Biomedical Engineering Reference
In-Depth Information
material. However, fluid-filled pore spaces occupy approximately 20% of a bone's
volume. Pores ranging in size include large millimeter-sized trabecular spaces,
vascular pores including Haverisan canals (
≈
20
µ
m), canaliculi and lacunae
(
m), and nanometer-sized pore spaces or ''matrix micropores'' [23] that
exist between and within the collagen and mineral crystals. Bound water may
stabilize the mineral crystallites by occupying OH
−
and possibly Ca
2
+
vacancy sites
[24] but likely plays a minor role in the mechanical behavior of the bone tissue.
Porosity in bone facilitates movement of the interstitial fluid (i.e., unbound
water) throughout the tissue that contributes to poroviscoelasticity. Fluid that exists
in smaller pore spaces between the mineral crystals and collagen fibrils [25] may
add plasticity to the mechanical response of bone. In addition, the proteins and
glycoproteins within the organic matrix interact with chemically unbound water
through charged interactions. The availability of charged sites on the organic
matrix has a profound effect on the stiffness of unmineralized matrix in tissues
containing other forms of collagen [26]. Similarly, the interaction between water
and the organic matrix of bone is subject to similar hydrostatic interactions, where
the bone tissue stiffens with occupation of charged sites by polar solvents [27].
≈
0
.
1
µ
3.3
Bone Phase Material Properties
Having established the three-phase nature of bone, we now examine what is known
about the individual phase material properties for each phase.
3.3.1
Organic Matrix
The organicmatrix within bone is composed primarily of fibrillar type I collagen that
is laid down by osteoblasts. While the resulting longitudinal, hierarchical structure
is well designed to undergo tension, as in the case of tendon and ligaments, it
also directs the pattern of mineralization along load-bearing directions in bone and
contributes to bone's resistance to tension, torsion, compression, and bending.
The material properties of collagen are scale dependent and vary with mea-
surement technique, hydration state, and source of the collagen material. Most
modeling for mineralized tissues has incorporated a modulus of 1-1.5GPa [28-31]
consistent with the value of 1.2GPa proposed by Gosline in a comparative analysis
of elastic proteins [32]. Young's modulus values of 3-9GPa were obtained for sin-
gle tropocollagen molecules via X-ray diffraction [33]. Cusack and Miller [34] used
Brillouin light scattering and obtained an elastic modulus value of 11.9GPa for
dry collagen and 5.1 GPa for wet collagen. The extremely large values are probably
due to the ultrahigh frequency (10
10
Hz) nature of the measurement since collagen
is viscoelastic and measured (complex) modulus in a viscoelastic solid depends
strongly on the measurement frequency. These values, therefore, would not be
appropriate for the quasistatic elastic modeling of mineralized tissues.
