Biomedical Engineering Reference
In-Depth Information
R
A
4
D
assuming that the reference point is the center of the circle (this is derived directly from
Equation 7.3
). Using measured values for the oxygen diffusion coefficient within air
(0.2 cm
2
/s) and a typical alveolar radius of 100
t
5
μ
m, the average diffusion time for oxygen
through the alveolus is 0.125 ms. This is a relatively accurate measurement for the time
required for oxygen diffusion, assuming that oxygen enters from the center of a uniform
alveolus. Also, this diffusion time is generally very fast as compared to the blood velocity
within the pulmonary capillaries, and therefore, it can be assumed that the gas concentra-
tion within the alveoli is uniform (i.e., there is no concentration gradient within the alveo-
lar space). Therefore, we do not need to consider the oxygen diffusion time throughout
the alveoli within the model of red blood cell oxygenation because it is not limiting the dif-
fusion process.
The second diffusion event that we will consider for red blood cell oxygenation is the
movement of oxygen across the respiratory boundary, which is primarily composed of the
alveolar epithelial cells and the capillary endothelial cells. In the simplest case, the diffu-
sion of oxygen across this boundary can be modeled by permeability laws. Assuming that
the permeability of oxygen is uniform throughout the entire respiratory boundary, then
the permeability can be defined in terms of the diffusion coefficient, the thickness of the
boundary, and the partition coefficient for oxygen, as follows:
p
c
D
x
P
5
ð
7
:
4
Þ
where
p
c
is the partition coefficient,
D
is the diffusion constant, and
x
is the thickness of
the boundary. The partition coefficient is the ratio of the diffusing concentration across the
diffusion boundary to the original concentration. In our example, it is the concentration of
oxygen in the alveolar space versus the concentration of oxygen within the blood. The
average thickness of the respiratory boundary is on the order of 2.2
μ
m, but can be as
small as 0.3
m. The diffusion coefficient for oxygen across the respiratory boundary is
approximately 2.3
μ
10
2
5
cm
2
/s. This simplified formula can be extended to the actual
respiratory boundary by a summation of the different permeabilities, which can be
assumed to be in series (i.e., the thickness and diffusion coefficients for each cell type
would be needed for this analysis). An average respiratory permeability can also be
obtained through a thickness weighted average for the individual permeabilities (i.e., the
thickness of the cell membrane, the thickness of the cytoplasm, among others). Under nor-
mal conditions, this process must be considered during red blood cell oxygenation.
The third diffusion event for oxygen is the diffusion of oxygen through the plasma in
order to reach the red blood cell membrane. This diffusion is actually a combination of con-
vection and diffusion because of the blood velocity through the pulmonary capillaries.
Diffusion of oxygen typically occurs tangent to the blood flow direction, and diffusion is the
only component that accounts for the movement of oxygen toward the red blood cell wall
(this is an assumption that is relatively accurate because the red blood cells typically traverse
a capillary in single file, and red blood cells do not have much freedom of movement in the
3
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