Skip to main page content
U.S. flag

An official website of the United States government

Dot gov

The .gov means it’s official.
Federal government websites often end in .gov or .mil. Before sharing sensitive information, make sure you’re on a federal government site.

Https

The site is secure.
The https:// ensures that you are connecting to the official website and that any information you provide is encrypted and transmitted securely.

Access keys NCBI Homepage MyNCBI Homepage Main Content Main Navigation
. 2025 Jan 8;20(1):e0313574.
doi: 10.1371/journal.pone.0313574. eCollection 2025.

Evaluation of keratometric and total corneal astigmatism measurements from optical biometers and anterior segment tomographers and mapping to reconstructed corneal astigmatism vector components

Achim Langenbucher  1 , Nóra Szentmáry  2   3 , Alan Cayless  4 , Peter Hoffmann  5 , Jascha Wendelstein  1   6 , Seth Pantanelli  7
Affiliations

Evaluation of keratometric and total corneal astigmatism measurements from optical biometers and anterior segment tomographers and mapping to reconstructed corneal astigmatism vector components

Achim Langenbucher et al. PLoS One. .

Abstract

Purpose: To investigate different measures for corneal astigmatism in the context of reconstructed corneal astigmatism (recCP) as required to correct the pseudophakic eye, and to derive prediction models to map measured corneal astigmatism to recCP.

Methods: Retrospective single centre study of 509 eyes of 509 cataract patients with monofocal (MX60P) IOL. Corneal power measured with the IOLMaster 700 keratometry (IOLMK), and Galilei G4 keratometry (GK), total corneal power (TCP2), and Alpin's integrated front (CorT) and total corneal power (CorTTP). Feedforward shallow neural network (NET) and linear regression (REG) prediction models were derived to map the measured C0 and C45 power vector components to the respective recCP components.

Results: Both the NET and REG models showed superior performance compared to a constant model correcting the centroid error. The mean squared prediction errors for the NET/REG models were: 0.21/0.33 dpt for IOLMK, 0.23/0.36 dpt for GK, 0.24/0.35 for TCP2, 0.23/0.39 dpt for CorT and 0.22/0.36 dpt for CorTTP respectively (training data) and 0.27/0.37 dpt for IOLMK, 0.26/0.37 dpt for GK, 0.38/0.42 dpt for TCP2, 0.35/0.36 dpt for CorT, and 0.44/0.45 dpt for CorTTP respectively on the test data. Crossvalidation with model optimisation on the training (and validation) data and performance check on the test data showed a slight overfitting especially with the NET models.

Conclusions: Measurement modalities for corneal astigmatism do not yield consistent results. On training data the NET models performed systematically better, but on the test data REG showed similar performance to NET with the advantage of easier implementation.

PubMed Disclaimer

Conflict of interest statement

Dr. Langenbucher reports speaker fees from Hoya Surgical and Johnson & Johnson Vision outside the submitted work Dr. Szentmáry and Dr. Cayless report no financial or proprietary interests. Dr. Hoffmann reports speaker fees from Hoya Surgical and Johnson & Johnson outside the submitted work. Dr. Wendelstein reports research grants from Carl Zeiss Meditec AG, speaker fees from Carl Zeiss Meditec AG, Alcon, Rayner, Bausch and Lomb, and Johnson & Johnson Vision outside of the submitted work Dr. Pantanelli reports research support from Alcon, Bausch & Lomb, and Carl Zeiss Meditec, unrelated to the present work. He is also a consultant for Bausch & Lomb, Carl Zeiss Meditec, and Hoya Surgical Optics. We confirm that this does not alter our adherence to PLOS ONE policies on sharing data and materials

Figures

Fig 1
Fig 1. Double angle plots for the keratometry measures of the Zeiss IOLMaster 700 device showing the 2 astigmatic power vector components (C0 and C45: Projection to the 0/90 degree and to the 45/135 degree meridian) for the differences between recCP and measured corneal power (graphs on the left) and the model prediction errors (prediction error: recCP—recCPpredicted) for the feedforward neural network based models (NET: Upper graphs on the right) and the linear regression based models (REG: Lower graphs on the right) for different measures modalities.
The data (blue dots referring to the training data and red dots referring to the test data) are shown together with the 95% error ellipses (green and yellow dash-dotted lines) and the centroids (green and yellow filled circle markers) for the training dataset (N = 305) and the test dataset (N = 102).
Fig 2
Fig 2. Double angle plots for the keratometry measures of the Ziemer Galilei G4 device (GK) showing the 2 astigmatic power vector components (C0 and C45: Projection to the 0/90 degree and to the 45/135 degree meridian) for the differences between recCP and measured corneal power (graphs on the left) and the model prediction errors (prediction error: recCP—recCPpredicted) for the feedforward neural network based models (NET: Upper graphs on the right) and the linear regression based models (REG: Lower graphs on the right) for different measures modalities.
The data (blue dots referring to the training data and red dots referring to the test data) are shown together with the 95% error ellipses (green and yellow dash-dotted lines) and the centroids (green and yellow filled circle markers) for the training dataset (N = 305) and the test dataset (N = 102).
Fig 3
Fig 3. Double angle plots for the total corneal power values of the Ziemer Galilei G4 device (TCP2) showing the 2 astigmatic power vector components (C0 and C45: Projection to the 0/90 degree and to the 45/135 degree meridian) for the differences between recCP and measured corneal power (graphs on the left) and the model prediction errors (prediction error: recCP—recCPpredicted) for the feedforward neural network based models (NET: Upper graphs on the right) and the linear regression based models (REG: Lower graphs on the right) for different measures modalities.
The data (blue dots referring to the training data and red dots referring to the test data) are shown together with the 95% error ellipses (green and yellow dash-dotted lines) and the centroids (green and yellow filled circle markers) for the training dataset (N = 305) and the test dataset (N = 102).
Fig 4
Fig 4. Double angle plots for the integrated corneal front surface power measures of the Galilei G4 device (CorT) according to the Alpin’s method showing the 2 astigmatic power vector components (C0 and C45: Projection to the 0/90 degree and to the 45/135 degree meridian) for the differences between recCP and measured corneal power (graphs on the left) and the model prediction errors (prediction error: recCP—recCPpredicted) for the feedforward neural network based models (NET: Upper graphs on the right) and the linear regression based models (REG: Lower graphs on the right) for different measures modalities.
The data (blue dots referring to the training data and red dots referring to the test data) are shown together with the 95% error ellipses (green and yellow dash-dotted lines) and the centroids (green and yellow filled circle markers) for the training dataset (N = 305) and the test dataset (N = 102).
Fig 5
Fig 5. Double angle plots for the integrated total corneal power measures of the Galilei G4 device (CorTTP) according to the Alpin’s method showing the 2 astigmatic power vector components (C0 and C45: Projection to the 0/90 degree and to the 45/135 degree meridian) for the differences between recCP and measured corneal power (graphs on the left) and the model prediction errors (prediction error: recCP—recCPpredicted) for the feedforward neural network based models (NET: Upper graphs on the right) and the linear regression based models (REG: Lower graphs on the right) for different measures modalities.
The data (blue dots referring to the training data and red dots referring to the test data) are shown together with the 95% error ellipses (green and yellow dash-dotted lines) and the centroids (green and yellow filled circle markers) for the training dataset (N = 305) and the test dataset (N = 102).
See this image and copyright information in PMC

Similar articles

See all similar articles

Cited by

References

    1. Koch DD, Wang L, Abulafia A, Holladay JT, Hill W. Rethinking the optimal methods for vector analysis of astigmatism. J Cataract Refract Surg 2021;47(1):100–105. doi: 10.1097/j.jcrs.0000000000000428 - DOI - PubMed
    1. Koch DD, Jenkins RB, Weikert MP, Yeu E, Wang L. Correcting astigmatism with toric intraocular lenses: effect of posterior corneal astigmatism. J Cataract Refract Surg 2013;39(12):1803–9. doi: 10.1016/j.jcrs.2013.06.027 - DOI - PubMed
    1. Langenbucher A, Hoffmann P, Cayless A, Wendelstein J, Szentmáry N. Evaluation of statistical correction strategies for corneal back surface astigmatism with toric lenses—a vector analysis. J Cataract Refract Surg 2023. doi: 10.1097/j.jcrs.0000000000001370 - DOI - PubMed
    1. Park DY, Lim DH, Hwang S, Hyun J, Chung TY. Comparison of astigmatism prediction error taken with the Pentacam measurements, Baylor nomogram, and Barrett formula for toric intraocular lens implantation. BMC Ophthalmol 2017;17(1):156. doi: 10.1186/s12886-017-0550-z - DOI - PMC - PubMed
    1. Preussner PR, Hoffmann P, Wahl J. Impact of posterior corneal surface on toric intraocular lens (IOL) calculation. Curr Eye Res 2015;40(8):809–14. doi: 10.3109/02713683.2014.959708 - DOI - PubMed

LinkOut - more resources