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 17

4.2 Finite Element Simulation of Proximal Femur
Elastic Behaviour

In the current study, the application of the multiscale FENN method was restricted
to the trabecular bone only. Nevertheless, the FENN method can be extended to
describe the multiscale fatigue crack accumulation process of cortical bone.
Trabeculae are composed of lamellae, lacunae, canaliculi and cement lines. The
lamellae are arranged longitudinally along the trabeculae within trabecular pack-
ets. Hence, trabecular bone exhibits anisotropic behaviour and its average (tra-
beculae level) properties depend on its microstructure. Since the investigation
scale of the present study corresponds to one or some trabeculae, it can be con-
sidered that the bone behaviour is purely elastic coupled to damage with isotropic
average properties from the nanoscale level.
At the macroscopic level model (whole proximal femur), fatigue damage was
not accounted for. Its coupling effect was considered in the mesoscopic formu-
lation at the trabecular level.
The behaviour law for cortical and cancellous bone at the macro (apparent)
level is expressed by:

r ij ¼ E ijkl e kl

ð 18 Þ

is the strain and E ijkl where r ij is the stress, e kl is the apparent (macro) isotropic

elasticity stiffness tensor.
The transition from the mesoscale to the macroscale is accomplished by
employing the trained NN. The mesoscale model (NN) able to predict detailed
responses was incorporated into the macroscale model as a material formulation on
the integration point level at every FE iteration—e.g. the behaviour law needed to
compute the outputs at the mesoscale was substituted by the trained NN (Fig. 2 ).
The NN model was incorporated into the Abaqus FE code via the user routine
UMAT to link the meso and the macro scales.

5 Multiscale Simulation of 3D Proximal Femur Fatigue
Crack Accumulation

To apply the proposed hybrid FENN method, a proximal femur (male, age = 77)
was imaged using the quantitative computed tomography (QCT) technique. The
3D FE mesh was generated from the reconstructed QCT images using 66680
tetrahedral elements (Fig. 7 ). Individual conversion of Hounsfield units (HU)to
equivalent ash density (q ash ð g = cm 3 Þ ) was performed based on the relation [ 11 ]:
q ash ¼ 9 10 3 þ 7 10 4 HU ð 19 Þ