We're unable to sign you in at this time. Please try again in a few minutes.
We were able to sign you in, but your subscription(s) could not be found. Please try again in a few minutes.
There may be a problem with your account. Please contact the AMA Service Center to resolve this issue.
Contact the AMA Service Center:
Telephone: 1 (800) 262-2350 or 1 (312) 670-7827  *   Email: subscriptions@jamanetwork.com
Error Message ......
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.
Text Size: A A A
Published online

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.

Figures in this Article


Place holder to copy figure label and caption
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.

Graphic Jump Location
Place holder to copy figure label and caption
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.

Graphic Jump Location
Place holder to copy figure label and caption
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.

Graphic Jump Location
Place holder to copy figure label and caption
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.

Graphic Jump Location




Also Meets CME requirements for:
Browse CME for all U.S. States
Accreditation Information
The American Medical Association is accredited by the Accreditation Council for Continuing Medical Education to provide continuing medical education for physicians. The AMA designates this journal-based CME activity for a maximum of 1 AMA PRA Category 1 CreditTM per course. Physicians should claim only the credit commensurate with the extent of their participation in the activity. Physicians who complete the CME course and score at least 80% correct on the quiz are eligible for AMA PRA Category 1 CreditTM.
Note: You must get at least of the answers correct to pass this quiz.
Please click the checkbox indicating that you have read the full article in order to submit your answers.
Your answers have been saved for later.
You have not filled in all the answers to complete this quiz
The following questions were not answered:
Sorry, you have unsuccessfully completed this CME quiz with a score of
The following questions were not answered correctly:
Commitment to Change (optional):
Indicate what change(s) you will implement in your practice, if any, based on this CME course.
Your quiz results:
The filled radio buttons indicate your responses. The preferred responses are highlighted
For CME Course: A Proposed Model for Initial Assessment and Management of Acute Heart Failure Syndromes
Indicate what changes(s) you will implement in your practice, if any, based on this CME course.


Some tools below are only available to our subscribers or users with an online account.

4 Citations

Sign in

Purchase Options

• Buy this article
• Subscribe to the journal
• Rent this article ?

Related Content

Customize your page view by dragging & repositioning the boxes below.

See Also...
Articles Related By Topic
Related Collections

The Rational Clinical Examination: Evidence-Based Clinical Diagnosis
Evidence Summary and Review 4

The Rational Clinical Examination: Evidence-Based Clinical Diagnosis