Bone Implant Design Using Optimization Methods - Biomechanics of Hard Tissues - page 264

cement mantle stresses and fatigue. However, in all these models the interface was
defined as fully bonded.
10.2.2
Uncemented Stems
In the studies mentioned above [15, 16], Katoozian and Davy also performed shape
optimization for uncemented stems. In this case, they minimized the stress in the
bone adjacent to the stem and the bone strain energy density. The finite element
model considered that the bone and the stem are fully bonded. The optimized
shapes presented a thin distal section and a large proximal part. These results are
similar to the ones obtained for cemented stems.
In 2001, Chang et al . [19] developed a three-dimensional model with frictional
contact at the bone-stem interface in order to minimize the difference in strain
energy density of the intact femur and implanted bone. The relative tangential
displacement between bone and implant was limited (to 50 µm) to avoid large
displacements. A reduced midstem implant design is optimized, where the two
design variables define the size of the middle part of the stem.
Kowalczyk [20] presented an optimization process to minimize the stress on
bone-stem interface. In this three-dimensional model, the stem has a proximal
collar and the interface is assumed to be fully bonded in coated regions. For the
uncoated surface the interface condition is frictionless contact. The design variables
define the coated region and stem axial length.
Fernandes et al . [21] presented a two-dimensional optimization procedure to
obtain the shape of a hip stem to minimize the relative displacement and normal
contact stress on stem-bone interface.
Ruben et al . [2] considered a multicriteria cost function in order to maxi-
mize initial stability. The 17 design variables are geometric parameters to define
three-dimensional stem shape, and some constraints were considered to obtain
clinically admissible implants. The multicriteria function permits the simultane-
ous minimization of relative tangential displacement and normal contact stress
on stem-bone interface. Frictional contact was considered in coated regions and
frictionless contact in uncoated ones. With this optimization process a set of non-
dominated points were computed, and in all cases the initial stability is better than
the initial shape defined based on a commercial prosthesis.
Besides these studies on shape optimization, other works on material optimiza-
tion applied to implant design are available. Usually, such models assume as
design variable the distribution of elastic modulus on the stem. An example of
this approach is the model presented by Kuiper and Huiskes [22], where the cost
function is the difference between the shear stress at stem-bone interface and a
reference value. Hedia et al . [23] used a two-dimensional model to minimize the
maximum shear stress value at the interface. In both cases, the optimized implants
are stiffer in the proximal part and the modulus of elasticity decreases up to the
distal part. Also, Katoozian et al . in 2001 presented a material optimization model
for hip stem using fiber reinforced polymeric composites [24].