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TECHNICAL PAPERS: Fluids/Heat/Transport

Mathematical Modeling of the Biomechanics of the Lamina Cribrosa Under Elevated Intraocular Pressures

[+] Author and Article Information
Tim Newson1

Geotechnical Research Centre, Department of Civil and Environmental Engineering, University of Western Ontario, London, Ontario, N6A 5B9, Canadatnewson@eng.uwo.ca

Ahmed El-Sheikh

Division of Civil Engineering, University of Dundee, Dundee DD1 4HN Scotland, United Kingdoma.i.h.elsheikh@dundee.ac.uk

1

Corresponding author.

J Biomech Eng 128(4), 496-504 (Feb 03, 2006) (9 pages) doi:10.1115/1.2205372 History: Received December 13, 2004; Revised February 03, 2006

Comprehensive understanding of the biomechanical performance of the lamina cribrosa (LC) and the optic nerve head is central to understanding the role of elevated intraocular pressures (IOP) in chronic open angle glaucoma. In this paper, six closed-from mathematical models based on different idealizations of the LC are developed and compared. This approach is used to create further understanding of the biomechanical behavior by identifying the LC features and properties that have a significant effect on its performance under elevated IOP. The models developed are based on thin circular plate and membrane theories, and consider influences such as in-plane pretension caused by scleral expansion and large deflections. Comparing the results of the six models against a full ocular globe finite element model suggests the significance of the in-plane pretension and the importance of assuming that the sclera provides the LC with a clamped edge. The model that provided the most accurate representation of the finite element model was also used to predict the behavior of a number of LC experimental tests presented in the literature. In addition to the deflections under elevated IOP, the model predictions include the distributions of stress and strain, which are shown to be compatible with the progression of visual field loss experienced in glaucoma.

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Copyright © 2006 by American Society of Mechanical Engineers
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Figures

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Figure 1

Cross section through the human optic nerve head

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Figure 2

Free body diagrams of the modeling idealizations in models 1–6

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Figure 3

Analysis of a laterally loaded circular plate (see Ref. 12)

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Figure 4

Equilibrium of the sclera

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Figure 5

Central displacement comparisons between the mathematical models

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Figure 6

Distribution of displacement across LC diameter under IOP=25mmHg (q=15mmHg or 0.002N∕mm2) as predicted by mathematical models

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Figure 7

Details of the finite element meshes used in analysis

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Figure 8

Central displacement comparisons between the FE and mathematical models

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Figure 9

Distribution of displacement across the LC diameter under IOP =25mmHg according to the finite element and the mathematical models

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Figure 10

Comparison between model 3 predictions and earlier experimental data

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Figure 11

Stress distribution on the anterior face of the lamina cribrosa at four different levels of IOP as obtained using model 3

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Figure 12

Strain distribution on the anterior face of the lamina cribrosa at four different levels of IOP as obtained using model 3

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