# Abstract

[This letter was peer-reviewed and published in the official journal of the American Academy of Ophthalmology. The citation is: Leffler C, Pradhan H, Nguyen N. Refraction after intraocular lens exchange. Ophthalmology. 2008;115:754.]

[This letter describes how to determine the appropriate power of intraocular lens when a lens exchange is required.]

### Refraction after intraocular lens exchange

Jin et al.[1] developed empiric relations for predicting the refraction after intraocular lens exchange from a sample of 22 eyes. These relations have some value, but also have some disadvantages. For hyperopic eyes, the proportion of variance explained by the regression was stated as r-squared = 0.76, and for myopic eyes r-squared = 0.95. In fact, the data from cases 3 and 4 were omitted from their Fig. 1.[1] With inclusion of these cases, the coefficient of determination for hyperopic eyes drops to r-squared = 0.53. Because the predictive equations did not have a zero intercept, replacing the lens with a lens of identical power was predicted to change the spherical equivalent (SE) refraction by +0.87 diopters in hyperopes, and by -0.41 diopters in myopes. The regression equations also do not apply to exchange for an intraocular lens with a different manufacturer’s A constant or a different effective lens position.[2]

A theoretical approach offers several advantages. We noted that double application of Holladay’s refractive vergence formula might apply (Equation 12 of Ref. [2]). This formula predicts the refraction after addition of refractive power to the eye, and was offered as a means to calculate the refraction after secondary or piggyback lens placement.[2] We used the formula once to determine the refraction after IOL removal. This predicted aphakic refraction and the new IOL power were input into the formula to determine the final refraction after IOL exchange. A similar approach was taken by Hideyuki et. al. in three patients.[3]

We applied this method to Jin et al’s data,[1] and plotted the actual change in refraction against the predicted change in refraction. The proportion of variance explained by the method was 0.93 (Fig 1). The regression equation was: Change in observed SE = 1.09 * (Change in predicted SE) – 0.026. When the three cases of Hideyuki et. al. were added to the analysis, the r-squared value was still 0.93. This method has several advantages. First, it provides a theoretical underpinning to the problem. The regression coefficient close to 1 and the intercept close to 0 mean that the theory predicts the observations without scaling coefficients or “fudge factors.” Second, the same equation applies to both myopes and hyperopes. Third, the method theoretically may apply to changes in intraocular lens A constant or in effective lens position (e.g. anterior chamber, sulcus fixation, or capsular fixation), although this dataset does not provide empirical validation of this possiblity. Finally, the low intercept value (0.026 D) correctly indicates that an IOL exchange with an identical lens will not change the refraction.

This method also complements traditional biometry formulas, based on axial length and keratometry. First, the presence of an unexpected refraction may indicate that traditional formulas are inaccurate in a particular patient. This refractive method does not use axial length, which may be difficult to accurately measure with a staphyloma, intraocular silicone oil, and other instances. Second, although keratometry enters the equation, the double-application method is very insensitive to changes in keratometry. Therefore, the method may be particularly useful when effective keratometry values are uncertain, such as after refractive surgery or with irregular astigmatism. Refractive vergence and traditional biometry equations can both be used prior to intraocular lens exchange to ensure that all information is considered.

**Christopher Leffler, MD, MPHShilpi Pradhan, MDNina Nguyen.**

Medical College of Virginia

Richmond, Virginia

**References.**

[1] Jin GJ, Crandall AS, Jones JJ. Intraocular lens exchange due to incorrect lens power. Ophthalmology 2007;114:417-24.

[2] Holladay JT. Standardizing constants for ultrasonic biometry, keratometry, and intraocular lens power calculations. J Cataract Refract Surg 1997;23:1356-70.

[3] Hideyuki T, Yoshiaki N, Yoshiaki H, Tomo N, Hiroshi U. A simple and accurate method to calculate emmetropic intraocular lens (IOL) power for IOL exchange. Folia Ophthalmologica Japonica 2005;56:765-7.

**Figure 1.** Double application of Holladay refractive vergence formula in intraocular lens exchange. D = diopters.