Accuracy of 24 IOL Power Calculation Methods.

PURPOSE: To scrutinize the accuracy of 24 intraocular lens (IOL) power calculation formulas in unoperated eyes. METHODS: In a series of consecutive patients undergoing phacoemulsification and implantation of the Tecnis 1 ZCB00 IOL (Johnson & Johnson Vision), the following formulas were evaluated: Barrett Universal II, Castrop, EVO 2.0, Haigis, Hoffer Q, Hoffer QST, Holladay 1, Holladay 2, Holladay 2 (AL Adjusted), K6 (Cooke), Kane, Karmona, LSF AI, Naeser 2, OKULIX, Olsen (OLCR), Olsen (standalone), Panacea, PEARL-DGS, RBF 3.0, SRK/T, T2, VRF, and VRF-G. The IOLMaster 700 (Carl Zeiss Meditec AG) was used for biometric measurements. With optimized lens constants, the mean prediction error (PE) and its standard deviation (SD), the median absolute error (MedAE), the mean absolute error (MAE), and the percentage of eyes with prediction erros within ±0.25, ±0.50, ±0.75, ±1.00, and ±2.00 D were analyzed. RESULTS: Three hundred eyes of 300 patients were enrolled. The heteroscedastic method revealed statistically significant differences (P < .05) among formulas. Newly developed methods such as the VRF-G (standard deviation [SD] ±0.387 D), Kane (SD ±0.395 D), Hoffer QST (SD ±0.404 D), and Barrett Universal II (SD ±0.405) were more accurate than older formulas (P < .05). These formulas also yielded the highest percentage of eyes with a PE within ±0.50 D (84.33%, 82.33%, 83.33%, and 81.33%, respectively). CONCLUSIONS: Newer formulas (Barrett Universal II, Hoffer QST, K6, Kane, Karmona, RBF 3.0, PEARL-DGS, and VRF-G) were the most accurate predictors of postoperative refractions. [J Refract Surg. 2023;39(4):249-256.].

Comparison of the prediction accuracy of 13 formulas in long eyes.

PURPOSE: To investigate the accuracy of modern intraocular lens (IOL) power calculation formulas in eyes with axial length (AL) ≥ 26.00 mm. METHODS: A total of 193 eyes with one type of lens were analysed. An IOL Master 700 (Carl Zeiss Meditec, Jena, Germany) was used for optical biometry. Thirteen formulas and their modifications were evaluated: Barrett Universal II, Haigis, Hoffer QST, Holladay 1 MWK, Holladay 1 NLR, Holladay 2 NLR, Kane, Naeser 2, SRK/T, SRK/T MWK, T2, VRF and VRF-G. The User Group for Laser Interference Biometry lens constants were used for IOL power calculation. The mean prediction error (PE) and its standard deviation (SD), the median absolute error (MedAE), the mean absolute error (MAE) and the percentage of eyes with PEs within ± 0.25 D, ± 0.50 D and < ± 1.00 D were calculated. RESULTS: The modern formulas (Barrett Universal II, Hoffer QST, Kane, Naeser 2 and VRF-G) produced the smallest MedAE among all methods (0.30 D, 0.30 D, 0.30 D, 0.29 D and 0.28 D, respectively). The percentage of eyes with a PE within ± 0.50 D ranged from 67.48% to 74.85% for SRK/T and Hoffer QST, Naeser 2 and VRF-G, respectively. CONCLUSIONS: Dunn's post hoc test of the absolute errors revealed statistically significant differences (P < 0.05) between some of the newer formulas (Naeser 2 and VRF-G) and the remaining ones. From a clinical perspective the Hoffer QST, Naeser 2 and VRF-G formulas were more accurate predictors of postoperative refraction with the largest proportion of eyes within ± 0.50 D.

Comparison of the Barrett Universal II, Kane and VRF-G formulas with existing intraocular lens calculation formulas in eyes with short axial lengths.

BACKGROUND: To compare the accuracy of recently developed modern intraocular lens (IOL) power formulas (Barrett Universal II, Kane and VRF-G) with existing IOL power formulas in eyes with an axial length (AL) ≤ 22 mm. METHODS: This analysis comprised 172 eyes of 172 patients operated on by one surgeon (LT) with one IQ SN60WF (Alcon Labs, Fort Worth, TX, USA) hydrophobic lens. Ten IOL formulas were evaluated: Barrett Universal II (BUII), Haigis, Hoffer Q, Holladay 1, Holladay 2, Kane, SRK/T, T2, VRF and VRF-G. The median absolute error (MedAE), mean absolute error (MAE), standard deviation (SD) and all descriptive statistics were evaluated. Percentages of eyes with a prediction error within ±0.25 D, ±0.50 D, ±0.75 D and ±1.00 D were calculated using standard optimised constants for the entire range of axial lengths. RESULTS: The VRF-G, Haigis and Kane produced the smallest MedAE among all formulas (0.242 D, 0.247 D and 0.263 D, respectively) and had the highest percentage of eyes with a PE within ±0.50 D (75.67%, 73.84% and 75.16%, respectively). The Barrett was less accurate (0.298 D and 68.02%, respectively). Statistically significant differences were found predominantly between the VRF-G (P < 0.05), Kane (P < 0.05) and Haigis (P < 0.05) and all other formulas. The percentage of eyes with a PE within ±0.50 D ranged from 66.28% to 75.67%. CONCLUSIONS: In eyes with AL ≤ 22.0 mm, the VRF-G, Haigis and Kane were the most accurate predictors of postoperative refraction, and the Barrett formula was less predictable.

A Critical Assessment of Friedenwald's Technique for Estimating the Coefficient of Rigidity of the Cornea.

Purpose: To determine if Friedenwald's technique for estimating the coefficient of corneal rigidity (Ko, units mmHg/µL), could differentiate between the cornea in keratoconus, normal eyes, and after crosslinking (CXL). Methods: Two operators (1 and 2) independently measured Ko in three groups (keratoconus, normal, and post-CXL corneas), and repeated the procedure in some where their care remained unchanged and others after routine CXL (>28 days postop, epi-off treatment, 3.0 mW/cm2, 30 min). The data were subsequently used to quantify interoperator error, test-retest/intersessional reliability for estimation of Ko, the significance of intergroup differences, and the effect of CXL on Ko. Results: The major findings were: (i) Ko values were not normally distributed; (ii) mean (±sd, 95% CI) interoperator error was -0.002 (±0.019, -0.006 to 0.003, n = 95) and the limit of agreement between the operators was ±0.039; (iii) RMS differences in the intersessional estimation of Ko values were 0.011 (operator 1) and 0.012 (operator 2); (iv) intergroup differences in Ko were not significant (p > 0.05); (v) intersessional change in Ko (y) was linearly related to Ko estimated (x) at 1st session (for operator 2 y = 1.187x-0.021, r = 0.755, n = 16, p < 0.01); and (vi) change in Ko (y 1) after CXL was linearly related to Ko (x 1) at preop (for operator 2 y 1 = 0.880x 1-0.016, r = 0.935, n = 20, p < 0.01). Conclusion: Friedenwald's technique for estimating the Ko is prone to substantial interoperator error and intersessional differences. According to the technique, the change in Ko following CXL is on par with the expected intersessional change observed in controls.

The relationship between angle kappa and astigmatism after phacoemulsification with implanting of spherical and aspheric intraocular lens.

PURPOSE: To determine the significance of any association between either change in angle kappa (Κ°) or the rectilinear displacement (L, mm) of the first Purkinje image relative to the pupil center and unexpected changes in astigmatism after phacoemulsification. METHODS: Orbscan II (Bausch and Lomb) measurements were taken at 1, 2, and 3 months after unremarkable phacoemulsification in patients implanted with spherical (group 1, SA60AT, Alcon) or aspheric (group 2, SN60WF, Alcon) nontoric IOLs. The outputs were used to calculate L. Astigmatism, measured by autorefractometry and subjective refraction, was subjected to vector analysis (polar and cartesian formats) to determine the actual change induced over the periods 1-2 and 2-3 months postop. RESULTS: Chief findings were that the mean (n, ±SD, 95%CI) values for L over each period were as follows: Group 1, 0.407 (38, ±0.340, 0.299-0.521), 0.315 (23, ±0.184, 0.335-0.485); Group 2, 0.442 (45, ±0.423, 0.308-0.577), 0.372 (26, ±0.244, 0.335-0.485). Differences between groups were not significant. There was a significant linear relationship between (A) the change in Κ (ΔΚ = value at 1 month-value at 2 months) and Κ at 1 month (x), where ΔΚ =0.668-3.794X (r = 0.812, n = 38, P = <0.001) in group 1 and ΔΚ = 0.263x -1.462 (r = 0.494, n = 45, P = 0.002) in group 2, (B) L and the J45 vector describing the actual change in astigmatism between 1 and 2 months in group 2, where J45 (by autorefractometry) =0.287L-0.160 (r = 0.487, n = 38, P = 0.001) and J45 (by subjective refraction) =0.281L-0.102 (r = 0.490, n = 38, P = 0.002), and (C) J45 and ΔΚ between 2 and 3 months in group 2, where J45 (by subjective refraction) =0.086ΔΚ-0.063 (r = 0.378, n = 26, P = 0.020). CONCLUSION: Changes in the location of the first Purkinje image relative to the pupil center after phacoemulsification contributes to changes in refractive astigmatism. However, the relationship between the induced change in astigmatism resulting from a change in L is not straightforward.

Spotlight on the Corneal Back Surface Astigmatism: A Review.

Recent evidence indicates that the corneal back surface astigmatism (CBSA) contributes to the refractive state of the eye in cataract surgery, especially with the implantation of toric intraocular lenses. But this has been met with some scepticism. A review of key studies performed over the past three decades shows that the mean CBSA power ranges from 0.18(±0.16)D to 1.04(±0.20)D. The clinical assessment of CBSA is problematic. There is poor agreement between the current automated systems for assessment of CBSA and it is assumed that these systems directly measure the CBSA. But CBSA cannot be measured directly in vivo. A historical review of methods used to quantify the curvature of the posterior corneal surface reveals that CBSA estimated by current systems is based on values for corneal front surface astigmatism, corneal refractive index, central corneal thickness, corneal thickness at peripheral locations and the exact distance between the corneal apex and each one of these peripheral locations. Doubts and errors in these values, coupled with the precise details of the algorithm incorporated to estimate CBSA, are the likely sources of the lack of agreement between current systems. These systematic errors cloud the assessment of CBSA. Mean CBSA may be low, but it varies from case to case. There is a clear need for a realistic, practical procedure for clinicians to independently calibrate systems for estimating CBSA. This would help to reduce uncertainty and the discrepancies between instruments designed to measure the same parameter.

The effect of corneal crosslinking on the rigidity of the cornea estimated using a modified algorithm for the Schiøtz tonometer.

Purpose: The aim of this study was to test a method for estimating corneal rigidity before and after cross-linking (CXL) using a Schiøtz tonometer. Methods: The study was performed in the Kyiv City Clinical Ophthalmological Hospital "Eye Microsurgical Center", Ukraine. This was a prospective, consecutive, randomized, masked, case-by-case, clinical study. Corneal rigidity, indicated by the gradient (G) between lg applied weight and corresponding lg scale reading during Schiøtz tonometry, were obtained by increasing (A-mode) then reducing (D-mode) weights by two operators [A] in keratoconus, post-CXL and control subjects for estimation of (i) interoperator and (ii) intersessional errors, (iii) intergroup differences; [B] before and after CXL. Central corneal thickness CCT was measured by scanning slit pachymetry. ANOVA, t tests, linear regression were the statistical tools used. Results: Average interoperator difference (ΔG) was -0.120 (SD = ±0.294, 95%CI = -0.175 to -0.066). A significant correlation between ΔG and the mean of each pair of G values was found (r = -0.196, n = 112, P = 0.038). Intersessional differences in mean G values were insignificant (P > 0.05). There was a significant correlation between G at first session (X1) and difference between sessions (ΔG) [Operator 1, ΔG = 0.598x1-0.461, r = 0.601, n = 27, P = 0.009]. Significant intergroup differences in G were found (Operator 1, one-way ANOVA, F = 4.489, P = 0.014). The difference (Δ) between the pre-(X2) and post-CXL treatment G values was significantly associated with the pre-CXL treatment value (Operator 1, Δ = 1.970x2-1.622, r = 0.642, n = 18, P = <.001). G values were correlated with CCT in keratoconus and post-CXL. Conclusion: Corneal rigidity (G) estimated using the Schiøtz tonometer can be useful for detecting changes after CXL. However, G values are linked to CCT, can vary from time-to-time and the procedure is operator dependent.

Clinical Accuracy of 18 IOL Power Formulas in 241 Short Eyes.

PURPOSE: To analyze the accuracy of 18 intraocular lens (IOL) power calculation formulas in eyes with axial length (AL) ≤ 22 mm. METHODS: We analyzed 241 eyes of 241 patients. Eighteen formulas were evaluated: Barrett Universal II (BUII), EVO 2.0, Haigis, Hoffer Q, Holladay 1 and 2, Cooke K6, Kane, LadasSuperFormula AI, Naeser 2, Olsen, Panacea, Pearl-DGS, RBF 2.0, SRK/T, T2, VRF and VRF-G. Optical biometry was performed with an IOLMaster 700 (Carl Zeiss Meditec, Jena, Germany). With lens constants optimized for the whole range of AL, the mean prediction error (PE) and its standard deviation (SD), the median absolute error (MedAE), the mean absolute error (MAE) and the percentage of eyes with PEs within ±0.25 D, ±0.50 D and <±1.00 D were calculated. RESULTS: Post-hoc analysis of the absolute PE revealed statistically significant differences (P < .05) between some of the newer formulas (K6, Kane, Naeser 2, Olsen and VRF-G), which obtained the lowest MedAE (respectively, 0.308, 0.300, 0.277, 0.310 and 0.276 D) and the remaining ones. These formulas yielded also the highest percentage of eyes with a PE within ±0.50 D (70.54%, 72.20%, 71.37%, 70.95% and 73.03%, respectively), whereas Panacea and SRK/T yielded the lowest percentage (62.24%), with a stastically significant difference (P < .05) with respect to most formulas. CONCLUSION: In eyes with AL ≤22.0 mm, new formulas (K6, Kane, Naeser 2, Olsen and VRF-G) offer the most accurate predictions of postoperative refraction.

The influence of routine uncomplicated phacoemulsification on the orthogonality of the cornea.

Purpose: The aim of this study was to determine the effect of routine uncomplicated phacoemulsification on the orthogonal distribution of mass within the central optical zone of the cornea. Methods: Astigmatism at both corneal surfaces was evaluated using Orbscan II (Bausch &and Lomb) before and up to 3 months after routine phacoemulsification (one eye/patient). The data were subjected to vector analysis to estimate the pre-and postoperative total astigmatism of the cornea (TCA). Results: Reporting the chief findings in minus cylinder (diopters, DC) over the central 3 mm (A) and 5 mm (B) optical zones. Mean TCA powers (±sd) at pre- and 3-months postop were A) -4.45DC (±2.00) and -5.69DC (±2.69), B) -2.91DC (±2.22) and -2.71DC (±1.60). Change in mean power was significant over 3 mm (P < 0.01, n = 49) but not over 5 mm. Inter-zonal differences were significant (P < 0.01). There was a significant linear relationship between the change in TCA power (y = preoperative-postoperative) and TCA at preoperative stage (x) where, A) y = 0.45x + 3.12 (r = 0.336, n = 49, P = 0.018), B) y = x + 2.65 (r = 0.753, n = 49, P = <0.01). Over the central 3 mm zone only, change (preoperative-postoperative) in axis (°) of TCA (y1) was significantly associated with TCA axis at preoperative stage (x1) where y1 = 1.391x1-0.008x12-0.701 (r = 0.635, n = 49, P < 0.01). Conclusion: Changes in TCA power and axis at 3 months postop, determined using Orbscan II, are indicative of orthogonal alterations in the distribution of corneal tissue. Over the central 3 mm zone, the association between y1 and x1 shows that a change in TCA axis is more profound when preoperative axis is near 90° i.e., against-the-rule.

The Impact of Changes in Corneal Back Surface Astigmatism on the Residual Astigmatic Refractive Error following Routine Uncomplicated Phacoemulsification.

PURPOSE: To determine the significance of any association between intersessional changes in ocular residual astigmatism (RA) and astigmatism at corneal front (FSA) and back (BSA) surfaces following uneventful routine phacoemulsification. METHODS: Astigmatism was evaluated by autorefractometry and subjective refraction and at both the corneal surfaces with Orbscan II™ (Bausch & Lomb) over central 3 mm and 5 mm optical zones at 1, 2, and 3 months after routine phacoemulsification in 103 patients implanted with monofocal nontoric intraocular lenses (IOLs, one eye/patient). Data were subjected to vector analysis to determine the actual change (Δ) in astigmatism (power and axis) for the refractive and Orbscan II findings. RESULTS: The number of cases that attended where ΔRA was ≥0.50 DC between 1 and 2 months was 52 by autorefractometry and 36 by subjective refraction and between 2 and 3 months was 24 by autorefractometry and 19 by subjective refraction. Vector analysis revealed significant correlations between ΔFSA and ΔRA for data obtained by autorefractometry but not by subjective refraction. At all times, ΔBSA was greater than ΔFSA (p < 0.01). Key findings for ΔBSA values over the central 3 mm zone were between (A) the sine of the axis of ΔRA (y) and sine of the axis of ΔBSA (x) for the data obtained by autorefractometry (between 1 and 2 months, y = 0.749 - 0.303x, r = 0.299, n = 52, p=0.031) and subjective refraction (between 2 and 3 months, y = 0.6614 - 0.4755x, r = 0.474, n = 19, p=0.040) and (B) ΔRA (y) and ΔBSA (x) powers between 2 and 3 months postoperatively for the data obtained by autorefractometry (ΔRA = 0.118 ΔBSA + 0.681 r = 0.467, n = 24, p=0.021) and subjective refraction (ΔRA = 0.072 ΔBSA + 0.545 r = 0.510, n = 19, p=0.026). CONCLUSION: Changes in the ocular residual refractive astigmatic error after implanting a monofocal nontoric IOL are associated with changes in astigmatism at the back surface of the cornea within the central optical zone.

The refractive index of the human cornea: A review.

The refractive index of the cornea and overlying tear film are key factors affecting refraction and overall optical properties of the eye. A figure of 1.376 is often quoted for the refractive index of the human cornea over the visible spectrum. In the 19th century estimates for the average refractive index of the human cornea ranged from 1.335 to 1.4391. Over the last two decades data obtained from either ex or in vivo corneas (under local anaesthesia with or without stromal resection) by contact Abbé refractometry show the refractive index of the cornea changes along its' depth undulating from around 1.400 at the epithelium to 1.380 at Bowman's layer, a low of 1.369 in the mid stroma and 1.373 at the endothelium. The mean refractive index of harvested tear samples is 1.337 rising to 1.482 for the overlying lipid layer. Contemporary measurements obtained in vivo by non-invasive methods reveal the average, or equivalent, refractive index of the tear film-cornea complex along the antero-posterior direction ranges from 1.423 to 1.436. Over the last 200 years calculations, with respect to the optics of the human eye, were based on values for the refractive index of the cornea obtained from invasive techniques. The refractive index of the cornea and overlying tear film appears to be higher than previously accepted and varies from case to case.

Effect of Cataract Surgery on the Refractive Index of the Cornea Estimated by Optical Pachymetry.

PURPOSE: To noninvasively estimate the refractive index (RI) of the central cornea along the antero-posterior direction before and after routine phacoemulsification. METHODS: Using 2 setups for a standard optical pachymeter, the ratio of observed optical section widths (OSWs) is a function of the RI. Thus, the corneal RI could be estimated using a calibration equating OSW ratios with known RI values. The OSW was measured by 2 observers for 1) normal subjects for estimating interoperator errors and effects of sex and age on the RI and 2) before and after patients underwent routine phacoemulsification. RESULTS: First, the average interoperator difference (ΔRI) was +0.0005 (SD = ±0.0044, 95% confidence limit, -0.0002 to +0.0012). The root mean square difference between measurements obtained by the observers was 0.0032. There was a significant correlation between the ΔRI and the mean of each pair of measured values (r = -0.172, n = 153, P = 0.003). The mean RI (±SD) was 1.435 (±0.005, n = 82) for females and 1.429 (±0.005, n = 71) for males. There was no significant between-sex difference or association between the RI and age (mean age, ±SD, and range, 44.31, 20.38, and 19-88 years, respectively). Second, the difference (y) between the preoperative (x) and postoperative RI was, y = 0.844x - 1.203 (r = 0.694, n = 31, P ≤ 0.001) according to observer 1 and according to observer 2, y = 0.755x - 1.108 (r = 0.681, n = 31, P ≤ 0.001). CONCLUSIONS: The RI of the human cornea along the antero-posterior axis can be estimated using a modified application of traditional optical pachymetry. The average values for the corneal RI were higher compared with those reported in previous reports. The change in the RI after phacoemulsification could be predicted from the preoperative value.