Clinical validation of an algorithm to correct the error in the keratometric estimation of corneal power for normal eyes

To validate clinically an algorithm for correcting the error in the keratometric estimation of corneal power by using a variable keratometric index of refraction (nk) in a normal healthy population.

Algorithm for Correcting the Keratometric Error in the Estimation of the Corneal Power in Eyes With Previous Myopic Laser Refractive Surgery

Purpose: To calculate theoretically the errors in the estimation of corneal power when using the keratometric index (nk) in eyes that underwent laser refractive surgery for the correction of myopia and to define and validate clinically an algorithm for minimizing such errors. Methods: Differences between corneal power estimation by using the classical nk and by using the Gaussian equation in eyes that underwent laser myopic refractive surgery were simulated and evaluated theoretically. Additionally, an adjusted keratometric index (nkadj) model dependent on r1c was developed for minimizing these differences. The model was validated clinically by retrospectively using the data from 32 myopic eyes [range, −1.00 to −6.00 diopters (D)] that had undergone laser in situ keratomileusis using a solid-state laser platform. The agreement between Gaussian (PGaussc) and adjusted keratometric (Pkadj) corneal powers in such eyes was evaluated. Results: It was found that overestimations of corneal power up to 3.5 D were possible for nk = 1.3375 according to our simulations. The nk value to avoid the keratometric error ranged between 1.2984 and 1.3297. The following nkadj models were obtained: nkadj= −0.0064286r1c + 1.37688 (Gullstrand eye model) and nkadj = −0.0063804r1c + 1.37806 (Le Grand). The mean difference between Pkadj and PGaussc was 0.00 D, with limits of agreement of −0.45 and +0.46 D. This difference correlated significantly with the posterior corneal radius (r = −0.94, P < 0.01). Conclusions: The use of a single nk for estimating the corneal power in eyes that underwent a laser myopic refractive surgery can lead to significant errors. These errors can be minimized by using a variable nk dependent on r1c.

New Approach for Correction of Error Associated With Keratometric Estimation of Corneal Power in Keratoconus

The aim of this study was to obtain the exact value of the keratometric index (nkexact) and to clinically validate a variable keratometric index (nkadj) that minimizes this error. Methods: The nkexact value was determined by obtaining differences (DPc) between keratometric corneal power (Pk) and Gaussian corneal power (PGauss c ) equal to 0. The nkexact was defined as the value associated with an equivalent difference in the magnitude of DPc for extreme values of posterior corneal radius (r2c) for each anterior corneal radius value (r1c). This nkadj was considered for the calculation of the adjusted corneal power (Pkadj). Values of r1c ∈ (4.2, 8.5) mm and r2c ∈ (3.1, 8.2) mm were considered. Differences of True Net Power with PGauss c , Pkadj, and Pk(1.3375) were calculated in a clinical sample of 44 eyes with keratoconus. Results: nkexact ranged from 1.3153 to 1.3396 and nkadj from 1.3190 to 1.3339 depending on the eye model analyzed. All the nkadj values adjusted perfectly to 8 linear algorithms. Differences between Pkadj and PGauss c did not exceed 60.7 D (Diopter). Clinically, nk = 1.3375 was not valid in any case. Pkadj and True Net Power and Pk(1.3375) and Pkadj were statistically different (P , 0.01), whereas no differences were found between PGauss c and Pkadj (P . 0.01). Conclusions: The use of a single value of nk for the calculation of the total corneal power in keratoconus has been shown to be imprecise, leading to inaccuracies in the detection and classification of this corneal condition. Furthermore, our study shows the relevance of corneal thickness in corneal power calculations in keratoconus.

Estimation of the Central Corneal Power in Keratoconus: Theoretical and Clinical Assessment of the Error of the Keratometric Approach

Purpose: The aim of this study was to analyze theoretically the errors in the central corneal power calculation in eyes with keratoconus when a keratometric index (nk) is used and to clinically confirm the errors induced by this approach. Methods: Differences (DPc) between central corneal power estimation with the classical nk (Pk) and with the Gaussian equation (PGauss c ) in eyes with keratoconus were simulated and evaluated theoretically, considering the potential range of variation of the central radius of curvature of the anterior (r1c) and posterior (r2c) corneal surfaces. Further, these differences were also studied in a clinical sample including 44 keratoconic eyes (27 patients, age range: 14–73 years). The clinical agreement between Pk and PGauss c (true net power) obtained with a Scheimpflug photography–based topographer was evaluated in such eyes. Results: For nk = 1.3375, an overestimation was observed in most cases in the theoretical simulations, with DPc ranging from an underestimation of 20.1 diopters (D) (r1c = 7.9 mm and r2c = 8.2 mm) to an overestimation of 4.3 D (r1c = 4.7 mm and r2c = 3.1 mm). Clinically, Pk always overestimated the PGauss c given by the topography system in a range between 0.5 and 2.5 D (P , 0.01). The mean clinical DPc was 1.48 D, with limits of agreement of 0.71 and 2.25 D. A very strong statistically significant correlation was found between DPc and r2c (r = 20.93, P , 0.01). Conclusions: The use of a single value for nk for the calculation of corneal power is imprecise in keratoconus and can lead to significant clinical errors.

Error induced by the estimation of the corneal power and the effective lens position with a rotationally asymmetric refractive multifocal intraocular lens

AIM: To evaluate the prediction error in intraocular lens (IOL) power calculation for a rotationally asymmetric refractive multifocal IOL and the impact on this error of the optimization of the keratometric estimation of the corneal power and the prediction of the effective lens position (ELP). METHODS: Retrospective study including a total of 25 eyes of 13 patients (age, 50 to 83y) with previous cataract surgery with implantation of the Lentis Mplus LS-312 IOL (Oculentis GmbH, Germany). In all cases, an adjusted IOL power (PIOLadj) was calculated based on Gaussian optics using a variable keratometric index value (nkadj) for the estimation of the corneal power (Pkadj) and on a new value for ELP (ELPadj) obtained by multiple regression analysis. This PIOLadj was compared with the IOL power implanted (PIOLReal) and the value proposed by three conventional formulas (Haigis, Hoffer Q and Holladay). RESULTS: PIOLReal was not significantly different than PIOLadj and Holladay IOL power (P>0.05). In the Bland and Altman analysis, PIOLadj showed lower mean difference (-0.07 D) and limits of agreement (of 1.47 and -1.61 D) when compared to PIOLReal than the IOL power value obtained with the Holladay formula. Furthermore, ELPadj was significantly lower than ELP calculated with other conventional formulas (P<0.01) and was found to be dependent on axial length, anterior chamber depth and Pkadj. CONCLUSION: Refractive outcomes after cataract surgery with implantation of the multifocal IOL Lentis Mplus LS-312 can be optimized by minimizing the keratometric error and by estimating ELP using a mathematical expression dependent on anatomical factors.

Errors Associated to Keratoconus Grading using Systems based on Corneal Power

Purpose: To analyze and define the possible errors that may be introduced in keratoconus classification when the keratometric corneal power is used in such classification. Materials and methods: Retrospective study including a total of 44 keratoconus eyes. A comprehensive ophthalmologic examination was performed in all cases, which included a corneal analysis with the Pentacam system (Oculus). Classical keratometric corneal power (Pk), Gaussian corneal power (Pc Gauss), True Net Power (TNP) (Gaussian power neglecting the corneal thickness effect), and an adjusted keratometric corneal power (Pkadj) (keratometric power considering a variable keratometric index) were calculated. All cases included in the study were classified according to five different classification systems: Alió-Shabayek, Amsler-Krumeich, Rabinowitz-McDonnell, collaborative longitudinal evaluation of keratoconus (CLEK), and McMahon. Results: When Pk and Pkadj were compared, differences in the type of grading of keratoconus cases was found in 13.6% of eyes when the Alió-Shabayek or the Amsler-Krumeich systems were used. Likewise, grading differences were observed in 22.7% of eyes with the Rabinowitz-McDonnell and McMahon classification systems and in 31.8% of eyes with the CLEK classification system. All reclassified cases using Pkadj were done in a less severe stage, indicating that the use of Pk may lead to the classification of a cornea as keratoconus, being normal. In general, the results obtained using Pkadj, Pc Gauss or the TNP were equivalent. Differences between Pkadj and Pc Gauss were within ± 0.7D. Conclusion: The use of classical keratometric corneal power may lead to incorrect grading of the severity of keratoconus, with a trend to a more severe grading.

Clinical Validation of Adjusted Corneal Power in Patients with Previous Myopic Lasik Surgery

Purpose. To validate clinically a new method for estimating the corneal power (P,) using a variable keratometric index (nkadj) in eyes with previous laser refractive surgery. Setting. University of Alicante and Medimar International Hospital (Oftalmar), Alicante, (Spain). Design. Retrospective case series. Methods. This retrospective study comprised 62 eyes of 62 patients that had undergone myopic LASIK surgery. An algorithm for the calculation of 11kadj was used for the estimation of the adjusted keratometric corneal power (Pkadj). This value was compared with the classical keratometric corneal power (Pk), the True Net Power (TNP), and the Gaussian corneal power (PcGauss). Likewise, Pkadj was compared with other previously described methods. Results. Differences between PcGauss and P, values obtained with all methods evaluated were statistically significant (p < 0.01). Differences between Pkadj and PcGauss were in the limit of clinical significance (p < 0.01, loA [ - 0.33,0.60] D). Differences between Pkadj and TNP were not statistically and clinically significant (p = 0.319, loA [- 0.50,0.44] D). Differences between Pkadj and previously described methods were statistically significant (p < 0.01), except with PcHaigisL (p = 0.09, loA [ - 0.37,0.29] D). Conclusion. The use of the adjusted keratometric index (nkadj) is a valid method to estimate the central corneal power in corneas with previous myopic laser refractive surgery, providing results comparable to PcHaigisL.

Positional accommodative intraocular lens power error induced by the estimation of the corneal power and the effective lens position

Purpose: To evaluate the predictability of the refractive correction achieved with a positional accommodating intraocular lenses (IOL) and to develop a potential optimization of it by minimizing the error associated with the keratometric estimation of the corneal power and by developing a predictive formula for the effective lens position (ELP). Materials and Methods: Clinical data from 25 eyes of 14 patients (age range, 52–77 years) and undergoing cataract surgery with implantation of the accommodating IOL Crystalens HD (Bausch and Lomb) were retrospectively reviewed. In all cases, the calculation of an adjusted IOL power (PIOLadj) based on Gaussian optics considering the residual refractive error was done using a variable keratometric index value (nkadj) for corneal power estimation with and without using an estimation algorithm for ELP obtained by multiple regression analysis (ELPadj). PIOLadj was compared to the real IOL power implanted (PIOLReal, calculated with the SRK-T formula) and also to the values estimated by the Haigis, HofferQ, and Holladay I formulas. Results: No statistically significant differences were found between PIOLReal and PIOLadj when ELPadj was used (P = 0.10), with a range of agreement between calculations of 1.23 D. In contrast, PIOLReal was significantly higher when compared to PIOLadj without using ELPadj and also compared to the values estimated by the other formulas. Conclusions: Predictable refractive outcomes can be obtained with the accommodating IOL Crystalens HD using a variable keratometric index for corneal power estimation and by estimating ELP with an algorithm dependent on anatomical factors and age.

Short-term and long-term changes in corneal power are not correlated with axial elongation of the eye induced by orthokeratology in children

PURPOSE: To assess the relationship between short-term and long-term changes in power at different corneal locations relative to the change in central corneal power and the 2-year change in axial elongation relative to baseline in children fitted with orthokeratology contact lenses (OK). METHODS: Thirty-one white European subjects 6 to 12 years of age and with myopia −0.75 to −4.00 DS and astigmatism ≤1.00 DC were fitted with OK. Differences in refractive power 3 and 24 months post-OK in comparison with baseline and relative to the change in central corneal power were determined from corneal topography data in eight different corneal regions (i.e., N[nasal]1, N2, T[temporal]1, T2, I[inferior]1, I2, S[superior]1, S2), and correlated with OK-induced axial length changes at two years relative to baseline. RESULTS: After 2 years of OK lens wear, axial length increased by 0.48±0.18 mm (P0.05). CONCLUSION: The reduction in central corneal power and relative increase in paracentral and pericentral power induced by OK over 2 years were not significantly correlated with concurrent changes in axial length of white European children.

Corneal changes following near work in myopic anisometropia

PURPOSE: To examine the symmetry of corneal changes following near work in the fellow eyes of non-amblyopic myopic anisometropes. METHODS: Thirty-four non-amblyopic myopic anisometropes (minimum 1 D spherical equivalent anisometropia) were recruited. Corneal topography was measured with the Medmont E300 Videokeratoscope before and after a controlled near task. Subjects were positioned to minimise head movements and read continuous text on a computer monitor for 10 minutes at an angle of 25 degrees downward gaze and an accommodation demand of 2.5 D. Measures of palpebral aperture morphology during primary and downward gaze were also obtained using digital photography and analysed with customised software. RESULTS: Significant changes in corneal topography were observed after ten minutes of reading. Localised superior regions of corneal topographical change (a hyperopic shift in corneal power) were typically exhibited in both eyes following the near task. The mean change in the corneal sphero-cylinder was +0.02/-0.11 x 113 and +0.02/-0.06 x 68 for the more and less myopic eyes respectively for a 6 mm corneal diameter. A significantly greater change in corneal astigmatism power vector J0 (a larger increase in against the rule astigmatism) was observed in the more myopic eyes (p < 0.01 for a 6 mm diameter). The more and less myopic eyes exhibited a high degree of interocular symmetry for measures of palpebral aperture morphology during both primary and downward gaze. Changes in corneal power vectors following reading were associated with eyelid position during downward gaze. CONCLUSIONS: Changes in corneal topography observed following a controlled reading task were highly symmetrical between the fellow eyes of myopic anisometropes due to the interocular symmetry of the palpebral aperture. However, the more myopic eye did exhibit a small but significantly greater magnitude of change in corneal astigmatism compared to the less myopic eye following reading. These findings may have implications for understanding the mechanism of development of non-amblyopic myopic anisometropia.

Corneal changes following near work in myopic anisometropia

Purpose: To examine the symmetry of corneal changes following near work in the fellow eyes of non-amblyopic myopic anisometropes. Methods: Thirty-four non-amblyopic, myopic anisometropes (minimum 1 D spherical equivalent anisometropia) had corneal topography measured before and after a controlled near work task. Subjects were positioned in a headrest to minimise head movements and read continuous text on a computer monitor for 10 minutes at an angle of 25 degrees downward gaze and an accommodation demand of 2.5 D. Measures of the morphology of the palpebral aperture during primary and downward gaze were also obtained. Results: The more and less myopic eyes exhibited a high degree of interocular symmetry for measures of palpebral aperture morphology during both primary and downward gaze. Following the near work task, fellow eyes also displayed a symmetrical change in superior corneal topography (hyperopic defocus) which correlated with the position of the upper eyelid during downward gaze. Greater changes in the spherical corneal power vector (M) following reading were associated with narrower palpebral aperture during downward gaze (p = 0.07 for more myopic and p = 0.03 for less myopic eyes). A significantly greater change in J0 (an increase in against the rule astigmatism) was observed in the more myopic eyes (-0.04 ± 0.04 D) compared to the less myopic eyes (-0.02 ± 0.06 D) over a 6 mm corneal diameter (p = 0.01). Conclusions: Changes in corneal topography following near work are highly symmetrical between the fellow eyes of myopic anisometropes due to the interocular symmetry of the palpebral aperture. However, the more myopic eye exhibits changes in corneal astigmatism of greater magnitude compared to the less myopic eye.

Minimizing the IOL Power Error Induced by Keratometric Power

Purpose. To evaluate theoretically in normal eyes the influence on IOL power (PIOL) calculation of the use of a keratometric index (nk) and to analyze and validate preliminarily the use of an adjusted keratometric index (nkadj) in the IOL power calculation (PIOLadj). Methods. A model of variable keratometric index (nkadj) for corneal power calculation (Pc) was used for IOL power calculation (named PIOLadj). Theoretical differences ($PIOL) between the new proposed formula (PIOLadj) and which is obtained through Gaussian optics (PIOL Gauss) were determined using Gullstrand and Le Grand eye models. The proposed new formula for IOL power calculation (PIOLadj) was prevalidated clinically in 81 eyes of 81 candidates for corneal refractive surgery and compared with Haigis, HofferQ, Holladay, and SRK/T formulas. Results. A theoretical PIOL underestimation greater than 0.5 diopters was present in most of the cases when nk = 1.3375 was used. If nkadj was used for Pc calculation, a maximal calculated error in $PIOL of T0.5 diopters at corneal vertex in most cases was observed independently from the eye model, r1c, and the desired postoperative refraction. The use of nkadj in IOL power calculation (PIOLadj) could be valid with effective lens position optimization nondependent of the corneal power. Conclusions. The use of a single value of nk for Pc calculation can lead to significant errors in PIOL calculation that may explain some IOL power overestimations with conventional formulas. These inaccuracies can be minimized by using the new PIOLadj based on the algorithm of nkadj.

Relationship among Corneal Biomechanics, Refractive Error, and Axial Length

Purpose: To evaluate the relationship between different ocular and corneal biomechanical parameters in emmetropic and ametropic healthy white children. Methods: This study included 293 eyes of 293 healthy Spanish children (135 boys and 158 girls), ranging in age from 6 to 17 years. Subjects were divided according to the refractive error: control (emmetropia, 99 children), myopia (100 children), and hyperopia (94 children) groups. In all cases, corneal hysteresis (CH) and corneal resistance factor (CRF) were evaluated with the Ocular Response Analyzer system. Axial length (AL) and mean corneal power were also measured by partial coherence interferometry (IOLMaster), and central corneal thickness (CCT) and anterior chamber depth were measured by anterior segment optical coherence tomography (Visante). Results: Mean (±SD) CH and CRF were 12.12 (±1.71) and 12.30 (±1.89) mm Hg, respectively. Mean (±SD) CCT was 542.68 (±37.20) μm and mean (±SD) spherical equivalent was +0.14 (±3.41) diopters. A positive correlation was found between CH and CRF (p < 0.001), and both correlated as well with CCT (p < 0.0001). Corneal resistance factor was found to decrease with increasing age (p = 0.01). Lower levels of CH were associated with longer AL and more myopia (p < 0.001 and p = 0.001, respectively). Higher values of CH were associated with increasing hyperopia. Significant differences in CH were found between emmetropic and myopic groups (p < 0.001) and between myopic and hyperopic groups (p = 0.011). There were also significant differences in CRF between emmetropic and myopic groups (p = 0.02). Multiple linear regression analysis showed that lower CH and CRF significantly associated with thinner CCT, longer AL, and flatter corneal curvature. Conclusions: The Ocular Response Analyzer corneal biomechanical properties seem to be compromised in myopia from an early age, especially in high myopia.

Theoretical evaluation of the cataract extraction-refraction-implantation techniques for intraocular lens power calculation

PURPOSE: To evaluate theoretically three previously published formulae that use intra-operative aphakic refractive error to calculate intraocular lens (IOL) power, not necessitating pre-operative biometry. The formulae are as follows: IOL power (D) = Aphakic refraction x 2.01 [Ianchulev et al., J. Cataract Refract. Surg.31 (2005) 1530]; IOL power (D) = Aphakic refraction x 1.75 [Mackool et al., J. Cataract Refract. Surg.32 (2006) 435]; IOL power (D) = 0.07x(2) + 1.27x + 1.22, where x = aphakic refraction [Leccisotti, Graefes Arch. Clin. Exp. Ophthalmol.246 (2008) 729]. METHODS: Gaussian first order calculations were used to determine the relationship between intra-operative aphakic refractive error and the IOL power required for emmetropia in a series of schematic eyes incorporating varying corneal powers, pre-operative crystalline lens powers, axial lengths and post-operative IOL positions. The three previously published formulae, based on empirical data, were then compared in terms of IOL power errors that arose in the same schematic eye variants. RESULTS: An inverse relationship exists between theoretical ratio and axial length. Corneal power and initial lens power have little effect on calculated ratios, whilst final IOL position has a significant impact. None of the three empirically derived formulae are universally accurate but each is able to predict IOL power precisely in certain theoretical scenarios. The formulae derived by Ianchulev et al. and Leccisotti are most accurate for posterior IOL positions, whereas the Mackool et al. formula is most reliable when the IOL is located more anteriorly. CONCLUSION: Final IOL position was found to be the chief determinant of IOL power errors. Although the A-constants of IOLs are known and may be accurate, a variety of factors can still influence the final IOL position and lead to undesirable refractive errors. Optimum results using these novel formulae would be achieved in myopic eyes.

Changes in ocular biometrics and refraction during near work in downward gaze over time

PURPOSE To investigate changes in the characteristics of the corneal optics, total optics, anterior biometrics and axial length of the eye during a near task, in downward gaze, over 10 min. METHODS Ten emmetropes (mean - 0.14 ± 0.24 DS) and 10 myopes (mean - 2.26 ± 1.42 DS) aged from 18 to 30 years were recruited. To measure ocular biometrics and corneal topography in downward gaze, an optical biometer (Lenstar LS900) and a rotating Scheimpflug camera (Pentacam HR) were inclined on a custom built, height and tilt adjustable table. The total optics of the eye were measured in downward gaze with binocular fixation using a modified Shack-Hartmann wavefront sensor. Initially, subjects performed a distance viewing task at primary gaze for 10 min to provide a "wash-out" period for prior visual tasks. A distance task (watching video at 6 m) in downward gaze (25°) and a near task (watching video on a portable LCD screen with 2.5 D accommodation demand) in primary gaze and 25°downward gaze were then carried out, each for 10 min in a randomized order. During measurements, in dichoptic view, a Maltese cross was fixated with the right (untested) eye and the instrument’s fixation target was fixated with the subject’s tested left eye. Immediately after (0 min), 5 and 10 min from the commencement of each trial, measurements of ocular parameters were acquired in downward gaze. RESULTS Axial length exhibited a significant increase with downward gaze and accommodation over time (p<0.05). The greatest axial elongation was observed in downward gaze with 2.5 D accommodation after 10 min (mean change from baseline 23±3 µm). Downward gaze also caused greater changes in anterior chamber depth (ACD) and lens thickness (LT) with accommodation (ACD mean change -163±12µm at 10 min; LT mean change 173±17 µm at 10 min) compared to primary gaze with accommodation (ACD mean change -138±12µm at 10 min; LT mean change 131±15 µm at 10 min). Both corneal power and total ocular power changed by a small but significant amount with downward gaze (p<0.05), resulting in a myopic shift (~0.10 D) in the spherical power of the eye compared with primary gaze. CONCLUSION The axial length, anterior biometrics and ocular refraction change significantly with accommodation in downward gaze as a function of time. These findings provide new insights into the optical and bio-mechanical changes of the eye during typical near tasks.