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Effect of corneal asphericity and spherical aberration on intraocular lens power calculations

Holladay, Jack T. MD, MSEE

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Journal of Cataract & Refractive Surgery: July 2015 - Volume 41 - Issue 7 - p 1553-1554
doi: 10.1016/j.jcrs.2015.06.021
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The effect of corneal asphericity on intraocular lens (IOL) power calculations found by Savini et al.1 is a direct consequence of the variation in corneal spherical aberration. The asphericity (Q-value), however, is only the minor component of the 2 variables needed to calculate spherical aberration; the most important variable is the corneal radius of curvature (r). de Ortueta and Arba Mosquera2 have independently shown that the formula for computing spherical aberration is proportional to the Q-value and inversely proportional to the third power of the corneal radius (1/r3). With the same Q-value, a steep cornea has much more spherical aberration than a flat cornea (my Table 1). Using the Q-value alone is why their findings with the Placido-disk topographer only explain 15% to 26% (R2) of their data and with the Scheimpflug and Scheimpflug–Placido 3% to 10%. The Q-value alone is a poor indicator of corneal spherical aberration and therefore of the residual ocular spherical aberration. If they had used the Zernike Z(4,0) value determined over a 6.0 mm zone, which is available on each of the devices used, their correlations and R2 values for prediction error would have been much higher.

Table 1
Table 1:
Longitudinal marginal spherical aberration* in diopters for typical apical K value and asphericity quotient (Q-value) of anterior cornea assuming surface is an aspheric conic.

The authors mistakenly state, “It is logical to expect a myopic outcome in prolate corneas, where the central curvature is higher than the paracentral curvature.” This is a common misconception that corneal refractive power is greatest where the corneal curvature is steepest; however, this is not true for normal Q-values from −0.53 to 0.00 (normal range) due to Snell’s law. For all prolate corneal Q-values greater than −0.53, the corneal refractive power is lowest at the apex even though the apical curvature is steepest. The average cornea has an apical radius of 7.71 mm, a Q-value over a 6.0 mm zone of −0.26 (prolate), and results in +1.03 diopters (D) longitudinal marginal spherical aberration as seen in my Table 1. The power at the apex (apical power at visual axis) is lowest (43.77 D) even though the apical radius is the steepest. The refractive power increases progressively by +1.03 to 44.80 D at the 6.0 mm diameter. As described by René Descartes in the 1620s, the Q-value that eliminates spherical aberration is −0.53 for the perfect aspheric cornea for any corneal apical radius. This is the only Q-value for which the corneal refractive power is constant over the entire optical zone with no spherical aberration. That the linear regression in Savini et al.’s Figure 1 crosses at a Q-value of −0.19 for the Placido-disk topographer is simply a result of the optimization of the IOL constant for this device. The authors will find that the zero prediction error will occur at the mean Q-value for each device with all formulas.

The IOL used was a spherical Acrysof SA60AT (Alcon Laboratories, Inc.). Today, most surgeons realize that the best visual outcome in normal and post-myopic refractive surgical corneas is with an aspheric IOL because it compensates for the positive spherical aberration in the cornea.3 The positive spherical aberration of the cornea can be measured directly with each of the topography or tomography devices used in their study using the Zernike Z(4,0) term over a 6.0 mm zone, for which the measured human average is +0.27 μm and accounts for all factors causing spherical aberration (my Table 2).3 Abbott Medical Optics, Inc. (−0.27 μm), Alcon Laboratories, Inc. (−0.18 μm), and Bausch & Lomb (0.0 μm) all have aspheric IOLs that can be matched to the patient’s measured corneal Zernike spherical aberration to achieve the minimum ocular spherical aberration.4 Wang and Koch4 also found that adding the Z(6,0) improved their results even further.

Table 2
Table 2:
Zernike Z(4,0) spherical aberration term* in microns for typical apical K value and asphericity quotient (Q-value) of anterior cornea assuming surface is an aspheric conic.

Finally and most important, the recommendation should be to use aspheric IOLs, not spherical IOLs, and then there is no need to compensate for the small portion of the prediction error from corneal asphericity. Matching the corneal spherical aberration to the closest available aspheric IOL will not only avoid the prediction error but also will significantly improve the quality of vision for visual acuity, contrast sensitivity, and nighttime driving as well as reducing patient reports of halos and glare.5,6


1. Savini G, Hoffer KJ, Piero Barboni P. Influence of corneal asphericity on the refractive outcome of intraocular lens implantation in cataract surgery. J Cataract Refract Surg. 2015;41:785-789.
2. de Ortueta D, Arba Mosquera S. Mathematical properties of asphericity: a method to calculate with asphericities. [letter] J Refract Surg 2008;24:119-121, reply by A Calossi, 121.
3. Holladay JT, Piers PA, Koranyi G, van der Mooren M, Norrby NES. A new intraocular lens design to reduce spherical aberration of pseudophakic eyes. J Refract Surg. 2002;18:683-691.
4. Wang L, Koch DD. Custom optimization of intraocular lens asphericity. J Cataract Refract Surg. 2007;33:1713-1720.
5. Packer M, Fine IH, Hoffman RS, Piers PA. Prospective randomized trial of an anterior surface modified prolate intraocular lens. J Refract Surg. 2002;18:692-696.
6. Kershner RM. Retinal image contrast and functional visual performance with aspheric, silicone, and acrylic intraocular lenses; prospective evaluation. J Cataract Refract Surg. 2003;29:1684-1694.
© 2015 by Lippincott Williams & Wilkins, Inc.