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Error of calculation of implant - keratometry after refractive surgery

The measure of keratometry (optical power of the cornea) is important to avoid miscalculations of implant after corneal refractive surgery.

The question "What will happen to my future cataract surgery if I'm having surgery for nearsightedness?" is sometimes in the preliminary interview and discussions around refractive surgery. Corneal refractive surgery for myopia does not make the more complicated cataract surgical, but exposed to the risk of lower precision in the calculation of the power of the implant (biometrics). In particular, there is a risk of money estimate the power of the implant, and to induce a farsightedness in a patient that we wanted to emmétropiser, which is correct to see from a distance without glasses. One of the reasons of this risk is to the limitations of some formulas of implant.  The understanding of the phenomena for the biometric calculation of the operated eyes of refractive surgery can address this problem and increase the accuracy of the calculation of the implant after corneal surgery for nearsightedness.

 Data necessary for biometric calculation

Calculate the power of the implant to replace the lens during the cataract surgery to at least collect the following data: the Dioptric power of the central cornea, axial length (length of the eye). The biometric calculation is to calculate how much optical power (vergence) somehow must supplement the corneal optical power (keratometry) to allow the incident light to be focused on the retina.

However, a setting importance remains inaccessible to the measure and must be the subject of an extrapolation: it comes from the distance between the cornea and the implant. This important data is called "Effective Position of the implant" (Effective Lens Position in English: ELP).

By definition, it is not possible to measure before the intervention, and this distance may vary depending on various factors, including anatomical, but also related to the geometry and behavior of the implant. With the formulas of third- and fourth-generation implant, the most important for predicting the position of the implant setting is the curvature of the cornea (keratometry) [1]

For a normal eye ' not operated for corneal surgery), the most frequent sources of error in the calculation of the power of the implant are related to an error of measurement of axial length (54%) and a poor estimate of the actual position of the postoperative implant (38%). The keratometry is a reliable measure since it is responsible for only 8% of errors.

After refractive surgery on the cornea, the keratometry measurement becomes the cause main error, followed by the poor estimate of the ELP [2]


The keratometry measurement error

In this context, the keratometry is the measurement of the optical power of the central cornea (vergence). If one knows the optical power of the central cornea and the length of the eye, we can deduce (for a given position of implant) the power that must be given to the implant so that the light emitted by the popular target is focused on the retina. To know the optical power of the center of the cornea, you need to know the radius of curvature, from which we can apply a simple formula of vergence.

vergence of the cornea

Vergence formula is used to calculate the optical power of the cornea from the measurement of the radius of curvature and the value of the refractive index

The measure of the curvature is accomplished through a keratometer, or a corneal topographer. These instruments have for principle of study of the corneal reflection of a focus, from which they measure the local radius of curvature in different points of the anterior corneal surface.

The Central corneal optical power is then estimated from measurement points from the corneal Summit by formulas that are based on simplifications such as the use of a less than the actual index refractive index, and the application of the formula of vergence. For technical reasons, it is not possible to measure the curvature at the geometric Center (top) of the cornea: in fact, the measurement of the radius of curvature is accomplished on points 1.5 mm from the Center. However, on a non operated cornea curvature in these points is very close to the Central curvature and 'paracentrale' measure does not induce a significant error.  However, these simplifications and approximations are no longer valid for operated corneas.

The normal cornea has a curvature which decreases slightly from the top (apex) to the periphery. A measurement to 1.5 mm and part of the Center on a Meridian provides a good estimate of the apical curvature, i.e. the Central curvature that dictates the optical power of the cornea.

Overestimation of the Central corneal power

After surgery for myopia, (radial keratotomy, laser photoablation), the cornea becomes oblate: the cornea is significantly more flat at the center of the cornea to 1.5 mm from the Center. These changes in curvature between the apex and the near periphery are reversed. The classic extrapolations of the topographical and keratometres are no longer valid when the cornea becomes flatter in the Center and in answers; the central optical power value is greater than the actual axial optical power of the cornea: given these changes, the corneal optical power is overrated.

Central keratometry

The paracentrale measurement of the radius of curvature allows to extrapolate the value of the power plant of the cornea (keratometry), provided that the previous corneal profile is not changed

After refractive surgery for myopia)LASIK(, PKR, etc.), the anterior corneal profile is changed and became oblate. The paracentrale measure of the power of the cornea provides significantly different values from the actual power plant (which is overrated).

horny keratometry oblate

The paracentrale measure of the cornea tends to overestimate the central value, which corresponds to the actual vergence of the cornea.

Effect of the reduced refractive index

This first source of error of measure k, must be added that related to the use of a "k" minus (1.333 instead of 1,376) said refractive index.  For a non surgery corneal posterior face of the cornea (inaccessible to the measure at the time of the development of forms of biometrics) is generally parallel to the anterior, which it mitigates the optical power of 10% approximately. The k index is an index whose value is reduced by 10% with respect to the real index (index of refraction physical). However, myopia laser surgery is only the front of the cornea. The relative effect of the optical power of the posterior face of the cornea towards the front is reduced by the use of the index of refraction k, which causes an overestimation of the Central corneal power.

An overestimation of the corneal power returns to give less power to the implant: this lack of power can cause a hyperopia after cataract surgery.


Prediction of the effective position of the implant error


The second source of error in the biometric calculation after refractive surgery comes from a lower quality for the prediction of the actual position of the implant. More implant tends to be located in more front (near the cornea, so more away from the retina) and lower is the calculated power for all other parameters (axial length, keratometry) equal.

In some formulas of implant, the position of the implant ("effective lens position" or ELP) is primarily predicted "statistically" from the keratometry measurement (i.e. of the radius of curvature of the front of the cornea): see this page For more explanations). In geometric terms, the distance between the top of the cornea and the implant is logically greater than the cornea is arched, because the "arrow" of a cornea snap is more important than that of a flat cornea. This assumption is at the heart of the calculation done by the formula called SRK - T.

actual position of the implant

Formula SRK / T: this formula predicts the position of the implant from the height of the corneal dome (and the "constant A", which is adjusted for different type of implants). If this strategy makes sense, it is justified in not operated corneas. A patient who had surgery myopia has an eye which the anatomic anterior Chamber is usually deep, although its cornea is (as the result of surgery) less arched.

After corneal surgery for myopia (LASIK, PKR, radial keratotomy), the cornea becomes less arched in the Center, while the depth of the anterior Chamber remains unchanged. Taking into account of the corneal curvature (keratometry) postoperative results in an underestimation of the actual position of the implant, which is predicted as "more forward" (closest to the cornea). This factor tends to lead to an underestimation of the power of the implant.

This error goes in the same direction and adds to that of the measure k, and thus increases the risk of hypermetropisation initially nearsighted eyes prior to refractive surgery.

The understanding of these mechanisms and the identification of sources of error to improve the accuracy of the calculation of implant surgery for myopia:

-improvement of the measure k

-better prediction of the actual position of the implant using the formulas of 5th generation.

2 responses to "implant calculation error – keratometry after refractive surgery"

  1. Suzanne poirier says:

    I had surgery in may 2018 for a cataract with the left eye. I'm confusing you and I had to have a lens re-set to my bezel to adjust my eyesight. Today in March 2019 I do not see any better. I went to see a second ophthalmologist for a second opinion. I have a refractive error.
    The ophthalmologist who operated me wants to make me laser.
    As I have already paid the intervention, to redo a lens do I have to pay more for laser?
    Is it a mistake of the ophthalmologist during the procedure?
    Thank you for answering me quickly

  2. Dr. Damien Gatinel says:

    There is not necessarily an error because the choice of the implant power that is posed during refractive surgery is done on the basis of a prediction (by a formula of implant calculation or biometric formula). Sometimes, even if we aim for a total correction from afar, and the implant is placed with the power predicted by the formula, a slightly different result is obtained (only because the biological measures are subject to some vagueness, and that it is not possible to know in advance the exact positioning of the implant in the eye). If a laser operation seems preferable to wearing a small correction in glasses, this will be considered as a comfort surgery and will have to be financed by yourself.

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