Biomedical Engineering Reference
In-Depth Information
Table 3.4
Mineralized tissue mineral volume fraction (
V
F
)
estimated in two ways and based on raw data in Table 3.3.
V
F
from weight % mineral
V
F
from mass density
Bone
0.49
0.38-0.48
Enamel
0.91
0.94
Dentin
0.43
0.54
The calculated mineral volume fractions for each tissue, obtained using the
composition data from Table 3.3, are presented in Table 3.4. The calculations differ
slightly, particularly in the composition of dentin relative to that of bone, but the
mineral volume fractions from either calculation are comparable. The reported
volume fraction of mineral in bone is approximately 50% [7], in good agreement
with either calculation. For simplicity, many model calculations and finite element
simulations of bone or dentin will assume a volume fraction of 50% mineral, in
good agreement with either calculation for both materials (Table 3.4).
Katz concluded that the simple examination of elastic modulus bounds based
on phase fractions and component moduli resulted in adequate prediction of
enamel properties but absolutely did not result in predictive capability for bone.
The modulus of bone increases dramatically at nearly constant mineral volume
fraction (in the region of mineral volume fraction 0.35-0.5). The result is that bone
modulus spans a region between the upper and lower H-S composite bounds, and
therefore cannot be predicted on the basis of the mineral volume fraction alone [5].
3.5
Bone as a Composite: Microscale Effects
There have really been few truly successful mechanical models for bone as a
composite. Part of the difficulty in modeling bone as a composite material is
in the uncertainty at the very finest levels of the ultrastructure. For example,
recent work has queried whether proteins or other organic components are directly
opposed against the bone mineral [76]. Manipulation of hydration state with polar
solvents dramatically alters the hydraulic permeability [77] in a manner which is
unclear - likely the organic-mineral interactions are affected due to alterations in
hydrogen bonding.
Such varied observations have been translated into a wide range of assumptions
about how the organic and mineral phases of bone interrelate. Mineral crystals
have been assumed to lie entirely within the collagen fibrils [73, 78], outside of
the fibrils to form interpenetrating phases between collagen and mineral [79, 80],
both within (
75%) of the collagen [81], or predominantly
outside of the collagen fibrils [82]. The specific relationship between the collagen
∼
25%) and outside (
∼
