Topography versus refraction

Most refractive surgeons perform corneal topography, keratometry and refraction before and after refractive surgery. As mentioned, corneal topography provides an image map based on the refractive power of the cornea at thousands of separate points on the corneal surface. Keratometry does the same at only a few points at an optical zone away from the center of the cornea. Corneal topography and keratometry are considered "objective" measures of corneal refractive power. Since corneal topography has come to be more widely used,(16) keratometry will be disregarded for the purpose of this discussion.

Refractive measurements are based on the subjective response of the patient to various lenses placed in front of the patient's eyes. A refraction identifies the myopic or hyperopic correction, as well as the magnitude and axis of astigmatic correction needed for clear vision.

Most people with astigmatism demonstrate differences in magnitude and axis between topographic astigmatism (T) and refractive astigmatism (R).(2) In other words, refractive power as measured at the surface of the cornea does not coincide with the refractive power that these people perceive as supplying good vision. The phenomenon may be related to the internal optics of the eye and the visual perception of the brain; clinicians sometimes refer to it as "lenticular astigmatism" (related to the lens of the eye). It presents a significant problem to current efforts to couple real-time corneal topography and laser treatment in an effort to "sphericize" the cornea. It also poses a common clinical quandary.

Faced with a discrepancy between T and R, most refractive surgeons treat the patient's spectacle astigmatism in the belief that reshaping the cornea to the patient's refractive preference will produce better visual results. It is apparent, however, that treating R may do nothing to alleviate T, and in fact can result in increased corneal topographic astigmatism. Increasing the corneal astigmatism violates fundamental principles of corneal surgery and may lead to spherical aberration.(17) For these reasons, Alpins does not dismiss the discrepancy so lightly, and offers a well-reasoned system for its management.

Figs. 4A, 4B and 4C demonstrate how the Alpins method can be used to approach a patient who has a discrepancy between T and R. Alpins describes the vector between T and R as ocular residual astigmatism (ORA), and sees ORA as an irreducible minimum astigmatism that can be achieved in any individual eye that has such a discrepancy.(2,18) If a surgeon chooses to treat the topographic astigmatism, the refractive astigmatism remains, and vice versa.



Fig. 4A: This DAVD shows a patient having a discrepancy between refractive astigmatism (R) and corneal topographic astigmatism (T), whose targeted treatment is based 100% on T. The vector between R and T is the ocular residual astigmatism (ORA), the minimal amount of astigmatism that can remain in the optical system of this eye. The target refraction is the amount of refractive astigmatism remaining after treatment to eliminate topographic astigmatism; that is, the cornea would be spherical but the patient would have a remaining refractive astigmatism equal to the target refraction (and ORA) shown. The treatment is shown as a vector of equivalent magnitude to T, but 180° away from T on the DAVD (actual steepening treatment on the cornea would be 90° away).



Fig. 4B: DAVD shows same patient as in Fig. 4A, but with correction targeted 100% on correcting refraction. Target topography is the corneal topographic astigmatism remaining after treatment to eliminate refractive astigmatism. The treatment vector has an equivalent magnitude to R, but is 180° away from R on the DAVD (actual steepening treatment on the cornea would be 90° away).



Fig. 4C: An intermediate TIA can be chosen between the boundaries of the topographic TIA and refractive TIA. The relative proximity of the intersection to either the topographic or refractive endpoints (heavy dashed line) is determined by the emphasis of treatment required (total will equal 100%). Any TIA that achieves the minimum target astigmatism for the prevailing topographic and refractive parameters will terminate on the ORA line. The surgical emphasis (topography versus refraction) can be selected using Alpins' "optimal treatment" (see Fig. 5), which is ultimately determined by the orientation of the ORA and the individual T and R values of each patient.

The ORA is equivalent in magnitude to the refractive (Fig. 4A) and topographic (Fig. 4B) targets. The maximum correction of astigmatism is achieved when the remaining astigmatism is at its minimum (the minimum target astigmatism) and is equal to the ORA. This remaining astigmatism will be refractive, topographic or a combination. The Alpins approach enables surgeons to calculate the ORA as well as the parameters (laser settings) for eliminating 100% of T, 100% of R or any combination of T and R equaling 100%, while leaving the absolute minimal amount of astigmatism in the eye's optical system. The Alpins method also helps surgeons choose these treatment parameters through the use of Alpins "optimal treatment."(2)

Alpins' optimal treatment is based on calculations that put more surgical emphasis on topographic astigmatism the more unfavorably the astigmatism falls on the cornea (toward an against-the-rule orientation). The surgical emphasis graph shown in Fig. 5 assumes a linear relationship (the heavy V-shaped lines); however, a nonlinear relationship may exist.



Fig. 5: Alpins' "optimal treatment," which is the optimal point of termination of the TIA with the ORA line, is determined from the surgical emphasis graph shown here. In this example, the meridian of target topography is 147°. As it lies 57° from a with-the-rule orientation of 90°, the surgeon may decide to apportion 57 of 90, or 63% emphasis, to a topography-based goal of zero astigmatism (and the remainder, 37%, to refractive astigmatism). If the meridian of target topography is 90°, a physiologically more favorable orientation, 100% of the treatment will be devoted to the correction of refractive astigmatism. If the meridian of target topography is 180°, or against-the-rule, 100% of the treatment will be devoted to correcting the topographic astigmatism ("sphericizing" the cornea and eliminating the unfavorable against-the-rule astigmatism).

Alpins performed an as-yet-unpublished study where astigmatic patients were randomly assigned to optimal treatment or the more conventional approach of treating only the refractive astigmatism. Optimal treatment produced better visual results even though it did not aim to treat 100% of the refractive astigmatism. The reasons cited above -- that is, the more physiologic orientation of with-the-rule astigmatism, the spherical aberration introduced by corneal astigmatism, etc. -- probably underlie these results. With optimal treatment, one appears to gain the advantage of less remaining corneal astigmatism without the penalty of increased refractive astigmatism.

Lasers and corneal topographers

Refractive lasers and corneal topography machines could include the Alpins method either as planning and analysis "add-ons" to their current software or as a basis for the development of custom applications. For lasers, it makes sense to consider use of the Alpins method in the programming of a laser's operating system. In this way, treatment parameters calculated by the Alpins method could directly guide the ablation pattern of a laser as opposed to the operator having to manually enter settings into the laser after using the Alpins method to calculate the settings.

Corneal topography machines, while benefiting from the add-on functions of the Alpins method, could use it to simulate prior to surgery the corneal image map that might be expected after any proposed refractive surgical correction. This would be especially helpful and dramatic for those patients in whom treatment of refractive astigmatism alone would actually exacerbate existing corneal astigmatism.

The visibility of the Alpins astigmatism-analysis method will continue to grow in the months ahead. Alpins' novel approach to irregular astigmatism was published in May.(4) He will present a number of papers at major ophthalmic meetings this year. His work is being increasingly cited as time goes by. In addition, the U.S. Food and Drug Administration recently expanded the labeling of currently available refractive excimer lasers, allowing the treatment of patients with astigmatism. As the performance of refractive surgery around the world increases, so too does the need for an encompassing, useful, well-defined approach to astigmatism analysis. Practitioners and industry will inevitably join in the widespread adoption of the Alpins method.

About the author

A well-known figure and commentator in the field of ophthalmology, Keith J. Croes is former editor-in-chief of Ocular Surgery News, Ocular Surgery News International Edition, Primary Care Optometry News and EyeWorld. Croes studied engineering and communications at Pennsylvania State University. He has written, ghostwritten or edited numerous formal papers and book chapters.

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