13. Thick lens IOL power calculation
This page is dedicated to predicting the IOL power intended to achieve the refractive objective sought after cataract surgery.
Thanks to an emmetropic pseudophakic eye model equipped with thick refractive structures (cornea and IOL), we have established a general formula, which incorporates the essential elements for a biometric calculation:
This expression also depends on the value of the corneal power (Dc), the power of the implant (Di), and those of the refractive indices considered (na, nv).
Here the schematic eye is represented as an optical system combining the cornea and the IOL, with each ‘lens’ being defined by its anterior and posterior radius of curvature, its refractive index, and its thickness.
For digital applications, distances should be expressed in meters.
Certain considerations are necessary before undertaking the calculation steps necessary to predict the power of an implant in a preoperative setting.
In the context of a biometric power calculation for a phakic eye, we do not know by definition the power of the IOL that one must place to reach the desired refractive target (this is what we are trying to predict! ). The position the IOL will take after surgery is also not known in advance.
It is also essential to distinguish the physical position of the implant from the « optical » position, ELPT, which appears in the formula cited above.
ELP is usually defined as the distance from the anterior corneal surface to the principal plane of an infinitely thin IOL. In the paraxial approximation using thick lenses, the implant position similar to a thick lens (ELPT) corresponds to the distance between the principal image plane of the cornea and the principal object plane of the IOL. This value depends on the physical position of the IOL in the eye but also on corneal thickness and IOL geometry. The latter varies between IOL models and power.
We can define the Actual lens position (ALP) as the physical distance measured from the anterior corneal surface to the anterior IOL surface. If we want a value independent of both corneal thickness and IOL geometry, we can define the internal lens position (ILP) as the physical distance between the posterior corneal surface and the anterior IOL surface.
We have established that the ALT length used in the formula differs slightly from the anatomical axial length (ALA). We must subtract from the latter the distance between the implant’s principal planes, which we do not know in advance either!
Let’s start by establishing an expression to predict the IOL’s power from the measured preoperative biometric data, a predicted value of the ELPT, and the target refraction (target SE).
For that, all we need is to solve the above equation for the IOL power (Di).
The formula for IOL power for targeting emmetropia (target SE =0)
The above expression refers to an emmetropic eye.
Solving it for the IOL power Di intended to make the eye emmetropic postoperatively gives:
We have already encountered this equation that we had obtained by using the vergence formula applied to an eye model with thin lenses. This is expected, as the difference between the eye models with thin vs. thick lenses mainly relates to the difference between the appreciation of the cornea and the IOL distance.
The formula for IOL power for targeting ametropia (target SE ≠0)
The value of the IOL power can be computed for a non-emmetropic target (SE≠0) after replacing Dc by Dce the preceding equation, where Dce is the sum of Dc and the vergence in the corneal plane of a spectacle lens of power equal to SE, placed at distance d from the corneal vertex:
We thus obtain the general formula:
Using the spreadsheet below, we can calculate a theoretical value of the IOL power intended to induce target refraction (SE) postoperatively from preoperative biometric data. Even if it provides realistic results, this online calculator should not be used in practice because it has certain simplifications (see below), and has not been the subject of a clinical evaluation.
We calculated the intraocular lens position (ILP: i.e., the distance comprises the posterior surface of the cornea to the anterior surface of the IOL) for the eyes comprising in a training set using the method described here. ILP was used as the designated target to predict using an algorithm, with the biometric parameters as features. In this example, a multiple linear regression was used, with the axial length, the anterior radius of curvature of the cornea, aqueous chamber depth, lens thickness, central corneal thickness (dc), and white-to-white diameter (WTW) as independent variables.
A first step makes it possible to obtain an estimate of the IOL power intended to obtain the desired postoperative refraction (SE) by using as a first approximation the value of the ILP as the anatomical AND optical position of the IOL (as would occur if a thin lens pseudophakic eye model was used). Once this value has been obtained, and from the values of the Coddington factor (assumed to be known), IOL’s refractive index, and thickness, it is then possible to predict the value of the ELPT.
The predicted value of the ELPT is obtained by adding to the ILP the value of the thickness of the cornea and the distance between the anterior face of the IOL and its principal object plane (S3Hi). The latter is calculated using paraxial formulas which use the geometric characteristics of the IOL envisaged to be implemented.
This value of the ELPT is then used to solve the equation again and obtain an IOL power value that considers the design characteristics of the latter in the context of a thick lens calculation.
As you will be able to see using this spreadsheet, an isolated variation of the Coddington factor is likely to vary the power of the IOL required to reach the refractive target.
A few remarks…
The calculation formula used for this spreadsheet assumes that the radius of the posterior surface of the cornea is known. This is often the case with modern biometers, but this value is not always measured and must be extrapolated. In thin-lens formulas, the total corneal power is inferred from the anterior radius of curvature, using the keratometric index. This method is based on the assumption that the relationship between the anterior radius and the posterior radius is the same along the entire anterior corneal radius. When the posterior radius is not measured, one can use a previously determined anterior radius / posterior radius relationship.
Certain studies have shown that it is preferable to modify the value of the axial length to gain refractive precision. This reflects the fact that modern biometric measurements, which rely on interferometric methods based on the optical path, do not always take into account the slight differences between the refractive indices of the components of the eye. These variations result in a slight difference between the axial length extrapolated from a single refractive index value for the intraocular path and the axial length extrapolated from a segmentation of the eye as a function of the value of the local refractive index.
Once the predicted value of the ILP is obtained, it is also possible to use an approach consisting of calculating the theoretical refraction of the pseudophakic eye with a series of IOLs of increasing power and to select the one whose power allows to achieve the refractive target. Each of these implants is positioned so that its anterior face coincides with the predicted ILP position.