper was 0.60 +/- 0.16 mm, whereas the mean width of Marxs line was 0.09 +/- 0.02 mm. The mean central upper eyelid pressure was calculated to be 3.8 +/- 0.7 mm Hg (assuming that the whole pressure cell was loaded), 8.0 +/- 3.4 mm Hg (derived using the pressure-sensitive paper imprint widths), and 55 +/- 26 mm Hg (based on contact widths equivalent to Marxs line). Conclusions. The pressure-sensitive paper measurements suggested that a band of the eyelid margin, significantly larger than the anatomic zone of the eyelid margin known as Marxs line, had primary contact with the ocular surface. Using these measurements as the contact between the eyelid margin and the ocular surface, the authors believe that the mean pressure of 8.0 +/- 3.4 mm Hg is the most reliable estimate of static upper eyelid pressure.

Eyelid pressure: inferences from corneal topographic changes.

Purpose: It is known that eyelid pressure can influence the corneal surface. However, the distribution of eyelid pressure and the eyelid contact area and the biomechanics of the changes are unknown. Although these factors are difficult to directly measure, analysis of eyelid-induced corneal topographic changes and eyelid morphometry enables some inferences to be drawn. Methods: Eighteen subjects, aged between 19 and 29 years, with normal ocular health were recruited. Corneal topographic changes were measured after 4 conditions consisting of 2 downward gaze angles (20 and 40 degrees) and 2 types of visual tasks (reading and steady fixation). Digital photography recorded the width of Marx line, the assumed region of primary eyelid contact with the cornea. Results: Significantly larger corneal changes were found after the 40-degree downward gaze conditions compared with 20-degree conditions because of the upper eyelid contact (P < 0.001). For the 40-degree downward gaze tasks, the lower eyelid changes were greater than those because of the upper eyelid (P < 0.01). The upper eyelid Marx line width was associated with the amplitude of corneal change (R2 = 0.32, P < 0.05). Conclusions: Analysis of the corneal topographic changes gives insight into the pressure applied by the upper and lower eyelids in different situations. These include greater upper eyelid pressure with increasing downward gaze and greater lower eyelid pressure compared with the upper eyelid in 40-degree downward gaze. There was some evidence that supports Marx line as the primary site of contact between the eyelid margins and the cornea.

Corneal refractive changes due to short-term eyelid pressure in downward gaze.

PURPOSE: To assess corneal refractive changes after 15‐minute visual tasks and their association with eyelid morphology. SETTING: Contact Lens and Visual Optics Laboratory, School of Optometry, Queensland University of Technology, Brisbane, Queensland, Australia. METHODS: Eighteen young subjects with normal ocular health were recruited. Corneal topography was measured with a videokeratoscope before and after 4 conditions consisting of 2 downward gaze angles (20 degrees and 40 degrees) and 2 types of visual tasks (reading and steady fixation). Anterior eye photography in downward gaze was used to determine the eyelid angle, tilt, and position with respect to the cornea. RESULTS: Corneal refractive power changed significantly after the 15‐minute downward gaze tasks. The largest mean corneal spherocylindrical change was +0.33 −0.30 × 84 after reading in the 40‐degree downward gaze (4.0 mm corneal diameter). The refractive changes were significantly larger after the 40‐degree tasks than after the 20‐degree tasks (P<.001). The changes in refractive root‐mean‐square error were significant for all conditions, except the 20‐degree steady fixation task, with 4.0 and 6.0 mm analysis diameters (P<.05). Significant correlations were found between some aspects of eyelid morphometry and corneal refractive change. CONCLUSIONS: The pressure of the eyelids on the cornea in short‐term downward gaze resulted in optically and clinically relevant corneal changes. Correlation between the refractive corneal changes and eyelid parameters suggests that the angle, shape, and position of the eyelids influence the nature of the corneal changes. When high accuracy is required, refraction should be qualified by the visual tasks undertaken before assessment.

Regional changes in corneal thickness and shape with soft contact lenses.

Purpose. To investigate the influence of soft contact lenses on regional variations in corneal thickness and shape while taking account of natural diurnal variations in these corneal parameters. Methods. Twelve young, healthy subjects wore four different types of soft contact lenses on four different days. The lenses were of two different materials (silicone hydrogel or hydrogel), designs (spherical or toric), and powers (3.00 or −7.00 diopter). Corneal thickness and topography measurements were taken before and after 8 h of lens wear and on 2 days without lens wear, using the Pentacam HR system. Results. The hydrogel toric contact lens caused the greatest level of corneal thickening in the central (20.3 ± 10.0 &mgr;m) and peripheral cornea (24.1 ± 9.1 &mgr;m) (p < 0.001) with an obvious regional swelling of the cornea beneath the stabilizing zones. The anterior corneal surface generally showed slight flattening. All contact lenses resulted in central posterior corneal steepening, and this was weakly correlated with central corneal swelling (p = 0.03) and peripheral corneal swelling (p = 0.01). Conclusions. There was an obvious regional corneal swelling apparent after wear of the hydrogel soft toric lenses because of the location of the thicker stabilization zones of the toric lenses. However, with the exception of the hydrogel toric lens, the magnitude of corneal swelling induced by the contact lenses over the 8 h of wear was less than the natural diurnal thinning of the cornea over this same period.