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Updated: Jan 6, 2022


Jaime Aramberri MD

Miranza Begitek Clinic. San Sebastian. Spain

Okular Clinic . Vitoria. Spain


Corneal refractive surgery (CRS) changes corneal shape and, therefore, corneal optics in order to focus the eye, eliminating all kinds of ametropia. Excimer and femtosecond laser techniques reshape only anterior cornea, while radial keratotomy flattens both anterior and posterior surfaces. These changes affect IOL power calculations and can lead to error depending on the calculation method.


There are three main sources of error:

1.- ELP (Estimated Lens Position) prediction error:

Most classical and modern formulas use corneal curvature as predictor of IOL position. The steeper the cornea the deeper the predicted pseudophakic ACD. However CRS will drive this relationship into error as IOL plane is not related to present corneal curvature anymore.

After myopic surgery, (LASIK, PRK, SMILE or RK) cornea is flattened and any K-dependent algorithm will predict a too low ELP value, underestimating IOL power and inducing some hyperopic refraction shift. After hyperopic surgery (LASIK, PRK) the effect is just the opposite and myopic refractive error will be induced.

The magnitude of this error will depend mainly on K and IOL power and, depending on the algorithm, will range from 1 D of spectacle plane refraction error for 1 mm ELP error with IOL power of 18 D up to 1.50 D with IOL power of 26 D (indicative average figures).

Figure 1: ELP as a function of K for the same AXL (28 mm). Estimations by three different formulas: SRK/T, Holladay 1 and Hoffer Q

Depending on its design, some algorithms are more or less affected. For example Hoffer Q induces less error than Holladay 1 and SRK/T because its algorithm reduces the ELP change/K change ratio as values reach the extremes of the range (Figure 1).

Several formulas don´t use corneal curvature as ELP predictor and avoid this error: Haigis, Okulix, Olsen C-constant, CSO formula, etc.

2.- Corneal power measurement error:

Total corneal power, as defined by keratometric K value or topographic Sim K value, becomes erroneous after CRS. This parameter is calculated from the measured anterior curvature radius using an arbitrary corneal index of refraction, 1.3375, that is called keratometric standard index of refraction. This figure is accurate as long as the anterior to posterior surface curvature ratio is normal: 1.21 ± 0.02 (in many papers the provided ratio is the inverse, posterior/anterior with a value of 0.82 ± 0.02).

After myopic LASIK/PRK corneal anterior surface is flattened while posterior remains unchanged. This moves the ratio upwards which functionally means that posterior power will be more relevant for the total value. As result, K and Sim K overestimate corneal power. I.e. 37 D K value should be 36 D. This error obviously leads to underestimation of IOL power and produces a hyperopic refractive error.

After hyperopic LASIK/PRK the effect is just the opposite and IOL power will be overestimated producing a myopic shift in the final refraction.

There is a good correlation between anterior corneal curvature, which is directly related to the induced shape change by the laser, and anterior/posterior ratio, which means that a function can predict one variable from the other.

After radial keratotomy both anterior and posterior surfaces flatten and this decreases the anterior/posterior ratio in the way hyperopic laser correction does. Final refractive error will be myopic. The main difference with respect to laser corrections is that variability is high and there is not a good correlation with anterior curvature.

Figure 2: Ant/post ratio after CRS

The anterior/posterior ratio change can be very high after myopic laser, as it is a function of the induced flattening which can remain for many years. We have seen cases as high as 1.55 for very high corrections. Hyperopic changes are normally lower because attempted corrections used to be so and there is some regression of the induced steepening through the years. So typical values are between 1.10 and 1.21, which is curiously the same range radial keratotomy corneas fall within. Therefore the highest errors due to this reason will normally be found among high myopic laser surgeries (Figure 2).

Beyond the anterior/posterior proportion issue there is another source of error: Enlargement of analysis area after corneal flattening and decrease after corneal steepening. This is due to the fact that keratometers and topographers measure corneal radius of a central area with an approximate diameter of 3 mm. However this is true for the normal range of human curvatures, radii range between 7.03 and 8.44 mm, but not for very flat or steep corneas, where the analyzed area will increase and decrease respectively. Moreover the change in asphericity present in these corneas, particularly old treatments, creates a high gradient of curvature in the paracentral area, which means that a measurement 1.5 mm from the optical axis changes significantly when measured, i.e., 1 mm further.

This means that steeper than correct readings are obtained both after myopic and hyperopic laser. The effect is normally more important after myopic laser where K values are further away from the normal range. The effect drives the error in the same sense that ant/post ratio issue does after myopic laser and in the opposite sense after hyperopic laser.

3.- Model error:

Most IOL power calculation formulas work on paraxial pseudophakic eye models. Higher order aberrations (HOA) are neglected and this is an acceptable assumption in normal corneas. After CRS HOA are usually higher, especially in old treatments with small optical zones, and the paraxial model misses their optical effect. The most frequently involved aberrations can be found in the third and fouth Zernike orders. The former affecting the spherical equivalent calculation and the latter the astigmatism.


Understanding the sources of error allows adopting the correct strategy to get an accurate IOL power calculation:

- Corneal measurements must be adapted to the adequate analysis area.

- Corneal power must be calculated accounting correctly for the contribution of the posterior surface either by direct measurement or by an empiric algorithm. In the latter it has to be stressed that different algorithms should be used for post-myopic laser and post-RK cases, as the anterior/posterior ratio change is very different between these two situations. As RK ant/post ratio is more variable direct measurement is definitely recommended over estimation.

- A way to skip the corneal power issue is to input directly the measured anterior and posterior radii in a thick lens model, like different raytracing programs do.

- Once corneal power error is solved the calculation method has to estimate IOL position not using the cornea as a predicting variable to avoid the formula error: I.e. Haigis, Shammas PL, Okulix, Olsen C constant, etc. If the cornea is still used to predict ELP, then a Double-K formulation of that formula should be used: K pre CRS is used for the ELP prediction and K post CRS, with its adequate power correction, for the subsequent optical calculation.

- It should be emphasized that most regular formulas are designed to input the keratometric K or Sim K. Therefore total corneal power calculated by raytracing of the anterior and posterior surfaces or by the Gaussian equivalent power formula is not a valid parameter for them, and should be converted to match the reference plane of K. This is what some equivalent K values do: EKR, equivalent K reading, and TK, total K. The first in Pentacam and Cassini and the second in IOL Master 700.

- Another option is to export the central corneal topographic data to an exact raytracing program which can calculate the IOL power avoiding the previously mentioned errors and taking account of the higher order aberrations. This can be particularly relevant when the CRS is decentered or there are complications like ectasia, scarring or interface epithelium ingrowth, that increase corneal irregularity. The only commercial software, to my knowledge, that can perform this sort of calculations are: Okulix and CSO tomographers with a proprietary method (Sirius and MS39).

- A completely different approach is to calculate IOL power based on intraoperative aphakic refraction. The ORA system can obtain a reliable measurement by Talbot-Moiré aberrometry and take the 2nd order aberration, sphere-cylinder, to the IOL plane. The calculation is empirically optimized by a huge database and good results have been reported after CRS.

Having understood the criteria to perform a correct calculation in these cases, some of the multiple methods published through the years are displayed to show the historic evolution of these calculations. Some of them just offer an empirical IOL power adjustment while others correct thoughtfully the different sources of error in the process.

1.- Methods that require preCRS data:

1..1 Clinical History (1989):

K value is corrected algebraically adding the refractive change (RC) of the CRS at the corneal plane. Some papers have defended not applying the vertex correction in order to provide a stronger effect (in myopia).

1.2 Feiz- Mannis (2001):

The IOL power calculated with pre-CRS K value is adapted with RC applying the ratio: 0.7D spectacle plane / 1 D IOL plane.

1.3 Hamed-Wang-Koch (2002):

K is again modified by RC. Two values are proposed: EyeSys topographer effective refractive power (EffRP) is modified with the formula: EffRPadj = EffRP-(0.15*RC)-0.05 and manual keratometer K: Kadj = K –(0.24*RC)+0.15 .

1.4. Wang-Booth-Koch (2004):

The previously described parameter EffRPadj is combined with the Double-K version of third generation formulas. They also proposed a slight change in the EffRPadj calculation when the Humprey topographer is used: EffRP-(0.19*RC). This shows that this RC modifying figure is device-dependent.

1.6 Masket (2006):

Regression formula adjusting the IOL power calculated by SRK/T (IOL) with the RC at the spectacle plane: IOLadj = IOL +(RC*0.326)+0.101

1.7 Savini (2007):

K value is adjusted changing the corneal index of refraction by RC: nc = 1.338 + 0.0009856*RC

This value has to be used in a Double K formula

The main problem with these methods is that normally accurate data are not available to the cataract surgeon. Pre-CRS corneal measurements are usually missing and refraction evolution through the years can be due to corneal, lens or axial length changes, which makes it impossible to calculate RC.

1.8 Barrett True K: This formula adjusts keratometry with the RC (non-published method) and then uses a Double-K Barrett Universal II formula

2.- Methods that don´t require clinical data:

2.1. Adjusted keratometry not measuring posterior cornea:

Different authors have proposed using a constant value for the posterior cornea added to the anterior corneal power calculated with the actual estromal index of refraction (1.376).

2.1.1. Seitz and Langenbucher (2000) proposed two formulas : Kadj= (K*(376/337.5))-5.90 and Kadj= K*(376/337.5)-6.20 .

2.1.2. Rosa (2002): Corneal power is modified by a factor related to AXL.

2.1.3. Maloney modified (2004): Kadj= (K*(376/337.5))-6.1. This value should be used in a Double-K formula according to Wang et al.

2.1.4. Savini (2006): Kadj= (K*(376/337.5))-4.98. This value should be used in a double-K formula.

2.1.5. Shammas PL(2007): Keratometry is adjusted with a formula similar to those previously seen: Kadj= K*1.14-6.8. Then Shammas PL (postLASIK) formula is used. This doesn´t use K as ELP predictor avoiding the formula error.

2.1.6. Haigis L (2008): Keratometry is adjusted with an empirical formula calculated from a clinical dataset of CRS patients. This value is used by Haigis formula, which doesn´t use K as ELP predictor.

2.1.7. Barrett True K No history: Keratometry is adjusted from the anterior curvature. The value is used in a Double-K Barrett Universal II formula. This formula can also work inputting the measured posterior corneal radii with Pentacam or with IOL Master 700 (then called Barrett True K TK). These options convert this formula in a real swiss-knife tool for this cases.

2.2 Adjusted keratometry measuring posterior cornea

2.2.1. OCT based formula (2015): K is calculated with the formula: K = 1.0208 *net corneal power-1.6622. Net corneal power is calculated with the Gaussian equivalent power formula using the measured anterior and posterior corneal radii by OCT (RTVue). Then K is used in the OCT IOL formula

2.2.2. Potvin-Shammas-Hill (2015): Pentacam True Net Power 4.0 , Gaussian equivalent power, is used in Shammas formula, with some modifications for AXL and ACD.

2.2.3. Besst formula(2006): Corneal power is calculated using the Gaussian equivalent power formula modified by postCRS results. This value should be used in Double-K formulas.

2.2.4. Equivalent K parameters: Corneal total power is calculated from measured anterior and posterior corneal radii and then converted to a value intended to match the regular keratometric K value. Therefore it can be directly used in any regular formula. The first was the Equivalent K reading published by Holladay (2009) where measurements were taken with Pentacam and the formula for conversion was: 376/rant – 31.65/rpost. It is also included in the Cassini topographer. Recently the Zeiss TK (total K) from the IOL Master 700 has been tested by Wang (2019).

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