J EMMETROPIA VOLUME 2 NUMBER 2 | << BACK |

UPDATE/REVIEW

Intraocular lens power calculation after myopic excimer
laser surgery with no previous data

Juan Carlos Mesa-Gutiérrez, MD, PhD, FEBO; Antonio Rouras-López, MD;
Isabel Cabiró-Badimón, MD; Vicente Amías-Lamana, MD; José Porta-Monnet, MD;
Laura Solanas-García, Opt.

ABSTRACT

How many ways are there to calculate intraocular lens (IOL) power in eyes
that have myopic laser in situ keratomileusis (LASIK)? The list is long, and growing. As is
always the case when there are several solutions to a problem, none is perfect.
In this review, we describe the most reliable methods in the worst scenario: no data prior to
LASIK available.When no preoperative corneal power and refractive change are available the
lowest mean absolute error is achieved with the methods of Masket, Seitz/Speicher/Savini,
Shammas, and Camellin/Calossi. When preoperative corneal power is unknown but the surgically
induced refractive change is known the lowest mean absolute error is achieved with
the Masket method followed by the the Savini method, Speicher/Seitz method modified by
Savini, and Shammas no-history method.
Ideally, it would be optimal to have a spreadsheet that allows the clinician to insert all values
available. The various formulas would then be calculated automatically. When faced
with a range of values for the IOL power, you'd better look for values that are consistent
with at least one other reading. Values that select higher IOL powers are preferable, leaving
the patient slightly myopic rather than hyperopic.
Resolution of this problem will require a method for accurately measuring posterior
corneal power or a technique for adjusting IOL power after implantation. Until then, surgeons
are faced with performing multiple calculations to ''guesstimate'' the correct IOL for
patients who, by their original decision to have LASIK, have demonstrated that they have
above-average refractive demands.

KEYWORDS:
Intraocular lens; refractive surgery; corneal refractive power; cataract surgery.

(J Emmetropia 2011; 2: 97-102 ©2011 SECOIR - Sociedad Española de Cirugía Ocular Implanto-Refractiva)

Hospital Esperit Sant, Barcelona, Spain.

Neither author has a financial or proprietary interest in any material
or method mentioned.

Corresponding author: Juan Carlos Mesa-Gutierrez. Servicio de
Oftalmología. Hospital Esperit Sant. Avda Mossèn Pons i Rabadà,
s/n. 08923 Santa Coloma de Gramenet, Barcelona, Spain. Tel: +34
93 3864241. E-mail: juancarlosmesa@excite.co.uk

INTRODUCTION

Intraocular power calculation after keratorefractive
surgery has been a major challenge for the ophthalmic
community and has generated numerous scholarly
works and efforts trying to optimize current formulas
and tailor new methods to better predict the correct
intraocular lens (IOL) power^{1-8}. Aramberri's work on
the double-K adjustment of third-generation IOL formulas
significantly improved the hyperopic results
stemming from inaccurate estimation of the effective
lens position by those formulas^{9}.

IOL power calculation can lead to unexpected refractive
outcomes for 2 primary reasons. The first is that the
surgically induced corneal power change is underestimated
because the standard keratometric refractive index
(usually 1.3375) is not valid once the laser modifies the
anterior to posterior corneal curvature ratio^{10-13}. The second
reason is that the IOL position is erroneously predicted
by third-generation theoretical formulas (eg,
Hoffer Q, Holladay 1, SRK/T) that derive the prediction
from the corneal curvature^{13-17}. A third reason may be partially
responsible for the inaccuracy of IOL power calculation
for eyes with a small optical zone and large correction;
in this case, the difference between the paracentral
corneal area (where keratometry [K] and simulated K
readings are taken) and the central cornea area (where the
visual axis passes) can be clinically relevant^{11,18-20}.

When no previous data are avaiable the calculations are more misleading as no double-K adjustment can be done. Various formulas have been described, and surgeons can now choose from many methods. This can easily generate confusion rather than accuracy. The aim of the present study was to provide with various methods of calculating IOL power in patients with no pre- LASIK data available. We address two possible scenarios with no preoperative corneal power known.

When neither preoperative corneal power nor refractive
change are available the lowest mean absolute error
is achieved with the methods of Masket, Seitz/
Speicher/Savini, Shammas, and Camellin/Calossi.
When preoperative corneal power is unknown but the
surgically induced refractive change is known the lowest
mean absolute error is achieved with the Masket method
followed by the the Savini method, Speicher/Seitz
method modified by Savini, and Shammas no-history
method. Good results can also be obtained with the
Awwad and Camellin/Calossi methods when the calculated
corneal power is entered into the double-K
Holladay 1 formula instead of the double-K SRK/T^{21}.

1. Preoperative corneal power and refractive change unknown

According to a recent paper these are the most reliable
methods^{21}:

KShammas = 1,14 x K - 6.8.

The main advantage of this method is that the corrected
corneal power is used in the Shammas post-LASIK
(Shammas-PL) formula and in this formula the effective
lens postion (ELP) does not vary with the corneal curvature,
which has been altered by the LASIK procedure^{22}.

The method of separately considering the anterior
corneal curvature and posterior corneal curvature, first
described by Seitz and Langenbucher and later
reviewed by Speicher, could be considered the most
accurate, at least when coupled with the double-K
SRK/T formula^{2,23}. If the preoperative corneal power is
unknown, the Seitz/Speicher method can be modified
according to Savini et al.,who suggest using a mean
value of -4.98 D for posterior corneal curvature^{21,24}.
The Seitz/Speicher/Savini method:

K = simulated K x 1.114 - 4.98,

is similar to other methods like the one proposed by
Maloney^{25}:

K = central corneal power x 1.114 - 4.9,
and the modified version developed by Wang^{4}:

K = central corneal power x 1.114 - 6.1,
equation 6 of Awwad^{11,26}.

SimKadj no history = 1.114 x SimK - 6.062
and, to a lesser extent, the Shammas et al.no-history
method^{22}:

K Shammas = simulated K x 1.14 - 6.8.

Ho et al.found that the Seitz/Speicher method modified
according to Savini et al. is highly accurate^{27,28}.
Obviously, this method (developed for eyes for which
the preoperative corneal power is not known) must be
used in conjunction with double-K formulas, which
require entry of the preoperative corneal power. There
are 3 possibilities to solve this contradiction: (1) calculate
the preoperative corneal power by adding the
refractive change to the postoperative corneal power (2),
use a mean value such as 43.13 or (3) estimate the effective
lens position (ELP), as suggested by Ho^{27-29}. The
good results obtained with the Seitz/Speicher method
(with or without the Savini modification) could be
related to its total independence of the surgically
induced refractive change (a likely source of errors)^{27}.

Refraction with Rosa method (Rrosa) = R x (0.0276
AL + 0.3635)

K(Rrosa) = 337.5/Rrosa

AL = Axial length; R=k/337.5

Another method proposed by Rosa is as follows^{30}:

KRosa = (1.3375-1)/[(K x RCF)/1000].

RCF: Rosa Correction Factor based on axial length

(mm):
22 - <23: 1.01

23 - <24: 1.05

24 - <25: 1.04

25 - <26: 1.06

26 - <27: 1.09

27 - <28: 1.12

28 - <29: 1.15

29:1.22

K = [(-0.0006 x AL2 + 0.0213 x AL + 1.1572] -1) /
(Kr/1000).

AL: Axial lengh.

Kr: Keratometry (radius of curvature in mm).

Rosa and Ferrara method may easily lead to postoperative
myopia^{32}.

The formula takes into account anterior and posterior
corneal radii and pachymetry (Pentacam, Oculus) and does
not require pre-keratorefractive surgery information^{33}.

Input Variables

rF: Front corneal radius (mm)

rB: Back corneal radius (mm)

CCT: central corneal thickness (microns)

Formula

n.air =1

n.vc = 1.3265

n.CCT = n.vc + (CCT x 0.000022)

K.conv = 337.5/rF

n.adj:

if K.conv <37,5 n.adj = n.CCT + 0.017

if K.conv <41,44 n.adj = n.CCT

if K.conv <45 n.adj = n.CCT - 0.015

ELSE;n adj EQUALS n CCT

n.acq = 1.336

d = d.cct /n.vc

d.cct = CCT /1000000

Fant = 1/rF x (n.vc - n.air)

Fpost = 1/rB (n.acq - n.vc)

Using the BESSt formula, 46% of eyes were

within +/-0.50 D of the intended refraction and

100% were within +/-1.00 D.

Output

KBESSt (corneal power after keratorefractive surgery,
D) =

{[1/rF x (n.adj - n.air)] + [1/rB x (n.acq - n.adj)] -

[d x 1/r x (n.adj - n.air) x 1/rB x (n.acq - n.adj)]} x

1000.

BESSt formula has been replaced by the BESSt2 algorithm. Corneal power is still estimated with gaussian optic formula as with BESST1 but some improvements can be found:

- prediction of preoperative anterior radius from postoperative posterior radius measurements.

- automatic application of double-K adjustment to the the predicted preoperative anterior radius.

- It uses a modified 3rd generation formula for IOL power calculation, preventing the cusp phenomenon which may happen using SRK/T formula.

- Automatic adjustments for extreme axial lengths.

- Contribution of corneal wavefront (espherical aberation) from Pentacam.

- It has two separate algoriths: one for myopia and other one for hyperopia.

According to his author BESSt2 is more accurate
than BESSt1 in hyperopia and more accurate than
Haigis-L in myopia^{34,35}.

In the absence of information about the change (D)
in spherical equivalent (ΔSE), a regression based solely
on average corneal power in the central 3.0 mm area
(ACCP3mm) should be used^{26}:

ACCPadj no history = 1.151 x ACCP3mm - 6.799 In the absence of topographic data a regression based on SimK is to be used:

SimKadj no history = 1.114 x SimK - 6.062

In 2004, Sónego-Krone et al reported that the
refractive change at the corneal plane after myopic
LASIK had a difference of -0.08+/-0.53 D with the
corneal power change determined by quantitative area
topography in a 4-mm-diameter central zone of
Orbscan II total-mean postoperative maps^{36}.

Quantitative area topography is distinct from quantitative
point topography, which assesses the average of
only two single steeper and flatter values. The total-mean
power maps represent the spherical equivalent refraction
of both corneal curvatures with regard to the corneal
thickness and are comparable to the equivalent power of
the cornea assessed by the thick lens formula. The totaloptical
power maps represent the ray tracing of light
through the whole cornea. The advantage of this method
is that the final total corneal powers to be used in IOL
calculation may be obtained directly from the topographic
maps, as measured after the previous corneal refractive
surgery without depending on regression formulas, artificial
refraction indices, contact lens over-refraction, aphakic
intraoperative refraction, previous refractive or topographic
data, algorithms, or correction factors^{36,37}.

It has been applied in a multicenter study using the
total mean power (equivalent power) and the total
optical power^{38,39}.Total optical power maps by the
Orbscan Topography System appear to be relatively
accurate in detecting the changes in corneal power
measured by refraction after LASIK. The correlation is
highest when averaging within the central 4.0 mm
zone. The corneal power change derived from axial
power maps correlates less well than that derived from
the TOP maps, as expected. Total optical power maps
appear to provide an accurate measure of corneal power
change in LASIK^{37-39}.

This same method has been applied with success
using the Galilei's total corneal power (TCP) by ray
tracing from a central zone of 0 to 4 mm diameter.
Similar to the Orbscan II total-optical power, the Galilei
uses a 4-mm diameter central zone for the TCP derived
from ray tracing. Galilei TCP represents the average
total corneal power fot the central 4 mm diameter of the
cornea. This TCP is calculated using the ray tracing
method, which takes the actual refractive indices of the
cornea into account. The post-LASIK corneal power is
estimated using the following formula^{40,41}:

Post-LASIK adjusted corneal power = 1.057 x TCP - 1.8348

2. Preoperative corneal power unknown and refractive change knownThe equation was determined to be as follows: IOL Power Adjustment = LSE x (-0.0.326) + 0.101 where LSE is the total prior laser treatment, adjusted for vertex distance, in spherical equivalent (SE).

Clinical example is as follows:

Previously myopic eye:

- SRK/T formula suggests 16.0 D for emmetropia after cataract surgery

- Prior laser correction (SE) = - 6.0 D

- Adjustment calculation: -6.0 D x (-0.326) + 0.101 = + 2.057 D

- IOL power adjusted by adding +2 D to the original + 16 D = +18 D for emmetropia

The Masket method had a great advantage in that it
omits the double-K step required by the Savini and
Seitz/Speicher/Savini methods. The latter methods can be
significantly influenced by the choice of the preoperative
corneal power to be entered into the double-K formulas.
In contrast, the Masket method (like the Shammas nohistory
method) does not have this drawback^{5}.

Ksavini = [(1.338+ 0.0009856 x ΔSEsp) -1] / Kr/1000)

ΔSEsp: Change in spherical equivalent at spectacle plane

Kr: Keratomety (radius of curvature in mm)^{20,21,24}.

See above.

KCamellin = [(1.3319 + 0.00113 x ΔSEsp) - 1] / (Kr/1000).

ΔSEsp: Change in SE at spectacle plane.

Kr: Keratometry (radius of curvature in mm).

When entered into the double-K SRK/T formula,
the corneal power calculated with the Camellin/Calossi
method results in a positive arithmetic error in IOL
power prediction, with a subsequent myopic outcome.
The suboptimal results are probably due to the fact
that this method was developed to be used with the
Camellin/ Calossi formula for IOL power calculation,
which is a modified Binkhorst II formula, and not with
the double-K SRK/T formula. The Camellin/ Calossi
formula calculates the ELP from the preoperative anterior
chamber depth. Considerably better results can be
obtained by entering the calculated corneal power into
the double-K Holladay 1 formula^{8,42}.

See above.

Two variables, ACCP3mm and ΔSE, were shown to
be vital and sufficient for accurate refractive power prediction.
The multiple regression based on these 2 independent
variables successfully predicted corneal refractive
power^{26}:

ACCPadj = ACCP3mm - 0.16 x (SEpostLASIK - SEpreLASIK)

adjusting for the fact that the measured ACCP3mm overestimates the true value by about 0.16 D for every diopter of myopic laser correction.

In the absence of topographic data, SimK and ΔSE
are to be used^{26}

SimKadj = SimK- 0.23 x (SEpostLASIK - SEpreLASIK).

as the measured SimK overestimates the true value by about 0.23 D for every diopter of laser correction26.

K = SimK - (0.15 x ΔSE) - 0.05

This method requires knowledge of the refractive
change from the surgery and the postoperative Sim-K
from the topography unit^{34}.

They also offered a second method to calculate true
corneal power by substituting 0.15 by 0.19^{43,44}.

K = Kflat + 0.25 x ΔSE

This method requires knowledge of the refractive
change from the surgery and the postoperative flattest
K reading measured now (Kflat)^{35}.

Requires knowing the surgically induced refractive
change at the corneal plane (ΔSEcp) and the average
radius of curvature of the cornea now (Kr)^{45}:

KJarade = [(1.3375 + 0.0014 x ΔSEcp) - 1]/(Kr/1000)

KHaigis = -5.1625 x Kr + 82.2603 - 0.35

This method requires only the postoperative K
reading form the Zeiss IOLMaster in radius of curvature
(or converted to diopters using the index of refraction
setting in the IOLMaster)^{46}.

Central power = (central topographic power x [376/337.5]) - 4.9

Koch and Wang obtained the best results using the
Maloney method using -6.1 instead of -4.9^{4}.

They also offered a second method to calculate true
corneal power if ΔSE is known^{44}. The formula is:
K = EffRp - (0.19 .x ΔSE)

K = 1.1141 x TK - 6.1

Koch and Wang obtained the best results using the Maloney method (discussed earlier) but only after increasing the constant from 5.5 to 6.1. They also offered a second method to calculate true corneal power if ΔSE is known (38). The formula is:

K = EffRp - (0.19 .x ΔSE)

Where EffRp is the effective refractive power obtained from topography.

This method utilizes the change in refractive error
to offset the calculated target IOL power^{47}.

P = PTARG - 0.595 x ΔSEcp + 0.231

P = IOL Power

PTARG = the target IOL power to produce the postoperative desired refractive error.

**FINAL ADVICE.**

The historical K method, although theoretically
considered the gold standard, is misleading in practice
because myopic or hyperopic errors in post-LASIK
refractions can easily translate into errors of the same
magnitude in the final post-cataract surgery refraction.
In addition, early occult cataractous stage can produce
myopic shift and potentially lead to a falsely overminused
post-LASIK refraction result, introducing an
error in corneal power estimation. We recommend
against using the historical K method^{48}.

This method is based on the fact that the final
change in refractive error the eye obtains from surgery
was due only to a change in the effective corneal power.
If this refractive change the patient experienced is algebraically
added to the presurgical corneal power, we
will obtain the effective corneal power the eye has now.
Obviously this requires knowledge of the K reading
and refractive error prior to refractive surgery^{48}.

K = KPRE + RPRE - RPO or [K = KPRE + RCC]

KPRE = refractive surgery preoperative corneal power

RPO = refractive surgery PO refractive error (spherical equivalent)

RPRE = refractive surgery preoperative refractive error (spherical equivalent)

RCC = surgical change in refractive error (SE) vertexed to Corneal Plane

Our concerns about the clinical history method are in
good agreement with several previous studies in which the
clinical history method obtained less accurate results than
other methods, even when the calculated corneal power
was entered into double-K formulas. Hence, we recommend
extreme caution when using the corneal power generated
by the clinical history method in any double-K formula
and agree with Awwad that this method should no
longer be considered the gold standard for IOL power calculation
after refractive surgery^{48,51}.

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