PURPOSE. We developed a combined biomechanical and hemodynamic model of the human eye to estimate blood flow and oxygen concentration within the lamina cribrosa (LC) and rank the factors that influence LC oxygen concentration. METHODS. We generated 5000 finite-element eye models with detailed microcapillary networks of the LC and computed the oxygen concentration of the lamina retinal ganglion cell axons. For each model, we varied the intraocular pressure (IOP) from 10 mm Hg to 55 mm Hg in 5-mm Hg increments, the cerebrospinal fluid pressure (13 ± 2 mm Hg), cup depth (0.2 ± 0.1 mm), scleral stiffness (±20% of the mean values), LC stiffness (0.41 ± 0.2 MPa), LC radius (1.2 ± 0.12 mm), average LC pore size (5400 ± 2400 μm 2), the microcapillary arrangement (radial, isotropic, or circumferential), and perfusion pressure (50 ± 9 mm Hg). Blood flow was assumed to originate from the LC periphery and drain via the central retinal vein. Finally, we performed linear regressions to rank the influence of each factor on the LC tissue oxygen concentration. RESULTS. LC radius and perfusion pressure were the most important factors in influencing the oxygen concentration of the LC. IOP was another important parameter, and eyes with higher IOP had higher compressive strain and slightly lower oxygen concentration. In general, superior-inferior regions of the LC had significantly lower oxygen concentration than the nasal-temporal regions, resulting in an hourglass pattern of oxygen deficiency. CONCLUSIONS. To the best of our knowledge, this study is the first to implement a comprehensive hemodynamical model of the eye that accounts for the biomechanical forces and morphological parameters of the LC. The results provide further insight into the possible relationship of biomechanical and vascular pathways leading to ischemia-induced optic neuropathy.

In this article, a free vibration analysis of the functionally graded porous piezoelectric (FGPP) microplates is firstly solved by using a combination of two variable refined plate theory (RPT), modified strain gradient theory (MSGT) and isogeometric analysis (IGA). The FGPP microplate is composed of piezoelectric material with pores, which are distributed across the plate thickness in uniform and non-uniform distributions. The modified strain gradient theory is used to capture the size effect on the natural frequency of the FGPP microplates. According to the variational principle of RPT with two variables, the governing equations are derived and solved by the IGA. The influence of the length scale parameters (LSPs), external electric voltage, power law index, length-to-thickness ratio, aspect ratio and boundary conditions (BCs) on the natural frequency of the FGPP microplates is studied. The numerical results show that a rise in the porosity coefficient makes a decrease in the microplate’s stiffness, while an increase in LSPs leads to a rise in the microplate’s stiffness.This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium provided the original work is properly cited.

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