We analyzed five datasets containing measurements from eyes from a cataractous population. In each dataset, the same IOL model was inserted among the following: FineVision Micro F (BVI Medical, USA), Acrysof SN60WF (Alcon, USA), Tecnis PCB00 Monofocal (Johnson & Johnson Vision, USA), and Vivinex XC1/XY1 (Hoya, Japan). The study adhered to the tenets of the Declaration of Helsinki and was approved by the Rothschild Foundation Hospital institutional review board (IRB 00012801) under the number CE_20211123_6_GDE. The datasets were anonymized and contained pre-operative biometric data derived with the Lenstar 900 (Haag-Streit AG, Koeniz, Switzerland; EyeSuite software i8.2.2.0) for the Finevision dataset, and the IOL-Master 700 (Carl-Zeiss-Meditec, Jena, Germany; version 7.5.3.0084) for the 3 others, including axial length (AL), anterior chamber depth (ACD; from the front corneal apex to the front apex of the crystalline lens), lens thickness (LT), corneal thickness (CCT), corneal diameter (CD), and the front corneal surface flat (R1) and steep (R2) radii. The corneal power in the flat and the steep corneal meridian (K1 = (nK-1)/R1 and K2 = (nK-1)/R2) was calculated from the corneal front surface radii R1 and R2, with a keratometer index nK as indicated in the formula definition. Postoperative refraction was measured at 6 meters 4 to 6 weeks after cataract surgery by an experienced optometrist and recorded in the dataset, which only included data with a postoperative Snellen decimal visual acuity of at least 0.8 (20/25) Snellen lines.
For all open-source, third-generation formulas, except SRK/T (single-optimized Haigis, Hoffer Q, Holladay 1), the lens constant corresponds to an increment in lens position, added directly to the eye-specific predicted lens position value.
13–17 Hence, the minus ΔELP value calculated using our method can be directly added to the original lens constant (a0, pACD, SF for single optimized Haigis, Hoffer Q, Holladay 1, respectively). However, in the SRK/T formula, the A constant is transformed into an increment in lens position value (ACDconst) using the following equation:
\begin{eqnarray}
{base\, ACDconst} = {base\, A\, constant\, x\, }0.62467 - 68.747\nonumber\\
\end{eqnarray}
ACDconst is then added to the eye-specific predicted lens position value (H), and an offset equal to −3.336 is applied to obtain the final lens position value (ACDest)
18,19:
Hence, when using our method, the original SRK/T A constant must first be converted to its ACDconst equivalent using
Equation 16. Subsequently, minus ΔELP can be added to the latter, followed by converting this adjusted value back to an updated A constant. This can be achieved by solving
Equation 16 for it:
\begin{eqnarray}
&& {Updated\, A\, constant}\nonumber\\
&& \,\,\,\, = \frac{{\left( {base\;ACDconst\; + \;minus\;\Delta ELP} \right) + 68.747\;}}{{0.62467}}\quad
\end{eqnarray}
This methodology can be applied to any formula using a transformation of the SRK/T A constant, in order to determine its lens position increment. As an example, in the PEARL-DGS formula,
20 the change in theoretical internal lens position (TILP) related to the baseline TILP prediction is correlated to the A-constant via the following formula:
\begin{eqnarray}
\Delta TILP &=& \left( {A\;constant\;x\;0.00061311} \right)\nonumber\\
&&\,\,\,\, - \;0.072931129\quad
\end{eqnarray}
For every dataset, the IOL constants respectively optimized for minimizing the mean PE, SD, and RMS were determined using the reference (iterative) method for the following formulas: SRK/T, Hoffer Q, Holladay 1, Haigis (single-optimized, with preset values for a1/a2 = 0.4/0.1), and PEARL-DGS. Starting from the value of the optimized constant (OC) zeroing the mean PE, the ELP increment leading to mean errors comprised between −0.5 diopters (D) and +0.5 D were calculated by 0.01 D steps.
All calculations and analysis were performed using Python version 3.11.15.
We first compared the linearly predicted values of the mean PE (
\(\bar E\)) against the change in ELP (ΔELP
0) derived from
Equation 9, against the values of mean PE obtained through the iterative process. This process allowed for a systematic evaluation of how closely the computed values from this linear model corresponded to the actual data point thereby facilitating a robust assessment of the model's predictive accuracy and efficacy in representing the observed data distribution.
Then, for each ME step, the values of the SD and RMS of the PE were calculated. This allowed us to obtain the respective reference values of the constant that minimizes the SD and the RMS. We could obtain an estimation of these values by computing ΔELP
SD and ΔELP
RMS using
Equations 12 and
15 and adding it to the constant zeroing out the mean PE. We then computed the difference between the reference and estimated constant values, and the differences between their corresponding SD and RMS values (i.e. the resulting values that would have been obtained by using the evaluated optimization method instead of the reference optimization method) were then determined. For each of the values of constants determined by the iterative method, we also indicated the corresponding values of ME, SD, RMS, whenever indicated.