Comparison of IOL Formulas and When to Utilize

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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 been since 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.

Table 2: Toric IOL Power Formulas

Formula Name Year Variables Advantages Disadvantages
Abulafia-Koch Toric[2] 2016
  • Toric IOL power at the corneal plane
    • As calculated by the Holladay 1 formula, using meridional method described by Fam and Lim [3]
  • Cylinder of post-op manifest refraction at the corneal plane
  • Anterior cornea-based K
  • Application of the Abulafia-Koch formula resulted in the lowest centroid error of all the nomograms (Baylor, Goggins)[4]
  • No statistically significant difference in MPE between Abulafia-Koch, Barrett, and EVO 2.0 [2] [5][6]
Barrett Toric 2015
  • AL
  • K
  • ACD
  • LT (optional)
  • WTW (optional)
  • Posterior corneal curvature (optional)
  • CCT (optional)
  • Lens factor
  • Pre-installed on the IOLMaster 700
  • Employs an algorithm that empirically accounts for posterior corneal astigmatism
  • May optionally utilize measured posterior corneal curvature
  • Uses the BUII formula to calculate ELP
  • No statistically significant difference in MPE between Abulafia-Koch, Barrett, and EVO 2.0 [2] [5][6]
  • Barrett and EVO had similar performance in terms of their astigmatism prediction accuracy [7]
Baylor Toric Nomogram [8] 2013
  • Anterior corneal astigmatism magnitude and axis
  • First toric IOL power calculation nomogram to account for posterior corneal astigmatism [8]
  • Improved median absolute error in predicted astigmatism amongst toric calculators[8]
  • Barrett Toric outperforms application of the Baylor nomogram[8]
EVO 2.0 Toric 2020
  • AL
  • K
  • ACD
  • LT (optional)
  • CCT (optional)
  • A-constant
  • Toric model
  • Posterior corneal curvature (optional)
  • SIA (optional)
  • Pre-LVC manifest refraction
  • Post-LVC manifest refraction
  • Combines theoretical posterior corneal astigmatism and thick lens modeling
  • No statistically significant difference in MPE between Abulafia-Koch, Barrett, and EVO 2.0 [2] [5][6]
  • Barrett and EVO had similar performance in terms of their astigmatism prediction accuracy[7]
Holladay 2 Toric[9] 2019 ***Formula not publicly available
  • Utilizes a total SIA correction to account for factors that lead to differences between preoperative K and postoperative astigmatism[9]
  • SIA is described as a factor that leads to residual astigmatism post-surgery [10]
Intraoperative Aberrometry (IA) [11][12]
  • AKA Intraoperative Optical Refractive Biometry (ORA)
  • AKA Intraoperative Refractive Biometry
2005[12]
  • Purely optical principles
  • One multi-center, RCT found a higher proportion of eyes in the IA group compared to pre-operative biometry to have 0.5 D or less astigmatism (89.2% vs. 76.6%), and lower mean magnitude of residual astigmatism (0.29 ± 0.28 D vs. 0.36 ± 0.35 D)[13]
  • Requires additional equipment: 
    • ORA
  • Unclear if IA holds clear advantage over modern toric IOL formulas
Kane Toric 2020
  • AL
  • K
  • ACD
  • Gender
  • LT (optional)
  • CCT (optional)
  • SIA (optional)
  • A-constant
  • 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 [6]

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

Formula Name Year Variables Advantages Disadvantages
Adjusted Atlas 9000
Adjusted EffRP
ASCRS Post-LVC IOL Power Calculator[14] 2007
  • Easily averages the predictions of multiple formulas
  • One of the most accurate methods of IOL power calculation in eyes post-LVC
  • Allows entry of as little or as much information available to the surgeon
Barrett True-K 2015
  • AL
  • Measured K1
  • Measured K2
  • ACD
  • LT (optional)
  • WTW (optional)
  • Lens factor
  • May be used with or without historical data
  • Improved using historical data and measured posterior corneal power [15]
  • Pre-installed on IOLMaster 700, thereby reducing potential for transcription error [16]
  • When using extended depth-of-focus IOLs, Barrett True-K No History outperformed other post-refractive formulas [17]
  • Performs equivalently to multi-formula approach in post-refractive eyes [16]
Clinical History Method (CHM)
  • Require pre-LVC keratometry and manifest refraction
  • Less accurate than methods requiring less information
Corneal Bypass Method
  • Require pre-LVC keratometry and manifest refraction
  • Less accurate than methods requiring less information
Feiz-Mannis
  • Require pre-LVC keratometry and manifest refraction
  • Less accurate than methods requiring less information
Haigis-L[18] 2008
  • AL
  • K
  • ACD
  • 3 constants:
    • a0
    • a1
      • Associated with measured ACD
    • a2
      • Associated with measured AL
  • 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[19])
  • Less accurate than Barrett True-K No History[20] [21]
Intraoperative Aberrometry[11][12]
  • AKA Intraoperative Optical Refractive Biometry (ORA)
  • AKA Intraoperative Refractive Biometry
  • AKA Intraoperative Autorefraction
2005[12]
  • Purely optical/refractive based
  • No AL required
  • No K required
  • Comparable to Barrett True-K in post-corneal refractive surgery and possibly better in post-hyperopic LVC [22]
  • Requires additional equipment:
    • ORA
Masket[23] 2006
  • Uses Holladay 1 formula for AL >23.0 mm[24]
  • Uses Hoffer Q formula for AL <23.0 mm[24]
  • Post-corneal refractive surgery power adjustment = [(laser-vision correction spherical equivalent, with vertex distance corrected) * (-0.326)] + (0.101)
  • Works for myopic and hyperopic LVC
  • Requires knowledge of the pre-LVC and post-LVC manifest refraction [23]
OCT (RTVue)[25] 2010
  • AL
  • ACD
  • CCT
  • Net Corneal Power
  • Posterior Corneal Power
  • Historical data not required
  • Requires special equipment:
    • Optovue RTVue
OKULIX[26] (Ray Tracing) 2002
  • AL
  • K
  • ACD
  • CCT
  • IOL design parameters
  • Can be used in post-LVC eyes, if corneal topographies available[27]
  • 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[28] 2015 ***Formula not publicly available
  • Historical data not required
  • Requires special equipment:
    • Oculus Pentacam
Schuster/Schanzlin-Thomas-Purcell (SToP)[29] 2016
  • AL
  • Ratio of posterior-to-anterior corneal radius
  • Anterior corneal radius
  • A-constant
  • Historical data not required
  • Requires specific equipment:
    • Scheimpflug imaging (Pentacam HR)
    • PCI-based optic biometer (IOLMaster)
Shammas[30] 2003 ***Formula not publicly available
  • Historical data not required
  • May be more accurate in long eyes (i.e. AL ≥ 30 mm) [31]
  • Significantly impacted by extreme ACDs [32]
Wang-Koch-Maloney[33] 2004

Table 1: Spherical IOL Power Formulas

Formula Name Year Formula Classification Variables Advantages Disadvantages
Barrett Universal (BU)[34][35] Version I: 1993[35]

Version II: 2010

Vergence
  • AL
  • K
  • ACD
  • LT (optional)
  • WTW (optional)

***Formula not publicly available

  • More accurate in long eyes [36]
  • More accurate in normal ranges AL:
    • Including implantaion of Panoptix IOL in normal ALs of 22.5mm-26mm [37]
    • Including implantation of Acrysof IQ SN60WF IOL in AL >22.0mm[38]
    • Including implantation of trifocal hydrophilic IOL [39]
  • Best in eyes with mild-moderate keratoconus[40] or K > 40 [41]
  • Easily accessible for free online
  • May be less accurate in short eyes (i.e. AL ≤22.0mm [42] or requiring implantation of a lens power ≥30D[43])
    • However, BU-II can still provide excellent refractive outcomes with AL <22.5mm[41] or AL 20.8mm-22.0mm[44]
  • Inaccessible without internet access or access to the formula programmed into the Lenstar LS900®
  • May be limited in pediatric populations[45]
EVO 2.0

2019

Vergence
  • AL
  • K
  • ACD
  • LT (optional)
  • CCT (optional)
  • More accurate in long eyes (26mm≤AL<28mm)[46]
  • Accounts for the optical dimensions of the eye and can handle different IOL geometry and powers
  • No inclusion of age, gender, or WTW as variables factored into calculations
Haigis 2004 Vergence
  • AL
  • K
  • ACD
  • 3 constants:
    • a0
    • a1
      • Associated with measured ACD
    • a2
      • Associated with measured AL
  • More accurate in short eyes (AL<22mm) [47]
  • More accurate for stage III keratoconus eyes [40]
  • Less accurate in long eyes:
    • Resulting hyperopic outcomes in long eyes using Haigis alone, which can be addressed using Haigis with Wang-Koch adjustment[48][49]
  • Less accurate in eyes with extreme LT values[41]
    • 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)[50]
Hill-RBF Version 2: 2018

Version 3: 2020

Artificial Intelligence
  • AL
  • K
  • ACD
  • LT (optional)
  • WTW (optional)
  • CCT (optional)
  • Continues to improve prediction accuracy as more data analyzed
  • May outperform BU-II [51][52]
  • 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)[50]
Hoffer Q[53] 1993 Vergence
  • AL
  • K
  • pACD
  • More accurate in short eyes:
    • Including implantation of Sofport AO and Akreos Fit IOLs in eyes with 20.00mm ≥ AL ≤ 20.09mm[54]
    • Including implantaion of Panoptix IOL in eyes with AL ≤22.5mm [55]
  • No use of ACD measurement, so theoretically less reliable in anatomically abnormal anterior segments
Hoffer QST 2021 Artificial Intelligence
  • AL
  • K
  • ACD
  • pACD
  • Post-operative refractive target
  • More accurate than Hoffer Q:
    • Including un-operated short eyes and un-operated long eyes [56]
  • Paucity of published evidence currently available
Holladay 1[57] 1988 Vergence
  • AL
  • K
  • Surgeon factor
  • More accurate for short eyes[54][58]:
    • Including implantaion of Panoptix IOL in AL ≤22.5mm [55]
  • 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[48][49]
  • No use of ACD measurement, so theoretically less reliable in anatomically abnormal anterior segments
Holladay 2 1995 Vergence
  • AL
  • K
  • ACD
  • LT
  • WTW
  • CCT
  • Age
  • May be more accurate in pediatric populations[45]
  • 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 2 with Wang-Koch adjustment[59]
Intraoperative Aberrometry (IA) [11][12]
  • AKA Intraoperative Optical Refractive Biometry (ORA)
  • AKA Intraoperative Refractive Biometry
2005 [12]
  • Not significantly different from the best preoperative biometry-based methods available for IOL power selection in short eyes [60]
Kane 2017 Blended (Vergence, Regression, and Artificial Intelligence-based)
  • AL
  • K
  • ACD
  • LT (optional)
  • CCT (optional)
  • Gender
  • Accurate in short eyes [39][42]
  • Accurate in long eyes (i.e. AL ≥26mm) [46]
  • Continues to improve prediction accuracy as more data analyzed
  • Accurate in extreme ACD (e.g. ≤3.0mm)[50]
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.)
  • Continues to improve prediction accuracy as more data analyzed
OKULIX[26] 2002 Ray-tracing
  • AL
  • K
  • ACD
  • CCT
  • IOL design parameters
  • Provides geometrical "most probable" IOL position (i.e. no estimation of ELP)[27]
  • Can be used in post-LASIK eyes, if corneal topographies available[27]
  • Calculating sum-of-segments AL is difficult in most clinical settings because vitreous thickness is not available to calculate in many optical biometers[61]
  • Less accurate in extremely short and long AL[26]
Olsen-C[62][63] 2014 Ray-tracing
  • AL (optional)
  • K (optional)
  • ACD
  • LT
  • Requires purchase of PhacoOptics® – IOL Power Calculation Software
SRK/T[64] 1990 Vergence-based
  • AL
  • K
  • A-constant
  • Accurate is eyes with normal axial lengths and mean keratometry values
  • More 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
  • Less accurate in long eyes than modern vergence-based formulas (i.e. BU-II, EVO, Hill-RBF, Kane) [46]
    • 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[48][49]
    • Including implantation of trifocal IOL in highly myopic Chinese patients [17]
  • Assumes normal ACD
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)
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
LT lens thickness
LVC laser vision correction
mm millimeter
OCT optic coherence tomography
OLCR optical low coherence reflectometry
ORA Optiwave Refractive Analysis
PCI partial coherence interferometry
pACD personalized anterior chamber depth
RCT randomized control trial
RBF radial basis function
SIA surgically induced astigmatism
SRK/T Sanders-Retzlaff-Kraff theoretical
WTR with-the-rule (corneal astigmatism)
WTW white-to-white corneal diameter distance
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