Reply: Pentacam keratometry and IOL power calculation

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The topic you have raised is very interesting, and I agree that the time might have come to revise some old concepts at the base of ophthalmology.

A great deal of research has recently been done on methods to better estimate corneal power following refractive surgery, and the BESSt formula is one of them. BESSt was developed with the thick lens equation in mind. However, with our approach, the index of refraction of the cornea, n, had to be modified to allow direct comparison with measurements taken with current topographers. As you correctly point out, this is because the ratio between the posterior and anterior radii of curvature of the cornea varies instead of always being 0.883 (as described in the schematic Gullstrand's eye) and because topographers convert radius to diopters using 1.3315 instead of 1.376 as the corneal refractive index. While our technique has led to a significant improvement in IOL power prediction, small scattering in outcomes still occurs, although it rarely exceeds 0.75 D. As a matter of fact, unexpected refractive outcomes also occur in eyes that have not had refractive surgery and are neither very long- nor very short-sighted.

If one thinks about the extraordinary number of assumptions and approximations in the formulas we currently use to work out corneal and IOL power, achieving the target refraction after a routine phaco appears to be a fortunate event. For example, let's look at Snell law, which is the basis of all our calculations. How can it be applied correctly when nobody knows how to directly measure n, not to mention its variations after laser refractive surgery?

What about the paraxial approximation (peripheral rays that are off the visual axis are ignored and the lens is treated as a flat surface) that is used in all biometry formulas? Laser keratorefractive surgery has taught us that highly oblate (or prolate) corneas resulting from aggressive correction of myopia (or hyperopia) can induce considerable amounts of negative (or positive) spherical aberration. Although peripheral, those aberrated rays can make the circle of least confusion shift back and forth on the retina and this should not be ignored in the IOL power calculation. Aberrations have also been shown to be affected (favorably or unfavorably) by changes in pupil size and pupil location (eg, pupil centroid shift). In my opinion, optical aberrations (at the least spherical aberration and coma) should be studied at different pupil sizes before surgery to simulate different postoperative lighting conditions and predict the final visual quality through the use of point spread functions (PSF).

What should be said about the beautiful pseudocolor refractive maps produced by the most advanced corneal topographers? Many recent formulas for estimating corneal power after laser refractive surgery are based on their measurements. All the peripheral values displayed on topography maps misrepresent corneal power and are meaningless from an optical point of view. They are the result of an attempt to convert local radius of curvature to dioptric power using the lens maker equation (LME) (n/o + P = n′/i). The LME cannot be applied to nonspherical surfaces such as the cornea (the normal cornea is slightly prolate). Power is a paraxial concept and can only be applied to a small area near the visual axis.

Although important, all the factors discussed above seem to play a marginal role compared with the real challenge of accurately predicting the postoperative position of the IOL. Scatter in outcomes is expected to remain until a single IOL design is universally adopted. I am referring in particular to shape, length, and inclination of the haptics. Precise information on the front and back radii of curvature, thickness, index of refraction, and spherical aberration of each IOL optics is also of crucial importance for accurate calculation using the thick lens equation. Such information, in conjunction with Scheimpflug imaging, can also be used to verify whether mislabeling of the IOL has occurred in cases of postoperative refractive surprise. A universal IOL design would have the benefit of achieving consistent anteroposterior (z) centration of the IOLs in the bag and minimizing confounding factors.

All current formulas for biometry also use A-constants (optically nonexisting entities) instead of advanced prediction algorithms to estimate the distance between the principal plane of the cornea and the front principal plane of the IOL. The anterior chamber depth (ACD) typically required by older biometry formulas had nothing to do with that distance either. Better prediction of this distance is at the basis of our research, BESSt II. Intraocular lenses typically come in 0.25 D intervals rather than being custom made for the desired target refraction. This disadvantage, added to the fact that the ANSI standard allows a 0.50 D tolerance from the labeled power, can lead to further inaccuracies.

Since precise assessment of true axial length (IOLMaster, Carl Zeiss Meditec), anterior and posterior corneal curvature (Pentacam, Oculus, Inc.), optical aberrations (various aberrometers), projection of pupil aperture on corneal and aberrometric map (Pentacam, topographers, aberrometers) is possible, it should also be possible to apply real ray-tracing calculations without fudge factors. Ray tracing is also the only way of predicting postoperative image quality via PSF.

Now that we have a better understanding of the refractive properties of the cornea and the human eye has the time came to go back to pure geometric optics? Maybe this is too much to expect from us since we are the ones who are still using a 180-degree system to analyze changes in a sphere.