Biomedical Engineering Reference
In-Depth Information
Blood compartment
Blood flow
direction
Semipermeable
membrane
Water/Toxins
F
iltrate
direction
Filtrate compartment
FIGURE 12.6
Typical arrangement of a dialyzer to remove toxins from blood. A dialyzer would contain a
semipermeable membrane that would be able to filter toxins from the blood and would leave all proteins, cells,
and other necessary organic molecules within the blood. A counter-current flow is used to maintain a concentra-
tion gradient along the entire membrane.
dialysate. The last is the membrane which is permeable to the substances of interest (e.g.,
toxins) and not permeable to other substances (e.g., plasma proteins).
Blood dialysis occurs in more than 300,000 patients in the United States. Prior to dialy-
sis, the patient's blood is anticoagulated and remains so during the entire dialysis period.
Blood is continually drawn from the body and enters the extracorporeal device. Water,
toxins, and potentially some ions are removed from the blood and enter water (which is
the dialysate) that contains ions in a similar concentration as the plasma. The semiperme-
able membrane used differs based on the patient's characteristics. Typically, membranes
are composed of poly(methyl methacrylate), polyacrylonitrile, and polysulfone. These
membranes allow the movement of molecules that are relatively small but block the move-
ment of larger molecules.
To initiate the flow of water and solutes between the two compartments of the dialyzer,
a hydrostatic pressure gradient and a concentration gradient is put into place across the
semipermeable membrane. Also, the flow through the dialyzer is typically slow, so that a
counter-current gradient is established. A counter-current gradient means that the blood
inflow is at the same location as the filtrate outflow. This location would have the largest
concentration gradient between the blood and the filtrate. At the blood outflow location,
which is aligned with the filtrate inflow, the concentration gradient exists but is smaller.
Using this approach, all of the toxins can be removed from the blood without multiple
passes through the dialyzer. In fact, the nephron uses a counter-current multiplier system
to efficiently transfer solutes from the nephron into the peritubular capillaries and vice
versa (although this was not discussed).
To mathematically model these types of systems, a modified compartmental analysis
method can be used to describe the convection of blood and dialysate through the extra-
corporeal device and the diffusion of solutes out of the blood. We would first need to con-
sider the rate at which the solute enters the compartment and the rate at which the solute
exits the compartment. These can be represented as
dq
in
dt
5
_
q
in
ð
12
:
5
Þ
dq
out
dt
5
_
q
out
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