Purpose The proper choice of an intraocular lens (IOL) power calculation formula is an important aspect of phacoemulsification. In this study, the formulas most commonly used today are described and their accuracy is evaluated. Methods This review includes papers evaluating the accuracy of IOL power calculation formulas published during the period from January 2015 to December 2022. The articles were identified by a literature search of medical and other databases (PubMed/MEDLINE, Crossref, Web of Science, SciELO, Google Scholar, and Cochrane Library) using the terms “IOL formulas,” “Barrett Universal II,” “Kane,” “Hill-RBF,” “Olsen,” “PEARL-DGS,” “EVO,” “Haigis,” “SRK/T,” and “Hoffer Q.” Twenty-nine of the most recent peer-reviewed papers in English with the largest samples and largest number of formulas compared were considered. Results Outcomes of mean absolute error and percentage of predictions within ±0.5 D and ±1.0 D were used to evaluate the accuracy of the formulas. In most studies, Barrett achieved the smallest mean absolute error and PEARL-DGS the highest percentage of patients with ±0.5 D in short eyes, while Kane obtained the highest percentage of patients with ±0.5 D in long eyes. Conclusions The third- and fourth-generation formulas are gradually being replaced by more accurate ones. The Barrett Universal II among vergence formulas and Kane and PEARL-DGS among artificial intelligence-based formulas are currently most often reported as the most precise.

Purpose To evaluate the accuracy of intraocular lens (IOL) power calculation in a patient cohort with short axial eye length to assess the performance of IOL power calculation schemes in strong hyperopes. Methodology The study was a single centre, single surgeon retrospective consecutive case series at the Augen- und Laserklinik, Castrop-Rauxel, Germany. Inclusion of patients after uneventful cataract surgery implanting either spherical (SA60AT) or aspheric (ZCB00) IOLs. Inclusion criteria were axial eye length 28.5 D. Lens constants were optimised on a separate patient cohort considering the full bandwidth of axial eye length. Data of one single eye per patient were randomly included. The outcome measures were: mean absolute prediction error (MAE), median absolute prediction error, mean prediction error with SD and median prediction error and the percentage of eyes with an MAE within 0.25 D, 0.5 D, 0.75 D and 1.0 D. Results A total of 150 eyes from 150 patients were assessed. Okulix, PEARL-DGS, Kane and Castrop provided a statistically significantly smaller MAE compared with the Hoffer Q and SRK/T formulae. Conclusion In our patient cohort with short axial eye length, the use of PEARL-DGS, Okulix, Kane or Castrop formulae showed the lowest MAE. The Castrop formula has not been published before, but will be disclosed with a ready-to-use Excel sheet as an addendum to this paper.

Background: To explain the concept of the Castrop lens power calculation formula and show the application and results from a large dataset compared to classical formulae. Methods: The Castrop vergence formula is based on a pseudophakic model eye with 4 refractive surfaces. This was compared against the SRKT, Hoffer-Q, Holladay1, simplified Haigis with 1 optimized constant and Haigis formula with 3 optimized constants. A large dataset of preoperative biometric values, lens power data and postoperative refraction data was split into training and test sets. The training data were used for formula constant optimization, and the test data for cross-validation. Constant optimization was performed for all formulae using nonlinear optimization, minimising root mean squared prediction error. Results: The constants for all formulae were derived with the Levenberg-Marquardt algorithm. Applying these constants to the test data, the Castrop formula showed a slightly better performance compared to the classical formulae in terms of prediction error and absolute prediction error. Using the Castrop formula, the standard deviation of the prediction error was lowest at 0.45 dpt, and 95% of all eyes in the test data were within the limit of 0.9 dpt of prediction error. Conclusion: The calculation concept of the Castrop formula and one potential option for optimization of the 3 Castrop formula constants (C, H, and R) are presented. In a large dataset of 1452 data points the performance of the Castrop formula was slightly superior to the respective results of the classical formulae such as SRKT, Hoffer-Q, Holladay1 or Haigis.

Although cataract extraction seems to be feasible without major technical obstacles, the surgical technique has changed completely, and patients are no longer satisfied with good spectacle-corrected vision but anticipate complete visual rehabilitation after cataract surgery, without correction. To fulfill this desire, toric or accommodative intraocular lenses are of increasing popularity, and the intraocular lens power calculation after keratorefractive surgery has been improved. In this review article, we provide an overview of different mathematical strategies of calculating the intraocular lens power with standard formulas and with new algorithms, such as paraxial or numeric ray-tracing. These enhanced techniques may improve the validity of lens power calculation due to reduction of the prediction error, especially in cases with high or excessive corneal astigmatism and after refractive laser surgery. Furthermore, a new calculation scheme for the determination of bitoric eikonic intraocular lenses allows a distortion-free imaging in astigmatic eyes. The biometric determinants for the different formulas and calculation schemes are discussed in detail. In difficult cases, standard calculation schemes are overemployed and new mathematical algorithms are necessary to adequately address these problems. Ray-tracing algorithms and other complex mathematical computation schemes are of increasing interest and will more and more replace conventional calculation formulas for determination of intraocular lens power.

To analyze different techniques of measuring accommodation after implantation of a new accommodative posterior chamber intraocular lens (PCIOL). In this comparative, nonrandomized interventional study, we analyzed 15 eyes of 15 patients (aged 44-84 years) at 6 months after cataract surgery and PCIOL implantation (Akkommodative 1CU; HumanOptics AG, Erlangen, Germany) and compared these results with those of an age-matched control group (n = 15). We used the following methods to measure accommodation: dynamic measurement with objective (videorefractometry [PowerRefractor; PlusOptix, Erlangen] and streak retinoscopy) and subjective (subjective near point [push-up test and accommodometer] and defocusing) techniques, as well as static measurement of the change in anterior chamber depth (ACD) using the IOLMaster (Zeiss, Jena, Germany) after pharmacological stimulation using 2% pilocarpine eye drops. Theoretical accommodation calculated from the forward shift of the lens optics (decrease of ACD) using paraxial geometrical optics and measured accommodation amplitude. Accommodation amplitude (mean +/- SD; range; median) results after 6 months in the study and control groups were as follows: 1.00 +/- 0.44; 0.75-2.13; 1 diopter (D); and 0.35 +/- 0.26; 0.10-0.65; 0.25 D, respectively, using the PowerRefractor; 0.99 +/- 0.48; 0.13-2.00; 0.88 D; and 0.24 +/- 0.21; -0.13-0.75; 0.25 D, respectively, using retinoscopy; 1.6 +/- 0.55; 0.50-2.56; 1.7 D; and 0.42 +/- 0.25; 0.00-0.75; 0.50 D, respectively, using subjective near point; and 1.46 +/- 0.53; 1.00-2.50; 1.75 D; and 0.55 +/- 0.33; 0.25-0.87; 0.50 D, respectively, using defocusing. Anterior chamber depth decreased in the study and control groups as follows: 0.78 +/- 0.12; 0.49-1.91; 0.65 mm; and 0.16 +/- 0.09; 0.00-0.34; 0.18 mm, respectively, after applying 2% pilocarpine eyedrops, indicating an accommodation of 1.16 +/- 0.22; 0.72-1.88; 1.05 D vs 0.22 +/- 0.13; 0.00-0.47; 0.23 D (P =.001). Accommodation after implantation of a presumably accommodative PCIOL can be measured with clinical methods or derived from the biometric data of the eye and the measured ACD decrease using geometrical optics. For clinical purposes, pseudophakic accommodation should be assessed with a variety of different techniques, including subjective and objective measurements. The theoretical approach using geometrical optics may be an additional indicator for the accommodative response in patients with pseudophakic eyes and may allow a subdivision of the measured accommodation into true pseudophakic accommodation and pseudoaccommodation.