Biomedical Engineering Reference
In-Depth Information
TABLE 11.3
Values of Parameters Estimated by the
Optimization Process [34]
Parameters
Values (nM)
K
D
11
4.8
K
D
21
5.2
K
D
12
222.1
K
D
22
5.7
c
s
BP
10
45
c
s
BP
20
101
Adding equations (11.59) and (11.60) leads to
∂
φ
f
c
j
∂t
c
j
+
φ
f
v
f
c
j
−φ
f
D
j
∇
+
∇•
+
2
=0
,j
=1
,
2
2
1
φ
f
1
φ
f
v
s
c
ji
∂
∂t
c
ji
+
−
∇•
−
(11.61)
i
=1
i
=1
which describes IGF-I and -II transported by diffusion and advection in a
deforming porous media with competition for binding sites.
Equation (11.61) can be further simplified to
φ
f
∂c
j
∂t
2
+
1
φ
f
∂c
ji
∂t
−
2
c
j
+
φ
f
v
s
−∇
φ
f
D
j
•∇
c
j
φ
f
D
j
∇
−
−
κ
∇
p
i
=1
2
=0
,j
=1
,
2
+
1
φ
f
v
s
•∇
c
ji
−
(11.62)
i
=1
Equation (11.62) is the governing transport equation for IGF-I and -II.
The mechanical quantities, such as fluid pressure, displacement, and velocity
can be determined using methods described in the previous sections.
11.4.2.5
Radial IGF-I and -II Transport in Cartilage under
Unconfined Dynamic Compression
To allow direct comparison with the studies presented in previous sections,
unconfined compressive loading between two impermeable platens will again
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