Biomedical Engineering Reference
In-Depth Information
Solution
r
K
R
4
D
r
2
2
r
C
r
K
1
r
C
r
CðrÞ
5
C
P
1
2
ln
2
2
cm
3
s
r
2
1
ð
35
μ
m
Þ
ð
5
E
2
8 mol
=
Þ
2
ð
4
μ
m
Þ
4
μ
m
cm
3
CðrÞ
5
4
E
2
8 mol
=
2
ln
1
4
ð
2
E
2
5cm
2
=
s
Þ
2
r
ð
35
μ
m
Þ
2
4
0
@
1
A
3
5
2
2
2
1
ð
35
μ
m
Þ
ð
5
E
2
8 mol
=
cm
3
=
s
Þ
ð
10
μ
m
Þ
2
ð
4
μ
m
Þ
4
μ
m
=
cm
3
2
ln
Cð
10
μ
m
Þ
5
4
E
2
8 mol
1
2
4
ð
2
E
2
5cm
2
=
s
Þ
10
μ
m
ð
35
μ
m
Þ
cm
3
2
:
65
E
2
8 mol
=
5
2
4
0
@
1
A
3
5
2
2
2
cm
3
s
1
ð
35
μ
m
Þ
ð
5
E
2
8 mol
=
Þ
ð
20
μ
m
Þ
2
ð
4
μ
m
Þ
4
μ
m
cm
3
Cð
20
μ
m
Þ
5
4
E
2
8 mol
=
2
ln
1
4
ð
2
E
2
5cm
2
=
s
Þ
2
20
μ
m
ð
35
μ
m
Þ
:
=
cm
3
5
1
78
E
2
8 mol
Although the Krogh method to calculate tissue oxygenation is possibly the most famous
and the most often used model, there are some limitations associated with this model.
First, Krogh did not consider the reduction in plasma oxygenation concentration along the
capillary length. This model also assumes that the capillaries are uniformly distributed in
a regular array throughout the tissue. This is fairly accurate for some tissue like skeletal
muscle, but for other tissues (especially the brain), the capillary distribution is seemingly
random. Krogh also assumed that diffusion only occurs within one direction in both the
plasma and the tissue (i.e., radial). If these assumptions are not met, there will be a drastic
effect on the movement of oxygen throughout the tissue, and it is likely that the tissue
oxygen concentration will not be uniform at one particular radial location.
The same analysis can be conducted for carbon dioxide exchange. The formulations are
the same, and it turns out that the same processes are the rate-limiting steps for carbon
dioxide movement. The following are experimentally determined diffusion coefficients/
kinetic rate constants for carbon dioxide. The diffusion coefficient for carbon dioxide
movement through the respiratory boundary is 8.3
10
2
4
cm
2
/s. The diffusion coefficient
for carbon dioxide through plasma is on the order of 4
3
10
2
4
cm
2
/s. Within the red blood
3
10
2
4
cm
2
/s and the kinetic associa-
tion constant for the formation of bicarbonate within the red blood cell is 0.13 s
2
1
cell, the diffusion coefficient for carbon dioxide is 1.6
3
(again,
recall that the majority of carbon dioxide does not associate with hemoglobin).
7.2 GLUCOSE TRANSPORT
Glucose diffusion out of the vascular system is similar to the diffusion of oxygen and
carbon dioxide; however, because glucose is not lipid soluble, there are other mechanisms
present to efficiently move glucose into the interstitial space. This is typically termed
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