Biomedical Engineering Department, Helwan University, Helwan, Egypt.
Information Technology and Computer Science School, Nile University, Sheikh Zayed City, Egypt.
BMC Ophthalmol. 2023 Jun 5;23(1):250. doi: 10.1186/s12886-023-02985-3.
Corneal biomechanics is of great interest to researchers recently. Clinical findings relate them to corneal diseases and to outcomes of refractive surgery. To have a solid understanding of corneal diseases' progression, it is important to understand corneal biomechanics. Also, they are essential for better explaining outcomes of refractive surgeries and their undesired consequences. There is a difficulty for studying corneal biomechanics in-vivo and multiple limitations arise for ex-vivo studies. Hence mathematical modelling is considered as a proper solution to overcome such obstacles. Mathematical modelling of cornea in-vivo allows studying corneal viscoelasticity with taking into consideration all boundary conditions existing in real in-vivo situation.
Three mathematical models are used to simulate corneal viscoelasticity and thermal behavior in two different loading situations: constant and transient loading. Two models of the three are used for viscoelasticity simulation which are Kelvin-Voigt and standard linear solid models. Also, temperature rise due to the ultrasound pressure push is calculated using bioheat transfer model for both the axial direction and as a 2D spatial map using the third model (standard linear solid model).
Viscoelasticity simulation results show that standard linear solid model is efficient for describing the viscoelastic behavior of human cornea in both loading conditions. Results show also that the deformation amplitude obtained from standard linear solid model is more reasonable for corneal soft-tissue deformation with respect to corresponding clinical findings than that obtained from Kelvin-Voigt model. Thermal behavior results estimated corneal temperature rise to be roughly 0.2 °C, which conforms with FDA regulations for soft tissue safety.
Standard Linear Solid (SLS) model is better describing the human corneal behavior in response to constant and transient load more efficiently. Temperature rise (TR) for the corneal tissue of about 0.2 °C is conforming with FDA regulations and even less than the FDA regulations for soft tissue safety.
角膜生物力学是近来研究人员非常感兴趣的领域。临床发现将其与角膜疾病和屈光手术的结果联系起来。为了深入了解角膜疾病的进展，了解角膜生物力学是很重要的。此外，它们对于更好地解释屈光手术的结果及其不良后果也是必不可少的。活体研究角膜生物力学存在困难，离体研究存在多种局限性。因此，数学建模被认为是克服这些障碍的一种合适的解决方案。活体角膜的数学建模允许在考虑到真实活体情况下存在的所有边界条件的情况下研究角膜粘弹性。
使用三种数学模型模拟两种不同加载情况（恒载和瞬态加载）下的角膜粘弹性和热行为。三种模型中的两种用于粘弹性模拟，即 Kelvin-Voigt 模型和标准线性固体模型。此外，还使用第三种模型（标准线性固体模型）计算了由于超声压力推动而导致的轴向和二维空间图中温度升高。
粘弹性模拟结果表明，标准线性固体模型在两种加载条件下都能有效地描述人眼角膜的粘弹性行为。结果还表明，与 Kelvin-Voigt 模型相比，标准线性固体模型获得的变形幅度更符合临床发现，更适合描述角膜软组织的变形。热行为结果估计角膜温升约为 0.2°C，符合 FDA 对软组织安全性的规定。
标准线性固体（SLS）模型在模拟恒载和瞬态载荷下人眼角膜的行为方面更有效。角膜组织的温升（TR）约为 0.2°C，符合 FDA 规定，甚至低于 FDA 对软组织安全性的规定。
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