Biomedical Engineering Reference
In-Depth Information
be considered. Thus, equation (11.62) can be rewritten as
∂
2
c
j
∂r
2
φ
f
∂c
j
∂t
∂c
j
∂r
2
+
1
− φ
f
∂c
ji
+
1
r
∂t
− φ
f
D
j
i
=1
+
φ
f
v
r
−
∂c
j
∂r
2
∂c
ji
∂r
+
1
φ
f
v
r
κ
r
∂p
∂r
−
=0
,j
=1
,
2
(11.63)
i
=1
The average free and bound (complexed) IGF uptake ratio become
r
0
2
πrc
i
dr
1
c
i
0
R
f
Free IGF uptake ratio :
ui
=
r
0
0
(11.64)
2
πrdr
⎡
⎤
⎦
r
0
2
πrc
ij
dr
2
1
c
i
0
R
s
⎣
Bound IGF uptake ratio :
ui
=
r
0
0
(11.65)
2
πrdr
j
=1
11.4.2.6
Free Diffusion with Competitor
Experiments showed a significant increase in the free IGF-I level in human
synovial fluid in both OA and rheumatoid arthritis patients in comparison
with normal cartilage (e.g., increasing from 20 to 80 ng/mL), but no change
in the level of IGF-II [62]. Shown in Figure 11.14 are results of a “math-
ematical experiment” to understand the bioavailability of free IGF-I under
various cartilage conditions. The IGF-I concentration (
c
f
10
) in the solute bath
(synovial fluid) is varied to explore the possible IGF-I transport behavior for
“OA” (i.e., “diseased”) conditions. The results show that the rate of free IGF-I
uptake is relatively high in the diseased condition (Figure 11.14[a]), whereas
a decrease of bound IGF-I uptake is observed.
11.4.2.7
Growth Factor Transport with Competitor and Cyclic
Deformation
In cartilage synovial fluid, free IGF-I concentration is low (around 20 ng/mL)
in comparison to that of free IGF-II (around 200 ng/mL) [62]. In previous sec-
tions it was shown that cyclic loading enhances IGF-I transport. However, the
combination of competitive binding and cyclic loading might further modify
the transport behavior of IGF-I. Figure 11.15 shows the percent increased in
time-dependent free and bound IGF-I uptake in normal cartilage condition,
in the absence (i.e.,
c
f
10
= 20 ng/mL,
c
f
20
= 0 ng/mL) or in the presence of
IGF-II competition (i.e.,
c
f
10
= 20 ng/mL,
c
f
20
= 200 ng/mL), after 5 h 0.1 Hz
at 6% strain cyclic deformation. The results indicate that cyclic loading still
enhances IGF-I uptake in both cases; however, the enhancement is reduced
when a competitor for binding sites is introduced. The competitor effectively
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