Universal IOL Formula Optimizer & Statistical Analyzer

Constant optimization and refractive outcomes analysis — works with any IOL formula using a positional constant

by Damien Gatinel, MD, PhDRothschild Foundation Hospital, Paris, France · gatinel.com · PEARL-DGS · Ophthalmic Tools

UFO

About the Optimization Method

This tool uses the sensitivity factor F to optimize IOL formula constants. The function F relates a small change in the effective lens position (ELP) to the resulting variation in refractive power at the spectacle plane (in diopters). Because F depends on both the implanted IOL power (P) and keratometry (K), the optimal constant adjustment is computed per-eye and then aggregated — making this approach universal and applicable to any IOL calculation formula that relies on a positional constant (A-constant, SF, pACD, a0, etc.).

Methodological note: The aggregate sensitivity factor F̄ used in the optimization is the arithmetic mean of the individual per-eye values Fᵢ = F(Kᵢ, Pᵢ), not the value computed from the sample means F(K̄, P̄). This distinction matters because the relationship between F and its inputs is nonlinear, so mean(F(Kᵢ,Pᵢ)) ≠ F(mean(K), mean(P)). Using the per-eye approach correctly weights each observation according to its own optical geometry.

Reference: Gatinel D, Debellemanière G, Saad A, Rampat R, Wallerstein A, Gauvin M, Malet J. A Simplified Method to Minimize Systematic Bias of Single-Optimized Intraocular Lens Power Calculation Formulas. Am J Ophthalmol. 2023 Sep;253:65-73. PMID: 37150337

Simplified guide to IOL formula optimization  ·  Understanding PE, MAE, SD & RMSE metrics

Medical Disclaimer & Data Privacy

IMPORTANT: This tool is intended for qualified ophthalmologists only. Results should be interpreted with clinical judgment. Always validate optimized constants with a separate dataset before clinical implementation.

DATA PRIVACY: All calculations are performed entirely in your browser. No data is transmitted to any server.

References

IOL Formula Optimization

  1. Gatinel D, Debellemanière G, Saad A, Rampat R, Wallerstein A, Gauvin M, Malet J. A simplified method to minimize systematic bias of single-optimized intraocular lens power calculation formulas. Am J Ophthalmol. 2023 Sep;253:65-73. PMID: 37150337
  2. Gatinel D, Debellemanière G, Saad A, Rampat R, Wallerstein A, Gauvin M, Malet J. A new method to minimize the standard deviation and root mean square of the prediction error of single-optimized IOL power formulas. Transl Vis Sci Technol. 2024;13(6):2. PMID: 38837172
  3. Gatinel D, Debellemanière G, Saad A, Brenner LF, Gauvin M, Wallerstein A, Malet J. Impact of the minimization of standard deviation before zeroization of the mean bias on the performance of IOL power formulas. Transl Vis Sci Technol. 2024;13(10):22. PMID: 39392436
  4. Langenbucher A, Wendelstein J, Szentmáry N, Cayless A, Hoffmann P, Debellemanière G, Gatinel D. Performance of a simplified strategy for formula constant optimisation in intraocular lens power calculation. Acta Ophthalmol. 2025;103(1):e10-e18. PMID: 38687054

Precision & Accuracy of IOL Formulas

  1. Gatinel D, Debellemanière G, Saad A, Wallerstein A, Gauvin M, Rampat R, Malet J. Impact of single constant optimization on the precision of IOL power calculation. Transl Vis Sci Technol. 2023;12(11):11. PMID: 37930666
  2. Gatinel D, Debellemanière G, Saad A, Rampat R, Malet J. Theoretical impact of intraocular lens design variations on the accuracy of IOL power calculations. J Clin Med. 2023;12(10):3404. PMID: 37240510
  3. Olsen T, Cooke DL, Findl O, Gatinel D, Koch D, Langenbucher A, Melles RB, Yeo TK. Surgeons need to know more about intraocular lens design for accurate power calculation. J Cataract Refract Surg. 2023;49(6):556-557. PMID: 36753322

PEARL-DGS Formula & ELP Calculation

  1. Debellemanière G, Dubois M, Gauvin M, Wallerstein A, Brenner LF, Rampat R, Saad A, Gatinel D. The PEARL-DGS formula: the development of an open-source machine learning-based thick IOL calculation formula. Am J Ophthalmol. 2021;232:58-69. PMID: 33992611
  2. Gatinel D, Debellemanière G, Saad A, Dubois M, Rampat R. Determining the theoretical effective lens position of thick intraocular lenses for machine learning-based IOL power calculation and simulation. Transl Vis Sci Technol. 2021;10(4):27. PMID: 34004006
  3. Gatinel D, Debellemanière G, Saad A, Rampat R. Determining the theoretical formula for the sensitivity factor (F) relating ELP displacement to refractive change. Transl Vis Sci Technol. 2022;11(9):5. PMID: 36069859

Optimization Strategies (Langenbucher et al.)

  1. Langenbucher A, Szentmáry N, Cayless A, Müller M, Eppig T, Schröder S, Fabian E. IOL formula constants: strategies for optimization and defining standards for presenting data. Curr Eye Res. 2023;48(3):263-269. PMID: 33530082
  2. Langenbucher A, Hoffmann P, Cayless A, Wendelstein J, Szentmáry N. Limitations of constant optimization with disclosed intraocular lens power formulae. J Cataract Refract Surg. 2024;50(3):201-208. PMID: 37847110

Data Requirements?

Minimum for optimization: IOL Power (D), Keratometry (K1/K2 or Km or R1/R2), Prediction Error (Error, PE, or prediction_error).

Recommended: IOL Model/Type, Eye (OD/OS), Formula name, Patient ID.

PE = Achieved Refraction − Predicted Refraction (D). Consistent column naming improves auto-detection.

Load Your Data?

Drag & Drop or Click to Select

CSV, XLSX

CSV OK

Paste Data

Example Datasets?

Load a built-in example to explore the tool's capabilities without uploading your own data.

Analysis Scope

Current: No data

Constant Optimization (Gatinel Method)?

F = 0.0006 (P² + 2KP) D/mm — computed per eye, then averaged: F̄ = mean(Fᵢ). Three targets: ME=0 (zeroing bias), SD-min, RMS-min.

Input Parameters?

Sign: In power prediction, negative ME → negative ΔELP. For known-P zeroing, opposite sign.

Load data or enter values, then click Calculate.

Multi-Metric (ME / SD / RMS)?

Per-eye F computation from dataset K & P columns.

References: Gatinel D, et al. A Simplified Method to Minimize Systematic Bias of Single-Optimized IOL Power Calculation Formulas. Am J Ophthalmol. 2023;253:65-73. PMID 37150337
Gatinel D, et al. A New Method to Minimize the Standard Deviation and Root Mean Square of the Prediction Error of Single-Optimized IOL Power Formulas. Transl Vis Sci Technol. 2024;13(6):2. — F = 0.0006(P² + 2KP) D/mm. ΔA = ΔELP / 0.62467. PMID 38837172

A-constant & Barrett Universal II: The Barrett formula uses an internal Lens Factor (LF), but accepts the SRK/T A-constant as input and converts it internally. Therefore, the optimized A-constant obtained here (ΔA = ΔELP / 0.62467) can be applied directly to the Barrett Universal II formula. This simplified optimization approach bypasses the need for the proprietary LF conversion. For formulas whose calculation is not publicly available (Barrett, Kane, EVO…), the method consists of: (1) computing ΔELP from your dataset, (2) converting to ΔA, and (3) adding ΔA to the current A-constant used in the formula. Two to three iterations typically suffice to reach ME ≈ 0.

Detailed methodology (gatinel.com) |  Barrett Universal II Calculator (APACRS)

Subgroup Analysis & Filtering?

Categorical

Load data first.

Numerical Range

Filters are cumulative: add multiple variables, click × to remove individually.

No active filters.
Outlier policy:

Error Statistics?

Distribution

Normality Testing?

Precision Thresholds

Threshold%NVisualization

Percentiles

PercentileValue (D)PercentileValue (D)

Column Statistics

ColumnNMeanSDMinQ1MedianQ3Max

Correlation Analysis?

Detailed Parameter Analysis?

Chart Controls

Export Results

Debug Console

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