Biomedical Engineering Reference
In-Depth Information
Table 3.6
Elastic coefficients (GPa) for single-crystal hy-
droxyapatite [52] and plexiform and osteonal bone [96] from
Table 3.5 normalized to the long axis coefficient (C
33
)value
for comparisons in anisotropy between materials.
HA single
Plexiform Osteonal
crystal
bone
bone
C
11
/C
33
0.80
0.64
0.73
C
22
/C
33
0.80
0.71
0.72
C
33
/C
33
1
1
1
C
44
/C
33
0.23
0.23
0.22
C
55
/C
33
0.23
0.20
0.22
C
66
/C
33
0.27
0.17
0.19
C
12
/C
33
0.25
0.42
0.40
C
23
/C
33
0.32
0.39
0.38
C
13
/C
33
0.32
0.45
0.44
ratio (
M
) in anisotropic materials [97, 106]. For bone, the
E
ratio of 1.75 (ratio
of longitudinal to transverse moduli) corresponds to an
M
ratio of
4 [106].
This analytical approach was used to demonstrate that bone mineral has greater
connectivity in the longitudinal versus the transverse direction [107].
Nanoindentation testing, performed in various directions, reveals properties that
vary significantly with direction. In one example, individual lamellae within dry
samples were
≈
1
.
≈
55% greater inmodulus than in the transverse direction: 25
.
7
±
1
.
0
and 16
1 GPa, respectively [98]. Equine cortical bone processed to remove
the organic phase remains highly anisotropic - with a 34% difference in transverse
versus longitudinal indentation modulus - and bone samples with the mineral
fraction removed show only a 10% difference [66] (Table 3.7). In comparison to the
.
6
±
1
.
Table 3.7
Anisotropy in equine cortical bone from nanoin-
dentation measurements for plane strain modulus (E
)in
planes that lie transverse and longitudinal to the long axis of
the bone. Student's
t
-test between directions
a
.
Condition
E
Longitudinal (GPa) E
Transverse (GPa)
Wet
11.7 (1.7), 326
11.8 (1.9), 68 (N.S.)
Ethanol dehydrated
15.0 (2.2), 309
24.8 (2.2), 68**
PMMA (polymethylmethacrylate) embedded 19.4 (2.1), 283
25.8 (2.1), 74**
Deproteinated (embedded)
13.4 (1.0), 62
20.4 (2.2), 62**
Decalcified (embedded)
4.9 (0.3), 59
5.5 (0.3), 49*
Data are from Bembey
et al
. [66]
a
Results reported as not significantly different (N.S.), significant (*), or highly significant (**).
