Application of Neural Network and Finite Element Method for Multiscale Prediction of Bone Fatigue Crack Growth in Cancellous Bone - Multiscale Computer Modeling in Biomechanics and Biomedical Engineering - page 3

applied stress and cycle frequency. The output data are the average crack density
and length computed at a given trabecular bone site.
1 Introduction
Bone is a hierarchically organized material at different length scales. At the
macroscopic scale, it is composed of cortical or compact bone and trabecular or
cancellous bone (Fig. 1 ).
Bone strength strongly depends on the trabecular structure of the bone, which
can be assessed by changes in its morphological and mechanical properties over
time [ 15 , 23 , 36 , 49 ]. In general, modelling the trabecular bone behaviour must
address changes in its structure, at multiple levels, allowing for a more accurate
description of the bone tissue. This process occurs hierarchically at different
spatio-temporal scales and involves interacting phenomena (deformation, damage,
adaptation, etc.) [ 15 , 23 , 36 , 49 ]. In particular, the adaptation of trabecular bone to
cyclic fatigue loads involves a complex physiological response that is targeted to
local sites of damage. Fatigue damage in bone results from the repetitive loading
of daily activities in the form of microcracks with an average crack length of about
100 lm[ 46 ] and diffusely damaged areas. Such alterations are relevant for can-
cellous bone with high metabolic activity and numerous bone quality changes [ 16 ,
30 ]. Physically, fatigue microcracks at the mesoscale are assessed by crack density
(Cr.Dn) and crack length (Cr.Le) [ 14 ]. Assessment of the hierarchical effect of the
Cr.Dn and Cr.Le accumulation within trabecular bone on the whole bone (organ)
quality is of major biological and clinical importance for the investigation of bone
diseases, fractures and their treatment. The effect of damage microcracks on the
mechanical properties of bone is complex since a crack can affect the mechanical
properties of the surrounding matrix, it can act as a local stress riser, and it can
further exacerbate the heterogeneous and anisotropic character of bone [ 40 ].
Moreover, evidence that fatigue damage decreases bone organ quality, increases
fracture susceptibility, and serves as a remodeling stimulus motivates the devel-
opment of numerical multiscale modeling approaches. Most theoretical and
numerical studies of bone damage evolution at the macroscopic level have focused
on the development of continuum approaches in which the total damage is a scalar
quantity defined either as the normalized number of cycles (D = f(N/Nf)) or in
terms of the changes in elastic modulus and residual strain during life [ 4 , 22 , 23 ,
32 , 43 , 47 ]. However, these approaches ignore the fact that the physical damage in
bone at the trabecular level takes the form of Cr.Dn and Cr.Le non-linear
accumulation.
Fracture mechanics laws have also been applied to investigate crack growth in
bone. Taylor and Lee [ 46 ] developed a theoretical model to predict fatigue damage
and failure in bone based on simulation of the growth of every crack in a piece of
bone material. The limitation of fracture mechanics based approaches is that it is