Biomedical Engineering Reference
In-Depth Information
first observed by Julius Wolff [32] at the end of the nineteenth century. From his
observations he stated the law of bone remodeling (Wolffs law), which assumes that
bone adapts to mechanical loading and that this adaptation follows mathematical
rules. Indeed, it is possible to say that bone structure is regulated by cells that react
to mechanical stimulus.
The stress shielding effect is a consequence of the mechanism of load transfer
from prosthesis to femur [5]. Before THA, load transfer from pelvic bone to femur
is carried out directly by the natural joint. After surgery, loads are transferred by
interaction forces from the implant to femur. However, the implant is stiffer than
bone and part of the total load is supported by the stem and the stress on bone
tissue is globally reduced. Consequently, the femur loses mass and it becomes less
dense. This stress shielding effect is greater for stiffer prostheses because fewer
loads are transferred to bone tissue [5, 33].
After THA, the load is transferred from the stem to bone, from the interior to the
outside part of the femur; thus there is formation of new bone next to the implant
[34, 35]. This fact is more evident near the stem tip because of maximum distal
stresses [33]. On the proximal region and away from the stem, the stress shielding
effect is stronger and can lead to excessive bone loss.
10.4
Multicriteria Formulation for Hip Stem Design
The design of an implant has to take into account the requirements for a good
primary stability (low stress and low relative displacement at the interface) and
reduced stress shielding. In the case of the hip stem, these requirements lead to
different geometries when they are considered alone. Thus, one needs to consider
all the requirements simultaneously.
To address this problem, a multicriteria optimization process is presented in this
chapter to obtain the three-dimensional femoral stem shape with better primary
stability and less stress shielding. The multicriteria objective function combines
three single cost functions. The first two are related to the primary stability, that
is, they are a measure of the relative tangential displacement between the bone
and implant and the normal contact stress. The third one is related to the stress
shielding.
The optimization problem can be stated in a general way, as,
min
d
f
(
d
)
such that
(
d
i
)
min
(10.1)
≤
d
i
≤
(
d
i
)
max
i
=
1, 2,
...
,14
h
j
(
d
)
≤
0
j
=
1, 2,
...
,10
where
d
represents the geometric design variables with (
d
i
)
min
and (
d
i
)
max
being the
lower and upper bound of these variables, and
h
j
is a set of geometric constraints
necessary to obtain clinically admissible stem shapes.
