Understanding and interpreting corneal topography maps for orthokeratology

Orthokeratology (ortho-k) lenses temporarily reshape the cornea’s anterior surface to correct refractive errors, with corneal topographers providing a quick, non-invasive way to measure and visualize corneal shape. Since the cornea is three-dimensional while computer screens are two-dimensional, depth and curvature need to be represented using color-coded maps. This article explores the principles of various map types, highlighting their utility in assessing changes in corneal topography from ortho-k lens wear.

If you were able to lay the cornea with its back surface down onto a flat base surface you would be able to measure the height from the base at any location on the cornea.

Because the corneal is largely spherical, height maps offer no useful information when viewed in this format, however, the height data used to form the map is used by software guided ortho-k lens designs to create a best fit empirical design.

Elevation maps follow the same process as the height map with the added step of removing the spherical component that makes up around 98% of the cornea's shape.

The topography software will overlay a best fit sphere to the height data and then display the difference in height between the anterior corneal and the fitted sphere. This time warmer (redder) colors typically indicate corneal locations that lie above the fitted sphere and cooler (bluer) colors below the fitted sphere.

Elevation maps are most useful for determining if toric ortho-k lenses are needed. Where the difference in elevation between flat and steep meridians at around 4mm from the corneal apex exceeds around 30 microns then a toric lens is likely to provide a better fit. The measurement location and elevation difference required to trigger toric lens selection is dependent on lens design, and should be readily available in the lens fitting guide or from calling the lens supplier.

Topographers vary in the term they use, but axial and sagittal maps are the same thing, only different in name. In tangential maps the ‘true’ curvature of each surface location is calculated relative to its neighbourhood locations.  

Tangential maps can be displayed in dioptres using the same keratometry calculations previously described for axial maps, however this can lead to confusion as tangential maps offer a truer representation of localized surface profile than refractive effect, and consequently best considered in mm’s. The same color profile as previously described is used, with redder colors indicating steeper curvature and bluer colors flatter curvature.

Tangential maps excel in visualizing localized fluctuations in curvature, making them particularly useful for highlighting the steep plus power ring that forms around the treatment zone and aligns with the worn ortho-k lens reverse curve zone.

Axial and sagittal are again different names for the same measurement. Axial curvature is calculated by the topographer's software at each corneal location as the distance between the surface normal and the central axis as shown in the image below.

This measurement to the central axis causes axial curvature to provide information on the overall shape of the eye, with larger eyes exhibiting flatter axial curvature compared to smaller eyes. It’s important to realize that this measurement process does not reflect the actual curvature of the surface at each location like display in the tangential map, but more the smoothed curvature profile across the surface.

Calculation of axial curvature reflects optical power calculations and therefore, axial curvature is calculated in the same way as keratometry curvature, which allows the curvature measurement in mm to be converted to the equivalent dioptre curvature using the keratometry formula: Curvature (D) = 0.3375 / curvature (m). Gaussian optics and thin lens assumption is used to simplify the calculation.

All curvature maps are most useful in ortho-k when calculated and displayed by subtracting the baseline (pre-lens wear) axial map from the map captured after lens removal. Topography software will perform this calculation to display the ‘difference’ map where corneal locations steepened by ortho-k lens wear will be displayed in redder colors and locations of flattening in bluer colors.

Recent research indicates that smaller central treatment zones may be beneficial in providing an enhanced myopia control effect, and it is in axial maps that this visualization is best made through evaluating the diameter of the central blue zone.

Refractive power maps display the true refractive power of the measured corneal shape by calculating how incident light parallel to the central axis is refracted using Snell’s law at each corneal location, adopting a thin lens approach to simplify the optical power calculation.

Refractive power maps are best utilized in ortho-k by creating a difference map between baseline and post-lens wear to determine effectiveness in correcting refractive error.

To this point the described maps relate to the anterior surface of the cornea in isolation, which is the measurement provided from placido disc style corneal topographers. Scanning instruments like the Oculus Pentacam are additionally able to capture the topography profile of the posterior cornea and corneal thickness at each measurement location.

Including the posterior corneal and corneal thickness in the refractive power calculation described above enables ray tracing of the total cornea, thus truer visualization of change to refractive change induced by ortho-k lens wear. Especially in treated corneas the additional information will change the outcome significantly.

Total corneal power maps offer a more realistic visualization on the refractive effect achieved from lens wear. While the posterior corneal curvature has been shown to be minimally affected by ortho-k lens wear, growing use of the Pentacam in ortho-k can only improve understanding of how ortho-k wear affects the cornea beyond the anterior surface alone, and consequently increased benefit over Placido disk style instruments that capture anterior corneal topography in isolation.

The Pentcam also displays a tangential map of the posterior corneal in isolation, following the same calculation process described above for anterior corneal maps. As previously described, the tangential map profile is particularly useful for highlighting local variation in shape profile.

Referring to published research showing minimal change to posterior corneal curvature from ortho-k lens wear, any change to the posterior corneal as a result of lens wear should be considered as unusual. Calculating the difference between the pre and post wear posterior corneal surface tangential map offers a safeguard warning system for detecting early development of keratoconus in children that may otherwise be masked by ortho-k, which becomes particularly relevant when taking increased ortho-k prescribing for myopia management into consideration.

Now that you have a better understanding of the different topographical maps, you should find corneal topography maps easier to interpret and comfortable with developing a workflow through the different map types to interpret treatment outcomes from ortho-k lens wear. Practice makes perfect, improved map interpretation will lead to better decision making and reduced likelihood of lens remakes. Open up the different map types for each of your post ortho-k lens wear assessments, refer to the ‘when to use..’ guidelines above, and you’ll quickly become an orthokeratology fitting aficionado.