The precision to estimate the corneal power to calculate the intraocular lens (IOL) in corneas that have been ablated by an excimer laser is still beyond what is needed to meet the expectations of an increasingly demanding patient following refractive surgery.1
The main reason for the common and undesirable hyperopic surprise after refractive surgery is related to incorrect measurements of the corneal power.2 Each diopter (D) of error in the estimation of corneal power can lead to nearly 1 D of error in the final outcome.3 The estimation of corneal power based on the radius of curvature found in Placido-disk based systems relies only on data acquired from the anterior surface of the cornea. In myopic ablations the flattening of the anterior surface of the cornea is not followed by a similar change in the posterior surface, therefore resulting in an overestimated power of the single refractive surface based on Gullstrand’s model eye.4
Another approach to estimate the corneal power is by using ray tracing through each surface of the cornea to calculate an average focal length. It assumes and propagates incoming parallel rays and uses Snell’s law to refract these rays through the anterior and posterior corneal surfaces.4 Considering that both surfaces of the cornea are actually measured in the ray tracing method, changes induced in the cornea after surgery will likely not affect its ability to provide an accurate corneal power.4
The purpose of this study was to evaluate changes in the corneal power (ΔK) induced by different magnitudes of myopic ablations estimated by Placido-disk and ray tracing methods.
Patients and Methods
This prospective and comparative study was performed at the Cole Eye Institute, Cleveland, Ohio, approved by an Institutional Review Board, and conducted in accordance with the tenets of the Declaration of Helsinki.
A total of 58 healthy eyes (35 patients) with myopia or myopic astigmatism were prospectively enrolled in this study when they previously met the standard criteria for LASIK after a screening evaluation.5 Inclusion criteria were consecutive eyes that were considered good for LASIK and myopic ablation. Patients with previous ocular history or ocular surgery or candidates for a hyperopic treatment were excluded from the study. Measurements where the minimum quality required by the system was not achieved and any patients lost to follow-up were excluded from the study.
All patients had a detailed preoperative ophthalmic evaluation including uncorrected visual acuity, corrected distance visual acuity, manifest and cycloplegic refraction, slit-lamp evaluation, applanation tonometry, and fundus examination. All eyes had a corneal topography assessment (Atlas corneal topographer; Carl Zeiss Meditec, Jena, Germany) preoperatively and 3 months after LASIK surgery. Simulated keratometry (SimK) data were collected each time.
In addition, eyes were also imaged at both time points (preoperatively and after 3 months) with the dual-Scheimpflug imaging system (GALILEI analyzer; Ziemer Ophthalmic Systems AG, Port, Switzerland) and SimK, and total corneal power (TCP) over the central 4 mm area was collected.
Eyes were divided into three groups based on the spherical equivalent in diopters in the spectacle plane before surgery. The low myopia group included patients with a spherical equivalent of −3 D or less; the moderate myopia group included patients with a spherical equivalent between −3 and −6 D; and the high myopia group included patients with a spherical equivalent greater than −6 D.
All surgeries were performed by a single experienced surgeon (RRK) with the wavefront optimized photoablation profile using the WaveLight Allegretto Wave Eye-Q (400-Hz) excimer laser (Alcon Laboratories, Fort Worth, TX). The LASIK procedures were performed with a 0.95-mm spot size, an optical zone of 6.25 mm, and a transition zone of 1.25 mm. The magnitude of the spherical and astigmatic correction was first determined using software nomogram suggestions from clinical refractive measurements that were entered in the SurgiVision DataLink Alcon Edition (SurgiVision Inc., Scottsdale, AZ) and then adjustments were made by the surgeon based on final assessment of all available clinical data.
Measurements were performed with the GALILEI analyzer (software version 5.2.1) according to the manufacturer’s guidelines. This system integrates a dual-Scheimpflug camera and Placido-based corneal topography to measure anterior and posterior corneal surfaces. Height data from the Scheimpflug images and slope data, converted into height data from the Placido, are merged to calculate a surface fitted to the anterior corneal surface. Posterior corneal surface is measured using only data provided by the Scheimpflug system. The GALILEI analyzer is a rotational scanning system acquiring between 15 and 60 Scheimpflug images per scan and two Placido top view images at 90° apart, as the cameras rotate around the central axis. Placido and Scheimpflug data are acquired simultaneously, and then a motion correction algorithm is applied to the combined dataset. This correction compensates for the patient’s eye motion during scanning by a tracker that locates and tracks a patch on the iris, matching its location on every scan.
All patients were imaged with the GALILEI analyzer as follows. The device was first brought into focus (Placido rings into sharp focus) and aligned with the patient visual axis (central fixation light). Then patients were asked to blink just before the measurement.
SimK from the corneal topography (Atlas SimK), SimK from the GALILEI analyzer (GALILEI SimK), the average TCP value over the central 4.0-mm area of the cornea (TCP Ave), and the average TCP of the steepest and flattest meridian between 0 and 4 mm (TCP SimK) were collected preoperatively and 3 months after surgery. They were then compared to each other and to the achieved spherical equivalent of the correction. The analyzed parameters were calculated as follows.
SimK parameters are calculated with the keratometric index (n = 1.3375). This does not correspond to the actual index of refraction of the cornea (n = 1.376) because it takes into account the negative dioptric power of the posterior corneal surface. The SimK value that was recorded by both Atlas topographer and GALILEI analyzer is the arithmetic mean of the steep and flat axis over the central cornea (0 to 4.0 mm) and deriving from the axial curvature map.
TCP is the actual power of the cornea including both the anterior and posterior surfaces. The TCP is calculated by tracking the path of incident rays of light through the three-dimensional cornea (anterior surface, corneal thickness, and posterior surface) using ray tracing. The ray tracing uses Snell’s Law to refract the incoming ray of light through both surfaces. Corneal power is then determined by n / f, where n is the index of refraction of the aqueous (n = 1.336) and f is the focal length, referenced to the anterior corneal surface.
We recorded the TCP over the central 0 to 4.0 mm area and distinguished two different values: the TCP Ave, which is the mean TCP value over the central 0 to 4.0 mm, and the TCP SimK, which is the arithmetic average power of the steep and flat axis in this area and is calculated as follows: TCP meridian = (Steep + Flat) / 2.
Spherical equivalent of the manifest refraction before and after surgery was corrected for the vertex distance of the cornea, presuming that the phoropter used in the test was 12 mm from the cornea. This was calculated using the formula spherical equivalent cornea = spherical equivalent phoropter/ 1 – (0.012) (spherical equivalent phoropter). The difference between the spherical equivalent in the corneal plane before and after surgery was considered the spherical equivalent change induced (ΔSE) by the laser surgery. This was done to allow a comparison between the changes in power observed in the different systems tested (which measure the power in the corneal plane) and the real change in manifest refraction.
The difference between ΔSE of the manifest refraction in the corneal plane and the changes observed in corneal power ΔK was evaluated for each parameter (ΔSE-ΔK). A positive number indicates the system overestimated the final power (which would lead to a hyperopic surprise if the number was used to calculate an IOL) and a negative number indicates the system underestimated the final corneal power.
Statistical analyses were performed using JMP software (version 8.0; SAS Institute, Inc., Cary, NC). Normality of data was evaluated with the Kolmogorov–Smirnov test. Differences between data were evaluated using the analysis of variance, Wilcoxon test, and Student’s t test. Data were expressed as mean ± standard deviation. The level of significance for each parameter was set at a P value less than .05.
The low myopia group included 19 eyes, the moderate myopia group included 26 eyes, and the high myopia group included 13 eyes. The mean change in the spherical equivalent in the corneal plane (ΔSE) after the laser surgery was −7.16 ± 1.23 D in the high myopia group, −4.30 ± 0.62 D in the moderate myopia group, and −1.28 ± 0.56 D in the low myopia group. No eyes were excluded from the study or lost to follow-up.
Table 1 and Figure 1 show the difference between the real change in spherical equivalent and the change in corneal power (ΔSE - ΔK) measured with each method. This difference between the real change in spherical equivalent and the change in corneal power quantify the magnitude of overestimation or underestimation of the corneal power after surgery (compared to the change in spherical equivalent). The Atlas SimK overestimated the corneal power after the procedure by 0.50 ± 0.53 D when compared to refractive change in the corneal plane induced by the laser surgery. The SimK of the GALILEI analyzer overestimated the power by 0.77 ± 0.47 D. The two parameters that were calculated using the ray tracing method showed the opposite, with the TCP average over the 0- to 4-mm zone showing an underestimation of the corneal power of −0.29 ± 0.54 D, and with TCP SimK of −0.25 ± 0.48 D.
Table 1: Analysis of the Difference Between the Real Change in Spherical Equivalent and the Change in Corneal Power (ΔSE-ΔK) Measured With Each Method
Figure 1. A bar graph showing the distribution of estimated changes in corneal power measured by each method after surgery (ΔK) subtracted from the real change in spherical equivalent (ΔSE) (n = 58). If the method estimated the exact change observed in the spherical equivalent, the result would be 0 (ΔSE – ΔK = 0). This was observed with the simulated keratometry from (A) the Atlas corneal topographer (Carl Zeiss Meditec, Jena, Germany) and (B) the GALILEI analyzer (Ziemer Ophthalmic Systems AG, Port, Switzerland). Negative values mean that the method underestimated the corneal power when compared to the change in spherical equivalent (ΔSE – ΔK < 0) as seen in (C) the average of the central 4-mm corneal power and (D) the mean of the steep and flat meridians of the central 4-mm power.
The eyes were then separated according to the level of myopia. In the low myopia group, there was no statistically significant difference despite the changes in parameters measured by the ray tracing method being closer to the ΔSE, and with a lower standard deviation. The SimK measured by the GALILEI analyzer showed a significant overestimation of the power when compared to the other three variables (Table 2, Figure 2). An inverse trend was observed between the Placido-disk and ray tracing methods when they were compared in increasing levels of myopia. In the moderate myopia group, the Atlas topographer overestimated the corneal power, which was not statistically different than the SimK with the GALILEI analyzer. The parameters measured by the ray tracing method showed an underestimation of the corneal power (Table 2, Figure 2). In the high myopia group, the overestimation of the corneal power with the Placido-disk technology demonstrated an increasing trend, whereas the underestimation with the ray tracing technology also increased (Table 2, Figure 2). Note the opposite trend between a Placido-disk based system such as the Atlas topographer (Table 1), in which there is a clear increasing overestimation of the corneal power with higher corrections, and a ray tracing method such as TCP SimK, in which there is a clear increasing underestimation of the power with higher corrections (Table 1).
Table 2: Statistical Comparison (P Value) Between the Methods Analyzed
Figure 2. Graphic representation of the difference found in the spherical equivalent change (ΔSE) and the values obtained by the systems analyzed (difference in corneal power before and after surgery [ΔK]) in the (A) low myopia group (n = 19), (B) moderate myopia group (n = 26), and (C) high myopia group (n = 13). Atlas topography = Atlas corneal topographer (Carl Zeiss Meditec, Jena, Germany); GALILEI SimK = simulated keratometry from the GALILEI analyzer (Ziemer Ophthalmic Systems AG, Port, Switzerland); TCP Ave = average total corneal power value over the central 4-mm area of the cornea; TCP SimK = average TCP of the steepest and flattest meridian between 0 and 4 mm
The results obtained demonstrated consistently that the TCP based on ray tracing does not show a progressive overestimation of the corneal power (directly related to the level of myopia), as seen in standard SimK measurements by corneal topographers or keratometers.2 It showed an opposite effect, where the TCP showed a trend to underestimate the corneal power in higher levels of myopia. There are three main reasons that can explain this underestimation.
First, the vertex distance was corrected using the standard 12-mm distance between the phoropter and the cornea. If the manifest refraction (which determines the preoperative spherical equivalent) was actually performed with a smaller distance (eg, 7 mm), the correction of the new vertex distance (7 mm instead of 12 mm) would lead to an average increase of 0.28 D in the ΔSE in the high myopia group, thus reducing the underestimation in the TCP SimK in this group to an average of −0.49 D and increasing the overestimation with the Atlas topographer to an average of +1.08 D.
The second reason is that the ray tracing measurement in the device that was tested is performed using the central 4 mm of the cornea. In high myopic ablations, the induction of positive spherical aberration can lead to a myopic shift when the patient has a larger pupil. All tests to measure the manifest refraction before and after surgery were performed under low light situations, which could have led to large pupil situation and a resulting myopic shift in the postoperative manifest refraction. This would mean a lower ΔSE and consequently an assumption of a higher corneal power in a large pupil situation than the one obtained only by measuring the central cornea. This could explain why we found lower corneal powers (underestimation) in higher levels of myopia when measuring the central cornea with the TCP than the ones obtained with the ΔSE.
The third reason is related to the fact that we compared the obtained results to manifest refraction before and after surgery. When refracting myopic patients there is always a concern about not overcorrecting the patients. Usually, the physician prefers the lens with less power if the patient is not sure which lens is the best (it is better to undercorrect than overcorrect a myopic patient in the manifest refraction before surgery). This is more pronounced in higher degrees of myopia and could account for a lower preoperative myopic level before surgery and consequently a lower ΔSE than reality. Compared to the higher ΔK obtained with the TCP, this would lead to the interpretation that the TCP underestimated the final corneal power.
These three factors are not mutually exclusive and each of them can account for a small magnitude of underestimation of corneal power.
It is important to consider that the formulas for IOL power calculation available today are based on keratometric and topographic corneal powers, which rely on a standard single refracting surface based on Gullstrand’s model eye. The power calculated from ray tracing uses the calculated bending of the light through the surfaces of the cornea. Also, the TCP is referenced to the anterior surface of the cornea (compared to the posterior surface in the keratometry); both of these situations lead to a lower absolute number.4 Despite a better agreement found before and after refractive surgery, the absolute number of a ray tracing measurement is approximately 1.3 D lower12 than the keratometry or topography SimK and cannot be used interchangeably with the current formulas, which are based on keratometry values.13 One option would be to optimize the formulas for a calculation based on ray tracing methods.
The accuracy and reproducibility of non-Placido-disk devices to measure corneal power has been reported in numerous studies in the peer-reviewed literature. Previous studies found that a Scheimpflug system is more reproducible and repeatable than a scanning slit system.6 The dual-Scheimpflug system used in this study also has shown an excellent repeatability,7 even in eyes after refractive surgery.8 The corneal power measurements with this system are highly reproducible, comparable, and correlated to automated keratometry, manual keratometry, and the Atlas topographer.9 Considering that the standard deviations among the different eyes observed with the TCP SimK were always lower than those measured with the Atlas topographer, it is not possible to attribute the results observed to variations or errors in measurements obtained with the dual-Scheimpflug system.
A previous study10 evaluated the ratio between the ΔK and the ΔSE in similar groups (low, moderate, and high myopia), using one of the devices (the same Placido-disk based system [Atlas topographer]) used in the current study. It supports the theory and results encountered with the Atlas topographer, showing the progressive overestimation of the final corneal power directly correlated to the level of ΔSE in a nonlinear relationship. This also supports that the methods evaluated in this study that use a Scheimpflug system behave in an opposite trend from what has been published with Placido-based systems.
Data from 3 months postoperatively were used in this study. Considering that the central cornea after refractive surgery remains stable even after several years of follow-up,11 it is not likely that the results would be different if performed a long period after the laser vision correction, when the cataract surgery would be needed.
SimK measurements by corneal topographers and keratometers assume the corneal power by the anterior curvature alone and estimate a fixed relation between the anterior and posterior surfaces of the cornea. When dealing with corneas after refractive surgery, this ratio changes (because the flattening of the anterior surface is not followed by that of the posterior surface) with the level of correction.4 This causes an overestimation of the corneal power that explains the findings with the Atlas and GALILEI SimK. There was a statistically significant difference between the Atlas and GALILEI SimK in the low myopia group (Table 2). This difference was not found in the moderate or high myopia groups and could be due to larger variation of ΔK and ΔSE in patients with low myopia as previously reported in a large sample study.10
One of the limitations of the study is that the changes in estimated power were calculated and then compared to the refractive changes in the corneal plane, which were determined by subjective refraction, so small changes in vertex distance during the test in patients with high myopia could have underestimated or overestimated the changes in the corneal plane. Because our results showed an overestimation in corneal power with the calculations made by topography, which match the methods and results of the peer-reviewed literature available,2,14 and all comparisons were based on the same ΔSE, the opposite trend (underestimation) found in the ray tracing method cannot be related to any limitations, such as small variabilities, that would affect all groups.
We believe, based on the results shown in this study, that a ray tracing method is not influenced by the flaws seen with methods based on anterior curvature alone. It has the potential to be the standard method to calculate corneal power after refractive surgery. However, ray tracing methods need be validated and optimized before it can be used routinely in IOL calculation.
- Wang L, Booth MA, Koch DD. Comparison of intraocular lens power calculation methods in eyes that have undergone laser-assisted in-situ keratomileusis. Trans Am Ophthalmol Soc. 2004;102:189–196.
- Coulibaly R. Underestimation of intraocular lens power for cataract surgery after myopic PRK. Ophthalmology. 2000;107:222–223. doi:10.1016/S0161-6420(99)00103-7 [CrossRef]
- Chen S, Hu FR. Correlation between refractive and measured corneal power changes after myopic excimer laser photorefractive surgery. J Cataract Refract Surg. 2002;28:603–610. doi:10.1016/S0886-3350(01)01323-2 [CrossRef]
- Wang L, Mahmoud AM, Anderson BL, Koch DD, Roberts CJ. Total corneal power estimation: ray tracing method versus gaussian optics formula. Invest Ophthalmol Vis Sci. 2011;52:1716–1722. doi:10.1167/iovs.09-4982 [CrossRef]
- Ciolino JB, Belin MW. Changes in the posterior cornea after laser in situ keratomileusis and photorefractive keratectomy. J Cataract Refract Surg. 2006;32:1426–1431. doi:10.1016/j.jcrs.2006.03.037 [CrossRef]
- Kawamorita T, Uozato H, Kamiya K, et al. Repeatability, reproducibility, and agreement characteristics of rotating Scheimpflug photography and scanning-slit corneal topography for corneal power measurement. J Cataract Refract Surg. 2009;35:127–133. doi:10.1016/j.jcrs.2008.10.019 [CrossRef]
- Wang L, Shirayama M, Koch DD. Repeatability of corneal power and wavefront aberration measurements with a dual-Scheimpflug Placido corneal topographer. J Cataract Refract Surg. 2010;36:425–430. doi:10.1016/j.jcrs.2009.09.034 [CrossRef]
- Savini G, Carbonelli M, Barboni P, Hoffer KJ. Repeatability of automatic measurements performed by a dual Scheimpflug analyzer in unoperated and post-refractive surgery eyes. J Cataract Refract Surg. 2011;37:302–309. doi:10.1016/j.jcrs.2010.07.039 [CrossRef]
- Shirayama M, Wang L, Weikert MP, Koch DD. Comparison of corneal power obtained from 4 different devices. Am J Ophthalmol. 2009;148:528–535. doi:10.1016/j.ajo.2009.04.028 [CrossRef]
- Moshirfar M, Christiansen SM, Kim G. Comparison of the ratio of keratometric change to refractive change induced by myopic ablation. J Refract Surg. 2012;28:675–681. doi:10.3928/1081597X-20120921-01 [CrossRef]
- Lombardo M, Lombardo G, Ducoli P, Serrao S. Long-term changes of the anterior corneal topography after photorefractive keratectomy for myopia and myopic astigmatism. Invest Ophthalmol Vis Sci. 2011;52:6994–7000. doi:10.1167/iovs.10-7052 [CrossRef]
- Savini G, Barboni P, Carbonelli M, Hoffer KJ. Agreement between Pentacam and videokeratography in corneal power assessment. J Refract Surg. 2009;25:534–538.
- Norrby S. Pentacam keratometry and IOL power calculation. J Cataract Refract Surg. 2008;34:3. doi:10.1016/j.jcrs.2007.08.015 [CrossRef]
- Leng C, Feiz V, Modjtahedi B, Moshirfar M. Comparison of simulated keratometric changes induced by custom and conventional laser in situ keratomileusis after myopic ablation: retrospective chart review. J Cataract Refract Surg. 2010;36:1550–1555. doi:10.1016/j.jcrs.2010.04.027 [CrossRef]
Analysis of the Difference Between the Real Change in Spherical Equivalent and the Change in Corneal Power (ΔSE-ΔK) Measured With Each Methoda
|Group||Atlas SimK||GALILEI SimK||TCP Ave||TCP SimK|
|All eyes||0.50 ± 0.53||0.77 ± 0.47||−0.30 ± 0.54||−0.25 ± 0.48|
|Low myopia||0.20 ± 0.38||0.76 ± 0.43||0.07 ± 0.33||0.05 ± 0.30|
|Moderate myopia||0.57 ± 0.46||0.75 ± 0.44||−0.28 ± 0.36||−0.22 ± 0.34|
|High myopia||0.79 ± 0.63||0.82 ± 0.60||−0.88 ± 0.57||−0.76 ± 0.50|
Statistical Comparison (P Value) Between the Methods Analyzed
|Group||Atlas SimK||GALILEI SimK||TCP Ave||TCP SimK|
| Atlas SimK||N/A||.0004a||.242||.179|
| GALILEI SimK||.0004a||N/A||< .0001a||< .0001a|
| TCP Ave||.242||< .0001a||N/A||.907|
| TCP SimK||.179||< .0001a||.907||N/A|
| Atlas SimK||N/A||0.161||< .0001a||< .0001a|
| GALILEI SimK||.161||N/A||< .0001a||< .0001a|
| TCP Ave||< .0001a||< .0001a||.436||N/A|
| TCP SimK||< .0001a||< .0001a||.436||N/A|
| Atlas SimK||N/A||.572||< .0001a||< .0001a|
| GALILEI SimK||.572||N/A||< .0001a||< .0001a|
| TCP Ave||< .0001a||< .0001a||N/A||.907|
| TCP SimK||< .0001a||< .0001a||1.000||N/A|