Determination of Effective Lens Position (ELP)
One of our main goals is to compute formulas to determine the estimated effective lens position of the thick intraocular lens (IOL) in a pseudophakic eye. Using such a formula for each eye in a training data set, we could generate data that could be utilized for training purposes for a machine learning algorithm. This algorithm would aim to predict the effective lens position of a thick IOL (ELPT ) from preoperative ocular biometry, allowing the suitable IOL power to be chosen for the desired refraction using a paraxial optical formula, ray tracing, or IA algorithm.
Thick lens paraxial model for the pseudophakic eye
We have designed a schematic eye model where the design of the IOL (its anterior and posterior radii) can vary for the same paraxial power. In this context, the value of the ELPT can be used to compute the anatomical lens position (ALP), which corresponds to the distance separating the anterior corneal and IOL vertices.
ALT is equal to the anatomical axial length of the emmetropic eye (ALA)reduced by the distance between the principal planes of the implant (HiH’i) and the distance between the anterior surface of the cornea and the secondary principal plane of the cornea (S1H’c).
ELPT is referred to here as the effective lens position of a thick IOL, i.e. the distance separating the principal image plane of the cornea from the principal object plane of the IOL (H’cHi).
The relationship between the thick lens position ELPT and the anatomical lens position of the IOL (S1S3 = ALP for anterior lens position) is expressed as follows:
The distance between the vertex of the corneal posterior surface and the vertex of the anterior surface of the IOL (ILP for internal lens position) is simply given by:
- na is the refractive index of the aqueous humor
- nv is the refractive index of the vitreous
- Dc is the total power of the cornea
- Di is the total power of the IOL
Determination of the ELPT
The preceeding equation can be solved for ELPT :
The ± sign must be replaced by – when Di>0 (IOL power is positive), and by + when Di<0 (IOL power is negative).
This equation provides the value of the ELPT in an emmetropic pseudophakic eye.
The ELPT value can be computed for a non-emmetropic pseudophakic eye after replacing Dc by Dce in the preceeding 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 (neglecting the distance S1Hc).
This amounts to giving the cornea an emmetropizing power so that the ELPT resolution equation can be used.
The ELPT resolution equation can be used to determine the effective thin lens position, denoted ELPt, which would be obtained in a thin lens model where the cornea and IOL have a null thickness (S1S2=S3S4=0) and ALA=ALT. Thus, when we use this formula, we calculate a distance which, in a thick lens context, corresponds to a distance between principal planes which depends not only on the anatomical position of the IOL with respect to the cornea but also on the geometry of the IOL (ratio between the anterior and posterior curvatures, central thickness).
Computation of the ELPT
The following spreadsheet is used to calculate the effective position of the thick IOL in a pseudophakic eye from biometric data, postoperative refraction, and IOL geometry (Coddigton shape factor). Rca and Rcp are the anterior and posterior corneal surface radii, respectively. di is the IOL central thickness. Ria and Rip are the anterior and posterior IOL surface radii, respectively, computed from the IOL power and Coddigton values.