Physics-Informed Neural Network Modeling of Corneal Inflation: Forward Prediction and Inverse Parameter Identification

Document Type : Research Paper

Authors
1 Britton Chance Center for Biomedical Photonics, Wuhan National Laboratory for Optoelectronics, Huazhong University of Science and Technology, Wuhan, Hubei, 430074, China
2 MOE Key Laboratory for Biomedical Photonics, Wuhan National Laboratory for Optoelectronics, Huazhong University of Science and Technology, Wuhan 430074, China
3 College of Life Science and Technology, Huazhong University of Science and Technology, Wuhan, Hubei, 430074, China
Abstract
The cornea is vital for the eye's optical function and structural integrity, with its biomechanics regulating intraocular pressure (IOP), preserving vision, and ensuring safe, effective refractive surgeries. Corneal inflation experiments serve as a vital approach to investigate the mechanical behavior of the cornea under physiological IOP by measuring displacement responses at varying pressure levels, thus providing key data that reflect its biomechanical characteristics. Accurate forward prediction of mechanical responses and inverse identification of mechanical parameters in these experiments are of significant value for the quantitative assessment of corneal biomechanics. In recent years, Physics-Informed Neural Networks (PINNs), an emerging approach that integrates physical prior knowledge with deep learning, have demonstrated strong capabilities in solving partial differential equations (PDEs). Based on the PINN framework, this study investigates forward mechanical response prediction and inverse parameter identification in corneal inflation experiments. Experimental validation using Polydimethylsiloxane (PDMS) artificial corneas demonstrated that the proposed method performs well in both forward prediction and inverse identification tasks, and its effectiveness was confirmed through comparison with the finite element method. This study provides an innovative solution for biomechanical modeling and material parameter identification in corneal inflation experiments.
Keywords
Subjects

Publisher’s Note Shahid Chamran University of Ahvaz remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

[1] Ruberti, J.W., Sinha Roy, A., Roberts, C.J., Corneal biomechanics and biomaterials, Annual Review of Biomedical Engineering, 13(1), 2011, 269-295.
[2] Ávila, F.J., Marcellán, M.C., Remón, L., On the relationship between corneal biomechanics, macrostructure, and optical properties, Journal of Imaging, 7(12), 2021, 280.
[3] Wilson, A., Marshall, J., A review of corneal biomechanics: Mechanisms for measurement and the implications for refractive surgery, Indian Journal of Ophthalmology, 68(12), 2020, 2679-2690.
[4] Wen, J., Chen, X., Yang, Y., Liu, J., Li, E., Liu, J., Zhou, Z., Wu, W., He, K., Acupuncture Medical Therapy and its Underlying Mechanisms: A Systematic Review, American Journal of Chinese Medicine, 49(1), 2021, 1-23.
[5] Matteoli, S., Virga, A., Paladini, I., Mencucci, R., Corvi, A., Investigation into the Elastic Properties of ex vivo Porcine Corneas Subjected to Inflation Test after Cross-Linking Treatment, Journal of Applied Biomaterials & Functional Materials, 14(2), 2016, 163-170. 
[6] Wang, L., Tian, L., Huang, Y., Huang, Y., Zheng, Y., Assessment of corneal biomechanical properties with inflation test using optical coherence tomography, Annals of Biomedical Engineering, 46(2), 2018, 247-256.
[7] Chang, S.H., Zhou, D., Eliasy, A., Li, Y.C., Elsheikh, A., Experimental evaluation of stiffening effect induced by UVA/Riboflavin corneal cross-linking using intact porcine eye globes, PLoS One, 15(11), 2020, e0240724. 
[8] Piñero, D.P., Alcón, N., Corneal biomechanics: a review, Clinical and Experimental Optometry, 98(2), 2015, 107-116.
[9] Zhou, Z., Wang, H., Zhang, Y., Lv, H., Zhang, Z., Li, H., Liu, X., Quan, T., Lv, X., Zeng, S., Biomechanical Characterization of Central Corneal Region Using Inflation Test and its Application to Predicting Central Corneal Response Under Intraocular Pressure, Annals of Biomedical Engineering, 54(1), 2016, 303-315.
[10] Zhou, Z., Wang, H., Wang, Z., Zhang, Y., Lv, H., Zhang, Z., Gao, Z., Liu, X., Lv, X., Quan, T., Chen, S., Non-invasive measurement of in vivo corneal steady-state biomechanical properties via controllable negative pressure inflation, IEEE Transactions on Biomedical Engineering, 73, 2025, 1289-1297.
[11] Lv, H., Zhou, Z., Qu, Y., Zhang, Z., Zhang, Y., Zhang, H., Wu, H., Zhao, D., Wang, Z., Lu, J., Wang, H., Measurement Device for Corneal Static Biomechanical Properties Based on Negative Pressure Adhesion, IEEE Transactions on Instrumentation and Measurement, 74, 2025, 4015006.
[12] Bao, F., Wang, J., Cao, S., Liao, N., Shu, B., Zhao, Y., Li, Y., Zheng, X., Huang, J., Chen, S., Wang, Q., Development and clinical verification of numerical simulation for laser in situ keratomileusis, Journal of the Mechanical Behavior of Biomedical Materials, 83, 2018, 126-134.
[13] Quan, T., Zhou, Z., Zhang, Z., Wei, Y., Feng, X., Liu, X., Lv, X., Zeng, S., Wang, H., Model control of corneal surface curvature during refractive surgery: validation on artificial eyes, 2024, DOI: 10.1364/opticaopen.26778595.v1.
[14] Zheng, X., Bao, F., Geraghty, B., Huang, J., Yu, A., Wang, Q., High intercorneal symmetry in corneal biomechanical metrics, Eye and Vision, 3(1), 2016, 7.
[15] Bao, F., Deng, M., Zheng, X., Li, L., Zhao, Y., Cao, S., Yu, A., Wang, Q., Huang, J., Elsheikh, A., Effects of diabetes mellitus on biomechanical properties of the rabbit cornea, Experimental Eye Research, 161, 2017, 82-88.
[16] Soize, C., An overview on uncertainty quantification and probabilistic learning on manifolds in multiscale mechanics of materials, Mathematics and Mechanics of Complex Systems, 11(1), 2023, 87-174.
[17] dell’Isola, F., D’Annibale, F., Luciano, R., Henze, T., Giorgio, I., A generalised plate with kinematically independent thickness for modelling shapes of corneas affected by keratoconus before and after penetrating keratoplasty, Mathematics and Mechanics of Solids, 2025, DOI: 10.1177/10812865251345814.
[18] Mazinani, P., Cardillo, C., Shear wave velocity and finite element modeling for understanding keratoconus biomechanics: Comparison with healthy cornea, Mathematics and Mechanics of Solids, 2025, DOI: 10.1177/10812865251347512.
[19] Yin, Z., Li, G.Y., Zhang, Z., Zheng, Y., Cao, Y., SWENet: A physics-informed deep neural network (PINN) for shear wave elastography, IEEE Transactions on Medical Imaging, 43(4), 2023, 1434-1448.
[20] Kamali, A., Sarabian, M., Laksari, K., Elasticity imaging using physics-informed neural networks: Spatial discovery of elastic modulus and Poisson's ratio, Acta Biomaterialia, 155, 2023, 400-409.
[21] Ragoza, M., Batmanghelich, K., Physics-informed neural networks for tissue elasticity reconstruction in magnetic resonance elastography, International Conference on Medical Image Computing and Computer-Assisted Intervention, 2023, 333-343
[22] Zhang, Y., Liao, J., Feng, Z., Yang, W., Perelli, A., Wang, Z., Li, C., Huang, Z., VP-net: an end-to-end deep learning network for elastic wave velocity prediction in human skin in vivo using optical coherence elastography, Frontiers in Bioengineering and Biotechnology, 12, 2024, 1465823.
[23] Gao, H., Zahr, M.J., Wang, J.X., Physics-informed graph neural Galerkin networks: A unified framework for solving PDE-governed forward and inverse problems, Computer Methods in Applied Mechanics and Engineering, 390, 2022, 114502.
[24] Cho, H.S., Jeoung, S.C., Yang, Y.S., Development of eye phantom for mimicking the deformation of the human cornea accompanied by intraocular pressure alterations, Scientific Reports, 12(1), 2022, 20670. 
[25] Pandolfi, A., Manganiello, F., A model for the human cornea: constitutive formulation and numerical analysis, Biomechanics and Modeling in Mechanobiology, 5(4), 2006, 237-246. 
[26] Defferrard, M., Bresson, X., Vandergheynst, P., Convolutional neural networks on graphs with fast localized spectral filtering, Advances in Neural Information Processing Systems, 29, 2016.
[27] Bower, A.F., Applied mechanics of solids (Chapter 5), CRC Press, 2010.
[28] Kerbl, B., Kopanas, G., Leimkühler, T., Drettakis, G., 3d gaussian splatting for real-time radiance field rendering, ACM Transactions on Graphics, 42(4), 2023, 139.
[29] Clayson, K., Pavlatos, E., Ma, Y., Liu, J., 3D Characterization of corneal deformation using ultrasound speckle tracking, Journal of Innovative Optical Health Sciences, 10(06), 2017, 1742005.
[30] Kingma, D.P., Ba, J., Adam: A method for stochastic optimization, arXiv preprint, arXiv:1412.6980, 2014.

Articles in Press, Corrected Proof
Available Online from 19 March 2026