Biomedical Engineering Reference
In-Depth Information
Table 9.1
The material properties reported
from different sources for the elastic mod-
uli, Poissons ratios, and so on. The super-
script d reflects the drained properties and
the superscript m reflects the matrix ma-
terial properties. The water compressibil-
ity (
K
f
)is2.3GPa,itsviscosity(
µ
) is 0.001
Pa s, and the amplitude of
ε
o
, the applied
strain, is taken as 0.0005. The transversely
isotropic elastic constant data is from Cowin
and Mehrabadi [93]. The modal value for land
mammal long bones for
R
i
/
R
o
was taken as
0.5, varying effectively from 0 (solid) to 0.73
[94]. Human bones are thought to be in the
same range.
Material parameters
PLC (
L
)
PV (
V
)
E
1
E
1
=
15.17 GPa
12.7 GPa
E
3
15.96 GPa
14.9 GPa
d
12
=
ν
d
21
ν
0.316
0.27
31
=
ν
32
ν
0.308
0.285
13
23
ν
=
ν
0.282
0.27
E
1
E
1
=
18.6 GPa
18.6 GPa
E
3
22.32 GPa
22.32 GPa
m
12
=
ν
m
21
ν
0.322
0.322
31
=
ν
32
ν
0.312
0.312
ν
m
13
=
ν
m
23
0.255
0.255
Outer radius (osteon, whole bone)
r
o
=
160 µm
R
o
=
0
.
03 m
Inner radius (osteon, whole bone)
r
i
=
40
µ
m
R
i
=
0
.
015 m
Porosity
φ
0.05 or 0.1 or 0.15
0.05
10
−
22
10
−
14
Permeability K
rr
2
.
2
×
m
2
to 2
.
2
×
6
.
35
×
m
2
to 6
.
35
×
10
−
24
m
2
10
−
8
m
2
9.7.4
Cancellous Bone Porosity
The cancellous bone porosity is the porosity external to, and surrounding, the
trabeculae. It is the bone porosity with the largest pores (up to 1 mm). The porosity
is well connected to the marrow cavity and it contains marrow, fat, and blood vessels.
The magnitude of the porosity varies with anatomical location; it is smaller near
the load-bearing surfaces and increases to its greatest magnitude as the medullary
canal is approached. The permeability associated with this porosity is surveyed in
[60]; the concentration in the present work is upon the porosity associated with the
interstitial bone fluid contained in the bone matrix, and not upon that associated
with the bone marrow.
9.7.5
The Interfaces between the Levels of Bone Porosity
There are two external boundaries to the several porosity domains of interest in
bones: the periosteum and endosteum. These are, mechanically and biologically,
very different structures. The endosteum is mechanically insignificant while the
periosteum is like a pretensioned, stiff, relatively impermeable fiber stocking
