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 one3 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?
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 Npost= 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.
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?
These method requires access to an accurate manifest refraction and keratometry prior to LASIK.
Contact Lens Overrefraction KCL= BC+ D+ (ORCL- MR)
KCL=corneal power; BC is the contact lens base curve ORCL 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:
• 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;
• 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).
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
(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.
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.
1. Wang Z, Chen J, Yang B. Posterior corneal surface topographic changes after laser in situ keratomileusis are related to residual corneal bed thickness. Ophthalmology 1999;106:406-09.
2. Naroo SA, Charman WN. Changes in posterior corneal curvature after photorefractive keratectomy. J Cataract Refract Surg 2000;26:872-78.
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;
5. Aramberri J. Intraocular lens power calculation after corneal refractive surgery: Double-K method. J Cataract Refract Surg 2003;29:2063-68.
6. Sanders DR, Kraff MC. Improvement of intraocular lens power calculation using empirical data. J Am Intraocul Implant Soc 1980;6:263-67.
7. Olsen T. Sources of error in intraocular lens power calculation.
J Cataract Refract Surg 1992;18:125-29.
8. Winkler-von-Mohrenfels C, Gabler B, Lohmann CP. Optical biometry before and after excimer laser epithelial kerato-mileusis (LASEK) for myopia. Eur J Ophthalmol 2003;
9. Cuaycong MJ, Gay CA, Emery J, et al. Comparision of the accuracy of computerized videokeratography and keratometry for use in intraocular lens calculations. J Cataract Refract Surg 1993;19:178-81.
10. Packer M, Brown LK, Hoffman RS, Fine IH. Intraocular lens power calculation after incisional and thermal keratorefractive surgery. J Cataract Refract Surg 2004;30:1430-34.
11. Seitz B, Langenbucher A. Intraocular lens power calculation in eyes after corneal refractive surgery. J Cataract Refract Surg 2000;16:349-61.
12. Cuaycong MJ, Gay CA, Emery J, et al. Comparison of the accuracy of computerized videokeratography and keratometry for use in intraocular lens calculation. J Cataract Refract Surg 1993;19(Suppl):178-81.
13. Celikkol L, Pavlopoulos G, Weinstein B, et al. Calculation of intraocular lens power after radial keratotomy with computerized videokeratography. Am J Ophthalmol 1995;
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.
15. Seitz B, Langenbucher A. Intraocular lens calculations status after corneal refractive surgery. Curr Opin Ophthalmol 2000;11:35-46.
16. Maeda N, Klyce SD, Smolek MK, McDonald MB. Disparity between keratometry-style readings and corneal power within the pupil after refractive surgery for myopia. Cornea 1997;
17. Srivannaboon S, Reinstein DZ, Sutton HFS, Holland SP.
Accuracy of orbscan total optical power maps in detecting
refractive change after myopic laser in situ keratomileusis. I Cataract Refract Surg 1999;25:1596-99.
18. Qazi MA, Cua IY, Roberts CJ, Pepose JS. Determining corneal power using Orbscan II videokeratography for intraocular lens calculation after excimer laser surgery for myopia. J Cataract Refract Surg 2007;33:21-30.
19. Bechmann M, Thiel MJ, Neubauer AS, et al. Central corneal thickness measurement with a retinal optical coherence tomography device versus standard ultrasonic pachymetry.
20. Maldonado MJ, Ruiz-Oblitas L, Munuera JM, et al. Optical coherence tomography evaluation of the corneal cap and stromal bed features after laser in situ keratomileusis for high myopia and astigmatism. Ophthalmology 2000;107:
21. Tang M, Li Y, Avila M, Huang D. Measuring total corneal power before and after laser in situ keratomileusis with high-speed optical coherence tomography. J cataract Refract Surg 2006;32:1843-50.
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.
23. Feiz V, Mannis MJ. Intraocular lens power calculation after corneal refractive surgery. Curr Opin Ophthalmol 2004;15:
24. Hamed AM, Wang L, Misra M, Koch DD. A comparative analysis of five methods of determining corneal refractive power in eyes that have undergone myopic laser in situ keratomileusis. Ophthalmology 2002;109:651–58.
25. Smith RJ, Chan WK, Maloney RK. The prediction of surgically induced refractive change from corneal topography. Am J Ophthalmol 1998;125:44-63.
An Update on IOL Power Calculation Formulas