Numerical procedure for multiscale bone adaptation prediction based on neural networks and finite element simulation

A human femur is composed of cortical and trabecular bone organized in a hierarchical way. In this paper, a multiscale procedure based on finite element simulation and neural network computation was developed to link mesoscopic and macroscopic scales to simulate trabecular bone adaptation process. The finite element calculation is performed at macroscopic level and trained neural networks are employed as numerical devices for substituting the finite element computation needed for the mesoscale prediction. Based on a set of mesoscale simulations of representative volume element of bone, a neural network is trained to approximate the responses. The input data for the artificial neural network are boundary conditions and the applied stress. The output data are some averaged bone properties. A macroscale constitutive model is obtained by homogenization of the mesoscale responses. The proposed approach is able to predict in rapid way some relevant outputs related to bone adaptation process such as trabecular bone density, elastic modulus and accumulation of apparent fatigue damage of 3D trabecular bone architecture at a given bone site. The proposed rapid multiscale method was able to predict final proximal femur trabecular bone adaption similar to the patterns observed in a human proximal femur.