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R. Grytz, G. Meschke, J. B. Jonas; A Mathematical Approach to Predict the Local Microarchitecture of the Lamina Cribrosa (LC) and Peripapillary Sclera (PPS). Invest. Ophthalmol. Vis. Sci. 2009;50(13):4892.
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To calculate and establish a mathematical multi-scale model to predict and explain the microarchitecture of collagen fibrils existing in the lamina cribrosa (LC) and peripapillary sclera (PPS), and to predict and explain its impact on IOP-related deformations.
The mechanical properties of LC and PPS were derived from a microstructure-oriented constitutive model that included the stretch-dependent stiffening and the statistical distribution of collagen fibril orientations. Biomechanically induced adaptation of the local microarchitecture was captured by allowing for continuous reorientation of collagen fibrils in response to the IOP-related loading conditions. The mathematical model was applied to a 3D finite element model of the scleral shell including the LC.
Starting from an isotropic distribution of collagen fibrils at the initial configuration the microstructure was adopted progressively until a homeostatic state was reached. At the homeostatic configuration the model predicted in accordance with experimental observations the existence of an annulus of fibrils around the scleral canal in the PPS, and a predominant radial orientation of fibrils in the periphery of the LC (Figure). The annulus of fibrils significantly shielded axons passing through the LC from IOP-related membrane deformations and high tensile stresses, while the radial oriented fibrils in the LC periphery reinforced the LC against bending deformations.
The mathematical model presents a novel, biomechanical explanation of the spatial orientation of LC and PPS fibrillar collagen. The numerical data suggest that the IOP-related LC deformation and the stress environment of axons passing through the LC are sensitive with respect to the microarchitecture of the PPS and LC.
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