Biomedical Engineering Reference
In-Depth Information
The prosthesis stem is inserted into a tube of bone which is relatively stiff,
by virtue of its thickness, rather than its young's modulus. The amount
by which this tube bends is determined by the applied load and is almost
unchanged by changes in the prosthesis material. Now, since the prosthesis
stem is located inside the bone tube, it is forced to bend by the same amount
as the tube. Knowing this, we can appreciate that if the prosthesis is made
from a relatively stiff material, then high stresses will arise in it. We say
that the prosthesis material is under strain control whilst the bone is under
stress control.
Figure 12.8(b) shows the maximum stress in the bone cement, as a
function of its young's modulus, assuming a constant young's modulus for
the prosthesis material of 200 GPa. There are various FE analyses in the
literature and they show much greater variation in cement stress values than
in the prosthesis stress values shown above (see Prendergast
et al
., 1989 for
a summary). Here, this author has deliberately chosen results which give
rather high stresses. This variation is largely caused by changes in prosthesis
design (some designs cause high local stress concentrations in the bone)
and also by variations in the thickness of the cement layer. The data in Fig.
12.8(b) also show an increase of stress with material stiffness, however there
is a significant downwards curvature of the line, implying conditions which
are intermediate between strain control and stress control. To complete the
picture, Fig. 12.8(c) shows that the stress in the cement material (using here
a normal PMMA bone cement with
E
= 2.3 GPa) decreases with increasing
prosthesis stiffness. This is to be expected since the stress is essentially
being shared between the prosthesis and the cement, so if the prosthesis
takes more, the cement will have less.
We can use these figures to compare different materials with regard to
their long-term performance in the AHJ. For example, Table 12.2 shows a
comparison of the fatigue behaviour of some prosthesis materials, calculated
by dividing the fatigue limit of each material by the maximum stress to give
a safety factor. as well as traditional metallic materials, included here are
Table 12.2
Safety factors for various AHJ stem materials (using standard bone
cement)
Material
Young's
Fatigue limit
Maximum
Safety factor
modulus
(MPa)
stress in
(GPa)
stem (MPa)
Particulate composite
25
30
18
1.7
Fibre composite
50
120
31
3.9
Titanium alloy
100
550
56
9.8
CoCr alloy (cast)
200
300
98
3.1
CoCr alloy (wrought)
200
670
98
6.8
Stainless steel
200
420
98
4.3
