Multiscale prediction of crack density and crack length accumulation in trabecular bone based on neural networks and finite element simulation

In this paper, a novel multiscale algorithm to simulate accumulation of trabecular bone crack density and crack length at macroscopic scale during cyclic loading is developed. The method is based on finite element analysis and neural network computation to link mesoscopic (trabecular level) and macroscopic (whole femur) scales. The finite element calculation is performed at the macroscopic level and a trained neural network incorporated into the finite element code Abaqus is employed as a numerical device to perform the local mesoscopic computation. Based on a set of mesoscale simulations of representative volume elements obtained by digital image-based modeling technique using mu-CT and voxel finite element, a neural network is trained to approximate the local finite element responses. The input data for the artificial neural network are the applied stress, the stress orientation and the cycle frequency. The output data are the averaged crack density and crack length at a given site of the bone. Copyright (C) 2010 John Wiley & Sons, Ltd.