IOL power formula classifications

Traditionally, intraocular lens (IOL) power formulas have been classified into generations. First-generation formulas referred to the earliest vergence formulas independently developed by Gernet and Fyodorov.1,2 Second-generation formulas referred to a wide range of formulas listed by Sanders et al., like those by Donzis et al. and Thompson et al. as well as the first Olsen formula.3–6 According to other authors, second-generation formulas are those including factors that scaled the IOL axial position prediction based on axial length (AL), such as the original Hoffer formula with pACD, based on measured preoperative anterior chamber depth (ACD) (from corneal epithelium to the anterior lens surface).7 Third-generation formulas referred to formulas predicting the IOL position from keratometry (K) and AL, such as the Hoffer Q, Holladay 1, and SRK/T.8–10 The confusion started with fourth-generation formulas, as these sometimes included both formulas, such as the Holladay 2, which predicted the IOL position from more than 2 preoperative parameters, and others, such as the Haigis formula, which predicted the IOL position from the AL and the preoperative ACD.11 Wisely, the classification into generations was replaced by a more descriptive classification in 2017, when Koch et al. proposed 5 categories: (1) historical/refraction-based formulas, (2) regression formulas, (3) vergence formulas, (4) artificial intelligence (AI) formulas, and (5) ray tracing.12 Since 2017, the number of IOL formulas for healthy unoperated eyes has dramatically increased, and we felt it is essential to provide an updated classification, which is shown in Figure 1. Given that the historical/refraction-based and the regression formulas are no longer used, we can still rely on the classification by Wang et al. for the remaining formulas, which can be included in vergence formulas, AI methods, and ray tracing. Some of these categories now require different subcategories. The aim of this article is not to provide a detailed description of each formula and method but only to update their classification in an organized manner.Figure 1.: Classification of IOL power formulas.Vergence formulas should be defined as either thin lens or thick lens formulas. The former consider both the cornea and the IOL as infinitely thin diopters, whereas the latter take their thickness into consideration. In addition, both thin lens and thick lens formulas can take advantage of AI. Therefore, the following 4 subcategories can be defined: (1) Thin lens vergence formulas without AI: these include the Haigis, Hoffer Q, Holladay 1, Holladay 2 (unpublished), and SRK/T.8–11 In recent years, several formulas entered this subcategory: Castrop, Cooke K6 (unpublished), Panacea (unpublished), T2, and VRF and VRF-G (unpublished).13–15 (2) Thin lens vergence formulas with AI: these include the 3C calculator by Massimo Camellin, Umberto Camellin, Antonio Calossi (unpublished), Hoffer QST, Kane (unpublished), and Ladas AI super formula, whose structure is unpublished.7,16 (3) Thick lens vergence formulas without AI: EVO 2.0 by TK Yeo (unpublished) and the Næser 2.17 (4) Thick lens vergence formulas with AI: the only formula in this subcategory is the Pearl-DGS, which was originally developed as a thin lens formula and then converted into a thick lens formula.18 Pure AI-based methods do not share any optical background but are data-driven only, using machine learning. The earliest method in this group was the Radial Basis Function, developed by Warren E. Hill, MD, and Haag-Streit (unpublished), whose latest evolution is v. 3.0. Recently, the Karmona and Nallasamy formulas, both developed using machine learning models, joined this subgroup.19,20 Ray-tracing methods, which calculate the path of light rays based on Snell's law at each interface and the refractive index of each diopter, can be classified into paraxial and exact methods. Exact ray tracing is not limited to the paraxial area, but also takes corneal asphericity and higher-order aberrations into account and can be calculated over different pupil diameters. In both paraxial and exact ray tracing, the exact design of the IOL is required, which is one of the major limitations of ray tracing, since IOL manufactures are reluctant to provide these data.21 Different from vergence formulas, all input to ray-tracing power calculation should be true physical parameters and no adjustable parameters (eg, lens constants) should be used. The IOL power by paraxial ray tracing can also be calculated on Excel.22 The following subcategories can be defined: (1) Paraxial ray tracing with no AI: the Barrett Universal II (unpublished), O formula, Olsen formula, and Z-Calc by Zeiss (unpublished).23,24 (2) Paraxial ray tracing with AI: the only method using this approach is the Zeiss AI IOL Calculator (unpublished), which is not yet commercially available, but whose preliminary results have been published.25 (3) Exact ray tracing with no AI: this subcategory includes the proprietary software developed by Costruzione Strumenti Oftalmici for Sirius and later for MS-39, Okulix, and Olsen ray tracing, which is available on the Pentacam (Oculus Optikgeräte GmbH).26–28 Further formulas and methods are currently being developed, and this classification, which does not include solutions specifically developed for postrefractive surgery eyes, will have to be updated regularly.