Biomedical Engineering Reference
In-Depth Information
10.2
Optimization Methods for Implant Design
Rapid development of computational facilities and numerical tools to solve
engineering problems resulted in the development of computational biomechan-
ics. Nowadays, this field plays a key role in the modeling of living tissues, analysis
and design of medical devices, and pre-clinical tests. The bone implant design has
benefited from these tools, such as development of some shape optimization pro-
cesses used to obtain geometries with better performance. Also, numerical bone
remodeling and osseointegration models have been applied to study the stress
shielding effects after a bone implant [12].
In the case of hip implant, some shape optimization models have been developed
to study the relation between stem geometry and prosthesis performance for both
cemented and uncemented stems.
10.2.1
Cemented Stems
Huiskes and Boeklagen [13] developed a model to optimize the shape of a cemented
stem with the objective of minimizing the strain energy density in the cement
mantle. This work was part of a research program with surgeons and bioengineers
to obtain a new stem, which culminated with the scientific hip prostheses (Biomet
Europe).
In the work of Yonn
et al
. [14] a two-dimensional model was used to obtain a
stem shape that minimized the maximum stress in the cement mantle.
Katoozian and Davy presented two optimization models [15, 16]. Both of them
considered a three-dimensional geometry of the bone with the implant. In the first
work, the optimal shape is obtained in order to minimize the von Mises stress in
the cement. In the second work, three single cost functions were considered. The
first two are related to the stress field in the cement mantle, and the third is the
cement strain energy density. In these studies, all optimized shapes have small
distal sections and a stiffer proximal part.
Hedia and coworkers [17] minimized the fatigue in cement mantle with a
constraint on the proximal bone stress.
Gross and Abel [5] optimized the thickness of a two-dimensional hollow stem.
In order to do that, three single functions were considered: minimization of the
cement mantle stress, maximization of the proximal bone stress with a constraint
on cement stress, and maximization of the proximal bone stress without any
constraint.
Tanino
et al
. [18] minimized the maximum principal stress on the distal half of
the cement mantle. In this case, a three-dimensional model was considered with
15 design variables and some geometric constraints to obtain clinically admissible
shapes.
These shape optimization models are important in developing a better under-
standing of the influence of stem shape on stress shielding effect and also on
