Efficient harmonic simulation of a trabecular bone finite element model by means of model reduction

Three-dimensional serial reconstruction techniques allow us to develop very detailed microfinite element (micro-FE) model of bones that can very accurately represent the porous bone micro-architecture. However, such models are of very high dimension and, at present, simulation is limited to a linear elastic analysis only. In the present paper, we suggest to use model reduction in order to enable harmonic simulation for micro-FE models. We take two bone models of dimensions 130 000 and 900 000 and report results for implicit moment matching based via the Arnoldi process. We demonstrate that for the fist model a low-dimensional subspace of dimension 10 allows us to accurately describe frequency response up to 190 Hz. For the second model, a low-dimensional subspace of dimension 25 is enough to accurately describe frequency response up to 30 Hz. We show that the time to perform model reduction and then to simulate the low-dimensional model is orders of magnitude less than that needed for harmonic simulation of the original model.