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 22

(a) Predicted fatigue damage contour. (b) measured fraction of damaged bone tissue.
Fig. 11 a Enlargement showing the predicted contour of the fatigue damage. b Fraction of
damaged bone tissue and localization in trabecular specimens from Wang et al. [ 50 ]
accumulated residual and maximum strains within a trabecular bone specimen
generate strain concentrations followed by the formation of a fracture line through
the specimen. Martin et al. [ 36 ] reported that relatively small amounts of micro-
damage can cause significant reductions in the bone's mechanical properties even
before the appearance of microcracks. Similar results were obtained with
numerical studies, which demonstrated that damage is visible below apparent
compressive yield strain and local tissue yielding initiates at low apparent stress
levels [ 38 , 39 ]. The predicted fatigue damage of single trabeculae (Fig. 12 a) lead
to a crack initiation and propagation (Fig. 12 b) which appears to be local, in
agreement with experimental observations (Fig. 12 c) [ 10 ].
After the training phase, the eight remaining trabecular bone samples were used
in order to check the validity of the NN prediction. First Cr.Dn and Cr.Le were
predicted with the NN and second, micro-CT FE fatigue simulations were per-
formed for verification. Figure 13 a, b shows an example of Cr.Dn and Cr.Le
evolution versus cycles predicted by both the NN and the FE methods (specimen:
BV = TV ¼ 25 : 035 %). One can observe that the accumulation of cracks increases
rapidly during the first cycles, followed by a reduced rate of accumulation and an
accelerated growth rate prior to the specimen failure. Similar experimental results
on cortical bone were obtained by O'Brien et al. [ 41 ]. The shape of the Cr.Dn
accumulation can be explained by the following three stages: (i) strain localization
due to trabeculae shapes and interconnections during the early cycles; (ii) accu-
mulation of local residual strain leading to damage growth and (iii) final cata-
strophic rupture of the localized bone tissue which triggers the growth of one
macroscopic crack through the trabecular structure.
It can be seen that very good agreement is obtained between the two predictions.
An average coefficient of correlation of 0.9984 was found between the NN