Biomedical Engineering Reference
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compute the outputs at mesoscale is substituted by the trained NN. The hierarchical
combination of trained NN (mesocale) and FE (macroscale) models for the
prediction of bone fatigue microcrack growth can be applied using other factors
(age, gender, drugs, …) integrating information extracted from available data and
experiments. The aim here was to illustrate the potential of the FENN method in the
field of bone biomechanics to incorporate local responses at continuum macroscopic
level both accurately and rapidly. Due to the restricted amount of clinical data, it was
very difficult to directly compare the proposed FENN numerical results to in vivo
experimental ones. Nevertheless, the results provide evidence for the capability of
the proposed FENN method to supply outputs of the fatigue microcrack behaviour of
trabecular bone. The FENN model advances current FE models by explicitly
describing the Cr.Dn and Cr.Le evolution under cyclic compressive loads and by the
rapid computation time (the NN approach was about 4.32e5 times faster than the FE
computation). Such a method can contribute toward the development of more
sophisticated multiscale FE models to predict the behaviour of living bone by
explicitly including the effects of fatigue crack influence.
The application of NN models is beneficial since a multilevel numerical
analysis of bone behaviour simulation is time-consuming. The complexity of the
NN is determined during training such that the minimal network is used that can
accurately represent the training data. However, despite the success of the pro-
posed hybrid FENN approach, certain limitations apply. First, for the sake of
simplification, the behaviour of the trabecular bone was considered to be isotropic
and fatigue data were obtained from published experimental results on human
vertebral trabecular bone. Since the scale of investigation of the present work
corresponds to one or some trabeculae, one can assume isotropic averaged prop-
erties from the nanoscale level. Alternatively, an anisotropic behaviour description
of trabecular bone tissue can be used to simulate the anisotropic fatigue damage
behaviour of bone. Furthermore, material anisotropy and fatigue data extracted
from the proximal femur can be assigned to the FE model. However, limited
experimental data are available to characterize such micromechanical properties of
trabecular bone. Third, the bone repair process resulting from bone remodeling
was not considered in the present study. Nevertheless, the overall structure of the
proposed multiscale FENN approach will remain unchanged. There will still be a
need to perform multiscale simulations to predict the accumulation of local fatigue
microcracks within the trabecular bone of human proximal femurs.
Acknowledgments This work was supported by the French National Research Agency (ANR)
through TecSan program (Project MoDos, no. ANR-09-TECS-018). The authors are grateful to
Dr Loulou H. for providing the micro-CT trabecular bone meshes.
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