Biomedical Engineering Reference
In-Depth Information
Table 3.5
Elastic coefficients (GPa) for single-crystal hydrox-
yapatite [52] and plexiform and osteonal bone [96]. All data
were collected using ultrasonic techniques. Indices 1 and 2
refer to the radial and circumferential directions, respectively,
and 3 refers to the long axis of the bone.
HA single
Plexiform
Osteonal
crystal
bone
bone
C
11
137
22.4
21.2
C
22
137
25.0
21.0
C
33
172
35.0
29.0
C
44
39.6
8.2
6.3
C
55
39.6
7.1
6.3
C
66
47.25
6.1
5.4
C
12
42.5
14.8
11.7
C
23
54.9
13.6
11.1
C
13
54.9
15.8
12.7
that becomes increasingly transversely isotropic as the bone undergoes osteonal
remodeling [96] - properties in the transverse direction (C
11
and C
22
)areof
similar values in single-crystal hydroxyapatite and osteonal bone but vary greatly in
plexiform bone (Table 3.5). Reorganization of bone with remodeling likely involves
increased organization of bone mineral onto a more highly organized and less
randomly deposited collagen structure.
There are clear differences between the overall pattern of anisotropy in the
mineral crystal and in the bone samples, as is apparent when the C
ij
values (from
Table 3.5) for each material are normalized by the largest stiffness coefficient, those
associated with the longitudinal axis (C
33
), as shown in Table 3.6. The numerical
values for C
11
,C
22
,andC
66
are relatively smaller in bone compared with apatite,
while C
12
,C
23
,andC
13
are all relatively greater in bone. Thus, and unsurprisingly,
the pattern of anisotropy in bone is not simply the result of anisotropy in the
mineral phase itself; other factors must contribute to the anisotropic response.
In contrast to suchmeasurements in healthy bone, metabolic diseasesmay have a
profound influence on anisotropy. Osteoporosis has little effect while osteopetrosis
reduces material anisotropy in bone [96]. The degree of anisotropy of this complex
structure is affected by changes in the bone due to normal growth [97], type
[97-101], and disease [96, 102].
Mineral crystals align with the collagen fibrils [15, 52] to contribute to anisotropy
at the level of the material. Acoustic microscopy of whole, demineralized, and
deproteinated bone samples showed the organic phase to possess near isotropy
while the mineral phase was anisotropic [103]. Knoop microindentation testing
revealed directionally dependent behavior on a planar bone surface [104, 105].
Through integration of measured elastic constants over the indented plane, an
anisotropy ratio (
E
) can be determined that accounts for the indentation modulus
