# Corneal topography: elevation maps

Corneal topography of elevation to collect information directly related to the spatial morphology, i.e. to the relief of the corneal surface. Measuring corneal relief allows representation in elevation, with respect to a reference surface, which is most often spherical by default.

The topography of elevation is a complementary diagnostic tool to the topography specular (topography of curvature). It allows access to the study of the posterior face of the cornea and provides information on the corneal thickness (optical product, establishing a study of corneal tomography) which is deducted from the distance between the front and back surfaces. Its relatively recent generalization was favoured by the development of refractive surgery, where it is particularly useful for the planning of photoablative corneal surgery, as well as screening for contraindications to the LASIK (screening of beginner infra clinical forms of Keratoconus, as Keratoconus fruste).

**Definition of rise in corneal topography **

Rise in corneal topography is simply refers to the distance above or below which are points of the corneal surface toward a reference surface: the surface is 'virtual' and must be calculated. It simply serves as a 'zero level '. In this, the topography of elevation is closer to the notion of "topography", which is the study of the relief of surfaces. The pre-eminence of the topography of curvature owes to its historical precedence.

Data processed in topography of elevation are directly the spatial coordinates of the surface analyzed in a 3 dimensional space, and not that of the local curvature. The corneal surface studied includes a mesh which points have an abscissa X, ordered Y and an elevation coordinate (Z).

Corneal elevation data can theoretically be calculated from the data of curvature (technology of specular reflection, which was the first technique used in the study of corneal topography). He must perform a mathematical operation that induced a loss of precision of the study of elevation with respect to direct measurement. Acquired more directly using the digitized images of a line of light (instrument Orbscan) scan, or a camera rotating Scheimpflug (Pentacam, Galilei, TMS 5 instruments).

The direct acquisition (independent of the technology by specular reflection type Placido) is more reliable that the calculation from the data of curvature, because it is not influenced by mathematical interpolation and/or smoothing of specular data, related to the calculation of integration necessary for curvature to rise. The curvature is indeed deducted from the rise, because the local radius of curvature of a surface is calculated from an operation of derivation (need to get the local slope and especially its changes; operation of second derivative).

This type of direct acquisition also provides elevation data of the posterior surface of the cornea, specular reflection techniques can analyze: indeed, the specular reflection is proportional to the difference in refractive index at the level of the reflective interface. case of the posterior surface and aqueous humor, this difference is too small to allow the study of the reflection of projected targets.

Images of the raw data collected by the detection system (camera Scheimpflug, or detection of "slots balayantes") is handled by a dedicated mathematical process (ex: triangulation) three-dimensional reconstruction of the surface of the cornea. Anterior and posterior corneal surface define corneal volume, which allows to record pachymetrique "point by point", then allowing the establishment of a Tomographic map.

Given the discrepancy between the total diameter of the cornea (millimetric scale) and the change in elevation to describe (micronique scale), the representation of the fine variations in elevation can not be made compared to a reference (SR) arbitrary horizontal as a plane surface.

As the cornea, the Earth is a body whose surface is close to the geometry of a sphere. In terrestrial topography, the average sea level is conveniently chosen as one the usual reference surface and 'zero level '. Land below the sea level and ditches - marine are then fitted with a 'negative' elevation

The representation of the corneal elevation also requires the use of a reference surface, against which the differences of elevation will be characterized. In order to highlight the small local variations, the reference surface must marry the overall profile of the measured surface. The sphere is the geometric surface chosen 'default' to represent the elevation of the cornea. It is important to understand that the Reference Surface used for the representation of the elevation of the cornea must be calculated: it corresponds to a geometric surface characterized (ex: sphere) whose points are closest to the analyzed surface.

**Calculation of the sphere of Reference:**

Once completed the acquisition of gross elevation data (X, Y, Z coordinates), the topographer software must calculate a reference sphere (commonly called even in France: 'best - fit sphere': BFS) using an appropriate algorithm. Schematically, several spheres (of RADIUS and variable position - so-called 'floating') are 'tested' and for each, the topographer software calculates the sum of the distances to the square between each of the points of the measured corneal surface and the anticipated sphere. The chosen sphere is one for which the sum of the square of the distance from the measured corneal surface is the lowest. Raise the measured distance squared can both cancel out the influence of the (upper or lower) position of the point measured with respect to the sphere tested, and give some weight to the most distant points of the test curve. The sphere of selected reference is that which the quadratic deviation to the measured corneal surface is the lowest.

It is necessary to calculate a sphere of reference for the front of the cornea, and another sphere of reference to the posterior side of the cornea: obviously, these areas will not have the same RADIUS.

The value of the radius of the sphere of reference has no optical significance, and does not correspond directly to the value of the average keratometry of the studied surface, even if it is usually larger that the average keratometry is low. The Asphericity and the degree of toricite or irregularity of the corneal surface represented also influence the radius of the sphere of reference. When analyzed corneal surface is dominated by the toricite, the radius of the sphere of reference tends to adopt an intermediate value between the respective values of curvature of the flattest Meridian and the Meridian the camber. As a result, points along the flattest meridians will be rather located above the sphere, while those located along the curved meridians will be located below. A reason for rise in 'X' (in 'cross') is then obtained.

**Rendering of the maps of elevation: **

After calculation of the sphere of reference on a given diameter of analysis, elevation data are rendered by using a suitable color scale. With most of the topographical and by analogy with the land maps of elevation, the dots above the sphere (positive elevation) are represented in warm colors, from yellow and dark red, while points below the sphere (negative elevation) are represented in cold color (from blue to purple). Points located at the level of the sphere are represented in green ('zero level'). E elevation topography, an area of 'red' must be seen as 'above' the sphere of reference, not as an arched area just.

Have the elevation anterior and posterior, knowing the difference between these surfaces allows a map of product, which provides a particularly comprehensive survey of changes in corneal thickness: it also defines this type of study as tomographic representation of the cornea. The color scale varies warm colors (thin corneas) to cooler colors (thick corneas). The value of the minimum thickness, its location, the existence of a thinning central or cancer are all information sought in refractive surgery, as part of the screening of Keratoconus infra clinical including.

**Alignment constraints**

The different choices for alignment are the following: 'float', 'axis', 'pinned' or 'apex')**Figure 11**). The "float" mode, in which no constraint is applied to the sphere of reference, is the default mode for most of the topographers. The 'axis' alignment forced the geometric centre of the sphere to be aligned with that of the cornea, with the possibility to move along it. The constraint "pinned" imposes an intersection of the sphere of reference with the surface on the line of sight. The "apex" mode combines two constraints, the "pinned" mode and the "axis" mode

By default, there is no alignment to the sphere of reference constraints (the calculated sphere is said to be "floating", or even in calculated 'float' mode '). The center of the BFS is not forced to lie on the geometric axis of the cornea, and the chosen sphere is simply one that marries the best reporting corneal surface.

**Not spherical reference surfaces **

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It is possible to select in the menu of the software as the Orbscan topographer, the Pentacam or Galilei a NON spherical reference surface. By default, the calculation of the reference surfaces is in mode "float". It is also possible to force the geometric axis of these surfaces to align with that of the cornea (ex: axial mode with the Orbscan). The interest of non-spherical surfaces is better "stick" to the geometric reality of the cornea, and allow to split qualitatively the effect of certain characteristics of the shape of the analyzed surface.

More alignment constraints can be added to the calculated reference sphere, and other geometrical surfaces of references can be selected, such as Ellipsoids, the toroides or any conicoide.

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