Chapter 4

Advanced Intraocular
Lens Power Calculations 4
John P. Fang, Warren Hill, Li Wang,
Victor Chang, Douglas D. Koch

Core Messages 4.1 Introduction

■ Accurate IOL power calculations are a Accurate intraocular lens (IOL) power calcula-
crucial element for meeting the ever in- tions are a crucial element for meeting the ever
creasing expectations of patients under- increasing expectations of patients undergoing
going cataract surgery. cataract surgery. As a direct result of techno-
■ Although ultrasound biometry is a well- logical advances, both our patients and our peers
established method for measuring axial have come to view cataract surgery as not only
length optical coherence biometry has a rehabilitative procedure, but a refractive pro-
been shown to be significantly more ac- cedure as well. The precision of IOL power cal-
curate and reproducible. culations depends on more than just accurate
■ The power adjustment necessary be- biometry, or the correct formula, but in reality
tween the capsular bag and the ciliary is a collection of interconnected nuances. If one
sulcus will depend on the power of the item is inaccurate, the final outcome will be less
intraocular lens. than optimal.
■ When the patient has undergone prior
corneal refractive surgery, or corneal
transplantation, standard keratometric
and topographic values cannot be used.
4.2 Axial Length Measurement
■ Several methods have been proposed to By A-scan biometry, errors in axial length mea-
improve the accuracy of IOL power cal- surement account for 54% of IOL power error
culation in eyes following corneal refrac- when using two-variable formulas [23]. Be-
tive surgery; these can be divided into cause of this, much research has been dedicated
those that require preoperative data and to achieving more accurate and reproducible
those that do not. axial lengths. Although ultrasound biometry is
■ Because it is impossible to accurately a well-established method for measuring ocular
predict the postoperative central power distances, optical coherence biometry has been
of the donor graft, there is presently shown to be significantly more accurate and re-
no reliable method for calculating IOL producible and is rapidly becoming the preva-
power for eyes undergoing combined lent methodology for the measurement of axial
corneal transplantation and cataract re- length.
moval with intraocular lens implanta-
tion.
■ The presence of silicone oil in the eye
4.2.1 Ultrasound
complicates intraocular lens power mea-
surements and calculations. Axial length has traditionally been measured
using ultrasound biometry. When sound waves
encounter an interface of differing densities,
a fraction of the signal echoes back. Greater dif-
32 Advanced Intraocular Lens Power Calculations

ferences in density produce a greater echo. By 1. Probe tip/cornea,

measuring the time required for a portion of the 2. Aqueous fluid/anterior lens,
sound beam to return to the ultrasound probe, 3. Posterior lens/vitreous,
the distance can be calculated (d = v × t)/2. Be- 4. Vitreous/retina,
cause the human eye is composed of structures 5. Retina/sclera,
of varying densities (cornea, aqueous, lens, vitre- 6. Sclera/orbital fat.
ous, retina, choroid, scleral, and orbital fat), the
axial length of each structure can be indirectly The axial length is the summation of the an-
4 measured using ultrasound. Clinically, applana- terior chamber depth, the lens thickness, and the
tion and immersion techniques have been most vitreous cavity.
commonly used. The y-axis shows peaks (known as spikes) rep-
resenting the magnitude of each echo returned to
the ultrasound probe. The magnitude or height
of each peak depends on two factors. The first is
4.2.1.1 Applanation Technique the difference in densities at the acoustic inter-
With the applanation technique, the ultrasound face; greater differences produce higher echoes.
probe is placed in direct contact with the cornea. The second is the angle of incidence at this inter-
After the sound waves exit the transducer, they face. The height of a spike will be at its maximum
encounter each acoustic interface within the eye when the ultrasound beam is perpendicular to
and produce a series of echoes that are received the acoustic interface it strikes. The height of
by the probe. Based on the timing of the echo and each spike is a good way to judge axiality and,
the assumed speed of the sound wave through hence, alignment of the echogram.
the various structures of the eye, the biometer Because the applanation technique requires
software is able to construct a corresponding direct contact with the cornea, compression will
echogram. In the phakic eye, the echogram has typically cause the axial length to be falsely short-
six peaks (Fig. 4.1), each representing the inter- ened. During applanation biometry, the com-
faces of: pression of the cornea has been shown to range

Fig. 4.1 Phakic axial length mea-

surement using the applanation
technique. a Initial spike (probe
tip and cornea), b anterior lens
capsule, c posterior lens capsule,
d retina, e sclera, f orbital fat
 4.2 Axial Length Measurement 33

from 0.14 to 0.33 mm [24, 29, 30]. At normal Although the immersion technique has been
axial lengths, compression by 0.1 mm results in shown to be more reproducible than the applana-
a postoperative refractive error toward myopia of tion technique, both require mindfulness of the
roughly 0.25 D. Additionally, this method of ul- properties of ultrasound. Axial length is calcu-
trasound biometry is highly operator-dependent. lated from the measured time and the assumed
Because of the extent of the error produced by average speed that sound waves travel through
direct corneal contact, applanation biometry has the eye. Because the speed of ultrasound varies
given way to noncontact methods, which have in different media, the operator must account
been shown to be more reproducible. for prior surgical procedures involving the eye
such as IOL placement, aphakia, or the presence
of silicone oil in the vitreous cavity (Table 4.1).
Length correction can be performed simply us-
4.2.1.2 Immersion Technique ing the following formula:
The currently preferred A-scan method is the
immersion technique, which, if properly per- True length = [corrected velocity/measured ve-
formed, eliminates compression of the globe. locity] × measured length
Although the principles of immersion biometry
are the same as with applanation biometry, the However, using a single velocity for axial
technique is slightly different. The patient lies su- length measurements in eyes with prior sur-
pine with a clear plastic scleral shell placed over gery is much less accurate than correcting each
the cornea and between the eyelids. The shell segment of the eye individually and adding to-
is filled with coupling fluid through which the gether the respective corrected length measure-
probe emits sound waves. Unlike the applanation ments. For example, in an eye with silicone oil,
echogram, the immersion technique produces an the anterior chamber depth would be measured
additional spike corresponding to the probe tip at a velocity of 1,532 m/s, the crystalline lens
(Fig. 4.2). This spike is produced from the tip of thickness at 1,641 m/s, and the vitreous cavity
the probe within the coupling fluid. at either 980 m/s or 1,040 m/s depending on the

Fig. 4.2 Phakic axial length mea-

surements using the immersion
technique. a Probe tip—echo
from tip of probe, has now
moved away from the cornea
and becomes visible; b cornea—
double-peaked echo will show
both the anterior and posterior
surfaces; c anterior lens capsule;
d posterior lens capsule; e retina;
f sclera; g orbital fat
34 Advanced Intraocular Lens Power Calculations

Table 4.1 Average velocities under various conditions By adding the CALF to or subtracting it from
for average eye length [16]. PMMA: polymethyl meth- the measured axial length, the true axial length
acrylate is obtained.
Another source of axial length error is that
Condition Velocity (m/s) the ultrasound beam has a larger diameter than
Phakic eye 1,555 the fovea. If most of the beam reflects off a raised
parafoveal area and not the fovea itself, this will
Aphakic eye 1,532 result in an erroneously short axial length read-
4 PMMA pseudophakic 1,556 ing. The parafoveal area may be 0.10–0.16 mm
Silicone pseudophakic 1,476 thicker than the fovea.
In addition to compression and beam width,
Acrylic pseudophakic 1,549
an off-axis reading may also result in a falsely
Phakic silicone oil 1,139 shortened axial length. As mentioned before, the
Aphakic silicone oil 1,052 probe should be positioned so that the magni-
tude of the peaks is greatest. If the last two spikes
Phakic gas 534
are not present (sclera and orbital fat), the beam
may be directed to the optic nerve instead of the
fovea.
density of the silicone oil (1,000 centistokes vs. In the setting of high to extreme axial myopia,
5,000 cSt). The three corrected lengths are then the presence of a posterior staphyloma should be
added together to obtain the true axial length. considered, especially if there is difficulty obtain-
Sect. 4.8 describes in greater detail IOL calcula- ing a distinct retinal spike during A-scan ultraso-
tions in eyes with silicone oil. nography. The incidence of posterior staphyloma
For pseudophakia, using a single instrument increases with increasing axial length, and it is
setting may also lead to significant errors be- likely that nearly all eyes with pathologic myopia
cause IOL implants vary in sound velocity and have some form of posterior staphyloma. Staphy-
thickness (Table 4.2). By using an IOL material- lomata can have a major impact on axial length
specific conversion factor (CF), a corrected axial measurements, as the most posterior portion of
length factor (CALF) can be determined using: the globe (the anatomic axial length) may not
correspond with the center of the macula (the
CF = 1 – (VE/VIOL) refractive axial length). When the fovea is situ-
CALF = CF × T ated on the sloping wall of the staphyloma, it may
where VE = sound velocity being used (such as only be possible to display a high-quality retinal
1,532 m/s), spike when the sound beam is directed eccentric
VIOL = sound velocity of the IOL material being to the fovea, toward the rounded bottom of the
measured, staphyloma. This will result in an erroneously
T = IOL central thickness. long axial length reading. Paradoxically, if the

Table 4.2 Velocities for indi-

PMMA 2,713 m/s (Alcon MC60BM)
vidual intraocular lens mate-
Acrylic 2,078 m/s (Alcon MA60BM) rials [13]. HEMA: hydroxy-
ethyl methylmethacrylate
First generation silicone 990 m/s (AMO SI25NB)
Second generation silicone 1,090 m/s (AMO SI40NB)
Another second generation silicone 1,049 m/s (Staar AQ2101V)
Hydrogel 2,000 m/s (B&L Hydroview)
HEMA 2,120 m/s (Memory lens)
Collamer 1,740 m/s (Staar CQ2005V)
 4.2 Axial Length Measurement 35

sound beam is correctly aligned with the refrac- Through noncontact means, the IOL Master
tive axis, measuring to the fovea will often result (Carl Zeiss Meditec, Jena, Germany) emits an
in a poor-quality retinal spike and inconsistent infrared laser beam that is reflected back to the
axial length measurements. instrument from the retinal pigment epithelium.
Holladay has described an immersion A/B- The patient is asked to fixate on an internal light
scan approach to axial length measurement in the source to ensure axiality with the fovea. When
setting of a posterior staphyloma [4, 33]. Using a the reflected light is received by the instrument,
horizontal axial B-scan, an immersion echogram the axial length is calculated using a modified
through the posterior fundus is obtained with the Michelson interferometer. There are several ad-
cornea and lens echoes centered while simulta- vantages of optical coherence biometry:
neously displaying void of the optic nerve. The A- 1. Unlike A-scan biometry, the optical coher-
scan vector is then adjusted to pass through the ence biometry can measure pseudophakic,
middle of the cornea as well as the middle of the aphakic, and phakic IOL eyes. It can also mea-
anterior and posterior lens echoes to assure that sure through silicone oil without the need for
the vector will intersect the retina in the region of use of the velocity cenversion equation.
the fovea. Alternatively, as described by Hoffer, if 2. Because optical coherence biometry uses
it is possible to visually identify the center of the a partially coherent light source of a much
macula with a direct ophthalmoscope, the cross shorter wavelength than ultrasound, axial
hair reticule can be used to measure the distance length can be more accurately obtained. Op-
from the center of the macula to the margin of tical coherence biometry has been shown to
the optic nerve head. The A-scan is then posi- reproducibly measure axial length with an ac-
tioned so that measured distance is through the curacy of 0.01 mm.
center of the cornea, the center of the lens, and 3. It permits accurate measurements when pos-
just temporal to the void of the optic nerve on terior staphylomata are present. Since the
simultaneous B-scan. patient fixates along the direction of the mea-
suring beam, the instrument is more likely to
display an accurate axial length to the center
of the macula.
Summary for the Clinician 4. The IOL Master also provides measurements
■ Because the applanation technique re- of corneal power and anterior chamber depth,
quires direct contact with the cornea, enabling the device to perform IOL calcula-
compression will typically cause the axial tions using newer generation formulas, such
length to be falsely shortened. as Haigis and Holladay 2.
■ The speed of ultrasound varies in differ-
ent media. To account for this, the op- The primary limitation of optical biometry is its
erator must alter ultrasound speed set- inability to measure through dense cataracts and
tings for eyes that are pseudophakic or other media opacities that obscure the macula;
aphakic or that contain silicone oil in the due to such opacities or fixation difficulties, ap-
vitreous cavity. proximately 10% of eyes cannot be accurately
■ In the setting of high to extreme axial measured using the IOL Master [21].
myopia, the presence of a posterior When both optical and noncontact ultra-
staphyloma should be considered. sound biometry are available, the authors rely on
the former unless an adequate measurement can-
not be obtained. Both the IOL Master and im-
mersion ultrasound biometry have been shown
to produce a postoperative refractive error close
4.2.2 Optical Coherence Biometry to targeted values. However, the IOL Master is
Introduced in 2000, optical coherence biom- faster and more operator and patient-friendly.
etry has proved to be an exceptionally accurate Though mostly operator-independent, some
and reliable method of measuring axial length. degree of interpretation is still necessary for op-
36 Advanced Intraocular Lens Power Calculations

timal refractive outcomes. During axial length

measurements it is important for the patient to
Summary for the Clinician
look directly at the small red fixation light. In this ■ Optical coherence biometry has proved
way, axial length measurements will be made to to be an exceptionally accurate and reli-
the center of the macula. For eyes with high to able method of measuring axial length.
extreme myopia and a posterior staphyloma, be- ■ The primary limitation of optical biom-
ing able to measure to the fovea is an enormous etry is its inability to measure through
advantage over conventional A-scan ultrasonog- dense cataracts and other media opaci-
4 raphy. The characteristics of an ideal axial length ties that obscure the macula.
display by optical coherence biometry are the fol-
lowing (Fig. 4.3):
1. Signal-to-noise ratio (SNR) greater than 2.0.
2. Tall, narrow primary maxima, with a thin,
well-centered termination.
4.3 Keratometry
3. At least one set of secondary maxima. How- Errors in corneal power measurement can be an
ever, if the ocular media is poor, secondary equally important source of IOL power calcula-
maxima may be lost within a noisy baseline tion error, as a 0.50 D error in keratometry will
and not displayed. result in a 0.50 D postoperative error at the spec-
4. At least 4 of the 20 measurements taken tacle plane. A variety of technologies are avail-
should be within 0.02 mm of one another and able, including manual keratometry, automated
show the characteristics of a good axial length keratometry, and corneal topography. These
display. devices measure the radius of curvature and
5. If given a choice between a high SNR and an provide the corneal power in the form of kera-
ideal axial length display with a lower SNR, tometric diopters using an assumed index of re-
the quality of the axial length display should fraction of 1.3375. The obtained values should be
always be the determining factor for measure- compared with the patient’s manifest refraction,
ment accuracy. looking for large inconsistencies in the magni-
tude or meridian of the astigmatism that should
prompt further evaluation of the accuracy of the
corneal readings.
Important sources of error are corneal scars
or dystrophies that create an irregular anterior
corneal surface. While these lesions can often be
seen with slit lamp biomicroscopy, their impact
on corneal power measurements can best be as-
sessed by examining keratometric or topographic
mires. The latter in particular give an excellent
qualitative estimate of corneal surface irregular-
ity (Fig. 4.4). In our experience, if the irregularity
is considered to be clinically important, we try
to correct it whenever feasible before proceeding
with cataract surgery. Examples would include
epithelial debridement in corneas with epithelial
basement disease, and superficial keratectomy in
eyes with Salzmann’s nodular degeneration.
When the patient has undergone prior cor-
neal refractive surgery, or corneal transplanta-
tion, standard keratometric and topographic
Fig. 4.3 An ideal axial length display by ocular coher- values cannot be used. This topic will be further
ence biometry in clear ocular media [12] discussed in Sect. 4.6.
 4.5 IOL Calculation Formulas 37

is empirically derived from linear regression

4.4 Anterior Chamber analysis of a large number of cases.
Depth Measurement The first IOL power formula was published by
A-scan biometers and the IOL Master calculate Fyodorov and Kolonko in 1967 and was based on
anterior chamber depth as the distance from the schematic eyes [7]. Subsequent formulas from
anterior surface of the cornea to the anterior sur- Colenbrander, Hoffer, and Binkhorst incorpo-
face of the crystalline lens. In some IOL calcu- rated ultrasound data [3, 5, 14]. In 1978, a regres-
lation formulas, the measured anterior chamber sion formula was developed by Gills, followed by
depth is used to aid in the prediction of the final Retzlaff, then Sanders and Kraff, based on analy-
postoperative position of the IOL (known as the sis of their previous IOL cases [8, 26, 28]. This
effective lens position, or the ELP). work was amalgamated in 1980 to yield the SRK I
formula [27]. All of these formulas depended on
a single constant for each IOL that represented
the predicted IOL position. In the 1980s, further
4.5 IOL Calculation Formulas refinement of IOL formulas occurred with the
There are two major types of IOL formulas. One incorporation of relationships between the posi-
is theoretical, derived from a mathematical con- tion of an IOL and the axial length as well as the
sideration of the optics of the eye, while the other central power of the cornea.

Fig. 4.4 Corneal surface irregularity shown on the Humphrey topographic map of an eye with epithelial base-
ment disease
38 Advanced Intraocular Lens Power Calculations

have perfectly normal anterior chamber anatomy

4.5.1 The Second and Third with normal anterior chamber depth. The error
Generation of IOL Formulas in this assumption accounts for the characteris-
The IOL constants in the second and third gen- tic limited axial length range of accuracy of each
eration of IOL formulas work by simply moving third generation two-variable formula. The Hol-
up or down the position of an IOL power pre- laday 1 formula, for example, works well for eyes
diction curve for the utilized formula. The shape of normal to moderately long axial lengths, while
of this power prediction curve is mostly fixed for the Hoffer Q has been reported to be better suited
4 each formula and, other than the lens constant, to normal and shorter axial lengths [15].
these formulas treat all IOLs the same and make
a number of broad assumptions for all eyes re-
gardless of individual differences.
For example, two hyperopic eyes with the
4.5.2 The Fourth Generation
same axial length and the same keratometry may
of IOL Formulas
require different IOL powers. This is due to two A recent exception to all of this is the Haigis for-
additional variables: of more importance, the ac- mula [9]. Rather than moving a fixed formula-
tual distance from the cornea that the IOL will specific IOL power prediction curve up or down,
sit in the pseudophakic state (i.e., ELP) and to the Haigis formula instead uses three constants
a lesser degree, the individual geometry of each (a0, a1, and a2) to set both the position and the
lens model. Commonly used lens constants do shape of a power prediction curve:
not take both of these variations into account.
These include: d = a0 + (a1 * ACD) + (a2 * AL)
SRK/T formula—uses an “A-constant,”
Holladay 1 formula—uses a “Surgeon Factor,” where d is the effective lens position, ACD is the
Hoffer Q formula—uses a “Pseudophakic An- measured anterior chamber depth of the eye (cor-
terior Chamber Depth” (pACD). neal vertex to the anterior lens capsule), and AL
These standard IOL constants are mostly in- is the axial length of the eye (the distance from
terchangeable—knowing one, it is possible to es- the cornea vertex to the vitreoretinal interface).
timate another. In this way, surgeons can move The a0 constant basically moves the power pre-
from one formula to another for the same intra- diction curve up, or down, in much the same way
ocular lens implant. However, the shape of the that the A-constant, Surgeon Factor, or pACD
power prediction curve generated by each for- does for the SRK/T, Holladay 1, and Hoffer Q
mula remains the same no matter which IOL is formulas. The a1 constant is tied to the measured
being used. anterior chamber depth, and the a2 constant is
Variations in keratometers, ultrasound ma- tied to the measured axial length. In this way,
chine settings, and surgical techniques (such as the value for d is determined by three constants,
the creation of the capsulorrhexis) can impact rather than a single number.
the refractive outcome as independent variables. The a0, a1, and a2 constants are derived by re-
“Personalizing” the lens constant for a given IOL gression analysis from a sample of at least 200
and formula can be used to make global adjust- cases and generate a surgeon and IOL-specific
ments for a variety of practice-specific variables. outcome for a wide range of axial lengths and
Popular third generation two-variable formu- anterior chamber depths. The resulting constants
las (SRK/T, Hoffer Q and Holladay 1) also as- more closely match actual observed results for
sume that the distance from the principal plane a specific surgeon and the individual geometry of
of the cornea to the thin lens equivalent of the an IOL implant. This means that a portion of the
IOL is, in part, related to the axial length. That is mathematics of the Haigis formula is individu-
to say, short eyes may have a shallower anterior ally adjusted for each surgeon/IOL combination.
chamber and long eyes may have a deeper ante- The Holladay 2 formula uses another inno-
rior chamber. In reality, this assumption may be vative approach, which is to use measurements
invalid. Short eyes and many long eyes typically of corneal power, corneal diameter, ACD, lens
 4.6 Determining IOL Power Following Corneal Refractive Surgery 39

thickness, refractive error, and axial length to fur- on the power of the capsular bag IOL (Table 4.3).
ther refine the ELP calculation. The Holladay 2 The important concept is that for stronger intra-
formula is based on previous observations from a ocular lenses, the reduction in power must be
35.000 patient data set and has been shown to be greater. For very low IOL powers, no reduction
advantageous in both long and short eyes. in IOL power is required. Table 4.3 will provide
good results for most, modern posterior cham-
ber IOLs.
Summary for the Clinician
■ The shape of the power prediction curve 4.6 Determining IOL Power
is mostly fixed for each second and third
generation formula.
Following Corneal
Refractive Surgery
■ Popular third generation two-variable
formulas may also assume that the dis- The true corneal power following corneal refrac-
tance from the corneal vertex to the thin tive surgery is difficult to obtain by any form of
lens equivalent of the IOL is, in part, re- direct measurement. This is because keratometry
lated to the axial length and/or central and topography measure the anterior corneal
corneal power. radius and convert it to total corneal power by
■ The fourth generation IOL power for- assuming a normal relationship between the
mulas address these issues. anterior and posterior corneal curvatures. How-
ever, unlike incisional corneal refractive surgery
for myopia, which flattens both the anterior and
the posterior corneal radius, ablative corneal re-
fractive surgery for myopia primarily alters an-
4.5.3 Capsular Bag to Ciliary Sulcus terior corneal curvature. Additionally, standard
IOL Power Conversion keratometry measures a paracentral region and
Intraocular lens power formulas typically calcu- assumes that this accurately reflects central cor-
late the power of the intraocular lens to be posi- neal power. For these reasons, keratometry and
tioned within the capsular bag. Occasionally, this simulated keratometry by topography typically
is not possible, as with an unanticipated intraop- under-estimate central corneal power following
erative tear in the posterior lens capsule. In order ablative corneal surgery for myopia and overes-
to achieve a similar postoperative refractive re- timate it for corneas that have undergone hyper-
sult with an IOL placed at the plane of the cili- opic ablation.
ary sulcus, a reduction in IOL power is typically There is a second and less commonly recog-
required. nized source of unanticipated postoperative re-
The power adjustment necessary between the fractive error. As a general rule, IOL power cal-
capsular bag and the ciliary sulcus will depend culations following all forms of corneal refractive
surgery should not be run using an uncorrected
two-variable, third-generation formula because
Table 4.3 Intraocular lens (IOL) power correction for they assume that the effective lens position is, in
unanticipated sulcus implantation [13] part, related to central corneal power. By using
axial length and keratometric corneal power to
Capsular bag Ciliary sulcus power estimate the postoperative location of the IOL,
IOL power adjustment or the ELP, the artifact of very flat Ks follow-
ing myopic corneal refractive surgery will cause
+35.00 D to +27.50 D –1.50 D
these formulas to assume a falsely shallow post-
+27.00 D to +17.50 D –1.00 D operative ELP and recommend less IOL power
+17.00 D to +9.50 D –0.50 D than required. To avoid this potential pitfall, the
double K feature of the Holladay 2 formula al-
+9.00 D to -5.00 D No change
lows direct entry of two corneal power values by
40 Advanced Intraocular Lens Power Calculations

checking the box “Previous RK, PRK…”; if the IOLpre + (ΔD / 0.7) = IOLpost
corneal power value before refractive surgery is where IOLpre = the power of the IOL as if no
unknown, the formula will use 43.86 D as the de- LASIK had been performed,
fault preoperative corneal value. Another option ΔD = the refractive change after LASIK at the
is to apply Aramberri’s “double K method” cor- spectacle plane,
rection to the Holladay 1, Hoffer Q or SRK/T for- IOLpost = the estimated power of the IOL to be
mulas [1] or refer to the IOL power adjustment implanted following LASIK.
nomograms published by Koch and Wang [19].
4 Several methods have been proposed to im-
prove the accuracy of IOL power calculation in
eyes following corneal refractive surgery; these
4.6.1.3 Masket IOL
can be divided into those that require preopera-
Power Adjustment Method
tive data and those that do not. Masket [22] has developed another method that
adjusts the IOL power based on the amount of
refractive laser correction. Instead of calculat-
ing IOL power with pre-LASIK data as above,
4.6.1 Methods Requiring this method modifies the predicted IOL power
Historical Data obtained using the patient’s post-laser correction
readings by using the following formula:
4.6.1.1 Clinical History Method
The clinical history method [18] for corneal IOLpost + (ΔD × 0.326) + 0.101 = IOLadj
power estimation requires accurate historical
data and was first described by Holladay as: where IOLpost = the calculated IOL power fol-
lowing ablative corneal refractive surgery,
Kp + SEp - SEa = Ka ΔD = the refractive change after corneal refrac-
tive surgery at the spectacle plane,
where Kp = the average keratometry power be- IOLadj = the adjusted power of the IOL to be im-
fore corneal refractive surgery, planted.
SEp = the spherical equivalent before corneal re-
fractive surgery,
SEa = the stable spherical equivalent after corneal
refractive surgery,
4.6.1.4 Topographic Corneal
Ka = the estimate of the central corneal power
Power Adjustment Method
after corneal refractive surgery. There are several approaches to modifying post-
LASIK corneal power measurements:

1. To adjust the effective refractive power (Ef-

4.6.1.2 Feiz-Mannis IOL fRP) of the Holladay Diagnostic Summary of
Power Adjustment Method the EyeSys Corneal Analysis System by using
Another method that is helpful to use when good the following formulas after myopic or hyper-
historical data are available is the IOL power ad- opic surgery respectively [11, 31]:
justment method of Feiz and Mannis et al. [6].
Using this technique, the IOL power is first cal- EffRP – (ΔD × 0.15) – 0.05 = post-myopic LASIK
culated using the pre-LASIK (laser-assisted in adjusted EffRP
situ keratomileusis) corneal power as though EffRP + (ΔD × 0.16) – 0.28 = post-hyperopic
the patient had not undergone keratorefractive LASIK adjusted EffRP
surgery. This pre-LASIK IOL power is then in-
creased by the amount of refractive change at the where ΔD = the refractive change after LASIK at
spectacle plane divided by 0.7. This approach is the corneal plane.
outlined as follows:
 4.6 Determining IOL Power Following Corneal Refractive Surgery 41

2. To average the corneal curvatures of the cen-

ter and the 1-mm, 2-mm, and 3-mm annu-
4.6.2.2 Modified Maloney Method
lar rings of the Numerical View of the Zeiss Another very useful method of post-LASIK cor-
Humphrey Atlas topographer (AnnCP) and neal power estimation is one that was originally
modify the result using the following formula described by Robert Maloney and subsequently
[31]: modified by Li Wang and Douglas Koch et al.
[32]. Using this technique, the central corneal
AnnCP + (ΔD × 0.19) – 0.4 = post-hyperopic power is obtained by placing the cursor at the
LASIK adjusted AnnCP exact center of the Axial Map of the Zeiss Hum-
phrey Atlas topographer. This value is then con-
3. To modify keratometry (K) values as follows verted back to the anterior corneal power by
[11]: multiplying this value by 376.0/337.5, or 1.114.
An assumed posterior corneal power of 6.1 D is
K – (ΔD × 0.24) + 0.15 = post-myopic LASIK then subtracted from this product:
adjusted K
(CCP × 1.114) – 6.1 D = post-LASIK adjusted
This latter approach is not as accurate as the two corneal power
above-mentioned topography-based methods.
where CCP = the corneal power with the cursor
in the center of the topographic map.
The advantage of this method is that it re-
4.6.2 Methods Requiring quires no historical data and has a low variance
No Historical Data when used with either the Holladay 2 formula or
a modern third generation two-variable formula
4.6.2.1 Hard Contact Lens Method combined with the “double K method” correction
This method does not require pre-LASIK data, nomogram published by Koch and Wang [19].
but can only be used if the visual acuity is better
than around 20/80 [34]:

Bc + Pc + SEc – SEs = Ka
4.6.3 Hyperopic Corneal
Refractive Surgery
where Bc = base curve of contact lens in diop- For eyes that have undergone hyperopic LASIK,
ters, it is easier to estimate central corneal power than
Pc = refractive power of contact lens in diopters, for myopic LASIK. This is presumably because
SEc = spherical equivalent with contact lens in the ablation takes place outside the central cor-
place, nea. The average of the 1-mm, and 2-mm an-
SEs = spherical equivalent without contact lens, nular power rings of the Numerical View of the
Ka = estimated corneal power following refrac- Zeiss Humphrey Atlas topographer can serve as
tive surgery. an estimate of central corneal power following
hyperopic LASIK. As an alternative, the adjusted
Unfortunately, the literature now suggests that EffRP of the EyeSys Corneal Analysis System
the hard contact lens method may be less accu- proposed by Drs. Wang, Jackson, and Koch also
rate than originally thought following all forms works well (see Sect. 4.6.1.4) [31].
of ablative corneal refractive surgery [2, 10, 17, Remember that some form of a “double K
32]. Better results may require the use of contact method” is still required for IOL power calcu-
lens designs with posterior curvatures that better lations following hyperopic LASIK in order to
fit the surgically modified corneal surface. avoid an inaccurate estimation of ELP.
42 Advanced Intraocular Lens Power Calculations

correction (IOL exchange or a piggyback IOL)

Summary for the Clinician until two reasonably stable refractions and to-
■ In eyes that have undergone ablative cor- pographies are obtained at the same time of the
neal surgery, IOL calculations are more day.
complex due to difficulty in calculating Because of both the relative inaccuracy of IOL
true corneal refractive power and poten- calculations in RK eyes and their tendency to ex-
tial errors in estimating the effective lens perience a long-term hyperopic drift, we usually
position. target IOL power calculations for –1.00 D. A de-
4
■ A variety of approaches can be used to tailed discussion with the patient regarding these
calculate corneal power (see Table 4.4). issues is required. Finally, if more than 6 months
passes before cataract surgery is required for the
fellow eye, the corneal measurements should be
repeated due to the fact that additional corneal
flattening frequently occurs over time following
4.6.4 Radial Keratotomy radial keratotomy.
Unlike the ablative forms of corneal refractive
surgery (LASIK and PRK) in which only the an-
terior radius is changed, eyes that have previously
undergone radial keratotomy experience flatten-
Summary for the Clinician
ing of both the anterior and posterior radii. This ■ Eyes that have previously undergone
approximate preservation of the ratio between radial keratotomy experience flattening
the anterior and posterior radii allows for a direct of both the anterior and posterior radii;
measurement of the central corneal power. Thus, this allows for a direct "averaging" mea-
any map that provides some average of anterior surement of the central corneal power.
corneal power over the central 2–3 mm gives an ■ Patients with previous radial keratometry
accurate estimation of corneal refractive power. will commonly show variable amounts
Examples include averaging the 0-mm, 1-mm, of transient hyperopia in the immediate
and 2-mm annular power rings of the Numeri- postoperative period following cataract
cal View of the Zeiss Humphrey Atlas topogra- surgery.
pher and the EffRP from the Holladay Diagnostic
Summary of the EyeSys Corneal Analysis System.
It is important to remember that one still needs
to compensate for potential errors in ELP by us-
ing the Holladay 2 formula or the double-K ap-
4.6.5 Accuracy
proach with third-generation formulas described
and Patient Expectations
in Sect. 4.6. It is important to explain to patients in that in-
Patients with previous radial keratometry will traocular lens power calculations following all
also commonly show variable amounts of tran- forms of corneal refractive surgery are, at best,
sient hyperopia in the immediate postoperative problematic. In spite of our best efforts, the final
period following cataract surgery [20]. This is refractive result may still end up more hyperopic
felt to be due to stromal edema around the ra- or more myopic than expected. In addition, astig-
dial incisions, which flattens the central cornea.
Although usually transient, it may be as high as
+6.00 D. It may be more likely to occur in eyes
with eight or more incisions, an optical zone of  Table 4.4 Example of post-corneal refractive sur-
less than 2.0 mm, or incisions that extend to the gery intraocular lens calculation: a 50 year-old male
limbus. The hyperopia may take 8–12 weeks to underwent cataract extraction and posterior chamber
IOL implantation in both eyes 5 years after myopic
resolve. Thus, we recommend following up these laser-assisted in situ keratomileusis (LASIK). The fol-
patients with refractions and topographic maps lowing data is from his left eye. EffRP: effective refrac-
obtained at 2-week intervals, deferring surgical tive power
 4.6 Determining IOL Power Following Corneal Refractive Surgery 43

Pre-cataract surgery data:

Pre-LASIK data:
– Pre-LASIK refraction: -8.50 D
– Pre-LASIK mean keratometry: 44.06 D
Post-LASIK data:
– Post-LASIK refraction: -0.50 D
– EffRP: 38.82 D
– Central topographic power (Humphrey Atlas): 39.00 D
– Contact lens over-refraction data: refraction without contact lens: -0.50 D, contact lens
base curve: 37.75 D, contact lens power: +1.75 D, refraction with contact lens: -2.00 D
Post-cataract surgery data:
– An Alcon SA60AT lens with power of 23.5 D was implanted in this eye,
and the manifest refraction after cataract surgery was +0.125 D
Corneal refractive power estimation:
Clinical history method:
– Pre-LASIK refraction at corneal plane (vertex distance: 12.5
mm): (-8.50)/{1-[0.0125*(-8.50)]} = -7.68 D
– Post-LASIK refraction at corneal plane: (-0.50)/{1-[0.0125*(-0.50)]} = -0.50 D
– Corneal power = 44.06 + (-7.68) - (-0.50) = 36.88 D
Hard contact lens method:
– Corneal power = 37.75 + 1.75 + [(-2.00) - (-0.50)] = 38.00 D
Adjusted EffRP:
– Adjusted EffRP = 38.82 - 0.15 * [(-0.50 - (-7.68)] - 0.05 = 37.69 D
Modified Maloney Method:
– Corneal power = 39.00 * (376/337.5) - 6.1 = 37.35 D
IOL power calculation (aiming at refraction of +0.125 D):
Clinical history method:
– IOL power using corneal power obtained from the clinical history method: 24.42 D
Hard contact lens method:
– IOL power using corneal power obtained from the hard contact lens method: 23.01 D
Adjusted EffRP:
– IOL power using Adjusted EffRP: 23.54 D
Modified Maloney method:
– IOL power using corneal power obtained from the Modified Maloney method: 23.94 D
Feiz-Mannis IOL power adjustment method:
– IOL power using pre-LASIK K: 14.55 D
– IOL power after LASIK: 14.55 + 7.18/0.7 = 24.81 D
Masket IOL power adjustment method
– IOL power using post-LASIK K (EffRP in this case): 20.19 D
– IOL power after LASIK: 20.19 + [-0.50 - (-7.68)] * 0.326 + 0.101 = 22.63 D
IOL power prediction error using different methods (Implanted – Predicted):
– Double-K clinical historical method: -0.92 D
– Double-K CL over-refraction: +0.49 D
– Double-K Adjusted EffRP: -0.04 D
– Double-K Modified Maloney method: -0.44 D
– Feiz-Mannis IOL power adjustment method: -1.31 D
– Masket IOL power adjustment method: +0.87 D
44 Advanced Intraocular Lens Power Calculations

matism may be present and may not respond as unacceptably high ametropia, options include
expected to corneal relaxing incisions. IOL exchange, a piggyback IOL, or corneal re-
The higher order optical aberrations and fractive surgery.
multifocality that often accompany the various 2. Defer cataract surgery until the graft has sta-
forms of corneal refractive surgery also remain bilized, preferably after suture removal. Al-
unchanged following cataract surgery. For exam- though more accurate, there would be a delay
ple, third- and fourth-order higher order aber- in visual rehabilitation and the second proce-
rations produced by radial keratotomy can be as dure may cause surgical trauma to the donor
4 much as 35 times normal values. Elevated higher cornea.
order aberrations are also seen following PRK 3. Perform cataract extraction alone without
and LASIK, particularly decentered ablations or IOL implantation in conjunction with the cor-
older treatments with small central optical zones. neal graft. With this approach, there is mini-
Although the positive spherical aberration in- mal risk of trauma to the graft with the second
duced by myopic procedures may be partially procedure. However, it essentially eliminates
ameliorated by implanting an IOL with negative the chance of implanting the IOL in the cap-
asphericity, moderate to high amounts of posi- sular bag.
tive spherical aberration usually remain. The vi-
sual consequence of these aberrations is loss of
best-corrected acuity and contrast sensitivity
Summary for the Clinician
and, understandably, some patients mistakenly ■ Because it is impossible to accurately
expect that cataract surgery will alleviate these predict postoperative central power of
symptoms. Thus, it is important to discuss this the donor graft, there is presently no re-
prior to surgery so that their expectations will be liable method for calculating IOL power
realistic. for eyes undergoing combined corneal
The active use of so many different methods transplantation and cataract removal
of IOL calculation following corneal refractive with IOL implantation.
surgery is eloquent testimony to how far we still
have to go in this area. To minimize the risk of
unexpected postoperative hyperopia, we gen-
erally recommend a refractive target of around
–0.75 D, depending on the refractive status of the
4.8 Silicone Oil
fellow eye. For eyes containing silicone oil, A-scan axial
See Table 4.4 for an example of an intraocular length measurements are best carried out with the
lens calculation following corneal refractive sur- patient seated as upright as possible, especially if
gery. the vitreous cavity is partially filled with silicone
oil. In the upright position, it is more likely that
the silicone oil will remain in contact with the
retina. In the recumbent position, the less dense
4.7 Corneal Transplantation silicone oil will shift away from the retina, toward
There is presently no reliable method for calcu- the anterior segment. This can lead to confusion
lating IOL power for eyes undergoing combined as to the correct interpretation of the position of
corneal transplantation and cataract removal the retinal spike.
with IOL implantation. This is because it is im- The refractive index of silicone oil is also
possible to accurately predict the central power higher than that of the vitreous, requiring an ad-
of the donor graft. There are several options: justment to IOL power. To prevent the silicone
1. Use a mean corneal power, based on evalua- oil from altering the refractive power of the pos-
tion of prior grafts, as a “best guess” of post- terior surface of the IOL, it is preferable to im-
operative corneal power and proceed with plant polymethyl methacrylate (PMMA) convex-
IOL implantation. In eyes with an acceptable plano lenses, with the plano side oriented toward
postoperative refractive error, additional lens the vitreous cavity and preferably over an intact
surgery will not be required. For eyes with posterior capsule. The additional power that
 References 45

must be added to the original IOL calculation for

a convex-plano IOL (with the plano side facing
4.9 Conclusion
toward the vitreous cavity) is determined by the The methodology for accurately calculating IOL
following relationship, as described in 1995 by power in normal and complex eyes has improved
Patel [25]: dramatically in recent years. Future advances are
needed in all areas, including methods of measur-
((Ns – Nv)/(AL – ACD)) × 1,000 = additional ing corneal power, predicting effective lens posi-
IOL power (diopters) tion, and perhaps even measuring axial length.
where Ns = refractive index of silicone oil The ultimate solution may be an IOL whose
(1.4034), spherical and astigmatic power and higher or-
Nv = refractive index of vitreous (1.336), der aberrations can be modified postoperatively.
AL = axial length in mm, Ideally, such an IOL could be modified multiple
ACD = anterior chamber depth in mm. times to adapt to the patient’s changing visual
needs and to compensate for aging changes of
For an eye of average dimensions, and with the the cornea.
vitreous cavity filled with silicone oil, the addi-
tional power needed for a convex-plano PMMA
IOL is typically between +3.0 D and +3.5 D.
However, if the silicone oil will not be left in the
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