Biomedical Engineering Reference
In-Depth Information
organic phase, the mineral phase is the major contributor to measured anisotropy
at the material level although, as discussed above, the pattern of anisotropy does
not precisely mimic that of the hydroxyapatite itself.
The porosity and density of bone can bemeasured either within the material itself
or within a region of the bonematerial that includes organic andmineral constituent
phases, pore spaces, and microcracks or other inherent structural flaws. Within
the larger structure of cortical bone, large Haversian canals (diameter
m)
run generally parallel to the long axis of the bone. Smaller pore spaces made
of networks of canaliculi (
≈
1 µm), Volkman's canals (
≈
5-10 µm), and osteocyte
lacunae (
≈
5 µm) permeate the bone material. Most measurements of bulk samples
cannot avoid the influence of porosity and so report an effective measurement of
mineralization (i.e., percent mineral) or density. The interpretation of the composite
nature of bone depends heavily on the inclusion or exclusion of voids within the
tissue. These voids are filled by soft tissue or water
in vivo
.
Further, the exact nature (e.g., shape, size, density) of the pore spaces within
bone may highly influence the material anisotropy. The influence of porosity on
material properties is directional anisotropy [108, 109]. Young's and shear modulus
in human femoral cortical bone samples correlate with porosity in the longitudinal,
but not the transverse, direction [109]. In addition, increasing porosity correlates
with decreased anisotropy [108, 109]. In general, pore spaces in bone preferentially
align with the long axis of the bone. As compared to the bone tissue, pores introduce
an additional anisotropy of 16-20% of the effective medium for human cortical
bone samples ranging in porosity from 2 to 15% [108].
Simple composites theory shows that no simple relationship exists between the
elastic modulus and mineral content for large specimens of bone [5]. Nanoin-
dentation, to examine the tissue level of bone, has helped to better elucidate the
relationship between modulus and mineral volume fraction (
V
F
) [50]. Analysis of
micrometer-sized volumes has extended the study of material heterogeneity to the
tissue level. Similar to the groundbreaking work of Katz [5], no simple relationship
exists between modulus and mineral content at the tissue level (Figure 3.3) [50].
Similar to the work of Katz in larger volumes of bone [5], the modulus-mineral
content relationship was examined in bone samples ranging from very poorly min-
eralized, osteomalacic bone to the exceptionally dense whale rostrum (Figure 3.3).
Data for nanoindentation modulus and mineral volume fraction (
V
F
)fellwithin
H-S composite bounds, which describe the continuity between stiff particles in a
continuous compliant phase (lower bound) and compliant particles in a continuous
stiff phase (upper bound) [69]. Elastic indentation modulus was shown to exist as
a function of mineral volume fraction (as calculated from calibrated quantitative
backscattered electron images of each indentation site) [110]. The heterogeneity
in the data, as demonstrated by the amorphous relationship between modulus
and
V
F
throughout the range of bone types, resulted from a complex interplay of
factors that include the composition of the mineral phase, crystallinity, collagen
orientation, and nano- to micrometer-sized pore spaces.
Anisotropy is mainly influenced by the intrinsic factors of tissue-level organiza-
tion: orientation of collagen fibers and mineral crystals within the bone material
≈
50
µ
