Page 259 - Biomedical Engineering and Design Handbook Volume 1, Fundamentals

236 BIOMECHANICS OF THE HUMAN BODY

It should be noted that the in vitro mechanical test methods most often used to date on trabecular
bone are known to introduce substantial errors in the data as a result of the porous anisotropic
trabecular structure. Damage preferentially occurs at the ends of machined specimens when they are
compressed between loading platens due to disruption of the trabecular network at the specimen
boundaries. 114–116 In addition, friction at the platen-specimen interface creates a triaxial stress state
that may result in an overestimation of modulus. 114,115,117 If strains are computed from the relative
displacement of the platens, substantial systematic and random errors in modulus on the order of
20 ± 12 percent can occur. 118 Strength and failure strain data are also affected. 119,120 The trabecular
anisotropy indicates that experimental measurements of the orthotropic elastic constants should be
done in the principal material coordinate system. Since off-axis moduli are functions of multiple
material elastic constants, substantial errors can be introduced from misalignment 121 if not corrected
for. Much of the data in the literature have been obtained in various types of off-axis configurations,
since specimens are often machined along anatomic rather than material axes. The difficulty in inter-
preting these off-axis measurements is heightened when intersite and interstudy comparisons are
attempted. For all these reasons, and since the in vitro test boundary conditions rarely replicate those
in vivo, interpretation and application of available data must be done with care.
An important development for structural analysis of whole bones is the use of quantitative
computed tomography (QCT) to generate anatomically detailed models of whole bone 122–127 or
bone-implant 128,129 systems. At the basis of such technology is the ability to use QCT to noninva-
sively predict the apparent density and mechanical properties of trabecular bone. Some studies have
2
reported excellent predictions (r ≥ 0.75) of modulus and strength from QCT density information for
various anatomic sites. 82,89,130,131 Since the mechanical properties depend on volume fraction and
architecture, it is important to use such relations only for the sites for which they were developed;
otherwise, substantial errors can occur. Also, since QCT data do not describe any anisotropic
properties of the bone, trabecular bone is usually assumed to be isotropic in whole-bone and bone-
implant analyses. Typically, in such structural analyses, cortical bone properties are not assigned
from QCT since it does not have the resolution to discern the subtle variations in porosity and
mineralization that cause variations in cortical properties. In these cases, analysts typically assign
average properties, sometimes transversely isotropic, to the cortical bone.

9.6 MECHANICAL PROPERTIES OF TRABECULAR
TISSUE MATERIAL

While most biomechanical applications at the organ level require knowledge of material properties
at the scales described earlier, there is also substantial interest in the material properties of trabecular
tissue because this information may provide additional insight into diseases such as osteoporosis
and drug treatments designed to counter such pathologies. Disease- or drug-related changes could
be most obvious at the tissue rather than apparent or whole-bone level, yet only recently have
researchers begun to explore this hypothesis. This is so primarily because the irregular shape and
small size of individual trabecula present great difficulties in measuring the tissue material properties.
Most of the investigations of trabecular tissue properties have addressed elastic behavior. Some
of the earlier experimental studies concluded that the trabecular tissue has a modulus on the order of
1 to 10 GPa. 132–135 Later studies using combinations of computer modeling of the whole specimen
and experimental measures of the apparent modulus have resulted in a wide range of estimated val-
ues for the effective modulus of the tissue (Table 9.6) such that the issue became controversial.
However, studies using ultrasound have concluded that values for elastic modulus are about 20 per-
cent lower than for cortical tissue. 136,137 This has been supported by results from more recent nanoin-
dentation studies. 61,62,138 The combined computer-experiment studies that successfully eliminated
end artifacts in the experimental protocols also found modulus values more typical of cortical bone
than the much lower values from the earlier studies. 139 Thus an overall consensus is emerging that
the elastic modulus of trabecular tissue is similar to, and perhaps slightly lower than, that of cortical
bone. 140 Regarding failure behavior, it appears from the results of combined computational-experimental