Page 255 - Biomedical Engineering and Design Handbook Volume 1, Fundamentals

232 BIOMECHANICS OF THE HUMAN BODY

FIGURE 9.11 Dependence of ultimate stress on age for
trabecular bone from the human vertebra and femur. For both
anatomic sites, strength decreases approximately 10 percent
per decade. (Data from Refs. 15 and 149.)

of trabecular bone mechanics research has been devoted to improving our understanding of the rel-
ative contributions and interplay of porosity, architecture, and tissue properties in the apparent level
properties.
The elastic and strength properties of trabecular bone display substantial heterogeneity with
respect to donor age and health, anatomic site, loading direction (with respect to the principal orien-
tation of the trabeculae), and loading mode. Both modulus and strength decrease with age, falling
approximately 10 percent per decade 15,78 (Fig. 9.11). Pathologies such as osteoporosis, osteoarthritis,
and bone cancer are also known to affect mechanical properties. 79,80 Young’s modulus can vary
81
100-fold within a single epiphysis and three fold depending on loading direction. 82–85 Typically, the
modulus of human trabecular bone is in the range 10 to 3000 MPa depending on the preceding
factors; strength, which is linearly and strongly correlated with modulus, 11,81,82 is generally 2 orders
of magnitude lower than modulus and is usually in the range 0.1 to 30 MPa.
In compression, the anisotropy of trabecular bone strength increases with age 78 and decreasing
density (Fig. 9.12). The strength also depends on loading mode, being highest in compression and
lowest in shear. 86,87 Ratios of compressive to tensile strength and compressive to shear strength are
87
not constant but rather depend on modulus and density (see Fig. 9.12). Both modulus and strength
depend heavily on apparent density, yet these relationships vary for different types of trabecular bone
because of the anatomic site-, age-, and disease-related variations in trabecular architecture. Linear
∗
and power-law relationships can be used to describe the dependence of modulus and compressive
strength on apparent density (Tables 9.4 and 9.5), with typical coefficients of determination
2
(r values) in the range 0.5 to 0.9.
Interestingly, the failure (yield and ultimate) strains of human trabecular bone have only a weak
dependence, if any, on apparent density and modulus. 11,13,78, 88–91 A recent study designed to test for
intersite differences found that yield strains were approximately uniform within anatomic sites, with
standard deviations on the order of one-tenth the mean value, but mean values could vary across
11
sites (Fig. 9.13). Thus, for analysis purposes, yield strains can be considered constant within sites
but heterogeneous across sites. Regardless of anatomic site, however, yield stains are higher in com-
11
pression than in tension. Ultimate strains are typically in the range of 1.0 to 2.5 percent. Evidence
from experiment on bovine bone indicates that yield strains are also isotropic 92,93 despite substantial
anisotropy of modulus and strength.

∗ Differences in the predictive power between the various linear and power laws are usually negligible within a single anatomic
site because the range of apparent density exhibited by trabecular bone is less than 1 order of magnitude.