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 10

Inputs

Apparent stress

Cycle number

Outputs
Cr.Dn &
Cr.Le

BV/TV

Apparent
density

Apparent
Young's modulus

Fig. 5 Neural network architecture composed of input, hidden and output layers

this does not help, try adding an extra hidden layer. If over-learning occurs
(verification error starts to rise) try removing hidden units (and possibly layers).

In the present work, the selected architecture is based on double hidden layers
with five neurons of each layer with a learning rate factor g ¼ 0 : 01 and momentum
coefficient a ¼ 0 : 01 (Fig. 5 ).

3.2 Trabecular Bone Specimens for Training

Fracture in trabecular bone is a complex process that depends strongly on the volume
fraction (the relative fraction of bone tissue vs. void space), the architecture (the
geometrical arrangement of the bone tissue, connectivity, and mean trabeculae
thickness), the mechanical properties of the bone tissue, and the applied loads. For a
realistic application of the multiscale approach proposed, different trabecular spec-
imens must be used and trained to cover the morphological ranges of the whole
trabecular zone of the proximal femur (lowest and highest porosities and densities).
From a biological perspective every bone site has a different morphology. Therefore,
different samples must be used to capture a realistic human proximal femur mor-
phology. In the current study 23 cylindrical cores (7.04 mm in diameter and
5.5-10 mm long) from fresh-frozen elderly human proximal femur (n = 12) and
greater trochanter (n = 11) trabecular bone were harvested from eleven males
(50-94 years old) (n = 12). All the specimens were machined such that the main
trabecular orientation was aligned with the axis of the core [ 37 ]. None of the donors
had a history of metabolic bone disease or cancer. Fifteen samples were used to
generate training data for the NN and eight samples were kept (not used in the
training phase) to validate the previously trained NN (comparison between FE and
NN predicted results). The 23 specimens were scanned using micro-computed
tomography using the Skyscan 1072 system at an approximate spatial resolution of