Biomedical Engineering Reference
In-Depth Information
Table 2 Loading factors levels used to perform FE simulation on 15 specimens (Table
1
)
Loading inputs
Level
Values
1.e
1
, 1.e
3
, 1.e
4
, 1.e
5
, 1.e
7
Number of cycles
5
Applied apparent stress (MPa)
5
25, 50, 70, 90, 110
The results of FE simulation were used as training data for the NN
(i) the bone volume fraction (BV
=
TV ),
(ii) the ash density,
(iii) the apparent elastic modulus.
and two loading factors:
(iv) the applied apparent stress amplitude,
(v) the number of cycles.
The outputs are Cr.Dn (#/mm
3
) and Cr.Le (lm/mm
3
). This set of outputs
represents one of the main fatigue damage parameters observed [
4
,
36
,
50
].
Five values for each factor were selected, generating full factorial combinations
of the inputs (5
5) applied to the 15 training specimens. Hence, 375 (5
5
15)
micro-CT FE simulations were performed on the 15 specimens with a total
computation time of about 350 h on a 64 GB dual-core computer to study the
effect of each input combination on every trabecular bone specimen.
The stress training values applied were based on a previously established
relation between volume fraction and the maximum stress measured in a mono-
tonic strength experiment [
45
]. The lower stress amplitude was chosen to be 10 %
of the ultimate stress (r
u
) while the upper stresses were assigned to four different
amplitudes, varying from 20 to 90 % of the ultimate stress. In addition, reported
S-N curves for human cancellous and cortical bone matrix show that the cycles to
failure vary from 1.e
1
to 1.e
7
[
7
,
45
]. Based on these results, five cycle values were
used here to train the NN, ranging from 1.e
1
to 1.e
7
(Table
2
).
The training data for the NN were extracted by homogenization from results of
FE simulations performed on 15 specimens. Eight specimens were not used to
prepare the training data but were kept to check the validity of the previously
trained NN (NN prediction first on the 15 training specimens followed by FE
predictions (using the 8 remaining specimens).
4 Finite Element Modeling Approaches
Two FE models were applied in the current investigation:
(i) Meso FE model needed to generate virtual data for the NN training based on
different trabecular specimen simulations coupled to fatigue damage.
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