Application of neural network and finite element method for multiscale prediction of bone fatigue crack growth in cancellous bone

Fatigue damage in bone in the form of microcracks results from the repetitive loading of daily activities. It is well known that the resistance of bone at the organ level to fatigue fracture is a function of its resistance to the initiation and propagation of local microcracks at a mesoscopic scale which can lead to macrocrack growth at the organ level. Multiscale investigation of the relationship between the effect of the fatigue microcrack growth at microscopic scales and the whole bone behaviour is a subject of great interest in the research field of the biomechanics of human bone. Several finite element models (FE) have been developed in recent years in order to provide better insight and description regarding bone fatigue microcrack growth. Despite the progress in this field, there is still a lack of models integrating multiscale approaches to assess the accumulation of apparent fatigue microcracks in relation with trabecular architecture into practical FE simulations. In this chapter, a trabecular bone multiscale model based on FE simulation and neural network (NN) computation is presented to simulate the accumulation of trabecular bone crack density and crack length at a given trabecular bone site during cyclic loading. The FE calculation is performed at macroscopic level and a trained NN incorporated into a FE code is employed as a numerical device to perform the local mesoscopic computation (the behaviour law needed to compute the outputs at mesoscale is substituted by the trained NN). The input data for the NN are some trabecular morphological and material factors, the applied stress and cycle frequency. The output data are the average crack density and length computed at a given trabecular bone site.