Biomedical Engineering Reference
In-Depth Information
−
u
n
M
=
0
Transition
zone
M
=
1
|
u
t
|
M
=
1
M
=
0
Figure 2.7
Graphic scheme of osteogenesis criterium.
or bone tissue so as to fulfill the adaptation criterion. Therefore, the constitutive
behavior of the interfacial tissue is dependent on the relative quantities of each
tissue present at the location. In parallel, the interfacial adaptation found in the
course of the periprosthetic remodeling process and, therefore, the density of the
interfacial elements, must vary according to the density of the bone attached to
the interface material point, according to Eq. (2.7).
2.4
Numerical Examples
The examples shown in this section were obtained using the code ABAQUS plus
user subroutines in FORTRAN and Python in order to include the proposed
models for bone, interface, and adaptation routines. Also, the geometric model of
a standard femur from Cheung
et al
. [53] was used.
A simulation of the femur alone is run first. The aim of this run is to obtain a
valid initial density distribution of bone that emulates a real one. Three load cases
are applied. The loadings due to the body weight are applied only in certain regions
by surface forces parabolically distributed along and normal to the surface of the
femoral head. The location of the loading surfaces is determined from the angles
referring to the gait cycle. According to Allard [54] they vary from
20
◦
to 25
◦
for
the hip joint. The application of load to a region greater than the surface is justified
by the fact that over time other activities, such as climbing steps and even sitting
on and getting up from a chair, must be taken into account during the simulations.
In the present simulations, the loadings due to the body weight are divided into
three load cases in order to represent, approximately, the forces to which the femur
is subjected. Each load case has a body mass (BM) value of 700 N.
The stresses due to the action of the gluteus maximus, medius, and minimum
muscles, applied to the greater trochanter (Figure 2.8), are also considered, as-
suming that these muscles with an insertion point close to the femoral head
are sufficient to obtain results that approximate real conditions [55]. The loads
referring to the action of each muscle are applied on the anterior, medial, and
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