Background and objective

Biomechanical stresses and strains can be simulated in the optic nerve head (ONH) using the finite element (FE) method, and various element types have been used. This study aims to investigate the effects of element type on the resulting ONH stresses and strains.

Methods

A single eye-specific model was constructed using 3D delineations of anatomic surfaces in a high-resolution, fluorescent, 3D reconstruction of a human posterior eye, then meshed using our simple meshing algorithm at various densities using 4- and 10-noded tetrahedral elements, as well as 8- and 20-noded hexahedral elements. A mesh-free approach was used to assign heterogeneous, anisotropic, hyperelastic material properties to the lamina cribrosa, sclera and pia. The models were subjected to elevated IOP of 45 mmHg after pre-stressing from 0 to 10 mmHg, and solved in the open-source FE package Calculix; results were then interpreted in relation to computational time and simulation accuracy, using the quadratic hexahedral model as the reference standard.

Results

The 10-noded tetrahedral and 20R-noded hexahedral elements exhibited similar scleral canal and laminar deformations, as well as laminar and scleral stress and strain distributions; the quadratic tetrahedral models ran significantly faster than the quadratic hexahedral models. The linear tetrahedral and hexahedral elements were stiffer compared to the quadratic element types, yielding much lower stresses and strains in the lamina cribrosa.

Conclusions

Prior studies have shown that 20-noded hexahedral elements yield the most accurate results in complex models. Results show that 10-noded tetrahedral elements yield very similar results to 20-noded hexahedral elements and so they can be used interchangeably, with significantly lower computational time. Linear element types did not yield acceptable results.

中文翻译：

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有限元类型在人类视神经乳头和后极的 3D 生物力学模型中的影响分析

背景与目的

可以使用有限元 (FE) 方法在视神经乳头 (ONH) 中模拟生物力学应力和应变，并且已使用各种元素类型。本研究旨在研究单元类型对由此产生的 ONH 应力和应变的影响。

方法

在高分辨率、荧光、3D 重建人类后眼中，使用解剖表面的 3D 轮廓构建单眼特定模型，然后使用我们的简单网格划分算法使用 4 节点和 10 节点四面体元素在各种密度下进行网格划分，以及 8 节点和 20 节点的六面体单元。使用无网格方法将异质、各向异性、超弹性材料特性分配给筛板、巩膜和软脑膜。模型在预应力从 0 到 10 mmHg 后承受 45 mmHg 的升高 IOP，并在开源 FE 包 Calculix 中解决；然后使用二次六面体模型作为参考标准，根据计算时间和模拟精度对结果进行解释。

结果

10节点四面体和20R节点六面体单元表现出相似的巩膜管和层流变形，以及层流和巩膜应力应变分布；二次四面体模型的运行速度明显快于二次六面体模型。与二次单元类型相比，线性四面体和六面体单元更硬，在筛板中产生低得多的应力和应变。

结论

先前的研究表明，20 个节点的六面体单元在复杂模型中产生最准确的结果。结果表明，10 节点四面体单元产生的结果与 20 节点六面体单元非常相似，因此它们可以互换使用，计算时间显着缩短。线性单元类型没有产生可接受的结果。