Biology Reference
In-Depth Information
cases of osteoporosis. Furthermore, rates of modeling and remodeling do not appear to be
consistent for all locations in the skeleton (
Bertram and Swartz, 1991
). Third, Wolff's law
does not account for hypertrophy and thresholding. To explain these terms, bone seems to
respond to some aspects of load thresholding, in which a load must reach a certain threshold
before the bone responds. Additionally, systemic bone hypertrophy (excessive bone forma-
tion throughout the body of some individuals) is not accounted for by Wolff's law (
Bertram
and Swartz, 1991
). Finally, Wolff's law implies that atrophy is equal to the reverse of hyper-
trophy, which is not true. The localized response of bones in terms of apposition and resorp-
tion must reflect the biomechanics of the whole element (
Bertram and Swartz, 1991
).
Pearson and Lieberman (2004)
further caution against assuming a relationship between
the direction of loading in long bone cross-sectional geometry without experimental testing
and validation in terms of cross-sectional geometry, bone density, and musculoskeletal
stress markers. Musculoskeletal stress markers are also part of the bones' functional response
to varying forces, and are discussed in both Smith (Chapter 7) and Kroman and Symes
(Chapter 8), this volume.
Engineering Beam Theory
Living bone is seldom loaded by a single force, which makes bone very complicated to
model mathematically. As a result of the nonuniform loading patterns from diverse activities
and from body weight, living bone is anisotropic, as mentioned earlier. Bone is ultimately
strongest under compression, but is loaded by tension, compression, shear, and bending
forces. Muscles create the largest forces on bones (
Frost, 1997
). Torsional forces are distrib-
uted over the entire surface of a bone in a circular fashion (
Frankel and Nordin, 1980
). The
polar moment of inertia is a measure of the torsional strength of a bone, which is directly
related to the distance from the surface of the bone to the neutral axis (an axis along the shaft
in which there are no longitudinal stresses). The neutral axis typically goes through the center
of the medullary canal (although this can fluctuate depending on the direction of the force(s)
being applied). Increasing surface area or cross-sectional area increases bone's strength to
both compression and tension. Area moments of inertia (e.g., I
x
,I
y
,I
max
,I
min
) measure the
bending strength of a bone, which is also related to the distance from the centroid (the
FIGURE 14.2
Ruler analogy for engineering beam theory.
