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geometric center of a three-dimensional object). If an object is symmetric, the neutral axis and
the centroid are one and the same.
A simple demonstration of bending strength can be given with a wooden ruler. Consider
the ease of bending a ruler in half along the 2 cm width compared to its 2 mm narrow edge
( Larsen, 1997 ). See Figure 14.2 . If you try to bend the ruler along its width, it yields quickly
and fails. However, if you try to bend it along the narrow edge of the ruler, it is more difficult
to bend and break. The analogy of the ruler is useful when considering the diaphysis of the
load-bearing long bones of the lower limb, because bones are typically harder to break in one
direction than another, if not circular in cross-section.
Manouvrier first recognized a difference in this cross-sectional ratio in 1888 from
nonhuman primates to modern humans, the latter having a more round diaphysis. The
purpose of a higher ratio or a more anteroposterior elongated shaft is to resist bending forces
in this AP direction. This elongation of the diaphysis has been shown to be the result of
greater flexion at the knee, related to crossing over steep or rough terrain ( Lovejoy et al.,
1976; Larsen, 1997 ; Ruff, 1987). 3 This ratio is useful because it automatically controls for
size differences facilitating comparison between individuals and populations ( Ruff and
Hayes, 1983a, b ).
Bone Density and Osteoporosis
Bone shafts increase in diameter with age, which reduces long bone cortical thickness and
gives the appearance of reduced bone density in radiographs. This essentially maintains and
increases bending strength into adulthood by increasing the distance from the bone surface to
the centroid, while simultaneously decreasing surface area, thus reducing the bone's strength
in compression. Women experience an accelerated bone loss following menopause due to
a reduction in the hormone estrogen (an intrinsic factor), which has been demonstrated in
prehistoric populations as well ( Bloom and Laws, 1970; Ericksen, 1976; Ruff and Hayes,
1982, 1984; Nelson et al., 2000 ).
During growth, osteoblast deposition of osteoid exceeds osteoclast resorption. When the
epiphyses fuse, growth ends and consolidation begins. Consolidation is the phase in which
the bone increases in density until peak bone mass is reached in the early or mid-thirties.
Involution is then the next stage when bone loss exceeds bone formation. Sex and age are
the number one factors affecting bone density cause by involution. Osteoporosis occurs
when bone loss in an individual is two and a half standard deviations lower than the
population mean peak bone mass and thus the bone is at an increased risk of fracture.
Osteopenia is a condition of low bone density, but without the risk of fracture and less severe
than osteoporosis. The rate of bone loss in osteoporosis is not the same for trabecular and
cortical bone. In general, the rate of loss in bone mineral density (BMD) is approximately
1% per year until the age of 65. The process is accelerated to 2% per year BMD lost for the
five years following menopause in women ( Zhang-Wong and Seeman, 2002 ). Trabecular
bone can be built up again, but cortical bone loss is relatively irreversible, as mentioned
earlier in the discussion on criticisms of Wolff's law. “Overall, women lose 35 e 50 percent
3 Manouvrier attributed the greater elongation in humans to our being more civilized compared to
nonhuman primates (1888).
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