Biomedical Engineering Reference
In-Depth Information
1/2a
3
A
1/2a
2
1/2a
1
B
1/8 of cell
1/2a
3
1/2a
2
Relative density
in each point
m =
1/2a
1
1-a
1
a
2
a
3
Figure 10.17
Bone material model. (Adapted from Fernandes
et al
.[12].)
In Eq. (10.9), (
f
i
)
P
is the applied load for the load case
P
,(
u
i
)
P
is the displacement
field for load case
P
,
κ
is the metabolic cost to maintain bone mass,
f
is the surface
whereloadsareapplied,and
b
is the total bone volume.
This remodeling model is combined with an ingrowth algorithm to predict the
ability of bone to attach to the stem surface. Actually, if a good primary stability is
achieved bone starts to grow into the porous coating. The bone ingrowth depends
on relative tangential displacement, contact stress, and the gap between bone
and stem. Moreover, after bone ingrowth starts the connection between bone and
implant can be disrupted if the mechanical conditions become adverse.
To take into account the mechanical factors mentioned above, an algorithm based
on previous ingrowth models [12, 31, 47, 48] is used. In this algorithm there are
five levels for the interface stiffness, from 0 to 30 N mm
−
1
, as shown in Table 10.7.
In each interface point bone ingrowth occurs if the following five conditions are
satisfied for every load cases:
Stiffness and shear stress threshold in bone-stem interface.
Table 10.7
Stiffness
K
(N mm
−
1
)
Osseointegration level
Shear stress threshold (MPa)
1
0
4.5
2
7.5
18
3
15
33
4
22.5
35
5
30
35
