IOL Power Calculations After LASIK and PRK

Calculating IOL power in eyes that underwent corneal refractive surgery is likely to remain a debated issue—until we can rely on a method that directly measures the corneal power after laser corneal surgery (ie, LASIK, LASEK, PRK). This ideal method should provide the clinician with the correct corneal power measurement, independent from the availability of perioperative data (eg, preoperative K-values, attempted correction). This method does not yet exist, but the number of patients needing cataract surgery after corneal refractive surgery is increasing. Patient expectations are also increasing.

As a result of the ongoing effort to provide patients with optimal refraction, ophthalmologists worldwide have contributed to developing and publishing an increasing number of formulas. By the end of 2006, we counted as many as 25 formulas and/or methods. Being able to choose from many possibilities may increase the chances of achieving the desired outcome, but it also raises concern for the ophthalmologist: Do I know all of them? Which one works best for my patient?

To better understand the issue of IOL power calculation, it is wise to look first for the reasons leading to miscalculation. Errors mainly depend on two factors. First, current keratometers and videokeratography systems do not correctly measure central corneal power in these eyes, because they instead measure the curvature of the anterior corneal surface. This measurement is converted into keratometric diopters, with a standardized keratometric index of refraction (usually 1.3375) on the basis of the paraxial equation P= (n-1)/r, where P is the corneal power (diopters), n is the standardized keratometric index of refraction, and r is the radius of the anterior corneal surface (meters). The keratometric index of refraction refers to a theoretical single refractive lens—representing the anterior and posterior corneal surfaces—and assumes a stable ratio of anterior-to-posterior corneal curvature. Of course, LASIK and PRK disrupt this ratio, making the standard keratometric index of refraction invalid. The second problem is that most IOL power calculation formulas incorrectly predict the effective lens position. Using the postrefractive surgery K-value causes effective lens position underestimation and contributes to IOL underestimation. Aramberri solved this problem by introducing the double-K method. The prerefractive surgery K is used to calculate the effective lens position, and the postrefractive surgery K produces the IOL power using the vergence formula.^1,2 The methods developed to calculate IOL power after LASIK and PRK are classified according to the required perioperative data (Table 1).

METHODS REQUIRING PREOP KERATOMETRY, PREOP REFRACTION, AND POSTOP REFRACTION

Clinical history method. This method calculates postoperative corneal power by algebraically adding the surgically induced refractive change to the preoperative K-readings.^3,4 The result is given by the formula: K = Kpre + Rpre – Rpo, where Kpre = preoperative corneal power, Rpre = preoperative refraction, and Rpo = postoperative refraction. It is still considered the gold standard to assess corneal power after corneal refractive surgery for myopic and hyperopic procedures, although refractive surprises cannot be excluded.^5-10 The application of the double-K method seems to remarkably improve the predictive power of the clinical history method and enhances the precision of its results using the refraction at the corneal plane, which is optically correct. Thus, making it no longer necessary to perform the correction at the spectacle plane, traditionally adopted to prevent hyperopic results in patients who underwent myopic correction.^1,5,11-13

Unfortunately, this method cannot be used when presurgical K-readings and the amount of refractive correction are unknown, or when the postoperative refraction is affected by nuclear sclerosis-induced or axial length progression myopia, which may significantly change the refraction and render the calculation invalid.

Corneal bypass method (Wake-Forest method). The corneal bypass method assumes that the patient has not had either LASIK or PRK; prerefractive surgery K-values and current axial length are used to calculate the IOL power, aiming the postoperative refraction at the surgically induced refractive change.^14,15 The IOL power achieved by this method is considered as equivalent to the power of the natural crystalline lens and is expected not to change the refraction in a patient who achieved emmetropia following excimer laser surgery and must later undergo phacoemulsification and IOL implantation.

The preliminary results seem interesting but need to be validated by larger studies. Additionally, this method has the same important limitation as the clinical history method, as its predictive power may be less in cases where the postoperative refraction is unreliable, thus making it hard to establish the net refractive change.¹⁴

Feiz-Mannis' formula. The formula developed by Feiz and Mannis is based on the assumption that for every diopter of change in IOL power, 0.70 D of refractive change will be achieved at the spectacle plane.¹³ Accordingly, Feiz and Mannis suggested calculating the IOL power for emmetropia using prerefractive surgery keratometry (ie, as if the patient had not undergone excimer laser surgery) and then adding (for previously myopic eyes) or subtracting (for previously hyperopic eyes) the value corresponding to the attempted correction divided by 0.7. Few studies have tested this formula; results were satisfactory in all but one case.^9,11-13 In eyes that underwent myopic laser correction, it may be necessary to aim for a final refraction of -0.50 D, as this formula may lead to a slight IOL power underestimation.¹²

METHODS REQUIRING ONLY PREOP KERATOMETRY

Separate consideration of anterior and posterior corneal curvature. The previously described methods cannot be adopted when preoperative keratometry is the only known parameter and if there are no sufficiently reliable data about the attempted correction. In this event, the best option is probably represented by separately considering anterior and posterior corneal curvatures, as described by Seitz and Speicher.^16,17 In this method, preoperative K-readings suffice on their own and are based on the assumption that the total refractive power of the cornea (P) may be considered as the sum of the power of the anterior (Pa) and posterior (Pp) corneal surfaces, as shown in the formula: P = Pa + Pp = (n2–n1)/r1 + (n3–n2)/r2, where n1 is the refractive index of the air (= 1); n2 is the refractive index of the cornea (= 1.376); and n3 is the refractive index of the aqueous humor (= 1.336). Both preoperatively and postoperatively, we can always calculate Pa by multiplying the corneal power (ie, measured by keratometry or simulated keratometry [Sim-K]) by 1.114.^11,18 Hence: Pa = Sim-K X 1.114. Once we know the preoperative Pa, the negative-valued Pp can be easily calculated as the difference between the total and the anterior surface corneal powers, as shown in the formula: Pp = P – Pa = Sim-K – (Sim-K X 1.114).

According to this method, the true corneal power (K) after LASIK or PRK can be calculated by adding the postoperative Pa to the preoperative Pp, which is assumed not to be significantly altered by surgery. The formula is: K = postop Pa + preop Pp = postop Sim-K X 1.114 + (preop Sim-K – preop Sim-K x 1.114). The reliability of this method still awaits clinical confirmation. Theoretically, results are promising, on condition that the double-K formula was also used.¹²

Jarade's formula. A quite similar alternative option is the formula published by Jarade and Tabbara.¹⁹ It is also based on the consideration of both anterior and posterior corneal surfaces. It requires the pre-LASIK K-value (Kpreop) and pre- and post-LASIK corneal radii measured by autokeratometry (respectively Ra-preop and Ra-post). The postexcimer laser K-value (K) is calculated as follows: K = Kpreop – [(Nc–1) X (Ra-post – Ra-preop) / (Ra-post – Ra-preop)], where Nc is the corneal refractive index of 1.376. Again, this method needs further validation in the clinical setting.

METHODS REQUIRING ONLY PREOP REFRACTION

Although the cataract surgeon may find it difficult to obtain pre-LASIK or PRK K-readings in many patients—especially if the clinical chart is unavailable—the preoperative refraction is easier to obtain, as this value may be retrieved even from an old pair of spectacles or a prescription. When the preoperative refraction is the only available parameter, we have several options for calculating postoperative corneal power. Some of these (ie, Feiz-Mannis' nomogram, Latkany's formulas, Masket's refractive history method)^7,20,21 are based on linear regression formulas, the results of which should be added to or subtracted from the IOL power calculated using post-LASIK/PRK K-readings (ie, as if the eye had not undergone photorefractive surgery). The remaining formulas aim to modify the post-LASIK/PRK K-readings, either by correcting the keratometric index of refraction on the basis of the refractive change,^22-24 or by adjusting the K-readings of videokeratography and keratometry.^8,11,25,26 Of course, all the following methods assume that the surgically induced refractive change corresponds to the preoperative refraction.

Feiz-Mannis' nomogram. After confirming that K-readings from manual keratometry lead to unwanted hyperopia in eyes that underwent myopic LASIK, Feiz et al explored the relationship between the surgically induced refractive change at the spectacle plane and the IOL power calculation error (performed using postoperative keratometry). They detected a statistically significant linear relationship for both myopic and hyperopic corrections.¹³ For previously myopic eyes, the diopters of underestimation are derived from the formula: diopters of underestimation = -0.231 + (0.595 X refractive change), where refractive change is the absolute value (ie, 4.5 for a patient with a preoperative defect of -4.50 D).

Hence, the corrected IOL power (P) is obtained by subtracting the resulting value from the target IOL power (PTARG) (eg, for emmetropia), calculated using the post-LASIK keratometry. The formula is: P = PTARG + 0.231 – (0.595 X refractive change). For previously hyperopic eyes, the formula is: P = PTARG + 0.751 – (0.862 X refractive correction).

Subsequent studies evaluating the formula have reported excellent results in about half of patients; refractive surprises have still occurred.^9,12,20

Latkany's regression formula. Latkany et al⁷ investigated the relationship between the error in IOL power estimation, as calculated on the basis of conventional keratometry and the amount of refractive correction performed by excimer laser. They found that such a relationship is linear and is expressed by the following formulas: using average K: -(0.46 X Pre-Rx + 0.21), and using flattest K: -(0.47 X Pre-Rx + 0.85), where Pre-Rx = prerefractive surgery myopic spherical equivalent.

The result of the regression formula is then added to the target IOL power, calculated using the corneal power measured by conventional keratometry. Although there is limited clinical experience, theoretical comparisons showed the formulas to be quite promising.¹²

Masket's refractive history method. The first step is the same as in the above-mentioned formulas by Feiz and Latkany, in that the IOL power is calculated as if the eye did not undergo previous refractive surgery. Thereafter, the target IOL power obtained is adjusted according to the formula: IOL power adjustment = -0.326 X refractive correction + 0.101.

This value is added to the target IOL power calculation in patients who previously underwent myopic laser correction, or subtracted in patients who underwent hyperopic laser correction. The final formula is: P = PTARG – 0.326 X refractive correction +0.101. Dr. Masket recommends using the SRK/T formula for myopic eyes and the Hoffer Q-formula for hyperopic eyes, on which his results are based. The first results appear promising in both hyperopic and myopic patients.²¹

Jarade, Savini, and Camellin's formulas to calculate postrefractive surgery keratometric index of refraction. We have already stated that the conventional keratometric refractive index (n=1.3375) adopted to convert the anterior corneal curvature into diopters, is inaccurate after LASIK and PRK. Several investigators have analyzed whether changing it—on the basis of the amount of myopic correction—may improve IOL power calculation predictability after excimer laser surgery. In all cases, once the new keratometric index of refraction is known, the corneal power (K) is obtained using the standard formula K=(n-1)/r, where r is the anterior corneal radius of curvature.

The proposed formulas to calculate post-LASIK/PRK keratometric index of refraction are the following: effective refractive index = 1.3375 + 0.0014 X AMC (Jarade);²² postrefractive surgery index of refraction = 1.338 + 0.0009856 X AMC (Savini);²³ and postrefractive surgery relative keratometric refractive index = 1.3319 + 0.00113 X AMC (Camellin),²⁴ where AMC = amount of myopic correction. With all formulas, the resulting refractive index progressively decreases as the amount of myopic correction increases.

Although preliminary results are interesting, clinical experience with these formulas is still limited. It is likely that satisfactory results are obtained only if the double-K method is used to calculate IOL power.

Shammas' refraction-derived corrected keratometric value. Shammas et al25 developed another method to correct the K-reading by keratometry. They observed a correlation between the amount of refractive correction at the corneal plane and the overestimation of corneal power by videokeratographer compared with the clinical history method. The corneal power is calculated by the formula: corrected keratometry = Kpost (-0.23 X CRc), where Kpost is the postrefractive surgery keratometry and CRc is the amount of myopia corrected at the corneal plane. To our knowledge, this method has never been tested in a clinical setting, whereas theoretically its predictive power is questionable.¹²

Adjusted effective refractive power. Another method is available for surgeons who have the EyeSys Corneal Analysis System (EyeSys Technologies, Inc., Houston). This was proposed in 2002 and reanalyzed by Koch et al in 2004.^8,11 When applied to patients who underwent myopic surgery, the corrected keratometric power is calculated by multiplying the refractive correction by 0.15 D and subtracting this value from the measured effective refractive power (EffRP), which is the calculated mean refractive power of the cornea over the central 3 mm. It is displayed in the Holladay Diagnostic Summary. The investigators showed that the adjusted EffRP offered the highest predictability after myopic LASIK. EffRP may also be adjusted to calculate corneal power in eyes that underwent hyperopic surgery,²⁷ according to the following formula: EffRP adjusted = EffRP + 0.162 (SEpre – SEpost) –0.279, where SEpre and SEpost are the pre- and postrefractive spherical equivalents, respectively.

Ronje method. Keratometry readings after myopic LASIK or PRK can be simply adjusted by subtracting 25% of the correction performed by the excimer laser from the flattest K value,²⁶ as shown in the following formula: K = KPOFLAT + 0.25 X refraction change.

METHODS THAT DO NOT REQUIRE PREOP DATA

The most challenging task is to obtain a reliable corneal power when no preoperative data are available. Several investigators have offered attempts, but a gold standard is still lacking.

Contact lens method. First described by Frederick Ridley and later by Joseph Soper, historically this is one of the most important methods. Until a few years ago, it was the only choice to calculate corneal power when both preoperative keratometry and refraction were not available.^3,4,28,29

Once the spherical equivalent at the spectacle plane is determined by trial spectacle lenses, a plano PMMA hard contact lens of known base curve (eg, 40.00 D) is placed on the patient's eye, and the refraction is reassessed (ie, contact lens over-refraction). The corneal power (K) is the result of the difference between the contact lens over-refraction (RCL) and the spherical equivalent refraction without the contact lens (RNoCL), as shown in the formula: K = BCL + PCL + RCL – RNoCL, where BCL is the contact lens base curve and PCL is the contact lens power, which is usually zero.

This method is strongly limited because it cannot be applied in patients with low visual acuity (ie, less than 20/80) induced by cataract.³⁰ Moreover, several investigators recently questioned its predictability theoretically and practically.^11,30-34

Separate consideration of anterior and posterior corneal curvature: Savini-Barboni-Zanini's method, Maloney's method, Koch's method. These methods are variations of the formula proposed by Seitz and Speicher, whereby the posterior corneal surface power is calculated from the preoperative K-reading and subsequently subtracted from the anterior corneal surface power.^16,17 They may be useful when the preoperative K-reading is missing, and we need a standard value for the posterior corneal surface power. This is -4.98 D, according to Savini-Barboni-Zanini, and -6.10 D according to Maloney and Koch.^11,12

The resulting formulas are: K = 1.114 KPO -4.98 and K = 1.114 KPO -6.1, where K is the calculated K-value and KPO is the post-LASIK/PRK K-value. It is important to note both Maloney and Koch recommend using the power at the center of the axial map instead of the Sim-K.

Although clinical experience with these methods is not extensive, it seems wise to use them in conjunction with the double-K formula by Aramberri.^11,12 Because the latter, to be applied, requires a preoperative keratometry or videokeratography, a reasonable solution may be offered by the Koch and Wang nomogram. This is designed to provide the values of the Double-K formulas by adjusting the IOL power on the basis of axial length and refractive correction.³⁵

Shammas' no-history method (clinically derived corrected keratometric value). This method, which derives the corneal power from the clinical history method, calculates it according to the equation: K = 1.14 KPO – 6.8. The investigators recommend entering the value obtained into the Shammas post-LASIK formula to finally calculate IOL power. By doing so, they recently reported excellent results that need to be validated by further studies.^25,36

Ferrara's theoretical variable refractive index (TRI). The formula developed by Ferrara et al³⁷ is based on the observed correlation between the change in the corneal refractive index after excimer laser surgery and the axial length (AL), as shown by the formula: TRI = -0.0006 X AL2 + 0.0213 X AL+ 1.1572, where TRI = theoretical refractive index and AL = axial length. Corneal power (P) can be calculated using the formula: P = (TRI –1)/r, where r is the corneal curvature in meters. Even if preliminary results look promising, there have not yet been conclusive studies confirming the predictability of this method. Theoretically, it seems to calculate a low corneal power, leading to a risk of myopic refraction after IOL implantation.¹²

Rosa's correcting factor method. This method is another worthwhile option in the event of missing preoperative data. The postoperative radius, as measured by videokeratographer, is multiplied by a correcting factor (range, 1.01 to 1.22) that depends on the axial length of the eye. The dioptric corneal power is then obtained by means of the formula: K = (1.3375-1)/corrected radius.³⁸

Rosa's method also seems to lead to a remarkably low mean corneal power with the consequent risk of myopic refraction after cataract surgery.^12,22,36

Aphakic refraction technique. During phacoemulsification, when the cataract has been removed and the IOL has not yet been implanted, it is possible to calculate the IOL power for emmetropia. There are two methods. Ianchulev et al³⁹ assess the aphakic refraction by a portable autorefractor (vertex distance, 13.1 mm) while the patient is on the operating table. Mackool waits 30 minutes and measures the aphakic refraction in an office examing room.⁴⁰

The formulas for IOL power calculation are slightly different: Ianchulev, P = 2.02 x AR + (A -118.84); and Mackool, P = 1.75 X AR + (A -118.84), where P = target IOL power; AR = aphakic refraction; and A = A-constant for intended IOL style. The results reported in small groups of patients seem excellent, but these concepts need further validation.

Gaussian optics formula (using posterior corneal curvature measurements by Orbscan [Bausch & Lomb, Rochester, New York] or Pentacam [Oculus Optikgeräte GmbH, Wetzlar, Germany]). All previously described methods involve assumptions to compensate for the unknown posterior corneal curvature or index of refraction, and thus provide only an indirect true corneal power estimate. Theoretically, it would be better to directly determine the corneal power (P) by using the Gaussian optics formula (or thick lens formula): P = P1 + P2 – (d/n) (P1P2), where P1 and P2 are the power of two lenses separated by a distance (d) in a medium of refractive index (n). If we refer to the corneal surfaces, the formula can be represented as: P = (n1-n0)/r1 + (n2-n1)/r2 – (d/n1) x [(n1-n0)/r1] X [(n2-n1)/r2], where r1 and r2 are the radius of curvature of the anterior and posterior corneal curvature, respectively.

Until recently, it was not possible to measure r2. Today, two instruments allow us to take such measurements: the Orbscan II and the Pentacam. The early results are encouraging. Cheng and Lam, in a theoretical study comparing the corneal power as calculated by clinical history method and the Gaussian optics formula with Orbscan II measurements in patients that had undergone LASIK, did not find any statistically significant differences.⁴¹

Alternatively, instead of being entered into the Gaussian optics formula to obtain the true corneal power, the Orbscan II data may be directly entered into modern IOL power calculation formulas.

A recent study evaluating this approach showed that several measurements by the Orbscan II closely reflected the actual changes of corneal power after refractive surgery and thus may be used to reliably calculate IOL power after LASIK or PRK. Among these measurements, the averaged total axial power in the central 5 mm of the cornea and the total optical power in the central 4 mm, using the Holladay 2 formula, were the most likely to prevent hyperopic refractive surprises.³⁴ Additionally, a previous investigation found that the 4-mm total optical power map of the Orbscan II closely reflected the refractive change induced by LASIK and should be used for IOL calculation after LASIK. The same investigators reported that the 2-mm total mean power should also be considered a reliable option.⁴² No one has yet demonstrated that these values lead to satisfactory results in the clinical settings, and caution is thus warranted.

Entering data from the Pentacam into the Gaussian optics formula resulted in an underestimation of the corneal power compared with data from videokeratography in nonoperated eyes. Similarly, the Gaussian optics formula underestimated corneal power with respect to the clinical history method in eyes that underwent myopic and hyperopic laser surgery. The reason for these discrepancies are still unknown. An external application (ie, the BESSt formula, See article on page 45) had to be developed to address these differences and gave promising preliminary results.⁴³

Numerical ray tracing. When all preoperative data are unknown, IOL power may, alternatively, be calculated by a new software using numerical ray tracing (Oculix; (Ingenieurbüro der Leu, Hillerse, Germany).⁴⁴ Explaining the technological basis of ray tracing is beyond the aim of this article; however, it is noteworthy that the preliminary results seem quite interesting, although postoperative hyperopia cannot be excluded, as it was noted in six of 10 eyes.

Until a direct, user-friendly, and precise method of calculating corneal power after excimer laser surgery becomes available, we have to become familiar with the formulas described previously. This task is not easy, as the number of options increases year after year. For this reason, we have developed a computer spreadsheet application that automatically calculates the corrected K-value and adjusts IOL power according to each of the methods. It also suggests the optimal choice. The Hoffer/Savini LASIK IOL Power Tool was presented at the 2006 American Academy of Ophthalmology Annual Meeting, in Las Vegas. We are now working out the kinks in the program, to be sure that there are no errors. We will be offering it free of charge to anyone who requests it by e-mail to KHofferMD@aol.com.

Kenneth J. Hoffer, MD, FACS, is Clinical Professor of Ophthalmology at the University of California, Los Angeles, and practices at St. Mary's Eye Center, in Santa Monica, California. He states that he does not have any financial interest in the products or companies mentioned. Dr. Hoffer may be reached at +1 310 451 2020; khoffermd@aol.com.

Giacomo Savini, MD, is in private practice at the Centro Salus, in Bologna, Italy. Dr. Savini states that he has no financial interest in the products or companies mentioned. He may be reached at +39 051 555311; fax +39 051 524486; or giacomo.savini@alice.it.

Maurizio Zanini, MD, is in private practice at the Centro Salus, in Bologna, Italy. Dr. Zanini states that he has no financial interest in the products or companies mentioned. He may be reached at +39 051 555311; m.zanini@eyeproject.com.