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E.A. Nauman, F. Woods, IV, E.A. Sander, J.C. Downs, C.F. Burgoyne; A Cellular Solid Model of the Lamina Cribrosa . Invest. Ophthalmol. Vis. Sci. 2004;45(13):5530.
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Purpose: To develop an idealized mathematical model of the human lamina cribrosa that can be used to estimate the structural stiffness and the microscale deformations in the laminar beams resulting from elevated intraocular pressure (IOP). Methods: Two hexagonal cellular solid models of the lamina cribrosa were considered. The first consisted of unit cells whose faces were open in the anterior–posterior direction and closed within the transverse plane; forming tubes for the passage of the axon bundles. The second was composed of open walls on all faces allowing for some tortuosity of the nerve fibers. In both cases, the lamina cribrosa was assumed to consist of 11 layers in the anterior–posterior direction, each 21 microns thick. The tissue modulus of the laminar beams was assumed to be 4100 kPa, similar to that of monkey peripapillary sclera. The structural modulus of the lamina cribrosa was predicted as a function of the laminar pore diameter for the range of 10 – 100 µm. Compressive strains in the laminar beams were also determined at a normal IOP of 10 mm of Hg and an elevated IOP of 45 mm of Hg. Results: At a fixed laminar volume fraction of 0.5, the modulus of the hexagonal closed cell remained constant, while that of the open cell varied from 414 kPa at a pore diameter of 100 microns to 1470 kPa for a pore diameter of 10 microns. The closed cell model predicted compressive strains of 0.0007 at normal IOP and 0.0029 at elevated IOP. The open cell model predicted a range of strains at normal IOP from 0.0009 to 0.0032 depending on pore size. At elevated IOP the peak strain increased to 0.0145. A sensitivity analysis showed that these values depend strongly on the assumed volume fraction. Conclusions:We developed an idealized mathematical model of the lamina cribrosa that can be used to study the effects of elevated intraocular pressure on the compressive strains in the optic nerve head and tested its sensitivity to various structural parameters. Combining these models with more detailed anatomical analyses of the lamina cribrosa could help elucidate the progression of glaucomatous degeneration.
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