A mathematical model for the corneal transparency problem

• Published in: Journal of mathematics in industry Vol. 12; no. 1; pp. 1 - 11
• Main Authors: Araújo, Adérito, Barbeiro, Sílvia, Bernardes, Rui, Morgado, Miguel, Sakić, Sunčica
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 06.05.2022; Springer Nature B.V; SpringerOpen
• Subjects: Applications of Mathematics; Backscattering; Biotechnology and Materials Science; Cornea; Corneal transparency; Discontinuous Galerkin method; Form and Patterns in Medicine; Galerkin method; Light scattering; Low-storage explicit Runge-Kutta method; Math. Appl. in Environmental Science; Mathematical and Computational Biology; Mathematical and Computational Engineering; Mathematical Methods in Physics; Mathematical Modeling and Industrial Mathematics; Mathematical models; Mathematics; Mathematics and Statistics; Maxwell’s equations; Propagation; Runge-Kutta method; Shape; Corneal transparency; Discontinuous Galerkin method; Low-storage explicit Runge-Kutta method; Light scattering; Maxwell’s equations
• ISSN: 2190-5983; 2190-5983
• DOI: 10.1186/s13362-022-00125-y

Understanding the physical basis of corneal transparency has been a subject of interest amongst physicists, basic scientists and ophthalmologists. Impairment of corneal clarity is a significant cause of visual morbidity worldwide. Thus, it is essential to understand the mechanisms behind corneal transparency and how the alterations due to corneal pathologies affect vision. We use Maxwell’s equations to model light propagation in ocular tissues and a nodal discontinuous Galerkin method combined with an explicit Runge-Kutta method to simulate light propagation in normal and pathological corneas. Our simulation results illustrate that an increase in the diameter of some fibres causes an increase in backscattering. Thus, these may represent some of the physical changes in the cornea that might result in loss of transparency and visual morbidity.