Biomedical Engineering Reference
In-Depth Information
These rates would also be equal to the volumetric flow rate of fluid into the compart-
ment multiplied by the inflow or outflow concentration of the solute:
q
in
5
Qc
in
_
ð
12
:
6
Þ
q
out
5
Qc
out
_
We can then describe the time rate of change of any solute within the compartment as
dq
dt
5
_
q
out
5
Q
q
in
2
_
ð
c
in
c
out
Þ
2
or
dc
dt
5
Q
V
compartment
ð
c
in
2
c
out
Þ
ð
12
:
7
Þ
assuming that the volume of the compartment does not change with time. To completely
model an extracorporeal device, a system of first-order linear ordinary differential equa-
tions would need to be coupled, such that the solute concentration in each compartment
would affect the net diffusion across the semipermeable barrier. Such a system would take
the form of
Q
1
-
2
V
1
Q
2
-
1
V
2
dc
1
dt
52
c
2
1
Q
1
c
1
1
ð
12
:
8
Þ
Q
1
-
2
V
1
Q
2
-
1
V
2
dc
2
dt
5
1
Q
2
c
1
c
2
2
Q
1
-
2
is the flow rate from compartment 1 into compartment 2.
where
Example
A patient is currently connected to an extracorporeal device to remove the excess salt from
his or her blood (see
Figure 12.7
). Imagine that the inflow blood contains 5 grams of salt and the
blood inflow flow rate is 5 mL/min. The blood outflow rate is also 5 mL/min. The inflow rate of
the dialysate is 2 mL/min, and the outflow flow rate is also 2 mL/min. There is a flow between
FIGURE 12.7
Flow through an
extracorporeal device for the in-
text example problem.
5 mL/min
5 mL/min
Blood compartment
100 mL, c
1
(0)
=
150 g
Blood flow
direction
1mL/min
2 mL/min
2 mL/min
F
iltrate
direction
Filtrate compartment
100 mL, c
2
(0)
=
0 g
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