1.3 Topographic Indices, Asphericity & Cone Localization

1.3 Topographic Indices, Asphericity & Cone Localization

Accurate interpretation of corneal topography requires moving beyond subjective visual color inspection to objective quantitative indices. For contact lens practitioners, numerical indices support pattern recognition, while asphericity and cone description help form a fitting hypothesis that must be tested on eye.

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Quantitative Topographic Indices

Modern topographers synthesize thousands of data points into standardized numerical indices designed to assist in screening, longitudinal monitoring, and lens selection.

Simulated Keratometry (SimK)

Simulated Keratometry emulates conventional manual keratometry by sampling curvature along two orthogonal meridians separated by 90 degrees at the 3.0 mm optical zone:

• SimK1 (Flat K): The flattest meridian at the 3.0 mm zone.
• SimK2 (Steep K): The meridian 90 degrees away from SimK1.
• $\Delta K$ (Corneal Astigmatism): $\text{SimK2} - \text{SimK1}$.

The SimK Trap in Ectasia: Because keratoconic cones are frequently decentered 3.0 mm to 5.0 mm away from the corneal center, the 3.0 mm SimK ring captures only the shoulder of the cone. Review the local curvature display, including the reported maximum value and its location, while recognizing that Kmax is device-dependent and does not alone establish diagnosis or lens geometry.

Optical Regularity and Asymmetry Indices

• Surface Regularity Index (SRI): Measures local optical regularity across 256 points within the central 4.5 mm pupillary aperture. In a healthy eye, SRI approaches zero ($< 0.20$). Elevated SRI values correlate directly with loss of spectacle best-corrected visual acuity (BCVA) caused by irregular astigmatism and higher-order optical aberrations (such as coma and trefoil).
• Surface Asymmetry Index (SAI): Compares corneal power between 128 pairs of points situated 180 degrees apart along identical radial distances. High SAI values ($> 0.50$) indicate pronounced asymmetry across the visual axis, characteristically observed in keratoconus, decentered refractive surgery ablations, and tilted penetrating keratoplasty (PKP) donor buttons.
• Keratoconus Prediction Index (KPI): A multivariate discriminant index combining eight distinct topographic indices (including SimK1, SimK2, SAI, SRI, and differential sector powers). A KPI value $> 0.23$ indicates a high statistical probability of keratoconus.

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The Rabinowitz-McDonnell Diagnostic Criteria

In 1989, Dr. Yaron Rabinowitz and Dr. Peter McDonnell established the clinical benchmark criteria for identifying keratoconus based on Placido topography.

The Inferior-Superior (I-S) Value

Keratoconus most commonly develops in the inferior corneal hemisphere. The I-S value quantifies vertical asymmetry by evaluating five points located 3.0 mm inferior to the center (at 210°, 240°, 270°, 300°, and 330°) and subtracting the average of five corresponding points located 3.0 mm superior to the center (at 30°, 60°, 90°, 120°, and 150°):

$I-S = \bar{K}_{\text{Inferior}} - \bar{K}_{\text{Superior}}$

Diagnostic Decision Rules

Historical Placido-screening publications described I–S and central-power cutoffs, with larger asymmetry or steeper values increasing suspicion. Treat these as method-specific screening aids. Modern assessment also considers scan quality, repeatability, anterior and posterior elevation, pachymetric progression, epithelial mapping, refraction, examination, and documented progression.

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Corneal Asphericity: Q-Value, Eccentricity, and Shape Factor

The human cornea is not spherical; it is an aspheric surface that changes in curvature from the center toward the limbus. Mathematically, the corneal cross-section is modeled as a conic section governed by three interrelated parameters:

$p = 1 - e^2 = 1 + Q \implies Q = -e^2$

• Shape Factor ($p$): Defines overall conic shape ($p = 1$ is spherical, $p < 1$ is prolate, $p > 1$ is oblate).
• Eccentricity ($e$): Quantifies the rate of radial flattening ($e = 0$ is spherical; normal cornea $e \approx 0.40$ to $0.60$).
• Asphericity ($Q$-Value): Measures deviation from a true sphere in dioptric terms.

Prolate vs. Oblate Geometries

PROLATE (Normal Cornea):         OBLATE (Post-Myopic LASIK / PRK / Ortho-K):
        |                                      |        
     /     \  (Steep Center)                \      /  (Flat Center)
   /         \  (Flattens Peripherally)      \    /   (Steepens Peripherally)
  |           |                               |  |    
   Q < 0 (avg -0.26)                           Q > 0

• Normal Prolate Cornea ($Q < 0$, average $Q \approx -0.26$, range $-0.10$ to $-0.35$): The central cornea is steepest and continuously flattens toward the periphery. In keratoconus, the cornea becomes hyperprolate ($Q < -0.80$ to $-1.50$), featuring an extraordinarily steep apex and dramatic peripheral flattening.
• Oblate Cornea ($Q > 0$): The central cornea is flat, while the mid-periphery and periphery steepen. Oblate geometries are created iatrogenically by myopic laser ablation (LASIK, PRK), radial keratotomy (RK), or orthokeratology (Ortho-K).

Contact Lens Design: Standard vs. Reverse Geometry

• Standard Alignment Lenses: Designed for prolate corneas; the base curve parallels the central cornea, and peripheral curves flatten progressively to provide edge lift.
• The Oblate Fitting Disaster: If a standard prolate lens is placed on an oblate post-LASIK cornea, the lens will rest heavily on the steeper mid-periphery while bridging far above the flat center. This creates massive central bubble entrapment, mid-peripheral bearing, and peripheral lens seal-off.
• Reverse Geometry Lenses: An oblate cornea may benefit from a reverse-geometry design in which a steeper secondary zone helps align with the midperipheral knee. The exact relationship is design-specific. This allows the lens to clear the steep mid-periphery and align evenly over the flat central ablation zone.

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Cone Morphological Classification

Keratoconic ectasias are classified clinically into three primary morphological profiles based on the geographic size, location, and boundaries of the cone:

1. Nipple Cones

• Dimensions: Small diameter, $\le 5.0\ \text{mm}$ (often 3.0 mm to 4.0 mm).
• Location: Central or paracentral, typically displaced slightly inferonasal or inferotemporal.
• Topographic Appearance: A round, circumscribed island of steep curvature surrounded by 360 degrees of normal, flat cornea. There is a high dioptric gradient between the cone and the surrounding tissue.
• Contact Lens Selection: Successfully managed with small-diameter corneal RGPs (8.5 mm to 9.2 mm) using a multi-curve or aspheric design. The small diameter allows the lens to center directly over the compact cone without rocking. If lid forces cause decentration, an intralimbal design (10.5 mm to 11.2 mm) provides enhanced stability.

2. Oval Cones

• Dimensions: Medium diameter, $5.0\ \text{mm}$ to $6.0\ \text{mm}$.
• Location: Markedly decentered inferotemporally, frequently drooping toward the mid-periphery.
• Topographic Appearance: An ellipsoid steep zone extending well beyond the central 4.0 mm zone, creating severe vertical and oblique asymmetry.
• Contact Lens Selection: Conventional small corneal RGPs frequently fail because they tilt and rock across the steep superior shoulder of the cone, leading to heavy superior bearing, severe inferior edge standoff, 3 and 9 o'clock staining, and frequent lens ejection. Optimal modalities include large intralimbal RGPs (10.8 mm to 11.8 mm), hybrid lenses (rigid gas permeable center with a soft silicone hydrogel skirt), or mini-scleral lenses (15.0 mm to 16.5 mm) that vault the decentered cone entirely.

3. Globus Cones

• Dimensions: Large diameter, $> 6.0\ \text{mm}$, involving $> 75%$ of the corneal surface.
• Location: Generalized, limbus-to-limbus thinning and protrusion.
• Topographic Appearance: Diffuse steepening encompassing nearly the entire anterior topography without a distinct transition zone.
• Contact Lens Selection: Small corneal GPs may be difficult to stabilize on an extensive or decentered pattern, but they are not categorically contraindicated. A larger corneal, intralimbal, hybrid, custom soft, piggyback, or scleral design may be selected after diagnostic assessment.

Differential Diagnosis: Pellucid Marginal Degeneration (PMD)

PMD is characterized by a narrow, crescentic band of stromal thinning located 1.0 mm to 2.0 mm superior to the inferior limbus. Topography shows high against-the-rule astigmatism with a characteristic but not exclusive "butterfly" or "crab-claw" pattern of inferior steepening wrapping upward around the mid-periphery. PMD often makes a small corneal GP difficult to stabilize, but modality selection remains individualized and can include larger corneal, custom soft, hybrid, piggyback, or scleral designs.

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Cone Morphology, Asphericity & Specialty Lens Selection