Corneal topography by keratometry

Agreement between Pentacam and handheld Auto-Refractor/Keratometer for keratometry measurement

OBJECTIVE

This study was conducted to evaluate the level of agreement in keratometry measurements between a rotating Scheimpflug imaging-based system (Pentacam) and a handheld auto-refractokeratometer (handheld NIDEK ARK-30).

METHOD

This analytical cross-sectional study was conducted in the right eyes of 579 subjects. Keratometry measurements were conducted with the Pentacam and the handheld NIDEK ARK-30 systems. The SPSS Software version 22 and MedCalc V3 were applied to estimate descriptive statistics using paired t-test, Pearson correlation coefficient, 95% limits of agreement (LoA), and Bland-Altman plot.

RESULTS

In the total sample, the inter-device difference in the mean flat and steep keratometry values was -0.266 diopter (D) (P-value<0.001) and 0.052D (P-value=0.093), respectively. There was a significant difference in mean flat keratometry between the two devices in all groups of refractive errors (paired difference <0.5D and P-value<0.001). The difference in mean steep keratometry was significant only in myopic subjects (P-value=0.046). The 95% LoA between the two devices measurements was 2.51D, 3.98D, and 6.37D for flat keratometry and 2.6D, 3.2D, and 3.9D for steep keratometry in emmetropic, myopic, and hyperopic subjects, respectively.

CONCLUSION

Our study showed relatively wide limits of agreement between handheld NIDEK ARK-30 and Pentacam; therefore, these devices cannot be used interchangeably for measuring corneal curvature.

Anterior corneal asphericity calculated by the tangential radius of curvature

We propose a method of calculating the corneal asphericity (Q) and analyze the characteristics of the anterior corneal shape using the tangential radius. Fifty-eight right eyes of 58 subjects were evaluated using the Orbscan II corneal topographer. The Q-values of the flat principal semi-meridians calculated by the sagittal radius were compared to those by the tangential radius. Variation in the Q-value with semi-meridian in the nasal and temporal cornea calculated by the tangential radius was analyzed. There were significant differences in Q-values (P<0.001) between the two methods. The mean Q-values of the flat principal semi-meridians calculated by tangential radius with -0.33 ± 0.10 in the nasal and -0.22 ± 0.12 in the temporal showed more negative than the corresponding Q-values calculated by the sagittal radius. The Q-values calculated by tangential radius became less negative gradually from horizontal semi-meridians to oblique semi-meridians in both nasal and temporal cornea. Variation in Q-value with semi-meridian was more obvious in the nasal cornea. The method of calculating corneal Q using the tangential radius could provide more reasonable and complete Q-value than that by the sagittal radius. The model of a whole anterior corneal surface could be reconstructed on the basis of the above method.

Origins of the keratometer and its evolving role in ophthalmology

The keratometer, or ophthalmometer as it was originally known, had its origins in the attempt to discover the seat of accommodation in the eye. Since that early beginning, it has been re-invented a number of times, with improvements and modifications made in the original principles of its design for new applications that arose as ophthalmology advanced. The cornea is not only responsible for the majority of the refraction in the eye, but is also readily accessible for measurement and modification. The keratometer's ability to measure the cornea has allowed it to play a central role in critical advances in ophthalmic history. This review describes the origins and principles of this instrument, the novel applications that led to the keratometer's continued resurgences over its nearly 250-year history, and the modern devices that have borrowed its basic principles and are beginning to replace it in common clinical practice.

Optical surface reconstruction technique through combination of zonal and modal fitting

Videokeratometers and Scheimpflug cameras permit accurate estimation of corneal surfaces. From height data it is possible to adjust analytical surfaces that will be later used for aberration calculation. Zernike polynomials are often used as adjusting polynomials, but they have shown to be not precise when describing highly irregular surfaces. We propose a combined zonal and modal method that allows an accurate reconstruction of corneal surfaces from height data, diminishing the influence of smooth areas over irregular zones and vice versa. The surface fitting error is decreased in the considered cases, mainly in the central region, which is more important optically. Therefore, the method can be established as an accurate resampling technique.

Curvature of ellipsoids and other surfaces

From differential geometry one obtains an expression for the curvature in any direction at a point on a surface. The general theory is outlined. The theory is then specialised for surfaces that are represented parametrically as height over a transverse plane. The general ellipsoid is treated in detail as a special case. A quadratic equation gives the principal directions at the point and, hence, the principal curvatures associated with them. Equations are obtained for ellipsoids in general that are generalisations of Bennett's equations for sagittal and tangential curvature of ellipsoids of revolution. Equations are also presented for the locations of umbilic points on the ellipsoid.

A comparison of the ARK-700A autokeratometer and Medmont E300 corneal topographer when measuring peripheral corneal curvature

PURPOSE

The purpose of this study was to evaluate if corneal topogometry measurements as taken with the ARK-700A autokeratometer are comparable with those measured by the Medmont E300 videokeratoscope at corresponding locations.

METHODS

Central and peripheral radius and eccentricity were measured in 122 right eyes of young normal subjects using autokeratometry and videokeratoscopy, obtained in a random order.

RESULTS

Curvature measurements obtained with the ARK700A and Medmont E300 correlated well for the central cornea. Larger differences were observed between peripheral autokeratometry readings and the empirically determined corresponding locations with the videokeratoscope. Correlations between the instruments are inconsistent, resulting in unacceptable confidence intervals. Corneal eccentricity was significantly different between the instruments for the vertical (t = 2.4; p = 0.018) and for the horizontal meridians. In the first case, the difference between the averaged values was not clinically significant, but in the horizontal meridian the AK significantly overestimated eccentricity values (t = -11.5; p < 0.001) with differences which were clinically significant.

CONCLUSIONS

Central corneal curvature data obtained by ARK700A and Medmont E300 can be interchanged but the same is not true of peripheral determinations of corneal shape. ARK700A probably measures peripheral corneal shape within an elliptical region between 5 and 7 mm in diameter, with the major axis in the vertical meridian.

Verification of aspheric contact lens back surfaces

PURPOSE

To suggest a tolerance level for the degree of asphericity of aspheric rigid gas-permeable contact lenses and to find a simple method for its verification.

METHODS

Using existing tolerances for the vertex radius, tolerance limits for eccentricity and p values and were calculated. A keratometer-based method and a method based on sag measurements were used to measure the vertex radius and eccentricity of eight concave progressively aspheric surfaces and six concave ellipsoidal surfaces. The results were compared with a gold standard measurement made using a high-precision mechanical instrument (Form Talysurf).

RESULTS

The suggested tolerance for eccentricity and p value and is +/-0.05. The keratometer method was very accurate and precise at measuring the vertex radius (mean deviation +/- SD from Talysurf results, -0.002 +/- 0.008 mm). The keratometer was more precise than and similar in accuracy to the sag method for measurement of asphericity (mean deviation of keratometer method results from Talysurf results, 0.017 +/- 0.018; mean deviation of sag method results from Talysurf results using five semichords, -0.016 +/- 0.032).

CONCLUSION

Neither method was precise enough to verify the asphericity within the suggested tolerance. The keratometer can be efficiently used to verify the back vertex radius within its International Organization for Standardization tolerance and the back surface asphericity within an eccentricity/p value tolerance of +/-0.1. The method is poor for progressive aspheres with large edge blending zones. Deriving the eccentricity from sag measurements is a potential alternative if the mathematical description of the surface is known. The limiting factor of this method is the accuracy and precision of individual sag measurements.

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).