Corneal asphericity and refractive error

Effect of Corneal Tilt on the Determination of Asphericity

Purpose: To quantify the effect of levelling the corneal surface around the optical axis on the calculated values of corneal asphericity when conic and biconic models are used to fit the anterior corneal surface. Methods: This cross-sectional study starts with a mathematical simulation proving the concept of the effect that the eye's tilt has on the corneal asphericity calculation. Spherical, conic and biconic models are considered and compared. Further, corneal asphericity is analysed in the eyes of 177 healthy participants aged 35.4 ± 15.2. The optical axis was determined using an optimization procedure via the Levenberg-Marquardt nonlinear least-squares algorithm, before fitting the corneal surface to spherical, conic and biconic models. The influence of pupil size (aperture radii of 1.5, 3.0, 4.0 and 5.0 mm) on corneal radius and asphericity was also analysed. Results: In computer simulations, eye tilt caused an increase in the apical radii of the surface with the increase of the tilt angle in both positive and negative directions and aperture radii in all models. Fitting the cornea to spherical models did not show a significant difference between the raw-measured corneal surfaces and the levelled surfaces for right and left eyes. When the conic models were fitted to the cornea, changes in the radii of the cornea among the raw-measured corneal surfaces' data and levelled data were not significant; however, significant differences were recorded in the asphericity of the anterior surfaces at radii of aperture 1.5 mm (p < 0.01). With the biconic model, the posterior surfaces recorded significant asphericity differences at aperture radii of 1.5 mm, 3 mm, 4 mm and 5 mm (p = 0.01, p < 0.01, p < 0.01 & p < 0.01, respectively) in the nasal temporal direction of right eyes and left eyes (p < 0.01, p < 0.01, p < 0.01 & p < 0.01, respectively). In the superior-inferior direction, significant changes were only noticed at aperture radii of 1.5 mm for both right and left eyes (p = 0.05, p < 0.01). Conclusions: Estimation of human corneal asphericity from topography or tomography data using conic and biconic models of corneas are affected by eyes' natural tilt. In contrast, the apical radii of the cornea are less affected. Using corneal asphericity in certain applications such as fitting contact lenses, corneal implant design, planning for refractive surgery and mathematical modelling when a geometrical centre of the eye is needed should be implemented with caution.

Predicting corneal refractive power changes after orthokeratology

This study aimed to characterise corneal refractive power (CRP) changes along the principal corneal meridians during orthokeratology (OK). Nineteen myopes (mean age 28 ± 7 years) were fitted with OK lenses in both eyes. Corneal topography was captured before and after 14 nights of OK lens wear. CRP was calculated for the central 8 mm cornea along the horizontal and vertical meridians. The central-paracentral (CPC) power ratio was calculated as the ratio between maximum central and paracentral CRP change from individual data. There was a significant reduction in CRP at all locations in the central 4 mm of the cornea (all p < 0.001) except at 2 mm on the superior cornea (p = 0.071). A significant increase in CRP was evident in the paracentral zone at 2.5, 3 and 3.5 mm on the nasal and superior cornea and at 3.5 and 4 mm on the temporal cornea (all p < 0.05). No significant change in CRP was measured in the inferior cornea except decreased CRP at 2.5 mm (p < 0.001). CPC power ratio in the nasal and temporal paracentral regions was 2.49 and 2.23, respectively, and 2.09 for both the inferior and superior paracentral corneal regions. Our results demonstrates that OK induced significant changes in CRP along the horizontal and vertical corneal meridians. If peripheral defocus changes are inferred from corneal topography, this study suggests that the amount of myopia experienced on the peripheral retina was greater than twice the amount of central corneal power reduction achieved after OK. However, this relationship may be dependent on lens design and vary with pupil size. CPC power ratios may provide an alternative method to estimate peripheral defocus experienced after OK.

Corneal asphericity and related factors in the geriatric population: A population-based study

PURPOSE

To determine the distribution of the corneal asphericity coefficient (Q value) and related factors in an Iranian geriatric population.

METHODS

This population-based study was conducted in 2019 in Tehran, using stratified multistage random cluster sampling. The study population was ≥60 years of age. Participants underwent corneal imaging using a Pentacam HR. Mean keratometry, corneal astigmatism, central corneal thickness, anterior chamber depth and the overall anterior and posterior Q values (for 8 mm chord diameter) were recorded. Axial length measurements were performed using the IOL Master 500.

RESULTS

2457 eyes of 2457 individuals were analysed. The mean age was 67.3 ± 5.82 years and 1479 (60.2%) were female. The mean Q value for the anterior corneal surface was -0.35 ± 0.17 (95% CI: -0.35 to -0.34). The anterior Q value showed a statistically significant inverse relationship with axial length and mean keratometry, and a significant direct association with anterior chamber depth and corneal astigmatism. The mean posterior Q value was -0.41 ± 0.15 (95% CI: -0.42 to -0.40). The posterior Q value had a significant direct relationship with age, anterior chamber depth, mean keratometry and corneal astigmatism.

CONCLUSION

The corneal Q values in this geriatric Iranian population were more negative than the values reported in most previous studies. Corneal asphericity was greater affected by ocular biometry and corneal curvature than demographic factors and refractive status.

<p>Ocular Manifestations and Biometrics in Marfan’s Syndrome from Eastern Nepal</p>

Purpose

To evaluate the ocular characteristics of Marfan’s syndrome (MFS) fulfilling the revised Ghent-2 nosology in Eastern Nepal.

Materials and Methods

A hospital-based observational and cross-sectional study was conducted. Ocular manifestations and biometrics were incorporated. Patients were subdivided into adults (16 years or older) and children (5–15 years). Ocular biometric parameters consisted of values of refractive error, keratometry readings, anterior chamber depth (ACD), central corneal thickness (CCT), lens thickness (LT) and axial length (AL).

Results

A total of 34 eyes of 17 patients with MFS were included, where 32 eyes were phakic. Mean age of the study participants was 14.5 ± 9.1 years. The mean best corrected visual acuity (BCVA) of phakic eyes was 0.99 ± 0.82 LogMAR. Myopia greater than −3 diopters (D) was present in 28/34 (82.35%) eyes. The average spherical equivalent was −12.34 ± 8.85 D. Ectopia lentis (EL) was present in 24/32 (75%) eyes where superonasal was the most common subluxation in 10/24 (41.7%) eyes. AL was longer in adults 26.54 ± 4.42 mm compared to 25.21 ± 1.93 mm in children. Likewise, LT in adults was 4.9 ± 0.70 mm and 4.40 ± 0.59 mm in pediatric participants. Flat corneas were noted in both the groups with an average of 41.53 ± 2.21 D. The mean CCT and ACD were 524.62 ± 21.74 μm and 3.64 ± 0.80 mm, respectively. There was a negative association between the AL and the average corneal curvature (K_med, correlation coefficient −0.11, p=0.54).

Conclusion

Myopia is the foremost ocular involvement with significant visual disability in MFS. Though, AL and corneal curvature are not included in the revised Ghent-2 nosology, we strongly recommend these parameters to be considered during ophthalmic evaluation in suspected and diagnosed cases of MFS in the absence of genetic testing.

Age- and Gender-Related Characteristics of Corneal Refractive Parameters in a Large Cohort Study

PURPOSE

To characterize age- and sex-related changes in corneal refractive parameters in myopic and hyperopic patients undergoing refractive surgery.

DESIGN

A retrospective cross-sectional study.

METHODS

Analysis of demographic and refractive parameters of myopic and hyperopic patients who underwent laser in situ keratomileusis (LASIK) or photorefractive keratectomy (PRK) between January 2000 and December 2014 at the Care-Vision Laser Centers, Tel-Aviv, Israel.

RESULTS

A total of 62,422 eyes of 31,211 patients were included. With advancing age, refractive surgery was performed for lower magnitudes of myopia and hyperopia. The magnitude of cylinder was higher in men than in women in both myopic and hyperopic patients. In comparison, women were significantly more myopic than men (spherical equivalent of -3.73 diopter [D] versus -4.07 D; P < 0.01). The myopic group sphere (r = 0.044; P < 0.001) had a positive correlation with age, whereas other parameters had a negative correlation with age: astigmatism (r = -0.09; P < 0.001), best-correct visual acuity (BCVA) (r = -0.04; P < 0.001), flat K (r = -0.09; P < 0.001), steep K (r = -0.06; P < 0.001), average K (r = -0.07; P < 0.001), and J0 (r = -0.05; P < 0.001). For hyperopic patients, astigmatism (r = 0.35; P < 0.001), BCVA (r = 0.11; P < 0.001), flat K (r = 0.30; P < 0.001), average K (0.14; P < 0.001), and central corneal thickness (r = 0.10; P < 0.001) correlated positively with age, whereas sphere (r = -0.23; P < 0.001), J0 (r = -0.31; P < 0.001), and overall blurring strength (r = -0.31; P < 0.001) had negative correlations with age.

CONCLUSIONS

This large cohort study shows age- and sex-related refractive parameters among myopic and hyperopic patients seeking refractive surgery. These parameters can explain and predict trends in patients attending refractive surgery.

Extended depth of focus contact lenses vs. two commercial multifocals: Part 1. Optical performance evaluation via computed through-focus retinal image quality metrics

PURPOSE

To compare the computed optical performance of prototype lenses designed using deliberate manipulation of higher-order spherical aberrations to extend depth-of-focus (EDOF) with two commercial multifocals.

METHODS

Emmetropic, presbyopic, schematic eyes were coupled with prototype EDOF and commercial multifocal lenses (Acuvue Oasys for presbyopia, AOP, Johnson & Johnson & Air Optix Aqua multifocal, AOMF, Alcon). For each test configuration, the through-focus retinal image quality (TFRIQ) values were computed over 21 vergences, ranging from -0.50 to 2.00D, in 0.125D steps. Analysis was performed considering eyes with three different inherent aberration profiles: five different pupils and five different lens decentration levels.

RESULTS

Except the LOW design, the AOP lenses offered 'bifocal' like TFRIQ performance. Lens performance was relatively independent to pupil and aberrations but not centration. Contrastingly, AOMF demonstrated distance centric performance, most dominant in LOW followed by MED and HIGH designs. AOMF lenses were the most sensitive to pupil, aberrations and centration. The prototypes demonstrated a 'lift-off' in the TFRIQ performance, particularly at intermediate and near, without trading performance at distance. When compared with AOP and AOMF, EDOF lenses demonstrated reduced sensitivity to pupil, aberrations and centration.

CONCLUSION

With the through focus retinal image quality as the gauge of optical performance, we demonstrated that the prototype EDOF designs were less susceptible to variations in pupil, inherent ocular aberrations and decentration, compared to the commercial designs. To ascertain whether these incremental improvements translate to a clinically palpable outcome requires investigation through human trials.

New Perspective on Myopia Control with Orthokeratology

PURPOSE

To compare peripheral refraction along both the horizontal and vertical retinal meridians before and after orthokeratology (OK) lens wear.

METHODS

Nineteen young adult myopic subjects (mean age, 28 ± 7 years) were fitted with OK lenses in both eyes. Central and peripheral refraction and corneal topography measurements were taken before and after 14 nights of OK. All measurements were taken with no correction or OK lens in place.

RESULTS

At baseline before OK, peripheral spherical equivalent refraction (M) across the horizontal meridian did not vary significantly from center. M across the vertical meridian was more myopic than the center (p < 0.05). After OK, there was a significant hyperopic shift in M (p < 0.001); both meridians now experienced myopic peripheral refraction. At baseline, J180 across the horizontal meridian was more negative than the center, and along the vertical meridian, it was more positive than the center (all p < 0.05). At baseline, J45 was more positive than center with increased eccentricity in the temporal and inferior retina and more negative than center with increased eccentricity in the nasal and superior retina. Orthokeratology caused greater rate of change of peripheral J180 across both retinal meridians (p < 0.001). Furthermore, compared with baseline, J45 became more positive in the nasal and superior retina and more negative in the temporal and inferior retina (all p < 0.05).

CONCLUSIONS

Orthokeratology lenses induced significant changes in peripheral refraction along the horizontal and vertical meridians. As peripheral myopia was measured at baseline along the vertical meridian, the results of our study suggest that inducing greater degrees of myopic defocus on to the peripheral retina, more than habitually experienced, may be required for effective myopia control. Further investigation into the critical threshold of retinal area receiving myopic defocus and the impact of duration of exposure is necessary to improve the efficacy of current myopia control treatments.

Analysis of age, refractive error and gender related changes of the cornea and the anterior segment of the eye with Scheimpflug imaging

PURPOSE

To assess age, refractive error and gender related changes occurring in the cornea and the anterior segment of the eye using a Scheimpflug system.

METHODS

The study included 666 healthy eyed subjects with a mean age of 39.3±19.7 years (range: 3-85 years). All analyses were based on the right eyes of the patients as all measured parameters correlated well between the right and left eyes. Each parameter was correlated with age and the right eye's spherical equivalent (SE) using Pearson correlations. Univariate linear regression models were constructed for analyses of parameters.

RESULTS

The anterior corneal surface asphericity showed significant positive correlations whereas posterior corneal surface asphericity showed significant negative correlations with age. Anterior chamber depth (ACD), volume (ACV) and angle (ACA) showed significant negative correlations with age and SE. Age explained 25% of the variance in anterior corneal surface asphericity, 22% of variance in posterior corneal surface asphericity, 26% of variance in ACV, 27% of variance in ACD, and 19% of variance in ACA. In the SE model SE was identified to account for 25% of variance in ACV, 22% of variance in ACD, each, and 17% of variance in ACA. Significant differences were detected in anterior and posterior keratometry values, ACV, ACD and ACA among gender groups (p<0.01).

CONCLUSIONS

The cornea shows a tendency for a decrease in anterior corneal surface asphericity and an increase in posterior corneal surface asphericity with advancing age. Men have flatter corneas and women have shallower anterior chambers and narrower anterior chamber angles.

Effect of anterior corneal surface asphericity modification on fourth-order zernike spherical aberrations

PURPOSE

To evaluate the theoretical influence of the change in corneal asphericity (ΔQ) on the change in fourth-order Zernike spherical aberration coefficient (ΔC(4)0) with customized aspheric refractive correction of myopia and hyperopia.

METHODS

The initial anterior corneal surface profile was modeled as a conic section of apical radius of curvature R0 and asphericity Q₀. The postoperative corneal profile was modeled as a conic section of apical curvature R1 and asphericity Q1, where R1 was computed from defocus D, and Q₁ selected for controlling the postoperative asphericity. The corresponding change in fourth-order spherical aberration (ΔC(0)4) was computed within a 6-mm optical zone using inner products applied to the incurred optical path changes. These calculations were repeated for different values of D, R₀, Q₀, and various intended ΔC(4)0 values.

RESULTS

Increasing negative spherical aberration (ΔC(4)(0) < 0) requires a change toward more negative values of asphericity (increased prolateness; ΔQ < 0) for hyperopic and low myopic corrections, but more positive values (ΔQ < 0) for high myopic correction. The larger the intended change in corneal spherical aberration (ΔC(4)(0)), the more myopic the threshold value for which the required change in asphericity, ΔQ, becomes positive. The influence of the magnitude of paraxial defocus correction is less pronounced when larger changes in C(4)(0) are intended.

CONCLUSIONS

These results provide a basis for controlling the direction (sign) and the magnitude of spherical aberration changes when using customized aspheric profiles of ablation.

Variations in corneal asphericity (Q value) between African-Americans and whites

PURPOSE

To search for differences in corneal asphericity on the basis of ethnicity between African-American and white populations.

METHODS

A prospective cohort design was used to analyze corneal asphericity (Q value) data obtained by Pentacam HR (Oculus, Wetzlar, Germany) on right eyes from African-American (n = 80) and white (n = 80). Subjects were stratified by ethnicity, age, and spherical equivalent (SE) refractive error. Q values were obtained from each quadrant (superior, nasal, inferior, and temporal) and two meridians (horizontal and vertical).

RESULTS

The mean Q values were African-Americans -0.26 ± 0.19 and whites -0.20 ± 0.12, indicating that the eyes of African-Americans were significantly more prolate (p = 0.003) than those of whites. There was a significant difference between mean Q values for ethnic groups only in the 30- to 39-year olds (p = 0.01) and there was a lack of correlation with age in both ethnic groups. Q value contrasts by gender were only significant between males (p = 0.01). There was a lack of correlation between Q value and SE for either ethnic group. Age group contrasts between ethnic groups found significant differences for those with SE greater than 0.00 D to -3.00 D (p = 0.05) and greater than 0.00 D to +3.00 D (p = 0.05). Comparison of mean Q values in opposing meridians within and across ethnic groups were significant, although neither group showed significant differences between horizontal and vertical meridians.

CONCLUSIONS

Corneal asphericity as represented by mean Q value varies significantly between African-Americans and whites. The greatest differences are evident in opposing quadrants and appear to be little influenced by age, gender, or SE.

Central and paracentral corneal curvature changes during orthokeratology

PURPOSE

To investigate regional changes in corneal curvature and power induced by overnight orthokeratology (OK) contact lens wear over a period of 2 weeks.

METHODS

Corneal topography data (Medmont E300) from 21 myopes (12 M, 9F, 20 to 40 years), who had worn BE OK lenses manufactured in Boston XO material for 14 nights, were analyzed retrospectively. Enrollment criteria were myopia up to 4.50 D and corneal toricity up to 1.50 D. Custom MATLAB programs were used to determine sectorial tangential curvature and refractive power, and to investigate changes from baseline after 1 and 14 nights, and between 1 and 14 nights of lens wear in the central circular zone (CCZ) and surrounding paracentral annular zone (PCZ), with each zone subdivided into nasal, superior, temporal, and inferior sectors.

RESULTS

After OK, significant asymmetry was found in tangential curvature across sectors. In the CCZ, by day 14 there was greater flattening in the temporal (-1.27 ± 0.62 D, p < 0.001) than nasal sector (0.05 ± 0.62 D, p = 0.893). In the PCZ, by day 14 there was greater steepening in the temporal (2.37 ± 1.09 D, p < 0.001) than nasal sector (0.30 ± 1.36 D, p = 0.326). In both zones, vertical sectors did not show any asymmetry. The variation in corneal curvature across sectors and the mirror asymmetry was also reflected in variations in the corneal refractive power.

CONCLUSIONS

OK induces non-uniform corneal changes to the central and paracentral regions. This non-uniformity may influence peripheral refraction profiles reported with OK that have been suggested to be influential in myopia control.

Time course of the effects of orthokeratology on peripheral refraction and corneal topography

PURPOSE

To describe the time course of changes in both peripheral refraction and corneal topography in myopic adults wearing myopic orthokeratology (OK) lenses.

METHODS

Nineteen adult myopes were fitted with OK lenses in both eyes for overnight wear. Central and peripheral refraction and corneal topography were measured along the horizontal meridian at baseline and after 1, 4, 7 and 14 nights of lens wear.

RESULTS

At baseline, refraction was myopic at all positions along the horizontal meridian. Two weeks of OK lens wear caused a significant change in refraction where the general trend was a hyperopic shift in spherical equivalent (M) except at 35° in the nasal visual field where there was instead a myopic shift in M. The most significant change in M occurred between baseline and after 1 night of OK lens wear and the effect became less dramatic across subsequent days of OK treatment. Similarly, OK caused significant change in corneal refractive power at all positions along the horizontal corneal chord. There was a reduction in corneal power or flattening of the cornea at all positions except at 2.4 mm and 2.8 mm on the nasal cornea where there was an increase in corneal refractive power or steepening of the cornea. This change was most apparent after 1 night of OK lens wear and, similar to changes in peripheral refraction, changes in corneal refractive power on subsequent days of OK treatment became less marked.

CONCLUSIONS

Orthokeratology caused significant changes in both peripheral refraction and corneal topography. The greatest change in refraction and corneal refractive power across the horizontal corneal meridian occurred during the first night of OK lens wear. Subsequent changes in both peripheral refraction and corneal topography were less dramatic, in the same manner as reported changes in apical radius and central refraction after OK. This study confirms that with OK treatment, the peripheral retina experiences myopic defocus, which is conjectured to underlie the observed slowing of myopia progression.

Total ocular, anterior corneal and lenticular higher order aberrations in hyperopic, myopic and emmetropic eyes

Total ocular higher order aberrations and corneal topography of myopic, emmetropic and hyperopic eyes of 675 adolescents (16.9 ± 0.7 years) were measured after cycloplegia using COAS aberrometer and Medmont videokeratoscope. Corneal higher order aberrations were computed from the corneal topography maps and lenticular (internal) higher order aberrations derived by subtraction of corneal aberrations from total ocular aberrations. Aberrations were measured for a pupil diameter of 5mm. Multivariate analysis of variance followed by multiple regression analysis found significant difference in the fourth order aberrations (SA RMS, primary spherical aberration coefficient) between the refractive error groups. Hyperopic eyes (+0.083 ± 0.05 μm) had more positive total ocular primary spherical aberration compared to emmetropic (+0.036 ± 0.04 μm) and myopic eyes (low myopia=+0.038 ± 0.05 μm, moderate myopia=+0.026 ± 0.06 μm) (p<0.05). No difference was observed for the anterior corneal spherical aberration. Significantly less negative lenticular spherical aberration was observed for the hyperopic eyes (-0.038 ± 0.05 μm) than myopic (low myopia=-0.088 ± 0.04 μm, moderate myopia=-0.095 ± 0.05 μm) and emmetropic eyes (-0.081 ± 0.04 μm) (p<0.05). These findings suggest the existence of differences in the characteristics of the crystalline lens (asphericity, curvature and gradient refractive index) of hyperopic eyes versus other eyes.

Peripheral refraction in myopic children wearing orthokeratology and gas-permeable lenses

PURPOSE

To investigate changes in peripheral refraction after orthokeratology (OK) and rigid gas-permeable (GP) lens wear in progressing myopic children and to compare these peripheral defocus changes with reported changes in adults wearing OK.

METHODS

Sixteen myopic children subjects were fitted with an OK lens in one eye for overnight wear and a GP lens in the other eye for daily wear. Central and peripheral refraction were measured at baseline and then after 3 mo of lens wear.

RESULTS

At baseline, myopic children showed relative peripheral hyperopia compared with central refraction at and beyond 20° in the temporal visual field (VF) and 30° in the nasal VF. Three months of OK lens wear produced hyperopic shifts in refraction between 30° in the temporal VF and 20° in the nasal VF. Peripheral refraction was similar to center at all positions in the temporal VF while remaining significantly myopic at all locations in the nasal VF. No change in either central or peripheral refraction was found after 3 mo in the eye assigned for GP lens wear.

CONCLUSIONS

OK significantly reduced myopia in the central 20° VF in myopic children, converting relative peripheral hyperopia measured at baseline to relative peripheral myopia. These changes in children are similar to changes reported in myopic adults wearing OK lenses. No change in either central or peripheral refraction was found after 3 mo of daily GP lens wear. OK lenses can be used to induce myopic defocus in the periphery in myopic children and may thus provide a potential mechanism for myopia control.

Corneal asphericity and spherical aberration after refractive surgery

PURPOSE

To evaluate changes in corneal asphericity (Q) and spherical aberrations after refractive surgery using Scheimpflug imaging.

SETTING

University of California, San Diego, Shiley Eye Center, La Jolla, California, USA.

DESIGN

Cohort study.

METHODS

After wavefront-guided laser in situ keratomileusis, patients within ± 0.50 diopter of plano and with an uncorrected distance visual acuity of at least 20/20 were evaluated. The Q values and corneal spherical aberration Zernike values were obtained using Scheimpflug imaging preoperatively and 1 to 3 months postoperatively.

RESULTS

The study enrolled 177 myopic eyes and 32 hyperopic eyes. The mean Q value was -0.28 ± 0.11 (SD) and -0.22 ± 0.15, respectively, preoperatively and +0.35 ± 0.44 and -0.64 ± 0.31, respectively, postoperatively. The asphericity change was highly correlated with preoperative spherical equivalent (r(2) = 0.81; P ≤ .001). The mean corneal spherical aberration was +0.21 ± 0.08 μm in myopic eyes and +0.36 ± 0.11 μm in hyperopic eyes preoperatively and +0.36 ± 0.17 μm and 0.00 ± 0.29 μm, respectively, postoperatively. The corneal spherical aberration changes were correlated with the amount of preoperative refractive error (r(2) = 0.34; P < .001). There was a tendency for Q values and spherical aberrations to become more positive after myopic ablation and more negative after hyperopic ablation.

CONCLUSIONS

Myopic and hyperopic corrections induced changes in the Q value and spherical aberrations in opposite directions (ie, positive and negative, respectively). The changes depended on the magnitude of the refractive correction.

FINANCIAL DISCLOSURE

No author has a financial or proprietary interest in any material or method mentioned.

Relationship between conjunctivochalasis and refractive error

OBJECTIVES

To assess the relation between the prevalence and grade of conjunctivochalasis and refractive error and to compare the grade of conjunctivochalasis between myopic and hyperopic patients.

METHODS

Consecutive patients aged from 3 to 94 years were chosen for this study. Exclusion criteria included a history of using contact lenses, ocular surgeries, infectious conjunctivitis, or corneal diseases. The age, gender, medical history, ocular history, the grade and other parameters of inferior conjunctivochalasis classified into three locations (nasal, middle, and temporal), and refractive error were determined in all subjects. Patients were divided into three groups as follows: a hyperopic group (≥0.0 D), an emmetropic group (<0.0 and ≥-2.0 D), and a myopic group (<-2.0 D). They were also divided into 10 groups according to age. One-way analysis of variance and the Scheffe multiple comparison test were used to compare the mean values among three groups. Relations among the variables were investigated by calculating Pearson correlation coefficients and partial correlation coefficients.

RESULTS

A total of 1,110 patients were included in the study. In each age group, the mean grade of conjunctivochalasis was higher in hyperopic patients than in myopic patients. There were no significant differences in both the downward gaze- and digital pressure-dependent changes of conjunctivochalasis between the myopic and hyperopic groups. The severity of conjunctivochalasis affecting the nasal and temporal bulbar conjunctiva, and parameters such as the changes of conjunctivochalasis caused by downward gaze or digital pressure, were correlated with the refractive error, especially in patients over 40 years old (P<0.05).

CONCLUSIONS

This was the first assessment of the relationship between refractive error and the grade of conjunctivochalasis in a large consecutive series of patients. Our results suggest that the prevalence and grade of conjunctivochalasis are dependent on refractive error, with hyperopia being an important risk factor for conjunctivochalasis.

Correlation among ocular spherical aberration, corneal spherical aberration, and corneal asphericity before and after LASIK for myopic astigmatism with the SCHWIND AMARIS platform

PURPOSE

To determine the spherical wave aberration of the human eye based on corneal topography.

METHODS

Based on the pre- and postoperative status of 146 consecutive eyes (median patient age 36 years), the correlations between spherical aberration and asphericity and between corneal and ocular spherical aberrations were determined using simple linear regression methods. The asphericity (Q) values for which spherical aberration equals zero as well as the reference Q values for which corneal spherical aberration equals ocular spherical aberration have been determined. Patients underwent LASIK using the AMARIS excimer laser platform (SCHWIND eye-tech-solutions). All ablations were based on aspheric aberration-neutral profiles.

RESULTS

Corneal and ocular spherical aberrations correlate well with Q value and the value p · R(-3) in patients before and after LASIK for myopic astigmatism. A Q value of -0.19 to -0.27 can provide zero ocular spherical aberration in patients before and after LASIK for myopic astigmatism. Ocular spherical aberration is induced at a rate of half the induced corneal spherical aberration. A reference Q value of -0.12 to +0.01 can provide corneal spherical aberration equal to ocular spherical aberration in patients before and after LASIK for myopic astigmatism.

CONCLUSIONS

Ocular and corneal wave aberrations are two different concepts that are not interchangeable. As for spherical aberration, a simple static model with a reference cornea deviating from a Cartesian oval can provide a 2:1 correspondence between corneal and ocular spherical aberration.

Asphericity analysis using corneal wavefront and topographic meridional fits

The calculation of corneal asphericity as a 3-D fit renders more accurate results when it is based on the corneal wavefront aberrations rather than on the corneal topography of the principal meridians. A more accurate prediction could be obtained for hyperopic treatments compared to myopic treatments. We evaluate a method to calculate corneal asphericity and asphericity changes after refractive surgery. Sixty eyes of 15 consecutive myopic patients and 15 consecutive hyperopic patients (n=30 each) are retrospectively evaluated. Preoperative and 3-month-postoperative topographic and corneal wavefront analyses are performed using corneal topography. Ablations are performed using a laser with an aberration-free profile. Topographic changes in asphericity and corneal aberrations are evaluated for a 6-mm corneal diameter. The induction of corneal spherical aberrations and asphericity changes correlates with the achieved defocus correction. Preoperatively as well as postoperatively, asphericity calculated from the topography meridians correlates with asphericity calculated from the corneal wavefront in myopic and hyperopic treatments. A stronger correlation between postoperative asphericity and the ideally expected/predicted asphericity is obtained based on aberration-free assumptions calculated from corneal wavefront values rather than from the meridians. In hyperopic treatments, a better correlation can be obtained compared to the correlation in myopic treatments. Corneal asphericity calculated from corneal wavefront aberrations represents a 3-D fit of the corneal surface; asphericity calculated from the main topographic meridians represents a 2-D fit of the principal corneal meridians. Postoperative corneal asphericity can be calculated from corneal wavefront aberrations with higher fidelity than from corneal topography of the principal meridians. Hyperopic treatments show a greater accuracy than myopic treatments.

Analysis of optimized profiles for 'aberration-free' refractive surgery

PURPOSE

To provide a model of an aberration-free profile and to clinically evaluate the impact of treatments based upon these theoretical profiles in the post-operative cornea.

METHODS

Aberration-free profiles were deduced from the Zernike expansion of the difference between two corneal cartesian-ovals. Compensation for the focus-shift effects of removing corneal tissue were incorporated by preserving the location of the optical focus of the anterior corneal surface. Simulation of the surgical performance of the profile was performed by means of simulated ray-tracing through a cornea described by its anterior surface and pachymetry. Clinical evaluation was retrospectively analysed in terms of visual outcomes, corneal wavefront aberration and asphericity changes at 3-month follow-up compared to the baseline on 100 eyes treated for compound myopic astigmatism.

RESULTS

The proposed 'aberration-free' profiles theoretically preserve aberrations, becoming more oblate asphericity after myopic treatments, and more prolate after hyperopic ones. In the clinical evaluation, 94% of eyes were within +/-0.50 D of emmetropia. BSCVA improved significantly (p < 0.001). Induced corneal aberrations at 6-mm were below clinically relevant levels: 0.123 +/- 0.129 microm for HO-RMS (p < 0.001), 0.065 +/- 0.128 microm for spherical aberration (p < 0.001) and 0.058 +/- 0.128 microm for coma (p < 0.01), whereas the rate of induced aberrations per achieved D of correction were -0.042, -0.031, and -0.030 microm D(-1) for HO-RMS, SphAb, and coma (all p < 0.001). Induction of positive asphericity correlated to achieved correction (p < 0.001) at a rate 3x theoretical prediction.

CONCLUSIONS

'Aberration-free' patterns for refractive surgery as defined here together with consideration of other sources of aberrations such as blending zones, eye-tracking, and corneal biomechanics yielded results comparable to those of customisation approaches. Having close-to-ideal profiles should improve clinical outcomes decreasing the need for nomograms, and diminishing induced aberrations after surgery.

Topography-based assessment of anterior corneal curvature and asphericity as a function of age, sex, and refractive status

PURPOSE

To assess corneal asphericity (Q) and evaluate potential factors influencing the shape of the anterior corneal surface.

SETTING

Medical Optics Research Group, Institute of Medical Physics, University of Erlangen-Nuremberg, Erlangen, Germany.

METHODS

In this cross-sectional consecutive study, 3 topographic measurements were taken. Eyes were grouped by age in years (A: <or=29; B: 30 to 39; C: 40 to 49; D: 50 to 59; E: 60 to 69; F: >or=70), sex, and refraction.

RESULTS

The study comprised 487 eyes (205 men, 288 women; age 17 to 81 years). The mean Q of the anterior corneal surface was -0.22 +/- 0.14 (SD) overall, -0.21 +/- 0.12 in Group A, -0.25 +/- 0.11 in Group B, -0.21 +/- 0.15 in Group C, -0.23 +/- 0.14 in Group D, -0.19 +/- 0.17 in Group E, -0.20 +/- 0.15 in Group F, -0.23 +/- 0.13 in men, -0.21 +/- 0.14 in women, -0.19 +/- 0.14 in hyperopes (n = 166; >+0.50 to +6.50 diopters [D]), -0.23 +/- 0.13 in emmetropes (n = 162; -0.50 to +0.50 D), and -0.23 +/- 0.15 in myopes (n = 165; <-0.50 to -8.00 D). There was no significant correlation between Q and age; Q differed significantly between men and women (P = .005), hyperopes and emmetropes (P<.0001), and hyperopes and myopes (P = .001).

CONCLUSIONS

There were high interindividual variations in the Q value. Thus, proper correction of spherical aberration with intraocular lenses (IOLs) requires sophisticated selection of the asphericity of IOL surfaces based on biometric data and individual corneal Q values.

Relationship between anterior corneal asphericity and refractive variables

BACKGROUND

The anterior corneal surface is closely modelled by a conic section that is fully described by asphericity (Q) and the apical radius of curvature. Computerized corneal topographers have allowed for more accurate and complete descriptions of corneal shape. Our objective was to compare anterior corneal asphericity (Q) values determined for different corneal diameters in eyes of different refractive state.

METHODS

Q-values were determined in 118 eyes of 118 subjects using both a videokeratoscope (Atlas Mastervue, Humphrey Instruments-Zeiss) and Vol-CT 6.89 software (Sarver & Associates Inc.), which estimates Q-values for several corneal diameters (3.0 mm, 4.0 mm, 5.0 mm, 6.0 mm, 7.0 mm and 8.0 mm) using topographic data obtained with the instrument. For comparisons, Q-values were stratified three ways: by refractive error (myopic, emmetropic or hyperopic eyes), corneal power (low, intermediate and high) and corneal astigmatism (low, intermediate and high).

RESULTS

Mean corneal asphericity was -0.35 +/- 0.03, differing significantly from reported data (Student's t-test). Asphericities determined using both methods did not vary significantly with regard to refractive error or corneal power, but did differ among the corneal astigmatism groups (p < 0.01). A trend was observed towards more negative Q-values with increasing corneal diameter, but differences in corneal asphericity according to corneal diameter were only significant in the astigmatism group (p < 0.01).

CONCLUSION

Q-values varied according to the refractive properties examined. However, the relationship between refractive state and corneal asphericity was found to be determined more by the geometric properties of the eye (corneal power and axial length) than by manifest refraction.

Wide-field schematic eye models with gradient-index lens

We propose a wide-field schematic eye model, which provides a more realistic description of the optical system of the eye in relation to its anatomical structure. The wide-field model incorporates a gradient-index (GRIN) lens, which enables it to fulfill properties of two well-known schematic eye models, namely, Navarro's model for off-axis aberrations and Thibos's chromatic on-axis model (the Indiana eye). These two models are based on extensive experimental data, which makes the derived wide-field eye model also consistent with that data. A mathematical method to construct a GRIN lens with its iso-indicial contours following the optical surfaces of given asphericity is presented. The efficiency of the method is demonstrated with three variants related to different age groups. The role of the GRIN structure in relation to the lens paradox is analyzed. The wide-field model with a GRIN lens can be used as a starting design for the eye inverse problem, i.e., reconstructing the optical structure of the eye from off-axis wavefront measurements. Anatomically more accurate age-dependent optical models of the eye could ultimately help an optical designer to improve wide-field retinal imaging.

Neural and optical limits to visual performance in myopia

We investigated the relative importance of neural and optical limitations to visual performance in myopia. A number of visual performance measures were made on all or subsets of 121 eyes of emmetropic and myopic volunteers aged 17-35 years. These tests included visual measures that are mainly neurally limited (spatial summation out to +/-30 degrees in the horizontal visual field and resolution acuity out to +/-10 degrees in the horizontal visual field) and central ocular aberrations. We found that myopia affected the neurally limited tests, but had little effect on central higher order aberration. The critical area for spatial summation increased in the temporal visual field at 0.03 log units/dioptre of myopia. Resolution acuity decreased at approximately 0.012 log units/dioptre of myopia. Losses of visual function were slightly greater in the temporal than in the nasal visual field. The observed visual deficit in myopia can be explained by either global retinal expansion with some post-receptor loss (e.g. ganglion cell death) or a posterior polar expansion in which the point about which expansion occurs is near the centre of the previously emmetropic globe.

Optical models for human myopic eyes

Data from the author's investigations and other studies are used to construct refractive dependent models. These models include a gradient index lens and aspheric corneal, lens and retinal surfaces. Elements that alter with refraction are anterior corneal radius, vitreous length and retinal shape (vertex radius of curvature and asphericity) and decentration. Two versions of the models are produced, one with centred and symmetrical optical elements, and one with tilts of the lens and decentrations and tilts of the retina. The centred model predicts increase in spherical aberration in myopia. It predicts the relative change in mean sphere in the periphery between the horizontal and vertical meridians that has been observed in a recent experimental study. It overestimates peripheral astigmatism by about 50%. The decentred version has limited success in predicting changes in peripheral refraction of average eyes.

Aberrations and myopia

It has been suggested that high levels of axial aberration or specific patterns of peripheral refraction could play a role in myopia development. Possible mechanisms involving high levels of retinal image blur caused by axial aberrations include form deprivation through poor retinal image quality in distance vision, enhanced accommodative lags favouring compensatory eye growth, and an absence of adequate directional cues to guide emmetropization. In addition, in initially emmetropic eyes, hyperopia in the retinal periphery may result in local compensatory eye growth, which induces axial myopia. Evidence in support of these ideas is reviewed and it is concluded that, for any fixed pupil diameter, evidence for higher levels of axial aberration in myopes in comparison with other refractive groups is weak, making involvement of axial aberrations in myopization through image degradation at the fovea unlikely. If, however, some potential myopes had unusually large pupil diameters, their effective aberration levels and associated retinal blur would be larger than those of the rest of the population. There is stronger evidence in favour of differences in patterns of peripheral refraction in both potential and existing myopes, with myopes tending to show relative hyperopia in the periphery. These differences appear to be related to a more prolate eyeball shape. Longitudinal studies are required to confirm whether the retinal defocus associated with the peripheral hyperopia can cause patterns of eyeball growth which lead to axial myopia.

Corneal asphericity after hyperopic laser in situ keratomileusis

PURPOSE

To analyze corneal asphericity after hyperopic laser in situ keratomileusis (LASIK) and its relationship to the clinical outcomes.

SETTING

Corneal and Refractive Surgery Service, Massachusetts Eye and Ear Infirmary, Boston, Massachusetts, USA.

METHODS

In a retrospective case series, 23 patients (33 eyes) with hyperopia or hyperopic astigmatism who had LASIK were evaluated. A computer program (Holladay Diagnostic Summary, EyeSys Laboratories) was used to analyze corneal asphericity (Q) before and after LASIK. Corneal asphericity was evaluated to determine the association with the postoperative refractive error, best spectacle-corrected visual acuity (BSCVA), uncorrected visual acuity (UCVA), achieved refractive correction, mean corneal power (K), refractive yield (achieved/attempted correction), and keratometric yield (change in keratometry/attempted correction).

RESULTS

After hyperopic LASIK, all corneas exhibited increased negative central Q. The postoperative corneal radius of curvature, BSCVA, and refractive and keratometric yields were not significantly correlated with the preoperative Q values. The asphericity change, Delta Q, was highly correlated with the achieved correction (r = 0.747, P <.0001). The postoperative Q value correlated well with the preoperative value (r = 0.534, P <.05) and the achieved correction (r = 0.601, P <.05) but not with the Delta Q. Neither the postoperative Q nor the Delta Q was correlated with the spherical equivalent, K, BSCVA, or UCVA.

CONCLUSIONS

Asphericity may be a useful quantitative descriptor of the corneal optical contour after hyperopic LASIK. Negative central Q increased after hyperopic LASIK, especially when greater degrees of refractive correction were attempted.

Application of linear regression to videokeratoscope data for tilted surfaces

PURPOSE

To investigate the use of linear regression analysis performed on the tabular data display of the EyeSys videokeratoscope (VK). When a radius squared vs distance squared scatterplot is produced from aspheric surface data the equivalent conic section can be deduced from the intercept and slope of the linear regression line. Non-linear plots are often produced. Linear regression may then be applied in a number of ways.

METHOD

Topographical data derived from both the EyeSys VK and a computer model of the instrument were analysed by three methods of linear regression. The resultant apical radii, p-values and predicted surface tilts were compared with known values.

RESULTS

The three methods predict different surface characteristics whose errors were found to vary depending upon the asphericity of the surface and its tilt.

CONCLUSIONS

Apical radius is most accurately predicted by linear regression method (1). Both p-value and tilt are best predicted by averaging the radius and position data for corresponding points in each semi-meridian before squaring the resultant points and performing linear regression (method 3).

Corneal topography by keratometry

AIMS

To investigate the ability of a telecentric keratometer to describe the asphericity and curvature of convex ellipsoidal surfaces and human corneas.

METHODS

22 conicoidal convex surfaces and 30 human corneas were examined by conventional keratometry. Additional keratometric measurements were made when the surface was tilted in the horizontal plane relative to the instrument optical axis. This resulted in a series of radius measurements derived from different regions of the surface. These measurements were used to determine the apical radius and the p value of the horizontal meridian of each surface. The results were compared with those derived from measurements using the EyeSys videokeratoscope and form Talysurf analysis. The method was repeated on 30 human corneas and the results compared with those of a videokeratoscope.

RESULTS

For the aspheric buttons, the keratometric and the EyeSys results tended to give higher values for both apical radius and the p values than those of the Talysurf analysis. The best agreement was between the Talysurf and the keratometer where the results were not significantly different. For the human corneas, the apical radii were significantly different comparing the keratometer with the videokeratoscope but the p values were not significantly different.

CONCLUSION

The keratometric method for assessing curvature and asphericity appears to hold promise as a method for quantifying the corneal topography.

Longitudinal changes in corneal asphericity in myopia

PURPOSE

To report the change in shape of the peripheral cornea (asphericity, Q) as it relates to myopia progression in adolescence.

METHODS

Forty-eight subjects with initial ages between 11 and 13 years of age were observed for 5 years. Each subject had participated in a variety of soft contact lens studies and all had worn daily wear soft contact lenses successfully for the 2 years before collection of the second data set.

RESULTS

Myopia increased by an average of 1.46 D and was strongly correlated with a 0.56-mm increase in axial length. There was no contribution to the change in myopia from the change in central radius of the cornea. A significant (p < 0.01, one tail) correlation was found between Q and the progression of myopia. Principal axis analysis yielded a slope of -0.04 in Q per diopter of increase in myopia.

CONCLUSION

These data show a shift to a more positive Q (in the oblate direction) with increased myopia.

The EyeSys videokeratoscopic assessment of apical radius and p-value in the normal human cornea

The EyeSys videokeratoscope was used to assess the corneal topography in 98 subjects. Scatterplots of distance squared versus radius squared were plotted for the near horizontal and near vertical principal meridians of the two eyes. The regression lines allowed calculation of the surface apical radius and the p-value. The group average apical radius was 7.93 mm (horizontal) and 7.78 mm (vertical). The group average p-value was 0.76 (horizontal) and 0.82 (vertical). Both apical radius and p-value were similar when comparing the two eyes for both the horizontal and the vertical meridians. The two meridians in a single eye, however, had different values for both apical radius and p-value. Male apical radii were longer than those of females but the p-values were the same. There is no apparent association between age and either apical radius or p-value for the subjects used in this study. The asphericity of the cornea does not show any apparent association with corneal curvature in this group of subjects.

Image quality in polypseudophakia for extremely short eyes

AIM

To evaluate the image quality produced by polypseudophakia used for strongly hypermetropic and nanophthalmic eyes.

METHODS

Primary aberration theory and ray tracing analysis were used to calculate the optimum lens shapes and power distribution between the two intraocular lenses for two example eyes: one a strongly hypermetropic eye, the other a nanophthalmic eye. Spherical aberration and oblique astigmatism were considered. Modulation transfer function (MTF) curves were computed using commercial optical design software (Sigma 2100, Kidger Optics Ltd) to assess axial image quality, and the sagittal and tangential image surfaces were computed to study image quality across the field.

RESULTS

A significant improvement in the axial MTF was found for the eyes with double implants. However, results indicate that this may be realised as a better contrast sensitivity in the low to mid spatial frequency range rather than as a better Snellen acuity. The optimum lens shapes for minimum spherical aberration (best axial image quality) were approximately convex-plano for both lenses with the convex surface facing the cornea. Conversely, the optimum lens shapes for zero oblique astigmatism were strongly meniscus with the anterior surface concave. Correction of oblique astigmatism was only achieved with a loss in axial performance.

CONCLUSIONS

Optimum estimated visual acuity exceeds 6/5 in both the hypermetropic and the nanophthalmic eyes studied (pupil size of 4 mm) with polypseudophakic correction. These results can be attained using convex-plano or biconvex lenses with the most convex surface facing the cornea. If the posterior surface of the posterior intraocular lens is convex, as is commonly used to help prevent migration of lens epithelial cells causing posterior capsular opacification (PCO), then it is still possible to achieve 6/4.5 in the hypermetropic eye and 6/5.3 in the nanophthalmic eye provided the anterior intraocular lens has an approximately convex-plano shape with the convex surface anterior. It was therefore concluded that consideration of optical image quality does not demand that additional intraocular lens shapes need to be manufactured for polypseudophakic correction of extremely short eyes and that implanting the posterior intraocular lens in the conventional orientation to help prevent PCO does not necessarily limit estimated visual acuity.

Evaluation of relationships among refractive and topographic parameters

PURPOSE

To examine the relationships among several refractive and topographic parameters.

SETTING

Cullen Eye Institute Department of Ophthalmology, Baylor College of Medicine, Houston, Texas, USA.

METHODS

Using computerized videokeratography (EyeSys Corneal Analysis System), 287 corneas of 150 patients were retrospectively analyzed. The Holladay Diagnostic Summary (HDS) refractive maps were used to evaluate relationships among variables of the HDS and refractive error.

RESULTS

Myopic spherical equivalent refraction (P = .0003) and more negative asphericity (Q-values) (P = .0119) were correlated with steeper corneas. The Q-values were less negative in eyes with moderate myopia (2.0 to 6.0 diopters [D]) than in those with hyperopia (1.0 D or greater). The Q-values below -0.3 were correlated with less favorable values for predicted corneal acuity and corneal uniformity index values. Mean corneal curvature measurements obtained by computerized videokeratography and standard keratometry showed a strong degree of correlation (P = .0001).

CONCLUSION

As the degree of myopia and negative asphericity increased, the corneal radius of curvature decreased. Corneal Q-values less than -0.3 were associated with reduced optical performance of the cornea.

Contact lens back surface specification derived from the EyeSys videokeratoscope

Rigid corneal lenses were designed for 36 subjects using the software available with the EyeSys Corneal Analysis System 2000 (software version 2.00W) and a program from the textbook 'Contact lens Optics and Lens Design' Both alignment and apical clearance designs were investigated. It was found that the EyeSys lenses produced tear layer thickness and axial edge clearance values that were excessive in some cases, especially for flatter corneas. In the case of an alignment mode of fitting, the designs were relatively steep in the back optic zone and flat in the periphery when compared with designs derived from the textbook.

The Shape of Bowman's Layer in the Human Cornea

PURPOSE

The aim of this investigation was to derive a mathematical model for Bowman's layer, the interface between the epithelium and stroma, in the human cornea.

METHODS

The central epithelial thickness distribution within 14 normal human corneas was measured in vivo using high frequency ultrasonic digital signal processing with a measurement precision of 2 microns. The results per eye were averaged and incorporated into existing algorithms for the estimation of the shape of the anterior surface of Bowman's layer using terminology in accordance with Baker's equation.

RESULTS

The average radius of Bowman's layer was 7.34 mm (SE +/- 0.17 mm). Descriptions of this boundary ranged from a steepening or prolate ellipse to a hyperbola. However, the typical Bowman's layer is hyperbolic with a shape factor, p = -0.22 (SE +/- 1.81).

CONCLUSION

The results support previous cadaver studies where Bowman's layer was found to be steeper than the anterior corneal surface but disagree with the concept that the average Bowman's layer is akin to a prolate ellipse. The hyperbolic nature of the average Bowman's layer has the potential to influence the optical performance of the eye.

Corneal shape in hyperopia

Background: A trend towards decreased peripheral corneal flattening with increasing myopia has recently been demonstrated. The present study was conducted to determine whether corneal asphericity also varies significantly with hyperopic refractive error. Methods: Thirty-five eyes with spherical equivalent refractive error ranging from -0.37 D to +6.00 D were examined. A conicoid equation was fitted to videokeratoscopic (Topographic Modeling System) data and corneal asphericity and apical radius of curvature values were calculated for each subject. Axial length measurements were made using a hand-held biometric ruler. Keratometry was also performed on each eye. Results: The relationship between corneal asphericity (Q) and spherical equivalent refractive error was not statistically significant (p = 0.7419). In addition, no association could be demonstrated between Q and corneal radius of curvature or between Q and axial length. Corneal radius of curvature was positively correlated with axial length (r = 0.367, p = 0.0298). Axial length was found to decrease as hyperopic refractive error increased (r = 0.753, p = 0.0001). Conclusions: For hyperopic eyes, corneal asphericity does not appear to be significantly correlated with refractive error, a finding that is at variance with previous data for myopic eyes showing an association between these two variables. The results suggest that there may be differences between hyperopic and myopic eyes with regard to the anterior segment changes that occur during refractive error development.

Model for Deriving the Optical Performance of the Myopic Eye Corrected With An Intracorneal Ring

BACKGROUND

The intracorneal ring has been advanced as a mechanical device for the correction of myopia. The device may reduce refractive error, but the effect on the overall optical performance of the eye has been neglected. This paper addresses this issue by presenting mathematical models that will predict the effect of the intracorneal ring on refractive error, corneal asphericity, and the spherical aberration of the eye.

MATERIALS AND METHODS

Algorithms are derived for predicting the corneal apical radius, asphericity, and the change in myopia after inserting intracorneal rings of any thickness and diameter.

RESULTS

The model predicts that the magnitude of myopia reduction is a function of both ring thickness and diameter. The large diameter (9 to 10 mm), thin (0.1 to 0.2 mm) intracorneal ring is less likely to adversely affect corneal asphericity and therefore not significantly enhance the spherical aberration of the eye.

CONCLUSIONS

An intracorneal ring cannot correct more than 4.00 diopters (D) of myopia without significantly increasing ocular spherical aberration, which, in turn, will compromise the final visual outcome.

Topographic determination of corneal asphericity and its lack of effect on the refractive outcome of radial keratotomy

PURPOSE

The normal human cornea flattens peripherally. The amount of flattening, or asphericity, has traditionally been calculated from multiple keratometric measurements. We devised a mathematical technique for determining asphericity from computed corneal topography. We then determined whether asphericity affects the refractive outcome of radial keratotomy.

METHODS

One eye each of 41 patients who underwent four- or eight-incision radial keratotomy and preoperative computed corneal topography was identified retrospectively and analyzed. The asphericity, P, of each cornea was calculated by fitting Baker's equation (y2 = 2r0x-Px2) to each meridian of the topographic map. For each patient, we calculated the difference between the refractive outcome in diopters for radial keratotomy and the prediction of a quadratic least-squares best-fit model involving optical zone size and age.

RESULTS

Aspericity could be calculated from the topographic maps in all 41 patients and ranged from 0.33 to 1.28, with mean +/- S.D. of 0.82 +/- 0.21. Aphericity varied among the meridians of a cornea, with an average standard deviation among meridians of 0.17. No statistical correlation was found between calculated asphericity and refractive outcome.

CONCLUSIONS

Corneal asphericity can be calculated from corneal topographic maps. Asphericity is not constant in the different meridians of a normal cornea. Corneal asphericity is not useful in predicting the refractive outcome of radial keratotomy.

The shape of the corneal apical zone after excimer photorefractive keratectomy

Applying an experimental photo-keratoscope, which assesses the shape of cornea within the pupillary region, to a group of subjects who have undergone excimer laser photorefractive keratectomy over a central 4 mm chord diameter of the cornea, we report the shape of the typical cornea within the ablated zone conforms to a steepening ellipse (average shape factor, 1.25). A statistically significant difference in the mean shape factor (asphericity) between the photoablated and the normal cornea (average shape factor 0.89) was not confirmed. However, there is more variability in the shape factors found in the photorefractive keratectomy group compared with normals, within the same distance from the corneal apex. Using the criterion of overlap within two standard deviations, averaging the vertical horizontal meridians, 75% of photorefractive keratectomy eyes fall within the shape factor limits of the normal eye group. In all cases the post-ablated corneal surface was found to be regular in terms of surface quality alone. The excimer photorefractive keratectomy technique is therefore a clinically acceptable method of refractive surgery.

An improved universal theoretical formula for intraocular lens power prediction

Although available empirically derived and theoretical formulas perform adequately for eyes of average axial length, both have been shown to be deficient for eyes that have unusually short and long axial lengths. I developed a formula based on a theoretical model eye in which anterior chamber depth is related to axial length and keratometry. A relationship between the A-constant and a "lens factor" is also used to determine anterior chamber depth. The location of the intraocular lens' principle planes of refraction is retained as a relevant variable in the formula, and the user need not know the material and construction of the lens and or its constant. I compared the new formula with the SRK II, Holladay, and SRK/T formulas in a group of 100 unselected patients and in selected subgroups of patients with average, short, and long axial lengths. The new formula was significantly more accurate than the other third-generation formulas and maintained its accuracy in the subgroups. The formula can be described as universal because it can be used for different lens styles and for eyes with short, medium, and long axial lengths.