Refractive indices used by the Haag-Streit Lenstar to calculate axial biometric dimensions

Long-range frequency-domain optical delay line based on a spinning tilted mirror for low-cost ocular biometry

Optical biometers are routinely used to measure intraocular distances in ophthalmic applications such as cataract surgery planning or myopia monitoring. However, due to their high cost and reduced transportability, access to them for screening and surgical planning is still limited in low-resource and remote settings. To increase patients' access to optical biometry we propose a novel low-cost frequency-domain optical delay line (FD-ODL) based on an inexpensive stepper motor spinning a tilted mirror, for integration into a time-domain (TD)-biometer, amenable to a compact footprint. In the proposed FD-ODL, the axial scan range and the A-scan rate are decoupled from one another, as the former only depends on the spinning mirror tilt angle, while the A-scan rate only depends on the motor shaft rotational speed. We characterized the scanning performance and specifications for two spinning mirror tilt angles, and compared them to those of the standard, more expensive FD-ODL implementation, employing a galvanometric scanner for group delay generation. A prototype of the low-cost FD-ODL with a 1.5 deg tilt angle, resulting in an axial scan range of 6.61 mm and an A-scan rate of 10 Hz was experimentally implemented and integrated in a dual sample beam optical low-coherence reflectometry (OLCR) setup with a detour unit to replicate the measurement window around the anterior segment and the retina. The intraocular distances of a model eye were measured with the proposed low-cost biometer and found to be in good agreement with those acquired by a custom swept-source optical coherence tomography (SS-OCT) system and two commercial biometers, validating our novel design.

Comparison of A-Scan ultrasonography and the Lenstar optical biometer in Guinea pig eyes

OBJECTIVE

To compare the biometric parameters provided by A-scan ultrasonography and the Lenstar optical biometer in guinea pig eyes, including anterior segment depth (ASD), lens thickness (LT), vitreous chamber depth (VCD), and axial length (AL), and differences of them between treated form deprivation (FD) eyes and untreated fellow eyes after 4 weeks of FD.

METHODS

Three-week-old guinea pigs (N = 41) were subjected to biometric measurements before monocular FD (baseline) and after a 4-week FD. Statistical analyses including within-subject standard deviation (SD_within), coefficient of variation (CV), and intraclass correlation coefficient (ICC), used to evaluate repeatability for both the A-scan ultrasonography and the Lenstar individually, and correlation and Bland-Altman analyses were used to assess agreement between the two methods. The absolute values of ASD, LT, VCD and AL as measured by the two devices were compared, and the differences of them between treated (T) and untreated fellow (F) eyes (ΔASD, ΔLT, ΔVCD and ΔAL) (Δ = T-F) were compared between the two devices after 4 weeks of FD.

RESULTS

Measurements by the Lenstar (ICC: 0.923-0.994) were more repeatable than A-scan ultrasonography (ICC: 0.825-0.870). There was a high correlation for AL (r = 0.851, P < 0.001), a moderate correlation for VCD (r = 0.571, P < 0.001) and LT (r = 0.423, P < 0.001), and a low correlation for ASD (r = 0.230, P < 0.01) between the two devices. The values for ASD, VCD and AL measured by A-scan ultrasonography were larger than those measured by the Lenstar (all, P < 0.001), while LT provided by A-scan ultrasonography was much smaller than that of the Lenstar (P < 0.001). Bland-Altman plots showed poor agreement of absolute values of the four parameters between the two devices. Moreover, there was a high correlation between both methods for ΔAL (r = 0.704, P < 0.001), a moderate correlation for ΔVCD (r = 0.534, P < 0.001) and ΔASD (r = 0.574, P < 0.001), and no correlation for ΔLT (r = 0.303, P = 0.054). The ΔASD, ΔLT, and ΔAL measurements obtained by A-scan ultrasonography were greater than those obtained by the Lenstar (all, P < 0.001), while ΔVCD was mildly smaller using A-scan ultrasonography (P < 0.05). Bland-Altman plots illustrated there is good agreement of ΔAL, ΔVCD, ΔASD, and ΔLT between the two devices.

CONCLUSIONS

The Lenstar exhibited better repeatability and provided smaller measurements for AL, VCD and ASD than A-scan ultrasonography. Furthermore, a high correlation and a good agreement for the ΔAL was observed between the two devices after a period of FD. In summary, the two devices cannot replace each other directly to obtain absolute values of ASD, LT, VCD and AL, but the Lenstar still can serve as an option in measuring ΔAL between eyes in guinea pig myopia model.

Standardizing sum-of-segments axial length using refractive index models

Optical biometry uses interferometry to measure the axial length (AL) of the eye. Traditionally, one-variable regression formulas have converted the optical path length measured by a biometer to a geometric AL. An alternate calculation of axial length sums the individual segments of the eye (sum-of-segments AL). This calculation has been shown to improve predictions of some intraocular lens power formulas when used in place of traditional axial length. Sum-of-segments ALs are determined from 13 refractive index models. As measured in 1695 eyes, these yield different ocular axial lengths. A path to standardization from these models is presented.

Age-related axial length changes in adults: a review

PURPOSE

To investigate the origins of age-related decreases in axial length in the literature.

METHODS

A literature review was performed, including all articles regarding axial length changes with age. These data were combined with mean body length and education level for the countries of each study to assess their influence in a multivariate analysis. Furthermore, analyses were performed of how optical path length, used by optical biometers to measure axial length, is affected by the known age-related changes in the crystalline lens. The influence of other factors mentioned in the literature was also investigated.

RESULTS

Seventeen cross-sectional studies were found that met the search criteria. The decrease in axial length over time was consistent across most of these studies. However, when plotted as a function of year of birth, mean body length and number of years in school, the data indicated an increase in length. Multivariate analysis confirmed the influence of body length (P = 0.005) and birth year (P = 0.017), but not age (P = 0.50). Meanwhile, the lenticular changes due to aging and cataract formation cause a minor bias in the form of increased axial length measurements. Finally, a gradual thinning of the choroidal arteries was reported to cause an increase in axial length.

CONCLUSION

The age-related decrease in axial length is mainly associated with gradual changes in increased body length and education level, while attenuated by minor biases in measurement procedure and thinning of the choroidal arteries.

Customized models of ocular aberrations across the visual field during accommodation

We aimed to create individual eye models that accurately reproduce the empirical measurements of wave-front aberrations across the visual field at different accommodative states, thus providing a mechanistic explanation for the changes in the eye's aberration structure due to accommodation. Structural parameters of a generic eye model were optimized using optical design software to account for published measurements of wave-front aberrations measured for 19 individuals at 37 test locations over the central 30°-diameter visual field at eight levels of accommodative demand. Biometric data for individual eyes were used as starting values and normative data were used to constrain optimizations to anatomically reasonable values. Customizations of the accommodating eye model accurately accounted for ocular aberrations over the central 30° of visual field with an averaged root mean square fitting error typically below 0.2 μm at any given field location. Optimized structural parameters of the eye models were anatomically reasonable and changed in the expected way when accommodating. Accuracy for representing spherical aberration was significantly improved by relaxing anatomical constraints on the anterior surface of the lens to compensate for not including gradient-index media. Use of the model to compute pan-retinal image quality revealed large penalties of accommodative lag for activating photoreceptor responses to the retinal image.

Matching the LenStar optical biometer to A-Scan ultrasonography for use in small animal eyes with application to tree shrews

We describe an analysis strategy to obtain ultrasonography-matched axial dimensions of small animal eyes using the LenStar biometer. The LenStar optical low-coherence reflectometer is an attractive device for animal research due to its high precision, non-invasiveness, and the ability to measure the axial dimensions of cornea, anterior chamber, lens, vitreous chamber, and axial length. However, this optical biometer was designed for clinical applications in human eyes and its internal analysis provides inaccurate values when used on small eyes due to species-dependent differences in refractive indices and relative axial dimensions. The LenStar uses a near infrared light source to measure optical path lengths (OPLs) that are converted by the LenStar's EyeSuite software into geometrical lengths (GLs) based on the refractive indices and axial dimensions of the human eye. We present a strategy that extracts the OPLs, determines refractive indices specific for the small animal eye of interest and then calculates corrected GLs. The refractive indices are obtained by matching the LenStar values to ultrasonography values in the same eyes. As compared to ultrasounography, we found that the internal calculations of the LenStar underestimate the axial dimensions of all ocular compartments of the tree shrew eye: anterior segment depth by 6.17±4.50%, lens thickness by 1.37±3.06%, vitreous chamber depth by 29.23±2.35%, and axial length by 10.62±1.75%. Using tree shrew-specific refractive indices, the axial dimensions closely matched those measured by ultrasonography for each compartment. Our analysis strategy can be easily translated to other species by obtaining a similar paired data set using ultrasonography and LenStar, and applying our step by step procedures.

Multi-Scale Modeling of Vision-Guided Remodeling and Age-Dependent Growth of the Tree Shrew Sclera During Eye Development and Lens-Induced Myopia

The sclera uses unknown mechanisms to match the eye's axial length to its optics during development, producing eyes with good focus (emmetropia). A myopic eye is too long for its own optics. We propose a multi-scale computational model to simulate eye development based on the assumption that scleral growth is controlled by genetic factors while scleral remodeling is driven by genetic factors and the eye's refractive error. We define growth as a mechanism that changes the tissue volume and mass while remodeling involves internal micro-deformations that are volume-preserving at the macroscale. The model was fitted against longitudinal refractive measurements in tree shrews of different ages and exposed to three different visual conditions: (i) normal development; (ii) negative lens wear to induce myopia; and (iii) recovery from myopia by removing the negative lens. The model was able to replicate the age- and vision-dependent response of the tree shrew experiments. Scleral growth ceased at younger age than scleral remodeling. The remodeling rate decreased as the eye emmetropized but increased at any age when a negative lens was put on. The predictive power of the model was investigated by calculating the susceptibility to scleral remodeling and the response to form deprivation myopia in tree shrews. Both predictions were in good agreement with experimental data that were not used to fit the model. We propose the first model that distinguishes scleral growth from remodeling. The good agreement of our results with experimental data supports the notion that scleral growth and scleral remodeling are two independently controlled mechanisms during eye development.

Effect of Accommodation on Peripheral Eye Lengths of Emmetropes and Myopes

PURPOSE

To investigate the effect of accommodation on central and peripheral axial lengths in young adult emmetropes and myopes.

METHODS

On-axis and peripheral axial lengths were measured with the Haag-Streit Lenstar in 83 young adult participants for 0D and 6D accommodation demands. A Badal system was used to both correct refractive errors and induce accommodation. Participants were emmetropes (n = 29, mean spherical equivalent refraction +0.35 ± 0.35D), low myopes (32, -1.38 ± 0.73D), and higher myopes (22, -4.30 ± 0.73D). Ages were similar for all groups (22 ± 2 years). Pupils were dilated with 2.5% phenylephrine to allow a large field of measurement while maintaining active accommodation. Axial lengths were measured in 5° steps to ±30° across the horizontal visual field.

RESULTS

With accommodation, axial length increased for all refractive groups at all positions, but with lessening effect away from fixation. Axial length changes were greater for higher myopes than for emmetropes on-axis (higher myopes 41 ± 14 μm, emmetropes 30 ± 12 μm, P = .005), for higher myopes than for low myopes at 30° nasal (P = .03), and for the higher myopes than for the other groups at 20° nasal (P < .05). There were significant correlations between myopia and changes in axial length at all positions, with the highest correlation on-axis (R = 0.30, P < .001).

CONCLUSIONS

During accommodation, eye length increased out to at least ±30° visual angle in young adult myopes and emmetropes. The increase was significantly greater for higher myopes than for the other groups at some positions. At all positions, there were significant correlations between myopia and accommodation-induced changes in axial length.

Variation of axial and oblique astigmatism with accommodation across the visual field

In this study we investigated the impact of accommodation on axial and oblique astigmatism along 12 meridians of the central 30° of visual field and explored the compensation of corneal first-surface astigmatism by the remainder of the eye's optical system. Our experimental evidence revealed no systematic effect of accommodation on either axial or oblique astigmatism for two adult populations (myopic and emmetropic eyes). Although a few subjects exhibited systematic changes in axial astigmatism during accommodation, the dioptric value of these changes was much smaller than the amount of accommodation. For most subjects, axial and oblique astigmatism of the whole eye are both less than for the cornea alone, which indicates a compensatory role for internal optics at all accommodative states in both central and peripheral vision. A new method for determining the eye's optical axis based on visual field maps of oblique astigmatism revealed that, on average, the optical axis is 4.8° temporal and 0.39° superior to the foveal line-of-sight in object space, which agrees with previous results obtained by different methodologies and implies that foveal astigmatism includes a small amount of oblique astigmatism (0.06 D on average). Customized optical models of each eye revealed that oblique astigmatism of the corneal first surface is negligible along the pupillary axis for emmetropic and myopic eyes. Individual variation in the eye's optical axis is due in part to misalignment of the corneal and internal components that is consistent with tilting of the crystalline lens relative to the pupillary axis.

Validation of a partial coherence interferometry method for estimating retinal shape

To validate a simple partial coherence interferometry (PCI) based retinal shape method, estimates of retinal shape were determined in 60 young adults using off-axis PCI, with three stages of modeling using variants of the Le Grand model eye, and magnetic resonance imaging (MRI). Stage 1 and 2 involved a basic model eye without and with surface ray deviation, respectively and Stage 3 used model with individual ocular biometry and ray deviation at surfaces. Considering the theoretical uncertainty of MRI (12-14%), the results of the study indicate good agreement between MRI and all three stages of PCI modeling with <4% and <7% differences in retinal shapes along horizontal and vertical meridians, respectively. Stage 2 and Stage 3 gave slightly different retinal co-ordinates than Stage 1 and we recommend the intermediate Stage 2 as providing a simple and valid method of determining retinal shape from PCI data.