Biomedical Engineering Reference
In-Depth Information
Table 10.4
Maximum normal contact stress (MPa). Minimization of stress function
f
t
.
Initial shape
Optimized
Totally coated
88.08
40.95
Half coated
135.1
40.36
4
3
Initial
Optimized
Totally
coated
Optimized
Half
coated
2
1
Figure 10.12
Initial and optimized stems. Minimization of stress function
f
t
.
because it stays surrounded by marrow and never directly touches the cortical
bone. In Table 10.4 the maximum stress values for initial and optimized shape
are presented. For initial shape the half coated stem has a greater peak stress than
the totally coated prosthesis. However, optimized shapes have almost the same
maximum contact stress, because the lack of friction is not relevant for small and
circular stem tips. In Figure 10.12 it is also possible to verify that sections 2 for
optimal shapes are almost circular in order to increase cortical bone contact at
middle stem. Finally, sections 3 and 4 are thicker (parameter
b
) than the initial
solution to increase the contact surface and thus to minimize stress at the medial
region, particularly in calcar region (see Figure 10.1).
10.6.3
Optimal Geometry for Remodeling -
f
r
In Table 10.5 numerical results for remodeling objective function are summarized.
In this case, optimized shapes have the same function value for totally and half
Table 10.5
Objective function values. Minimization of remodeling function
f
r
.
f
−
initial
f
−
final
r
r
Totally coated
50.34
17.93
Half coated
49.61
17.93
