Biomedical Engineering Reference
In-Depth Information
Fig. 1 Sketch of idealized a diaphyseal and b metaphyseal cross-sections of bones. For the
hollow circular cross-section of a: total area, TA = pD
2
/4; medullary area, MA = pD
2
/4;
cortical bone area, CA = TA-MA = p(D
2
-D
2
)/4; bone moment of inertia = p(D
4
-D
4
)/64
equations we note that structural strength depends directly on r
fail
(material) and
either A or I (geometry), which in turn depend on diameter squared or raised to the
power four. Area is essentially a measure of the amount of bone in the cross-
section, while moment of inertia is a measure reflecting both the amount of bone
and how it is distributed. These simple relationships motivate our interest in area
and moment of inertia as two key measures of bone size. Also of interest are
diameter and section modulus, defined as I/c.
Bones are dynamic structures that change throughout life. In this chapter, we
review the published data on changes in bone structure with aging. We consider
changes in the diaphyseal regions of long bones (e.g., femur, tibia, radius), which
are comprised mostly of cortical bone, and changes at the ends of long bones and
in short bones (e.g., vertebra), which are comprised of a mix of cortical and
trabecular bone. These latter sites are of particular clinical relevance as the most
common fracture sites are the vertebra, distal radius and proximal femur. We focus
primarily on bone geometry, but also consider whole-bone mechanical properties
where data are available. We also discuss recent work showing that material and
geometric properties, often considered to be independent contributors to whole-
bone strength, are probably not independent.
2 Diaphyseal Changes with Age
2.1 Cross-Sectional Geometry
Even after rapid skeletal growth ends in the third decade of life, the diaphyses of
long bones continue to change via periosteal and endocortical expansion. The net
changes in geometry indicate that bone apposition prevails at the periosteum,
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