Haigis Formula Research Articles

Impact of the Minimization of Standard Deviation Before Zeroization of the Mean Bias on the Performance of IOL Power Formulas.

In cataract surgery, accurate intraocular lens (IOL) power calculations are crucial for optimal postoperative refractive outcomes. This study explores the impact of prioritizing the reduction of the standard deviation (SD) of prediction errors before mean prediction error (PE) adjustment on IOL calculation formula precision and accuracy. We conducted a retrospective analysis of 4885 eyes from 2611 patients, all implanted with the same IOL model, comparing four traditional IOL power calculation formulas: SRK/T, Holladay 1, Haigis, and Hoffer Q. We introduced new constants aiming to minimize the SD of PE (new_const) against traditionally optimized constants (classic_const), using a heteroscedastic statistical method for comparison. Validation of precision improvements used a secondary dataset of 262 eyes from 132 patients. We observed significant reductions in mean absolute error (MAE) across training and test sets for Hoffer Q, Holladay, and Haigis formulas, indicating accuracy enhancements. Optimized constants significantly reduced SDs for Haigis from 0.3255 to 0.3153 and for Hoffer Q from 0.3521 to 0.3387. These optimizations also increased the proportion of eyes achieving PE within ±0.25D. SRK/T showed improved SD from 0.3596 to 0.3585. However, Holladay 1 showed minimal change with no significant improvement. In the test dataset, significant reductions in SD were observed for Haigis and Hoffer Q. Prioritizing SD minimization before adjusting mean PE significantly improves the precision of selected IOL power formulas, enhancing postoperative refractive outcomes. The effectiveness varies among formulas, underscoring the need for formula-specific adjustments. The study presents a novel two-step approach for optimizing IOL power calculations.

Prediction of refraction error after toric lens implantation with biometric input data uncertainties and power labelling tolerances.

The purpose of this study was to simulate the impact of biometric measure uncertainties, lens equivalent and toric power labelling tolerances and axis alignment errors on the refractive outcome after cataract surgery with toric lens implantation. In this retrospective non-randomised cross sectional Monte-Carlo simulation study we evaluated a dataset containing 7458 LenStar 900 preoperative biometric measurements. The biometric uncertainties from literature, lens power labelling according to ISO 11979, and axis alignment tolerances of a modern toric lens (Hoya Vivinex) were taken to be normally distributed and used in a Monte-Carlo simulation with 100 000 samples per eye. The target variable was the defocus equivalent (DEQ) derived using the Castrop (DEQC) and the Haigis (DEQH) formulae. Mean/median / 90% quantile DEQC was 0.22/0.21/0.36 D and DEQH was 0.20/0.19/0.32 D. Ignoring the variation in lens power labelling and toric axis alignment the respective DEQC was 0.20/0.19/0.32 D and DEQH was 0.18/0.17/0.29 D. DEQC and DEQH increased with shorter eyes, steeper corneas, equivalent lens power and highly with toric lens power. According to our simulation results, uncertainties in biometric measures, lens power labelling tolerances, and axis alignment errors are responsible for a significant part of the refraction prediction error after cataract surgery with toric lens implantation. Additional labelling of the exact equivalent and toric power on the lens package could be a step to improve postoperative results.

Evaluation of repeatability and agreement of two optical biometers for intraocular lens power calculation.

The repeatability of two biometers (Lenstar-LS900 and Eyestar-900) to measure ocular parameters and intraocular lens (IOL) power calculation, and their agreement were evaluated. 134 eyes of 134 participants were measured thrice with each biometer. Axial length (AL), anterior chamber depth (ACD), lens thickness (LT) and keratometry (K) were evaluated. The IOL power was calculated using different formulas. The repeatability limit (RLimit), the mean differences (MD) and the limits of agreement (LoA) were calculated. The RLimits for all parameters were higher with Lenstar compared to Eyestar. RLimits were lower than 0.50 D except for Barrett Universal II (0.54 D) and Haigis (0.51 D) formulas with the Lenstar. Mean differences were lower than 0.01mm for AL, ACD and LT, and lower than 0.03 D for K. MD ranged from 0 to 0.02 D for all formulas except for Barrett and Hill. When dividing the sample into subgroups (short, normal and long eyes), the MDs were similar for the IOL power and were lower than 0.03 D, except for the Barrett and Hill formulas. Both biometers provide repeatable biometry and IOL power calculations. The LoA interval for the IOL power calculation was between 0.75 and 1.50D, which was similar among the subgroups.

Performance Evaluation of a Simple Strategy to Optimize Formula Constants for Zero Mean or Minimal Standard Deviation or Root-Mean-Squared Prediction Error in Intraocular Lens Power Calculation

PurposeTo investigate the performance of a simple prediction scheme for the formula constants optimized for a mean (MPE), standard deviation (SDPE) or root-mean-squared refractive prediction error (RMSPE). DesignRetrospective cross-sectional study. MethodsUsing IOLMaster 700 biometric data from 888 eyes treated with the Hoya Vivinex lens and 821 eyes treated with the Alcon SA60AT lens, plus the power of the implanted lens and postoperative spherical equivalent refraction, optimized constants for SRKT, Hoffer Q, Holladay 1, Haigis, and K6 formulae were calculated using an iterative nonlinear optimization for zero MPE and minimal SDPE and RMSPE. Start values were detuned by ±1.5 from the MPE optimized constants and formula constants generated using the simple prediction scheme were compared to the corresponding directly optimized constants. ResultsFor all 5 formulae under test and with both datasets, constants optimized using the simple scheme showed excellent agreement with those from the iterative method with either MPE or RMSPE used as the optimization metric, and good agreement with SDPE as the metric. Constants optimized for zero MPE or minimal RMSPE agreed within 0.05, whereas constants for minimal SDPE could be systematically off by up to 0.6 from the MPE values, making SDPE unsuitable as an optimization metric. ConclusionsThis simple formula constant optimization scheme performs excellently for 4 disclosed formulae and one nondisclosed formula in our 2 monocentric datasets with zero MPE or minimal RMSPE as metrics. Multicentric studies with other study populations and biometers are required to further investigate the clinical applicability.

Does blepharospasm effect biometric parameters and intraocular lens power calculations?

To investigate the effect of botulinum toxin-A (BTX-A) treatment on corneal topography, ocular biometry and keratometry in patients with benign essential blepharospasm (BEB) and hemifacial spasm (HFS). This study comprised 66 eyes of 33 patients with BEB and 5 eyes of 5 patients with HFS who underwent BTX-A injections consecutively. Refractive error values, tear break-up time (TBUT), corneal topography [corneal power of flat axis (K1) and steep axis (K2), mean corneal power (Km), corneal astigmatism (K2-K1)] and ocular optical biometry [axial length (AL), anterior chamber depth (ACD)] were recorded before BTX-A treatment and 1 month after BTX-A treatment. The researchers calculated the expected emmetropic intraocular lens power (emm-IOL) using the SRK-T, Holladay, Hoffer-Q and Haigis formulas at each examination. K1 (43.48 ± 2.02 vs. 43.57 ± 2.08, p = 0.036), Km (43.91 ± 1.99 vs. 43.99 ± 2.06, p = 0.024) and ACD (3.22 (2.77-3.76) vs. 3.41 (2.99-4.02), p < 0.001) values were found to be significantly higher. The expected emm-IOL according to the SRK-T (21.04 ± 1.6 vs. 20.93 ± 1.6, p = 0.048), Holladay (21.05 ± 1.6 vs. 20.91 ± 1.62, p = 0.037) and Hoffer-Q (21.08 ± 1.65 vs. 20.94 ± 1.68, p = 0.038) decreased significantly. The expected emm-IOL according to the Haigis formula slightly decreased, but it was not significant (p = 0.386). Additionally, TBUT was found to be significantly lower (p < 0.001) after BTX-A injection. Other parameters were not statistically significant (p > 0.05). Our study is the first in the literature to compare optic biometry data and intraocular lens power calculation formulas before and after BTX-A injection in eyes with BEB and HFS. BTX-A injection could play an important role in changing the keratometric and ACD values. It should be considered that IOL power calculations that might be unpredictable due to blepharospasm, so repeated measurements and especially measurements after releasing the spasm with BTX-A injections, are necessary in BEB and HFS.

Accuracy comparison of total keratometry and standard keratometry in intraocular lens power calculations for post-corneal refractive surgery cataract patients

Objective: To compare the accuracy of intraocular lens (IOL) power calculations using total keratometry (TK) versus standard keratometry (K) in post-corneal refractive surgery cataract patients. Methods: This retrospective case series study included 30 patients (36 eyes) with a history of laser corneal refractive surgery who underwent cataract extraction and IOL implantation at Qingdao Eye Hospital, Affiliated to Shandong First Medical University, from September 2022 to December 2023. The cohort comprised 16 males and 14 females, with an average age of (53.6±8.1) years. IOL power was calculated using the K-based Haigis-L and Barrett True-K formulas, as well as the TK-based Haigis and Barrett Universal Ⅱ formulas. Postoperative objective refraction was performed to obtain the actual refractive status of the operated eyes. The refractive prediction error (RPE) was defined as the difference between the actual spherical equivalent and the predicted refraction. The absolute value of the RPE was taken as the refractive absolute error (RAE). Differences in errors calculated by the four formulas were compared. Results: TK showed good consistency with K, with TK being on average 0.50 D lower than K. Analysis of variance revealed statistically significant differences in RPE among the four formulas (P<0.001). The RPE for the TK-based Haigis formula was (0.17±0.09) D, and for the Barrett Universal Ⅱ formula, it was (0.21±0.11) D, both significantly better than the K-based Haigis-L formula (-0.61±0.12) D and Barrett True-K formula (-0.57±0.11) D (all P<0.001). The percentage of eyes with postoperative RPE<±1.00 D was higher for the TK-based Haigis (92%, 33 eyes) and Barrett Universal Ⅱ (86%, 31 eyes) formulas compared to the TK-based Barrett True-K (75%, 27 eyes) and Haigis-L formulas (67%, 24 eyes), with statistically significant differences (P<0.05). Conclusions: Compared with K, TK improves the accuracy of IOL power calculation in post-corneal refractive surgery patients. Both the TK-based Barrett Universal Ⅱ and Haigis formulas demonstrate high accuracy.

Impact and Correction of an Anterior Phakic Intraocular Lens on Swept-Source Optical Coherence Tomography Biometry.

To evaluate the impact of anterior chamber phakic intraocular lens (pIOL) on swept-source optical coherence tomography (SS-OCT) biometric measurements and IOL power calculation. This retrospective analysis of 67 eyes of 49 patients with previous anterior chamber pIOL implantation analyzed the accuracy of automatic segmentation of the anterior surface of the crystalline lens and its impact on anterior chamber depth (ACD, measured from epithelium to lens), lens thickness measurements, and IOL power calculation. The sample was divided into two groups: correct detection of the anterior surface of the crystalline lens and inaccurate detection. Segmentation of eyes from the inaccurate detection group was manually corrected and ACD and lens thickness were calculated using ImageJ software. IOL power was calculated using 7 formulas for both measurements. The anterior surface of the crystalline lens was mis-identified in 13 (19.4%) eyes. ACD was underestimated (Δ -0.85 ± 0.33 mm, P < .001) and lens thickness was overestimated (Δ +0.81 ± 0.25 mm, P < .001). Manual correction changed the target spherical equivalent only in the Haigis formula (P = .009). After correction for segmentation bias, the Pearl DGS, Cooke K6, and EVO 2.0 formulas showed the lowest prediction error, with the Pearl DGS showing greatest accuracy within ±1.00 diopters of prediction error range (81.0%). SS-OCT biometry misidentifies the anterior surface of the crystalline lens in a significant proportion, resulting in significant IOL power calculation error in the Haigis formula. Manual proofing of segmentation is mandatory in every patient with anterior chamber pIOL implantation. After correct segmentation, the Pearl DGS, Cooke K6, and EVO seem to be the best formulas. [J Refract Surg. 2024;40(8):e562-e568.].

Analysis of the Effective and Actual Lens Position by Different Formulas. Postoperative Application of a Ray-Tracing-Based Simulated Optical Model

(1) Background: This study compares the effective lens position (ELP) and intraocular lens power (IOLP) derived from SRK/T, Hoffer Q, Holladay I, and Haigis formulas with the actual lens position (ALP) and the implanted IOLP after cataract surgery. Additionally, it aims to optimize ALP using a ray-tracing-based simulated optical model to achieve emmetropia. (2) Methods: A retrospective observational study was conducted on 43 eyes implanted with the same monofocal intraocular lens (IOL). Preoperative and postoperative biometric data were collected using the Lenstar LS900. Postoperative measurements included ALP, subjective refraction, and refraction error (RE). Optical simulations (OSLO EDU 6.6.0) were utilized to optimize ALP for emmetropia (ALPIDEAL). (3) Results: Paired t-test results between REOSLO-REOBJ (p-value = 0.660) and REOSLO-RESUB (p-value = 0.789) indicated no significant statistical differences. However, statistically significant differences were found between ALP and ALPIDEAL (p &lt; 0.05), with a difference of −0.04 ± 0.45 mm [ranging from −1.00 to 1.20 mm]. A significant correlation was observed between ΔALP (ΔALP = ALP − ALPIDEAL) and RESUBJ. (4) Conclusions: This customized ray-tracing eye model effectively achieves refractive outcomes similar to those obtained both subjectively and objectively post-surgery. Additionally, it has enabled optical simulations to optimize the IOL position and achieve emmetropia.

Accuracy of intraocular lens power formulas in patients with average keratometry greater than 46 diopters

ObjectiveTo compare the accuracy of Kane, Barrett Universal II, Haigis, and SRK-T formulas in eyes with average keratometry greater than 46 diopters (D). MethodsA retrospective analysis was conducted on 101 eyes of 101 patients with average keratometry greater than 46 D. The absolute prediction error (EA) was obtained for each patient one month after surgery. The mean absolute prediction error (MEA), median absolute prediction error (MedEA) and the percentage of patients with absolute refractive error less than 0.25 D, 0.50 D, and 1.00 D were calculated for each formula analyzed. ResultsThe Kane formula achieved the lowest MEA (0.53 ± 0.43) and the lowest MedEA (0.41), followed by Barrett Universal II (MEA: 0.56 ± 0.42, MedEA: 0.49), SRK-T (MEA: 0.59 ± 0.44, MedEA: 0.54), and Haigis (MEA: 0.77 ± 0.47, MedEA: 0.69), showing a significant difference in the results. It was also observed that the Kane formula was the most accurate, with the highest percentage of patients, with EA less than 0.25 D, 0.50 D, and 1.00 D (30.7%, 54.4%, and 86.1%, respectively), while the Haigis formula was the least accurate (12.9%, 33.7%, and 69.3%, respectively). ConclusionIn eyes with corneas having average keratometry greater than 46 D, the Kane formula proves to be a useful tool in intraocular lens (IOL) power calculation and demonstrates higher precision compared to the Barrett Universal II, SRK-T, and Haigis formulas.

Comparison of keratometry and total corneal power, as measured by an SS-OCT-based optical biometer, for intraocular lens power calculation in Asian eyes.

To investigate whether standard keratometry (K) or total corneal power (TCP) leads to more accurate refractive outcomes for intraocular lens (IOL) power calculation. Public hospital. Retrospective evaluation of a diagnostic test instrument. Preoperatively, all patients underwent optical biometry with Anterion, a swept-source optical coherence tomography device providing both K and TCP. The same IOL model was implanted in all cases. The whole sample was divided into a training dataset, used to optimize the formula constants, and a testing dataset, used to investigate the spherical equivalent prediction error (SEQ-PE) of 8 IOL power formulas. Trueness, precision, and accuracy were evaluated by means of the robust 2-sample t test. Cochran Q test was performed to assess whether the percentage of eyes with an SEQ-PE within each threshold was significantly different; in such an event, the McNemar test was then applied. Both the training and testing datasets included 317 eyes. No significant differences were detected for trueness because of constant optimization. Precision and accuracy were better when K was entered, although a statistically significant difference was observed only with the EVO (precision: P = .02 and accuracy: P = .03) and Haigis ( P < .01 for both precision and accuracy) formulas. No significant differences were observed for the percentage of eyes with an absolute SEQ-PE within any threshold. With most formulas, IOL power calculation is not more accurate when TCP is used instead of K.

The VRF-L and VRF-GL IOL power calculation methods after radial keratotomy.

To investigate the accuracy of the VRF-L and VRF-GL IOL power calculation methods in cataract surgery after radial keratotomy (RK). The VRF-L and VRF-GL methods were collated with nine formulas: Barrett True K (No History), Haigis, Hoffer Q, Hoffer Q (Double-K), Holladay 1 (Double-K), Holladay 2 (Double-K), PEARL-DGS (RK), SRK/T (Double-K), and T2 (Double-K). With SS-OCT biometry (IOLMaster 700, Carl Zeiss Meditec), data of 78 eyes from 78 patients with previous RK was included. Optimised lens constants were sourced from the IOL Con website. Subjective refraction was obtained at 4 to 5 months postoperatively. The root mean square absolute error (RMSAE) and median absolute error (MedAE) were chosen as primary outcomes and the percentage of eyes with PEs within ±0.25 D, ±0.50 D, ±0.75 D, and ±1.00 D were analysed. Statistical significance (Bootstrap-t test, P < 0.05) was shown by VRF-GL, VRF-L, and Haigis formulas with the lowest RMSAE (0.813 D, 0.816 D and 0.824 D) and MedAE (0.511 D, 0.497 D and 0.533 D) values. The Barrett True K formula was less predictable (0.836 and 0.580, respectively). The VRF-L, VRF-GL, and Haigis achieved the highest percentage of eyes with a PE within ±0.50 D (52.56%, 50.00%, and 46.15%) and ±1.00 D (79.49%, 79.49%, and 80.77% respectively). The VRF-L and VRF-GL methods demonstrated higher accuracy and were comparable with existing methods in eyes after RK. The Haigis was an alternative option with a higher percentage of eyes with a PE within ±1.00 D (80.77%).

Investigation of the myopic outcomes of the newer intraocular lens power calculation formulas in Korean patients with long eyes

This study investigated the underlying causes of the myopic outcomes of the optic-based newer formulas (Barrett Universal II, EVO 2.0, Kane, Hoffer-QST and PEARL-DGS) in long Korean eyes with Alcon TFNT intraocular lens (IOL) implantation. Postoperative data from 3100 randomly selected eyes of 3100 patients were analyzed to compare the reference back-calculated effective lens positions (ELPs) based on the Haigis formula using conventional axial length (AL) and Cooke-modified AL (CMAL) with the predicted ELP of each single- and triple-optimized Haigis formula applied to AL- and CMAL. Contrary to the AL-applied Haigis formula, the predicted ELP curve of the CMAL-applied, single-optimized Haigis formula, simulating the methods of the newer formulas, exhibited a significant upward deviation from the back-calculated ELP in long eyes. The relationship between the AL and anterior chamber depth in our long-eyed population differed from that in the base population of the PEARL-DGS formula. The myopic outcomes in long eyes appeared to stem from the substantial overestimation of the postoperative IOL position with AL modification, leading to the implantation of inappropriately higher-powered IOLs. This discrepancy may be attributed to the ethnic differences in ocular biometrics, particularly the relatively smaller anterior segment in East Asian patients with long AL.

Особенности расчета оптической силы недифракционной интраокулярной линзы с расширенной глубиной фокуса

Purpose. Retrospective analysis of the accuracy of 7 formulas for calculating the optical power of a non-diffractive intraocular lens (IOL) with extended depth of focus. Material and methods. The retrospective study included 48 patients (81 eyes) with AcrySof IQ Vivity EDOF IOL implantation. The IOL optical power range was +15.0 to +30.0 D, and the target refraction was –0.25 to 0.25 D. The mean age of the patients was 59.1±7.7 (40–84) years.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 = 2.18, a0 = 1.39, a1 = 0.41, a2 = 0.13, personalized ACD = 5.74, ACD (Hoffer Q/Holladay 2) = 5.64/5.50, A-constant (SRK/T/Kane) = 119.2/119.3. The lowest MAE is determined for Kane, Barrett Universal II, and SRK/T formulas (p&lt;0.05). The use of Haigis and Olsen formulas was characterized by a lower MAE compared to Holladay 2 and Hoffer Q formulas (p&lt;0.05). With the exception of the Haigis and Hoffer Q formulas, all other formulas are shown to fall within the target refraction of ±2.00 D. With the Kane, Barrett Universal II and SRK/T formulas, 100% target refraction of ±1.00 D, 98‒99% target refraction of ±0.50 D, and greater than 80% target refraction of ±0.20 D were determined. Conclusion. In this study, we retrospectively evaluated the performance of seven formulas for calculating the optical power of the Acrysof IQ Vivity EDOF non-diffractive intraocular lens. The best results were shown for the Kane, Barrett Universal II and SRK/T formulas. Key words:cataract, phacoemulsification, EDOF, Symfony, IOL optical power calculation, constant optimization

Performance of a simplified strategy for formula constant optimisation in intraocular lens power calculation.

To investigate the performance of a simple prediction scheme for the formula constants optimised for a mean refractive prediction error. Analysis based on a dataset of 888 eyes before and after cataract surgery with IOL implantation (Hoya Vivinex). IOLMaster 700 biometric data, power of the implanted lens and postoperative spherical equivalent refraction were used to calculate the optimised constants (.)opt for SRKT, HofferQ, Holladay and Haigis formula with an iterative nonlinear optimisation. For detuning start values by ±1.5 from (.)opt, the predicted formula constants (.)pred were calculated and compared with (.)opt. Formula performance metrics mean (MPE), median (MEDPE), mean absolute (MAPE), median absolute (MEDAPE), root mean squared (RMSPE) and standard deviation (SDPE) of the formula prediction error were analysed for (.)opt and (.)pred. (.)pred - (.)opt showed a 2nd order parabolic behaviour with maximal deviations up to 0.09 at the tails of detuning and a minimal deviation up to -0.01 for all formulae. The performance curves of different metrics of PE as functions of detuning variations show that the formula constants for zeroing MPE and MEDPE yield almost identical formula constants, optimisation for MAPE, MEDAPE and RMSPE yielded formula constants very close to (.)opt, and optimisation for SDPE could result in formula constants up to 0.5 off (.)opt which is unacceptable for clinical use. This simple prediction scheme for formula constant optimisation for zero mean refraction error performs excellently in our monocentric dataset, even for larger deviations of the start value from (.)opt. Further studies with multicentric data and larger sample sizes are required to investigate the performance in a clinical setting further.

Surrogate optimisation strategies for intraocular lens formula constant optimisation.

To investigate surrogate optimisation (SO) as a modern, purely data-driven, nonlinear adaptive iterative strategy for lens formula constant optimisation in intraocular lens power calculation. A SO algorithm was implemented for optimising the root mean squared formula prediction error (rmsPE, defined as predicted refraction minus achieved refraction) for the SRKT, Hoffer Q, Holladay, Haigis and Castrop formulae in a dataset of N = 888 cataractous eyes with implantation of the Hoya Vivinex hydrophobic acrylic aspheric lens. A Gaussian Process estimator was used as the model, and the SO was initialised with equidistant datapoints within box constraints, and the number of iterations restricted to either 200 (SRKT, Hoffer Q, Holladay) or 700 (Haigis, Castrop). The performance of the algorithm was compared to the classical gradient-based Levenberg-Marquardt algorithm. The SO algorithm showed stable convergence after fewer than 50/150 iterations (SRKT, HofferQ, Holladay, Haigis, Castrop). The rmsPE was reduced systematically to 0.4407/0.4288/0.4265/0.3711/0.3449 dioptres. The final constants were A = 119.2709, pACD = 5.7359, SF = 1.9688, -a0 = 0.5914/a1 = 0.3570/a2 = 0.1970, C = 0.3171/H = 0.2053/R = 0.0947 for the SRKT, Hoffer Q, Holladay, Haigis and Castrop formula and matched the respective constants optimised in previous studies. The SO proves to be a powerful adaptive nonlinear iteration algorithm for formula constant optimisation, even in formulae with one or more constants. It acts independently of a gradient and is in general able to search within a (box) constrained parameter space for the best solution, even where there are multiple local minima of the target function.

Limitations of constant optimization with disclosed intraocular lens power formulae.

To investigate the effect of formula constants on predicted refraction and limitations of constant optimization for classical and modern intraocular lens (IOL) power calculation formulae. Tertiary care center. Retrospective single-center consecutive case series. This analysis is based on a dataset of 888 eyes before and after cataract surgery with IOL implantation (Hoya Vivinex). Spherical equivalent refraction predSEQ was predicted using IOLMaster 700 data, IOL power, and formula constants from IOLCon ( https://iolcon.org ). The formula prediction error (PE) was derived as predSEQ minus achieved spherical equivalent refraction for the SRKT, Hoffer Q, Holladay, Haigis, and Castrop formulae. The gradient of predSEQ (gradSEQ) as a measure for the effect of the constants on refraction was calculated and used for constant optimization. Using initial formula constants, the mean PE was -0.1782 ± 0.4450, -0.1814 ± 0.4159, -0.1702 ± 0.4207, -0.1211 ± 0.3740, and -0.1912 ± 0.3449 diopters (D) for the SRKT, Hoffer Q, Holladay, Haigis, and Castrop formulas, respectively. gradSEQ for all formula constants (except gradSEQ for the Castrop R) decay with axial length because of interaction with the effective lens position (ELP). Constant optimization for a zero mean PE (SD: 0.4410, 0.4307, 0.4272, 0.3742, 0.3436 D) results in a change in the PE trend over axial length in all formulae where the constant acts directly on the ELP. With IOL power calculation formulae where the constant(s) act directly on the ELP, a change in constant(s) always changes the trend of the PE according to gradSEQ. Formulae where at least 1 constant does not act on the ELP have more flexibility to zero the mean or median PE without coupling with a PE trend error over axial length.

Comparison of the formula accuracy for calculating multifocal intraocular lens power: a single center retrospective study in Korean patients.

This study evaluated the accuracy of newer formulas (Barrett Universal II, EVO 2.0, Kane, Hoffer QST, and PEARL-DGS) and the Haigis formula in Korean patients with the Alcon TFNT multifocal intraocular lens. In total, 3100 randomly selected eyes of 3100 patients were retrospectively reviewed. After constant optimization, the standard deviation (SD) of the prediction error was assessed for the entire group, and the root mean square error was compared for short and long axial length (AL) subgroup analysis. The Cooke-modified AL (CMAL) was experimentally applied to the Haigis formula. All the newer formulas performed well, but they did not significantly outperform the Haigis formula. In addition, all the newer formulas exhibited significant myopic outcomes (- 0.23 to - 0.29 diopters) in long eyes. Application of the CMAL to the Haigis formula with single constant optimization produced similar behavior and higher correlation with the newer formulas. The CMAL-applied triple-optimized Haigis formula yielded a substantially smaller SD, even superior to the Barrett and Hoffer QST formulas. The AL modification algorithms such as the CMAL used in newer formulas to cope with optical biometry's overestimation of the AL in long eyes seemed to overcompensate, particularly in the long eyes of the East Asian population.

Accuracy of Intraocular Lens Power Prediction Using 9 Formula

Purpose: To compare the accuracy of nine intraocular lens (IOL) power calculation formulas.Methods: This study is retrospective consecutive case series. A total of 228 eyes of 228 patients who underwent uncomplicated cataract surgery between October 2015 and March 2021 were included. The accuracy of nine IOL calculation formulas (Kane, Emmetropia verifying optical version, Hill-radial basis function, Olsen, Barrett Universal II [Barrett II], Haigis, Holladay, Hoffer, and SRK/T) was compared and analyzed using differences between the predicted refractive power and actual refractive power at 2 months after cataract surgery. Mean prediction error (ME), mean absolute error (MAE), median absolute error (MedAE), and the percentage of eyes that were within ± 0.50 diopters (D), ± 0.75 D, and ± 1.00 D of the target refraction were calculated for each formula.Results: For all eyes, Haigis formula was the most accurate in MAE, followed by Barrett II formula. Comparing the probability of MAE within 0.50 D, Haigis formula showed the highest accuracy. A total of 20 eyes of 20 patients had more than 25 mm axial length. Regarding MAE, Hoffer Q was the most accurate, followed by the Olsen formula. Comparing the probability of MAE within 0.50 D, the Hoffer Q formula was the most accurate. A total of 24 eyes of 24 patients had more than 46 D keratometry. Regarding MAE and MedAE, Haigis was the most accurate, followed by the Barrett II formula. Comparing the probability of MAE within 0.5 D, Holladay formula was the most accurate.Conclusions: Barrett II and Haigis formulas showed greater accuracy for all patients when we determined IOL power before cataract surgery. Hoffer Q, Olsen, and Barrett II formulas showed higher accuracy for long axial length. And Haigis and Barrett II were the most accurate for steep keratometry.

Comparison of Biometric Formulae for Intra Ocular Lens Power Calculation

Purpose: To determine the accuracy of different biometric formulae for intraocular lens power (IOL) calculation in predicting a target postoperative refraction within ± 1.0 diopters in patients with long axial length undergoing phacoemulsification. Study Design: Cross sectional study. Place and Duration of Study: Department of Ophthalmology and visual sciences, Unit 1 Dow University of Health Sciences, Dr. Ruth KM Phau Civil Hospital Karachi from February 2019 to August 2019. Methods: The study included 45 eyes with cataract and preoperative uncorrected visual acuity ranging from 6/60-6/12, axial length of 24.5 to 27.0 mm with no other ocular problem. IOL power was calculated with SRK-T, Holladay 1 and Haigis formula installed in optical biometer AL-Scan (Nidek Co, Ltd., Gamagori, Japan) and by Barrett universal 2 formula from http://www.apacrs.org/barrett_universal2/. Patients underwent phacoemulsification by single surgeon. Follow up included refractive status using Autorefractokertometer, URK-700 (Unicos Co., Ltd., Korea) at 6th week post-operatively. Deviation of actual postoperative refraction from the predicted target preoperative refraction were calculated and values within ± 1.0 diopter were considered accurate. Data was analyzed using SPSS version 22. Results: Outcome in terms of postoperative refractive error (+1D to -1D) with respect to biometric formula showed 100% accuracy using Haigis formula, 90% accuracy using SRK-T formula, 72.72% accuracy using Barrett universal II formula and 66.67% accuracy using Holladay-1 formula. Conclusion: Haigis formula proved to be more reliable and accurate than SRK-T, Holladay 1 and Barrett universal II formulae for calculation of intraocular lens power in eyes with long axial length.

Refractive Status after Phacoemulsification with Biometry Done by Haigis and SRK-T Formulae in Myopic Patients

Background: Optimum refractive outcome is the key indicator for assessing the success of cataract surgery. Accurate biometric calculation of IOL is an important contributor of post-operative refractive status. There are several formulae for calculation of IOL power depending on axial length of eyes. Haigis is the formula of choice for calculating IOL power in myopic patients, whereas, SRK-T is a versatile formula irrespective of axial length. For IOL power calculation by Haigis formula needs expensive instrument. On the other hand, biometry by SRK-T formula can be done by less expensive and easily available instrument. Objective: To assess and compare post-operative refractive status after phacoemulsification where biometry done by Haigis and SRK-T formulae. Methods: This prospective observational study was conducted over 60 diagnosed patients of cataract with axial length more than 24 mm attending in the cataract clinic of NIO&amp;H for phacoemulsification. Patients were selected based on specific selection criteria. Selected patients underwent detail ophthalmic and systemic examination as well as relevant investigation. Biometric calculation of IOL power was done by a single skilled technician by using Haigis formula (group A) in 30 patients and SRK-T formula (group B) in 30 patients. Visual acuity was assessed by LogMAR unit after 4 weeks of surgery and compared between two groups, p value ≤0.05 was considered as significant. Results: Mean age of the study subjects were 57.7±6.0 (SD) years in group A and 57.27±5.48 (SD) years in group B. In group A 14(46.7%) were male and 16(53.3%) were female and in group B 16(53.3%) were male and 14(46.7%) were female. Mean axial length was 25.05±0.45 (SD) mm in group A and 24.88±0.32 (SD) mm in group B. Mean IOL power was 18.23±0.76 (SD) diopter in group A and 18.23±0.65 (SD) diopter in group B. Post-operative mean visual acuity was 0.19±0.26 (SD) LogMAR unit in group A and 0.18 ±0.27 (SD) LogMAR unit in group B. Regarding post-operative refractive status of the study subjects, in group A, out of 30 patients 14(46.7%) were emmetropic, 7(23.3%) were myopic, 5(16.7%) were hypermetropic and the rest 4(13.3%) patients had astigmatism and in group B, out of 30 patients 16(53.3%) were emmetropic, 5(16.7%) were myopic, 4(13.3%) were hypermetropic and the rest 5(16.7%) patients had astigmatism. Conclusion: Quantitative assessment and statistical analysis shows there was no significant difference in post-operative refractive status and mean visual acuity between two groups. J.Natl.Inst.Ophthalmol.2023;6(1): 42-47