Biomedical Engineering Reference
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energy (a measure of fracture resistance) was negatively correlated with age, albeit
weakly (p = 0.037; r 2 = 0.10). This finding is consistent with the view that
diaphyseal stiffness does not change with age due to negligible changes in moment
of inertia and elastic modulus (a measure of stiffness at the tissue/material level),
whereas diaphyseal fracture energy declines with age due to decreases in bone
material toughness (see '' Cortical Bone Mechanics and Composition: Effects of
Age and Gender '').
Burr and Martin [ 15 ] torsionally tested 86 radii from donors (approx. equal
numbers female, male) aged 18-95 year. They reported only elastic properties.
Radii from females were approx. 40 % less stiff (torsional rigidity) than males.
With aging, the whole-bone stiffness did not change in females, whereas it
increased by approx. 6 %/decade in males. These changes were consistent with the
corresponding changes in moment of inertia (Table 2 ), whereas there were no
changes in estimated shear modulus.
Clearly, additional data at the whole-bone level are needed to determine how
changes in morphology and material properties influence diaphyseal fracture
resistance at different sites with aging.
2.3 Coordinated Variations in Geometric and Material
Properties in Mice and Men
Functional adaptation within the skeletal system can coordinate morphological
traits and tissue-level mechanical properties so the particular combination results
in a bone that is sufficiently stiff and strong to support the loads imposed during
daily activities [ 21 ]. The interaction among morphological traits and tissue-level
mechanical properties results in each person acquiring not a single trait, but a
particular set of traits. The particular set of traits acquired by a person will vary
with their height and body weight, as expected. Importantly, even when correcting
for body size there remains tremendous variation among individuals of the same
height and weight. Thus, bone size not only varies with body size [ 22 , 23 ], but the
relationship between bone width and bone length (i.e., robustness) also varies
widely among individuals [ 24 ].
Because bone stiffness is proportional to the fourth power of diameter, the
natural variation in bone diameter [ 25 ] appears to be accompanied by coordinated
variations in cortical area and tissue-modulus in order to maximize the stiffness of
slender bones (narrow relative to length) and minimize the mass of robust bones
(wide relative to length). This phenomenon, which was consistent with a theo-
retical understanding of the functional adaptation process [ 26 ], was observed in
mouse long bone [ 27 , 28 ] and translated to human long bone [ 29 , 30 ] and also to
more complex, cortico-cancellous sites like the proximal femur [ 31 , 32 ] and
vertebral body [ 33 ].
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