Biomedical Engineering Reference
In-Depth Information
TABLE 11.4
Parameters Used in Model Validation [89]
Parameters
Values
N
3
K
30% total-receptor concentration
10
−
5
mg/mL/sec
β
3.8
×
Initial aggrecan content
16 mg/mL
1.0
0.8
1 day
0.6
3 days
0.4
5 days
0.2
6 h
10 h
2 h
0.0
0
0.2
0.4 0.6
Radial distance from center of the cartilage (mm)
0.8
1
1.2
1.4
FIGURE 11.18
Normalized IGF-I mediated aggrecan production rate, as a function of radial
distance from the center of cartilage undergoing free diffusion. The calculated
aggrecan production rate is normalized to the value of parameter
β
.(
K
=
0
.
3
c
RT
,
β
= 3.8
= 16 mg/mL, and
c
I
0
=
10
−
5
mg/mL/sec,
n
=3,
c
a
0
×
40 nM.)
stimulation extends into the inner region of the domain at an intermediate
frequency (i.e., 0.01 Hz).
Figure 11.18 shows predictions of the spatial dependence of IGF-I induced
aggrecan synthesis rate in the presence of 300 ng/mL bath IGF-I concentra-
tion undergoing free diffusion. It can be seen that a strong spatially dependent
aggrecan production develops at early times (i.e., time
<
1 day) when IGF-I
initially diffuses into the cartilage with a steep concentration gradient from the
outer edge of the cartilage. Over time, as IGF-I gradually saturates the carti-
lage disc, aggrecan production rate becomes uniform throughout the disc and
reaches its maximum level. Eventually aggrecan production is “switched off”
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