Biomedical Engineering Reference
In-Depth Information
does not limit the red blood cell oxygenation. The second diffusion event is the movement of
the gas across the respiratory boundary. This would be modeled with a partition coefficient
for each of the boundaries that are included within the model (i.e., alveolus epithelial cells
and capillary endothelial cells), as
p c D
x
P 5
The third diffusion event is the convection and diffusion of oxygen to the red blood cell
within the pulmonary capillaries. The dimensionless Sherwood number can be used to
model this convection-diffusion event, as
Kx
D
Sh 5
and
Sh
Sh 0 : 25 1
0
:
84
ð
Hct
0
:
25
Þ
5
2
The fourth diffusion event is the diffusion of oxygen across the red blood cell membrane,
which occurs approximately 100 times faster than the diffusion across the respiratory bound-
ary. This event is also not a rate limiting step in diffusion. The last diffusion event is the dif-
fusion of oxygen to hemoglobin and the kinetic association of oxygen to hemoglobin. This is
modeled with a Thiele modulus, which is defined as
r
kx 2
D
φ 5
A model of tissue oxygenation should also be formulated and perhaps the most famous
model is the Krogh model. Assuming that oxygen diffusion through tissue is homogeneous
in all directions and that the capillaries are regularly spaced in three dimensions, the Krogh
radius quantifies the area of tissue oxygenation per capillary. The relationship of the capil-
lary radius to the Krogh radius is represented as
r K R
4 C P D
r 2
2 r C
r K 1
C ð r Þ
C P 5
r C
r
1
2 ln
1
7.2
Glucose transport is also a salient transport mechanism to discuss within the microcircula-
tion. Under most normal conditions, glucose cannot freely diffuse through the capillary wall.
Its movement is coupled to the movement of a second ion (such as sodium), where the
energy gained by moving this second ion down its electrochemical gradient is used to move
glucose up its concentration gradient. Co-transporters are typically used in these processes.
7.3
Lipid soluble molecules can freely permeate the endothelial cells that line the capillaries.
Non-lipid soluble molecules cannot diffuse freely through the endothelial cells, but typically
they move through the intercellular cleft. It has been experimentally determined that physio-
logically important molecules generally have a permeability through the intercellular cleft
that is in the range of water's permeability through the intercellular cleft. For instance,
sodium chloride has a permeability approximately 96% of water's permeability. Large
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