Biomedical Engineering Reference
In-Depth Information
Atomistic modeling for stretching single tropocollagen molecules has been
used to generate comparable values of 2.4-7 GPa [35-37]. Collagen fibrils yielded
modulus values of 1-2.7 GPa via X-ray diffraction [38] and AFM testing [39],
respectively. In addition, a microelectromechanical system (MEMS) device used to
stretch hydrated individual collagen fibers revealed modulus values of 0.4-0.5 GPa
at small strains (more relevant for mineralized tissues) and
12 GPa at large strains
[40, 41]. Molecular multiscale modeling of comparable individual collagen fibers
produced modulus values of 4.36-38GPa for small and large strains, respectively
[35, 42].
The scale dependence of collagen is a current subject of controversy. In some
works, collagen shows a reduction of the modulus from the tropocollagen level
to the fibril level by
≈
80%
[42]. However, other authors have come to opposite conclusions concerning both
scale dependence and the relative range of numerical values for the collagen
modulus. Two studies [43, 44] discussed the advances in measuring fundamental
collagen elastic properties, taking advantage of technological developments such
as the optical tweezers and sophisticated computational techniques. Both these
works report extremely low modulus values for collagen at molecular scales, in
the single- to double-digit megapascal range and in contrast to many of the
values listed above. Both works also note an increased elastic modulus values
for larger structural units of collagenous soft tissues, such as whole tendons,
typically in the hundreds of megapascal to single-digit gigapascal range. This
increase in modulus for larger structural units is attributed to cross-linking [44]. A
comparison of the approximate stress-strain for four different hierarchical levels
of collagen from [44] gives approximate values of elastic modulus for tendon
E
=
636 MPa, collagen fascicle
E
=
162 MPa, collagen fiber
E
=
43 MPa, and
procollagen molecule
E
=
27 MPa. Modulus values for demineralized bone matrix
also have been reported as generally lower than those presented for individual
collagen structures: from hundreds of megapascals [45] to
≈
1-2 GPa [46]. Clearly,
there are fundamental issues outstanding concerning the appropriate value to use
for the elastic modulus of collagen, and this will affect the fidelity of any composite
models used to simulate the mechanical behavior of bone.
≈
40% [33, 42] and from the fibril to the fiber level by
≈
3.3.2
Mineral Phase
The elastic modulus of both single-crystal hydroxyapatite and mineralogical fluo-
roapatite is reported in the range from100 to 150GPa depending on the test method
and specimen orientation [47-51]. The Poisson's ratio was reported as
28
[48]. Biological apatite is an analog of mineral apatite, and so its mechanical prop-
erties are quite well known if the mineral is fully dense - which may not be the
case in biological systems [29]. The heterogeneity of bone mineral complicates
the measurement of properties. Not only is bone mineral heterogeneous within
the bone material itself but also localized differences in bone mineral exist within
the regions of varying age and in different bone types.
ν
=
0
.
