A Cellular Solid Model for Analysis of the Microstructural Mechanics of the Lamina Cribrosa

Abstract

Abstract: : Purpose: To investigate the transmission of geometrically dependent macro–scale loads in the sclera to the microstructure of the lamina cribrosa through the use of idealized cellular solid models. Methods: The state of in–plane IOP induced macro–scale stress in the lamina cribrosa was determined by combining the law of Laplace with the method of sections over a strip of the eye that bisected the lamina cribrosa. A relationship between the macro–scale level biomechanics of the lamina cribrosa and its microstructural behavior was constructed using a cellular solid model. The model was composed of regular octagonal unit cells that matched both the laminar solid volume fraction (SVF) and average pore area of morphological data from the lamina cribrosa. The effect of porosity was then investigated by fixing the laminar plate thickness and varying the plate length. Results: The macro–scale modulus of the lamina cribrosa, normalized by the micro–scale modulus of the laminar plates, decreased monotonically from 0.48 to 0.05 over the SVF range of 0.7 to 0.1. The macro–scale stresses in the lamina cribrosa were dependent on the SVF and the ratio of the scleral modulus to the macro–scale modulus of the lamina cribrosa. The stress decreased with decreasing SVF but the stiffer the lamina cribrosa became in relation to the sclera, the more load was shared between the two tissues. Transmission of macro–scale load in the lamina cribrosa to the laminar microstructure resulted in stress amplifications between 5.3 and 7.5 x IOP, which corresponds to stresses of 10 and 15 kPa under an IOP of 15 mm Hg. For a change in IOP from 15 to 45 mm Hg, micro–scale strains of 0.005 and 0.007 developed in the axial and oblique plates, respectively. Conclusions: In the absence of posterior laminar deflection, high levels of stress exist in the idealized models of the lamina cribrosa even for normal levels of IOP. But these stresses are not substantially greater than the stress in the sclera far from the scleral canal. The most important parameter in determining the IOP–induced stress in the lamina cribrosa was the stiffness of the laminar microstructure relative to the sclera.

Keywords: lamina cribrosa • sclera • optic disc