Biomedical Engineering Reference
In-Depth Information
waste metabolite concentration in the blood and the dialysate creates a flux of the
metabolite from the blood to the dialysate. Electrolytes are not removed because
the dialysate and blood have similar electrolyte concentrations. In this model, two
compartments are considered (Figure 10.8).
The
blood compartment
is assumed to have a given volume (
V
B
). To predict
the changes in the blood (or plasma) urea concentration (
C
BU
) with time during
dialysis, the plasma urea change is written, similar to compartments before as
(
)
dVC
BBU
=
QC
−
QC
B out
,
B out
,
B in
,
B
dt
where
Q
B,in
and
Q
B,out
are the volumetric inlet and outlet flow rates of blood
through the dialyzer, respectively, and
C
BU, out
is the “blood” urea concentration
exiting the dialyzer (and entering the CST). For the blood compartment, the inlet
urea concentration to the dialyzer is the same as the outlet concentration of the CST
(
C
BU
,
in
=
C
BU
). Unlike other two-compartmental models, a certain volume of water
is removed in the urine. Hence volume of blood is a function of time and cannot be
treated as a constant. Using the chain rule,
dC
dV
(10.30)
V
BU
+
C
B
=
Q
C
−
Q
C
B
BU
B out
,
BU out
,
B in
,
BU
dt
dt
For the changing blood volume, material balance with constant density is rep-
resented by:
dV
(10.31)
B
=
QQ
−
B out
,
B in
,
dt
The substitution of (10.30) into (10.31) and simplification gives:
Figure 10.8
Modeling countercurrent (opposite direction fl ow with the blood) dialysis unit.
