Intraocular lens power calculation after corneal refractive surgery

Purpose of review Keratorefractive procedures designed to decrease refractive errors have gained enormous popularity among ophthalmologists and patients. As the post–refractive surgery patient population ages, visually significant cataracts will develop. With advances in techniques for cataract extraction and intraocular lens implantation, cataract surgery has evolved into a refractive surgical procedure as well as an operation to improve best corrected visual acuity. This raises expectations in terms of desired postoperative refractive status and uncorrected visual acuity. Although performing modern cataract surgery in post–refractive surgery eyes is technically no more complicated than operating on virgin eyes, the calculation of intraocular lens power for a desired refractive target can be challenging and complicated. This has become increasingly apparent as case reports of “refractive surprises” after cataract surgery appear in the literature more frequently. Recent findings This paper reviews the current clinical experience with intraocular lens power determination after cataract surgery in post-keratorefractive patients, provides an overview of possible sources of error in intraocular lens power calculation in these patients, and analyzes methods to minimize intraocular lens power errors. Summary The clinical and routine methods of intraocular lens power determination after keratorefractive surgery need to be modified to improve accuracy. Our knowledge of this subject is still evolving. Given the enormous impact of this problem on clinical practice, awareness of the shortcomings and suggested methods to improve accuracy can be valuable to clinicians.


Introduction
Increasing numbers of patients undergo corneal surgical procedures to decrease dependence on refractive aids. Most of these procedures permanently and irreversibly alter corneal shape and its effective power. Excimer keratectomy (laser-assisted in situ keratomileusis [LASIK], laser-assisted subepithelial keratomileusis [LASEK], photorefractive keratectomy [PRK]) has quickly become the procedure of choice, replacing older incisional surgeries such as radial keratotomy (RK). In 2002, an estimated 818,000 LASIK procedures were performed in the United States, compared with 250,000 RK procedures performed annually at the height of its popularity [1,2].
Patients who have undergone keratorefractive surgery are typically in their mid-30s [3••]. As this population ages, unavoidable development of visually significant cataracts will occur. With the evolution of modern cataract surgery, we have refined methods of intraocular lens (IOL) power determination so that current formulas are highly accurate in matching desired refractive status after IOL implantation. Increased accuracy has heightened both patient and surgeon expectations for precise outcomes, particularly among those who have already undergone refractive surgery.
As surgeons gain experience with cataract extraction in post-refractive surgery patients, they are finding that standard IOL formulas and keratometry can lead to "refractive surprises," which may require subsequent surgical correction. Common results are underestimation of IOL power and unexpected hyperopia in patients who have undergone corneal refractive surgery to correct myopia, regardless of the procedure (RK, PRK, LASIK) [4][5][6][7][8][9][10][11]. Refractive surprises seem directly related to the amount of keratectomy performed, so greater refractive correction correlates with greater underestimation of IOL power [12][13][14].
Experience with IOL power determination after corneal surgery to correct hyperopia remains limited. A few reported cases of cataract surgery after hexagonal keratectomy (now abandoned) resulted in myopic surprises [15]. As procedures like hyperopic LASIK/PRK, conductive keratoplasty, and laser thermokeratoplasty gain wider acceptance, refractive surprises after cataract surgery may increase. Therefore, more accurate methods to determine IOL power after keratorefractive surgery are needed.

Intraocular lens power determination
IOL power calculation relies on three measurements: axial length, based on ultrasound or optical biometry; corneal power, using manual/automated keratometry; and anterior chamber depth, which is not independently measured. These values are used collectively in theoretic or regression formulas to determine an IOL power for a desired refractive status. Axial length measurements have been the source of most refractive surprises, although refinements in biometry techniques and instruments have decreased these errors [16,17].

Axial length
When biometry is accurate, axial length measurements are unlikely to contribute significantly to IOL power errors after corneal refractive surgery. Two studies analyzing axial length before and after radial keratotomy and excimer keratectomy found no significant differences [18,19]. If axial length is significantly changed after myopic LASIK/PRK, shortening would be expected as tissue is removed from the central cornea. This shortening should result in IOL power overestimation with unexpected myopia, which counters clinical experience.

Anterior chamber depth (effective lens position)
Effective lens position or anterior chamber depth affects post-cataract surgery refraction, so that a greater myopic shift is observed with more anterior IOL position after implantation. Anterior chamber depth cannot be independently measured because even after in-the-bag implantation it is hard to predict the exact distance between the cornea and IOL. If corneal surgery significantly changes anterior chamber depth and therefore the effective lens position, the result can effectively change post-cataract surgery refraction. Several investigators have looked at anterior chamber depth after refractive surgery. One study reported a small forward shift of the posterior cornea after myopic LASIK [20]. This observation, however, has not been confirmed in a similar study [21]. These changes, even if real, appear too small to account for changes in refraction and therefore probably do not significantly contribute to IOL power errors after myopic treatments.

Corneal power
Corneal power calculations rely on determining radius of curvature of the anterior cornea in meters (r), which is converted into a diopteric power (P) using an index of refraction (n) according to the following formula. P = (n − 1)/r Radius of curvature is measured by keratometry units or topography. Keratometry is based on the principle that distance between reflected mires on the cornea increases as corneal curvature decreases. These mires are projected onto the paracentral cornea rather than the cornea's true center.
Topography works similarly, with topography units projecting concentric mires onto the corneal surface. Measuring distances between mires in the paracentral 3 to 4 mm of the cornea at ∼1000 points yields a radius of curvature that units automatically convert into diopteric power (simulated keratometry [Sim-K],TMS topography, Tomey, Erlangen, Germany) using a preprogramed refractive index. Two assumptions regarding topography or keratometry are that (1) the cornea is a true spherical surface and (2) the power of the cornea's paracentral 3 to 4 mm is not significantly different from that of the central cornea. These assumptions are clinically acceptable because keratometry and topography yield values that predict accurate IOL power in most normal eyes. In reality, the cornea is a prolate, aspheric refractive media with progressive flattening toward the periphery.
In most keratometry and topography units, the cornea's refractive index is assumed to be 1.3375. This value is convenient because a cornea with a 7.5-mm radius of curvature has a diopteric power of 45.00 mm on the keratometer scale. However, the index is based on Gullstrand's model eye rather than on actual measurements [22]. In this model, 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 until recently the posterior corneal curvature could not be directly measured. To compensate, the eye model assumes a fixed ratio between anterior and posterior surfaces, then uses this ratio to determine posterior corneal curvature and subsequently posterior corneal power (Fig. 1).

Sources of error in corneal power determination
Considering that different types of refractive surgery fundamentally alter corneal shape and power, the usual assumptions may not be valid and may be the sources of error in determining corneal power. In this review of possible error sources, we have divided corneal refractive surgery into RK and excimer keratectomy (PRK, LASIK, LASEK).

Radial keratotomy
In RK, deep radial incisions are made in the peripheral cornea while sparing the central cornea. RK steepens the peripheral cornea and flattens the central cornea, resulting in a hyperopic shift and a proportionally greater flattening of the cornea in the center compared with the paracentral cornea [23]. This creates an abrupt change from treated to untreated cornea. Attempting larger corrections with RK increases the number and length of incisions, effectively decreasing the size of the optical zone. Because keratometry and topography units measure radius of curvature in the cornea's paracentral 3 to 4 mm, measured diopteric power represents the paracentral cornea, which in post-RK eyes is significantly steeper than the central cornea. The measured zone also increases in size further from the central cornea as the cornea becomes flatter, resulting in overestimation of cornea power [24,25].

Excimer keratectomy: myopic LASIK and photoreactive keratotomy
The ability of large optical zones to decrease postoperative glare and halos has become evident with increased LASIK and PRK experience, and optical zones greater than 5 to 6 mm are now considered routine. As a result, the paracentral radius of curvature determined by topography or keratometry would be expected to closely approximate central corneal curvature. In clinical experience, however, when the radius of curvature is converted into diopteric power, this calculated value overestimates central corneal power [4][5][6][7][8][9][10][11][12]. The key to understating this error is the cornea's refractive index, assumed to be 1.3375. This number works well for normal prolate corneas but is not applicable to corneas that have undergone LASIK or PRK for two reasons.
First, after eximer keratectomy, anterior corneal surface changes, but the posterior corneal surface remains unaltered. Seitz et al. [26] studied posterior corneal power using Orbscan (Bausch & Lomb-Orbtek Inc., Salt Lake City, UT, USA) before and after LASIK, showing that with a residual bed thickness of 250 µm or more, changes in posterior corneal power after LASIK were minimal, although borderline statistically significant. Sonergo-Krone et al. [27••] found small changes in posterior corneal power after LASIK but large changes in anteriorposterior power ratio. These studies indicate a fundamental deviation from the traditional Gullstrand's model with its fixed anterior-posterior ratio. Changing anterior-posterior power alters the cornea's effective refractive index in direct relation to the amount of keratectomy. In the original Gullstrand model, for every 9% change in ratio, effective corneal power is changed by 0.5 diopters [22].
Another factor that contributes to change in refractive index after refractive keratectomy is variation in corneal refractive index, as shown by Patel et al. [28], who found the index of refraction to be slightly different in different layers. Because excimer laser selectively removes anterior stromal layers and leaves the posterior stroma intact, it can change the cornea's total refractive index. Removing more tissue is also expected to produce greater change in refractive index. This is supported by the observed correlation between depth of ablation and underestimation of IOL power after myopic PRK [12,29].

Excimer keratectomy: hyperopic procedures
Little, if any, experience with cataract surgery after hyperopic excimer keratectomy has been reported. Because these treatments cause steepening of the central cornea with large optical zones, paracentral radius of curvature, measured by manual keratometry or topography, should be a fairly accurate estimation of central curvature. As in myopic treatments, the anterior-posterior corneal power ratio is expected to change, although in the opposite direction. Therefore, using the standard refractive index would theoretically underestimate corneal power and result in unexpected myopia after IOL implantation.
In a recent study, we analyzed eight eyes after hyperopic LASIK, using pre-LASIK keratometry and amount of hyperopic treatment to predict a fictitious post-LASIK IOL power. In each case, predicted IOL power was Used with permission from Olsen [22]. lower than IOL power determined by standard post-LASIK keratometry [13]. Despite lack of actual implantation, this study indicated that using post-hyperopic LASIK standard keratometry could theoretically result in IOL power overestimation and unexpected myopia.

Conductive keratoplasty and laser thermokeratoplasty
A literature search for cataract surgery and IOL power determination after conductive keratoplasty and laser thermokeratoplasty found no case reports. Data are not available to evaluate the similarity of conductive keratoplasty and laser thermokeratoplasty with hyperopic LASIK or PRK. To our knowledge, anterior-posterior corneal curvature in these patients has not been studied.

Summary
Manual keratometry after myopic LASIK, PRK, and RK overestimates corneal power and underestimates IOL power. The causes differ for RK and LASIK/PRK. In LASIK/PRK, error is directly proportional to the amount of keratectomy. Manual keratometry after hyperopic LASIK and PRK theoretically underestimates corneal power and results in IOL power overestimation, also in direct proportion to the amount of correction.

Methods to improve intraocular lens power determination
Several methods can improve IOL power accuracy after corneal refractive surgery. No single approach has been studied in a large sample, and some are based purely on theory. Most cases also require knowledge of prerefractive surgery data that may not be available to cataract surgeons. Proposed methods include use of topography to measure central corneal power, advanced IOL calculation formulas, contact lens overrefraction, clinical history, nomogram-based adjustment, corneal power determination by directly determining posterior curvature, and intentional overcorrection targeting for myopia.

Topography/videokeratography
Topography and simulated videokeratoscopy are suggested to improve central corneal power measurements in post-refractive surgery eyes. Maeda et al. [25] developed a videokeratographic method to calculate corneal power within the pupil. The study showed that average central power differed from standard keratometry in post-refractive surgery eyes having small optical zones and large attempted corrections; yet, values in normal corneas were equivalent. Theoretically, this method offers advantages in eyes with small optical zones. Cuaycong et al. [29] compared manual keratometry with keratometry derived from computerized videokeratography to determine IOL power in normal eyes without prior refractive surgery and found that the computerized videokeratography values were more accurate. However, a follow-up study of normal corneas by Husain et al. [30] found that the corneal powers derived from computerized videokeratography were less accurate than those from standard keratometry. In a small case series of cataract surgery in post-RK eyes, Celikkol et al. [31] concluded that corneal powers derived from computerized videokeratography were more accurate than routine methods. By contrast, Ladas et al. [32] reported a case in which topographyderived corneal power resulted in inaccurate IOL power determination, and Seitz et al. found manual keratometry to be superior to topography-derived values in postmyopic PRK eyes [12,33].
In summary, using videokeratography with programs like EyeSys System 2000 Software [EyeSys Vision, Houston, TX, USA] to determine central corneal power may be beneficial after RK with small optical zones. However, videokeratography has not been found to be superior to manual keratometry in post-PRK/LASIK corneas, and its reliability and accuracy have not been verified. Odenthal et al. [34] noted that using the Hoffer Q formula after myopic LASIK decreased but did not eliminate IOL power underestimation. Nevertheless, these studies offer no clear-cut conclusions regarding the accuracy of different modern theoretic formulas, although their use is probably advantageous in post-refractive surgery eyes.

Contact lens overrefraction
This method uses a hard contact lens of known power and base curve to determine true corneal power. After patients have undergone refraction, a plano hard contact lens is placed on the eye, and overrefraction is performed. If no difference exists between refractions, corneal diopteric power is the same as the contact lens base curve. If overrefraction is more myopic than refraction without the contact lens, the lens is steeper than the cornea. The change in refraction is subtracted from the contact lens base curve to yield corneal power. If overrefraction is more hyperopic than the contact lens refraction, the cornea is steeper than the lens. Change in refraction is added to the contact lens base curve to calculate corneal power. Contact-lens-derived corneal powers have been shown to correlate well with manual keratometry in normal corneas when visual acuity is better than 20/70 [35]. Once the visual acuity is lower than 20/70, which may be the case in many patients with cataract, the correlation is poor. The accuracy of this technique is not established in post-refractive surgery eyes.

Clinical history
Originally proposed by Holladay [36] to determine corneal power after radial keratotomy, this method was advocated by Hoffer [37] for use in post-LASIK/PRK eyes [37]. Using this method requires a knowledge of keratometry prior to refractive surgery as well as induced refractive change (change in SE) before the development of cataract. These values are used to determine a calculated corneal power as follows. Calculated corneal power is then used for IOL power determination. Originally, change in SE induced by refractive surgery was determined at the corneal level. However, a recent study found increased accuracy when using change in SE at the spectacle level instead [34]. In a follow-up editorial, Hoffer [38] recommended calculating change in SE at the spectacle level. The following actual case example shows a calculated corneal power lower than manual keratometry readings after LASIK, which should decrease IOL power underestimation. The major shortcomings of this approach are that accuracy and reliability have not been established in large series, and it requires a knowledge of keratometry values prior to refractive surgery, which cataract surgeons may not have. Its major flaw, however, is assuming a one-toone relation between corneal diopteric power and refraction (ie, if corneal power changes by one diopter, refraction changes by one diopter). Studies by Patel et al. [39] and Hugger et al. [40] analyzed changes in refraction and corneal power after refractive surgery in a large sample. Both studies found less change in corneal power than in refraction and concluded that this was due to change in the cornea's effective refractive index. This indicates that the clinical history method reduces IOL power errors, but the degree of accuracy is not yet established.

Nomogram-based correction
By analyzing eyes after myopic and hyperopic LASIK, we developed a theoretic nomogram to correct IOL power after these procedures [13]. The nomogram is based on four established clinical premises.
1. IOL power after myopic corneal surgery has to be higher than before surgery. 2. IOL power after hyperopic corneal surgery is expected to be lower than before surgery. 3. To maintain emmetropia, the difference between IOL powers before and after refractive surgery must compensate for refraction changes. 4. For every diopter of change in IOL power, refraction at the spectacle plane with a vertex distance of 12.5 mm changes by only 0.67 diopters.
The fourth and most important premise is based on the following formula, with E as resultant refractive error, P as IOL power for emmetropia, and I as implanted IOL. The formula is based on analysis of 2500 eyes by Sanders and Kraff [41].
Taking these basic premises into account, the following formulas can predict IOL power to maintain emmetropia after refractive surgery.
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) Using these formulas, we predicted IOL powers for 19 eyes after myopic LASIK and 8 after hyperopic LASIK, and compared predicted IOL with an IOL power by post-LASIK manual keratometry. We calculated the differences between predicted and manual keratometry IOL power values. After performing linear regression, we found the following.
Post-myopic LASIK: Step 1: Use standard post-LASIK keratometry, axial length, and SRK-T formula to determine IOL power. 14.76 diopters for a PCIOL with A constant 118.9 Step 2: Use nomogram (Table 1) to adjust IOL power. 14.76 + 2. 15 = 16.91 Step 3: Implant a 17.50 acrylic lens model SA60AT (Alcon Laboratories, Fort Worth TX). Postoperative refraction: plano The shortcomings of this approach are that it is purely theoretic and has not been tested in large series. Moreover, the relation between IOL power and refraction, observed by Sanders and Kraff [41], may not apply to post-LASIK eyes. At the time of writing this manuscript, we had used this nomogram for IOL implantation in 13 eyes after myopic LASIK with excellent results (unpub-lished data). Further prospective data of this method's accuracy are currently being collected.

Optical formula corneal power calculations
Using Gaussian optics, the cornea's true power can theoretically be determined regardless of previous surgical procedures. This approach considers the cornea to have two refractive surfaces, anterior and posterior. The theoretic power of the cornea is calculated using corneal thickness and refractive indexes of air, cornea, and aqueous humor through a series of formulas. Hamed et al. [42] used this method to look at 100 post-myopic LASIK eyes. The authors used the following optical formula to directly calculate corneal refractive power, where n 0 = refractive index of air, n 1 = refractive index of anterior surface of cornea, n 2 = refractive index of aqueous humor, r 1 = anterior radius of curvature, r 2 = posterior radius of curvature, and d = corneal thickness (Fig. 1). Good correlation was noted between this calculated corneal power and the clinical history method. However, the study assumed a fixed ratio between anterior and posterior curvature of the cornea based on the Gullstrand eye model because posterior corneal curvature could not be directly measured. In reality, the ratio between posterior and anterior corneal curvature is not constant and changes significantly after refractive surgery [26,27••]. The authors also had to calculate an effective index of refraction utilizing the historical method. This circular reasoning could explain the strong correlation with the clinical history method. To our knowledge, no actual IOL implantations based on this formula have been performed.

Direct corneal power measurements
The major shortcoming with most of these techniques is the need to know pre-refractive surgery values, such as refraction and keratometry. An ideal method would determine corneal power accurately without these values. True corneal power could be determined regardless of refractive status if anterior and posterior corneal curvatures could be directly measured. However, direct mea-   [44] found that the cornea's central 4.0-mm zone after myopic LASIK measured by Orbscan correlated best with expected corneal power after LASIK. Although intriguing, this approach is purely theoretic and, to our knowledge, has not been used for actual IOL implantation. In addition, the actual measurement of the cornea's central 2 mm was difficult even for the studies' authors. So, despite promising technology, the accuracy and applicability of these power measurements have not been established clinically.

Targeting myopia
When regular keratometry is performed after myopic refractive surgery, selective choice of an IOL to target myopia when other data are not available may reduce refractive surprises. In analyzing eyes undergoing cataract surgery after RK, Chen et al. [45] found that selecting an IOL targeting −1.50 in post-RK eyes reduced the frequency of postcataract hyperopia by 60%. Some initial hyperopia immediately after cataract surgery also regresses over several weeks, possibly because of inherent instability of the post-RK cornea [46,47].

Conclusion
Current methods of IOL power determination after corneal refractive surgery are limited by a lack of actual clinical experience on a large scale and by the theoretic nature of all the calculation methods. However, based on accumulated clinical experience, several useful guidelines can be followed. In addition to the recommendations below, the surgeon can consider providing patients with pre-refractive surgery keratometry and refraction and having them keep these records for possible cataract surgery in the future.
1. If only pre-and post-corneal surgery refraction are available, use post-refractive surgery keratometry and axial length and adjust IOL power using a theoretic nomogram (Tables 1 and 2). 2. If pre-refractive surgery keratometry values and refraction are available, predict IOL power theoretically using clinical history or nomogram-based methods. If using the clinical history method, determine changes in spherical equivalent at the spectacle plane rather than the corneal level. 3. If data are not available and patients have visual acuity >20/70, consider the contact lens method. 4. If data are not available and patients have visual acuity <20/70, consider targeting −1.50 to −2.00 for postmyopic refractive surgery patients and +1.00 for posthyperopic refractive surgery patients. 5. Some hyperopia in the immediate post-cataract surgery can regress in RK patients, so delay intervention through lens exchange or further refractive surgery until the refraction is stable. 6. Inform patients who have had previous corneal refractive surgery of limitations in accurate IOL power calculations. As part of their informed consent for cataract surgery, specifically discuss the possible need for corrective refractive aids, repeat corneal refractive surgery, or IOL exchange.