Biomedical Engineering Reference
In-Depth Information
b-Spline with
negative slope
Concave
b-spline
a
b
Nonadmissible
Admissible
Nonadmissible
Figure 10.5
Two examples of nonadmissible stem shapes.
considered as the objective function,
NC
1
c
m
d
f
t
=
α
c
|
(τ
)
P
|
(10.5)
P
n
P
=
1
where (
τ
n
)
P
is the normal contact stress on stem-bone interface
c
for load case
P
.
Here,
P
is again the load weight factors, and
m
is constant taken equal to 2. It
should be noted that the value of
m
can control the contribution of peak stress
values for the function. When
m
increases the relevance of the peak values also
increases.
For both functions (Eqs. 10.4 and 10.5), the state variables, tangential displace-
ment and contact stress, are the solution of the equilibrium problem with contact
conditions.
α
10.4.4
Objective Function for Bone Remodeling
After surgery bone starts a new remodeling process in order to adapt to the new load
conditions. In fact, a smaller stress shielding effect promotes a smaller proximal
bone loss. A femoral stem that minimizes the bone loss is the one that maintains
the mechanical conditions of the intact bone. To achieve this, a common criterion
