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8 Axial Length Dependenceof IOL Constants

INTRODUCTION

In formulas to calculate the necessary power for an intraocular lens (IOL) implant, the IOL itself is represented by its respective lens constants. While the A-constant is the most popular one, it is not the only one: each formula has its own way and hence, its own constant(s) to represent a given IOL type. Table 8.1 gives an overview on popular IOL formulas with their respective constants.

A-constants or ACD-constants are usually stated by the lens manufacturers and are meant for an average measurement set-up. In the literature (e.g. there are simple transformation formulas (‘standard’ relations)1-3 to translate one IOL constant into another. This is the standard situation and the respective constants may be considered as default constants.

For a given surgeon’s measurement set-up it is highly probable that the manufacturers’ constants are less than optimum. Thus, it is commonly agreed (e.g. that the published constants must be customized (individualized, personalized, optimized)4,5 in order to make allowance for different surgeon-specific measurement conditions (e.g.

different combinations of A-scans and keratometers).

Once constants are optimized, the classical (‘standard’) relations between them break down and are replaced by new ones (namely ‘relations between optimized IOL constants’).6, 7 For optical biometry with the Zeiss IOLMaster, such optimized IOL constants are e.g. published in the internet within the framework of the ULIB project.8

With customized constants for a given IOL type and measurement setup, one would expect that these should work equally well for all surgeons with the same instruments and lenses. Optimized IOLMaster constants, for example, are expected to produce the same quality of refractive results for all surgeons. This, however, is not the case in general due to the fact that apart from instrumentation there are additional conditions defining the surgeon’s working environment. Among them is the patients’ axial length distribution.

This article tries to elucidate the influence of axial length on optimized IOL constants.

MATERIAL AND METHODS

To assess the effect of axial length on different IOL constants, two methods were applied:

1. Model calculations on theoretical ametropic eyes derived from the standard Gullstrand eye.

2. Comparison of clinical results for different surgical centers.

Model Calculations

Theoretical ametropic eyes were derived from the Gullstrand eye (#2)9 as already described to some extent in a previous paper.10 The anterior segment (corneal radius, anterior chamber depth and lens thickness) was left

Table 8.1: Popular IOL formulas with their respective IOL constants

Formula SRK II SRK/T Holladay-I HofferQ Haigis Holladay-II

IOL constant A A sf pACD a0, a1, a2 ACD

Table 8.2: Axial and vitreous lengths, refractions and emmetropia IOL powers of the model eyes used, derived from Gullstrand eye #2. The anterior segment was the same for all eyes: ACD (anterior corneal vertex to anterior lenticular vertex): 3.6 mm; corneal radius: 7.7 mm, (phakic) lens power: 20.282 D. An effective IOL position of 4.419 mm was assumed for all model eyes

Model eye Axial length Vitreous length Refraction Emmetropia IOL

[mm] [mm] [D] power [D]

Hyperopic 10 (h10) 20.149 12.944 +11.007 36.385

Hyperopic 5 (h5) 22.149 14.944 +5.403 26.281

Emmetropic (em) 24.149 16.944 0.00 18.272

Myopic 5 (m5) 26.149 18.944 - 5.214 11.767

Myopic 10 (m10) 28.149 20.944 -10.248 6.379

unchanged. Axial myopia or hyperopia was created by increasing or decreasing the standard vitreous length (16.944 mm) by 2 or 4 mm. Axial and vitreous lengths for each model eye can be found in Table 8.2. Paraxial ray tracing with a custom-made PC program as well as a commercial software package (WinLens Plus, V.1.1.5, Linos, Goettingen, Germany) were applied to determine the refractions of the model eyes. The same technique was used to calculate the equivalent (total) power of an equiconvex PMMA lens (center thickness: 0.8 mm, refractive index: 1.490) positioned 4.819 mm11 behind the anterior corneal vertex which made the respective model eye emmetropic. The same lens thickness of 0.8 mm was used for the IOLs for all eyes. (In real life, lens thickness is a function of its refractive power. The error, however, caused by assuming a constant thickness is considered neglectable within the context of these model calculations).

In a second step, ‘clinical’ IOL calculations were performed for all model eyes using the following formulas:

SRK II,12 SRK/T,13 Holladay-I,14 HofferQ,15,16 Haigis2: for each formula, the respective IOL constants were iteratively adjusted to give the very emmetropia IOL power which was derived earlier from paraxial ray tracing.

The same procedure was applied to study the effect of immersion and contact ultrasound on the IOL constants to be used with these two biometry modes. For the standard emmetropic Gullstrand eye it was assumed that immersion ultrasound measures the correct axial length (24.149 mm), while contact ultrasound produces a value 0.30 mm shorter (i.e. 23.849 mm). Again, the respective IOL constants were iteratively varied to give the same emmetropia IOL power for both biometry techniques.

Clinical Data

The results of the model calculations were compared to clinical results, which were retrospectively derived from patient data sent to the author by 11 surgeons from Australia (n=1), Germany (n=2) and the USA (n=8) within the ULIB (User Group for Laser Interference Biometry) project to optimize IOL constants for optical biometry.17 A total of 2095 datasets of patients with an Alcon SN60WF lens were evaluated; further statistical details can be found in Table 8.5. Each set consisted of preoperative biometry (axial length, anterior chamber depth) and keratometry (corneal radii) data obtained with the Zeiss IOLMaster, the spherical equivalent of the stable postoperative refraction at BCDVA and the IOL power implanted.

Optimized constants of all popular IOL formulas were derived for each center. For this purpose, custom-made computer programs were applied performing an iterative mathematical process in which the respective IOL cons-tants were incrementally varied until the mean prediction error (achieved – calculated refraction) was zero.

RESULTS

Model Calculations

Together with biometric data, Table 8.2 lists the primary refractions (‘preoperative’) of the model eyes as well as the respective emmetropia IOL powers determined from paraxial ray-tracing. The IOL constants of the different power formulas necessary to come up with the correct emmetropia IOL are summarized in Table 8.3. Figure 8.1 shows the axial length dependences, thus obtained for the A-constants of the SRK II and SRK/T formulas, Figure 8.2 for the constants sf, pACD and a0 of the Holladay-1, HofferQ and Haigis formulas respectively.

Axial Length Dependence of IOL Constants

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Fig. 8.1: Model calculations: A-constants for the SRK II and SRK/T formulas to produce the correct emmetropia IOLs for model eyes of different axial lengths

Fig. 8.2: Model calculations: IOL constants sf, pACD and a0 for the Holladay-I, HofferQ and Haigis formulas to produce the correct emmetropia IOLs for model eyes of different axial lengths

Table 8.3: Lens constants of the respective IOL formulas necessary to obtain the correct emmetropia IOL power for each model eye

Model eye A SRK2 A SRKT sf pACD a0

Hyperopic 10 (h10) 124.20 120.49 2.524 6.067 1.417

Hyperopic 5 (h5) 121.10 119.55 2.055 5.732 1.225

Emmetropic (em) 118.09 118.38 1.508 5.392 1.040

Myopic 5 (m5) 117.09 117.75 1.308 5.269 0.865

Myopic 10 (m10) 116.70 117.48 2.079 5.893 0.721

The results of the simulations of different biometry techniques (immersion and contact ultrasound) are compiled in Table 8.4 for each biometry mode.

Clinical Results

The results of the individual constants’ optimizations at the different ophthalmosurgical centers are listed in Table 8.5, together with the axial length means and standard deviations in each center. The optimized constants of the Alcon SN60WF for the pooled data—as they are published on the ULIB website8 (in rounded form)—are also given in Table 8.5.

Figure 8.3 shows the customized A-constants for the SRK/T formula derived from the individual patient data in the 11 ophthalmosurgical centers vs the mean axial length of the respective patient population which was used for the optimization. The corresponding results for the constant a0 in the Haigis formula are plotted in Figure 8.4.

DISCUSSION

Our calculations simulating the use of immersion and contact ultrasound clearly demonstrate that constants for

Table 8.4: IOL constants necessary to calculate the correct emmetropia IOL power (18.272 D, cf Tab 8.2) for the standard Gullstrand eye with all IOL power formulas after simulated immersion (24.149 mm) and contact ultrasound (23.849 mm) measurements of the axial length

A SRK2 A SRKT sf pACD a0

Immersion ultrasound 118.09 118.38 1.508 5.392 1.040

Contact ultrasound 117.34 117.56 0.961 4.811 0.415

Fig. 8.3: Customized SRK/T A-constants for the Alcon SN60WF in 11 ophthalmosurgical centers vs mean axial length of the respective patient populations

Fig. 8.4: Customized a0 constants of the Haigis formula for the Alcon SN60WF in 11 ophthalmosurgical centers vs mean axial length of the respective patient populations

Table 8.5: Optimized IOL constants for the different ophthalmosurgical centers, together with the respective numbers of datasets used for constants’ optimization and the axial length means and standard deviations for each center. Extreme values in bold. *): a1=0.4, a2=0.1 . **): published on the ULIB website8

Center n Mean axial A SRK2 A SRKT sf pACD a0 *)

# length [mm]

1 325 23.54 ± 0.97 119.12 118.90 1.756 5.549 1.352

2 50 23.26 ± 0.84 119.87 119.30 1.971 5.712 1.546

3 210 23.76 ± 1.19 119.29 119.05 1.858 5.660 1.521

4 279 23.91 ± 1.25 119.09 119.00 1.846 5.654 1.471

5 199 23.73 ± 1.19 119.38 119.08 1.869 5.654 1.508

6 204 24.13 ± 1.21 119.01 118.99 1.824 5.631 1.321

7 50 23.44 ± 0.89 118.97 118.88 1.739 5.514 1.302

8 301 23.70 ± 1.02 119.17 119.02 1.835 5.642 1.502

9 268 23.47 ± 0.94 119.25 118.97 1.801 5.584 1.408

10 144 23.53 ± 0.99 119.49 119.05 1.835 5.613 1.458

11 65 23.49 ± 0.70 119.42 119.13 1.897 5.677 1.427

All **) 2090 23.68 ± 1.09 119.22 119.01 1.829 5.619 1.439

immersion biometry need to be stronger than for contact ultrasound. Since laser interference biometry with the Zeiss IOLMaster was calibrated against immersion ultrasound2 this argument also holds for optical biometry: accordingly, IOL constants for optical biometry must be stronger than for contact ultrasound ! This is the basis of the ULIB constants’ optimization project.17

The model calculations furthermore show a definite dependency of the IOL constants of the different power formulas on axial length. It is strongest for the SRK II

A-constant (Fig. 8.1) and weakest for the a0 A-constant of the Haigis formula (Fig. 8.2). This behavior is caused by and corresponds to the well-known axial length dependence of the arithmetic refraction prediction errors of these IOL power formulas.18 From the model calculations it follows that the SRK/T A-constant decreases by ≈ 0.4 D per mm axial length, the Haigis a0 constant by ≈ 0.1 mm per mm axial length.

The clinical observations are qualitatively and quantitatively in good agreement with these findings: all clinical constants decreased with increasing axial length.

Axial Length Dependence of IOL Constants

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The customized SRK/T A-constants from different centers were found to vary between 119.3 and 118.9 D in the axial length range of 23.2 to 24.2 mm, while the Haigis a0 constant changes between 1.30 and 1.55 mm. The author is aware of some shortcomings of the presented model calculations: the Gullstrand eye serving as a basis for the model eyes is a theoretical eye for optical and not for biometrical purposes. Also, apart from axial length no other factors (like e.g. corneal radii or anterior chamber depth) influencing refraction predictions and thus, IOL constants were made allowance for. Axial length, however, is the predominant factor in IOL power calculation, and the simplifying model calculations help in understanding why IOL constants necessarily depend upon the axial length average of the patient population from which the constants were derived.

CONCLUSION

Best refractive results will only be obtained if indivi-dualization is done on the surgeon level. Published constants like the ULIB constants for optical biometry8 are nevertheless a good starting point until enough data for individual optimization is available.

ACKNOWLEDGEMENT

The author wishes to thank the following surgeons for providing patient data: Australia: A.Rivett; Germany: U Reinking, R Wiedemann; USA: R Arleo, PC Campanella, J Chappell, DL Cooke, H Geggle, W Hill, WG Myers, P Parden.

REFERENCES

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2. 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;238:765-73.

3. Holladay, JT. International intraocular lens implant registry 2003. J Cataract Refract Surg 2003;29:176-97.

4. Gale RP, Saldana M, Johnston RL, Zuberbuhler B, McKibbin M. Benchmark standards for refractive outcomes after NHS cataract surgery. Eye advance online publication, 24 August 2007, doi:10.1038/sj.eye.6702954.

5. Bissmann W, Haigis W. How to optimize biometry for best visual outcome. In: Methods to achieving best uncorrected vision for your patients. Ocular Surgery News International Edition, May 2000, Slack Inc, Thorofare NJ, USA 2000;

13-15.

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7. www.augenklinik.uni-wuerzburg.de/uslab/iolcone.htm, as of March 24, 2005.

8. www.augenklinik.uni-wuerzburg.de/ulib/c1.htm, as of Nov 22, 2007.

9. Le Grand, El Hage SG. Physiological Optics, Springer, 1980.

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Optik und Refraktion. Kampik A (Hrsg), Biermann-Verlag, Zülpich, 1995;123-40.

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13. Retzlaff J, Sanders DR, Kraff MC. Development of the SRK/

T intraocular lens implant power calculation formula. J Cataract Refract Surg 1990;16(3):333-40.

14. Holladay JT, Musgrove KH, Prager TC, Lewis JW, Chandler TY, Ruiz RS. A three-part system for refining intraocular lens power calculations. J Cataract Refract Surg 1988;14:17-24.

15. Hoffer KJ. The Hoffer Q formula: a comparison of theoretic and regression formulas. J Cataract Refract Surg 1993;19:

700-12.

16. Hoffer KJ. Errata in printed Hoffer Q formula. J Cataract Refractive Surg 2007;33:2-3.

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18. Haigis W. IOL calculations in long and short eyes. In:

Mastering intraocular lenses (IOLs). Ashok Garg, JT Lin (eds).

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