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S. Kodiyalam, B.A. Hirons, R.T. Hart, C.F. Burgoyne, M.D. Roberts, R.K. Kalia, A. Nakano, P. Vashishta, J.C. Downs; Development of Large–Scale Parallel Finite Element Simulations of the Lamina Cribrosa Microstructure in the Optic Nerve Head (ONH) . Invest. Ophthalmol. Vis. Sci. 2005;46(13):1267.
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© ARVO (1962-2015); The Authors (2016-present)
Purpose:Develop a finite element code for computing on a parallel machine to determine stresses and strains in large–scale voxel–based models of a monkey optic nerve head (ONH). Validate the results of the parallel code against tetrahedra–based models from previous studies. Methods: Currently, biomechanical models of the laminar microstructure are limited to small regions due to limitations of commercial software. Based on a molecular dynamics simulation approach, we developed parallel finite element code to handle large–scale, voxel–based models of 3–D reconstructions of the lamina cribrosa. Computations for each region of the spatially decomposed system are handled by one CPU of the parallel machine, and the 6 steps of message passing involve communication of nodal displacements and forces between CPUs handling neighboring regions. The iterative Conjugate Gradient algorithm was used to determine the equilibrium configuration of the system, and stresses and strains were computed as elemental volume averages. These computations were carried out for voxel–based laminar microstructure from a small region of a monkey ONH corresponding to a single element from a macro–scale continuum finite element calculation of a full ONH. Displacement boundary conditions were derived from the parent continuum model using a sub–structuring approach developed in previous studies. Results: Elemental stresses and strains were found to be superconvergent (converge as (element size)4 to their exact values) in the case of a regular grid of hexahedral elements under sinusoidal body forces. The parallel code was found to be perfectly scalable with an efficiency >99% for up to 224 CPUs handling over half a million elements (voxels) per CPU. Results from voxel–based computations are consistent with a previous models using tetrahedral elements models run using commercial software and similar displacement boundary conditions. The average von Mises stress over all elements in this region of the lamina is over 100 x IOP. Conclusions: The quantitative agreement with the results from a previous study validates the custom parallel finite element code we have developed. The scalability of the parallel code will allow us to simulate the biomechanical behavior of the entire laminar microstructure in one model.
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