Biomedical Engineering Reference
In-Depth Information
Fig. 6.11
Isomap representing the trabecular architecture of the femoral bone
As it is understandable, decreasing the size of the infinitesimal subdivisions
permits to increase the detail of the analysis, however it will increase also the
computational cost of the analysis. As represented in Fig.
6.10
c each integration
point will probably present a distinct local apparent densitiy.
Similarly it is possible to obtain the local apparent density of each field node x
i
,
which can be determined using the following expression,
P
k
_
j
q
ð
q
j
Þ
app
j¼1
q
ð
x
i
Þ
app
¼
ð
6
:
26
Þ
P
k
_
j
j¼1
where
_
j
is the integration weight of an integration point q
j
belonging to the
Voronoï cell V
i
of the field node x
i
. With Eq. (
6.26
) the local apparent density field
can be defined, which can be represented in isomaps. Therefore, the results
regarding the evolution of the trabecular architecture, in all numerical examples
studied in this topic, are presented as grey tone isomaps. In those grey tone
isomaps the white colour represents the considered maximum apparent density
q
0
¼ 2
:
1 g/cm
3
and the dark-grey colour represents the minimum apparent density
q
0
¼ 0
:
1 g/cm
3
admitted in the analysis. All the other gray tones in the middle
represent transitional apparent densities. In each isomap presented in this topic it is
also indicated the domain medium apparent density, which is obtained applying
Eq. (
6.16
).
In Fig.
6.11
it presented an isomap example. This isomap was obtained with the
proposed remodelling algorithm combined with the NNRPIM [
27
,
28
]. The ana-
lysed femur domain was discretized in 5,991 nodes and the three load cases
suggested in the literature were considered [
64
,
65
]. Apparently the result obtained
