Haigis Formula Research Articles

A Comparative Study on the Accuracy of IOL Calculation Formulas in Nanophthalmos and Relative Anterior Microphthalmos

We sought to compare the prediction accuracy of 6 intraocular lens (IOL) formulas, namely, the Haigis, Hoffer Q, Holladay I, SRK/T, Barrett Universal II and Hoffer QST formulas, in microphthalmic eyes, including those with nanophthalmos and relative anterior microphthalmos (RAM). Retrospective case series. Twenty-six eyes with nanophthalmos (axial length [AL] 16.84 ± 1.36 mm, range 15.25 mm-19.82 mm) and 12 eyes with RAM (corneal diameter 8.41 ± 0.92 mm, range 7.00 mm-9.50 mm) receiving cataract surgery were included. The IOL Master 500 was used for biometry; thus, lens thickness (LT) was omitted in the IOL power calculation. The mean and median arithmetic and absolute prediction errors (PEs) of the 6 original calculation formulas, the absolute PEs of the 6 formulas after optimization, and the proportion of PEs within ±0.25 diopters (D), ±0.5 D, ±1 D, and ±2 D with each formula were compared. The factors influencing PE were analyzed by multivariate regression. In the nanophthalmos group, the overall prediction results were shifted to myopia. The original Haigis formula had the smallest median absolute PE (1.61 D, P < 0.001), and the optimized Haigis formula had the highest proportion of PEs within ±0.25 D, ±0.5 D, and ±1 D. In the RAM group, the overall prediction results were not significantly different from 0 (P > .05). No significant difference was found among the formulas before optimization (P=.146) and after optimization (P=.161), but the optimized Barrett Universal II formula had the highest proportion of PEs within ±1 D and ±2 D. When omitting the LT parameter in the calculation, the Haigis formula was the most accurate in cataract patients with nanophthalmos (AL <20 mm) among the 6 IOL calculation formulas, and the Barrett Universal II formula had the highest accuracy in cataract patients with RAM (corneal diameter ≤9.5 mm).

Assessment of the influence of keratometry on intraocular lens calculation formulas in long axial length eyes.

Hyperopic surprises tend to occur in axial myopic eyes and other factors including corneal curvature have rarely been analyzed in cataract surgery, especially in eyes with long axial length (≥ 26.0mm). Thus, the purpose of our study was to evaluate the influence of keratometry on four different formulas (SRK/T, Barrett Universal II, Haigis and Olsen) in intraocular lens (IOL) power calculation for long eyes. Retrospective case series. A total of 180 eyes with axial length (AL) ≥ 26.0mm were divided into 3 keratometry (K) groups: K ≤ 42.0 D (Flat), K ≥ 46.0 D (Steep), 42.0 < K < 46.0 D (Average), and all the eyes were underwent phacoemulsification cataract surgery with Rayner (Hove, UK) 920H IOL implantation. Prediction errors (PE) were compared between different formulas to assess the accuracy of different formulas. Multiple regression analysis was performed to investigate factors associated with the PE. The mean absolute error was higher for all evaluated formulas in Steep group (ranging from 0.66 D to 1.02 D) than the Flat (0.34 D to 0.67 D) and Average groups (0.40 D to 0.74D). The median absolute errors predicted by Olsen formula were significantly lower than that predicted by Haigis formula (0.42 D versus 0.85 D in Steep and 0.29 D versus 0.69 D in Average) in Steep and Average groups (P = 0.012, P < 0.001, respectively). And the Olsen formula demonstrated equal accuracy to the Barrett II formula in Flat and Average groups. The predictability of the SRK/T formula was affected by the AL and K, while the predictability of Olsen and Haigis formulas was affected by the AL only. Steep cornea has more influence on the accuracy of IOL power calculation than the other corneal shape in long eyes. Overall, both the Olsen and Barrett Universal II formulas are recommended in long eyes with unusual keratometry.

Evaluation of Refractive Accuracy of ORA and the Factors Impacting Residual Astigmatism in Patients Implanted with Trifocal IOLs During Cataract Surgery: A Retrospective Observational Study

PurposeTo assess the refractive accuracy of the intraoperative aberrometer Optiwave Refractive Analysis (ORA) and evaluate factors impacting residual astigmatism in eyes implanted with PanOptix (TFNT) trifocal intraocular lenses (IOLs) during cataract surgery.Patients and MethodsThis retrospective study examined 180 eyes implanted with a toric or non-toric trifocal IOL during cataract surgery. The mean refractive prediction error (RPE), median absolute RPE, and percentage of eyes with an absolute RPE ≤0.25, ≤0.50, ≤0.75, and ≤1.00 diopter (D) were determined for ORA and each of the IOL power formulas (Sanders–‍Retzlaff–Kraft/Theoretical [SRK/T], Barrett Universal II, and Haigis). Correlation analysis of postoperative residual astigmatism and factors associated with it was performed using Pearson’s and Spearman correlations in eyes with non-toric trifocal IOLs.ResultsAfter optimization, the median absolute RPE was 0.19 D, 0.25 D, 0.20 D, and 0.26 D in eyes measured using ORA and the SRK/T, Barrett Universal II, and Haigis formulas, respectively. An absolute RPE ≤0.50 D after optimization was noted in 92.8%, 83.3%, 88.3%, and 81.1% of the eyes using ORA and the SRK/T (p=0.0093), Barrett Universal II (p=0.2071), and Haigis (p=0.0018) formulas, respectively, showing significant differences between ORA and the SRK/T and Haigis formulas. The mean±standard deviation subjective residual astigmatism in non-toric IOL eyes (N=76) was 0.46±0.39 D and showed a strong positive correlation with preoperative objective refractive astigmatism (r=0.2925, p=0.0109), intraoperative ORA–measured astigmatism (r=0.5555, p<0.0001), postoperative objective refractive astigmatism (r=0.8188, p<0.0001), and postoperative total corneal astigmatism (TCA) (r=0.4051, p=0.0003) and a negative correlation with preoperative anterior corneal astigmatism (r=−0.3541, p=0.0017).ConclusionORA is a salient tool for improving the postoperative refractive accuracy of trifocal IOL power calculations and may help in determining the need for toric IOL use in astigmatic eyes with cataracts. Residual astigmatism correlated with objective refractive astigmatism, ORA-measured astigmatism, and postoperative TCA.

The Effect of Anterior Segment Depth on the Accuracy of 7 Different Intraocular Lens Calculation Formulas.

Objectives:To evaluate the effect of anterior segment depth (ASD; sum of anterior chamber depth and lens thickness) on the accuracy of 7 intraocular lens formulas calculated in patients with axial length (AL) between 22.5 and 24.5 mm.Materials and Methods:In this retrospective study, patients who underwent cataract surgery were divided into three groups based on their ASD measurements (Group I: ASD <7.30 mm, Group II: ASD between 7.30-7.90 mm, Group III: ASD >7.90 mm). The mean predictive error (MPE), mean absolute error (MAE), and median absolute error (MedAE) values of each group were compared. The effect of ASD on the predictive error (PE) of each lens formula was additionally tested in subgroups based on mean keratometry (K) values (Subgroup I: K <42.0 D, Subgroup II: K between 42.0-44.5 D, Subgroup III: K >44.5 D).Results:The study included 184 eyes of 184 patients. In Group I, all formulas except Olsen OLCR and Barrett II had clinically myopic MPEs. In Group II, the MPEs of all lens formulas except Barrett II were statistically non-different from zero (p>0.05). In Group III, the MPEs of all lens formulas were found to be statistically hyperopic. In Group III, all formulas except Olsen OLCR were significantly shifted to more hyperopic results when compared with Groups I and II (p<0.05). ASD was positively correlated with the PEs of the SRK/T, Holladay I, Hoffer Q, Barrett II, Hill-RBF, and Haigis formulas. In cases with mean K greater than 42.0 D, ASD was similarly correlated with PE for all formulas except Olsen OLCR.Conclusion:In eyes with AL between 22.5 and 24.5 mm, the predictions of lens formulas were significantly hyperopic in cases with greater ASD.

Biometry and Intraocular Lens Power Calculation in Eyes with Prior Laser Vision Correction (LVC) - A Review.

An intraocular lens (IOL) calculation in eyes that have undergone laser vision correction (LVC) poses a significant clinical issue in regards to both patient expectation and accuracy. This review aims to describe the pitfalls of IOL power calculation after LVC and give an overview of the current methods of IOL power calculation after LVC. Problems after LVC derive from the measurement of anterior corneal radii, central corneal thickness, asphericity, and the predicted effective lens position. A central issue is that most conventional 3rd generation formulas estimate lens position amongst other parameters on keratometry, which is altered in post-LVC eyes. An IOL power calculation results in eyes with prior LVC that are notably impaired in eyes without prior surgery. Effective corneal power including anterior corneal curvature, posterior corneal curvature, CCT (central corneal thickness), and asphericity is essential. Total keratometry in combination with the Barrett True-K, EVO (emmetropia verifiying optical formula), or Haigis formula is relatively uncomplicated and seems to provide good results, as does the Barrett True-K formula with anterior K values. The ASCRS ( American Society of Cataract and Refractive Surgery) calculator combines results of various formulae and averages results, which allows a direct comparison between the different methods. Tomography-based raytracing and the Kane and the Castrop formulae need to be evaluated by future studies.

Biometry and intraocular power calculation using a swept-source optical coherence tomography: A repeatability and agreement study.

To evaluate the repeatability of biometry and intraocular lens (IOL) power using Galilei G6 and to determine the agreement of its measurements with those of IOL Master 700 and IOL Master 500. Hundred mature cataract eyes were examined twice with Galilei G6 and the results were compared with those of other two devices. Axial length (AL), minimum (K1), maximum (K2), and mean keratometry, anterior chamber depth (ACD), white-to-white (WTW) diameter, lens thickness (LT), and the calculated IOL power were the studied parameters. The correlation coefficient, within-subject standard deviation (Sw), Bland-Altman method, and 95% limits of agreement (LoA) were used for statistical analysis. The intraclass correlation coefficient (ICC) was above 0.9 for all indices, and the LoA ranged from a minimum of 0.08 mm for AL to a maximum of 0.50 D for K1. Sw also ranged between a minimum of 0.02 for AL, ACD, and WTW and a maximum of 0.13 for K1. In the Galilei G6-IOL Master 700 pair, the narrowest and widest LoA were calculated for AL (0.07 mm) and K2 (0.49 D), respectively. In the Galilei G6-IOL Master 500 pair, the narrowest and widest widths of LoA were calculated for AL (0.17 mm) and K2 (0.92 D), respectively. In the first pair, the LoA of IOL power (0.57 D) were the best for Haigis formula and in the second pair, the best agreement (LoA: 0.35 D) was observed for Holladay-1. Galilei G6 provided repeatable biometric measurements. The agreement between biometry and IOL power calculation was better in the Galilei G6-IOL Master 700 pair compared to the Galilei G6-IOL Master 500.

Evaluation of IOL power calculation with the Kane formula for pediatric cataract surgery.

To assess the accuracy of the Kane formula for intraocular lens (IOL) power calculation in the pediatric population. The charts of pediatric patients who underwent cataract surgery with in-the-bag IOL implantation with one of two IOL models (SA60AT or MA60AC) between 2012 and 2018 in The Hospital for Sick Children, Toronto, Ontario, CanFada, were retrospectively reviewed. The accuracy of IOL power calculation with the Kane formula was evaluated in comparison with the Barrett Universal II (BUII), Haigis, Hoffer Q, Holladay 1, and Sanders-Retzlaff-Kraff Theoretical (SRK/T) formulas. Sixty-two eyes of 62 patients aged 6.2 (IQR 3.2-9.2) years were included. The SD values of the prediction error obtained by Kane (1.38) were comparable with those by BUII (1.34), Hoffer Q (1.37), SRK/T (1.40), Holaday 1 (1.41), and Haigis (1.50), all p > 0.05. A significant difference was observed between the Hoffer Q and Haigis formulas (p = 0.039). No differences in the median and mean absolute errors were found between the Kane formula (0.54 D and 0.91 ± 1.04 D) and BUII (0.50 D and 0.88 ± 1.00 D), Hoffer Q (0.48 D and 0.88 ± 1.05 D), SRK/T (0.72 D and 0.97 ± 1.00 D), Holladay 1 (0.63 D and 0.94 ± 1.05 D), and Haigis (0.57 D and 0.98 ± 1.13 D), p = 0.099. This is the first study to investigate the Kane formula in pediatric cataract surgery. Our results place the Kane among the noteworthy IOL power calculation formulas in this age group, offering an additional means for improving IOL calculation in pediatric cataract surgery. The heteroscedastic statistical method was first implemented to evaluate formulas' predictability in children.

Accuracy of new-generation intraocular lens calculation formulas in eyes with variations in predicted refraction.

To investigate the characteristics of eyes with large variations in predicted refraction using four traditional intraocular lens (IOL) formulas and evaluate the accuracy of new-generation intraocular lens power calculation formulas. Eyes that had variationin predicted refraction (≥ 0.75 D) using four traditional formulas (SRK/T, Holladay 1, Hoffer Q, and Haigis formulas) were included. Axial length (AL), anterior chamber depth (ACD), average keratometry (AK), and the ratio of axial length to corneal radius (AL/CR) were measured. New-generation formulas (Barrett Universal II, Emmetropia Verifying Optical2.0, Kane, and Pearl-DGS formulas) and traditional formulas were compared. The median absolute error (MedAE) was the main parameter to evaluate the accuracy of formulas. A total of 79 participants (79 eyes) who had variation in predicted refraction of (≥ 0.75 D) using four traditional formulas out of 510 eyes (510 patients) underwent uncomplicated cataract surgeries. The Barrett Universal II (0.29 D), EVO 2.0 (0.31 D), Kane (0.30 D), and Pearl-DGS (0.33 D) formulas produced significantly lower median absolute errors (MedAEs) than the Hoffer Q (0.61 D) and Holladay 1 (0.59 D) formulas (P < 0.01). The Wang-Koch (WK) adjustment significantly improved the accuracy of the Holladay 1 formula in long eyes (P < 0.001). Abnormal AL, ACD, and AK are more likely to lead to prediction errors using traditional formulas. New-generation formulas and traditional formulas with WK adjustment showed satisfactory prediction accuracy.

IOL Power Calculation Features after Radial Keratotomy

IOL power calculation after keratorefractive surgery is an important applied aspect of cataract surgery. The probability of refractive error is especially high when calculating in patients with a history of radial keratotomy. There is no unified approach to the tactics and methodology of calculation for this category of patients at the moment. The studies were conducted in a group of 17 patients (26 eyes) with a history of RK. The Haigis formula, which does not use keratometry to predict ELP, was chosen as the main one for the calculation. IOL calculation and biometrics were carried out on the IOL-Master, but corrected TCP IOL (Ray Traced) data obtained on the Galilei keratotomograph were manually entered into the optional keratometry fields. Thу Burrett True-K and Hoffer Q were used as verification formulas, the calculation was also carried out on IOL-Master, using corrected Galilei data. In all cases, postoperative refraction close to emmetropic was obtained. The spherical component of refraction ranged from +0.5 to -1.0 D, cylindrical — from 0.0 to 4.0 D, according to autorefractometry. Visual acuity without correction ranged from 0.4 to 1.0. Uncorrected visual acuity of 0.8 and higher was obtained in 65.38% of cases. The calculation algorithm implemented by us using the Haigis formula in combination with the use of individually adjusted keratometric TCP IOL data (Ray Traced, Galilei), allowed us to significantly improve the accuracy of IOL power calculating in patients with a history of RK and achieve target refraction even in cases of complex and irregular corneal topography.

Calculation of Intraocular Lens Optical Power with Enhanced Depth of Focus

Relevance. The new Increased Depth of Focus (EDOF) Intraocular Lens (IOL) technology is designed to improve the correction of visual acuity at a medium distance without compromising distance vision correction and provides a restoration of visual acuity in the distance and at an average distance, but at the same time a lower frequency of side optical phenomena and better contrast sensitivity compared to other multifocal IOLs (MIOL). Regardless of the technology used and the type of lens, the result of surgery and patient satisfaction depend on the optimization of the calculation of the optical strength of the IOL. To date, there is no consensus in the available literature on the choice of a formula for calculating the optical power of known EDOF IOLs.Aim. Retrospective analysis of the accuracy of 7 formulas for optical power calculation of a new extended depth of focus intraocular lens.Methods. The retrospective study included 34 patients (62 eyes) with implantation of a new EDOF Tecnis Symfony IOL ZXR00. The mean age of the patients was 61.9 ± 9.4 (39–87) years. IOL optical power range was +5.0 to +30.0 D, target refraction was –0.25 to 0.25 D. The average follow-up period for the patients was 12.3 ± 1.8 months. The SRK/T, Barrett Universal II, Haigis, Hoffer Q, Holladay 2, Olsen, and Kane formulas were retrospectively analyzed for effectiveness using appropriate constants. Each formula was optimized for the study group of patients to achieve an average refractive error as close to zero as possible. For each formula, the mean error (ME), mean absolute error (MAE), standard deviation (SD), median absolute error (MedAE), maximum absolute error (MaxAE), and percentage of eyes within the error range of 0.25, 0.5, 1.0, and 2.0 D were calculated.Results. The optimized constants were LF = 2.21, a0 = 1.43, a1 = 0.39, a2 = 0.12, personalized ACD=5.68, ACD (Hoffer Q / Holladay 2) = 5.68/5.66, A-constant (SRK/T / Kane) = 119.5/119.4. For the SRK/T, Barrett Universal II, Kane and Haigis formulas the lowest MAE is shown. Application of the Hoffer Q and Holladay 2 formulas are associated with the highest MAE. The Barrett Universal II, SRK/T, Kane, and Haigis formulas were characterized by the highest percentage of reaching refraction of ±0.25 D (64, 62, 59, and 53, respectively). For all of the formulas examined, the frequency of reaching refraction of ±1.00 D was greater than 90% and within ±2.00 D greater than 97%.Conclusion. This study was the first to retrospectively compare seven formulas for calculating the optical power of a new intraocular lens with an enhanced depth of focus. The SRK/T, Barrett Universal II, Haigis, and Kane formulas are recommended for calculating the optical power of the indicated IOL in clinical practice.

Comparison of Accuracy in Keratometries Measured by Different Camera Devices for Predicting the Intraocular Lens Power in Lens-Dislocated Patients

Introduction: This is a cross-sectional cohort study focused on assessing the influence of ocular biometric parameters of different camera devices for accurately predicting the intraocular lens (IOL) power in congenital ectopia lentis (EL) patients. Methods: This study includes a total of 91 eyes of 60 patients with congenital EL from June 2018 to April 2021. All patients underwent lens subluxation surgery with Cionni modified capsular tension rings implantation. Ocular parameters measured by partial coherence interferometry (IOLMaster 700; Carl Zeiss Meditec AG, Jena, Germany) and rotating Scheimpflug camera (Pentacam HR system; Oculus Optikgeräte GmbH, Wetzlar, Germany) were acquired from the database. The authenticity of the different keratometries (Ks) was analyzed by comparing the prediction error in spherical equivalent under controlled formula SRK/T, Haigis, and after Wang-Koch (WK) adjustment. Results: We observed significant greater K values were obtained in IOLMaster than Pentacam, resulting in more significant hyperopia error while calculating SRK/T. The IOL power calculated with the total corneal refractive power (TCRP) from Pentacam revealed the highest prediction accuracy, indicating that TCRP is the closest to the actual refractive power of the cornea. However, in an exceptional case for long eye patients, total K from IOLMaster was better recommended when using formula Haigis with WK adjustment. Conclusions: For most instances, TCRP is the best-recommended source of K value while calculating IOL power for EL patients. However, the total K from IOLMaster preferably fits for long eye patients, who require WK adjustment for Haigis formula.

Meridional ocular magnification after cataract surgery with toric and non-toric intraocular lenses

BackgroundOverall ocular magnification (OOM) and meridional ocular magnification (MOM) with consequent image distortions have been widely ignored in modern cataract surgery. The purpose of this study was to investigate OOM and MOM in a general situation with an astigmatic refracting surface.MethodsFrom a large dataset containing biometric measurements (IOLMaster 700) of both eyes of 9734 patients prior to cataract surgery, the equivalent (PIOLeq) and cylindric power (PIOLcyl) were derived for the HofferQ, Haigis, and Castrop formulae for emmetropia. Based on the pseudophakic eye model, OOM and MOM were extracted using 4 × 4 matrix algebra for the corrected eye (with PIOLeq/PIOLcyl (scenario 1) or with PIOLeq and spectacle correction of the residual refractive cylinder (scenario 2) or with PIOLeq remaining the residual uncorrected refractive cylinder (blurry image) (scenario 3)). In each case, the relative image distortion of MOM/OOM was calculated in %.ResultsOn average, PIOLeq/PIOLcyl was 20.73 ± 4.50 dpt/1.39 ± 1.09 dpt for HofferQ, 20.75 ± 4.23 dpt/1.29 ± 1.01 dpt for Haigis, and 20.63 ± 4.31 dpt/1.26 ± 0.98 dpt for Castrop formulae. Cylindric refraction for scenario 2 was 0.91 ± 0.70 dpt, 0.89 ± 0.69 dpt, and 0.89 ± 0.69 dpt, respectively. OOM/MOM (× 1000) was 16.56 ± 1.20/0.08 ± 0.07, 16.56 ± 1.20/0.18 ± 0.14, and 16.56 ± 1.20/0.08 ± 0.07 mm/mrad with HofferQ; 16.64 ± 1.16/0.07 ± 0.06, 16.64 ± 1.16/0.18 ± 0.14, and 16.64 ± 1.16/0.07 ± 0.06 mm/mrad with Haigis; and 16.72 ± 1.18/0.07 ± 0.05, 16.72 ± 1.18/0.18 ± 0.14, and 16.72 ± 1.18/0.07 ± 0.05 mm/mrad with Castrop formulae. Mean/95% quantile relative image distortion was 0.49/1.23%, 0.41/1.05%, and 0.40/0.98% for scenarios 1 and 3 and 1.09/2.71%, 1.07/2.66%, and 1.06/2.64% for scenario 2 with HofferQ, Haigis, and Castrop formulae.ConclusionMatrix representation of the pseudophakic eye allows for a simple and straightforward prediction of OOM and MOM of the pseudophakic eye after cataract surgery. OOM and MOM could be used for estimating monocular image distortions, or differences in overall or meridional magnifications between eyes.

Intraocular lens constant optimization in toric intraocular lens calculation using keratometry and total corneal power.

To evaluate intraocular lens (IOL) constant optimization in toric IOL calculation with keratometry (K) and total corneal refractive power (TCRP). Predicted spherical equivalent (SE) and residual astigmatism (RA) with K and TCRP were retrospectively calculated using the Haigis, Holladay 1, and SRK/T formulae and optimized IOL constants. The results of the Barrett calculator and the Abulafia-Koch formula with K were also calculated. The median absolute error in SE (MedAE-SE), mean absolute error in RA (MAE-RA), and centroid error (CE) were analyzed. Seventy-nine eyes of 71 patients implanted with toric IOLs were included. With K, there were no significant differences between the results before and after constant optimization using all the formulae. With TCRP, constant optimization significantly reduced MedAE-SE; however, significantly increased MAE-RA and CE using the Holladay 1 and SRK/T formulae. MedAE-SE, MAE-RA, and CE using the Haigis formula did not show significant differences. The difference in the predicted RA before and after constant optimization increased with IOL toricity. The MedAE-SE predicted by TCRP was significantly higher than that predicted by K despite constant optimization. The MAE-RA and CE predicted by TCRP were significantly lower than those predicted by K without posterior corneal astigmatism optimization; however, were not significantly different from those predicted by the Barrett and Abulafia-Koch formulae. Constant optimization is recommended when using the TCRP in toric IOL calculations, particularly for patients with large astigmatism. However, TCRP did not yield more accurate results than optimized K in toric IOL calculations despite constant optimization.

Prediction of ocular magnification and aniseikonia after cataract surgery.

Ocular magnification and aniseikonia after cataract surgery has been widely ignored in modern cataract surgery. The purpose of this study was to analyse ocular magnification and inter-individual differences in a normal cataract population with a focus on monovision. From a large dataset containing biometric measurements (IOLMaster 700) of both eyes of 9734 patients prior to cataract surgery, eyes were indexed randomly as primary (P) and secondary (S). Intraocular lens power (IOLP) was derived for the HofferQ, Haigis and Castrop formulae for emmetropia for P and emmetropia or myopia (-0.5 to -2 dpt) for S to simulate monovision. Based on the pseudophakic eye model in addition to these formulae, ocular magnification was extracted using matrix algebra (refraction and translation matrices and a system matrix describing the optical property of the entire spectacle corrected or uncorrected eye). With emmetropia for P and S the IOLP differences (S-P) showed a standard deviation of 0.162/0.156/0.157 dpt and ocular magnification differences yielded a standard deviation of 0.0414/0.0405/0.0408 mm/mrad for the HofferQ/Haigis/Castrop setting. Simulating monovision, the myopic eye (S) showed a systematically smaller mean absolute spectacle corrected ocular magnification than the emmetropic eye (-0.0351/-0.0340/-0.0336, respectively, relative magnification around 2%). If myopia in the S eye remains uncorrected, the reduction of ocular magnification is much smaller (around 0.2-0.3%). Vergence formulae for IOLP calculation sometimes implicitly define a pseudophakic eye model which can be directly used to predict ocular magnification after cataract surgery. Despite a strong similarity of both eyes, ocular magnification does not fully match between eyes and the prediction of ocular magnification and aniseikonia might be relevant to avoid eikonic problems in the pseudophakic eye.

Accuracy of segmented measurement of axial length in ultra-high myopia filled with silicone oil using immersion B-scan ultrasonography.

To evaluate the accuracy of segmented measurement of axial length (AL) in high myopia filled with silicone oil by immersion B-scan ultrasonography (immersion B-scan). From June 2016 to June 2020, a total of 67 ultra-high myopia inpatients (67 eyes) who underwent silicone oil removal combined with cataract extraction and intraocular lens (IOL) implantation were retrospectively enrolled. The preoperative axial length (AL) of 31 patients with severe cataract were segmented measured using immersion B-scan (B-scan group) and another 36 patients with mild or moderate cataract were measured using IOLMaster 500 (IOLMaster group). The post-operative ALs in two groups were both measured using IOLMaster 500. The IOL power was calculated with Haigis formula. The differences in ALs between pre- and post-surgery, as well as the postoperative refractive spherical equivalent, absolute refractive error, the prediction deviation of postoperative refraction and best corrected visual acuity (BCVA) were compared. The pre- and post-operative ALs were 30.46±1.63 mm (range 28.09-33.51 mm) and 30.42±1.70 mm (range 28.03-33.90 mm) in B-scan group (t=0.644, P=0.542) and 30.51±1.21 mm (range 28.03-33.90 mm) and 30.43±1.27mm (range 28.54-33.50 mm) in IOLMaster group (t=1.843, P=0.074), respectively. Three months after surgery, BCVA were 0.45±0.13 (range 0.3-0.9) and 0.44±0.20 (range 0.2-1.0) in B-scan and IOLMaster group respectively (t=0.086, P=0.932). There was no significant difference of the postoperative spherical equivalent (-3.11±0.65 D vs -3.21±0.51 D, t=0.671, P=0.505) and the absolute refractive error (0.589±0.340 vs 0.470±0.245 D, t=1.615, P=0.112) between two groups. In B-scan group, absolute refractive error within ±0.50 D was found in 18 eyes (58.1%), within ±1.00 D in 26 eyes (83.9%), and within ±1.50 D in 31 eyes (100%). In IOLMaster group, absolute refractive error within ±0.50 D was found in 23 eyes (63.9%), within ±1.00 D in 34 eyes (94.4%), and within ±1.50 D in 36 eyes (Z=0.757, P=0.449). The segmented measurement of ALs by immersion B-scan shows comparable measurement accuracy with that of IOLMaster 500 in ultra-high myopia patients with severe cataract secondary to silicone oil filling and can obtain an ideal postoperative refractive state.

Comparison of accuracy of intraocular lens power calculation for eyes with an axial length greater than 29.0mm.

PurposeTo evaluate and compare the accuracy of six different formulas (Emmetropia Verifying Optical version 2.0, Kane, SRK/T, Barrett Universal II, Haigis and Olsen) in intraocular lens (IOL) power calculation for extremely long eyes.MethodsRetrospective case-series. Seventy-three eyes with axial length (AL) ≥ 29.0 mm and underwent phacoemulsification cataract surgery with Rayner (Hove, UK) 920H IOL implantation from January 2018 to March 2020 were included. Prediction errors (PE) were calculated and compared between different formulas to evaluate the accuracy of formulas. Multiple regression analysis was performed to investigate factors associated with the PE.ResultsThe Kane formula had mean prediction error close to zero (– 0.01 ± 0.51 D, P = 0.841), whereas the EVO 2.0, SRK/T, Barrett Universal II, Haigis and Olsen formulas produced hyperopic outcomes (all P < 0.001). The median absolute error [inter-quartile range] produced by the EVO 2.0, Kane, Barrett Universal II and Olsen formulas showed no significant difference (0.33 D [0.48], 0.30 D [0.44], 0.34 D [0.39], 0.29 D [0.37], respectively, pairwise comparison P > 0.05), but was significantly lower than that of the SRK/T and Haigis formulas (0.85 D [0.66], 0.80 D [0.54], respectively, pairwise comparison P < 0.001). The AL and the PE produced by the SRK/T formula were significantly positively correlated in extremely myopic eyes (β = 0.248, P < 0.001), whereas the trend was not demonstrated in other formulas.ConclusionsFor cataract patients with axial length greater than 29.0 mm, the accuracy of the EVO 2.0, Kane, Barrett Universal II and Olsen formulas is comparable and significantly better than that of the SRK/T and Haigis formulas.

Strategies for formula constant optimisation for intraocular lens power calculation

BackgroundTo investigate modern nonlinear iterative strategies for formula constant optimisation and show the application and results from a large dataset using a set of disclosed theoretical-optical lens power calculation concepts.MethodsNonlinear iterative optimisation algorithms were implemented for optimising the root mean squared (SoSPE), the mean absolute (SoAPE), the mean (MPE), the standard deviation (SDPE), the median (MEDPE), as well as the 90% confidence interval (CLPE) of the prediction error (PE), defined as the difference between postoperative achieved and formula predicted spherical equivalent power of refraction. Optimisation was performed using the Levenberg-Marquardt algorithm (SoSPE and SoAPE) or the interior point method (MPE, SDPE, MEDPE, CLPE) for the SRKT, Hoffer Q, Holladay 1, Haigis, and Castrop formulae. The results were based on a dataset of measurements made on 888 eyes after implantation of an aspherical hydrophobic monofocal intraocular lens (Vivinex, Hoya).ResultsFor all formulae and all optimisation metrics, the iterative algorithms showed a fast and stable convergence after a couple of iterations. The results prove that with optimisation for SoSPE, SoAPE, MPE, SDPE, MEDPE, and CLPE the root mean squared PE, mean absolute PE, mean PE, standard deviation of PE, median PE, and confidence interval of PE could be minimised in all situations. The results in terms of cumulative distribution function are quite coherent with optimisation for SoSPE, SoAPE, MPE and MEDPE, whereas with optimisation for SDPE and CLPE the standard deviation and confidence interval of the PE distribution could only be minimised at the cost of a systematic offset in mean and median PE.ConclusionNonlinear iterative techniques are capable of minimising any statistical metrics (e.g. root mean squared or mean absolute error) of any target parameter (e.g. PE). These optimisation strategies are an important step towards optimising for the target parameters which are used for evaluating the performance of lens power calculation formulae.

Ray Tracing versus Thin-Lens Formulas for IOL Power Calculation Using Swept-Source Optical Coherence Tomography Biometry

PurposeTo evaluate the ray tracing method's accuracy employing Okulix ray tracing software and thin-lens formulas to calculate intraocular lens (IOL) power using a swept-source optical coherence tomography (SS-OCT) biometer (OA2000).MethodsA total of 188 eyes from 180 patients were included in this study. An OA-2000 optical biometer was used to collect biometric data. The predicted postoperative refraction based on thin-lens formulas including SRK/T, Hoffer Q, Holladay 1, and Haigis formulas and the ray tracing method utilizing the OKULIX software was determined for each patient. To compare the accuracy of approaches, the prediction error and the absolute prediction error were determined.ResultsThe mean axial length (AL) was 23.66 mm (range: 19–35). In subgroup analysis based on AL, in all ranges of ALs the ray tracing method had the lowest mean absolute error (0.56), the lowest standard deviation (SD; 0.55), and the greatest proportion of patients within 1 diopter of predicted refraction (87.43%) and the lowest absolute prediction error compared to the other formulas (except to SRK/T) in the AL range between 22 and 24 mm (all P 0.05). In addition, the OKULIX and Haigis formulas had the least variance (variability) in the prediction error in different ranges of AL.ConclusionThe ray tracing method had the lowest mean absolute error, the lowest standard deviation, and the greatest proportion of patients within 1 diopter of predicted refraction. So, the OKULIX software in combination with SS-OCT biometry (OA2000) performed on par with the third-generation and Haigis formulas, notwithstanding the potential for increased accuracy in the normal range and more consistent results in different ranges of AL.

Challenges in pediatric cataract surgery: comparison of intraocular lens power calculation formulas using optical biometry.

Comparison of the accuracy of intraocular lens (IOL) power calculation formulas (SRK II, SRK/T, Holladay 1, Hoffer Q and Barrett II Universal, Haigis) in pediatric cataract surgery using optical biometry. This prospective study included seventy eyes of 70 patients between ages of 3-15 who had undergone cataract surgery with IOL implantation. Anterior segment parameters and axial length (AL) were measured with an optical biometer. Barrett II Universal formula results were used to determine the diopter of implanted IOL. Postoperative refraction was taken at first month, and differences from the estimated refractive value [mean absolute predictive error (APE)] were compared between formulas. Formulas were also compared according to AL. The lowest APE was achieved with Barrett II formula (0.64 ± 0.73D) and the highest with Haigis formula (1.06 ± 0.84D) in the whole study population (p < 0.01). APE values were lowest with Holladay 1 (0.79 ± 0.71D) and highest with Haigis (1.44 ± 0.92D) in patients with an AL ≤ 22mm; lowest APE was achieved with Barrett II (0.47 ± 0.54D) and highest with Haigis (0.84 ± 0.72D) in patients with an AL > 22mm. Barrett II formula had the best results in eyes with average AL, and SRK/T and Holladay 1 formulas were better in eyes with shorter AL. Haigis formula statistically had the highest predictive error in all formulas.

Refractive prediction error in cataract surgery using an optical biometer equipped with anterior segment OCT.

To evaluate refractive error after cataract surgery using an optical biometer equipped with anterior segment optical coherence tomography (AS-OCT). Chukyo Eye Clinic, Nagoya, Japan. Retrospective observational design. In total, 150 patients with cataract (150 eyes, mean age 73.4 ± 8.2 years, men 76, women 74), who underwent measurement of parameters with the AS-OCT scanners ANTERION (AS-OCTB) and IOLMaster 700 (OCTB) before cataract surgery, were enrolled in the study. Refractive prediction error was compared between the 2 devices using the SRK/T, Haigis, and Barrett Universal II (UII) formulas for intraocular lens (IOL) power calculation. There were significant differences between AS-OCTB and OCTB in axial length, mean corneal refractive power, anterior chamber depth, lens thickness, and corneal diameter (n = 150). In the SRK/T formula, the arithmetic means of refractive prediction errors for AS-OCTB and OCTB were -0.06 ± 0.46 diopters (D) and 0.02 ± 0.42 D, respectively. In the Haigis formula, the arithmetic means of refractive prediction errors for AS-OCTB and OCTB were -0.23 ± 0.40 D and -0.08 ± 0.35 D, respectively. In the Barrett UII formula, the arithmetic means of refractive prediction errors for AS-OCTB and OCTB were -0.02 ± 0.38 D and 0.11 ± 0.36 D, respectively. AS-OCTB showed significantly larger refractive prediction error toward myopia than OCTB in all 3 formulas (P < .0001). The refractive prediction error using AS-OCTB showed a small difference from that using OCTB. While clinically comparable, the 2 methods could drive meaningful differences in IOL selection.