Biomedical Engineering Reference
In-Depth Information
1
1. Alveolar diffusion
Alveolus
2
2. Respiratory boundary diffusion
3
Pulmonary
capillary
5
Hb
3. Blood diffusion
4
4. Red blood cell membrane diffusion
Alveolus
5. Diffusion to hemoglobin
FIGURE 7.1
The five salient diffusion events for red blood cells within the pulmonary capillaries to become
oxygenated. By comparing the relative rates of diffusion of these five events, we can see that respiratory bound-
ary diffusion, blood diffusion, and diffusion/association with hemoglobin are the rate-limiting steps of red blood
cell oxygenation. Models of red blood cell oxygenation would assume a homogenous distribution of air within
the alveolus and a rapid diffusion across the red blood cell membrane.
for one-dimensional diffusion examples. Fick's second law of diffusion can be directly
obtained from Fick's first law of diffusion as
@x
-
@
-
-
@x
2
2
@t
52
@
Þ
5
@
@x
D
@
5
D
@
@x
ð
-
The general form for Fick's second law of diffusion would use the gradient operator for
the concentration differences, shown as
@
-
@t
5
r
U
ðDr
-
Þ
or
@
-
@t
5
Dr
-
2
if the diffusion coefficient is constant in all directions. Solving the differential
equation
(7.2)
for a one-dimensional diffusion example, the concentration of a species will vary
with time and distance, as given by the following function:
x
2
p
Cðx; tÞ
5
Cð
0
Þ
ð
7
:
3
Þ
Dt
where
C
(0) is the initial concentration at some point in space at time zero. The denomina-
tor of the expression in
Equation 7.3
is termed the diffusion length and is used to provide
a relative measure of how far the molecules move within a given time. The diffusion
length can be used to compare the diffusion of different molecules; molecules with a larger
diffusion length will typically diffuse more freely than those with a smaller diffusion
length (under the particular tissue conditions). For an alveolus, which is assumed to be cir-
cular with a radius of
R
A
, the diffusion length will be equal to
2
p
R
A
5
Dt
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