Biomedical Engineering Reference
In-Depth Information
1193-1205. The results obtained with 235 specimens with ages between 20 and
102 years showed that the deterioration for each decade of compact bone is 5 % in
the strength and 9 % in the maximum strain. Also, Yamada (1970) has measured the
deterioration of the compact bone of the femur with age. He used fresh femurs of
female and male cadavers, separated in three groups with ages between 20 and
39, 40 and 59 and 60 and 89 years and measured the compression that fracture them.
He obtained for the above sequence the following results: 51, 48, and 43 kN for men
and 42, 40, and 35 kN for women. These results explain why older women are more
likely to have their femur fractured than men.
Exercise 7.4
A hair breaks under a tension of 1.2 N. Supposing that its tensile
strength is 1.96
10
8
Pa, find the radius of the hair. This hair belongs to an oriental
whose cross-section is a circle, while that of a white occidental is slightly elliptical
and that of negroes, a pronounced ellipse.
Example 7.4
The leg bones that break more frequently when compressed are the
tibia immediately above the ankle, where the cross-sectional area is about 3 cm
2
.
Find the compressive load (mass) that causes a fracture of the tibia of one of
the legs.
We assume that the tibia has the same elastic properties as the femur.
T
c
¼ σ
c
A
10
7
Pa)(3
10
4
m
2
)
¼
(16.7
10
4
T
c
¼
5.0
N. This
force is equivalent
to supporting a load of
5,000 kg
¼
5 tons.
Exercise 7.5
Find the maximum compressive force that a femur supports before it
breaks, in the cases of an adult male and an adult female, knowing that the effective
cross-sectional area of the thin part of the femur of a man is 6.5 cm
2
and of a
woman, 5.2 cm
2
.
7.6 Pressure or Stress on Intervertebral Discs
Intervertebral discs are located between two vertebrae of the spinal column. These
discs have a wall called the fibrous annulus that is composed of about a dozen
collagen fibers. The fibers of adjacent layers have different orientations that give
strength to the discs under shear motion. At the internal part of a disc, there is a
nucleus made of a viscoelastic gel composed of about 80 % of water and proteins.
A little of this water is lost during the day due to compression of the discs by
standing or by walking which is recovered after a night of sleep.
The elasticity of a disc is due to its wall that can degenerate with age or with
repeated overloads. The herniation of the wall followed by nucleus extrusion can
compress the nerve which is one of the reasons for back pain. The discs, when
subject to a very large pressure, can be forced from their normal location, when it is
said that a sequestrum occurred.
