Biomedical Engineering Reference
In-Depth Information
DC
BIL
DZ
C
ALB
C
ALB
−C
BIL
!
C
BIL
K
0
A
LQ
Β
=
C
ALB
−C
BIL
−
(20)
where
A
is the membrane area,
L
the module length and
Q
is the volumetric flow rate.
Equations (19) and (20) can be integrated with the boundary conditions:
C
BIL
= C
Α,IN
C
BIL
= C
Β,IN
Z = 0
;
Z = L
(21)
B
B
Assuming that no albumin transfer occurs through the membrane, the total albumin con-
centration in the each phase is constant and equations (19)-(21) can be rewritten in terms of
dimensionless variables
X = C
BIL
/C
ALB
and
Ζ = Z/L
:
DX
Α
DΖ
X
Α
1−X
Α
−
X
Β
1−X
Β
K
0
A
Q
Α
C
ALB
=−
(22)
DX
Β
DΖ
X
Α
1−X
Α
−
X
Β
1−X
Β
K
0
A
Q
Β
C
ALB
=−
(23)
with the boundary conditions:
X
Α
= X
Α,IN
;
X
Β
= X
Β,IN
Ζ = 0
Ζ = 1
(24)
In SPAD or for a perfectly efficient dialysate regeneration system, the influent dialysate
is bilirubin-free (
X
Β
0
= 0
). In this case, the above equations show that, for an as-
signed bilirubin-to-albumin molar ratio in the feed, the fraction of bilirubin removed
/X
Α,IN
depends only on two dimensionless parameters:
Κ = K
0
A/Q
Α
C
ALB
,
and
1/Z = Q
Β
C
ALB
/Q
Α
C
ALB
. Fig. 3 reports a plot of module dimensionless clearance
X
Α,IN
−X
Α,OUT
C
Α,IN
−C
Α,OUT
C
Α,IN
CL
Q
Α
=
(25)
Vs.
1/Z
for different
Κ
and
X
Α,IN
values. Fig. 3 clearly shows that:
• the higher the albumin concentration in the solution to be dialyzed, the lower the
clearance that can be obtained, since both the values of
1/Z
and
Κ
decrease.
• clearance increases with increasing
1/Z
, i.e. increasing the dialysate flow rate or its
albumin concentration; nevertheless a clearance limiting value,
CL
∞
, is obtained for
1/Z≫1
.
CL
∞
can be determined by the solution of the following equation
CL
∞
Q
Α
1−
CL
∞
Q
Α
X
Α,IN
+ ln
=−Κ
(26)
From a practical point of view, if
1/Z
is above 1-1.5, a further increase of this pa-
rameter should produce a negligible improvement of module clearance.
• substantial improvement can be obtained with larger
K
0
A
values, i.e with larger mod-
ules or more permeable membranes.
