**INTRODUCTION**

*The refractive surgery such as laser in situ keratomileusis*
(LASIK) is very popular in recent years. An increasing
number of cataract surgeries in eyes after LASIK
proce-dures become to be problematic due to the difficulty in
intraocular lens (IOL) power calculation. Application of
the measured average keratometric readings (central
keratometric diopters) after LASIK into standard IOL
power calculation formulas commonly results in
substantial undercorrection and postoperative hyperopic
or even anisometropia.In this chapter, different methods
for improved assessment of central keratometric diopters
to minimize IOL power miscalculations after LASIK are
introduced.

**ERRORS IN IOL POWER CALCULATION**
Prediction formulas of IOL power in cataract surgery is
based on measurements of radius of corneal curvature,
axial length, and estimation of postoperative anterior
chamber depth (effective lens position, ELP).However,
after LASIK surgery, the anterior corneal curvature
becomes flatter, whereas the posterior curvature seems
no changes or much less change,^{1,2} which overestimates
central keratometric readings using the routine
keratometers or the autorefractors. This overestimation
may also be caused by different factors and becomes one^{3}
of the reasons for IOL power miscalculations (Fig. 10.1).

**1. The ratio between anterior and posterior curvature, measured***by standard keratometry or computerized videokeratography,*
*may markedly alter and the central corneal thickness decreases*
*after LASIK procedure.*

Previously many measurements of corneal power suppose central sphericity and a radius of curvature of

the posterior cornea 1.2 mm steeper than the anterior radius. After LASIK, there may be significant change of asphericity and there is a flattening of the anterior corneal surface with little or no impact on the posterior radius.

This change in relation leads to inaccurate estimations of net corneal power (the difference between anterior and posterior curvature).

**2. Inaccurate calculation of anterior corneal power using the***standardized value for refractive index of the cornea (1.3375).*

The index is based on Gullstrand’s model eye rather
than on actual measurements.^{5} In the Gullstrand’s model
eye, the cornea is replaced by an ideal thin lens with power
equivalent to the cornea and one refractive surface. The
total power of the lens is determined using the radius of
curvature of anterior and posterior cornea. The anterior
corneal curvature is determined using the keratometer,
but the posterior corneal curvature could not be directly
measured. To overcome this problem, the eye model

**Fig. 10.1: Schematic eye**

**How to Measure a Correct Central Keratometric Reading?**

### 47

assumes a fixed ratio between anterior and posterior
surfaces, then this ratio is applied to determine posterior
corneal curvature. Savini and coworkers presented that
myopic PRK and LASIK induce reduction of the
keratometric refractive index which is correlated to the
amount of attempted correction by excimer laser by the
factor of N^{post}= 1.338+ 0.0009856x attempted correction.^{4}
In recent advancement of measurement of posterior
curvature, such as Pentacam and Orbscan, the net power
of anterior and posterior cornea could be determined and
the refractive index can be recalculated according to the
amount of refractive corrections.

* 3. Incorrect estimation of effective lens position (ELP): One*
reason for the underestimated for IOL power calculation
after LASIK surgery is based on the incorrect effective lens
position (ELP) estimation calculated by third-generation
theoretical formulas in which the post LASIK surgery
K-value is applied. Aramberri presented that Double-K
modification of the SRK/T formula improved the accuracy
of IOL power calculation after LASIK and PRK.

^{5}This method used the pre-refractive surgery K-value (Kpre) for the effective lens position (ELP) calculation and the post-refractive surgery K-value (Kpost) for IOL power calculation by the vergence formula. The Kpre value was obtained by keratometry or topography and the Kpost, by the clinical history method. This method helped in the correction of underestimates the ELP and IOL power, resulting in hyperopia between 1.0 D and 3.0 D.

* 4. Incorrect axial length measurement: If the biometry is*
accurate, axial length measurements are unlikely to
contribute significantly to IOL power errors after LASIK
surgery. Axial length measurements have decreased these
errors by refinements in biometry techniques and
instruments.

^{6,7}Winkler-von-Mohrenfels and his collegues analyzed axial length before and after excimer keratectomy and found no significant differences.

^{8}Shortening axial length would be expected as tissue is removed from the central cornea after myopic LASIK/PRK,. This may result in IOL power overestimation with unexpected myopia.

**METHODS TO MEASURE**
**KERATOMETRIC DIOPTERS**
**Keratometry**

Manual and Automated

Manual and automated keratometry are the most frequently utilized methods for measuring central corneal power to calculate intraocular lens (IOL) power. Although

manual keratometry is a simple, reliable methods for determining K values for eyes with unaltered corneas.

However, manual keratometry is generally considered to be the least accurate of these methods, because it measures only four points approximately 1.5 mm from the corneal apex. This method assumes that the anterior central cornea is spherical and the radius of posterior corneal curvature is 1.2 mm. This measured zone may be more peripheral to the central flattened area leading to a lower power intraocular lens calculation and postoperative hyperopia.

Manual or automated keratometry will both overestimate the change in central refractive power following these procedures. Most keratometers use a corneal index of refraction of 1.3375. (M) However, LASIK surgery changes the fixed ratio based on anterior to posterior curvature and central corneal sphericity (Fig. 10.2). The ratio between anterior and posterior curvature could increase markedly and the central corneal thickness decreases after PRK/ LASIK procedure. Therefore, the default index of refraction used in maual keratometry is no longer accurate in determining the true power of the cornea after LASIK procedure. Rouitne single standard keratometry is not suitable for measuring corneal power after LASIK.

**Fig. 10.2: Flatter changes of anterior**
corneal curvature after PRK/LASIK

Manual keratometry after myopic LASIK overestimates corneal power and underestimates IOL power. Manual keratometry after hyperopic LASIK and PRK theoretically underestimates corneal power and results in IOL power overestimation, For LASIK/PRK, the error causes is directly proportional to the amount of keratectomy.

**Topography Access**

Placido-based Videokeratography

Videokeratoscopes, based on the Placido disk principle, is important to estimate the corneal keratometry.

Videokeratoscopes measure more than 5000 points over
entire cornea and more than 1000 points within the central
3.0 mm and yield a radius of curvature that units
automatically convert into diopteric power (simulated
keratometry [Sim-K]. Topography uses a preprogrammed
refractive index. Although the default index of refraction
is 1.3375, Placido-based videokeratography still can
provide greater accuracy than manual keratometry in
normal eyes and in eyes after radial keratotomy (RK).^{9, 10}
However, the true corneal power in eyes after PRK was
overestimated due to the change of the ratio of anterior to
posterior curvature.^{11} These reasons may be due to (1) the
cornea is a “true” spherical surface and (2) the power of
the paracentral 3 to 4 mm is not significantly different
from that of the central cornea. In fact, the cornea is a
prolate, aspheric refractive media with progressive
flattening toward the periphery.

*Cuaycong et al compared manual keratometry with*
keratometry derived from computerized
videokerato-graphy to determine IOL power in normal eyes without
refractive surgery and found that the computerized
videokeratography values were more accurate.^{12} Celikkol
*et al. showed that corneal powers derived from*
computerized videokeratography were more accurate
than routine methods.^{13}* In contrast, Husain et al.*

concluded that the corneal powers derived from
computerized videokeratography were less accurate than
that from standard keratometry.^{14}* Seitz et al. also found*
manual keratometry to be superior to topography-derived
values in postmyopic PRK eyes .^{15}

Average Central Power

Maeda and Klyce presented the concept of average central
power (ACP) which is obtained by the average of corneal
powers from Topographic Modeling System (TMS).^{16} They
showed a videokeratographic method to calculate corneal
power within the pupil. This method offers advantages
in eyes with small optical zones.

Slit-scanning Videokeratography ( Orbscan II) Slit-scanning-based corneal topography systems such as the Orbscan (Orbtek), Orbscan II (Bausch & Lomb) and Pentacam (Oculus GmbH) have the capacity to measure both corneal surfaces to calculate the total corneal power.

The Orbscan II system is a Placido-based, slit scanning instrument that projects 20 slits from the right and 20 slits from the left during each 2.1-second scan at a fixed angle of 45 degrees onto the cornea. Each slit was captured by video camera and used to construct mathematical

representations of the ture topographic surfaces. However,
the ability of Orbscan II to accurately map the surfaces of
human cornea remains unknown due to uncertain
variances like microsaccades, light scatter, tear instability
and surface irregularities. Srivannaboon et al presented
that the Orbscan topography system (Bausch & Lomb)
provides K-values that correlate closely with changes in
manifest refraction produced by LASIK.^{17} Qazi et al
showed that the Orbscan II 5.0 mm total axial power and
4.0 mm total optical power can be used to more accurately
predict true corneal power than the history-based method
and may be particularly useful while pre-LASIK data are
unavailable.^{18}

**Optical Coherence Tomography (OCT)**

Optical coherence tomography (OCT) is an alternative
method to directly measure both corneal surfaces. Current
commercial retinal OCT scanners with scan rates of 100
or 400 axial scans (A-scans)/second have been used to
measure corneal thickness and LASIK flap.^{19, 20} However,
the results of measurement in anterior corneal power are
variable due to the motion error. This motion error could
be reduced by using higher scanning speed. Therefore, a
high –speed cornea and anterior segment OCT (CAS-OCT,
Carl Zeiss Meditec, Inc.) which is capable of 2000 A-scans/

second and operated at a 1.3 um wavelength seems to be
better choice to measure corneal power. In 2006, Tang
and LI presented that the repeatability of hybrid method
that the optical powers of the anterior and posterior
surfaces were calculated by the combination of corneal
thickness map from OCT and anterior corneal surface
from Placido ring corneal topography which was 3 times
better than that of the direct method that both corneal
surfaces was measured directed by the OCT.^{21}

**METHODS TO IMPROVE THE PREDICTION**
**OF INTRAOCULAR POWER**

Each of these methods has practical limitations.

**Clinical History Method**

*K= Pre-RS K+ (Pre-RS SE- Post-RS SE)*

*K: current keratometric reading; Pre-RS K is prerefractive*
surgery keratometry

*Pre-RS SE and Post-RS SE are the prerefractive and*
postrefractive surgery spherical equivalents (SEs).

**How to Measure a Correct Central Keratometric Reading?**

### 49

These method requires access to an accurate manifest refraction and keratometry prior to LASIK.

**Contact Lens Overrefraction**
*KCL= BC+ D+ (OR*_{CL}*- MR)*

*KCL=corneal power; BC is the contact lens base curve*
*OR*_{CL}* is the SE of the overrefraction, and MR is the SE*
without contact lens.

The contact lens method loses accuracy when visual
acuity is lower than 20/80 or worse.^{22}

**Single-K versus double-K Method**

• Equation 1: Preoperative corneal radius of curvature:

rpre 337.5/Kpre

• Equation 2: Corrected axial length (LCOR): If L < 24.2, LCOR= L. If L > 24.2, LCOR= 3.446 +1.716x L-0.0237xL2

• Equation 3: Computed corneal width (Cw): Cw=5.41 + 0.58412 x LCOR + 0.098 x Kpre

• Equation 4: Corneal height (H): H=rpre-Sqrt[rpre2-(Cw2/4)]

• Equation 5: Offset value: Offset=ACDconst-3.336

• Equation 6: Estimated postoperative ELP (ACD):

ACDest=H + Offset

• Equation 7: Constants: V=12; na=1.336; nc=1.333;

ncm1=0.333

• Equation 8: Retinal thickness (RETHICK) and optical axial length (LOPT): RETHICK = 0.65696 - 0.02029 x L. LOPT = L + RETHICK

• Equation 10: Emmetropia IOL power (IOLemme):

*IOLemme = [1000 x na x (n x rpost - ncm1 x LOPT)]/*

*[(LOPT - ACDest) x (na x rpost - ncm1 x ACDest)]*

*• Variables L = axial length; Kpre = pre-refractive surgery*
K-value; Kpost = post-refractive surgery K-value;

ACDconst = IOL constant (can be computed from A-constant).

**Feiz–Mannis Method**

After myopic LASIK: Post-myopic LASIK IOL = pre-LASIK IOL+ (change in SE/0.67)

After hyperopic LASIK: Post-hyperopic LASIK IOL =
pre-LASIK IOL - (change in SE/0.67) ^{23}

**Adjusted Effective Refractive Power (EffRPadj)**
The EffRPadj is calculated by multiplying the
LASIK-induced refractive change by 0.15 diopters (D) and
subtracting this value from the measured EffRP, which is
displayed in the Holladay Diagnostic Summary of the

EyeSys Corneal Analysis System (effective refractive index,
1.3375; EyeSys Technologies, Inc., Houston, TX).^{24}
**Maloney Methods**

The corneal power at the center of the topographic map is
modified according to the formula Central power= (central
topographic powerx[376/337.5])-4.9.^{25}

**IOL Formulas**

**(SRK/T, Hoffer Q, Holladay I, and Holladay II)**
Holladay, Hoffer Q, or SRK/T, appear to improve the
accuracy of intraocular lens power calculations following
LASIK surgery while compared with regression formulas
such as the SRK or SRK II.

These methods will discuss in detail in other charpters.

**CONCLUSION**

To avoid underestimation of intraocular lens power after cataract surgery in eyes that previously receiving LASIK refractive surgery, the central corneal power should be measured correctly. Although there are no absolutely reliable methods in determining corneal power in these eyes, different measurements could be considered into the prediction of IOL power. Finally, long-term effects of LASIK on the stability of refraction are not known, and these could have an impact on IOL power calculations and the selection of the postoperative target of refraction.

**REFERENCES**

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3. Olsen T: On the calculation of power from curvature of the cornea. Br J Ophthamol 1986;70:152-54.

4. Savini G, Barboni P, Zanini M. Correlation between attempted correction and keratometric refractive index of the cornea after myopic excimer laser surgery. J of Refractive Surg 2007;

23:461-66.

5. Aramberri J. Intraocular lens power calculation after corneal refractive surgery: Double-K method. J Cataract Refract Surg 2003;29:2063-68.

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120:739-50.

14. Husain SE, Kohnen T, Maturi R, et al. Computerized videokeratography and keratometry in determining intraocular lens calculations. J Cataract Refract Surg 1996;22:362-66.

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22. Zeh WG, Koch DD. Comparison of contact lens overrefraction and standard keratometry for measuring corneal curvature in eyes with lenticular opacity. J Cataract Refract Surg 1999;25:898-903.

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**An Update on IOL Power Calculation Formulas**

**JT Lin (Taiwan), Ashok Garg (India)** 51

## 11 **An Update on IOL Power**

**An Update on IOL Power**