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# Understanding different corneal maps of the Pentacam

In this article, we will interpret some topography maps derived by Scheimflug based Pentacam, namely the Sagittal or axial map, True Net Power (TNP) map, Equivalent-K Reading (EKR) map, and the True Corneal Refractive Power (TCRP) map.

Before we describe the different corneal power maps described in the Pentacam, it is important that we appreciate the differnence between Placido based topography and scheimflug based tomgraphy in deriving corneal power maps. The corneal placido based topographers analyse the reflection of the placido mires from anterior surface of cornea and understand the slope of the cornea deriving the curvature power map. The curvatue is first displayed in millimeter (mm) and then converted into dioptric values through an equation where D= (1.3375-1)/r x 1000.

The scheimflug based tomography instruments like Pentacam measure the height or elevation of both anterior and posterior cornea and the curvature of the cornea is derived from the elevation.

Before we go ahead in describing the different cornea maps generated by Pentacam, it is necessarey to appreciate the following:

A) The Refractive Effect of Cornea : The cornea may be regarded as part of a sphere, though the best way of describing the cornea is a toric ellipsoid. If we regard the cornea as a part of a sphere, then its radius of curvature along the sphere would be the same everywhere. Even if the cornea is regarded as a sphere, its power is not the same everywhere, and generally increases as we move from the centre to the periphery. This is because of the effect of spherical aberration.

If spherical aberration is not taken into consideration, then an average radius of curvature of cornea of 7.5 mm will have a power of 45 dioptre everywhere in its anterior surface. In Pentacam, all refractive power maps of cornea takes Snell's Law of refraction into consideration and therefore accounts for positive spherical aberration of cornea as we move from the centre to the periphery. Ray tracing is an option to understand the power of the cornea as we move from the centre to periphery and therefore takes into consideration the effect of spherical aberration of the cornea.

If ray tracing is used to calculate the total or net power of cornea, parallel light is sent through the cornea. Each beam of light is then refracted and therefore studied implementing the true refractive indices of the cornea. The refractive indices of the air (1.0), anterior cornea (1.336) and aqueous ( 1.376) is taken into consideration calculate the principle plane of refraction of both anterior and posterior cornea.

B) Taking into account Anterior/Posterior Curvature values of Cornea : Cornea is meniscus in shape. That is, it has a convex shape in the anterior and concave shape in the posterior. The traditional keratometers/optical biometry or the placido based topograpy, does not measure the posterior cornea. It accounts for the power of the posterior cornea through a fudge factor called K index, where K index is commonly taken as 1.3375. This is often thought to correctly account for the anterior and posterior ratio of the cornea and give us the power of cornea without measuring the posterior cornea.

The K index that account for anterior posterior cornea ration may largely work for normal corneas (virgin corneas) but fail to work in post lasik patients or patients with an altered anterior posterior ratio. Thus some of the maps in the Pentacam use the true refractive index of the cornea (1.376), the aqueous and the air, and use Gaussian optics to derive the true power of cornea ( anterior plus posterior )

Corneal Readings from Placido based topography providing Simulated K(simK) or Sagittal Curvature of Pentacam

The Pentacam is not a placido based topography machine. It is based on Scheimflug principle and provides for both anterior and posterior curavature power maps of cornea. The corneal power derived from Sagittal (axial) power map is however only related to anterior cornea and does not take into account the posterior cornea, nor does it take into account the refractive power of the cornea ( the effect of spherical aberration ). The Sagittal (axial) power map mimics the common placido style map of anterior cornea.

The anterior corneal power values are provided according to Gaussian Optics formula:

The Holladay Equivalent K Reading or the EKR - The EKR comes with the Pentacam which is Scheimflug based topography ( tomography ). In the EKR mode, the true indices of the cornea and the aqueous is used. That is, in the EKR mode, as light passes through the air and enters the anterior cornea passing the tear film, and thereby leaves refracted passing through the posterior cornea to the aqueous, the true index of refraction of each medium is taken into consideration. It uses Snell's Law of Refraction to account for the spherical aberration ( refractive effect ) that adds to the positive power of cornea at each of the points when you move from the center to the periphery. This is not accounted by Keratometers or simulated Ks from Saggital or axial maps.

The average anterior and posterior corneal power are 48 D and -6.8 D (approximately). Let us assume that the patient in question has anterior/posterior corneal ratio lower than average. The Pentacam measures both anterior and posterior curvature of cornea, and measures posterior cornea as -6.5 D for this patient. Thus the patient's posterior cornea is -.3 D lower (less negative) than an average cornea. The EKR will therefore consider this and compensate for a weaker posterior corneal power and add .3D (adjust) to the anterior corneal values. The back surface of cornea has a negative power and therefore negates anterior corneal power. However, because the back surface of this patient's cornea is less negative (.3) than an average cornea, therefore the EKR will add to the anterior corneal power. The value derived of the anterior cornea ( K reading ) can then be directly input into any two variable IOL power calculation, regardless of the fact that this patient may have gone through a previous lasik or has an abnormal anterior posterior ratio.

The EKR Report also states the corneal power in the 1 to 7 mm zones of the cornea.

True Net Power of the Cornea ( TNP ) - This is measured by Scheimflug based devices and uses the original corneal refractive indices together with the measurement of both anteiror and posterior corneal curvature. Since the true corneal refractive indices are used, you cannot use this measurement with IOL calculation formulas like Holladay II or SRK T or Hoffer Q, as they are all based on the refractive indices of 1.3375. Since it derives the net power of the cornea, if you key this value to these formulas, it would lead to double correction as all IOL formulas assume the anterior to posterior ratio as 82.5%.

TNP does not account for the spherical aberration of cornea ( refractive effect ) and therefore cannot totally be relied for peripheral corneal power.

The equation for deriving TNP is :

Total Corneal Refractive Power Map ( TCRP ) - If you are interested in calculating corneal readings for simple IOL calculation, you need not look beyond EKR. The TCRP is however an accurate measurement of the True Refractive Power of cornea as it accounts for not only the correct corneal indices of refraction, but also account for spherical aberration ( refractive effect ), that is the change in corneal power as you move from center to periphery of the cornea despite the cornea having a regular curvature.

The TCRP Map uses ray tracing to calculate power . The True Net Power described earlier assumes that all rays passing through the cornea and emerging in aqueous are running parallel. In TCRP parallel light beams are transmitted through the cornea and focal length resulting from their refraction at the anterior and posterior cornea is calculated using Snell's Law of refraction. This refraction is based on true indices of air, cornea and the aqueous. In this way the ray tracing simulation takes into account principle planes of refraction of both sides of cornea. From this focal length one can then calculate the power at each point in cornea in diopters.

Thus TCRP takes into account - True Indices of Cornea and aqueous , refractive effect resulting from Spherical Aberration and anterior to posterior corneal curvature ratio. Needless to say, the TCRP map should show higher power towards the periphery due to spherical aberration.

However, unlike the EKR, you cannot use this into two variable standard IOL calculation formula. Again like TRP it uses true corneal indices of refraction and not the indices of refraction used by IOL calculation of formulas which therefore would amount to double correction if applied on formaulas like SRK T, Holladay I, etc.

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