Biomedical Engineering Reference
In-Depth Information
propagation from perpendicular to the loading direction to parallel to the
loading direction. The final stage of fatigue fracture occurs because cracks
coalesce and become so large that the weak interfaces can no longer absorb
them. The cracks can thus cross the bone and induce bone failure.
4.2.2 Trabecular bone
Material properties of trabecular bone vary widely depending mainly on the
anatomic location and age, for which the apparent density and the architecture
can be markedly different (Ding
et al
., 1997; Gibson, 1985) Trabecular bone
is best described as an open-celled porous foam. Since trabecular bone is
made up of a series of interconnecting trabeculae, it can be idealized as a
combination of rod-rod, rod-plate, or plate-plate basic cellular structures
where rods and plates represent thin and thick trabeculae, respectively. The
mechanical properties can vary by a factor of ten depending on the type and
orientation of these basic cellular structures (Fig. 4.5).
The architecture of trabecular bone depends on the thickness of individual
trabeculae and the spacing between trabeculae. The architecture of trabecular
bone results in anisotropic elastic properties found in elderly lumbar spine.
However, in contrast to cortical bone, trabecular bone is nearly isotropic at
some anatomic sites like the proximal humerus. For isotropic bones, the elastic
modulus and the ultimate strength of trabecular bone in any direction are
related to its apparent density
r
by a power-law relationship of the form:
E
=
a
+
br
c
1000
100
10
0.01
0.10
1.00
Apparent density g cm
-3
4.5
Compressive modulus as a function of apparent density for
trabecular bone. (adapted from Keaveny and Hayes, 1993).
