Biomedical Engineering Reference
In-Depth Information
equivalent rates of decline. In conclusion, there are important age-related changes
in bone structure and density that affect whole-bone strength. Additional studies
measuring whole-bone strength with aging are needed.
1 Introduction
Bones are structural entities that are increasingly susceptible to fracture with aging.
Age-related/osteoporotic fractures occur at an estimated rate of 2 million per year in
the U.S. with corresponding high costs in economic terms, quality of life, and
increased mortality [
1
]. The causes of the increase in fracture incidence with age are
multifactorial, but can generally be grouped into factors affecting applied loading
(e.g., body weight, impact from falls or other trauma) and factors affecting structural
(whole-bone) strength. Because the mechanical behavior of a structure depends on
its geometric and its material properties, changes in geometry and material prop-
erties of bones with age influence whole-bone strength. The changes that occur in the
material properties of bone with age include density, microstructure, composition,
etc., and are considered in other chapters in this volume (''
Characterisation of
Age and Gender
, Bone Microdamage and its Contributions to Fracture, Changes in
and Microstructure with Aging and Osteoporosis
'
'). Of primary interest in this
chapter are the changes in bone structure (i.e., size and shape, also called mor-
phology) that are documented to occur with aging. We also consider the limited
available data on whole-bone mechanical properties and aging.
There are many descriptors of bone morphology, but based on engineering
mechanics we focus on two geometric properties of particular relevance to whole-
bone strength: cross-sectional area and moment of inertia. For example, for a
cylindrical structure like the diaphysis (shaft) of a long bone (Fig.
1
), the theo-
retical strength under axial and bending loading are given by:
F
fail
¼
r
fail
xA
M
fail
¼
r
fail
xI
=
c
where F
fail
is the axial failure force (structural strength as it pertains to failure
under purely compressive or tensile loads), M
fail
is the bending failure moment
(structural strength as it pertains to failure under bending loads), r
fail
is the failure
stress (material strength), A is the cross-sectional area, I is the cross-sectional
moment of inertia (also called the second moment of area), and c is the distance
from the center of the cross-section to the outer most point on the surface. For a
solid cylinder with a circular cross-section: A = pD
2
/4, I = pD
4
/64, and c = D/2,
where D is the diameter. (See Fig.
1
for additional equations.) From these two
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