Compilation of IOL Power Calculation Formulas and When to Utilize

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Article initiated by:
Ian Hidinger, Jeremy Kudrna, MD, MS, Seth M. Pantanelli, MD, MS
All contributors:
Derek W DelMonte, MD, Jeremy Kudrna, MD, MS, Seth M. Pantanelli, MD, MS
Assigned editor:
Derek W DelMonte, MD
Review:
Assigned status Up to Date
 by Derek W DelMonte, MD on July 17, 2024.


Introduction

An increasingly important objective of cataract surgery is the minimization of refractive error. Achieving this requires that the surgeon choose an appropriate IOL power calculation formula, which is not a trivial task. Substantial progress has been made since Fyodorov introduced the classical vergence formula [1] and a myriad of methods have since been developed to handle unique populations of patients. Herein, we seek to compile a list of formulas for use in surgery naïve eyes (Table1), those with clinically significant astigmatism in which a toric IOL is anticipated (Table 2), and those with a history of corneal refractive surgery (Table 3).

While IOL power calculation formula selection is a critical component of the pre-surgical planning process, it should always be used in conjunction with an optimization of the optic media including adequate surface lubrication, validation of diagnostic testing for quality, lens constant optimization, meticulous intraoperative technique, tailoring of the IOL model to the patient's needs and desires, and careful post-operative manifest refractions to evaluate for unexpected outcomes.

Tables can be expanded or collapsed by clicking the Expand/Collapse link at the upper right hand corner of the particular table.

Table 1: Spherical IOL Power Formulas

Formula Name Year Formula Classification Variables Advantages Disadvantages
Barrett Universal (BU)[2][3] Version I: 1993[3]

Version II: 2010

Vergence
  • AL
  • K
  • ACD
  • LT (optional)
  • WTW (optional)
  • LF/DF or A-constant
  • Post-operative refractive target

***Formula not publicly available

  • Accurate in long eyes [4]
  • Accurate in normal ranges AL:
    • Including implantaion of Panoptix IOL in normal ALs of 22.5mm-26mm [5]
    • Including implantation of Acrysof IQ SN60WF IOL in AL >22.0mm[6]
    • Including implantation of trifocal hydrophilic IOL [7]
  • Along with Holliday 2, accurate in pediatric populations[8]
  • Best in eyes with mild-moderate keratoconus[9] or K > 40 [10]
  • Easily accessible for free online
  • Pre-installed on:
    • AL-Scan (Nidek)
    • Aladdin (Topcon)
    • Anterion (Heidelberg Engineering)
    • EQ Workplace (Zeiss)
    • IOLMaster 700 (Zeiss)
    • OA-2000 (Tomey)
    • Veracity Surgery Planner (Zeiss)
    • Vision Planner (Alcon)
  • May be less accurate in short eyes (i.e. AL ≤22.0mm [11] or requiring implantation of a lens power ≥30D[12])
    • However, BU-II can still provide excellent refractive outcomes with AL <22.5mm[10] or AL 20.8mm-22.0mm[13]
EVO 2.0

2019

Vergence
  • AL
  • K
  • ACD
  • A-constant
  • LT (optional)
  • CCT (optional)
  • Corneal refractive LVC status
  • Post-operative refractive target
  • Easily accessible for free online
  • Accurate in long eyes (26mm≤AL<28mm)[14]
  • Accurate in eyes requiring insertion of IOL ≥ 30D[12]
  • Similar in accuracy to Barrett Universal II [15]
  • Accounts for the optical dimensions of the eye and can handle different IOL geometry and powers
  • The EVO IOL calculator is solely intended for use with a pseudophakic IOL during cataract surgery and not for use with a refractive phakic IOL (e.g. as Staar Surgical's EVO Visian ICL)
  • Does not come pre-installed on any optic biometers
  • Performance has not extensively been reported in the literature
Haigis 2004 Vergence
  • AL
  • K
  • ACD
  • 3 constants:
    • a0
    • a1
      • Associated with measured ACD
    • a2
      • Associated with measured AL
  • Post-operative refractive target
  • Accurate in short eyes (AL<22mm) [16]
  • Accurate for stage III keratoconus eyes [9]
  • Pre-installed on:
    • Aladdin (Topcon)
    • Anterion (Heidelberg Engineering)
    • EQ Workplace (Zeiss)
    • Galilei G6 (Zeimer)
    • IOLMaster 700 (Zeiss)
    • OA-2000 (Tomey)
    • Vision Planner (Alcon)
  • Less accurate in long eyes:
    • Resulting hyperopic outcomes in long eyes using Haigis alone, which can be addressed using Haigis with Wang-Koch adjustment[17][18]
  • Less accurate in eyes with extreme LT values[10]
    • Haigis and Hill-RBF V.2.0 were significantly influenced by LT, independently of the ACD (myopic shift with thin lenses and a hyperopic shift with thick lenses)[19]
Hill-RBF Version 2: 2018

Version 3: 2020

Artificial Intelligence
  • AL
  • K
  • ACD
  • LT (optional)
  • WTW (optional)
  • CCT (optional)
  • A-constant
  • Post-operative refractive target
  • Prediction accuracy continues to improve as more data is analyzed
  • May outperform BU-II [20][21]
  • Haigis and Hill-RBF V.2.0 were significantly influenced by LT, independently of the ACD (myopic shift with thin lenses and a hyperopic shift with thick lenses)[19]
Hoffer Q[22] 1993 Vergence
  • AL
  • K
  • pACD
  • Post-operative refractive target
  • Accurate in short eyes:
    • Including implantation of Sofport AO and Akreos Fit IOLs in eyes with 20.00mm ≥ AL ≤ 20.09mm[23]
    • Including implantaion of Panoptix IOL in eyes with AL ≤22.5mm [24]
  • Pre-installed on:
    • AL-Scan (Nidek)
    • Anterion (Heidelberg Engineering)
    • EQ Workplace (Zeiss)
    • Galilei G6 (Zeimer)
    • IOLMaster 700 (Zeiss)
    • OA-2000 (Tomey)
    • Veracity Surgery Planner (Zeiss)
    • Vision Planner (Alcon)
  • No use of anatomic ACD, so theoretically less reliable in anatomically abnormal anterior segments
  • Recommended to be replaced by Hoffer QST
Hoffer QST 2021 Artificial Intelligence
  • AL
  • K
  • ACD
  • pACD
  • Post-operative refractive target
  • Easily accessible for free online
  • More accurate than Hoffer Q:
    • Including un-operated short eyes and un-operated long eyes [25]
  • Pre-installed on:
    • Optopol biometer
  • Paucity of published evidence currently available
Holladay 1[26] 1988 Vergence
  • AL
  • K
  • SF
  • Post-operative refractive target
  • Accurate for short eyes[23][27]:
    • Including implantaion of Panoptix IOL in AL ≤22.5mm [24]
  • Unique relationships of AL and K adjust for anterior segments accurately
  • Pre-installed on:
    • AL-Scan (Nidek)
    • Aladdin (Topcon)
    • Anterion (Heidelberg Engineering)
    • EQ Workplace (Zeiss)
    • Galilei G6 (Zeimer)
    • IOLMaster 700 (Zeiss)
    • OA-2000 (Tomey)
    • Veracity Surgery Planner (Zeiss)
    • Vision Planner (Alcon)
  • Less accurate in long eyes:
    • Resulting hyperopic outcomes in long eyes (i.e. AL >26.5mm) using Holladay 1 alone, which can be addressed using Holladay 1 with Wang-Koch adjustment[17][18]
Holladay 2 1995 Vergence
  • AL
  • K
  • ACD
  • LT
  • WTW
  • CCT
  • Age
  • A-constant/ACD/SF
  • Post-operative refractive target
  • Open Access Calculator Button on website permits Forward and Back Calculation of Holladay 2 Formula
  • Along with BU, accurate in pediatric populations[8]
  • Pre-installed on:
    • EQ Workplace (Zeiss)
    • IOLMaster 700 (Zeiss)
    • Veracity Surgery Planner (Zeiss)
    • Vision Planner (Alcon)
  • Less accurate in long eyes:
    • Resulting hyperopic outcomes in long eyes (i.e. AL >24.0mm) using Holladay 2 alone, which can be addressed using Holladay 1 with Wang-Koch adjustment and Holladay Nonlinear axial length adjustment[28]
  • Requires IOL Consultant Software (works for 30 days before UNLOCK KEY is necessary; after 30 days, one must use another computer for an additional 30 days) [29]
Intraoperative Aberrometry (IA) [30][31]
  • AKA Intraoperative Optical Refractive Biometry
  • AKA Intraoperative Refractive Biometry
  • AKA Intraoperative Autorefraction
 2005 [31] Vergence
  • AL
  • K
  • Corneal diameter
  • Post-operative refractive target
  • During patient fixation, each ORA reading average 40 measurements in several seconds to recommend predicted implanted IOL sphere and cylinder power [32]
  • Pre-installed on:
    • ORA (Alcon)
  • Not significantly different from the best preoperative biometry-based methods available for IOL power selection in short eyes [33]
  • No clear consensus regarding utility in routine cataract surgery (i.e. outside of post-LVC and astigmatic eyes)
  • Requires additional equipment: 
    • ORA (Alcon)
Kane 2017 Blended (Vergence, Regression, and Artificial Intelligence-based)
  • AL
  • K
  • ACD
  • LT (optional)
  • CCT (optional)
  • Gender
  • A constant (developed to be similar to SRK/T A-constant)
  • Post-operative refractive target
  • Accurate in short eyes [7][11][12]
  • Accurate in long eyes (i.e. AL ≥26mm) [14][34]
  • Prediction accuracy continues to improve as more data is analyzed
  • Accurate in extreme ACD (e.g. ≤3.0mm)[19]
  • Easily accessible for free online
  • Pre-installed on:
    • Veracity Surgery Planner (Zeiss)
    • EQ Workplace (Zeiss)
Ladas Super Formula 2015 Artificial Intelligence
  • Depending on biometry/variables, Ladas super formula applies most ideal calculations from other formulas (SRK/T, Hoffer Q, Holladay 1, Holladay with WK adjustment, Haigis with deep learning, etc.)
  • Post-operative refractive target
  • Prediction accuracy continues to improve as more data is analyzed
  • Newer versions including Toric and Post-LASIK calculators
OKULIX[35] 2002 Ray-tracing
  • AL
  • K
  • ACD
  • CCT
  • IOL design parameters
  • Post-operative refractive target
  • Provides geometrical "most probable" IOL position (i.e. no estimation of ELP)[36]
  • Can be used in post-LASIK eyes, if corneal topographies available[36]
  • Pre-installed on:
    • Anterion (Heidelberg Engineering)
    • OA-2000 (Tomey)
  • Calculating sum-of-segments AL is difficult in most clinical settings because vitreous thickness is not available to calculate in many optical biometers[37]
  • Demands that the precise optical profile of the IOL be known, which is proprietary and may not be shared by the IOL manufacturer, thus available for use for limited number of IOLs
Olsen-C[38][39] 2014 Ray-tracing
  • ACD
  • LT
  • Post-operative refractive target
  • Accurate in short eyes [7][11]
  • Accurate in long eyes [10]
  • Pre-installed on:
    • Aladdin (Topcon)
    • OA-2000 (Tomey)
  • Requires purchase of PhacoOptics® – IOL Power Calculation Software
PEARL-DGS[40] 2021 Artificial Intelligence
  • AL
  • K
  • ACD
  • LT
  • WTW
  • CCT
  • A constant
  • Uses machine learning models to predict:
    • Posterior corneal radius
    • Theoretical internal lens position
  • Post-operative refractive target
  • IOL constants are adjustable
  • No re-training required for new IOL models
  • Can also be used for toric and post-corneal refractive surgery eyes
  • Uses Python code, readily available on Github
  • Paucity of published evidence currently available
SRK/T[41] 1990 Vergence
  • AL
  • K
  • A-constant
  • Post-operative refractive target
  • Accurate in eyes with normal axial lengths and mean keratometry values
  • Accurate in axial myopes than other traditional vergence-based formulas (i.e. Holladay 1, Holladay 2, Hoffer Q)
  • Wang-Koch adjustment can be easily applied to further enhance outcomes in axial myopes
  • Pre-installed on:
    • AL-Scan (Nidek)
    • Aladdin (Topcon)
    • Anterion (Heidelberg Engineering)
    • EQ Workplace (Zeiss)
    • Galilei G6 (Zeimer)
    • IOLMaster 700 (Zeiss)
    • OA-2000 (Tomey)
    • Veracity Surgery Planner (Zeiss)
  • Less accurate in long eyes than modern vergence-based formulas (i.e. BU-II, EVO, Hill-RBF, Kane) [14]
    • Resulting hyperopic outcomes in long eyes (i.e. AL >27.0mm) using SRK/T alone, can be addressed using SRK/T with Wang-Koch adjustment[17][18]
    • Including implantation of trifocal IOL in highly myopic Chinese patients [42]
  • Assumes normal ACD

Table 2: Toric IOL Power Formulas

Formula Name Year Variables Advantages Disadvantages
Abulafia-Koch Toric[43] 2016
  • Toric IOL power at the corneal plane
    • As calculated by the Holladay 1 formula, using meridional method described by Fam and Lim [44]
  • Cylinder of post-op manifest refraction at the corneal plane
  • Anterior cornea-based K
  • SF
  • Post-operative refractive target
  • Application of the Abulafia-Koch formula resulted in the lowest centroid error of all the nomograms (Baylor, Goggins)[45]
  • Pre-installed on:
    • Veracity Surgery Planner (Zeiss)
  • No statistically significant difference in MPE between Abulafia-Koch, Barrett, and EVO 2.0 [43] [46][47]
Barrett Toric 2015
  • AL
  • K
  • ACD
  • LT (optional)
  • WTW (optional)
  • Posterior corneal curvature (optional)
  • CCT (optional)
  • LF
  • Post-operative refractive target
  • Employs an algorithm that empirically accounts for posterior corneal astigmatism
  • May optionally utilize measured posterior corneal curvature
  • Uses the BUII formula to calculate ELP
  • Pre-installed on the Vision Planner (Alcon )
  • Pre-installed on:
    • AL-Scan (Nidek)
    • Anterion (Heidelberg Engineering)
    • EQ Workplace (Zeiss)
    • Galilei G6 (Zeimer)
    • IOLMaster 700 (Zeiss)
    • Veracity Surgery Planner (Zeiss)
  • No statistically significant difference in MPE between Abulafia-Koch, Barrett, and EVO 2.0 [43] [46][47]
  • Barrett and EVO had similar performance in terms of their astigmatism prediction accuracy [48]
Baylor Toric Nomogram [49] 2013
  • Anterior corneal astigmatism magnitude and axis
  • Post-operative refractive target
  • First toric IOL power calculation nomogram to account for posterior corneal astigmatism [49]
  • Improved median absolute error in predicted astigmatism amongst toric calculators[49]
  • Barrett Toric outperforms application of the Baylor nomogram[49]
EVO 2.0 Toric 2020
  • AL
  • K
  • ACD
  • LT (optional)
  • CCT (optional)
  • A-constant
  • Toric model
  • Posterior corneal curvature (optional)
  • SICA (optional)
  • Pre-LVC manifest refraction
  • Post-LVC manifest refraction
  • Post-operative refractive target
  • Combines theoretical posterior corneal astigmatism and thick lens modeling
  • No statistically significant difference in MPE between Abulafia-Koch, Barrett, and EVO 2.0 [43] [46][47]
  • Barrett and EVO had similar performance in terms of their astigmatism prediction accuracy[48]
  • Does not come pre-installed on any optic biometers
Holladay 2 Toric[50] 2019
  • AL
  • K
  • ACD
  • LT
  • WTW
  • Age
  • Pre-LVC manifest refraction
  • Post-operative refractive target
  • Utilizes a total SICA correction to account for factors that lead to differences between preoperative K and postoperative astigmatism[50]
  • Must use Non-Linear Adjustment in AL for eyes >24.0 mm [28]
  • Must use Preoperative Ks, not Postoperative Ks to accurately determine the Prediction Error (Predicted Refraction minus Actual Refraction)
  • Software can use either Standard K or Total K or both
  • SICA is described as a factor that leads to residual astigmatism post-surgery [51]
    • To accurately calculate total SICA, one must use the 'check box' for small incision (allow for any location, though usually temporal) [52]
  • Easily implemented using IOL Consultant Software (works for 30 days before UNLOCK KEY is necessary; after 30 days, one must use another computer for an additional 30 days) [29]
  • Requires the actual observed axis of toric IOL at time of post-operative refraction (i.e. intended axis is not as important as the true orientation of the implanted IOL)
Intraoperative Aberrometry (IA) [30][31]
  • AKA Intraoperative Optical Refractive Biometry
  • AKA Intraoperative Refractive Biometry
  • AKA Intraoperative Autorefraction
 2005[31]
  • Based purely on optical principles
  • Post-operative refractive target
  • Accurate in post-LVC [53] and eyes in need of astigmatic correction[54]
  • Accurate compared to manual ink toric markings [55]
  • Pre-installed on:
    • ORA (Alcon)
  • Requires additional equipment: 
    • ORA (Alcon)
  • Unclear if IA holds clear advantage over modern toric IOL formulas
Kane Toric 2020
  • AL
  • K
  • ACD
  • Gender
  • LT (optional)
  • CCT (optional)
  • SICA (optional)
  • A-constant
  • Post-operative refractive target
  • Uses Kane formula to calculate ELP and then an algorithm utilizing artificial intelligence, regression, and theoretical optics to calculate astigmatism
  • Statistically significant lower mean absolute prediction error and a significant lower variance of PE compared with other toric formulas [47]
  • Pre-installed on:
    • EQ Workplace (Zeiss)
    • Veracity Surgery Planner (Zeiss)
Naeser-Savini [46] 2021
  • AL
  • K
  • TCA
  • SICU
  • Post-operative refractive target
  • Considers anterior and posterior corneal astigmatism
  • Easily accessible for free online
  • Paucity of published evidence currently available

Table 3: Post-Corneal Refractive Surgery IOL Power Calculation Formulas

Formula Name Year Variables Advantages Disadvantages
Adjusted Atlas 9000 [56] 2007
  • Post-operative refractive target
  • Requires specific equipment:
    • Atlas Corneal Topographer (Zeiss)
Adjusted EffRP [57] 2002
  • Post-operative refractive target
  • Post-PRK corneal powers measured using the adjusted EffRP formula were the most similar to values obtained using CHM [58]
  • Requires specific equipment:
    • EyeSys System 2000 Corneal Topographer (EyeSys)
ASCRS Post-LVC IOL Power Calculator[59] 2007
  • Allows entry of as little or as much information available to the surgeon
  • Post-operative refractive target
  • Easily averages the predictions of multiple formulas
  • One of the most accurate methods of IOL power calculation in eyes post-LVC
Barrett True-K 2015
  • AL
  • Measured K1
  • Measured K2
  • ACD
  • LT (optional)
  • WTW (optional)
  • LF
  • Post-operative refractive target
  • May be used with or without historical data
  • Improved using historical data and measured posterior corneal power [60]
  • More accurate compared to other popular post-refractive surgery formulas: Adjusted Atlas 9000, Masket, Modified Masket, Wang-Koch-Maloney, Shammas, Haigis-L [61]
  • When using extended depth-of-focus IOLs, Barrett True-K No History outperformed other post-refractive formulas [42]
  • Performs equivalently to multi-formula approach in post-refractive eyes [62]
  • Pre-installed on:
    • AL-Scan (Nidek)
    • Aladdin (Topcon)
    • EQ Workplace (Zeiss)
    • IOLMaster 700 (Zeiss)
    • OA-2000 (Tomey)
    • Veracity Surgery Planner (Zeiss)
    • Vision Planner (Alcon)
Clinical History Method [63] 1989
  • Post-operative refractive target
  • Post-PRK corneal powers measured using the adjusted EffRP formula were the most similar to values obtained using CHM [58]
  • Require pre-LVC keratometry and manifest refraction [61]
  • Less accurate than methods requiring less information [61]
  • Dependent on accuracy of historical data [61]
Corneal Bypass Method [64] 2006
  • Post-operative refractive target
  • Post-refractive corneal power is not required
  • Require pre-LVC keratometry and manifest refraction [61]
  • Less accurate than methods requiring less information [61]
  • Dependent on accuracy of historical data [61]
EVO 2.0 2019 Vergence
  • AL
  • K
  • ACD
  • LT (optional)
  • CCT (optional)
  • Corneal refractive LVC status
  • Post-operative refractive target
  • Accurate in long eyes (26mm≤AL<28mm)[14]
  • Accounts for the optical dimensions of the eye and can handle different IOL geometry and powers
  • The EVO IOL calculator is solely intended for use with a pseudophakic IOL during cataract surgery and not for use with a refractive phakic IOL (e.g. as Staar Surgical's EVO Visian ICL)
  • Does not come pre-installed on any optic biometers
  • Performance has not extensively been reported in the literature
Feiz-Mannis [65] 2001
  • Post-operative refractive target
  • Least likely of all post-corneal LVC surgery IOL calculation methods to lead to post-operative hyperopic surprise (i.e. Feiz-Mannis can be used as upper limit of possible IOL powers) [66]
  • Require pre-LVC keratometry and manifest refraction [61]
  • Less accurate than methods requiring less information [61]
  • Dependent on accuracy of historical data [61]
  • Susceptible to myopic outcomes [61] and large variance [67]
Haigis-L[68] 2008
  • AL
  • K
  • ACD
  • 3 constants:
    • a0
    • a1
      • Associated with measured ACD
    • a2
      • Associated with measured AL
  • Post-operative refractive target
  • Historical data not required
  • Identical IOL power calculations as Haigis formula, with the only difference being that Haigis-L first calculates a new corneal radius based on the myopic Haigis-L algorithm (this calculation is described by Warren Hill, MD[69])
  • Pre-installed on:
    • EQ Workplace (Zeiss)
    • IOLMaster 700 (Zeiss)
  • Less accurate than Barrett True-K No History[70] [71]
Intraoperative Aberrometry[30][31]
  • AKA Intraoperative Optical Refractive Biometry
  • AKA Intraoperative Refractive Biometry
  • AKA Intraoperative Autorefraction
 2005[31]
  • Based purely on optical principles
  • Post-operative refractive target
  • Comparable to Barrett True-K in post-corneal refractive surgery and possibly better in post-hyperopic LVC [72]
  • Accurate in post-LVC [53] and eyes in need of astigmatic correction[54]
  • Pre-installed on:
    • ORA (Alcon)
  • Requires additional equipment:
    • ORA (Alcon)
Masket[73] 2006
  • Uses Holladay 1 formula for AL >23.0 mm[74]
  • Uses Hoffer Q formula for AL <23.0 mm[74]
  • Post-corneal refractive surgery power adjustment = [(laser-vision correction spherical equivalent, with vertex distance corrected) * (-0.326)] + (0.101)
  • Post-operative refractive target
  • Works for myopic and hyperopic LVC
  • Requires knowledge of the pre-LVC and post-LVC manifest refraction [73]
OCT (RTVue)[75] 2010
  • AL
  • ACD
  • CCT
  • Net Corneal Power
  • Posterior Corneal Power
  • Post-operative refractive target
  • Historical data not required
  • Requires special equipment:
    • Optovue RTVue
OKULIX[35] (Ray Tracing) 2002
  • AL
  • K
  • ACD
  • CCT
  • IOL design parameters
  • Post-operative refractive target
  • Can be used in post-LVC eyes, if corneal topographies available[36]
  • Calculating sum-of-segments AL is difficult in most clinical settings because vitreous thickness is not available to calculate in many optical biometers[37]
  • Demands that the precise optical profile of the IOL be known, which is proprietary and may not be shared by the IOL manufacturer, thus available for use for limited number of IOLs
Potvin-Hill[76] 2015
  • Post-operative refractive target

***Formula not publicly available

  • Historical data not required
  • Requires special equipment:
    • Pentacam AXL (OCULUS)
Schuster/Schanzlin-Thomas-Purcell (SToP)[77] 2016
  • AL
  • Ratio of posterior-to-anterior corneal radius
  • Anterior corneal radius
  • A-constant
  • Post-operative refractive target
  • Historical data not required
  • Requires specific equipment:
    • Scheimpflug imaging (Pentacam HR)
    • PCI-based optic biometer (IOLMaster)
Shammas-PL[78] 2003
  • Post-operative refractive target

***Formula not publicly available

  • Historical data not required
  • Pre-installed on:
    • AL-Scan (Nidek)
    • Galilei G6 (Zeimer)
    • OA-2000 (Tomey)
  • Accurate in long eyes (i.e. AL ≥ 30 mm) [79]
  • Significantly impacted by extreme ACDs [80]
Wang-Koch-Maloney[67] 2004
  • Post-operative refractive target
  • Historical data not required
  • More accurate than Feiz-Mannis [61] [81]
  • Low variance among post-refractive formulas [67]
  • Requires specific equipment:
    • Atlas Corneal Topography (Zeiss)
  • Less accurate than OCT (RTVue) [70]

Abbreviation Table

Abbreviation Terminology
ACA anterior corneal astigmatism
ACD anterior chamber depth
AKA also known as
AL axial length
ATR against-the-rule (corneal astigmatism)
BUII Barrett Universal II
CCT central corneal thickness
D diopter(s)
DF design factor
DGS Debellemanière, Gatinel, Saad (last names of PEARL-DGS formula authors)
EffRP effective refractive power
ELP effective lens position
EVO Emmetropia Verifying Optical
Hoffer QST Hoffer Q Savini Taroni
IA intraoperative aberrometry
IOL intraocular lens
K keratometry
LASIK laser-assisted in-situ keratomileusis
LF lens factor
LT lens thickness
LVC laser vision correction
mm millimeter
OCT optic coherence tomography
OLCR optical low coherence reflectometry
ORA Optiwave Refractive Analysis
pACD personalized anterior chamber depth
PEARL Postoperative spherical Equivalent Prediction using ARtificial Intelligence and Linear algorithms

OR

Prediction Enhanced by ARtificial Intelligence and output Linearization

PCI partial coherence interferometry
PRK photorefractive keratectomy
RCT randomized control trial
RBF radial basis function
SICA surgically-induced corneal astigmatism
SRK/T Sanders-Retzlaff-Kraff theoretical
SF surgeon factor
TCA total corneal astigmatism
WTR with-the-rule (corneal astigmatism)
WTW white-to-white corneal diameter distance
  1. ↑ Fyodorov SN, Galin MA, Linksz A. Calculation of the optical power of intraocular lenses. Invest Ophthalmol. 1975 Aug;14(8):625-8. PMID: 1150402.
  2. ↑ Barrett GD. Intraocular lens calculation formulas for new intraocular lens implants. J Cataract Refract Surg. 1987;13(4):389-396. doi:10.1016/s0886-3350(87)80037-8
  3. ↑ 3.0 3.1 Barrett GD. An improved universal theoretical formula for intraocular lens power prediction. J Cataract Refract Surg. 1993;19(6):713-720. doi:10.1016/s0886-3350(13)80339-2
  4. ↑ Abulafia A, Barrett GD, Rotenberg M, et al. Intraocular lens power calculation for eyes with an axial length greater than 26.0 mm: Comparison of formulas and methods. J Cataract Refract Surg. 2015;41(3):548-556. doi:10.1016/j.jcrs.2014.06.033
  5. ↑ Choi A, Kwon H, Jeon S. Accuracy of theoretical IOL formulas for Panoptix intraocular lens according to axial length. Sci Rep. 2021;11(1):7346. doi:10.1038/s41598-021-86604-5
  6. ↑ Kane JX, Van Heerden A, Atik A, Petsoglou C. Intraocular lens power formula accuracy: Comparison of 7 formulas. J Cataract Refract Surg. 2016;42(10):1490-1500. doi:10.1016/j.jcrs.2016.07.021
  7. ↑ 7.0 7.1 7.2 Rocha-de-Lossada C, Colmenero-Reina E, Flikier D, et al. Intraocular lens power calculation formula accuracy: Comparison of 12 formulas for a trifocal hydrophilic intraocular lens. Eur J Ophthalmol. 2021;31(6):2981-2988. doi:10.1177/1120672120980690
  8. ↑ 8.0 8.1 Eppley SE, Arnold BF, Tadros D, Pasricha N, de Alba Campomanes AG. Accuracy of a universal theoretical formula for power calculation in pediatric intraocular lens implantation. J Cataract Refract Surg. 2021;47(5):599-605. doi:10.1097/j.jcrs.0000000000000495
  9. ↑ 9.0 9.1 Wang KM, Jun AS, Ladas JG, Siddiqui AA, Woreta F, Srikumaran D. Accuracy of Intraocular Lens Formulas in Eyes With Keratoconus. Am J Ophthalmol. 2020;212:26-33. doi:10.1016/j.ajo.2019.11.019
  10. ↑ 10.0 10.1 10.2 10.3 Melles, R. B., Holladay, J. T. & Chang, W. J. Accuracy of intraocular lens calculation formulas. Ophthalmology 125, 169–178 (2018).
  11. ↑ 11.0 11.1 11.2 Voytsekhivskyy OV, Tutchenko L, Hipólito-Fernandes D. Comparison of the Barrett Universal II, Kane and VRF-G formulas with existing intraocular lens calculation formulas in eyes with short axial lengths. Eye Lond Engl. Published online January 15, 2022. doi:10.1038/s41433-021-01890-7
  12. ↑ 12.0 12.1 12.2 Kane JX, Melles RB. Intraocular lens formula comparison in axial hyperopia with a high-power intraocular lens of 30 or more diopters. J Cataract Refract Surg. 2020;46(9):1236-1239. doi:10.1097/j.jcrs.0000000000000235
  13. ↑ Cooke DL, Cooke TL. Comparison of 9 intraocular lens power calculation formulas. J Cataract Refract Surg. 2016;42(8):1157-1164. doi:10.1016/j.jcrs.2016.06.029
  14. ↑ 14.0 14.1 14.2 14.3 Lin L, Xu M, Mo E, et al. Accuracy of Newer Generation IOL Power Calculation Formulas in Eyes With High Axial Myopia. J Refract Surg Thorofare NJ 1995. 2021;37(11):754-758. doi:10.3928/1081597X-20210712-08
  15. ↑ Melles RB, Kane JX, Olsen T, Chang WJ. Update on Intraocular Lens Calculation Formulas. Ophthalmology. 2019;126(9):1334-1335. doi:10.1016/j.ophtha.2019.04.011
  16. ↑ Shrivastava AK, Behera P, Kumar B, Nanda S. Precision of intraocular lens power prediction in eyes shorter than 22 mm: An analysis of 6 formulas. J Cataract Refract Surg. 2018;44(11):1317-1320. doi:10.1016/j.jcrs.2018.07.023
  17. ↑ 17.0 17.1 17.2 Wang L, Shirayama M, Ma XJ, Kohnen T, Koch DD. Optimizing intraocular lens power calculations in eyes with axial lengths above 25.0 mm. J Cataract Refract Surg. 2011;37(11):2018-2027. doi:10.1016/j.jcrs.2011.05.042
  18. ↑ 18.0 18.1 18.2 Wang L, Koch DD. Modified axial length adjustment formulas in long eyes. J Cataract Refract Surg. 2018;44(11):1396-1397. doi:10.1016/j.jcrs.2018.07.049
  19. ↑ 19.0 19.1 19.2 Hipólito-Fernandes D, Luís ME, Serras-Pereira R, et al. Anterior chamber depth, lens thickness and intraocular lens calculation formula accuracy: nine formulas comparison. Br J Ophthalmol. Published online November 23, 2020:bjophthalmol-2020-317822. doi:10.1136/bjophthalmol-2020-317822
  20. ↑ Nemeth G, Modis L. Accuracy of the Hill-radial basis function method and the Barrett Universal II formula. Eur J Ophthalmol. 2021;31(2):566-571. doi:10.1177/1120672120902952
  21. ↑ Nemeth G, Kemeny-Beke A, Modis L. Comparison of accuracy of different intraocular lens power calculation methods using artificial intelligence. Eur J Ophthalmol. 2022;32(1):235-241. doi:10.1177/1120672121994720
  22. ↑ Hoffer KJ. The Hoffer Q formula: a comparison of theoretic and regression formulas. J Cataract Refract Surg. 1993;19(6):700-712. doi:10.1016/s0886-3350(13)80338-0
  23. ↑ 23.0 23.1 Aristodemou, P., Knox Cartwright, N. E., Sparrow, J. M. & Johnston, R. L. Formula choice: Hoffer Q, Holladay 1, or SRK/T and refractive outcomes in 8108 eyes after cataract surgery with biometry by partial coherence interferometry. J. Cataract. Refract. Surg. 37, 63–71 (2011).
  24. ↑ 24.0 24.1 Choi A, Kwon H, Jeon S. Accuracy of theoretical IOL formulas for Panoptix intraocular lens according to axial length. Sci Rep. 2021;11(1):7346. doi:10.1038/s41598-021-86604-5
  25. ↑ Shammas HJ, Taroni L, Pellegrini M, Shammas MC, Jivrajka RV. ACCURACY OF NEWER IOL POWER FORMULAS IN SHORT AND LONG EYES USING SUM-OF-SEGMENTS BIOMETRY. J Cataract Refract Surg. 2022 Apr 27. doi: 10.1097/j.jcrs.0000000000000958. Epub ahead of print. PMID: 35473887.
  26. ↑ Holladay JT, Prager TC, Chandler TY, Musgrove KH, Lewis JW, Ruiz RS. A three-part system for refining intraocular lens power calculations. J Cataract Refract Surg. 1988;14(1):17-24.
  27. ↑ Kane, J. X., Van Heerden, A., Atik, A. & Petsoglou, C. Accuracy of 3 new methods for intraocular lens power selection. J. Cataract. Refract. Surg. 43, 333–339 (2017).
  28. ↑ 28.0 28.1 Wang L, Holladay JT, Koch DD. Wang-Koch axial length adjustment for the Holladay 2 formula in long eyes. J Cataract Refract Surg. 2018;44(10):1291-1292. doi:10.1016/j.jcrs.2018.06.057. Errata: January 2019 JCRS Jan 45 117.
  29. ↑ 29.0 29.1 https://www.hicsoap.com/
  30. ↑ 30.0 30.1 30.2 Tang M, Li Y, Huang D. An intraocular lens power calculation formula based on optical coherence tomography: a pilot study. J Refract Surg Thorofare NJ 1995. 2010;26(6):430-437. doi:10.3928/1081597X-20090710-02
  31. ↑ 31.0 31.1 31.2 31.3 31.4 31.5 Ianchulev T, Salz J, Hoffer K, Albini T, Hsu H, Labree L. Intraoperative optical refractive biometry for intraocular lens power estimation without axial length and keratometry measurements. J Cataract Refract Surg. 2005 Aug;31(8):1530-6. doi: 10.1016/j.jcrs.2005.01.035. PMID: 16129287.
  32. ↑ Kane JX, Chang DF. Intraocular Lens Power Formulas, Biometry, and Intraoperative Aberrometry: A Review. Ophthalmology. 2021;128(11):e94-e114. doi:10.1016/j.ophtha.2020.08.010
  33. ↑ Sudhakar S, Hill DC, King TS, Scott IU, Mishra G, Ernst BB, Pantanelli SM. Intraoperative aberrometry versus preoperative biometry for intraocular lens power selection in short eyes. J Cataract Refract Surg. 2019 Jun;45(6):719-724. doi: 10.1016/j.jcrs.2018.12.016. Epub 2019 Mar 8. PMID: 30853316.
  34. ↑ Kane, Jack X. MBBS; Melles, Ronald B. MD. Intraocular lens formula comparison in axial hyperopia with a high-power intraocular lens of 30 or more diopters. Journal of Cataract & Refractive Surgery: September 2020 - Volume 46 - Issue 9 - p 1236-1239 doi: 10.1097/j.jcrs.0000000000000235
  35. ↑ 35.0 35.1 Preussner PR, Wahl J, Lahdo H, Dick B, Findl O. Ray tracing for intraocular lens calculation. J Cataract Refract Surg. 2002;28(8):1412-1419. doi:10.1016/s0886-3350(01)01346-3
  36. ↑ 36.0 36.1 36.2 Preussner PR, Wahl J, Weitzel D. Topography-based intraocular lens power selection. J Cataract Refract Surg. 2005 Mar;31(3):525-33. doi: 10.1016/j.jcrs.2004.09.016. PMID: 15811740.
  37. ↑ 37.0 37.1 Cooke DL, Cooke TL. Approximating sum-of-segments axial length from a traditional optical low-coherence reflectometry measurement. J Cataract Refract Surg. 2019;45(3):351-354. doi:10.1016/j.jcrs.2018.12.026
  38. ↑ Olsen T, Hoffmann P. C constant: new concept for ray tracing-assisted intraocular lens power calculation. J Cataract Refract Surg. 2014;40(5):764-773. doi:10.1016/j.jcrs.2013.10.037
  39. ↑ Olsen T, Inventor; IOL Innovations ApS (Arhus, DK), assignee. System and method for determining and predicting IOL power in situ. US patent 8,657,4452014.
  40. ↑ Debellemanière G, Dubois M, Gauvin M, Wallerstein A, Brenner LF, Rampat R, Saad A, Gatinel D. The PEARL-DGS Formula: The Development of an Open-source Machine Learning-based Thick IOL Calculation Formula. Am J Ophthalmol. 2021 Dec;232:58-69. doi: 10.1016/j.ajo.2021.05.004. Epub 2021 May 13. PMID: 33992611.
  41. ↑ Retzlaff JA, Sanders DR, Kraff MC. Development of the SRK/T intraocular lens implant power calculation formula. J Cataract Refract Surg. 1990;16(3):333-340. doi:10.1016/s0886-3350(13)80705-5
  42. ↑ 42.0 42.1 Tan Q, Lin D, Wang L, et al. Comparison of IOL Power Calculation Formulas for a Trifocal IOL in Eyes With High Myopia. J Refract Surg Thorofare NJ 1995. 2021;37(8):538-544. doi:10.3928/1081597X-20210506-01
  43. ↑ 43.0 43.1 43.2 43.3 Abulafia A, Koch DD, Wang L, et al. New regression formula for toric intraocular lens calculations. J Cataract Refract Surg. 2016;42(5):663-671. doi:10.1016/j.jcrs.2016.02.038
  44. ↑ Fam HB, Lim KL. Meridional analysis for calculating the expected spherocylindrical refraction in eyes with toric intraocular lenses. J Cataract Refract Surg. 2007 Dec;33(12):2072-6. doi: 10.1016/j.jcrs.2007.07.034. PMID: 18053907.
  45. ↑ Ferreira TB, Ribeiro P, Ribeiro FJ, O’Neill JG. Comparison of astigmatic prediction errors associated with new calculation methods for toric intraocular lenses. J Cataract Refract Surg. 2017;43(3):340-347. doi:10.1016/j.jcrs.2016.12.031
  46. ↑ 46.0 46.1 46.2 46.3 Savini G, Næser K, Schiano-Lomoriello D, Ducoli P. Optimized keratometry and total corneal astigmatism for toric intraocular lens calculation. J Cataract Refract Surg. 2017;43(9):1140-1148. doi:10.1016/j.jcrs.2017.06.040
  47. ↑ 47.0 47.1 47.2 47.3 Kane JX, Connell B. A Comparison of the Accuracy of 6 Modern Toric Intraocular Lens Formulas. Ophthalmology. 2020;127(11):1472-1486. doi:10.1016/j.ophtha.2020.04.039
  48. ↑ 48.0 48.1 Pantanelli SM, Sun A, Kansara N, Smits G. Comparison of Barrett and Emmetropia Verifying Optical Toric Calculators. Clin Ophthalmol Auckl NZ. 2022;16:177-182. doi:10.2147/OPTH.S346925
  49. ↑ 49.0 49.1 49.2 49.3 Koch DD, Jenkins RB, Weikert MP, Yeu E, Wang L. Correcting astigmatism with toric intraocular lenses: effect of posterior corneal astigmatism. J Cataract Refract Surg. 2013;39(12):1803-1809. doi:10.1016/j.jcrs.2013.06.027
  50. ↑ 50.0 50.1 Holladay JT, Pettit G. Improving toric intraocular lens calculations using total surgically induced astigmatism for a 2.5 mm temporal incision. J Cataract Refract Surg. 2019;45(3):272-283. doi:10.1016/j.jcrs.2018.09.028
  51. ↑ Goggin M, Moore S, Esterman A. Toric Intraocular Lens Outcome Using the Manufacturer’s Prediction of Corneal Plane Equivalent Intraocular Lens Cylinder Power. Arch Ophthalmol. 2011;129(8):1004-1008. doi:10.1001/archophthalmol.2011.178
  52. ↑ Holladay JT. Calculation of total surgically induced astigmatism with a toric intraocular lens. J Cataract Refract Surg. 2020 May;46(5):793-794. doi: 10.1097/j.jcrs.0000000000000124. PMID: 32358279.
  53. ↑ 53.0 53.1 Ianchulev T, Hoffer KJ, Yoo SH, Chang DF, Breen M, Padrick T, Tran DB. Intraoperative refractive biometry for predicting intraocular lens power calculation after prior myopic refractive surgery. Ophthalmology. 2014;121(1):56-50
  54. ↑ 54.0 54.1 Hatch KM, Woodcock EC, Talamo JH. Intraocular lens power selection positioning with and without intraoperative aberrometry. J Refract Surg. 2015;31(4)237-42.
  55. ↑ Comparative meta-analysis of toric intraocular lens alignment accuracy in cataract patients: Image-guided system versus manual marking
  56. ↑ Koch DD, Wang L, “IOL Calculations Following Refractive Surgery,” presented at the ASCRS Symposium on Cataract, IOL and Refractive Surgery, San Diego, California, USA, April 2007.
  57. ↑ Hamed AM, Wang L, Misra M, Koch DD. A comparative analysis of five methods of determining corneal refractive power in eyes that have undergone myopic laser in situ keratomileusis. Ophthalmology. 2002;109(4):651-658. doi:10.1016/s0161-6420(01)01001-6
  58. ↑ 58.0 58.1 Baradaran-Rafii A, Fekri S, Rezaie M, et al. Accuracy of Different Topographic Instruments in Calculating Corneal Power after Myopic Photorefractive Keratectomy. J Ophthalmic Vis Res. 2017;12(3):254-259. doi:10.4103/jovr.jovr_74_16
  59. ↑ https://iolcalc.ascrs.org/
  60. ↑ Savini G, Hoffer KJ, Barrett GD. Results of the Barrett True-K formula for IOL power calculation based on Scheimpflug camera measurements in eyes with previous myopic excimer laser surgery. J Cataract Refract Surg. 2020 Jul;46(7):1016-1019. doi: 10.1097/j.jcrs.0000000000000205. PMID: 32271267.
  61. ↑ 61.00 61.01 61.02 61.03 61.04 61.05 61.06 61.07 61.08 61.09 61.10 61.11 Wang L, Hill WE, Koch DD. Evaluation of intraocular lens power prediction methods using the American Society of Cataract and Refractive Surgeons Post-Keratorefractive Intraocular Lens Power Calculator. J Cataract Refract Surg. 2010;36(9):1466-1473. doi:10.1016/j.jcrs.2010.03.044
  62. ↑ Ferguson TJ, Downes RA, Randleman JB. IOL Power Calculations after LASIK or PRK: Barrett True-K Biometer Only Calculation Strategy Yields Equivalent Outcomes as a Multiple Formula Approach. J Cataract Refract Surg. Published online January 18, 2022. doi:10.1097/j.jcrs.0000000000000883
  63. ↑ Holladay JT. Consultations in refractive surgery. Refract Corneal Surg 1989;5:203
  64. ↑ Walter KA, Gagnon MR, Hoopes PC, Dickinson PJ. Accurate intraocular lens power calculation after myopic laser in situ keratomileusis, bypassing corneal power. J Cataract Refract Surg. 2006;32(3):425-429. doi:10.1016/j.jcrs.2005.12.140
  65. ↑ Feiz V, Mannis MJ, Garcia-Ferrer F, et al. Intraocular lens power calculation after laser in situ keratomileusis for myopia and hyperopia: a standardized approach. Cornea. 2001;20(8):792-797. doi:10.1097/00003226-200111000-00003
  66. ↑ Feiz-Mannis Method. East Valley Ophthalmology. Accessed June 23, 2022. https://doctor-hill.com/iol-power-calculations/post-keratorefractive-surgery/myopic-lasik-lasek-prk/feiz-mannis-method/
  67. ↑ 67.0 67.1 67.2 Wang L, Booth MA, Koch DD. Comparison of intraocular lens power calculation methods in eyes that have undergone LASIK. Ophthalmology. 2004;111(10):1825-1831. doi:10.1016/j.ophtha.2004.04.022
  68. ↑ Haigis W. Intraocular lens calculation after refractive surgery for myopia: Haigis-L formula. J Cataract Refract Surg. 2008 Oct;34(10):1658-63. doi: 10.1016/j.jcrs.2008.06.029. PMID: 18812114.
  69. ↑ https://doctor-hill.com/iol-main/haigis-l.htm
  70. ↑ 70.0 70.1 Wang L, Tang M, Huang D, Weikert MP, Koch DD. Comparison of Newer Intraocular Lens Power Calculation Methods for Eyes after Corneal Refractive Surgery. Ophthalmology. 2015;122(12):2443-2449. doi:10.1016/j.ophtha.2015.08.037
  71. ↑ Abulafia A, Hill WE, Koch DD, Wang L, Barrett GD. Accuracy of the Barrett True-K formula for intraocular lens power prediction after laser in situ keratomileusis or photorefractive keratectomy for myopia. J Cataract Refract Surg. 2016;42(3):363-369. doi:10.1016/j.jcrs.2015.11.039
  72. ↑ Gouvea L, Sioufi K, Brown CE, Waring Iv G, Chamon W, Rocha KM. Refractive Accuracy of Barrett True-K vs Intraoperative Aberrometry for IOL Power Calculation in Post-Corneal Refractive Surgery Eyes. Clin Ophthalmol. 2021 Oct 27;15:4305-4315. doi: 10.2147/OPTH.S334489. PMID: 34737545; PMCID: PMC8558044.
  73. ↑ 73.0 73.1 Masket S, Masket SE. Simple regression formula for intraocular lens power adjustment in eyes requiring cataract surgery after excimer laser photoablation. J Cataract Refract Surg. 2006 Mar;32(3):430-4. doi: 10.1016/j.jcrs.2005.12.106. PMID: 16631051.
  74. ↑ 74.0 74.1 https://www.doctor-hill.com/iol-main/masket_method.htm
  75. ↑ Tang M, Li Y, Huang D. An intraocular lens power calculation formula based on optical coherence tomography: a pilot study. J Refract Surg. 2010 Jun;26(6):430-7. doi: 10.3928/1081597X-20090710-02. Epub 2010 Jun 17. PMID: 20677729; PMCID: PMC2916192.
  76. ↑ Potvin R, Hill W. New algorithm for intraocular lens power calculations after myopic laser in situ keratomileusis based on rotating Scheimpflug camera data. J Cataract Refract Surg. 2015;41(2):339-347. doi:10.1016/j.jcrs.2014.05.040
  77. ↑ Schuster AK, Schanzlin DJ, Thomas KE, Heichel CW, Purcell TL, Barker PD. Intraocular lens calculation adjustment after laser refractive surgery using Scheimpflug imaging. J Cataract Refract Surg. 2016 Feb;42(2):226-31. doi: 10.1016/j.jcrs.2015.09.024. PMID: 27026446.
  78. ↑ Shammas HJ, Shammas MC, Garabet A, Kim JH, Shammas A, LaBree L. Correcting the corneal power measurements for intraocular lens power calculations after myopic laser in situ keratomileusis. Am J Ophthalmol. 2003;136(3):426-432. doi:10.1016/s0002-9394(03)00275-7
  79. ↑ Whang WJ, Hoffer KJ, Kim SJ, Chung SH, Savini G. Comparison of intraocular lens power formulas according to axial length after myopic corneal laser refractive surgery. J Cataract Refract Surg. 2021 Mar 1;47(3):297-303. doi: 10.1097/j.jcrs.0000000000000445. PMID: 32991505.
  80. ↑ Christopher KL, Patnaik JL, Miller DC, Lynch AM, Taravella MJ, Davidson RS. Accuracy of Intraoperative Aberrometry, Barrett True-K With and Without Posterior Cornea Measurements, Shammas-PL, and Haigis-L Formulas After Myopic Refractive Surgery. J Refract Surg. 2021 Jan 1;37(1):60-68. doi: 10.3928/1081597X-20201030-02. PMID: 33432996.
  81. ↑ Yang R, Yeh A, George MR, Rahman M, Boerman H, Wang M. Comparison of intraocular lens power calculation methods after myopic laser refractive surgery without previous refractive surgery data. J Cataract Refract Surg. 2013;39(9):1327-1335. doi:10.1016/j.jcrs.2013.03.032
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