Limitations of Reconstructing Pentacam Rabbit Corneal Tomography by Zernike Polynomials
The study aims to investigate the likelihood of Zernike polynomial being used for reconstructing rabbit corneal surfaces as scanned by the Pentacam segment tomographer, and hence evaluate the accuracy of corneal power maps calculated from such Zernike fitted surfaces. The study utilised a data set o...
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| Format: | Article |
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MDPI AG
2022-12-01
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| Series: | Bioengineering |
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| Online Access: | https://www.mdpi.com/2306-5354/10/1/39 |
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| author | Mohamed Baraya Jessica Moore Bernardo T. Lopes Richard Wu FangJun Bao XiaoBo Zheng Alejandra Consejo Ahmed Abass |
| author_facet | Mohamed Baraya Jessica Moore Bernardo T. Lopes Richard Wu FangJun Bao XiaoBo Zheng Alejandra Consejo Ahmed Abass |
| author_sort | Mohamed Baraya |
| collection | DOAJ |
| description | The study aims to investigate the likelihood of Zernike polynomial being used for reconstructing rabbit corneal surfaces as scanned by the Pentacam segment tomographer, and hence evaluate the accuracy of corneal power maps calculated from such Zernike fitted surfaces. The study utilised a data set of both eyes of 21 rabbits using a reverse engineering approach for deductive reasoning. Pentacam raw elevation data were fitted to Zernike polynomials of orders 2 to 20. The surface fitting process to Zernike polynomials was carried out using randomly selected 80% of the corneal surface data points, and the root means squared fitting error (RMS) was determined for the other 20% of the surface data following the Pareto principle. The process was carried out for both the anterior and posterior surfaces of the corneal surfaces that were measured via Pentacam scans. Raw elevation data and the fitted corneal surfaces were then used to determine corneal axial and tangential curvature maps. For reconstructed surfaces calculated using the Zernike fitted surfaces, the mean and standard deviation of the error incurred by the fitting were calculated. For power maps computed using the raw elevation data, different levels of discrete cosine transform (DCT) smoothing were employed to infer the smoothing level utilised by the Pentacam device. The RMS error was not significantly improved for Zernike polynomial orders above 12 and 10 when fitting the anterior and posterior surfaces of the cornea, respectively. This was noted by the statistically non-significant increase in accuracy when the order was increased beyond these values. The corneal curvature calculations suggest that a smoothing process is employed in the corneal curvature maps outputted by the Pentacam device; however, the exact smoothing method is unknown. Additionally, the results suggest that fitting corneal surfaces to high-order Zernike polynomials will incur a clinical error in the calculation of axial and tangential corneal curvature of at least 0.16 ± 01 D and 0.36 ± 0.02 D, respectively. Rabbit corneal anterior and posterior surfaces scanned via the Pentacam were optimally fitted to orders 12 and 10 Zernike polynomials. This is essential to get stable values of high-order aberrations that are not affected by Zernike polynomial fittings, such as comas for Intracorneal Ring Segments (ICRS) adjustments or spherical aberration for pre-cataract operations. Smoothing was necessary to replicate the corneal curvature maps outputted by the Pentacam tomographer, and fitting corneal surfaces to Zernike polynomials introduces errors in the calculation of both the axial and tangential corneal curvatures. |
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| publishDate | 2022-12-01 |
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| spelling | doaj.art-4f8f981cf270431aac82c0ce354ba6b92023-11-30T21:14:36ZengMDPI AGBioengineering2306-53542022-12-011013910.3390/bioengineering10010039Limitations of Reconstructing Pentacam Rabbit Corneal Tomography by Zernike PolynomialsMohamed Baraya0Jessica Moore1Bernardo T. Lopes2Richard Wu3FangJun Bao4XiaoBo Zheng5Alejandra Consejo6Ahmed Abass7Department of Production Engineering and Mechanical Design, Faculty of Engineering, Port Said University, Port Said 42526, EgyptDepartment of Civil Engineering and Industrial Design, School of Engineering, University of Liverpool, Liverpool L69 3GH, UKDepartment of Civil Engineering and Industrial Design, School of Engineering, University of Liverpool, Liverpool L69 3GH, UKBrighten Optix Corporation, Shilin District, Taipei 11167, TaiwanEye Hospital, Wenzhou Medical University, Wenzhou 325035, ChinaEye Hospital, Wenzhou Medical University, Wenzhou 325035, ChinaDepartment Applied Physics, University of Zaragoza, 50009 Zaragoza, SpainDepartment of Production Engineering and Mechanical Design, Faculty of Engineering, Port Said University, Port Said 42526, EgyptThe study aims to investigate the likelihood of Zernike polynomial being used for reconstructing rabbit corneal surfaces as scanned by the Pentacam segment tomographer, and hence evaluate the accuracy of corneal power maps calculated from such Zernike fitted surfaces. The study utilised a data set of both eyes of 21 rabbits using a reverse engineering approach for deductive reasoning. Pentacam raw elevation data were fitted to Zernike polynomials of orders 2 to 20. The surface fitting process to Zernike polynomials was carried out using randomly selected 80% of the corneal surface data points, and the root means squared fitting error (RMS) was determined for the other 20% of the surface data following the Pareto principle. The process was carried out for both the anterior and posterior surfaces of the corneal surfaces that were measured via Pentacam scans. Raw elevation data and the fitted corneal surfaces were then used to determine corneal axial and tangential curvature maps. For reconstructed surfaces calculated using the Zernike fitted surfaces, the mean and standard deviation of the error incurred by the fitting were calculated. For power maps computed using the raw elevation data, different levels of discrete cosine transform (DCT) smoothing were employed to infer the smoothing level utilised by the Pentacam device. The RMS error was not significantly improved for Zernike polynomial orders above 12 and 10 when fitting the anterior and posterior surfaces of the cornea, respectively. This was noted by the statistically non-significant increase in accuracy when the order was increased beyond these values. The corneal curvature calculations suggest that a smoothing process is employed in the corneal curvature maps outputted by the Pentacam device; however, the exact smoothing method is unknown. Additionally, the results suggest that fitting corneal surfaces to high-order Zernike polynomials will incur a clinical error in the calculation of axial and tangential corneal curvature of at least 0.16 ± 01 D and 0.36 ± 0.02 D, respectively. Rabbit corneal anterior and posterior surfaces scanned via the Pentacam were optimally fitted to orders 12 and 10 Zernike polynomials. This is essential to get stable values of high-order aberrations that are not affected by Zernike polynomial fittings, such as comas for Intracorneal Ring Segments (ICRS) adjustments or spherical aberration for pre-cataract operations. Smoothing was necessary to replicate the corneal curvature maps outputted by the Pentacam tomographer, and fitting corneal surfaces to Zernike polynomials introduces errors in the calculation of both the axial and tangential corneal curvatures.https://www.mdpi.com/2306-5354/10/1/39corneal tomographyPentacamZernike polynomialsrabbit eyecurve fitting |
| spellingShingle | Mohamed Baraya Jessica Moore Bernardo T. Lopes Richard Wu FangJun Bao XiaoBo Zheng Alejandra Consejo Ahmed Abass Limitations of Reconstructing Pentacam Rabbit Corneal Tomography by Zernike Polynomials Bioengineering corneal tomography Pentacam Zernike polynomials rabbit eye curve fitting |
| title | Limitations of Reconstructing Pentacam Rabbit Corneal Tomography by Zernike Polynomials |
| title_full | Limitations of Reconstructing Pentacam Rabbit Corneal Tomography by Zernike Polynomials |
| title_fullStr | Limitations of Reconstructing Pentacam Rabbit Corneal Tomography by Zernike Polynomials |
| title_full_unstemmed | Limitations of Reconstructing Pentacam Rabbit Corneal Tomography by Zernike Polynomials |
| title_short | Limitations of Reconstructing Pentacam Rabbit Corneal Tomography by Zernike Polynomials |
| title_sort | limitations of reconstructing pentacam rabbit corneal tomography by zernike polynomials |
| topic | corneal tomography Pentacam Zernike polynomials rabbit eye curve fitting |
| url | https://www.mdpi.com/2306-5354/10/1/39 |
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