Biomedical Engineering Reference
In-Depth Information
Clearly, depending on the particular conditions and the kinetics of the reaction, this for-
mulation can differ significantly. The assumption of first-order kinetics is a reasonably
accurate representation for many of the reactions that occur within capillary blood flow.
Using the few fairly accurate assumptions made about the species concentration within
the fluid phase of the plug flow, the Conservation of Mass simplifies for species within the
microcirculation to an exponential relationship depending on the kinetics of the reaction.
Example
Consider the change in oxygen concentration and carbon dioxide concentration along a
500
m blood vessel (see Figure 6.6). Assume that the kinetics for each of these two molecules
are described by first-order reactions. The blood velocity within this particular capillary is
10 mm/s. The kinetic rate constant for each reaction is
μ
17 mol/s (for oxygen consumption) and
1.17 mol/s (for carbon dioxide formation). For these particular reactions, one oxygen molecule is
consumed or two carbon dioxide molecules are formed. The inlet blood concentration of oxygen
and carbon dioxide is 400 mL and 120 mL, respectively (dissolved gas concentration). Plot the
change in concentration as a function of distance along the capillary. What is the outlet concen-
tration of oxygen and carbon dioxide?
2
Solution
Oxygen concentration at the outlet would be
400 mLO
2
e
0
:
5mm
1
2
17 mol
=
s
=
10mm
=
s
C
O
2
ð
0
:
5mm
Þ
5
171 mLO
2
5
Carbon dioxide concentration at the outlet would be
120 mLCO
2
e
0
:
5mm
2
1
:
17 mol
=
s
=
10 mm
=
s
C
CO
2
ð
0
:
5mm
Þ
5
135 mLCO
2
5
The change in concentration over the distance of the blood vessel is shown in Figure 6.6.
FIGURE 6.6
Change in oxygen and car-
bon dioxide concentration within a capillary,
as modeled with first-order kinetic reactions.
This figure is associated with the in-text
example.
450
400
350
300
250
200
150
100
50
0
Oxygen concentration
Carbon dioxide concentration
0
0.05
0.1
0.15
0.2 0.25
Distance (mm)
0.3
0.35
0.4
0.45
0.5
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