Biomedical Engineering Reference
In-Depth Information
single pass (SPAD) or closed loop with albumin regeneration (MARS). The beneficial ef fect
of albumin in the dialysate for bilirubin removal in conventional renal replacement therapy
has also been suggested (Chawla et al., 2005).
Starting from the first work of Stange and Mitzner (1993) that suggested the use of
albumin dialysis for the treatment of liver failure, several studies have been devoted to the
in-vitro and in-vivo investigation of this detoxification process (for instance, Dammer et
al., 2007 and other papers in the same collection). Despite the big amount of literature
on this subject, only few papers report data that can be used for a quantitative analysis of
the process and for design purposes. Experimental data on albumin-dialysis of bilirubin in
a two-compartment closed-loop system are reported by Stange et al. (1993, 1996): these
authors compare the behavior of a standard polysulphone and a polyammide membrane pre-
treated with albumin. Abe et al. (2004) compare the performance of different membrane
modules for the removal of bilirubin. The rationale of albumin bound toxin removal by
albumin dialysis has been discussed byPatzer (2006), while Meyer et al. (2004) report a
theoretical model to evaluate albumin-bound toxin clearance in conventional hemodialysis.
In vitro transport of bilirubin and other protein bound compounds has been analyzed by
Raff et al. (2006).
In order to evaluate the bilirubin clearance obtained by an albumin dialysis device, a
mathematical model is presented here that combines the bilirubin transfer rate across the
membrane with the bilirubin mass balance in the feed and dialysate solution.
As for bilirubin transfer, diffusion through the membrane is considered as the rate-
controlling step. In the framework of a diffusion-solution model, bilirubin transmembrane
flux is given by
J
BIL
=
D
BIL
Δ
C
M,Α
BIL
−C
M,Β
(17)
BIL
where superscript
M
refers to the membrane phase;
C
M,Α
and
C
M,B
BIL
are the bilirubin concen-
trations in the membrane at the interface with phase
Α
and
Β
, respectively;
D
BIL
is bilirubin
diffusivity inside the membrane and
Δ
is the membrane thickness. Assuming equilibrium
conditions (equations 15 or 16) at the interfaces, the bilirubin flux may be rewritten in terms
of bilirubin and albumin concentrations in the liquid phases as
BIL
!
!
C
AB
C
A
C
BIL
C
ALB
−C
BIL
C
AB
C
BIL
J
BIL
= K
0
C
A
−
= K
0
C
ALB
−C
BIL
−
(18)
where
K
0
= S
BIL
D
BIL
/Δ
is a characteristic transport coefficient of the membrane. It is worth
noting that the driving force for bilirubin transfer is the difference between bilirubin to free
albumin ratios in the two phases and, obviously, the flux becomes zero when equilibrium
is achieved. At low bilirubin concentration (
C
ALB
≫C
BIL
) the driving force reduces to the
difference between bilirubin to albumin molar ratios, as suggested by Steiner et al. (2004)
and Dammeir et al. (2008) on the basis of experimental evidence.
The model of the albumin dialysis module is then obtained by combining the mass
transfer rate equation (18) with bilirubin mass balances in the feed (
Α
) and dialysate (
Β
);
for a counter-current hollow fiber module, the result is
!
C
BIL
C
ALB
−C
BIL
DC
BIL
DZ
C
BIL
K
0
A
LQ
Α
=
C
ALB
−C
BIL
−
(19)
