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S. Kodiyalam, R.T. Hart, C.F. Burgoyne, M.D. Roberts, J.C. Downs; Large–Scale Parallel Finite Element Simulations of the Monkey Lamina Cribrosa Microarchitecture . Invest. Ophthalmol. Vis. Sci. 2006;47(13):1229.
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© ARVO (1962-2015); The Authors (2016-present)
To compare IOP–related stress and strain within large–scale voxel–based models of a monkey optic nerve head (ONH) computed on a parallel machine to those generated by tetrahedra–based models run with commercial software.
We have developed novel parallel finite element code to handle large–scale, voxel–based models of 3–D reconstructions of the lamina cribrosa. Computations are carried out for voxel–based laminar microstructure from a small region of a monkey ONH containing ∼100,000 laminar voxels. These results are compared to results from a tetrahedral mesh for the same region obtained from commercial software. Another small region of the actual nerve head spanning 75x77x41 voxels in xyz size is used to construct cylindrical ONH–like structures containing ∼400,000 laminar voxels that are studied under different boundary conditions. In order to balance the load on the CPUs of the parallel machine an automated load–balancing scheme has been developed and tested with an entire monkey lamina containing ∼7 million laminar voxels.
Results from voxel–based computations are consistent with those from the tetrahedral–based mesh run using commercial software: the best–case average relative error in the displacement components is ∼3.0%. For this case, while the relative error in the stress–strain components is 11–26%, the spatial correlation is very strong: > 0.95 for all components. For the ONH–like configurations, a linear trend is observed in the anterior–to–posterior variation of average hydrostatic pressure within the lamina (translaminar pressure gradient) under IOP loading and fixed anterior–to–posterior displacement at the cylindrical lamina boundary. When applied to the entire lamina configuration (∼7 million laminar voxels), the automated load–balancing scheme results in a small load imbalance of 6% on 24 CPU's.
Quantitative agreement with the results from tetrahedra–based calculation achieves a first validation of our voxel–based methodology. The observed translaminar pressure gradient in the ONH–like configurations is similar to the trend in experimental measurements of the pressure within the lamina [Morgan W.H. et al, IOVS 1995, Vol 36, No. 6, 1163–72]. With a linear, IOP–induced, translaminar pressure gradient as the loading input load balanced computations will allow us to simulate the biomechanical behavior of the entire laminar microstructure in a single model.
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