Biomedical Engineering Reference
In-Depth Information
influences its mechanical properties. To a first approximation, detailed under-
standing of the organic matrix-mineral interactions is limited by intrinsically
small length scales, and there exists a clear need for new tools and experimental
approaches to examine materials at these scales. The ability to model - and thus
predict - the mechanical properties of bonelike composites are currently limited
by our lack of knowledge about mineral-matrix interactions at molecular length
scales.
We know that the apatite in bone deposits onto the organic matrix by
heterogeneous nucleation, but it is unclear as to what is the nature of the
nucleation sites - collagen, noncollagenous proteins (including glycoproteins
such as biglycan). Recent examination of natural bone by solid-state NMR has
indicated hydroxyapatite-sugar interfaces as the fundamental interaction, and
not hydroxyapatite-protein interfaces [76]. Obviously, this degree of uncertainty
influences our ability to model bone as a composite material.
Further complicating matters is the significant lack of uncertainty in the elastic
modulus of collagen. With a large value for
E
collagen
, lower-bounds-type models
with discontinuous mineral ''particles'' or ''platelets'' embedded in a continuous
collagen matrix result in reasonable elastic modulus values compared with the
known values for bone (Table 3.2). However, these models are inconsistent with
the known continuous nature of bone mineral, as can be demonstrated by the
existence of the porous solid that remains following removal of the organic
component of bone.
Current composites models of bone have primarily emphasized two-phase
behavior with the two components, the lumped water plus the organic and mineral
phases. A second common approach is to consider a poroelastic model in which
the organic plus mineral phases are lumped into a single ''solid skeleton'' that is
porous, where the second phase is the water. What is truly missing is a model
that considers individually the three phases - mineral, organic, and water - at
fundamental length scales without lumping two of the components together. This
provides opportunity for further research into bone as a composite.
In reality, there is no single model likely to predict
the
elastic modulus of
bone. Small-scale, local measurements of mineral content (volume fraction) and
mechanical properties (elastic modulus) demonstrate substantial point-to-point
variability in both values even in the same bone sample (Figure 3.3). A model for
bone consistent with the observed local variations in both mineral content and
stiffness [50, 111] must include a stochastic element and some sort of averaging
process to arrive at the macroscopic bone modulus from the very small-scale,
fundamental measurements. It has been speculated that this local randomness is
a key mechanism in obtaining the toughness of bone [111] such that any model
incorporating a single value of
V
F
or obtaining a single global value of
E
cannot
be realistic. With computational capabilities increasing all the time, it is entirely
possible to increase the complexity of bone composites models, to perhaps someday
achieve the aim of fully modeling macroscopic behavior based on the composition
and individual phase properties for a material as hierarchical and complicated as
bone.
