Determining postoperative anterior chamber depth

Determining postoperative anterior chamber depth Katharina Kriechbaum, MD, Oliver Findl, MD, Paul Rolf Preussner, MD, PhD, Christina Ko¨ppl, MD, Jochen Wahl, MD, Wolfgang Drexler, PhD Purpose: To compare measured and calculated postoperative anterior chamber depths (ACDs). Setting: Department of Ophthalmology and Institute of Medical Physics, University of Vienna, Vienna, Austria, and Department of Ophthalmology, University of Mainz, Mainz, Germany. Methods: The postoperative ACD was measured in 189 pseudophakic eyes using a laboratory prototype of partial coherence interferometry (PCI). In 6 intraocular lens (IOL) groups, the mean ACD was calculated by ray tracing based on the best-known A-constants of the SRK formulas. In addition, for each IOL type, each measured ACD was compared with a value calculated using the individual spherical equivalent of the postoperative refraction. Results: The measured and the calculated ACD values were close and did not show systematic differences. The ACD values obtained in the study, however, differed significantly from the values published by the IOL manufacturers. A comparison of the PCI-assessed ACDs and the calculated values using the postoperative refraction showed more scattered results for the refraction-based data, which was probably the result of higher measurement errors with the autorefractometer than with PCI. Conclusions: High-precision interferometry measurements and ray-tracing calculations confirmed each other. The resulting mean ACD values should be used instead of the manufacturers’ values. The refractive outcome of cataract surgery can be improved by combining preoperative high-precision PCI biometry and numerical ray tracing for IOL power calculations. J Cataract Refract Surg 2003; 29:2122–2126  2003 ASCRS and ESCRS

C

ataract surgery is one of the most frequently performed ophthalmic surgical procedures. The aim of the surgery is not only to restore clear media and vision but also to achieve the predicted postoperative refractive status. To date, the best intraocular lens (IOL)

Accepted for publication March 20, 2003. From the Department of Ophthalmology (Kriechbaum, Findl, Ko¨ppl) and Institute of Medical Physics (Drexler), University of Vienna, Vienna, and the Department of Ophthalmology, University of Mainz (Preussner, Wahl), Mainz, Austria. Dr. Drexler is a consultant to Carl Zeiss Meditec AG. None of the other authors has a financial or proprietary interest in any material or method mentioned. Reprint requests to Oliver Findl, MD, Department of Ophthalmology, University of Vienna, Wa¨hringer Gu¨rtel 18-20, 1090 Vienna, Austria. E-mail: [email protected].  2003 ASCRS and ESCRS Published by Elsevier Inc.

power predictions are calculated using various formulas based on measured intraocular parameters; however, inaccurate IOL power calculation remains a problem. In general, there are 2 major formula categories: theoretical and regression. In theoretical formulas, a simplified, theoretic, geometric 2-lens system of the eye consisting of the cornea and lens is assumed. Theoretical calculations are based on Gaussian optics (ie, paraxial approximation), which is an analytic approach to solving the equations of optics. However, this approach is valid only for small angles around the optical axis. Regression formulas are derived by retrospective analyses of a large number of patients who had IOL implantation. Their data were subjected to regression analyses, resulting in IOL power calculation formulas such as the SRK II.1 0886-3350/03/$–see front matter doi:10.1016/S0886-3350(03)00414-0

POSTOPERATIVE ACD PREDICTION

The accuracy of existing formulas is limited for various reasons. The most critical step in obtaining the best IOL power calculation is precise preoperative biometry. Studies based on ultrasound (US) biometry found that approximately 54% of the deviation between the predicted refraction and obtained refraction was caused by errors in preoperative axial length (AL) measurement. A preoperative AL measurement error of 100 ␮m would cause a corresponding postoperative refractive error of approximately 0.28 diopter (D).2,3 Another source of error is the prediction of the postoperative ACD, defined as the distance between the posterior corneal surface (some authors use the anterior corneal surface) and the anterior surface of the implanted IOL. Binkhorst4 originally introduced ACD as the distance between the anterior vertex of the cornea and the posterior principal plane of a convex-plano lens; however, no other author uses this definition. Some, for example Olsen and coauthors,5 measure the ACD from the anterior corneal surface instead of the posterior corneal surface. Another approach, suggested by Holladay,6 is to use the distance between the posterior corneal surface and the position of a theoretical ideal thin lens; that is, the effective lens position (ELP). Because many parameters, mainly interpatient anatomical differences and capsular bag shrinkage, are uncertain, the prediction of postoperative ACD from preoperative data is often unsatisfactory. Considering that inaccuracies in predicting the ELP may account for approximately 20% to 40% of the total refractive prediction error,7 the importance of new solutions for this problem is obvious. Older theoretical IOL calculation formulas disregard the influence of the variability in postoperative ACD on the calculated refractive status and assume a constant ACD value. Newer theoretical formulas seek to improve accuracy by replacing this ACD constant with one that conforms with AL8,9 or by varying ACD with corneal curvature and AL.10,11 Olsen,3 Haigis,12 and Holladay (Holladay 2 formula10) suggest measuring the ACD preoperatively and placing this individual value directly into the formula. A component of modern regression formulas that is necessary to equalize residual errors is the A-constant, which is mainly determined by the ELP after cataract surgery. Because IOL design influences the ELP,13 the IOL constant is used to adjust for variations and must

be adapted for different IOL models.14,15 Usually, the manufacturer supplies the A-constant as well as the most probable mean ACD value for a large number of patients. The greater the deviation of individual eye dimensions from the mean values, the more inaccurate the constants and therefore the formula. Some authors have developed analytical formulas to transform A-constants into ACDs and vice versa.16 However, in the case of a realistic thick IOL and not an ideal thin-lens assumption, as defined by Gaussian optics, such general transformation formulas may give incorrect results. A numerical ray-tracing method was recently introduced to improve the accuracy of IOL power calculations.17–19 In this method, the course of individual rays, refracted on the intraocular surfaces, is defined exactly according to Snell’s law (not to paraxial approximation). To estimate the most probable postoperative ACD for an IOL type, numerical methods are applied to recalculate the postoperative ACD from the given A-constants of the SRK formula. This study evaluated ACDs calculated with numerical methods from the best-known A-constants supplied by IOL manufacturers. The ACDs were compared with the values measured postoperatively using partial coherence interferometry (PCI). In addition, the actual postoperative ACD in each patient was compared with that calculated with ray tracing using the spherical equivalent (SE) of the postoperative refraction.

Patients and Methods One hundred eighty-nine eyes of nonselected consecutive patients scheduled for cataract surgery were included in the study. Silicone-filled eyes and a history of ocular disease other than cataract or previous surgery were exclusion criteria. Preoperatively, the IOLMaster (Carl Zeiss Meditec AG) was used to measure AL, ACD, and keratometry. The IOLMaster biometry unit uses PCI to measure AL,20,21 a photographic technique for ACD, and an autokeratometer for corneal radii. Intraocular lens power was calculated using the SRK/T formula included in the IOLMaster software. Small-incision cataract surgery with IOL implantation in the capsular bag was performed by different surgeons in a standardized fashion. The following foldable IOLs were used: AMO AR40e (74 eyes), Pharmacia 911A (48 eyes), Alcon MA60BM (20 eyes), Alcon MA30BA (19 eyes), Alcon SA30AL (17 eyes), and Alcon SA60AT (11 eyes). From 6 months to 1 year postoperatively, a follow-up examination was performed including objective determina-

J CATARACT REFRACT SURG—VOL 29, NOVEMBER 2003

2123

POSTOPERATIVE ACD PREDICTION

tion of refractive status with an autorefractometer (KR 3500 Auto Kerato-Refractometer, Topcon) and assessment of individual ACD with the laboratory prototype of dual-beam PCI. The ACD value was calculated using ray-tracing software that computes the mean ACD for an IOL using numerical methods17 and SRK formula A-constants as follows:

backward until an ACD that produces the eye’s refraction (SE) is attained. This ACD is compared with the measured ACD using PCI.

1. For the given A-constant, calculate the power of the emmetropic IOL for the mean eye with the SRK formula. (The SRK I, SRK II, and SRK/T give the same results.) 2. Find (by numerical iteration) the power label for the IOL type for which the data set (IOL radii, central thickness, refractive index) in the calculation gives a paraxial power for a thick lens closest to the result in step 1. This is not necessarily the nearest power label available from the manufacturer. 3. Find (by numerical iteration) the ACD for which this IOL, inserted into the mean eye, gives the same power difference to emmetropia as the IOL in step 2. Inside and outside the eye, power differences are approximated by each other by ⌬Poutside ⬇ 0.686 ⫻ ⌬Pinside. This approximation is true for eyes close to the mean eye, proved by the numerical calculations. 4. Repeat step 3 for the 2 IOL power labels above and below the first label. 5. Calculate the arithmetic means of these 5 values, which normally differ less than 0.1 mm from each other.16

The mean ALs in the IOL subgroups were similar and close to the overall mean value (Table 1). The numerical calculations were verified by the independent determination of ACD with PCI. There was good agreement between the recalculated ACDs using the manufacturer-supplied A-constants and the mean values by PCI (Table 1). Table 1 shows the recalculated ACD values using the postoperative refraction. The focus was mainly on the AR40e and 911A groups because they had the largest data samples. In the AR40e group, the mean ACD measured postoperatively with PCI was 4.096 mm ⫾ 0.345 (SD) (range 3.219 to 5.120 mm). The corresponding computer-calculated value based on the postoperative SE was 3.92 ⫾ 0.61 mm (range 2.77 to 6.07 mm). The mean difference between the measurement and calculation expressed as a numerical error was 0.17 mm (range –1.68 to 1.91 mm) and as an absolute error, 0.39 mm (range 0.00 to 1.91 mm). In the 911A group, the mean PCI-measured ACD was 4.001 ⫾ 0.291 mm (range 3.290 to 4.705 mm) and the mean calculated ACD, 3.93 ⫾ 0.58 mm (range 2.44 to 5.37 mm). The numerical difference was 0.07 mm (range –1.09 to 0.86 mm) and the absolute difference, 0.34 mm (range 0.03 to 1.09 mm).

The mean of these values is valid for a defined IOL type. In the second part of the study, the preoperative data set, consisting of the mean corneal radius, AL, and type and dioptric power of the implanted IOL, was used with the SE of the stable postoperative refraction to calculate an ACD value with ray tracing. The computer program simulates the individual eye and places the lens in a “virtual” anterior chamber. The course of rays, refracted onto intraocular surfaces, is calculated exactly according to Snell’s law. Then, the computer program changes the lens position forward and

Results

Table 1. Results of numerical calculations and PCI. IOL

n

Mean AL* (mm)

ACDMan (mm)

Mean ACDPCI ⫾ SD (mm)

ASRK

ACDS (mm)

Mean ACDRef ⫾ SD (mm)

AR40e

74

23.60

5.20

4.096 ⫾ 0.345

118.4

4.09

3.92 ⫾ 0.61†

911A

48

22.97

5.14

4.001 ⫾ 0.291

118.3

3.97

3.93 ⫾ 0.58

MA60BM

20

23.38

5.50

4.253 ⫾ 0.335

118.9

4.24

4.57 ⫾ 0.46†

MA30BA

19

23.44

5.49

4.294 ⫾ 0.243

118.9

4.39

4.53 ⫾ 0.56†

SA30AL

17

23.41

5.00

4.198 ⫾ 0.299

118.4

4.30

4.07 ⫾ 1.20

SA60AT

11

23.41

5.00

4.000 ⫾ 0.231

118.4

4.31

4.05 ⫾ 0.38

ASRK ⫽ A-constant used in SRK formula; ACDS ⫽ ACD value as derived from the A-constant; ACDMan ⫽ ACD values supplied by the manufacturers; ACDPCI ⫽ ACD value measured with PCI; ACDRef ⫽ ACD recalculated with numerical methods using the postoperative SE; AL ⫽ axial length (IOLMaster) *Mean of all ALs ⫽ 23.37 mm † ACDRef value differs significantly from ACDPCI

2124

J CATARACT REFRACT SURG—VOL 29, NOVEMBER 2003

POSTOPERATIVE ACD PREDICTION

Discussion In this study, there was high accordance between the mean ACDs assessed postoperatively with PCI and the mean values obtained by numerical ray tracing. This approach gave valid mean values for a specific IOL type. The IOL manufacturer-supplied ACD values, at least for the IOLs we investigated, differed significantly from the actual measured values. In cases in which the manufacturer’s values are determined from the position of an ideal thin lens calculated in Gaussian optics, this approach leads to an intolerably high error. Our software allows recalculation of the individual ACD based on biometry data, the measured postoperative refraction, and the implanted IOL power. Comparison of these calculations with the actual ACD measured in each eye also showed convincing results. Numerical ray tracing describes the course of rays refracted on intraocular surfaces exactly according to Snell’s law. It is not only valid for the small angles around the optical axis but also for off-axis rays. In addition, the exact determination of the course of light penetrating the eye is independent of AL and enables better IOL power calculation than the SRK formula in very long or short eyes.17 To understand the limits of IOL power calculation accuracy, the following must be considered: errors in manufacturers’ IOL data and fabrication limits, inaccurate preoperative ocular biometry, and incorrect estimation of postoperative ACD. Intraocular lens manufacturers determine A-constants based on the analyses of large collections of patient data. The high agreement of numerically recalculated ACD values based on these A-constants and the mean of PCI-measured ACDs confirm good statistical processing of A-constants on one hand and the high quality and accuracy of the PCI measurements on the other hand. The inaccuracy of preoperative measurement can be minimized when high-precision measurement methods such as PCI are used. A noninvasive, high-resolution technique,23–26 PCI performs accurate biometry in pseudophakic eyes, with a precision of 2.5 ␮m for ACD measurements.13,15 Thus, the precision of PCI is more than 10 times better than that of optical pachymetry or US, which has been shown to have a precision of 240 to 360 ␮m27–29 for ACD measurement. The labora-

tory prototype of PCI provides precise AL and anterior segment measurements. Measurements with the commercially available IOLMaster show lower but still acceptable precision. Another factor, whose importance has been underestimated, is exact calculation of the postoperative ACD, which has a major influence on postoperative refraction. Exact ACD prediction based on preoperative biometry data is, in principle, impossible because of the effect of several uncertain parameters; for example, a change in the axial IOL position, which is dependent on capsular bag shrinkage. Clearly, it has to be differentiated between the most probable mean ACD value for an IOL type as we present in our study and the ACD predicted for an individual eye. Prediction of the latter is far less exact; however, accuracy could be increased by new algorithms based on our results. To calculate individual postoperative ACD, knowledge of the postoperative refraction is necessary. Without a known refraction, the calculation becomes unsolvable because of an additional unknown variable. When we calculated individual ACDs based on the autorefractometer-assessed postoperative refraction, the results were more scattered than when we compared the mean ACDs; however, there was no systematic bias. The larger scattering can be explained by the higher measurement error of the autorefractometer than of PCI. Serial measurements with the autorefractometer and subjective refraction are known to differ by approximately 0.5 D and therefore have rather poor precision or reproducibility, leading to inaccurate calculations. An error not covered by our investigations results from inaccurate IOL manufacturing. The IOL’s radius and thickness and the refractive index of the optic material vary in the manufacturing process. Fortunately, these errors are assumed to be randomly distributed and thus should not influence the measured or calculated mean ACD values as determined in our study or the mean individual bias relative to these values (eg, as proposed in the algorithm by Olsen and coauthors30). They do, however, influence the resulting mean accuracy of IOL power adaptation. In conclusion, the importance of the correct determination of postoperative ACD has been underestimated and should play a more important role in IOL calculation in the future. Preoperative ocular biometry should profit from high-precision methods such as PCI.

J CATARACT REFRACT SURG—VOL 29, NOVEMBER 2003

2125

POSTOPERATIVE ACD PREDICTION

The accurate data should be processed using numerical ray tracing to calculate IOL power. The combination of high-precision biometry and numerical ray tracing should increase the accuracy of IOL power calculation and, therefore, the refractive outcome of cataract surgery.

References 1. Retzlaff J, Sanders D, Kraff M. A Manual of Implant Power Calculation; SRK Formula. Santa Monica, CA, American Intra-Ocular Implant Society, 1981; 17a, 17b 2. Olsen T. Sources of error in intraocular lens power calculation. J Cataract Refract Surg 1992; 18:125–129 3. Olsen T. Theoretical approach to intraocular lens calculation using Gaussian optics. J Cataract Refract Surg 1987; 13:141–145 4. Binkhorst RD. The optical design of intraocular lens implants. Ophthalmic Surg 1975; 6(3):17–31 5. Olsen T, Corydon L, Gimbel H. Intraocular lens power calculation with an improved anterior chamber prediction algorithm. J Cataract Refract Surg 1995; 21:313– 319 6. Holladay JT. Standardizing constants for ultrasonic biometry, keratometry, and intraocular lens power calculations. J Cataract Refract Surg 1997; 23:1356–1370 7. Olsen T, Gimbel H. Phacoemulsification, capsulorhexis, and intraocular lens power prediction accuracy. J Cataract Refract Surg 1993; 19:695–659 8. Hoffer KJ. The effect of axial length on posterior chamber lens and posterior capsule position. Curr Concepts Ophthalmic Surg 1984; 1(1):20–22 9. Shammas HJF. The fudged formula for intraocular lens power calculations. Am Intra-Ocular Implant Soc J 1982; 8:350–352 10. Holladay JT, Prager TC, Chandler TY et al. A three-part system for refining intraocular lens power calculations. J Cataract Refract Surg 1988; 14:17–24 11. Hoffer KJ. Clinical results using the Holladay 2 intraocular lens power formula. J Cataract Refract Surg 2000; 26:1233–1237 12. Haigis W, Lege B, Miller N, Schneider B. Comparison of immersion ultrasound biometry and partial coherence interferometry for IOL calculation according to Haigis. Graefes Arch Clin Exp Ophthalmol 2000; 238:765–773 13. Findl O, Drexler W, Menapace R, et al. Accurate determination of effective lens position and lens-capsule distance with 4 intraocular lenses. J Cataract Refract Surg 1998; 24:1094–1098

2126

14. Findl O, Drexler W, Menapace R, et al. Improved prediction of intraocular lens power using partial coherence interferometry. J Cataract Refract Surg 2001; 27:861–867 15. Findl O, Drexler W, Menapace R, et al. High precision biometry of pseudophakic eyes using partial coherence interferometry. J Cataract Refract Surg 1998; 24:1087–1093 16. Holladay JT. International Intraocular Lens & Implant Registry 2003. J Cataract Refract Surg 2003; 29:176–197 17. Preussner P-R, Wahl J, Lahdo H, et al. Ray tracing for intraocular lens calculation. J Cataract Refract Surg 2002; 28:1412–1419 18. Preußner P-R, Wahl J. Konsistente numerische Berechnung der Optik des pseudophaken Auges. Ophthalmologe 2000; 97:126–141 19. Preußner P-R, Wahl J, Lahdo H, Findl O. KonsistenteIOL Berechnung. Ophthalmologe 2001; 98:300–304 20. Kiss B, Findl O, Menapace R, et al. Biometry of cataractous eyes using partial coherence interferometry; clinical feasibility study of a commercial prototype I. J Cataract Refract Surg 2002; 28:224–229 21. Kiss B, Findl O, Menapace R, et al. Refractive outcome of cataract surgery using partial coherence interferometry and ultrasound biometry; clinical feasibility study of a commercial prototype II. J Cataract Refract Surg 2002; 28:230–234 22. 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 23. Fercher AF, Roth E. Ophthalmic laser interferometer. Proc SPIE 1986; 658:48–51 24. Fercher AF, Mengedoht K, Werner W. Eye-length measurement by interferometer with partially coherent light. Opt Lett 1988; 13:186–188 25. Hitzenberger CK. Optical measurement of the axial eye length by laser Doppler interferometry. Invest Ophthalmol Vis Sci 1991; 32:616–624 26. Drexler W, Baumgartner A, Findl O, et al. Submicrometer precision biometry of the anterior segment of the human eye. Invest Ophthalmol Vis Sci 1997; 38:1304–1313 27. Mutti DO, Zadnik K, Egashira S, et al. The effect of cycloplegia on measurement of the ocular components. Invest Ophthalmol Vis Sci 1994; 35:515–527 28. Zadnik K, Mutti DO, Adams AJ. The repeatability of measurement of the ocular components. Invest Ophthalmol Vis Sci 1992; 33:2325–2333 29. Koranyi G, Lydahl E, Norrby S, Taube M. Anterior chamber depth measurement: A-scan versus optical methods. J Cataract Refract Surg 2002; 28:243–247 30. Olsen T, Corydon L, Gimbel H. Intraocular lens power calculation with an improved anterior chamber depth prediction algorithm. J Cataract Refract Surg 1995; 21:313– 319

J CATARACT REFRACT SURG—VOL 29, NOVEMBER 2003