Biomedical Engineering Reference
In-Depth Information
fibrils and mineral crystals has a tremendous influence on accurately predicting
bone stiffness. Experimentally, mineral has been demonstrated to lie both within
and outside of the collagen in dentin [83], mineralized tendon [20], and bone
[22], where the distribution of mineral in mature tissues is predominantly in the
extrafibrillar compartment. Functionally, the intrafibrillar material in dentin likely
plays a dominant role over extrafibrillar material in sustaining load [84].
The most successful attempts to relate bone macroscopic mechanical behavior
to the response of individual components at fundamental (ultrastructural) length
scales has been via sophisticatedmultiscale computational modeling [82]. However,
it is unclear that this model presents a true solution to the problem, as an extremely
large (tens of gigapascals) elastic modulus value is used for the collagen phase. With
the collagen essentially as stiff as bone, and a strong influence in overall modulus
due to porosity, this model likely represents a first step toward a full description of
bone at multiple-length scales based on the nanometer-scale constituent phases.
3.6
Bone as a Composite: Anisotropy Effects
Bone is anisotropic throughout each level of its hierarchical structure. At the
macroscopic scale, trabecular (or cancellous) bone possesses a three-dimensional
structural organization that is driven by loading patterns. The orientation and
spacing of trabeculae determine the degree of anisotropy, which accounts for
72-94% of the variability in the elastic constants for trabecular bone [85-87]. At
levels below that of the whole bone, the material behavior is itself directionally
dependent [88]. What is known, and not known, about each constituent phase has
a profound influence on our ability to understand the true composite nature of
bone and also to develop accurate, high-quality composite models. The remainder
of this section therefore focuses on anisotropy in osteonal cortical bone, as that is
the focus of most composite models of bone.
Bone exhibits directional dependence at multiple scales and within various bone
types [89, 90]. Cortical bone, within long bones, demonstrates transverse isotropic
behavior in conventional load-deformation testing of macroscopic sections [90-92]
and in ultrasound measurements [89]. The elastic modulus and ultimate strength
are both greater in the longitudinal than in the transverse direction and show
little difference between the radial and transverse directions [89, 90, 92, 93]. Bone
loaded in tension also demonstrates a substantially greater strain to failure in
the longitudinal versus the transverse direction [90]. Overall, these properties are
explained by the longitudinal alignment of osteons and Haversian canals [94]
and in that the collagen fibrils [93] and, consequently, the
c
-axis of the mineral
crystals [92] generally align with the long axis of the bone. Properties may also
vary with the orientation of lamellae, blood vessel networks, and laminae, as well
as with anatomical site and age [90, 95]. Stiffness values, measured via ultrasonic
measurements, change significantly with bone type and maturity: the elastic
coefficients that describe bovine plexiform bone reveal an orthotropic material
