Corneal Shape

A basic premise of refractive surgery is that the cornea’s optical properties are intimately related to its shape. Consequently, manipulation of the corneal shape changes the eye’s refractive status. Although this assumption is true, the relationship between corneal shape and the cornea’s optical properties is more complex than is generally appreciated.

The normal human cornea has a prolate shape (Fig 7-1), similar to that of the pole of an egg. The curvature of the human eye is steepest in the central cornea and gradually flattens toward the periphery. This configuration reduces the optical problems associated with simple spherical refracting surfaces, which produce a nearer point of focus for peripheral rays than for paraxial rays—a refractive condition known as spherical aberration. Corneal asphericity, the relative difference between the peripheral and central cornea, is represented by the Q factor. In an ideal visual system, the curvature at the center of the cornea would be steeper than at the periphery (ie, the cornea would be prolate), and the asphericity factor Q would have a value close to −0.50; at this value of negative Q, the degree of spherical aberration would approach zero. However, in the human eye, such a Q value is not anatomically possible (because of the junction between the cornea and the sclera). The Q factor for the human cornea has an average value of −0.26, allowing for a smooth transition at the limbus. The human visual system, therefore, suffers from minor spherical aberrations, which increase with increasing pupil size.

Figure 7-1 An example of meridional (tangential, left) and axial (right) maps of a normal cornea.

(Used with permission from Roberts C. Corneal topography. In: Azar DT, ed. Gatinel D, Hoang-Xuan T, associate eds. Refractive Surgery. 2nd ed. St Louis: Elsevier-Mosby; 2007:103–116.)

Ablative procedures, incisional procedures, and intracorneal rings change the natural shape of the cornea to reduce refractive error. Keratometry readings in eyes conducted before they undergo keratorefractive surgery typically range from 38.0 D to 48.0 D. When refractive surgical procedures are being considered, it is important to avoid changes that may result in excessively flat (<33.0 D) or excessively steep (>50.0 D) corneal powers, which decrease vision quality and increase aberrations. A 0.8 D change in keratometry value (K) corresponds to approximately a 1.00 D change of refraction. The following equation is often used to predict corneal curvature after keratorefractive surgery:

K postop = Kpreop + (0.8 · RE)

where Kpreop and Kpostop are preoperative and postoperative K readings, respectively, and RE is the refractive error to be corrected at the corneal plane. For example, if a patient’s preoperative keratometry readings are 45.0 D (steepest meridian) and 43.0 D (flattest meridian), then the average K value is 44.0 D. If the amount of refractive correction at the corneal plane is −8.50 D, then the predicted average postoperative K reading is 44.0 + (0.8 × −8.50) = 37.2 D, which is acceptable.

The ratio of dioptric change in refractive error to dioptric change in keratometry approximates 0.8:1 owing to the change in posterior corneal surface power after excimer ablation. The anterior corneal surface produces most of the eye’s refractive power. In the Gullstrand model eye (see Table 3-1), the anterior corneal surface has a power of +48.8 D and the posterior corneal surface has a power of −5.8 D, so the overall corneal refractive power is +43.0 D. Importantly, standard corneal topography instruments and keratometers do not measure corneal power precisely because they do not assess the posterior corneal surface. Instead, these instruments estimate total corneal power by assuming a constant relationship between the anterior and posterior corneal surfaces. This constancy is disrupted with surgical removal or surgical addition procedures, causing a change in the effective refractive index of the cornea. For example, after myopic excimer surgery, the anterior corneal curvature is flattened. At the same time, the posterior corneal surface remains unchanged or, owing to the reduction in corneal pachymetry and weakening of the cornea, the posterior corneal surface may become slightly steeper than the preoperative posterior corneal curvature, increasing its negative power.

The removal of even a small amount of tissue (eg, a few micrometers) during keratorefractive surgery may cause a substantial change in refraction (Fig 7-2). The Munnerlyn formula approximates the depth of the ablation based on the optical zone and the refractive correction:

where t is the depth of the central ablation in micrometers, S is the diameter of the optical zone in millimeters, and D is the degree of refractive correction in diopters.

Figure 7-2 Comparison of a 43 D cornea with a 45 D cornea. Numbers below the vertical arrows indicate distance from the optical axis in millimeters; numbers to the right of the horizontal arrows indicate the separation between the corneas in micrometers. A typical pupil size of 3.0 mm is indicated. A typical red blood cell has a diameter of 7 μm. Within the pupillary space (ie, the optical zone of the cornea), the separation between the corneas is less than the diameter of a red blood cell.

(Courtesy of Edmond H. Thall, MD. Modified by C. H. Wooley.)

An ideal LASIK ablation or PRK removes a convex positive meniscus in corrections of myopia (Fig 7-3A) and a concave positive meniscus in simple corrections of hyperopia (Fig 7-3B). Intracorneal rings flatten the corneal surface to correct myopia while arcuate incisional procedures cause localized flattening to reduce myopic astigmatism. LTK and CK cause focal stromal contraction and central steepening, correcting hyperopia. Finally, pinhole corneal inlays, like the KAMRA corneal inlay (AcuFocus Inc, Irvine, CA), do not change the shape but increase depth of focus on the retina by decreasing the size of the entrance pupil.

• Azar DT, Primack JD. Theoretical analysis of ablation depths and profiles in laser in situ keratomileusis for compound hyperopic and mixed astigmatism. J Cataract Refract Surg. 2000;26(8):1123–1136.

• Holladay JT, Janes JA. Topographic changes in corneal asphericity and effective optical zone after laser in situ keratomileusis. J Cataract Refract Surg. 2002;28(6):942–947.

• Koller T, Iseli HP, Hafezi F, Mrochen M, Seiler T. Q-factor customized ablation profile for the correction of myopic astigmatism. J Cataract Refract Surg. 2006;32(4):584–589.

Figure 7-3 Myopic photorefractive keratectomy (PRK) and hyperopic laser in situ keratomileusis (LASIK). A, Schematic illustration of myopic PRK. The shaded area refers to the location of tissue subtraction. More stromal tissue is removed in the central than in the paracentral region (convex positive meniscus). B, Schematic illustration of hyperopic LASIK. A superficial corneal flap is raised. The shaded area refers to the location of tissue subtraction under the thin flap (concave positive meniscus). After treatment, the flap is repositioned.

(Used with permission from Poothullil AM, Azar DT. Terminology, classification, and history of refractive surgery. In: Azar DT, ed. Gatinel D, Hoang-Xuan T, associate eds. Refractive Surgery. 2nd ed. St Louis: Elsevier-Mosby; 2007:5–6. Figs 1-4, 1-5.)

Excerpted from BCSC 2020-2021 series : Section 3 - Clinical Optics. For more information and to purchase the entire series, please visit https://www.aao.org/bcsc.