Grytz Rafael, Krishnan Kapil, Whitley Ryan, Libertiaux Vincent, Sigal Ian A, Girkin Christopher A, Downs J Crawford
Department of Ophthalmology and Visual Sciences, University of Alabama at Birmingham, Birmingham, Alabama, United States.
Equine Clinic, Department of Companion Animals and Equids, Faculty of Veterinary Medicine, University of Liège, Liège, Belgium.
Comput Methods Appl Mech Eng. 2020 Jan 1;358. doi: https://doi.org/10.1016/j.cma.2019.112654. Epub 2019 Oct 1.
Commercial finite element modeling packages do not have the tools necessary to effectively incorporate the complex anisotropic and heterogeneous material properties typical of the biological tissues of the eye. We propose a mesh-free approach to incorporate realistic material properties into finite element models of individual human eyes. The method is based on the idea that material parameters can be estimated or measured at so called control points, which are arbitrary and independent of the finite element mesh. The mesh-free approach approximates the heterogeneous material parameters at the Gauss points of each finite element while the boundary value problem is solved using the standard finite element method. The proposed method was applied to an eye-specific model a human posterior pole and optic nerve head. We demonstrate that the method can be used to effectively incorporate experimental measurements of the lamina cribrosa micro-structure into the eye-specific model. It was convenient to define characteristic material orientations at the anterior and posterior scleral surface based on the eye-specific geometry of each sclera. The mesh-free approach was effective in approximating these characteristic material directions with smooth transitions across the sclera. For the first time, the method enabled the incorporation of the complex collagen architecture of the peripapillary sclera into an eye-specific model including the recently discovered meridional fibers at the anterior surface and the depth dependent width of circumferential fibers around the scleral canal. The model results suggest that disregarding the meridional fiber region may lead to an underestimation of local strain concentrations in the retina. The proposed approach should simplify future studies that aim to investigate collagen remodeling in the sclera and optic nerve head or in other biological tissues with similar challenges.
商业有限元建模软件包没有有效纳入眼部生物组织典型的复杂各向异性和非均匀材料特性所需的工具。我们提出一种无网格方法，将逼真的材料特性纳入个体人眼的有限元模型。该方法基于这样一种理念，即材料参数可以在所谓的控制点处进行估计或测量，这些控制点是任意的，且与有限元网格无关。在使用标准有限元方法求解边值问题时，无网格方法在每个有限元的高斯点处近似非均匀材料参数。所提出的方法应用于一个特定于眼睛的人类后极和视神经乳头模型。我们证明该方法可用于有效地将筛板微结构的实验测量结果纳入特定于眼睛的模型。根据每个巩膜的特定于眼睛的几何形状，在巩膜前表面和后表面定义特征材料方向很方便。无网格方法有效地近似了这些特征材料方向，并且在巩膜上实现了平滑过渡。该方法首次能够将视乳头周围巩膜的复杂胶原结构纳入特定于眼睛的模型，包括最近在前表面发现的子午线纤维以及巩膜管周围环向纤维随深度变化的宽度。模型结果表明，忽略子午线纤维区域可能导致视网膜局部应变浓度的低估。所提出的方法应会简化未来旨在研究巩膜和视神经乳头或其他具有类似挑战的生物组织中胶原重塑的研究。
