Analysis of the effects of finite element type within a 3D biomechanical model of a human optic nerve head and posterior pole

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.