Received 27.12.2024, Revised 15.03.2025, Accepted 24.04.2025

Mathematical modelling of eye condition in glaucoma: Approaches to parameter analysis and their interactions

Vladimir Vychuzhanin, Alexey Vychuzhanin, Olga Guzun , Oleg Zadorozhny

Mathematical modelling of physiological processes is a key component of intelligent medical systems, as it describes disease mechanisms in greater detail and contributes to early diagnosis. This study presents an analytical model for assessing eye health, incorporating key ophthalmological parameters: intraocular pressure (IOP), perfusion coefficient (Pperf), best-corrected visual acuity (BCVA), visual field index (VFI), retinal nerve fibre layer thickness (RNFL), and neuroretinal rim area (Rim_area). The study aimed to develop a model that can accurately evaluate the nonlinear interactions between these parameters, improving diagnostic accuracy and predicting glaucoma progression. The study also aimed to determine critical threshold values of these ophthalmological indicators to improve clinical decision-making. The results demonstrated that application of numerical optimisation techniques such as L-BFGS-B and logarithmic-exponential transformations significantly improves the accuracy of glaucoma risk prediction; critical threshold values of ophthalmological parameters have been identified, improving precision of detection of glaucoma stages. Additionally, the study facilitates a systematic evaluation of the association between intraocular pressure and optic nerve condition, a factor deemed critical for accurate prediction of disease progression. The practical significance of this research is determined by the potential integration into medical IT systems for automated glaucoma screening and patient monitoring. The proposed approach can assist ophthalmologists in clinical decision-making by optimising treatment strategies and preventing irreversible vision loss. The model’s adaptability also enables its use in telemedicine applications, facilitating remote diagnostics and continuous patient assessment

analytical model; ophthalmological parameters; optimisation; medical diagnostics; adaptability
10-19
Vychuzhanin, V., Vychuzhanin, A., Guzun , O., & Zadorozhny, O. (2025). Mathematical modelling of eye condition in glaucoma: Approaches to parameter analysis and their interactions. Information Technologies and Computer Engineering, 22(1), 10-19. https://doi.org/10.63341/vitce/1.2025.09

References

[1] Chen, R., Lei, J., Liao, Y., Jin, Y., Li, X., Wu, D., Li, H., Bi, Y., & Zhu, H. (2024). Predicting 24-hour intraocular pressure peaks and averages with machine learning. Frontiers in Medicine, 11. doi: 10.3389/fmed.2024.1459629.

[2] Dube, T., Takawale, T., Devgirikar, P., Saste, A., & Gaikwad, V. (2023). Glaucoma detection using deep learning: A review. International Journal of Creative Research Thoughts, 11(12), e525-e528.

[3] Guidoboni, G., Harris, A., Arciero, J.C., Siesky, B.A., Amireskandari, A., Gerber, A.L., Huck, A.H., Kim, N.J., Cassani, S., & Carichino, L. (2013). Mathematical modeling approaches in the study of glaucoma disparities among people of African and European descents. Journal of Coupled Systems and Multiscale Dynamics, 1(1), 1-21. doi: 10.1166/jcsmd.2013.1004. [4] Huang, X., Islam, M. R., Akter, S., Ahmed, F., Kazami, E., Abu Serhan, H., Abd-alrazaq, A., & Yousefi, S. (2023). Artificial intelligence in glaucoma: Opportunities, challenges, and future directions. Biomedical Engineering Online, 22(1), article number 126. doi: 10.1186/s12938-023-01187-8.

[4] Hussain, S., Chua, J., Wong, D., Lo, J., Kadziauskiene, A., Asoklis, R., Barbastathis, G., Schmetterer, L., & Yong, L. (2023). Predicting glaucoma progression using deep learning framework. Scientific Reports, 13, article number 19960. doi: 10.1038/s41598-023-46253-2.

[5] Jin, Y., Liang, L., Li, J., Xu, K., Zhou, W., & Li, Y. (2024). Artificial intelligence and glaucoma: A lucid and comprehensive review. Frontiers in Medicine, 11, article number 4238. doi: 10.3389/fmed.2024.1423813. 

[6] Kashyap, R., Nair, R., Gangadharan, S. M. P., Botto-Tobar, M., Farooq, S., & Rizwan, A. (2022). Glaucoma detection and classification using improved U-Net deep learning model. Healthcare, 10, article number 2497. doi: 10.3390/ healthcare10102497.

[7] Ling, X. C., Chen, H. S.-L., Yeh, P.-H., Cheng, Y.-C., Huang, C.-Y., Shen, S.-C., & Lee, Y.-S. (2025). Deep learning in glaucoma detection and progression prediction. Biomedicines, 13(2), article number 420. doi: 10.3390/ biomedicines13020420.

[8] Liu, Y., Wu, R., & Yang, A. (2023). Research on medical problems based on mathematical models. Mathematics, 11(13), article number 2842. doi: 10.3390/math11132842.

[9] Nocedal, J., & Wright, S. J. (2006). Numerical optimization (2nd ed.). Cham: Springer.

[10] Qian, X., et al. (2023). External validation of a deep learning detection system for glaucomatous optic neuropathy. Eye, 37, 3813-3818. doi: 10.1038/s41433-023-02622-9.

[11] Raju, M., Shanmugam, K.P., & Shyu, C.-R. (2023). Application of machine learning predictive models for early detection of glaucoma. Applied Sciences, 13(4), article number 2445. doi: 10.3390/app13042445.

[12] Shoukat, A., Akbar, S., Hassan, S.A., Iqbal, S., Mehmood, A., & Ilyas, Q.M. (2023). Automatic diagnosis of glaucoma from retinal images. Diagnostics, 13(10), article number 1738. doi: 10.3390/diagnostics13101738.

[13] Siesky, B., Harris, A., Verticchio Vercellin, A., Arciero, J., Fry, B., Eckert, G., Guidoboni, G., Oddone, F., & Antman, G. (2023). Heterogeneity of ocular hemodynamic biomarkers. Journal of Clinical Medicine, 12(4), article number 1287. doi: 10.3390/jcm12041287.

[14] Tarcoveanu, F., Leon, F., Curteanu, S., Chiselita, D., Bogdanici, C.M., & Anton, N. (2022). Classification algorithms used in predicting glaucoma progression. Healthcare, 10(10), article number 1831. doi: 10.3390/ healthcare10101831.

[15] Tonti, E., Tonti, S., Mancini, F., Bonini, C., Spadea, L., D’Esposito, F., Gagliano, C., Musa, M., & Zeppieri, M. (2024). Artificial intelligence and advanced technology in glaucoma. Journal of Personalized Medicine, 14(10), article number 1062. doi: 10.3390/jpm14101062.

[16] Tong, Y., Lu, W., Yu, Y., & Shen, Y. (2020). Application of machine learning in ophthalmic imaging. Eye and Vision, 7, article number 22. doi: 10.1186/s40662-020-00183-6.

[17] Moudgil, T., & Gupta, D. (2024). Advancements in antiglaucoma medications: A comprehensive review. Tropical Ophthalmology, 1(1), 12-16. doi: 10.4103/TOPH.TOPH_4_23.

[18] Vychuzhanin, V., Rudnichenko, N., Guzun, O., Zadorozhnyy, O., Korol, A., & Gritsuk, I. (2024). Artificial intelligence Integration in the diagnosis, prognosis and diabetic neovascular glaucoma treatment. CEUR Workshop Proceedings, 3790, 238-249.

[19] Wagner, I. V., Stewart, M. W., & Dorairaj, S. K. (2022). Updates on glaucoma diagnosis and management. Mayo Clinic Proceedings: Innovations, Quality & Outcomes, 6(6), 618-635. doi: 10.1016/j.mayocpiqo.2022.09.007.

[20] Zuo, H., Huang, B., He, J., Fang, L., & Huang, M. (2025). Machine learning approaches in high myopia. Journal of Medical Internet Research, 27, article number e57644. doi: 10.2196/57644.