Corneal Biomechanics

The cornea consists of collagen fibrils arranged in approximately 200 parallel lamellae that extend from limbus to limbus. The fibrils are oriented at angles to the fibrils in adjacent lamellae. This network of collagen is responsible for the mechanical strength of the cornea. The fibrils are more closely packed in the anterior two-thirds of the cornea and in the axial, or prepupillary, cornea than they are in the peripheral cornea. (See BCSC Section 8, External Disease and Cornea.)

Structural differences between the anterior and posterior stroma affect the biomechanical behavior of the cornea. These include differences in glycosaminoglycans as well as more lamellar interweaving in the anterior corneal stroma; thus, the anterior cornea swells far less than the posterior cornea does. Stress within the tissue is partly related to intraocular pressure (IOP) but not in a linear manner under physiologic conditions (normal IOP range). When the cornea is in a dehydrated state, stress is distributed principally to the posterior layers or uniformly over the entire cornea. When the cornea is edematous, the anterior lamellae take up most of the strain. Most keratorefractive procedures alter corneal biomechanical properties either directly (eg, radial keratotomy weakening the cornea to induce refractive change) or indirectly (eg, excimer laser surgery weakening the cornea by means of tissue removal). The lack of uniformity of biomechanical load throughout the cornea explains the variation in corneal biomechanical response to different keratorefractive procedures. For instance, LASIK has a greater overall effect than does photorefractive keratectomy (PRK) on corneal biomechanics, not only because a lamellar flap is created but also because the laser ablation occurs in the deeper, weaker corneal stroma (a more detailed discussion can be found later in this chapter and in Chapter 5).

Corneal Imaging for Keratorefractive Surgery

Corneal shape, curvature, and thickness profiles can be generated from a variety of technologies such as Placido disk–based systems and elevation-based systems (including scanning-slit systems and Scheimpflug imaging). Each technology conveys different information about corneal curvature, anatomy, and biomechanical function. In addition, computerized topographic and tomographic systems may display other data: pupil size and location, indices estimating regular and irregular astigmatism, estimates of the probability of having keratoconus, simulated keratometry, and corneal asphericity. Other topography systems may integrate wavefront aberrometry data with topographic data. Although this additional information can be useful in preoperative surgical evaluations, no automated screening system can supplant clinical experience in evaluating corneal imaging.

The degree of asphericity of the cornea can be quantified by determining the Q value, with Q = 0 for spherical corneas, Q < 0 for prolate corneas (relatively flatter periphery), and Q > 0 for oblate corneas (relatively steeper periphery). A normal cornea is prolate, with an asphericity Q value of – 0.26. Prolate corneas minimize spherical aberrations by virtue of their relatively flat peripheral curve. Conversely, oblate corneal contours, in which the peripheral cornea is steeper than the center, increase the probability of having induced spherical aberrations. After conventional refractive surgery for myopia, with the resulting flattening of the corneal center, corneal asphericity increases in the oblate direction, which may cause degradation of the optics of the eye.

Corneal Topography

Corneal topography provides highly detailed information about corneal curvature. Topography is

evaluated using keratoscopic images, which are captured from Placido disk patterns that are reflected from the tear film overlying the corneal surface and then converted to computerized color scales (Fig 1-7). Because the image is generated from the anterior surface of the tear film, irregularities in tear composition or volume can have a major impact on the quality and results of a Placido disk–based system. Because of this effect, reviewing the Placido image (image of the mires) prior to interpreting the maps and subsequent numerical data is a wise approach. Additionally, Placido disk–based systems are referenced from the line that the instrument makes to the corneal surface (termed the vertex normal). This line may not necessarily be the patient’s line of sight or the visual axis, which may lead to confusion in interpreting topographic maps. For a more extensive discussion of other uses of computerized corneal topography, refer to BCSC Section 3, Clinical Optics, and Section 8, External Disease and Cornea. Generally, data from the reflection of the mires from the topographic instruments are presented not only numerically but—more important for clinical evaluation—also as an image, with corneal curvature typically represented utilizing axial and tangential methods.

Figure 1-7 Placido imaging of the cornea. A, The raw Placido disk image; B, computer-generated color map derived from data in A. (Courtesy of J. Bradley Randleman, MD.)

Axial power and curvature

Axial power representation comes from the supposition that the cornea is a sphere and that the angle of incidence of the instrument is normal to the cornea. Axial power is based on the concept of “axial distance” (Fig 1-8). As can be seen from the illustration, axial power underestimates steeper curvatures and overestimates flatter curvatures. This representation also is extremely dependent on the reference axis employed—optical or visual.

Figure 1-8 Schematic representation of the difference between axial distance (axial curvature) and radius of curvature for 2 points on a curved surface. Points C1 and C2 represent the centers of curvature of their respective surface points. Points A1

and A2 represent the endpoints of the axial distances for the given axis. As can be seen, local, steeper areas of curvature are

underestimated, whereas flatter areas are overestimated. (Adapted from Roberts C. Corneal topography: a review of terms and concepts. J Cataract Refract Surg. 1996;22(5):624–629, Fig 3.)

Maps generated from the same cornea but using different reference axes look very different from one another. Axial power representations actually average the corneal powers and thereby provide a “smoother” representation of corneal curvature than does the tangential, or “instantaneous,” method. Recall that the curvature and power of the central 1–2 mm of the cornea are generally not well imaged by Placido disk techniques but can be closely approximated by the axial power and curvature indices (formerly called sagittal curvature); however, the central measurements are extrapolated and thus are potentially inaccurate. These indices also fail to describe the true shape and power of the peripheral cornea. Topographic maps displaying axial power and curvature provide an intuitive sense of the physiologic flattening of the cornea but do not represent the true refractive power or the true curvature of peripheral regions of the cornea (Fig 1-9).

Figure 1-9 Examples of curvature maps. A, Axial (sagittal); B, instantaneous (tangential). (Courtesy of J. Bradley Randleman, MD.)

Instantaneous power and curvature

A second method of describing the corneal curvature on Placido disk–based topography is the instantaneous radius of curvature (also called meridional or tangential power). The instantaneous radius of curvature is determined by taking a perpendicular path through the point in question from a plane that intersects the point and the visual axis, while allowing the radius to be the length necessary to correspond to a sphere with the same curvature at that point. The curvature, which is expressed in diopters, is estimated by the difference between the corneal index of refraction and 1.000, divided by this tangentially determined radius. A tangential map typically shows better sensitivity to peripheral changes with less “smoothing” of the curvature than an axial map shows (see Fig 1-9). In these maps, diopters are relative units of curvature and are not the equivalent of diopters of corneal power. The potential benefit of this method’s increased sensitivity is balanced by its tendency to document excessive detail (“noise”), which may not be clinically relevant.

For routine refractive screening, most surgeons have the topographic output in the axial (sagittal) curvature mode rather than the instantaneous (tangential) mode.

Corneal topography and astigmatism

A normal topographic image of a cornea without astigmatism demonstrates a relatively uniform color pattern centrally with a natural flattening in the periphery (Fig 1-10). Regular astigmatism is uniform steepening along a single corneal meridian that can be fully corrected with a cylindrical lens. Topographic imaging of regular astigmatism demonstrates a symmetric “bow-tie” pattern along a single meridian with a straight axis on both sides of center (Fig 1-10B). The bow-tie pattern on topographic maps is an artifact of Placido-based imaging; that is, because the Placido image cannot detect curvature at the central measurement point, the corneal meridional steepening seems to disappear centrally and become enhanced as the imaging moves farther from center.