ARTICLE
New equivalent keratometry reading calculation with a rotating Scheimpflug camera for intraocular lens power calculation after myopic corneal surgery Kyoung Yul Seo, MD, Chan Young Im, MD, Hun Yang, MD, Tae-im Kim, MD, Eung Kweon Kim, MD, Terry Kim, MD, Sang Min Nam, MD
PURPOSE: To calculate the keratometric (K) reading in corneas modified by myopic keratorefractive surgery using the total corneal refractive power (TCRP) of the Pentacam rotating Scheimpflug camera. SETTING: University hospitals and private clinics, South Korea DESIGN: Evaluation of diagnostic test or technology. METHODS: The study comprised healthy eyes, eyes having myopic keratorefractive surgery, and eyes having cataract surgery after myopic keratorefractive surgery. The conversion equation from the TCRP in the central 4.0 mm zone (TCRP4) to a K reading was derived in normal corneas. This equation was rechecked and its application range extended in corneas modified by myopic keratorefractive surgery. Then, the predictability of the TCRP method, combining the K reading derived from the TCRP4 and the Holladay 2 formula, was evaluated in a case series of cataract surgery patients who had previous myopic keratorefractive surgery. RESULTS: The K reading derived from the TCRP4 was obtained by adding 0.7 diopter (D). This conversion factor was applicable after myopic keratorefractive surgery because changes in TCRP4 were equal to changes in refraction in the 4.0 mm zone. The TCRP method predicted intraocular lens power within G0.5 D in 83% and within G1.0 D in 94% of eyes having cataract surgery after myopic keratorefractive surgery. CONCLUSION: The TCRP4 of the rotating Scheimpflug camera was successfully converted into the equivalent K reading, and the TCRP method showed good predictability in corneas modified by myopic keratorefractive surgery. Financial Disclosure: No author has a financial or proprietary interest in any material or method mentioned. J Cataract Refract Surg 2014; 40:1834–1842 Q 2014 ASCRS and ESCRS
The power of the cornea is conventionally measured by manual keratometry or autokeratometry (K reading). The keratometer measures the anterior radius of corneal curvature and uses an arbitrary index of refraction of 1.3375 so that a radius of 7.5 mm would yield 45.0 diopters (D).1,2 Therefore, the K reading is the standardized power of the cornea and applicable only if the cornea thickness is 500 mm and the ratio of the back to front surface central radius is approximately 82%.3 Although the K reading does not represent the equivalent corneal power, current formulas for intraocular lens (IOL) 1834
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power calculation in cataract surgery are based on K readings and are reliable for the majority of eyes with a physiologic and prolate cornea.3–5 This reliability can be obtained by adjusting formulas using many clinical cases. For example, the SRK/T formula was optimized using an iterative process on 5 data sets consisting of 1677 posterior chamber IOL cases.6 The Holladay 2 formula, which was used in this study, is based on previous observations from a 35 000 patient data set.7 In corneal refractive surgery, the anterior surface is intended to be modified and there is no longer a 0886-3350/$ - see front matter http://dx.doi.org/10.1016/j.jcrs.2013.11.044
EQUIVALENT K FOR IOL POWER CALCULATION AFTER MYOPIC CORNEAL SURGERY
physiologic ratio between the front and back corneal radii; this results in an unreliable K reading for IOL power calculation with current formulas.2,8 In addition, keratometers have an unmeasured central zone that is approximately 3.2 mm in diameter.2,9 Therefore, the central region of the cornea, which is more flattened or steepened by keratorefractive surgery, is essentially ignored.3 The Pentacam (Oculus Optikger€ ate GmbH) a rotating Scheimpflug camera that measures the entire central area of the cornea as well as the posterior corneal surface.2 Techniques that use the Scheimpflug camera for IOL power calculation in cataractous eyes that had previous myopic keratorefractive surgery have been developed. One is the true corneal net power, an approximation of the Gaussian equivalent power, which is the arithmetic sum of the front and back surface powers according to the Gaussian formula.5,10 The Gaussian equivalent power is significantly less than the K reading in virgin corneas and is not appropriate for current IOL formulas.2,3,11,12 However, studies13,14 have incorporated the true net power into the SRK/T formula without effective lens position (ELP) correction. In addition, the Holladay equivalent K reading (EKR) is an adjusted K reading for the difference in the posterior radius from normal.2,5 The Pentacam software (version 1.20r02) calculates the equivalent K reading with anterior and posterior powers by Snell's law. There have been some discussions about the validity of the equivalent K reading in the Pentacam system.5,15,16 The total corneal refractive power (TCRP) is the equivalent corneal power of the Scheimpflug camera
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using a ray-tracing method rather than the Gaussian formula.5,A The Gaussian formula depends on the assumption of paraxial optics, but ray tracing does not rely on paraxial optics and hence produces an accurate method of measuring the corneal power with respect to both the anterior and posterior corneal curvature.10,A To the best of our knowledge, the TCRP has not been used for IOL power calculation, especially in eyes with an altered anterior corneal curvature following myopic refractive surgery. However, the equivalent corneal power would produce inaccurate results with current IOL power calculation formulas, which are accustomed to standard K readings. The equivalent corneal power should be customized for these formulas with some type of conversion. We postulated that each K reading would represent a specific equivalent corneal power for the formula. If we knew the relationship between them, we could pick an equivalent K reading for a given equivalent corneal power. We expected a simple relationship between them because current formulas are successfully adapted to K readings despite their arbitrariness. To verify our hypothesis, we evaluated the simple relationship in the normal cornea, rechecked it, and then expanded the range of its application in myopic keratorefractive surgery patients. Lastly, the converted power from TCRP was coupled with the Holladay 2 formula, and the accuracy of IOL power calculation was evaluated in cataract surgery cases after myopic keratorefractive surgery. PATIENTS AND METHODS This retrospective clinical practice study prospectively obtained approval of the Institutional Review Board, CHA University. It adhered to the tenets of the Declaration of Helsinki.
Submitted: July 5, 2013. Final revision submitted: November 13, 2013. Accepted: November 30, 2013.
Measurement of Total Corneal Refractive Power
From the Department of Ophthalmology (Seo, T-i. Kim, E.K. Kim), Eye and Ear Hospital, Severance Hospital, Institute of Vision Research, Yonsei University College of Medicine; the Ian Eye Center (Im); the SU Yonsei Eye Clinic (Yang); the Corneal Dystrophy Research Institute (T-i. Kim, E.K. Kim), Yonsei University College of Medicine, Seoul; the Department of Ophthalmology (Nam), CHA Bundang Medical Center, CHA University, Seongnam, South Korea; the Department of Ophthalmology (T. Kim), Duke Eye Center, Durham, North Carolina, USA. Supported by the Converging Research Center Program through the Ministry of Science, ICT and Future Planning, Korea (2013K000373). Corresponding author: Sang Min Nam, MD, Department of Ophthalmology, CHA Bundang Medical Center, CHA University, 59 Yatap-ro, Bundang-gu, Seongnam-si, Gyeonggi-do 463-712, South Korea. E-mail: [email protected].
Each patient was seated with the head in a headrest and was asked to focus on the target at the center of the Scheimpflug system (Pentacam or Pentacam HR). Every Scheimpflug system in this study was calibrated and technically supported by the regional branch of Oculus. The operator moved the joystick until arrows on the display were aligned with the horizontal, vertical, and anterior– posterior axes. As soon as the image was aligned perfectly, the patient was asked to keep his or her eye open, after which the scanning process started. Automatic release was used to reduce variables. The 25-images mode was chosen so that the rotating camera acquired 25 scans in 1 second. In the power distribution display of the Scheimpflug system software (version 1.18r04), the zone, apex, and total corneal refractive power options were selected and the zone diameter was set as 4.0 mm. Then, Km in “power calculations in actual zone” was read as the total corneal refractive power in the central 4.0 mm zone (TCRP4).
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Basic Concept of the Total Corneal Refractive Power Method If TCRP4pre is the correctly computed power of the cornea before refractive surgery, the K reading of the cornea before refractive surgery (Kpre) and TCRP4pre is as follows: Kpre TCRP4pre Z C ðconstantÞ
(1)
From the clinical history method, the power of the postrefractive surgery cornea (Kch) is given by4,17 Kch Z Kpre ðR4c:post R4c:preÞ
(2)
where R4c.pre is the refraction before refractive surgery measured at the apex-centered 4.0 mm zone of the corneal plane and R4c.post is refraction after refractive surgery measured at the apex-centered 4.0 mm zone of the corneal plane. If the next equation is proven, R4c:post R4c:pre Z TCRP4pre TCRP4post
(3)
(TCRP4post is the TCRP4 of the cornea after refractive surgery) Kch will be calculated from TCRP4post, where Kch Z Kpre ðR4c:post R4c:preÞ Z Kpre ðTCRP4pre TCRP4postÞ Z ðTCRP4pre þ CÞ ðTCPR4pre TCRP4postÞ Z TCRP4post þ C (4) Now, both effective cornea powers for pre-refractive and post-refractive surgery (Ktcrp4) can be generally expressed with TCRP4 by equations 1 and 4: Ktcrp4 Z TCRP4 þ C
the K reading with a keratometric index of 1.3375.11 Finally, healthy eyes of healthy subjects (20 subjects for each subset in the 20, 30, 40, 50, and 60 years of age range) who had visited between 2007 and 2012 were recruited. To verify equation 1, the agreement between Ka and TCRP4 was studied with the Bland-Altman plot. The C constant of equation 1 was calculated by averaging (Ka TCRP4). It was confirmed with the Pearson product moment correlation that the C constant was independent of the patient’s age and corneal power.
(5)
Study Procedure First, equation 1 was proved and the C constant of equation 1 was determined through a retrospective review of medical records of healthy subjects. Second, equation 3 was verified by reviewing the preoperative and postoperative records of patients who had photorefractive keratectomy (PRK) or laser in situ keratomileusis (LASIK) for myopia. Then, Ktcrp4 for post-refractive surgery was calculated with equation 5, and the compatibility of Kch and Ktcrp4 was studied. Lastly, the cases of cataract surgery after PRK, LASIK, or laser-assisted subepithelial keratectomy (LASEK) for myopia were reviewed and the IOL prediction error with Ktcrp4 was estimated.
Verification of Equation 1 and Determination of the Constant One eye of each healthy subject who had visited the Ian Eye Center was randomly selected and reviewed. The inclusion criteria were as follows: no history of corneal surgery or ocular surface abnormalities; mean K power of autokeratometry (Ka) ranging from 40.0 D to 45.0 D; difference between mean corneal front power of the Scheimpflug camera (Kp) and Ka less than 0.5 D; Ka greater than TCRP4. Because Kp is developed to produce the same value as Ka, any difference implies that an unreliable measurement was taken with the Scheimpflug camera or with autokeratometry. In addition, TCRP4 rarely exceeds Ka in healthy corneas because the true corneal power in the principle plane is less than
Verification of Equation 3 and Calculation of Refraction for the 4.0 mm Zone One eye of each patient who had PRK or LASIK at B&VIIT Eye Center between 2009 and 2011 was randomly selected and reviewed. The Allegretto Wave Eye-Q laser (Wavelight Laser Technologie AG) or the Amaris excimer laser (Schwind eye-tech-solutions GmbH and Co. KG) was used for the surgery. The wavefront-optimized treatment of the Allegretto Wave Eye-Q laser or the aberration-free treatment of Amaris excimer laser was implemented to preserve the cornea's asphericity and avoid additional higher-order aberrations (HOAs).18,19 Data from more than 6 months after surgery were used. The eye was included in the study based on the following criteria: corrected visual acuity not worse than 20/20 preoperatively and postoperatively; cornea healthy before the surgery and not accompanied by any postoperative complication; difference between Kp and corresponding Ka less than 0.5 D preoperatively and postoperatively. For verifying equation 3, the manifest refraction was converted to the refraction measured at the apex-centered 4.0 mm zone of corneal plane (R4c). Because the manifest refraction had been measured under mesopic conditions, it was presumed that the corresponding pupil size of the patients was approximately 6.5 mm.20 The total corneal refractive power of the apex-centered 6.5 mm zone (TCRP6.5) was obtained from the power distribution display of the Scheimpflug camera after the zone diameter in the lower box was edited as 6.5. Then, R4c was calculated with the manifest refraction measured at the corneal plane (Rc), TCRP4, and TCRP6.5, where R4c Z Rc þ ðTCRP6:5 TCRP4Þ
(6)
By the equation 6, R4c:post R4c:pre Z Rc:post þ ðTCRP6:5post TCRP4postÞ ðRc:pre þ ðTCRP6:5pre TCRP4preÞÞ Z ðRc:post Rc:preÞ þ ðTCRP6:5post TCRP4postÞ ðTCRP6:5pre TCRP4preÞ (7) where Rc.pre and TCRP6.5pre are preoperative Rc and TCRP6.5, respectively, and Rc.post and TCRP6.5post are the postoperative Rc and TCRP6.5, respectively. Rc was calculated from the refractive error at spectacle plane (R) with the formula1,17 Rc Z R=ð1 0:012 RÞ
(8)
Then, equation 3 was confirmed by the Bland-Altman plot between (R4c.post R4c.pre) and (TCRP4pre TCRP4post). Finally, equation 4 was checked by the BlandAltman plot between Kch and (TCRP4post C C).
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Accuracy Test for Equation 5 with Cataract Surgery Cases after Refractive Surgery The cases of cataract surgery after PRK, LASIK, and LASEK for myopia performed between 2009 and 2012 at several clinics were reviewed. The cases were included if there were no significant complications during cataract surgery; postoperative manifest refraction was taken after more than 30 days; the difference between Kp and Ka was less than 0.5 D. The spherical aberration of the 6.0 mm total corneal wavefront aberration was calculated using the Zernike analysis of the Scheimpflug camera. The spherical equivalent (SE) of the predicted refraction (Rcalc) according to Ktcrp4 and the Holladay 2 formula was compared with the SE of the postoperative manifest refraction (Rtrue) through calculation of the arithmetic prediction error, Rtrue Rcalc. The percentages of correct refraction predictions within G0.5 D and G1.0 D were calculated. The Holladay 2 formula is available as part of the Holladay IOL Consultant software.B The “Previous RK, PRK, ALK, LASIK.” box was checked, and Ktcrp4 was input as the surgeonentered K value for alternate K. The horizontal white-towhite length and ultrasound measurements of the phakic anterior chamber depth (ACD), lens thickness, and axial length (AL) were entered. The results of Ktcrp4 and Holladay 2 formula were compared with results obtained with the no-history method of Shammas and Shammas.21 The no-history method of Shammas and Shammas is 1 of the 5 most accurate methods of the 25 formula combinations and uses only postoperative biometry.8 For the Shammas method, the corrected K value (Shammas.cd) and the predictive refraction were calculated with the clinically derived method and the Shammas post-LASIK formula (Shammas-PL), respectively. In addition, the prediction error of the Holladay EKR with the Holladay 2 formula (“Previous RK, PRK, ALK, LASIK.” on) was calculated. In the Holladay report of the Pentacam system, the Holladay EKR is displayed for pupil-centered 4.5 mm zone.
Statistical Analysis
Figure 1. Bland-Altman plot of the difference between the mean keratometric power of autokeratometry (Ka) and the total corneal refractive power of apex-centered 4.0 mm zone (TCRP4) in healthy subjects; Ka TCRP4 was not correlated with the mean of Ka and TCRP4 (Pearson r Z 0.116, PZ.251).
Ka TCRP4 Z 0:7
(1-1)
The C constant could be deviated G0.5 D from 0.7 D (Figure 1). Equation 3: Statistically Equivalence of Refractive Changes at Central 4.0 mm of Cornea Plane and Changes in Total Corneal Refractive Power of Scheimpflug Camera The medical records of 63 patients (30 cases of PRK and 33 cases of LASIK) were reviewed. The mean age was 26 G 5 years, and the mean preoperative manifest refraction was 5.37 G 1.93 D. The postoperative manifest refraction was taken after a median time of 284 days (interquartile range, 201 to 336 days). The mean difference between the refractive changes at the central 4.0 mm of the corneal plane and the
SPSS software (version 20, International Business Machines Corp.) was used for general statistical analysis. Bland-Altman plots and scatterplots were drawn and analyzed using Sigmaplot software (version 12.0, Systat Software, Inc.).
RESULTS Equation 1: Relationship between Keratometric Power of Autokeratometry and Total Corneal Refractive Power of the Scheimpflug Camera in Healthy Corneas The mean age of 100 healthy patients (45 men and 55 women) was 44 years G 15 (SD). The difference between Ka and TCRP4 in healthy corneas was independent of corneal power and patient's age (Figures 1 and 2). The mean difference between Ka and TCRP4 was 0.7 G 0.3 D (range 0.7 to 0.8 D; 95% confidence interval [CI]), and equation 1 was completed as:
Figure 2. Correlation between age and Ka TCRP4. No significant correlation was found (Pearson r Z 0.005, PZ.963) (Ka Z mean keratometric power of autokeratometry; TCRP4 Z total corneal refractive power of apex-centered 4.0 mm zone).
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Figure 3. Bland-Altman plot of the difference between postoperative changes in manifest refraction for the central 4.0 mm zone of corneal plane (R4cpost-pre) and the total corneal refractive power of the apexcentered 4.0 mm zone (TCRP4pre-post).
TCRP4 changes was 0.0 G 0.5 D (95% CI, 0.1 to 0.1 D), and the absolute value of the limits of agreement (LoA) was less than 1.0 D (Figure 3). Equation 4: Verification of Equation 1 in a Different Group Via Combination of Equation 3 The group for the equation 3 demonstration was applied again to prove equation 4. By equation 3, the refractive changes at the central 4.0 mm of the corneal plane could be replaced with the TCRP4 changes. If equation 1 and equation 3 were accurate, Kch and (TCRP4post C 0.7) in equation 4 would show no significant difference between them. The mean difference between Kch and (TCRP4post C 0.7) was 0.1 G 0.5 D (95% CI, 0.2 to 0.0 D), and the LoA were 1.0 D and 0.8 D (Figure 4). Accuracy of Equation 5 with Holladay 2 Formula (Total Corneal Refractive Power Method) in Cataract Surgery after Corneal Refractive Surgery In 18 cases of 14 patients, 9 cases (50%) were correctly predicted within G0.50 D and 14 cases (78%) were within G1.0 D by the Shammas method (Table 1). By the TCRP method, 15 cases (83%) and 17 cases (94%) of patients were properly predicted within G0.5 D and G1.0 D, respectively (Table 1). The difference between Ktcrp4 and Shammas.cd strongly correlated with the difference between Rcalc of Ktcrp4/Holladay 2 and Rcalc of Shammas.cd/ Shammas-PL (Spearman r Z 0.786, P!.001) (Figure 5). Neither method gave a hyperopic prediction error greater than 1.0 D (Table 1). In cases 3 and 14, the centers of the pupil in the Scheimpflug camera were erroneously measured and the Holladay EKRs were not reliable (Figure 6). Without both cases, 5 cases (31%) and 12 cases (75%)
Figure 4. Bland-Altman plot of the difference between the correct K value derived by the clinical history method (Kch) and the effective corneal power calculated with the total corneal refractive power of the apex-centered 4.0 mm zone (Ktcrp4). For the clinical history method, postoperative changes in manifest refraction for the central 4.0 mm zone of corneal plane were calculated.
had a prediction error within G0.5 D and G1.0 D, respectively, when the Holladay EKR was joined with Holladay 2 formula (Table 1). DISCUSSION The new equivalent K reading (Ktcrp4) for the IOL power calculation formula was obtained with the simple addition of 0.7 D to TCRP4 (equation 5). The Ktcrp4 could apply to the healthy cornea (equation 1) and the modified cornea with PRK or LASIK for myopia correction (equation 4). Refraction changes with PRK or LASIK were well reflected by TCRP4 (equation 3). When Ktcrp4 was incorporated in the Holladay 2 formula in eyes after myopic PRK, LASIK, or LASEK, the calculated IOL power was accurate enough to comply with a benchmark standard.22 The TCRP method was devised to be compatible with current IOL calculation formulas that depend on the K reading. The standard manual keratometer measures a 3.2 mm ring area for a 44.0 D cornea.2 The size of the measured ring area changes according to the radius of curvature of the cornea because a fixed size ring is emitted and mirrored by the anterior surface of the cornea.23 The 4.0 mm zone of TCRP4 embraces the group of various sizes of the ring area but is still close to the measured ring area of the standard keratometer. For the accuracy of TCRP to be guaranteed, the mean corneal front power of the Pentacam (Kp) should be within G0.5 D of the mean keratometric power of autokeratometry (Ka). According to the manufacturer of the Pentacam Scheimpflug camera (software version 1.18r04), Kp is the anterior simulated K reading on a ring that is 15 degrees around the corneal apex and developed to accord with Ka. If the
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Table 1. Comparison of prediction errors between the Shammas method, the total corneal refractive power method, and the Holladay equivalent keratometry reading method. Arithmetic Prediction Error (D)z Refraction Corneal IOL Power after Ktcrp4 EKR Age SA AL Implanted Cataract Shammas. Ktcrp4 EKR Shammas.cd (D) (D) Shammas-PL Holladay 2 Holladay2 Case (Y) Surgery (mm)* (mm) IOL Type (D) Surgery (D)† cd (D) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
42 62 47 41 38 62 60 55 55 35 42 44 53 47 51 54 53 53
PRK 1.841 29.90 ZA9003 LASEK 0.327 24.63 ZA9003 LASIK 1.110 28.65 ZA9003 PRK NA 26.54 ZA9003 PRK 0.479 27.32 ZA9003 LASIK 0.975 27.28 ZA9003 LASIK NA 27.19 ZA9003 PRK 0.937 29.08 ZCB00 PRK 0.394 26.76 ZCB00 LASIK 0.755 26.72 ZCB00 PRK 0.003 30.46 920H LASIK 0.899 26.53 PC-60 AD LASIK 0.528 28.69 SN60WF LASIK 0.325 25.04 SN60T4 LASIK 0.33 27.57 SN6AD1 PRK 0.271 26.19 ZMB00 LASIK 1.136 26.45 LISA 809M LASIK 0.901 26.49 LISA 809M
17.0 21.5 18.0 19.5 19.5 14.0 15.5 13.5 17.5 18.5 2.0 20.5 18.0 19.5 16.5 18.5 17.0 17.0
0.50 0.75 0.50 0.13 0.25 0.50 0.13 2.00 1.63 3.38 0.63 1.00 0.75 0.00 0.13 0.25 0.50 0.25
33.8 40.4 35.4 37.0 36.1 39.9 38.9 39.7 40.2 41.4 45.5 36.4 35.4 40.2 38.1 38.9 39.1 38.9
33.9 41.6 36.3 38.3 37.1 40.9 40.5 39.6 41.2 41.5 46.4 37.0 36.1 41.0 38.6 39.6 38.9 38.9
34.9 41.7 42.3 38.5 38.0 41.4 40.6 40.9 41.5 42.3 46.1 38.1 37.2 42.7 39.4 40.0 40.1 40.0
0.35 1.07 0.40 1.20 0.72 0.33 0.95 0.14 0.35 0.22 2.10 1.49 0.34 0.54 0.25 0.15 0.74 0.55
0.41 0.22 0.10 0.54 0.10 0.56 0.31 0.21 0.42 0.39 0.40 1.27 0.00 0.02 0.18 0.40 0.35 0.37
1.41 0.12 6.34 0.35 0.81 1.45 0.93 1.15 0.73 0.48 0.10 0.17 1.12 1.69 0.99 0.80 0.67 0.84
AL Z axial length; EKR Z Holladay equivalent keratometry reading; IOL Z intraocular lens; Ktcrp4 Z corneal power calculated by the adjusted total corneal refractive power in the central 4.0 mm zone; LASEK Z laser-assisted subepithelial keratectomy; LASIK Z laser in situ keratomileusis; NA Z not available; PRK Z photorefractive keratectomy; SA Z spherical aberration; Shammas-PL Z Shammas post-LASIK formula; Shammas.cd Z corrected keratometric value calculated by the clinically derived Shammas method *6.0 mm zone total corneal wavefront aberration cornea † Spherical equivalent (SE) of manifest refraction z SE of manifest refraction – predicted refraction
Scheimpflug camera measures at the same region with standard keratometry, Kp would be equal to Ka. Actually, Kp was not statistically different from Ka in a
Figure 5. Strong positive correlation between differences of cornea powers and predicted refraction (Rcalc). One outlier was observed (Case 11 in Table 1). (Ktcrp4 Z cornea power calculated with the TCRP4 method; Shammas.cd Z corrected keratometry power of the clinically derived Shammas method; TCRP4 Z total corneal refractive power of apex-centered 4.0 mm zone).
recent study.24 Because the TCRP method is an adaptation of Ka, the alignment between the Scheimpflug camera and keratometry was critical. In addition, the Scheimpflug camera measurement might be imperfect as a result of blinking or extraneous light influences.25 Recently, fluorescein staining of the tear film was reported to cause more intense backscattering of light, resulting in a measurement error with the Pentacam Scheimpflug camera.26 Therefore, Kp should be reviewed carefully when pathologic conditions of the cornea affecting backscattering are suspected. Even in the healthy cornea, a significant Kp outlier can be encountered as a measurement error.24 The C constant in equation 1 was determined with good accuracy; 95% of the difference from the C constant was as small as 0.5 D (Figure 1). Because Kp was allowed to differ from Ka up to 0.5 D, 0.5 D was the least deviation to be obtained. To the contrary, 95% of difference (LoA) for equation 3 validation might reach 1.0 D (Figure 3). For the verification of equation 3, the direct measurement of refraction in the central 4.0 mm zone was technically impossible; therefore, TCPR4 and TCRP6.5 were used to calculate R4c (equation 6). Because of this limitation, the LoA for
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Figure 6. Holladay equivalent K reading detail report of case 3. The red ring represents the 4.5 mm calculation zone of the Holladay equivalent K reading. The pupil edge (black dotted line) is irregular, and the pupil center is erroneously displaced.
equation 3 validation seemed to increase but the mean changes in R4c were statistically equal to those in TCRP4 (Figure 3). Equation 4 was verified with the group of patients for used in the equation 3 demonstration (Figure 4). Because equation 4 was derived from equations 1 and 3, the validity of equation 4 meant that equation 1 was adequate not only in the specified group but in another group (ie, that used for equation 3). Finally, equations 1 and 4 were generalized into equation 5. By equation 5, a proper K reading for the current IOL formula could be acquired from the TCRP4 of a healthy or excimer laser–modified cornea. By equation 3, which implied that the TCRP4 was a correct refractive power of the cornea, equation 5 could be validated beyond the included corneal power in equation 1 (40.0 to 45.0 D). If equation 3 is true, equation 5 may be applicable in a variety of altered corneas, such those after post-hyperopic PRK or LASIK, those with keratoconus, or those with trauma. However, TCRP varies according to the type of instrument used. Equation 1 meant the real corneal power was 0.7 D less than the K reading in healthy corneas. If the corneal power is calculated with the Gaussian formula in a 7.5 mm anterior corneal radius, a 0.822 ratio of the back to front surface central radius, and 550 mm
thickness, the Gaussian equivalent power would be 43.8 D whereas the K reading would be 45.0 D.2 Because the theoretical corneal power is 1.2 D less with the Gaussian formula, the corneal power by the Gaussian formula would be smaller than that calculated with TCRP. In contrast to this conjecture, ray tracing calculates a lower power of the cornea than the Gaussian formula for normal eyes with the Galilei dual Scheimpflug analyzer (Ziemer Ophthalmic Systems AG).10 Therefore, our results must be considered with respect to the Pentacam system only. The Holladay 2 is a fourth-generation formula and uses measurements of corneal power, corneal diameter, ACD, lens thickness, refraction, AL, and age to refine the ELP.7,27 Because the third-generation formula assumes that the ELP is related to central corneal power, the artifact of low corneal power after myopic corneal refractive surgery will cause the formula to presume a falsely shallow ELP and recommend a lower IOL power than required.7,28 To avoid this pitfall, the Holladay 2 formula uses the mean power of the normal cornea for the ELP calculation in consideration of other factors by checking “Previous RK [radial keratometry], PRK, ALK [automated lamellar keratoplasty], LASIK.” box.7,29 In addition, the Holladay 2 formula21 is recommended for the accurate estimation in cases outside the usual range of corneal
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power or AL.7,27,C A patient who has myopic LASIK frequently has a longer AL. Our TCRP method was tested for various ranges of age (35 to 62 years) and AL (24.63 to 30.46 mm) in eyes after PRK, LASIK, and LASEK surgery. Diverse types of IOL (eg, 1-piece monofocal, 3-piece monofocal, multifocal, and toric) were included. A benchmark standard of refractive outcomes after normal cataract surgery without previous refractive surgery is 85% of patients achieving a final SE within G1.0 D and 55% achieving within G0.5 D.22 In a recent study,8 the Shammas method predicted 53.5% of eyes within G0.5 D and 80.9% of eyes within G1.0 D of the target refraction. When the prediction accuracy of the Shammas method was similar with a previous study,8,22 the TCRP method satisfied the benchmark standard with good predictability. The predicted refraction of each method was well correlated with each corneal power except in case 11, which had a very long AL. Because the TCRP method was better than the Shammas method in case 11, the Holladay 2 formula may be more accurate than the Shammas-PL formula in patients with a very long AL (Table 1). However, a small number of cases were used to test the accuracy of the TCRP method. This could lead to a selection bias; thus, a larger scale study is should be performed. Because the prediction accuracy of the Shammas method in our cases was as good as the one previously reported,8 serious bias is not expected. The Ktcrp4 in equation 5 was an equivalent K reading for a given equivalent corneal power, TCRP4. However, the Ktcrp4 was different from the Holladay equivalent K reading of the Scheimpflug camera (Table 1). Although the Holladay EKR represents the corneal zone in the pupil center, TCRP4 represents the zonal power around the corneal apex. The Holladay EKR shows low repeatability because of the dynamic nature of the pupil as the pupil center changes position.30 Sometimes, the Pentacam Scheimpflug camera measured the pupil center incorrectly (Figure 6 and Table 1). In addition, the radius of the corneal back surface should be preserved in the preoperative state for the Holladay EKR calculation.2 However, Ktcrp4 may be applicable in subclinical or manifest ectasia of the posterior cornea if TCRP4 would accurately reflect corneal refractive power. The TCRP method seemed to work well in corneas with high spherical aberration (Table 1). Because optimized laser profiles were used to keep normal corneal asphericity and HOAs in verification of equation 3, this equation might not be valid for abnormally oblate corneas treated with old laser profiles. In our case series, spherical aberration up to 1.8 mm did not affect the accuracy of the TCRP method (case 1 in Table 1).
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In conclusion, TCRP4 was successfully converted into an equivalent K reading by the simple addition of 0.7 D in the corneal status after myopic keratorefractive correction. The TCRP4 method might be applicable to various corneal profiles if the TCRP represents the true refractive power of the cornea. WHAT WAS KNOWN The total corneal refractive power of the Pentacam Scheimpflug camera is calculated by ray tracing to provide an equivalent corneal power but has not been applicable for IOL power calculation because current formulas are optimized to the standard K reading. WHAT THIS PAPER ADDS By addition of 0.7 D to the total corneal refractive power at the 4.0 mm zone of the Scheimpflug camera, the total corneal refractive power was converted to the equivalent K reading in the normal and modified corneas after myopic keratometric surgery. After myopic keratometric surgery, the IOL power was successfully calculated using the Holladay 2 formula and the corneal power that was derived from the total corneal refractive power at the 4.0 mm zone.
REFERENCES 1. Shammas HJ, Shammas MC, Garabet A, Kim JH, Shammas A, LaBree L. Correcting the corneal power measurements for intraocular lens power calculations after myopic laser in situ keratomileusis. Am J Ophthalmol 2003; 136:426–432 2. Holladay JT, Hill WE, Steinmueller A. Corneal power measurements using Scheimpflug imaging in eyes with prior corneal refractive surgery. J Refract Surg 2009; 25:862–868; erratum, 2010; 26:387 3. Borasio E, Stevens J, Smith GT. Estimation of true corneal power after keratorefractive surgery in eyes requiring cataract surgery: BESSt formula. J Cataract Refract Surg 2006; 32:2004–2014 4. Hamilton DR, Hardten DR. Cataract surgery in patients with prior refractive surgery. Curr Opin Ophthalmol 2003; 14:44–53 5. Savini G, Hoffer KJ. Pentacam equivalent K-reading [letter]. J Refract Surg 2010; 26:388–389; reply by JT Holladay, WE Hill, A Steinmueller, 389–391 6. Retzlaff JA, Sanders DR, Kraff MC. Development of the SRK/T intraocular lens implant power calculation formula. J Cataract Refract Surg 1990; 16:333–340; correction, 528 7. Fang JP, Hill W, Wang L, Chang V, Koch DD. Advanced intraocular lens power calculations. In: Kohnen T, Koch DD, eds, Cataract and Refractive Surgery (Essentials in Ophthalmology). Berlin, Germany, Springer-Verlag, 2005; 38–40 8. McCarthy M, Gavanski GM, Paton KE, Holland SP. Intraocular lens power calculations after myopic laser refractive surgery: a comparison of methods in 173 eyes. Ophthalmology 2011; 118:940–944
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9. Haigis W. Intraocular lens calculation after refractive surgery for myopia: Haigis-L formula. J Cataract Refract Surg 2008; 34:1658–1663 10. 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. Available at: http://www.iovs.org/content/52/3/ 1716.full.pdf. Accessed April 19, 2014 11. Norrby S. Pentacam keratometry and IOL power calculation [letter]. J Cataract Refract Surg 2008; 34:3; reply by E Borasio, 4 12. Savini G, Barboni P, Carbonelli M, Hoffer KJ. Agreement between Pentacam and videokeratography in corneal power assessment. J Refract Surg 2009; 25:534–538 13. Kim SW, Kim EK, Cho B-J, Kim SW, Song KY, Kim T-i. Use of the Pentacam true net corneal power for intraocular lens calculation in eyes after refractive corneal surgery. J Refract Surg 2009; 25:285–289 14. Yi J-H, Shin JY, Ha BJ, Kim SW, Cho BJ, Kim EK, Kim T-i. The comparison of central and mean true-net power (Pentacam) in calculating IOL-power after refractive surgery. Korean J Ophthalmol 2009; 23:1–5. Available at: http://www.ncbi.nlm. nih.gov/pmc/articles/PMC2655745/pdf/kjo-23-1.pdf. Accessed April 19, 2014 15. Holladay JT. Accuracy of Scheimpflug Holladay equivalent keratometry readings after corneal refractive surgery [letter]. J Cataract Refract Surg 2010; 36:182–183; reply by Q Tang, KJ Hoffer, MD Olson, KM Miller, 183–184 16. Tang Q, Hoffer KJ, Olson MD, Miller KM. Accuracy of Scheimpflug Holladay equivalent keratometry readings after corneal refractive surgery. J Cataract Refract Surg 2009; 35:1198–1203 €chle M. Un17. Seitz B, Langenbucher A, Nguyen NX, Kus MM, Ku derestimation of intraocular lens power for cataract surgery after myopic photorefractive keratectomy. Ophthalmology 1999; 106:693–702 18. Gambato C, Catania AG, Vujosevic S, Midena E. Wavefrontoptimized surface ablation with the Allegretto Wave Eye-Q excimer laser platform: 12-month visual and refractive results. J Refract Surg 2011; 27:792–795 19. McAlinden C, Skiadaresi E, Moore JE. Visual and refractive outcomes following myopic laser-assisted subepithelial keratectomy with a flying-spot excimer laser. J Cataract Refract Surg 2011; 37:901–906 lez-Me ijome JM, 20. Alfonso JF, Ferrer-Blasco T, Gonza sGarcıa-Manjarres M, Peixoto-de-Matos SC, Monte R. Pupil size, white-to-white corneal diameter, and Mico anterior chamber depth in patients with myopia. J Refract Surg 2010; 26:891–898 21. Shammas HJ, Shammas MC. No-history method of intraocular lens power calculation for cataract surgery after myopic laser in situ keratomileusis. J Cataract Refract Surg 2007; 33:31–36 22. Gale RP, Saldana M, Johnston RL, Zuberbuhler B, McKibbin M. Benchmark standards for refractive outcomes after NHS cataract surgery. Eye 2009; 23:149–152. Available at: http://
23. 24.
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www.nature.com/eye/journal/v23/n1/pdf/6702954a.pdf. Accessed April 19, 2014 Khurana AK. Theory and Practice of Optics and Refraction, 2nd ed. Noida, UP, India, Elsevier India, 2008 Gonen T, Cosar CB, Sener B, Keskinbora KH. Comparison of keratometric data obtained by automated keratometer, Dicon CT 200, Allegro Topolyzer, and Pentacam. J Refract Surg 2012; 28:557–561 Wheeldon CE, McGhee CNJ. Corneal tomography and anterior chamber imaging. In: Brightbill FS, McDonnell PJ, McGhee CNJ, Farjo AA, Serdarevic O, eds, Corneal Surgery: Theory Technique and Tissue, 4th ed. St. Louis, Mo, Mosby/ Elsevier, 2009; 83–93 Hirnschall N, Crnej A, Gangwani V, Findl O. Effect of fluorescein dye staining of the tear film on Scheimpflug measurements of central corneal thickness. Cornea 2012; 31:18–20 Howes FW. Patient work-up for cataract surgery. In: Yanoff M, Duker JS, eds, Ophthalmology, 3rd ed. St. Lous, MO, Mosby, 2009; 416–417 Koch DD, Wang L. Calculating IOL power in eyes that have had refractive surgery [editorial]. J Cataract Refract Surg 2003; 29:2039–2042 Packer M, Fine IH, Hoffman RS. Biometry for refractive lens surgery. In: Fine IH, Packer M, Hoffman RS, eds, Refractive Lens Surgery. Berlin, Germany, Springer-Verlag, 2005; 11–20 McAlinden C, Khadka J, Pesudovs K. A comprehensive evaluation of the precision (repeatability and reproducibility) of the Oculus Pentacam HR. Invest Ophthalmol Vis Sci 2011; 52:7731–7737. Available at: http://www.iovs.org/content/52/ 10/7731.full.pdf. Accessed April 19, 2014
OTHER CITED MATERIAL
€ te GmbH. The PentacamÒ. The gold standard A. Oculus Optikgera in anterior segment tomography. Calculation of corneal power. Available at: http://www.pentacam.com/sites/calc_corneal_ power.php. Accessed April 19, 2014 B. Holladay IOL Consultant User’s Guide and Reference Manual. Houston TX, Holladay Lasik Institute, 1999 C. Holladay JT. Holladay Consulting, Inc., 2008. Advanced IOL calculations. Available at: http://www.docholladay.com/ handouts/ADVANCED%20IOL%20CALCS%202h%20BW%20 Handout.pdf. Accessed April 19, 2014
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First author: Kyoung Yul Seo, MD Department of Ophthalmology, Eye and Ear Hospital, Severance Hospital, Institute of Vision Research, Yonsei University College of Medicine, Seoul, South Korea
New equivalent keratometry reading calculation with a rotating Scheimpflug camera for intraocular lens power calculation after myopic corneal surgery Kyoung Yul Seo, MD, Chan Young Im, MD, Hun Yang, MD, Tae-im Kim, MD, Eung Kweon Kim, MD, Terry Kim, MD, Sang Min Nam, MD
PURPOSE: To calculate the keratometric (K) reading in corneas modified by myopic keratorefractive surgery using the total corneal refractive power (TCRP) of the Pentacam rotating Scheimpflug camera. SETTING: University hospitals and private clinics, South Korea DESIGN: Evaluation of diagnostic test or technology. METHODS: The study comprised healthy eyes, eyes having myopic keratorefractive surgery, and eyes having cataract surgery after myopic keratorefractive surgery. The conversion equation from the TCRP in the central 4.0 mm zone (TCRP4) to a K reading was derived in normal corneas. This equation was rechecked and its application range extended in corneas modified by myopic keratorefractive surgery. Then, the predictability of the TCRP method, combining the K reading derived from the TCRP4 and the Holladay 2 formula, was evaluated in a case series of cataract surgery patients who had previous myopic keratorefractive surgery. RESULTS: The K reading derived from the TCRP4 was obtained by adding 0.7 diopter (D). This conversion factor was applicable after myopic keratorefractive surgery because changes in TCRP4 were equal to changes in refraction in the 4.0 mm zone. The TCRP method predicted intraocular lens power within G0.5 D in 83% and within G1.0 D in 94% of eyes having cataract surgery after myopic keratorefractive surgery. CONCLUSION: The TCRP4 of the rotating Scheimpflug camera was successfully converted into the equivalent K reading, and the TCRP method showed good predictability in corneas modified by myopic keratorefractive surgery. Financial Disclosure: No author has a financial or proprietary interest in any material or method mentioned. J Cataract Refract Surg 2014; 40:1834–1842 Q 2014 ASCRS and ESCRS
The power of the cornea is conventionally measured by manual keratometry or autokeratometry (K reading). The keratometer measures the anterior radius of corneal curvature and uses an arbitrary index of refraction of 1.3375 so that a radius of 7.5 mm would yield 45.0 diopters (D).1,2 Therefore, the K reading is the standardized power of the cornea and applicable only if the cornea thickness is 500 mm and the ratio of the back to front surface central radius is approximately 82%.3 Although the K reading does not represent the equivalent corneal power, current formulas for intraocular lens (IOL) 1834
Q 2014 ASCRS and ESCRS Published by Elsevier Inc.
power calculation in cataract surgery are based on K readings and are reliable for the majority of eyes with a physiologic and prolate cornea.3–5 This reliability can be obtained by adjusting formulas using many clinical cases. For example, the SRK/T formula was optimized using an iterative process on 5 data sets consisting of 1677 posterior chamber IOL cases.6 The Holladay 2 formula, which was used in this study, is based on previous observations from a 35 000 patient data set.7 In corneal refractive surgery, the anterior surface is intended to be modified and there is no longer a 0886-3350/$ - see front matter http://dx.doi.org/10.1016/j.jcrs.2013.11.044
EQUIVALENT K FOR IOL POWER CALCULATION AFTER MYOPIC CORNEAL SURGERY
physiologic ratio between the front and back corneal radii; this results in an unreliable K reading for IOL power calculation with current formulas.2,8 In addition, keratometers have an unmeasured central zone that is approximately 3.2 mm in diameter.2,9 Therefore, the central region of the cornea, which is more flattened or steepened by keratorefractive surgery, is essentially ignored.3 The Pentacam (Oculus Optikger€ ate GmbH) a rotating Scheimpflug camera that measures the entire central area of the cornea as well as the posterior corneal surface.2 Techniques that use the Scheimpflug camera for IOL power calculation in cataractous eyes that had previous myopic keratorefractive surgery have been developed. One is the true corneal net power, an approximation of the Gaussian equivalent power, which is the arithmetic sum of the front and back surface powers according to the Gaussian formula.5,10 The Gaussian equivalent power is significantly less than the K reading in virgin corneas and is not appropriate for current IOL formulas.2,3,11,12 However, studies13,14 have incorporated the true net power into the SRK/T formula without effective lens position (ELP) correction. In addition, the Holladay equivalent K reading (EKR) is an adjusted K reading for the difference in the posterior radius from normal.2,5 The Pentacam software (version 1.20r02) calculates the equivalent K reading with anterior and posterior powers by Snell's law. There have been some discussions about the validity of the equivalent K reading in the Pentacam system.5,15,16 The total corneal refractive power (TCRP) is the equivalent corneal power of the Scheimpflug camera
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using a ray-tracing method rather than the Gaussian formula.5,A The Gaussian formula depends on the assumption of paraxial optics, but ray tracing does not rely on paraxial optics and hence produces an accurate method of measuring the corneal power with respect to both the anterior and posterior corneal curvature.10,A To the best of our knowledge, the TCRP has not been used for IOL power calculation, especially in eyes with an altered anterior corneal curvature following myopic refractive surgery. However, the equivalent corneal power would produce inaccurate results with current IOL power calculation formulas, which are accustomed to standard K readings. The equivalent corneal power should be customized for these formulas with some type of conversion. We postulated that each K reading would represent a specific equivalent corneal power for the formula. If we knew the relationship between them, we could pick an equivalent K reading for a given equivalent corneal power. We expected a simple relationship between them because current formulas are successfully adapted to K readings despite their arbitrariness. To verify our hypothesis, we evaluated the simple relationship in the normal cornea, rechecked it, and then expanded the range of its application in myopic keratorefractive surgery patients. Lastly, the converted power from TCRP was coupled with the Holladay 2 formula, and the accuracy of IOL power calculation was evaluated in cataract surgery cases after myopic keratorefractive surgery. PATIENTS AND METHODS This retrospective clinical practice study prospectively obtained approval of the Institutional Review Board, CHA University. It adhered to the tenets of the Declaration of Helsinki.
Submitted: July 5, 2013. Final revision submitted: November 13, 2013. Accepted: November 30, 2013.
Measurement of Total Corneal Refractive Power
From the Department of Ophthalmology (Seo, T-i. Kim, E.K. Kim), Eye and Ear Hospital, Severance Hospital, Institute of Vision Research, Yonsei University College of Medicine; the Ian Eye Center (Im); the SU Yonsei Eye Clinic (Yang); the Corneal Dystrophy Research Institute (T-i. Kim, E.K. Kim), Yonsei University College of Medicine, Seoul; the Department of Ophthalmology (Nam), CHA Bundang Medical Center, CHA University, Seongnam, South Korea; the Department of Ophthalmology (T. Kim), Duke Eye Center, Durham, North Carolina, USA. Supported by the Converging Research Center Program through the Ministry of Science, ICT and Future Planning, Korea (2013K000373). Corresponding author: Sang Min Nam, MD, Department of Ophthalmology, CHA Bundang Medical Center, CHA University, 59 Yatap-ro, Bundang-gu, Seongnam-si, Gyeonggi-do 463-712, South Korea. E-mail: [email protected].
Each patient was seated with the head in a headrest and was asked to focus on the target at the center of the Scheimpflug system (Pentacam or Pentacam HR). Every Scheimpflug system in this study was calibrated and technically supported by the regional branch of Oculus. The operator moved the joystick until arrows on the display were aligned with the horizontal, vertical, and anterior– posterior axes. As soon as the image was aligned perfectly, the patient was asked to keep his or her eye open, after which the scanning process started. Automatic release was used to reduce variables. The 25-images mode was chosen so that the rotating camera acquired 25 scans in 1 second. In the power distribution display of the Scheimpflug system software (version 1.18r04), the zone, apex, and total corneal refractive power options were selected and the zone diameter was set as 4.0 mm. Then, Km in “power calculations in actual zone” was read as the total corneal refractive power in the central 4.0 mm zone (TCRP4).
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EQUIVALENT K FOR IOL POWER CALCULATION AFTER MYOPIC CORNEAL SURGERY
Basic Concept of the Total Corneal Refractive Power Method If TCRP4pre is the correctly computed power of the cornea before refractive surgery, the K reading of the cornea before refractive surgery (Kpre) and TCRP4pre is as follows: Kpre TCRP4pre Z C ðconstantÞ
(1)
From the clinical history method, the power of the postrefractive surgery cornea (Kch) is given by4,17 Kch Z Kpre ðR4c:post R4c:preÞ
(2)
where R4c.pre is the refraction before refractive surgery measured at the apex-centered 4.0 mm zone of the corneal plane and R4c.post is refraction after refractive surgery measured at the apex-centered 4.0 mm zone of the corneal plane. If the next equation is proven, R4c:post R4c:pre Z TCRP4pre TCRP4post
(3)
(TCRP4post is the TCRP4 of the cornea after refractive surgery) Kch will be calculated from TCRP4post, where Kch Z Kpre ðR4c:post R4c:preÞ Z Kpre ðTCRP4pre TCRP4postÞ Z ðTCRP4pre þ CÞ ðTCPR4pre TCRP4postÞ Z TCRP4post þ C (4) Now, both effective cornea powers for pre-refractive and post-refractive surgery (Ktcrp4) can be generally expressed with TCRP4 by equations 1 and 4: Ktcrp4 Z TCRP4 þ C
the K reading with a keratometric index of 1.3375.11 Finally, healthy eyes of healthy subjects (20 subjects for each subset in the 20, 30, 40, 50, and 60 years of age range) who had visited between 2007 and 2012 were recruited. To verify equation 1, the agreement between Ka and TCRP4 was studied with the Bland-Altman plot. The C constant of equation 1 was calculated by averaging (Ka TCRP4). It was confirmed with the Pearson product moment correlation that the C constant was independent of the patient’s age and corneal power.
(5)
Study Procedure First, equation 1 was proved and the C constant of equation 1 was determined through a retrospective review of medical records of healthy subjects. Second, equation 3 was verified by reviewing the preoperative and postoperative records of patients who had photorefractive keratectomy (PRK) or laser in situ keratomileusis (LASIK) for myopia. Then, Ktcrp4 for post-refractive surgery was calculated with equation 5, and the compatibility of Kch and Ktcrp4 was studied. Lastly, the cases of cataract surgery after PRK, LASIK, or laser-assisted subepithelial keratectomy (LASEK) for myopia were reviewed and the IOL prediction error with Ktcrp4 was estimated.
Verification of Equation 1 and Determination of the Constant One eye of each healthy subject who had visited the Ian Eye Center was randomly selected and reviewed. The inclusion criteria were as follows: no history of corneal surgery or ocular surface abnormalities; mean K power of autokeratometry (Ka) ranging from 40.0 D to 45.0 D; difference between mean corneal front power of the Scheimpflug camera (Kp) and Ka less than 0.5 D; Ka greater than TCRP4. Because Kp is developed to produce the same value as Ka, any difference implies that an unreliable measurement was taken with the Scheimpflug camera or with autokeratometry. In addition, TCRP4 rarely exceeds Ka in healthy corneas because the true corneal power in the principle plane is less than
Verification of Equation 3 and Calculation of Refraction for the 4.0 mm Zone One eye of each patient who had PRK or LASIK at B&VIIT Eye Center between 2009 and 2011 was randomly selected and reviewed. The Allegretto Wave Eye-Q laser (Wavelight Laser Technologie AG) or the Amaris excimer laser (Schwind eye-tech-solutions GmbH and Co. KG) was used for the surgery. The wavefront-optimized treatment of the Allegretto Wave Eye-Q laser or the aberration-free treatment of Amaris excimer laser was implemented to preserve the cornea's asphericity and avoid additional higher-order aberrations (HOAs).18,19 Data from more than 6 months after surgery were used. The eye was included in the study based on the following criteria: corrected visual acuity not worse than 20/20 preoperatively and postoperatively; cornea healthy before the surgery and not accompanied by any postoperative complication; difference between Kp and corresponding Ka less than 0.5 D preoperatively and postoperatively. For verifying equation 3, the manifest refraction was converted to the refraction measured at the apex-centered 4.0 mm zone of corneal plane (R4c). Because the manifest refraction had been measured under mesopic conditions, it was presumed that the corresponding pupil size of the patients was approximately 6.5 mm.20 The total corneal refractive power of the apex-centered 6.5 mm zone (TCRP6.5) was obtained from the power distribution display of the Scheimpflug camera after the zone diameter in the lower box was edited as 6.5. Then, R4c was calculated with the manifest refraction measured at the corneal plane (Rc), TCRP4, and TCRP6.5, where R4c Z Rc þ ðTCRP6:5 TCRP4Þ
(6)
By the equation 6, R4c:post R4c:pre Z Rc:post þ ðTCRP6:5post TCRP4postÞ ðRc:pre þ ðTCRP6:5pre TCRP4preÞÞ Z ðRc:post Rc:preÞ þ ðTCRP6:5post TCRP4postÞ ðTCRP6:5pre TCRP4preÞ (7) where Rc.pre and TCRP6.5pre are preoperative Rc and TCRP6.5, respectively, and Rc.post and TCRP6.5post are the postoperative Rc and TCRP6.5, respectively. Rc was calculated from the refractive error at spectacle plane (R) with the formula1,17 Rc Z R=ð1 0:012 RÞ
(8)
Then, equation 3 was confirmed by the Bland-Altman plot between (R4c.post R4c.pre) and (TCRP4pre TCRP4post). Finally, equation 4 was checked by the BlandAltman plot between Kch and (TCRP4post C C).
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Accuracy Test for Equation 5 with Cataract Surgery Cases after Refractive Surgery The cases of cataract surgery after PRK, LASIK, and LASEK for myopia performed between 2009 and 2012 at several clinics were reviewed. The cases were included if there were no significant complications during cataract surgery; postoperative manifest refraction was taken after more than 30 days; the difference between Kp and Ka was less than 0.5 D. The spherical aberration of the 6.0 mm total corneal wavefront aberration was calculated using the Zernike analysis of the Scheimpflug camera. The spherical equivalent (SE) of the predicted refraction (Rcalc) according to Ktcrp4 and the Holladay 2 formula was compared with the SE of the postoperative manifest refraction (Rtrue) through calculation of the arithmetic prediction error, Rtrue Rcalc. The percentages of correct refraction predictions within G0.5 D and G1.0 D were calculated. The Holladay 2 formula is available as part of the Holladay IOL Consultant software.B The “Previous RK, PRK, ALK, LASIK.” box was checked, and Ktcrp4 was input as the surgeonentered K value for alternate K. The horizontal white-towhite length and ultrasound measurements of the phakic anterior chamber depth (ACD), lens thickness, and axial length (AL) were entered. The results of Ktcrp4 and Holladay 2 formula were compared with results obtained with the no-history method of Shammas and Shammas.21 The no-history method of Shammas and Shammas is 1 of the 5 most accurate methods of the 25 formula combinations and uses only postoperative biometry.8 For the Shammas method, the corrected K value (Shammas.cd) and the predictive refraction were calculated with the clinically derived method and the Shammas post-LASIK formula (Shammas-PL), respectively. In addition, the prediction error of the Holladay EKR with the Holladay 2 formula (“Previous RK, PRK, ALK, LASIK.” on) was calculated. In the Holladay report of the Pentacam system, the Holladay EKR is displayed for pupil-centered 4.5 mm zone.
Statistical Analysis
Figure 1. Bland-Altman plot of the difference between the mean keratometric power of autokeratometry (Ka) and the total corneal refractive power of apex-centered 4.0 mm zone (TCRP4) in healthy subjects; Ka TCRP4 was not correlated with the mean of Ka and TCRP4 (Pearson r Z 0.116, PZ.251).
Ka TCRP4 Z 0:7
(1-1)
The C constant could be deviated G0.5 D from 0.7 D (Figure 1). Equation 3: Statistically Equivalence of Refractive Changes at Central 4.0 mm of Cornea Plane and Changes in Total Corneal Refractive Power of Scheimpflug Camera The medical records of 63 patients (30 cases of PRK and 33 cases of LASIK) were reviewed. The mean age was 26 G 5 years, and the mean preoperative manifest refraction was 5.37 G 1.93 D. The postoperative manifest refraction was taken after a median time of 284 days (interquartile range, 201 to 336 days). The mean difference between the refractive changes at the central 4.0 mm of the corneal plane and the
SPSS software (version 20, International Business Machines Corp.) was used for general statistical analysis. Bland-Altman plots and scatterplots were drawn and analyzed using Sigmaplot software (version 12.0, Systat Software, Inc.).
RESULTS Equation 1: Relationship between Keratometric Power of Autokeratometry and Total Corneal Refractive Power of the Scheimpflug Camera in Healthy Corneas The mean age of 100 healthy patients (45 men and 55 women) was 44 years G 15 (SD). The difference between Ka and TCRP4 in healthy corneas was independent of corneal power and patient's age (Figures 1 and 2). The mean difference between Ka and TCRP4 was 0.7 G 0.3 D (range 0.7 to 0.8 D; 95% confidence interval [CI]), and equation 1 was completed as:
Figure 2. Correlation between age and Ka TCRP4. No significant correlation was found (Pearson r Z 0.005, PZ.963) (Ka Z mean keratometric power of autokeratometry; TCRP4 Z total corneal refractive power of apex-centered 4.0 mm zone).
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Figure 3. Bland-Altman plot of the difference between postoperative changes in manifest refraction for the central 4.0 mm zone of corneal plane (R4cpost-pre) and the total corneal refractive power of the apexcentered 4.0 mm zone (TCRP4pre-post).
TCRP4 changes was 0.0 G 0.5 D (95% CI, 0.1 to 0.1 D), and the absolute value of the limits of agreement (LoA) was less than 1.0 D (Figure 3). Equation 4: Verification of Equation 1 in a Different Group Via Combination of Equation 3 The group for the equation 3 demonstration was applied again to prove equation 4. By equation 3, the refractive changes at the central 4.0 mm of the corneal plane could be replaced with the TCRP4 changes. If equation 1 and equation 3 were accurate, Kch and (TCRP4post C 0.7) in equation 4 would show no significant difference between them. The mean difference between Kch and (TCRP4post C 0.7) was 0.1 G 0.5 D (95% CI, 0.2 to 0.0 D), and the LoA were 1.0 D and 0.8 D (Figure 4). Accuracy of Equation 5 with Holladay 2 Formula (Total Corneal Refractive Power Method) in Cataract Surgery after Corneal Refractive Surgery In 18 cases of 14 patients, 9 cases (50%) were correctly predicted within G0.50 D and 14 cases (78%) were within G1.0 D by the Shammas method (Table 1). By the TCRP method, 15 cases (83%) and 17 cases (94%) of patients were properly predicted within G0.5 D and G1.0 D, respectively (Table 1). The difference between Ktcrp4 and Shammas.cd strongly correlated with the difference between Rcalc of Ktcrp4/Holladay 2 and Rcalc of Shammas.cd/ Shammas-PL (Spearman r Z 0.786, P!.001) (Figure 5). Neither method gave a hyperopic prediction error greater than 1.0 D (Table 1). In cases 3 and 14, the centers of the pupil in the Scheimpflug camera were erroneously measured and the Holladay EKRs were not reliable (Figure 6). Without both cases, 5 cases (31%) and 12 cases (75%)
Figure 4. Bland-Altman plot of the difference between the correct K value derived by the clinical history method (Kch) and the effective corneal power calculated with the total corneal refractive power of the apex-centered 4.0 mm zone (Ktcrp4). For the clinical history method, postoperative changes in manifest refraction for the central 4.0 mm zone of corneal plane were calculated.
had a prediction error within G0.5 D and G1.0 D, respectively, when the Holladay EKR was joined with Holladay 2 formula (Table 1). DISCUSSION The new equivalent K reading (Ktcrp4) for the IOL power calculation formula was obtained with the simple addition of 0.7 D to TCRP4 (equation 5). The Ktcrp4 could apply to the healthy cornea (equation 1) and the modified cornea with PRK or LASIK for myopia correction (equation 4). Refraction changes with PRK or LASIK were well reflected by TCRP4 (equation 3). When Ktcrp4 was incorporated in the Holladay 2 formula in eyes after myopic PRK, LASIK, or LASEK, the calculated IOL power was accurate enough to comply with a benchmark standard.22 The TCRP method was devised to be compatible with current IOL calculation formulas that depend on the K reading. The standard manual keratometer measures a 3.2 mm ring area for a 44.0 D cornea.2 The size of the measured ring area changes according to the radius of curvature of the cornea because a fixed size ring is emitted and mirrored by the anterior surface of the cornea.23 The 4.0 mm zone of TCRP4 embraces the group of various sizes of the ring area but is still close to the measured ring area of the standard keratometer. For the accuracy of TCRP to be guaranteed, the mean corneal front power of the Pentacam (Kp) should be within G0.5 D of the mean keratometric power of autokeratometry (Ka). According to the manufacturer of the Pentacam Scheimpflug camera (software version 1.18r04), Kp is the anterior simulated K reading on a ring that is 15 degrees around the corneal apex and developed to accord with Ka. If the
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Table 1. Comparison of prediction errors between the Shammas method, the total corneal refractive power method, and the Holladay equivalent keratometry reading method. Arithmetic Prediction Error (D)z Refraction Corneal IOL Power after Ktcrp4 EKR Age SA AL Implanted Cataract Shammas. Ktcrp4 EKR Shammas.cd (D) (D) Shammas-PL Holladay 2 Holladay2 Case (Y) Surgery (mm)* (mm) IOL Type (D) Surgery (D)† cd (D) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
42 62 47 41 38 62 60 55 55 35 42 44 53 47 51 54 53 53
PRK 1.841 29.90 ZA9003 LASEK 0.327 24.63 ZA9003 LASIK 1.110 28.65 ZA9003 PRK NA 26.54 ZA9003 PRK 0.479 27.32 ZA9003 LASIK 0.975 27.28 ZA9003 LASIK NA 27.19 ZA9003 PRK 0.937 29.08 ZCB00 PRK 0.394 26.76 ZCB00 LASIK 0.755 26.72 ZCB00 PRK 0.003 30.46 920H LASIK 0.899 26.53 PC-60 AD LASIK 0.528 28.69 SN60WF LASIK 0.325 25.04 SN60T4 LASIK 0.33 27.57 SN6AD1 PRK 0.271 26.19 ZMB00 LASIK 1.136 26.45 LISA 809M LASIK 0.901 26.49 LISA 809M
17.0 21.5 18.0 19.5 19.5 14.0 15.5 13.5 17.5 18.5 2.0 20.5 18.0 19.5 16.5 18.5 17.0 17.0
0.50 0.75 0.50 0.13 0.25 0.50 0.13 2.00 1.63 3.38 0.63 1.00 0.75 0.00 0.13 0.25 0.50 0.25
33.8 40.4 35.4 37.0 36.1 39.9 38.9 39.7 40.2 41.4 45.5 36.4 35.4 40.2 38.1 38.9 39.1 38.9
33.9 41.6 36.3 38.3 37.1 40.9 40.5 39.6 41.2 41.5 46.4 37.0 36.1 41.0 38.6 39.6 38.9 38.9
34.9 41.7 42.3 38.5 38.0 41.4 40.6 40.9 41.5 42.3 46.1 38.1 37.2 42.7 39.4 40.0 40.1 40.0
0.35 1.07 0.40 1.20 0.72 0.33 0.95 0.14 0.35 0.22 2.10 1.49 0.34 0.54 0.25 0.15 0.74 0.55
0.41 0.22 0.10 0.54 0.10 0.56 0.31 0.21 0.42 0.39 0.40 1.27 0.00 0.02 0.18 0.40 0.35 0.37
1.41 0.12 6.34 0.35 0.81 1.45 0.93 1.15 0.73 0.48 0.10 0.17 1.12 1.69 0.99 0.80 0.67 0.84
AL Z axial length; EKR Z Holladay equivalent keratometry reading; IOL Z intraocular lens; Ktcrp4 Z corneal power calculated by the adjusted total corneal refractive power in the central 4.0 mm zone; LASEK Z laser-assisted subepithelial keratectomy; LASIK Z laser in situ keratomileusis; NA Z not available; PRK Z photorefractive keratectomy; SA Z spherical aberration; Shammas-PL Z Shammas post-LASIK formula; Shammas.cd Z corrected keratometric value calculated by the clinically derived Shammas method *6.0 mm zone total corneal wavefront aberration cornea † Spherical equivalent (SE) of manifest refraction z SE of manifest refraction – predicted refraction
Scheimpflug camera measures at the same region with standard keratometry, Kp would be equal to Ka. Actually, Kp was not statistically different from Ka in a
Figure 5. Strong positive correlation between differences of cornea powers and predicted refraction (Rcalc). One outlier was observed (Case 11 in Table 1). (Ktcrp4 Z cornea power calculated with the TCRP4 method; Shammas.cd Z corrected keratometry power of the clinically derived Shammas method; TCRP4 Z total corneal refractive power of apex-centered 4.0 mm zone).
recent study.24 Because the TCRP method is an adaptation of Ka, the alignment between the Scheimpflug camera and keratometry was critical. In addition, the Scheimpflug camera measurement might be imperfect as a result of blinking or extraneous light influences.25 Recently, fluorescein staining of the tear film was reported to cause more intense backscattering of light, resulting in a measurement error with the Pentacam Scheimpflug camera.26 Therefore, Kp should be reviewed carefully when pathologic conditions of the cornea affecting backscattering are suspected. Even in the healthy cornea, a significant Kp outlier can be encountered as a measurement error.24 The C constant in equation 1 was determined with good accuracy; 95% of the difference from the C constant was as small as 0.5 D (Figure 1). Because Kp was allowed to differ from Ka up to 0.5 D, 0.5 D was the least deviation to be obtained. To the contrary, 95% of difference (LoA) for equation 3 validation might reach 1.0 D (Figure 3). For the verification of equation 3, the direct measurement of refraction in the central 4.0 mm zone was technically impossible; therefore, TCPR4 and TCRP6.5 were used to calculate R4c (equation 6). Because of this limitation, the LoA for
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Figure 6. Holladay equivalent K reading detail report of case 3. The red ring represents the 4.5 mm calculation zone of the Holladay equivalent K reading. The pupil edge (black dotted line) is irregular, and the pupil center is erroneously displaced.
equation 3 validation seemed to increase but the mean changes in R4c were statistically equal to those in TCRP4 (Figure 3). Equation 4 was verified with the group of patients for used in the equation 3 demonstration (Figure 4). Because equation 4 was derived from equations 1 and 3, the validity of equation 4 meant that equation 1 was adequate not only in the specified group but in another group (ie, that used for equation 3). Finally, equations 1 and 4 were generalized into equation 5. By equation 5, a proper K reading for the current IOL formula could be acquired from the TCRP4 of a healthy or excimer laser–modified cornea. By equation 3, which implied that the TCRP4 was a correct refractive power of the cornea, equation 5 could be validated beyond the included corneal power in equation 1 (40.0 to 45.0 D). If equation 3 is true, equation 5 may be applicable in a variety of altered corneas, such those after post-hyperopic PRK or LASIK, those with keratoconus, or those with trauma. However, TCRP varies according to the type of instrument used. Equation 1 meant the real corneal power was 0.7 D less than the K reading in healthy corneas. If the corneal power is calculated with the Gaussian formula in a 7.5 mm anterior corneal radius, a 0.822 ratio of the back to front surface central radius, and 550 mm
thickness, the Gaussian equivalent power would be 43.8 D whereas the K reading would be 45.0 D.2 Because the theoretical corneal power is 1.2 D less with the Gaussian formula, the corneal power by the Gaussian formula would be smaller than that calculated with TCRP. In contrast to this conjecture, ray tracing calculates a lower power of the cornea than the Gaussian formula for normal eyes with the Galilei dual Scheimpflug analyzer (Ziemer Ophthalmic Systems AG).10 Therefore, our results must be considered with respect to the Pentacam system only. The Holladay 2 is a fourth-generation formula and uses measurements of corneal power, corneal diameter, ACD, lens thickness, refraction, AL, and age to refine the ELP.7,27 Because the third-generation formula assumes that the ELP is related to central corneal power, the artifact of low corneal power after myopic corneal refractive surgery will cause the formula to presume a falsely shallow ELP and recommend a lower IOL power than required.7,28 To avoid this pitfall, the Holladay 2 formula uses the mean power of the normal cornea for the ELP calculation in consideration of other factors by checking “Previous RK [radial keratometry], PRK, ALK [automated lamellar keratoplasty], LASIK.” box.7,29 In addition, the Holladay 2 formula21 is recommended for the accurate estimation in cases outside the usual range of corneal
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power or AL.7,27,C A patient who has myopic LASIK frequently has a longer AL. Our TCRP method was tested for various ranges of age (35 to 62 years) and AL (24.63 to 30.46 mm) in eyes after PRK, LASIK, and LASEK surgery. Diverse types of IOL (eg, 1-piece monofocal, 3-piece monofocal, multifocal, and toric) were included. A benchmark standard of refractive outcomes after normal cataract surgery without previous refractive surgery is 85% of patients achieving a final SE within G1.0 D and 55% achieving within G0.5 D.22 In a recent study,8 the Shammas method predicted 53.5% of eyes within G0.5 D and 80.9% of eyes within G1.0 D of the target refraction. When the prediction accuracy of the Shammas method was similar with a previous study,8,22 the TCRP method satisfied the benchmark standard with good predictability. The predicted refraction of each method was well correlated with each corneal power except in case 11, which had a very long AL. Because the TCRP method was better than the Shammas method in case 11, the Holladay 2 formula may be more accurate than the Shammas-PL formula in patients with a very long AL (Table 1). However, a small number of cases were used to test the accuracy of the TCRP method. This could lead to a selection bias; thus, a larger scale study is should be performed. Because the prediction accuracy of the Shammas method in our cases was as good as the one previously reported,8 serious bias is not expected. The Ktcrp4 in equation 5 was an equivalent K reading for a given equivalent corneal power, TCRP4. However, the Ktcrp4 was different from the Holladay equivalent K reading of the Scheimpflug camera (Table 1). Although the Holladay EKR represents the corneal zone in the pupil center, TCRP4 represents the zonal power around the corneal apex. The Holladay EKR shows low repeatability because of the dynamic nature of the pupil as the pupil center changes position.30 Sometimes, the Pentacam Scheimpflug camera measured the pupil center incorrectly (Figure 6 and Table 1). In addition, the radius of the corneal back surface should be preserved in the preoperative state for the Holladay EKR calculation.2 However, Ktcrp4 may be applicable in subclinical or manifest ectasia of the posterior cornea if TCRP4 would accurately reflect corneal refractive power. The TCRP method seemed to work well in corneas with high spherical aberration (Table 1). Because optimized laser profiles were used to keep normal corneal asphericity and HOAs in verification of equation 3, this equation might not be valid for abnormally oblate corneas treated with old laser profiles. In our case series, spherical aberration up to 1.8 mm did not affect the accuracy of the TCRP method (case 1 in Table 1).
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In conclusion, TCRP4 was successfully converted into an equivalent K reading by the simple addition of 0.7 D in the corneal status after myopic keratorefractive correction. The TCRP4 method might be applicable to various corneal profiles if the TCRP represents the true refractive power of the cornea. WHAT WAS KNOWN The total corneal refractive power of the Pentacam Scheimpflug camera is calculated by ray tracing to provide an equivalent corneal power but has not been applicable for IOL power calculation because current formulas are optimized to the standard K reading. WHAT THIS PAPER ADDS By addition of 0.7 D to the total corneal refractive power at the 4.0 mm zone of the Scheimpflug camera, the total corneal refractive power was converted to the equivalent K reading in the normal and modified corneas after myopic keratometric surgery. After myopic keratometric surgery, the IOL power was successfully calculated using the Holladay 2 formula and the corneal power that was derived from the total corneal refractive power at the 4.0 mm zone.
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First author: Kyoung Yul Seo, MD Department of Ophthalmology, Eye and Ear Hospital, Severance Hospital, Institute of Vision Research, Yonsei University College of Medicine, Seoul, South Korea
