letters to the editor

This section is an open forum and consists of the opinions and personal commentary of the writers. The views expressed are exclusively those of the writers and do not purport to reflect those of ASCRS or the Journal. ·

REFRACTION FACTOR IN IOL POWER CALCULATION

To the Editor: In the article by Thomas Cravy, "Using the Intraocu­

lar Lens Refraction Factor to Improve Refractive Prediction Accuracy" (] Cataract Refract Surg 15:519-525, 1989), an attempt was made to improve the accuracy of intraocular lens (IOL) calculations by using an individual refraction factor, which was determined empirically by computer iteration in a series of patients.

The history of IOL calculation shows that surgeons want to believe in constants. The refraction factor is such a constant, which was assumed in the SRK approach1·2 to calculate in retrospect the emmetropic IOL power from the actual refraction obtained with a given IOL according to

Po = Pi + Rx X R (1)

where Po = (calculated) power of IOL to give em­metropia, Pi = actual implant power, Rx = refraction error, and R = the conversion factor ( = refraction factor). The factor R was the important theoretical assumption made by the authors of the SRK formula to come up with an empirical formula for Po. As such, R is the a priori assumption of the A-constant.

In the original works by Sanders, Retzlaff and Kraff, 1 ·2 R was assumed to be 1. 25. Later, for unknown reasons, it was changed to 1.50. 3 In the newer SRK II approach, it has been further modified to be 1.0 in some cases.4 And now Cravy believes it should be less than 1.0.

The analysis by Cravy failed to clarify this field for the following reasons:

1. It should be realized that it is not possible by empirical means to determine the one and only theo­retical assumption underlying the SRK formula. If it were, we would have a case of merry-go-round reasoning.

2. If R is changed, the basic calculation of the emmetropic IOL power is changed according to equa­tion 1. In that case we have changed the basis of the SRK formula, and we need to repeat the entire multiple regression analysis in order to reevaluate the linear regression equation. It is not certain that the regression coefficients in the formula Po = A - 0.9 X

Fe- 2.5 X Ax still apply. This is especially the case when the result shows a correlation with the axial length, as was the observation of Cravy. (This criticism also applies to the newer SRK formula.)

3. Care should be exercised when heavy computer iteration is made on any data set to come up with a predictive formula. Each time a new iteration is made, the degrees offreedom are reduced, and the predictive value is decreased.

J CATARACT REFRACT SURG-VOL 16, JANUARY 1990 129

Table I. The refraction factor R as a function of various biometric data. Average ocular dimensions were assumed, unless specified otherwise.

Eye Type Anterior Chamber Depth of IOL

3.0 mm 4.0 mm 5.0mm

Normal eye 1.21 1.30 1.40

Axial length 26 mm 1.21 1.30 1.40

Axial length 21 mm 1.21 1.30 1.40

Corneal power 48 D 1.24 1.34 1.46

Corneal power 38 D 1.19 1.26 1.36

Refraction error - 10 D 0.92 0.97 1.04

Refraction error + 10 D 1.65 1.82 2.01

4. As Cravy himself points out, there is a problem regarding the estimation of R according to equation 1. As Rx now becomes the denominator, R becomes high when refractive errors are low. Most refractive errors after IOL implantation are close to emmetropia and this will make the estimation of R quite haphazard. Setting a lower limit does not solve the problem, as the distribution of estimated R's will not be a normal distribution. Statistical treatment using distributional methods is therefore a troublesome business.

As previously reported in this journal,.5 optical analysis shows the refraction factor to be composite in nature. Among other factors, it depends on the refrac­tion, the vertex distance, the corneal power, the position of the IOL, and the actual power of the implant. When IOL calculation is made according to an assumption-free computerized model based on an optical formalism, 6 the following figures are obtained as shown in Table l. As can be seen, the IOL chamber depth is the most important factor for the refraction factor. The axial length plays an insignificant role. A refraction factor below unity only occurs when the refraction error is beyond - 10 diopters.

Thomas Olsen, M.D., dr. med. Vejle, Denmark

REFERENCES l. Retzlaff]: A new intraocular lens calculation formula. Am Intra­

Ocular Implant Soc 1 6:148-1.52, 1980 2. Sanders DR, KraffMC: Improvement of intraocular lens power

calculation using empirical data. Am Intra-Ocular Implant Soc 1 6:263-267, 1980

3. Sanders DR, Retzlaff J, Kraff M, Kratz R, eta!: Comparison of the accuracy of the Binkhorst, Colenbrander, and SRK"' implant power prediction formulas. Am Intra-Ocular Implant Soc 1 7:337-340, 1981

4. Sanders DR, Retzlaff J, Kraff MC: Comparison of the SRK II'" formula and other second generation formulas. 1 Cataract Refract Surg 14:136-141, 1988

5. Olsen T: Theoretical, computer-assisted prediction versus SRK prediction of postoperative refraction after intraocular lens implantation. 1 Cataract Refract Surg 13:146-150, 1987

6. Olsen T: Theoretical approach to intraocular lens calculation using Gaussian optics. 1 Cataract Refract Surg 13:141-145, 1987

Thomas V. Cravy, M.D., replies: Upon reading Dr. Olsen's critique and reviewing his

references, I read his paper, "Theoretical, Computer­Assisted Prediction Versus SRK Prediction of Post­operative Refraction After Intraocular Lens Implanta­tion." In this paper he reported a 62% refraction prediction accuracy within one diopter with his com­puter assisted method, while achieving 69% and 65% with the SRK (RF = 1.5) and his modified SRK (RF = 1.25), respectively. Phase 3 of my paper reported a refraction prediction accuracy of 93% within one diopter in 61 consecutive Jaffe IOLs implanted in the bag. If this improvement (50%) in refraction prediction accuracy does not "clarify this field," I wonder what will.

I would like to clarify for Dr. Olsen that while the SRK basic formula was based upon multiple linear regression analysis techniques, it is not the product of a single such analysis. The B and C constants of the regression formula were a compromise, based upon numerous regression formulas, to permit lenses of all types and all manufacturers to be represented by a single equation (Olsen's reference 2). The A-constant was intended to be a variable to be individualized for a myriad oflens styles and manufacturers. Since empiri­cal formulas are based upon the concept of using what works rather than what should theoretically happen, my use of optimized A constant and refraction factor pairs represents a legitimate extension of the empirical formula concept. Solving a single equation for two unknowns is shown to be a case of the computer being mightier than the pen.

GLARE NOT CAUSED BY RIDGE

To the Editor: This is to congratulate the authors (Friedberg HL,

Kline OR, FriedbergAH: Comparison of the unwanted optical images produced by 6 mm and 7 mm intraocular lenses. ] Cataract Refract Surg 15:541-544, 1989) for carefully evaluating what has been a rather enigmatic and anecdotal subject. Glare and unwanted optical images such as circles, crescents, and halos have been noted by patients and discussed by many authors. These phenomena have been blamed on positioning holes, tabs, haptic insertion points, the edge of the lens, laser bumps, annular ridge, and YAG damage spots in the lens. Apple has clearly demonstrated that lens decentration allows peripheral design elements to enter the pupillary area and cause unwanted visual aberrations. It therefore makes sense to ensure perfect centration or use the largest lens implant diameter possible.

In their study, the authors recorded complaints of unwanted images in groups of patients with 20/40

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