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Artificial liver devices A chemical engineering analysis.

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ASIA-PACIFIC JOURNAL OF CHEMICAL ENGINEERING
Asia-Pac. J. Chem. Eng. 2011; 6: 639–648
Published online 17 June 2010 in Wiley Online Library
(wileyonlinelibrary.com) DOI:10.1002/apj.464
Research article
Artificial Liver Devices: A Chemical Engineering Analysis
M. C. Annesini, V. Piemonte* and L. Turchetti
Department of Chemical Engineering Materials & Environment University of Rome, ‘‘La Sapienza’’ via Eudossiana 18, 00184 Rome, Italy
Received 24 September 2009; Revised 15 April 2010; Accepted 27 April 2010
ABSTRACT: All the most widely used liver support devices implement the same elementary unit operations, mainly
membrane separation and adsorption, to remove albumin-bound toxins. Mathematical modeling of these operations is a
well-consolidated knowledge of chemical engineering, and the evaluation of the performance of these apparatus can be
confidently carried out once equilibrium conditions and transport phenomena kinetics are known. In this work, a devicefocused analysis of liver support devices is presented, with the aim of providing a framework for the quantitative and
semiquantitative assessment of their performance. The analysis is based on simple mathematical models of the single
unit operations implemented in the detoxification processes. A preliminary validation of the models against data obtained
during a clinical molecular adsorbent recirculating system (MARS) session, and referring to bilirubin detoxification
was performed; the results showed that the models used are consistent and possess a very good order-of-magnitude
prediction capability.  2010 Curtin University of Technology and John Wiley & Sons, Ltd.
KEYWORDS: albumin dialysis; artificial liver device; mathematical model; adsorption
INTRODUCTION
Hemodialysis and related processes like hemofiltration
and hemodiafiltration are widely used for the therapy
of kidney failure. In the last 20 years, several works
have been devoted to the analysis of these processes
and, nowadays, mathematical modeling of hemodialysis units as well as patient-unit systems during a clinical
treatment is a well consolidated practice[1] ; indeed this
theoretical effort largely contributed to improve the performance of these devices and the efficiency of the clinical treatment, also reducing the negative side effects.
As for artificial liver devices, the scenario is completely different. First, liver provides for several physiological functions which cannot be replaced by a simple
artificial device (not biologically supported) so that,
until now, artificial extracorporeal devices can only
make up for the lack of liver detoxification[2,3] ; therefore, these devices only suit for the time-limited clinical
treatment of acute and acute-on-chronic liver failure or
to bridge the patient to an organ transplantation. As a
second and more important point, blood detoxification
needed in support therapies is more difficult in liver
failure, rather than kidney failure: as a matter of fact,
liver failure involves the accumulation of both small
*Correspondence to: V. Piemonte, Department of Chemical Engineering Materials & Environment University of Rome “La Sapienza”
via Eudossiana 18, 00184 Rome, Italy.
E-mail: piemonte@ingchim.ing.uniroma1.it
 2010 Curtin University of Technology and John Wiley & Sons, Ltd.
Curtin University is a trademark of Curtin University of Technology
hydrophilic toxins and albumin-bound toxins in plasma.
While a conventional dialysis (CD) over rather selective
membranes can remove the former class of toxins, both
effectively and selectively, more complex processes are
required to remove the toxins of the latter class without
depleting blood of valuable macromolecules.
At present, the most widely used artificial liver
devices are the molecular adsorbent recirculating system
(MARS) (Teraklin AG, Rostok, Germany now Gambro
AB, Lund, Sweden)[4 – 7] and the Prometheus (Fresenius
Medical Care AG, Bad Homburg, Germany)[8 – 11] (see
Fig. 1). In spite of the differences between these processes, under a chemical engineering point of view,
it is evident that all of them implement the same
unit operations, mainly including membrane separation
and adsorption. More specifically, MARS implements
the albumin-dialysis process that consists in dialysis
of blood against an albumin rich solution (albumin
dialysate) that is, in turn, depurated before being recirculated to the main dialysis unit. Albumin dialysate
regeneration is carried out by three operation in series,
each aimed at removing a different class of toxins: CD
against a saline solution, fixed-bed adsorption on activated carbon (AC) and fixed-bed adsorption on anionic
resin (AR). Modeling of all the aforementioned unit
operations is a well-consolidated knowledge of chemical engineering, so that the evaluation of the performance of these apparatus can be confidently carried out
once equilibrium conditions and transport phenomena
kinetics related to the processes considered are known.
640
M. C. ANNESINI, V. PIEMONTE AND L. TURCHETTI
(a)
Asia-Pacific Journal of Chemical Engineering
(b)
Figure 1. Liver support devices. (a) MARS (AD, albumin dialyzer; CD, conventional dialyzer;
AR, anionic resin column, AC, activated carbon column); a similar scheme, excluding
dialysate regeneration and recirculation, applies to SPAD (Single Pass Albumin Dialysis).
(b) Prometheus (NR, polymeric nonionic resin column; AF, plasma fractionator; HF, high
flux dialyzer); adsorption is performed directly after plasma filtration on a polysulfone
membrane.
An extensive literature on the clinical performance of
liver support devices is presently available,[12 – 14] while
only few works are aimed at studying the fundamental phenomena occurring in the devices and acquiring information devoted to a rational design of these
systems.[15,16]
In this work, a device-focused analysis of liver support devices is presented, with the aim of providing
a framework for the quantitative and semiquantitative assessment of their performance. The analysis is
based on simple mathematical models of the single unit
operations implemented in the detoxification processes.
A preliminary validation of the models against data
obtained during a clinical MARS session and referring
to bilirubin detoxification was performed; the results
showed that the models used are consistent and possess
a very good order-of-magnitude prediction capability.
It is certainly evident that all the biomedical devices,
that work on living biological systems, are very complex and cannot be studied exclusively by means of
mathematical methods and computer simulations; nevertheless, the approach presented in this paper can be
useful for a preliminary assessment of existing liver
support devices, in order to compare different configurations and operating conditions, detect and address
design issues and, possibly, design new, more efficient, devices.
the performance of each detoxification process respect
to a given toxin is evaluated in terms of detoxification
efficiency η, defined as the fractional reduction of the
toxin concentration that is achieved by the process
η=
in
out
− ctox
ctox
in
ctox
(1)
where ctox is the toxin concentration and superscripts
in and out refer to process inlet and outlet conditions,
respectively.
From the definition (1), it can be easily shown that
the overall efficiency ηo of n detoxification processes
in series is given by
ηo = 1 −
n
(1 − ηi )
(2)
i =1
where ηi is the detoxification efficiency of the i th
process.
The following sections present simple models for
the evaluation of the efficiency of the detoxification
units most commonly included in liver support devices,
namely membrane units (both for conventional and
albumin dialysis) and fixed-bed adsorption columns.
Finally, the expressions of the efficiencies of the single
units are combined to evaluate the overall efficiency of
an albumin dialysis process with regeneration.
MATHEMATICAL MODELING
General approach
Membrane units
Artificial liver support devices implement a single or a
combination of unit detoxification processes whose aim
is to remove a toxin from a liquid stream. In this paper,
Membrane processes are widely used for blood detoxification, both for the treatment of kidney and liver
failure. Hollow fiber modules containing 10 000–15 000
 2010 Curtin University of Technology and John Wiley & Sons, Ltd.
Asia-Pac. J. Chem. Eng. 2011; 6: 639–648
DOI: 10.1002/apj
Asia-Pacific Journal of Chemical Engineering
ARTIFICIAL LIVER DEVICES ANALYSIS
fibers with very high specific surface area (1 − 2 m2 ;
50–150 ml priming volume) are used.[1] Low molecular weight solutes are primarily removed by diffusion
through low flux membranes operating without significant transmembrane solvent flux; on the other hand,
convection is found to be useful for the removal of
average and high molecular weight solutes in high flux
modules operating with large ultrafiltration rate. In liver
support devices, dialysis is applied to purify blood
against a dialysate solution, or to regenerate a dialysate
solution against a secondary dialysate. In any case, subscript B will be hereafter used for quantities related to
the solution that must be purified, while D will be used
for quantities related to the cleansing solution.
Referring to a pure dialysis process, with no solvent
flux across the membrane, the overall performance of
a membrane module is usually described in terms of
clearance, CL, and dialysance, DL, defined as:
in
out
ctox,B
− ctox,B
DL = QB
in
ctox,B
Js = P (ctox,B − ctox,D )
x =0
in
out∗
ctox,B
− ctox,B
DL = QB
(3)
where Q is the volumetric flow rate, subscript B refers
out∗
is the
to the stream to purify (usually blood); ctox,B
limiting toxin concentration that can be theoretically
obtained in the outlet stream, i.e. the toxin concentration
at thermodynamic equilibrium with the inlet dialysate
stream. While the clearance is a measure of the efficiency of the detoxification process, the dialysance is
related to the intrinsic module efficiency; in fact, the
ratio DL/QB is a measure of the approach to the maximum theoretical detoxification that can be obtained with
particular operating conditions. Of course, clearance and
dialysance coincide if fresh dialysate is fed to the membrane module (cD,in = 0), like in the case of single pass
dialysis.
Conventional dialysis of free toxins
Mathematical models of CD units for simple watersoluble toxins, assuming no solvent flux across the
membrane and countercurrent flow of blood and
dialysate, are well consolidated in the literature[1] ; these
models are obtained by coupling the differential mass
balance equation for the toxin in the two liquid streams
(here b stands for the membrane area per unit length of
the module)
dctox,B
dctox,D
= QD
= −Js b
QB
dx
dx
in
ctox,B = ctox,B
in
x = L cD = ctox,D
(6)
to obtain the following expression for the dialysance of
the membrane module:
= QB ηdial
in
out
ctox,B
− ctox,B
(5)
where P is the overall mass transfer coefficient including blood-side, dialysate-side and membrane mass
transfer resistance.
By substituting Eqn (5) into Eqn (4), a set of two
differential equations is obtained, that can be integrated
with the boundary conditions
1 − exp[R(1 − Z )]
Z − exp[R(1 − Z )]
(7)
where Z = QB /QD e R = P A/QB , A being the membrane area. It is worth noting that Z is a dimensionless
parameter that depends only on the operating conditions, while R includes information on the membrane
characteristics; more specifically, R gives a measure of
the ratio of toxin transfer rate across the membrane to
toxin axial convection rate.
Figure 2 shows DL vs 1/Z plots corresponding to
different R values. It can be seen that a limiting
dialysance value, DL∞ , is attained for high dialysate-toblood flow rates, i.e. for negligible toxin concentration
in the dialysate:
DL∞ = QB (1 − e −R )
(8)
1
R=0.1
R=0.5
R=1
R=2
0.75 R=10
DL/QB
CL = QB
toxin concentrations in the solution to be detoxified and
dialysate, so that the driving force for toxin transfer is
simply the difference in toxin concentration between the
two liquid phases; therefore:
0.5
0.25
(4)
and the expression of the toxin flux across the membrane. For simple water-soluble toxins, which do not
interact with other components in the system, the thermodynamic equilibrium condition corresponds to equal
 2010 Curtin University of Technology and John Wiley & Sons, Ltd.
0
0
0.5
1
1.5
2
2.5
3
QD/QB
Figure 2. Dialysance for free toxins.
Asia-Pac. J. Chem. Eng. 2011; 6: 639–648
DOI: 10.1002/apj
641
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M. C. ANNESINI, V. PIEMONTE AND L. TURCHETTI
Asia-Pacific Journal of Chemical Engineering
while for low 1/Z , DL approaches a value DL0 such
that
(9)
DL0 = QD
corresponding to an outlet dialysate stream in equilibrium with inlet blood.
Dialysis of albumin-bound toxins
In artificial liver devices, removal of albumin-bound
toxins is also required. In this case, CD is definitely
ineffective[17] and albumin dialysis was introduced by
adding a toxin binder, i.e. albumin, to the dialysate
in order to lower the free toxin concentration in the
dialysate solution and, therefore, enhance the toxin
concentration gradient across the membrane.
Therefore, it is useful to extend the model of the
dialysis module to such class of toxins in order to
evaluate the performance of conventional or albumindialysis process. For the sake of simplicity, toxins that
form 1 : 1 complex with albumin will be considered:
A+T AT
KB =
cAT
cA cT
(10)
where KB is the binding equilibrium constant, cA and
cT stand for free albumin and free toxin concentrations, respectively, while cAT is the albumin–toxin complex concentration. Total toxin and albumin concentrations are given as ctox = cT + cAT and calb = cA + cAT ,
respectively. To further simplify the problem, it can be
assumed that ctox calb , therefore in this case:
KB ctox
cAT
cAT = KB calb cT
cT calb
= cT (1 + KB calb )
(11)
and the toxin partition equilibrium between two liquid
phases at different albumin concentration is given by
ψ=
1 + KB calb,B
ctox,B
=
ctox,D
1 + KB calb,D
(12)
It is reasonable to assume that only the free toxin can
cross the membrane and no albumin flux or change in
blood or dialysate concentration occur in the membrane
module. The driving force for toxin flux through the
membrane can therefore be considered as the difference
between the blood-side and dialysate-side free toxin
concentrations:
Js = P (cT ,B − cT ,D ) =
P
(ctox,B − ψctox,D )
1 + KB calb,B
(13)
 2010 Curtin University of Technology and John Wiley & Sons, Ltd.
It can be proved (see Appendix A) that coupling
Eqn (13) with toxin mass balances (4), Eqn (7) is still
obtained with:
R
P A
=
QB (1 + KB calb,B )
1 + KB calb,B
QB 1 + KB calb,B
1 + KB calb,B
Z =
=Z
QD 1 + KB calb,D
1 + KB calb,D
R =
(14)
(15)
Therefore, Eqns (7) and (8) still apply to the calculation of dialysance of an albumin dialysis unit if R and
Z are substituted for R and Z , respectively.
Equations (14) and (15) show that R and Z are a
decreasing and increasing function of KB calb,B , respectively; as a consequence, DL is a decreasing function of
KB calb,B . This confirms that, all other conditions being
equal, it is more difficult to remove albumin-bound than
free toxins by CD. Albumin dialysis can indeed improve
the dialysance of albumin-bound toxins (Z can be lowered by increasing calb,D ); nevertheless, the limiting
value DL∞ , that is unaffected by calb,D (see eqns 8 and
14), can still be very low, especially for toxins characterized by a very high binding constant such as bilirubin
(KB 108 M−1 ),[18,19] for which mass transfer kinetics
across the membrane are likely to be the controlling
kinetic step in the albumin-dialysis process.
Adsorption units
Adsorption units are used in liver support devices to
remove toxins directly from blood or plasma, like
in hemoperfusion and plasmaperfusion devices, or to
regenerate the dialysate solution in recirculating devices
like MARS. In both cases, detoxification by adsorption
is performed on an albumin-concentrated liquid phase
and, depending on the adsorptive medium used, different classes of toxins can be removed, including both
free and albumin-bound toxins.[16,20 – 23]
Though some devices implement fluidized and
suspended-bed adsorption units,[24] fixed-bed is the
most common configuration used for the adsorption
units in liver support devices and, therefore, only fixedbed adsorption will be considered here.
Fixed-bed adsorption is a well-known unit operation of the process industry, and several mathematical
models of this process are available; furthermore, specific models for fixed-bed adsorption of albumin-bound
toxins from albumin-containing solutions have been
developed.[16,25] Though these models provide a thorough description of the process, they are quite complex
and require a numerical solution, so that they are not
suitable for the type of analysis presented in this paper;
for this reason, a simplified model will be presented
here. Before discussing this simplified model, the main
results reported in the literature about albumin-bound
Asia-Pac. J. Chem. Eng. 2011; 6: 639–648
DOI: 10.1002/apj
Asia-Pacific Journal of Chemical Engineering
toxin adsorption equilibrium and fixed-bed kinetics will
be briefly reviewed.
Details on the adsorption isotherm of bilirubin and
tryptophan on an ion exchange resin and AC are
reported by Annesini et al .[15,21] Those papers showed
that AR is a suitable adsorptive medium for bilirubin,
whereas AC has a higher affinity for tryptophan, but, in
both cases, the toxin-adsorbed amount decreases with
increasing albumin concentration in the liquid solution.
This effect is clearly due to the competitive binding of
toxins between albumin and the solid sorbent and, possibly, to other phenomena affecting adsorption capacity.
A general framework for the analysis of albumin-bound
toxins is also proposed in Ref. [21], in which apparent adsorption isotherms, expressed in terms of total
toxin concentrations, are obtained. For highly albuminbound toxins such as bilirubin, the apparent isotherm
has a Langmuir-like form, with parameters depending on albumin concentration; furthermore, for bilirubin adsorption on AC[21] , it has been obtained a linear apparent isotherm with a slope that decreases with
increasing albumin concentration.
Fixed-bed adsorption of albumin-bound toxins has
been previously investigated, considering operating
conditions similar to those used in MARS. More specifically, bilirubin adsorption on AR[16] and tryptophan on
AC[25] have been studied.
For these two toxin-sorbent systems, two opposite
kinetic regimes were observed; these two different
conditions will be hereafter referred to as ‘fast’ and
‘slow’ adsorption regime, respectively.
In the ‘fast’ adsorption regime (observed for the
tryptophan-activated carbon system) the characteristic
time of the toxin transfer from the liquid to the solid
phase is much shorter than the column residence time.
In this case, the column behavior is characterized by
a typical sigmoidal breakthrough curve, and the toxin
concentration in the column effluent is nearly zero
until complete saturation of the solid phase is reached.
In these conditions, the saturation of the solid phase
occurs progressively from the inlet to the outlet of the
column so that the axial toxin concentration profile in
the adsorbed phase is strongly nonuniform. A simple
model that describes the behavior of a column operating
in this regime in terms of detoxification efficiency is
therefore
1 t < tbt
ηads (t) =
0 t > tbt
∗
in
Mntox
/Qctox
where tbt =
is the column breakthrough
time, M the sorbent mass, Q the liquid phase volumetric
∗
the toxin adsorbed amount per unit
flow rate and ntox
sorbent mass in equilibrium with the feed solution.
From an engineering point of view, adsorption columns
of liver support devices should be operated in the
fast adsorption regime, in order to grant complete
toxin removal until saturation occurs. Furthermore, in
 2010 Curtin University of Technology and John Wiley & Sons, Ltd.
ARTIFICIAL LIVER DEVICES ANALYSIS
such regime, the only concern for the column design
is to ensure that the time needed to saturate the
solid phase, i.e. tbt , is longer than the duration of a
single treatment session. The column breakthrough time
depends strongly on the solid adsorption capacity that
is, in this regime, an important design parameter.
On the other hand, in the ‘slow’ adsorption regime
(observed for the bilirubin-AR system), the toxin transfer characteristic time is longer than the column residence time. As a consequence, the toxin concentration
in the column effluent is nonnegligible even in the early
operating-time of the column, when the solid phase
is still far from saturation. In this case, the saturation
of the solid phase proceeds in an rather uniform fashion throughout the column bed, so that the axial toxin
concentration gradient in the adsorbed phase is small.
Therefore, following a quasi-steady-state approach, the
steady-state toxin balance in the liquid phase, accounting for purely convective axial transport and toxin transfer to the solid phase
v
3
dctox
∗
+ (1 − ε)kc (ctox − ctox
)=0
dz
R
(16)
can be coupled with the transient toxin mass balance in
the solid phase
in
out
− ctox
)=M
Q(ctox
dntox
dt
(17)
In Eqns (16) and (17), ctox is the toxin concentration
∗
the toxin concentration in the
in the liquid phase, ctox
liquid phase at equilibrium with the solid phase, kc
the mass transfer coefficient, R the radius of adsorbent
particles, v the liquid superficial velocity, ntox the toxin
adsorbed amount per unit sorbent mass and ε is the bed
void fraction.
For the sake of simplicity, a linear adsorption
isotherm will be assumed, so that
∗
ntox = Kctox
(18)
where the adsorption equilibrium constant K is a
decreasing function of albumin concentration.
By substituting Eqn (18) into Eqn (17), a system of
two ordinary differential equations is obtained which
can be analytically integrated with the initial and
boundary conditions
t = 0 ntox = 0;
to obtain
out
ctox
in
ctox
t >0
z =0
in
ctox = ctox
(19)
t
= 1 − e− τ (1 − e−St )
(20)
where
St =
V
3
(1 − ε)kc ;
R
Q
τ=
KM
1
Q 1 − e −St
Asia-Pac. J. Chem. Eng. 2011; 6: 639–648
DOI: 10.1002/apj
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M. C. ANNESINI, V. PIEMONTE AND L. TURCHETTI
Asia-Pacific Journal of Chemical Engineering
and V is the column volume. It is worth noting that,
assuming a linear isotherm, a complex analytical solution of a rigorous model accounting for nonuniformity
of the adsorbed phase can be obtained[26] ; nevertheless,
Eqn (20) provides an excellent approximation of this
solution for values of St up to the order of unity. Indeed,
St gives a measure of the ratio of the toxin adsorption
rate to the toxin axial transport rate and, since Eqn (20)
was derived assuming slow adsorption regime, its validity is limited to low values of St.
As for the efficiency of the adsorption process, from
Eqn (20)
t
ηads (St, t/τ ) = (1 − e −St )e− τ
(21)
Eqn (21) shows that the efficiency of the adsorption
process has an initial, maximum value that depends
strongly on St and then decays exponentially with
time as adsorption equilibrium is approached. The time
constant τ is proportional to K : it is clear that, the
lower the adsorbed amount of toxin at equilibrium, the
faster the column saturation. Again, it is worth noting
that for albumin-bound toxins a decrease of K may
be caused by an increase of albumin concentration. In
Fig. 3, Eqn (21) is plotted for different values of St.
Albumin dialysis and regeneration
In recirculating systems like MARS, after extracting
toxins from blood, the albumin dialysate is regenerated
and recirculated to the albumin-dialysis unit. This
solution is clearly aimed at reducing the albumin
consumption and, therefore, the treatment cost. Since
toxins with different physicochemical properties are
removed from blood and transferred to the albumin
dialysate, different units are required to regenerate this
stream: in the case of MARS, the regeneration is
performed by one CD module, one activated carbon
column (AC) and one AR column in series. In order
to evaluate the performance of MARS albumin-dialysis
process, the efficiency of the regeneration line, ηreg , will
be considered first. To that end Eqn (2) can be applied:
ηreg = 1 − (1 − ηdial,CD )(1 − ηads,AC )(1 − ηads,AR )
(22)
The regeneration efficiency of each unit is different
for each toxin to be cleared. As for the elimination
of hydrophilic, low molecular weight toxins, such as
urea or creatinine, the most efficient unit is definitely
the secondary dialysis unit CD, while the adsorption
columns play a minor role; therefore, in this case ηreg ηdial,CD and the regeneration efficiency is almost timeindependent. On the other hand, high binding constant
toxins are virtually not removed by CD, so that the
regeneration efficiency is determined by the adsorption
columns and, therefore, is a decreasing function of time.
Lower binding constant toxins, such as tryptophan[28,29] ,
are removed both in the CD unit and in the adsorption
columns. It is worth noting that, if at least one ideal
regeneration unit with unit efficiency is present in the
regeneration system (i.e. a fast adsorption column that
produces a clean outlet stream until saturation of the
column is approached), a clean dialysate stream is
recirculated to the membrane module.
The efficiency of recirculating albumin-dialysis process, ηAD , can be obtained by combining the dialysance
of the albumin-dialysis module (DLAD ) with the effectiveness of the regeneration circuit (see Appendix B)
1
ηAD
1
0.8
0.6
ηads
644
calb
0.4
30 g/l
0.6 St
120 g/l
0.2
0
1.6
0
50
100
150
200
250
300
350
400
t (min)
Figure 3. Time evolution of the detoxification efficiency of
the adsorption column for different St numbers and albumin
concentrations in the dialysate solution. The bold line refers
to the basic case: St = 0.6, τ = 400 and calb = 30 g/l.
 2010 Curtin University of Technology and John Wiley & Sons, Ltd.
=
1 − ηreg
QD
+ Z
DLAD
ηreg
(23)
Equation (23) shows how the efficiency of the recirculating albumin-dialysis process depends both on
membrane properties and regeneration line efficiency.
For a high regeneration performance (ηreg → 1), the
overall system efficiency is controlled by the AD membrane properties, while, for a poor regeneration efficiency (ηreg → 0), ηAD is strongly affected by the regeneration performance.
As an example of application of Eqn (23), it is
possible to estimate the detoxification efficiency of
the MARS system with respect to bilirubin, that is
commonly considered a reference toxin for the evaluation of the performance of liver support devices.
Because bilirubin is strongly albumin-bound and negatively charged, its removal from the albumin dialysate
occurs almost exclusively in the AR column. Therefore
it may be assumed that ηdial,CD 0 and ηads,AC 0.
The results of the calculation are reported in Figs 4
and 5 along with the values of the parameters[15,16] used
Asia-Pac. J. Chem. Eng. 2011; 6: 639–648
DOI: 10.1002/apj
Asia-Pacific Journal of Chemical Engineering
ARTIFICIAL LIVER DEVICES ANALYSIS
rapidly and this causes a faster decay of the overall
system clearance with time.
0.06
St = 5
0.05
ηAD
0.04
ANALYSIS OF CLINICAL DATA
St
0.03
0.02
0.01
R0 = 0.06
0
0
50
calb,D = 100 g/l
100
150
200
Z0 = 1
250
St = 0.35
300
350
400
t (min)
Figure 4. Detoxification efficiency, with respect to bilirubin,
of a recirculating albumin-dialysis system (MARS): effect of
St number in the adsorption column.
0.06
calb,D
0.05
R0 = 0.06
St = 0.35
calb,D = 20 g/l
0.04
ηAD
Z0 = 1
In order to validate the considerations presented in the
previous paragraphs, preliminary data were obtained
during clinical MARS sessions.[27] Blood and albumin
dialysate samples (withdrawn at the points indicated
in Fig. 1) were collected and analyzed to measure
the concentration of albumin and bilirubin (Table 1).
Sample collection was performed before and at different
times after the beginning of the treatment. During the
treatment, the flow rates of the blood and dialysate
circuit were set to 170 ml/min, and the concentration
of albumin in the dialysate was about 100 g/l.
The data reported in Table 1 show that, although a
decrease of bilirubin plasma concentration was actually
observed, the efficiency of the treatment for the removal
of this toxin was very low during the session considered.
This can be most clearly shown by calculating the
experimental albumin-dialysis efficiency with respect to
bilirubin as follow:
ηAD =
0.03
0.02
0.01
calb,D = 200 g/l
0
0
50
100
150
200
250
300
350
400
t (min)
Figure 5. Detoxification efficiency, with respect to bilirubin,
of a recirculating albumin-dialysis system (MARS): effect of
albumin concentration in the dialysate.
for the calculation of ηads,AR and DLAD . The plots are
obtained considering a flow rate of 170 ml/min both in
the blood and albumin dialysate circuit.
Figure 4 shows the effect of the Stanton number St of
the AR column on the overall system performance. For
high St values, the column outlet stream is completely
regenerated and the system works with an almost
unitary efficiency, that is also fairly constant with time.
It is also interesting to discuss the effect of albumin concentration in the dialysate calb,D (figure 5): an
increase of this parameter determines an increase of ηAD
in the early treatment period, when adsorption columns
are far from saturation, and the membrane module performance controls the efficiency of the whole recirculating albumin-dialysis process; on the other hand,
when calb,D is increased, column saturation occurs more
 2010 Curtin University of Technology and John Wiley & Sons, Ltd.
QD c(1) − c(4)
QB
cpatient
(24)
where c(i ) is the toxin concentration measured at point
(i ) of the albumin dialysate circuit and cpatient is the
bilirubin concentration in patient’s blood samples (see
Fig. 1 and Table 1). The values obtained (see Table 1)
have an order of magnitude of 10−2 , in agreement with
the prediction of the model.
In order to test the model ability to describe the
time evolution of the system performance, Eqn (23)
was fit to the experimental data using R and St as
adjustable parameters (optimal values obtained: R =
0.035 ± 0.0002 and St = 0.52 ± 0.01). Figure 6 shows
that the calculated curve exhibits a very good agreement
Table 1. Total bilirubin concentration in patient’s blood
and albumin dialysate at different points of the MARS
circuit (see Fig. 1) measured during a clinical MARS
session.
Total bilirubin [mg/dl]
Patient
Point 1
Point 2
Point 3
Point 4
ηAD
Before
After 1 h
After 3 h
After 6 h
16.57
–
–
–
–
–
15.56a
1.3
1.3
1.2
0.8
0.032
13.74
1.6
1.6
1.5
1.2
0.029
11.48
1.1
1.0
0.9
0.9
0.018
a
Extrapolated on the basis of the time course of plasmatic
concentration.
Asia-Pac. J. Chem. Eng. 2011; 6: 639–648
DOI: 10.1002/apj
645
M. C. ANNESINI, V. PIEMONTE AND L. TURCHETTI
Asia-Pacific Journal of Chemical Engineering
with the experimental data. Clearly, a sound experimental validation of the models requires a higher number of experimental data; nevertheless, this preliminary
test showed that the model has a very good order-ofmagnitude prediction capability.
Furthermore, the comparison of concentrations measured at points 2, 3 and 4, confirms that, in the albumin
dialysate circuit, bilirubin is mainly cleared in the AR
column and, to a much lesser extent, in the AC column,
while the conventional dialyser is virtually ineffective
for the removal of this toxin. It is significant to point out
that the effluent of the resin column contains a nonnegligible bilirubin concentration even at early operating
times, when the sorbent is far from saturation. This
finding shows that the albumin dialysate is never completely cleared from bilirubin. As a consequence, the
device performance decreases during the treatment.
CONCLUSIONS
This paper presented the application of an engineering
analysis to liver support devices, with the aim of providing a framework for the quantitative and semiquantitative assessment of their performance. The performance
was evaluated in terms of detoxification efficiency with
respect to a given toxin, defined as the fractional toxin
concentration that is achieved by the device.
The analysis was based on simplified mathematical
models of the detoxification processes carried out by
liver support devices, even though, for some of the
systems considered, more rigorous models requiring a
complex analytical or numerical solution are available.
The logic behind this choice was to obtain simple
analytical solutions that are more readily interpretable
and to focus on the approach and physical implication of
the results rather than on the mathematics. Furthermore,
0.06
0.05
0.04
ηAD
646
0.03
0.02
0.01
0
R0 = 0.035
0
50
100
calb,D = 100 g/l
150
200
Z0 = 1
250
300
St = 0.52
350
400
t (min)
Figure 6. Comparison between experimental and calculated recirculating albumin-dialysis process efficiency. Solid
line, mathematical model; circles, experimental data.
 2010 Curtin University of Technology and John Wiley & Sons, Ltd.
in many relevant conditions, the simplified models
used to provide an excellent approximation of the
solution of the more rigorous models and, in any case,
account for all the essential features of the modeled
processes. Following a typical bottom–up approach,
the models were built starting from the description
of the elementary processes occurring in the device
units, and seeing a complex detoxification process as
a combination of elementary processes.
The models were subsequently used to calculate the
efficiency for bilirubin removal of an albumin dialysis
recirculating device such as MARS with different
operating conditions. The analysis was focused on
bilirubin removal, because this toxin is an important
marker of the clinical state of liver failure patients
and can also be considered as representative of a wide
class of strongly albumin-bound toxins. This approach
proved to be helpful in gaining a deeper insight into
the working principles of liver support devices, leading
to the detection of design issues. In particular, the
possible existence of an optimum dialysate albumin
concentration emerged. The optimal value should be
determined as a trade-off between two opposing effects
of an increase of this parameter: the improvement
of albumin-dialysis efficiency on one hand, and the
impairment of dialysate regeneration by adsorption on
the other hand. The simulations, based partially on
parameters determined by in vitro experiments, showed
that, for a device operating in conditions similar to
those of MARS and referring to bilirubin, the effect
of a further increase of dialysate albumin concentration
would be an initial improvement of the detoxification
efficiency in the early treatment time, followed by
a more rapid decay of the device performance with
time. Furthermore, for such a device, the detoxification
efficiency did not exceed 5%, this poor performance
being limited by the slow bilirubin mass transfer across
the membrane.
Some preliminary experimental data obtained during
a MARS clinical session were also used for a first
validation of the approach presented in this paper to
the analysis of liver support devices. It is evident that a
sound experimental validation of the models requires a
higher number of experimental data; nevertheless, this
preliminary test showed that the model is consistent
with the time evolution of the system efficiency and has
a very good order-of-magnitude prediction capability.
The information presented in this paper can be helpful
for the optimization of existing liver support devices
and for the design of new ones; to that end, the
modularity of the model can be helpful to analyze and
compare with the same approach used here different
configurations and operating conditions. Finally, for a
complete assessment of the performance of a given
device, a similar analysis should be extended to the
clearance of other toxins.
Asia-Pac. J. Chem. Eng. 2011; 6: 639–648
DOI: 10.1002/apj
Asia-Pacific Journal of Chemical Engineering
NOMENCLATURE
MARS molecular adsorbent recirculating
system
Jv
JS
CL
DL
QB
QD
cBin
cBout
cBout,∗
cin,D
cout,D
calb,D
calb,B
b
P
L
A
KB
cA
cT
cAT
ctox
∗
ctox
cpatient
ntox
∗
ntox
kc
R
v
ψ
ρ
ηdial
ηads
ηreg
ηAD
ηo
H
Solvent flux across the membrane module, m/s
solute flux across the membrane module,
mol/m2 s
Membrane module clearance, m3 /s
Membrane module dialysance, m3 /s
Flow rate of the solution to be purified (dialysis),
m3 /s
Flow rate of cleansing solution (dialysis), m3 /s
Toxin concentration at membrane module inlet
(blood-side), mol/m3
Toxin concentration at membrane module outlet
(blood-side), mol/m3
Minimum toxin concentration obtainable in the
solution to purify (blood-side), mol/m3
Toxin concentration at membrane module inlet
(dialysate side), mol/m3
Toxin concentration at membrane module outlet
(dialysate-side), mol/m3
Albumin concentration in the dialysate solution,
mol/m3
Albumin concentration in the blood, mol/m3
Membrane area per unit length of module, m
Overall mass transfer coefficient of membrane
module, m/s
Membrane module length, m/s
Membrane area, m2
Albumin–toxin binding equilibrium constant,
m3 /mol
Free albumin concentration, mol/m3
Free toxin concentration, mol/m3
Albumin–toxin complex concentration, mol/m3
Toxin concentration in the liquid phase, mol/m3
Toxin concentration in the solid phase at equilibrium with the liquid phase, mol/m3
Bilirubin concentration in patient’s blood,
mol/m3
Toxin adsorbed amount per unit sorbent mass,
mol/g
Toxin adsorbed amount at the equilibrium with
the feed solution, mol/g
Column mass transfer coefficient, m/s
Sorbent particle radius, m
Liquid superficial velocity, m2 /s
Adsorption column bed porosity
Binding equilibrium parameter
Sorbent intrinsic density, kg/m3
Membrane module efficiency
Adsorption column efficiency
Regeneration circuit efficiency
Recirculating albumin-dialysis process efficiency
Overall efficiency
Column height, m
 2010 Curtin University of Technology and John Wiley & Sons, Ltd.
ARTIFICIAL LIVER DEVICES ANALYSIS
K
St
Q
V
M
tbt
Adsorption equilibrium constant, m3 /g
Stanton number
Adsorption column feed flow rate, m3 /s
Column volume, m3
Sorbent mass, g
Column breakthrough time, min
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Asia-Pac. J. Chem. Eng. 2011; 6: 639–648
DOI: 10.1002/apj
647
648
M. C. ANNESINI, V. PIEMONTE AND L. TURCHETTI
Asia-Pacific Journal of Chemical Engineering
APPENDIX A
For albumin bound toxins, mass balance equation (4)
may be rewritten as
dctox,B
QB
dx
∗
QD dctox,B
=
= −Js b
ψ dx
(A1)
Coupling these equations with the toxin flux through
the membrane (13) results in the same set of differential
equations (4) and (5), if QD /ψ and P /(1 + KB calb,B )
are substituted for QD and P , respectively.
According to the definition (1), the efficiency of the
recirculating albumin-dialysis system is:
ηAD
+
=
in
out
out
in
− ctox,B
) = QD (ctox,D
− ctox,D
)
QB (ctox,B
(B2)
last term in the right-hand side of (26) may be written
as
out∗
ctox,B
=
in
out
ctox,B
− ctox,B
in
ctox,D
ψQB
out
in
QD ctox,D
− ctox,D
(B3)
Finally, since the outlet dialysate of the albumindialysis module is the inlet to the regeneration line and
vice versa,
APPENDIX B
1
where superscript in and out refer to the inlet and outlet
of the albumin-dialysis module. Considering that the
toxin balance at the albumin dialysis module
in
ctox,B
in
ctox,B
−
out
ctox,B
out∗
ctox,B
in
out
ctox,B
− ctox,B
=
in
out∗
− ctox,B
ctox,B
in
ctox,B
−
in
ctox,D
out
ctox,D
−
in
ctox,D
=
1 − ηreg
ηreg
(B4)
and therefore Eqn. (23) is obtained.
out
ctox,B
(B1)
 2010 Curtin University of Technology and John Wiley & Sons, Ltd.
Asia-Pac. J. Chem. Eng. 2011; 6: 639–648
DOI: 10.1002/apj
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