Biomedical Engineering Reference
In-Depth Information
contact mechanics for spherical tips.
51,52,72
Further, bone's complex
construction produces time-dependent, or viscoelastic, behavior. While
conventional analysis techniques enable a first order approximation of
indentation modulus, advanced approaches are needed to accurately
quantify the behavior of bone. This section provides an overview of the
advances, and current limitations, in our understanding of bone at the
tissue-level that have been enabled by nanoindentation.
3.1.
Anisotropy
The elastic response of bone is anisotropic. Cortical bone, found within
the mid-shaft of a long bone, is transversely isotropic
113
where the
osteons and Haversian canals generally align with the long axis of the
bone.
14
In one study of anisotropy in machined, millimeter-dimensioned
sections of human cortical Haversian bone tested in compression and
tension, elastic moduli were
40% greater in the longitudinal versus the
transverse direction in tension and
55% greater in compression.
113
Other
bone types also possess anisotropy where the properties vary with
direction and with the directionality of lamellae, blood vessel networks,
and laminae, as well as with anatomical site and age.
113,114
At smaller scales, bone also possesses anisotropy. The organization of
collagen fibrils and mineral crystals within the osteons and lamellar
structure create an elastic anisotropy where a large percentage of mineral
lies outside of the collagen fibrils.
115,116
Microhardness indentations,
sampling areas containing many lamellae and other structures (
e.g.
,
osteocyte lacunae), clearly demonstrate anisotropy using a Knoop
indenter tip on selected bone surfaces.
117,118
One key benefit of nanoindentation lies in the ability to measure
properties at the level of individual structures within bone, such as within
individual lamellae. By conducting nanoindentation testing in different
directions, the anisotropy of individual microstructural components can
be assessed. Similar to results in bulk sections of bone in compression,
113
Berkovich nanoindentation measurements on dry, cortical bone revealed
an elastic modulus for longitudinally-tested interstitial lamellae (25.7 ±
1.0 GPa) that was 55% greater than that measured in the transverse
direction (16.6 ± 1.1 GPa).
119
Nanoindentation measurements in osteonal
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