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Original Investigation |

A 3-D “Super Surface” Combining Modern Intraocular Lens Formulas to Generate a “Super Formula” and Maximize Accuracy

John G. Ladas, MD, PhD1; Aazim A. Siddiqui, MD1; Uday Devgan, MD2; Albert S. Jun, MD, PhD1
[+] Author Affiliations
1Wilmer Eye Institute, Johns Hopkins Medical Institutions, Baltimore, Maryland
2Jules Stein Eye Institute, University of California, Los Angeles, School of Medicine
JAMA Ophthalmol. 2015;133(12):1431-1436. doi:10.1001/jamaophthalmol.2015.3832.
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Importance  Cataract surgery is the most common eye surgery. Calculating the most accurate power of the intraocular lens (IOL) is a critical factor in optimizing patient outcomes.

Objectives  To develop a graphical method for displaying IOL calculation formulas in 3 dimensions, and to describe a method that uses the most accurate and current information on IOL formulas, adjustments, and lens design to create one “super surface” and develop an IOL “super formula.”

Design, Setting, and Participants  A numerical computing environment was used to create 3-D surfaces of IOL formulas: Hoffer Q, Holladay I, Holladay I with Koch adjustment, Haigis, and SRK/T. The surfaces were then analyzed to determine where the IOL powers calculated by each formula differed by more than 0.5, 1.0, and 1.5 diopters (D) from each of the other formulas. Next, based on the current literature and empirical knowledge, a super surface was rendered that incorporated the ideal portions from 4 of the 5 formulas to generate a super formula. Last, IOL power values of a set of 100 eyes from consecutive patients at an eye institute were calculated using the 5 formulas and super formula. The study was performed from December 11, 2014, to April 20, 2015. Analysis was conducted from February 18 to May 6, 2015.

Main Outcomes and Measures  Intraocular lens power value in diopters and the magnitude of disparity between an existing individual IOL formula and our super formula.

Results  In the 100 eyes tested, the super formula localized to the correct portion of the super surface 100% of the time and thus chose the most appropriate IOL power value. The individual formulas deviated from the optimal super formula IOL power values by more than 0.5 D 30% of the time in Hoffer Q, 16% in Holladay I, 22% in Holladay I with Koch adjustment, 48% in Haigis, and 24% in SRK/T.

Conclusions and Relevance  A novel method was developed to represent IOL formulas in 3 dimensions. An IOL super formula was formulated that incorporates the ideal segments from each of the existing formulas and uses the ideal IOL formula for an individual eye. The expectation is that this method will broaden the conceptual understanding of IOL calculations, improve clinical outcomes for patients, and stimulate further progress in IOL formula research.

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Figures

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Figure 1.
The SRK I and SRK/T Formulas in 3 Dimensions

A-C, SRK I, SRK/T, and superimposed SRK I and SRK/T formulas demonstrate the value of 3-D comparison. The following inputs were used: corneal power 37-47 diopters (D), axial length 20-30 mm, target refraction 0 D, manufacturer’s A-constant 115.3 (chosen to approximate values in Holladay et al3). IOL indicates intraocular lens.

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Figure 2.
Third-Generation Intraocular Lens Formulas in 3 Dimensions

Superimposed surfaces of Hoffer Q, Holladay I, Holladay I with Koch adjustment, Haigis, and SRK/T formulas highlighting the differences and value of 3-D comparison. Same inputs were used as in Figure 1, and for the Haigis formula, a mean value for anterior chamber depth (3.37 mm) from Haigis4 rather than a measured value of a particular patient was used. D indicates diopters; IOL, intraocular lens.

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Figure 3.
The Ladas-Siddiqui Graph

Graphical representation of regions where each formula differs by 0.5 (A), 1.0 (B), and 1.5 (C) diopters (D) from any 1 of the other 4 formulas. Green represents areas within the specified range of agreement and red represents areas outside the range of agreement. Same inputs and formulas as in Figure 2 were used.

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Figure 4.
The Super Surface

A 3-D surface composed of the ideal portions from Hoffer Q (for axial length 20-21.49 mm), Holladay I (for axial length 21.49-25 mm), Holladay I with Koch adjustment (for axial length >25 mm), and Haigis (for any negatively powered intraocular lens [IOL] values). Same inputs as in Figure 2 were used. A, Raw form of super surface where ideal segments taken from existing IOL formulas are denoted by the different colors. B, Further amalgamation and continuity of the super surface. C, A single, unified, super surface in its final form. D indicates diopters.

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