OCULUS maps for evaluating ortho-k: Epithelial Reshaping Power Map

When applied to corneas reshaped by ortho-k, conventional refractive maps derived from Placido disk topography are subject to several sources of inaccuracy. These include the effect of spherical aberration, reliance on assumed rather than measured posterior corneal curvature, and the use of a simplified refractive index. The following sections describe each of these factors and how the Pentacam addresses them.

Both the Pentacam and Placido disk topography systems apply Snell's law of refraction to measure refraction at discrete locations on the corneal surface.

In the cornea, as in other non-spherical refractive surfaces, peripheral light rays refract differently to more central rays, with this difference defined as spherical aberration.

Placido disk-based topographers calculate corneal curvature by projecting a pattern of known dimensions onto the anterior corneal surface and analyzing the reflected image. A limitation of this approach is that measurements are restricted to the anterior surface. To calculate the refractive power of the total cornea, assumptions about the posterior surface curvature need to be incorporated.

For untreated eyes, an assumed constant ratio between the radii of the posterior and anterior surfaces is usually sufficiently accurate.¹  When this ratio is altered, for example in response to ortho-k lens wear, it is beneficial to actually measure both corneal surfaces.

The OCULUS Pentacam uses Scheimpflug scanning technology to capture both the anterior and posterior surfaces of the cornea, enabling calculation of true posterior corneal curvature. This measured rather than assumed posterior curvature provides a more accurate calculation of total corneal power in both untreated and treated corneas.

The Pentacam can also account for the slightly different positions of the principal planes of the anterior and posterior corneal surfaces — a consequence of the finite thickness of the cornea that further refines the refractive power calculation.

To bring together the effect of spherical aberration, the curvature and position of both corneal surfaces, and the specific refractive indices, the ray tracing method can be used. In this approach, parallel light is sent through the cornea and each beam is refracted according to the correct refractive index, the slope of the surfaces, and the exact location of the refraction.

This is the basis of the Total Corneal Refractive Power (TCRP) method in the Pentacam software and represents a significant improvement over simplified power calculations.

When evaluating ortho-k outcomes specifically, further refinement can be made to the refractive index used in the calculation. By convention, most Placido topographers and keratometers use the refractive index n=1.3375 when calculating corneal refractive power, treating the cornea as a single refractive surface.¹  For a more precise calculation that includes the posterior curvature, the refractive index n=1.376 is used.² 

To more accurately quantify the refractive changes created by ortho-k, OCULUS has developed a new difference map called 'epithelium reshaping power (ERP)' and the corresponding parameter 'ΔERP'.

The ERP map builds on the ray tracing method, accounting for spherical aberration, both corneal surfaces, real refractive indices (Air: n = 1.000; Epithelium: n=1.401; Stroma/Endothelium: n = 1.376; Aqueous n = 1.336), and the positions of the principal planes.

What sets the ERP map apart from other ray tracing maps is the inclusion of the corneal epithelium as a separate refractive layer, with its own refractive index (n=1.401) that is higher than the value conventionally assigned to the cornea as a whole (n=1.376). This is particularly relevant in ortho-k, where the refractive change is achieved through redistribution of the epithelial layer rather than reshaping of the underlying stroma. Central epithelial thinning and mid-peripheral thickening alter the geometry of the epithelial-stromal interface, and because the epithelium has a higher refractive index than the stroma, these thickness changes carry a greater refractive effect than a single-index corneal model would predict.

By modeling the epithelium as its own refractive layer, the ERP map captures this additional contribution. The result is a more accurate representation of the true dioptric change induced by ortho-k, which might otherwise be underestimated by conventional ray tracing methods that treat the cornea as optically homogeneous.

In practice, the ERP map is used as a difference map comparing corneal power at baseline (before ortho-k lens wear) with follow-up measurements. At each visit, the map calculates corneal power using the measured anterior epithelial surface and the measured posterior corneal surface. The position of the posterior epithelial surface (the epithelial-stromal interface) is derived from baseline measurement data, as this boundary cannot be directly measured by the Pentacam at follow-up.

The resulting difference map displays the change in corneal refractive power attributable to epithelial reshaping, expressed in diopters. The ΔERP parameter provides a single summary value of the central refractive change, which can be compared directly to the change in manifest refraction to evaluate how accurately the topographic findings reflect the actual treatment effect.

the ERP map offers several advantages over conventional Placido disk-derived refractive maps when evaluating ortho-k outcomes:

• It includes the measured posterior corneal surface rather than relying on an assumed anterior-to-posterior curvature ratio that may no longer be valid after ortho-k reshaping.
• It uses ray tracing to account for spherical aberration and the true positions of the refracting surfaces.
• It models the corneal epithelium as a separate refractive layer with its own refractive index (n=1.401), capturing the full dioptric effect of epithelial thickness redistribution.

Together, these refinements give practitioners a more precise tool for evaluating the refractive changes induced by ortho-k, and for making more meaningful comparisons between topographic and refractive findings at baseline and follow-up.