Biomedical Engineering Reference
In-Depth Information
by the nephron epithelial cells (K
2
) and the reabsorption of glucose into the peritubular capillar-
ies (K
3
), where the Ks are defined as the transfer rate, which account for the diffusion coefficient
and the membrane parameters. The initial quantity of glucose within the nephron is defined as
q
0
. Solve for the time rate of change of the quantity of glucose within the nephron.
Solution
The mass balance of glucose quantity can be defined as the accumulation of glucose within
the nephron is equal to the input of glucose minus the output of glucose. Therefore, the mass
balance equation is
dq
dt
5
q
in
2
q
out
The input quantity is defined as
K
1
q
The output quantity is defined as
ð
K
2
1
K
3
Þ
q
Using this definition within the differential equation
dq
dt
5
K
1
q
2
ð
K
2
1
K
3
Þ
q
dq
q
5
ð
K
1
2
K
2
2
K
3
Þ
dt
ln
q
5
ð
K
1
2
K
2
2
K
3
Þ
t
1
c
Ce
ðK
1
2
K
2
2
K
3
Þt
q
o
e
ðK
1
2
K
2
2
K
3
Þt
q
ð
t
Þ
5
5
where
C
is the initial concentration of glucose within the nephron. With increasing complexity,
these methods can still be applied, but it is necessary to quantify the time rate of change of each
substance, within each compartment. This can lead to multiple differential equations that must
be solved simultaneously.
12.6 EXTRACORPOREAL FLOWS: DIALYSIS
Dialysis is a method to separate solutes within a solution by means of diffusion through
a semipermeable membrane. Blood dialysis is needed when the kidneys can no longer
remove the toxins from blood. When the kidneys fail, the patients must be maintained on
dialysis; otherwise, they will die. As with any dialysis, there are three major components
of the system (
Figure 12.6
). The first is a compartment for the solution which will have
substances removed. In our case, this will be blood. The second is a compartment contain-
ing a fluid with which the solutes will enter. The fluid in this compartment is termed the
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