Measurement of Corneal Curvature

the center of the pupil. The corneal vertex is the point located at the intersection of the patient’s line of fixation and the corneal surface. It is represented by the corneal light reflex when the cornea is illuminated coaxially with fixation. The corneal vertex is the center of the keratoscopic image and does not necessarily correspond to the point of maximum curvature at the corneal apex (Fig 2-10).

Figure 2-10 Corneal vertex and apex. (Illustration by Christine Gralapp.)

Shape, Curvature, and Power

Three topographic properties of the cornea are important to its optical function: the underlying shape, which determines its curvature and, hence, its refractive power. Shape and curvature are geometric properties of the cornea, whereas power is a functional property. Historically, power was the first parameter of the cornea to be described, and a unit representing the refractive power of the central cornea, the diopter, was accepted as its basic unit of measurement. However, with the advent of contact lenses and refractive surgery, knowing the overall shape and the related property of curvature has become increasingly important.

The refractive power of the cornea is determined by Snell’s law, the law of refraction. Snell’s law

is based on the difference between 2 refractive indices (in this case, of the cornea and of air), divided by the radius of curvature. The anterior corneal power using air and corneal stromal refractive indices is higher than clinically useful because it does not take into account the negative contribution of the posterior cornea. Thus, for most clinical purposes, a derived corneal refractive index of 1.3375 is used in calculating central corneal power. This value was chosen to allow 45 D to equate to a 7.5- mm radius of curvature. Average refractive power of the central cornea is about +43 D, which is the sum of the refractive power at the air–stroma interface of +49 D minus the endothelium–aqueous power of 6 D. The refractive index of air is 1.000; aqueous and tears, 1.336; and corneal stroma, 1.376. Although the air–tear interface of the cornea is responsible for most of the eye’s refraction, the difference between total corneal power based on stroma alone and with tears is only –0.06 D.

BCSC Section 3, Clinical Optics, covers these topics in greater depth.

Keratometry

The ophthalmometer (keratometer) empirically estimates, but does not directly measure, the central corneal power. It reads 4 points in the 2.8- to 4.0-mm zone. A simple vergence formula used in computing the corneal power in this region is then utilized to calculate the radius of curvature. Results are reported as radius of curvature in millimeters or refracting power in diopters. This estimation of central corneal power is useful for contact lens fitting or intraocular lens (IOL) power calculation in the normal cornea; however, it is not accurate in the patient who has previously undergone refractive surgery.

Computerized Corneal Topography

Corneal topography is based on keratoscopy, in which reflected images of multiple concentric circles can be digitally captured and the analysis performed by computer software. Placido disk–based topographers are the most commonly available type. In general, on steeper parts of the cornea, the reflected mires appear closer together and thinner, and the axis of the central mire is shorter (Fig 2- 11). Conversely, along the flat axis, the mires are farther apart and thicker, and the central mire is longer. These units assume the angle of incidence to be nearly perpendicular and the radius of curvature to be the distance from the surface to the intersection with the line of sight or visual axis of the patient (axial distance) (Fig 2-12). However, the assumption that the visual axis is coincident to the corneal apex may lead to some misinterpretations, such as the overdiagnosis of keratoconus. Axial curvature closely approximates the power of the central 1–2 mm of the cornea but fails to describe the true shape and power of the peripheral cornea.

Figure 2-11 Videokeratoscopic mires are closer together in the axis of steep curvature (arrow), and farther apart in the flat axis (arrowhead) in this post–penetrating keratoplasty patient. Major axes are not orthogonal.

Figure 2-12 Placido imagery for calculating the corneal curvature. The assumption that the perpendicular to the videokeratograph, the patient’s line of sight, and the corneal apex are coincident is rarely correct. (Courtesy of Michael W. Belin,

MD; rendered by C. H. Wooley.)

Another method of describing the corneal curvature uses the instantaneous radius of curvature (also called tangential power) at a certain point. This radius is determined by taking a perpendicular path, through the point in question, from a plane that intersects the point and the visual axis, but allowing the radius to be the length necessary to correspond to a sphere with the same curvature at that point. The instantaneous radius of curvature, with curvature given in diopters, is estimated by the difference between the corneal index of refraction and 1.000 divided by this tangentially determined radius. The tangential map typically shows better sensitivity to peripheral changes with less “smoothing” of the curvature than the axial maps (Fig 2-13). (In these maps, diopters are relative units of curvature and not the equivalent of diopters of corneal power.)

Figure 2-13 Topography of a patient with keratoconus. The top image shows axial curvature, the bottom, tangential curvature. Note that the steeper curve on the bottom is more closely aligned to the cone. (Courtesy of John E. Sutphin, MD.)

A third map, the mean curvature map, does not require the perpendicular ray to cross the visual axis. It uses an infinite number of spheres to fit the curvature at that point. The algorithm determines a minimumand maximum-size best-fit sphere and, from their radii, determines an average curvature (arithmetic mean of principal curvatures) known as the mean curvature for that point. These powers are then mapped using standard colors to represent diopter changes, allowing for more sensitivity to peripheral changes of curvature (Fig 2-14).

Figure 2-14 The top image shows mean curvature in keratoconus for the same patient as in Figure 2-13. The local curvature outlines the cone, as shown by the thinnest point in the pachymetry map in the bottom figure. (Courtesy of John E. Sutphin, MD.)

In addition to power maps, computerized topographic systems may display other data: pupil size and location, indexes estimating regular and irregular astigmatism, estimates of the probability of having keratoconus, simulated keratometry, and more.

About two-thirds of patients with normal corneas have a symmetric pattern that is round, oval, or bowtie-shaped (Fig 2-15). The others are classified as having an asymmetric pattern: inferior steepening, superior steepening, asymmetric bowtie patterns, or nonspecific irregularity. However, many corneas are found to have a complex shape whose representation is oversimplified by the use of such qualitative pattern descriptions. Besides the limitations of the algorithms and the variations in terminology by manufacturers, the accuracy of corneal topography may be affected by various other problems:

misalignment

stability (test-to-test variation) sensitivity to focus errors tear-film effects

distortions

area of coverage (central and limbal) nonstandardized data maps

colors that may be absolute or varied (normalized)