Page 170 - Biomedical Engineering and Design Handbook Volume 2, Applications

DESIGN OF ARTIFICIAL KIDNEYS 149

The extraction coefficient for countercurrent flow dialysis without significant ultrafiltration can
be expressed as 23
E = (1 – exp (k A (1 – Z)/Q )/(Z – exp (k A (1 – Z) Q )) (5.6)
D B D B
The term (k A/Q ) is a dimension-less quantity and is referred to as the number of mass trans-
D B
fer units N .Therefore,
T
E = (1 – exp (N (1 – Z))/(Z – exp (N (1 – Z))) (5.7)
T T
where Z is the ratio of blood flow rate (Q ) to the dialysate flow rate (Q ):
B D
Z = Q /Q (5.8)
B D
The extraction coefficient E increases with decreasing Z. When Z = 0, regardless of the dialyzer
(countercurrent, cocurrent, or mixed flow), the extraction coefficient can be expressed as

E = 1 – exp (– N ) (5.9)
T
The clearance for countercurrent flow low flux dialysis can be expressed as

K = Q E = Q (1 – exp (N (1 – Z))/(Z – exp (N (1 – Z)) (5.10)
B B T T
In the conventional or low flux dialysis, the blood flow rates are in the range of 200 to 250 mL/min.
In the high flux dialysis, the blood flow rates are above 400 mL/min. For low flux as well as high flux
dialysis, clearance depends on extraction and therefore on k and k . These parameters in turn depend
D
U
on the type of membrane used.

5.4 MEMBRANES FOR DIALYSIS

The properties of the semipermeable membrane play a major role in dialysis. The membrane should have
high permeability to water and organic metabolites and at the same time should be able to retain plasma
proteins. In particular, the membrane should be able to remove middle molecules such as β -microglobulins
2
and advanced glycation end products (AGE), and at the same time should not cause any depletion of serum
albumin and other proteins. 7,24 In addition, the membrane should be biocompatible and blood compatible.
25
An ideal membrane does not adsorb blood proteins or hormones. C. P. Sharma provides an excellent
review of membranes for hemodialysis.
Cellulose, modified cellulose, and synthetic polymers are the three types of membranes used in
dialysis. Cellulose membranes were used initially as they have good permeability with uniform pore
25
size and are hydrophilic. Protein adsorption decreases with increasing hydrophilicity. However, cel-
lulose membranes are known for biocompatibility and hemocompatibility problems. 25–27 Cellulose
and regenerated cellulose membranes lead to the release of thromboxane, histamine, interleukin-1,
26
and tumor necrosis factor, etc. In addition, significant transient leucopenia has been observed with
these membranes. Cellulose is a long-chain molecule containing hydroxyl (OH) groups. The free
hydroxyl groups have been associated with the complement activation and leucopenia observed when
using cellulose or regenerated cellulose membranes. 27
Substituted cellulose has been developed to reduce the hemocompatibility problems associated
with cellulose. 25 Cellulose acetate (diacetate and triacetate) membranes are formed by bonding
acetate to the hydroxyl groups. This modified cellulose membranes have tertiary amino compounds