Biomedical Engineering Reference
In-Depth Information
6), the stem
tip is small to avoid direct contact with cortical bone, and section 4 is thick and
almost rectangular, also to reduce stress objective function. But, in Figures 10.15
and 10.16 it is also possible to see that section 3 is thinner and larger to reduce
both the displacement and the remodeling cost functions.
Finally, non-dominated shapes, when the weight for the remodeling objective is
bigger (
When the weight for the contact stress objective is bigger (
β
=
0
.
t
6), have a very small stem tip, and sections 2 and 3 are very thin in
order to improve proximal load transfer. However, section 4 is thicker to reduce
contact stress and almost rectangular to improve rotational stability.
Finally, in the same Figures 10.15 and 10.16 a wedge design is observed in
all nondominated points. In fact, the wedge design is important to improve axial
stability and a small stem tip is also essential to reduce maximum contact stress
and to increase proximal load transfer.
β
=
0
.
r
10.7
Long-Term Performance of Optimized Implants
With the multicriteria shape optimization process nondominated points with better
primary stability and less stress shielding after surgery were obtained. However,
the prediction of the long-term performance of optimized hip stems is necessary
to confirm the relation between initial conditions and implant success. Therefore,
an integrated model for bone remodeling and osseointegration was used in order
to study the long-term effect of optimized stem shapes.
The remodeling model presented by Fernandes
et al
. was used [12, 45]. In this
model bone tissue is considered a porous material with a periodic microstructure
that is obtained by the repetition of cubic cells with prismatic holes with dimensions
a
1
,
a
2
,and
a
3
, as shown in Figure 10.17. The orthotropic elastic properties are
obtained by the homogenization method [46]. Relative density at each point of
femur is solution to an optimization problem, and depends on local porosity,
µ
=
1
−
a
1
a
2
a
3
(10.8)
with the extreme values
a
i
1 corresponding to cortical bone and mar-
row, respectively. Intermediate values for relative density correspond to trabecular
bone. Assuming that bone adapts according to applied loads in order to maximize
its stiffness, the law of bone remodeling is derived by considering an optimization
process where the holes dimensions (
a
) at each bone finite element are the design
variables, and the objective is the minimization of a linear combination of the
compliance (inverse of the stiffness) and the metabolic cost to maintain bone mass.
Considering a multiple load formulation the optimization function is,
=
0and
a
i
=
NC
µ
(
a
)
2
d
f
remo
=
1
α
(
f
i
)
P
(
u
i
)
P
d
+
κ
(10.9)
P
f
b
P
=
