Open Journal of Nephrology, 2013, 3, 161-167
http://dx.doi.org/10.4236/ojneph.2013.33029 Published Online September 2013 (http://www.scirp.org/journal/ojneph)
Study of Dialyzer Membrane (Polyflux 210H) and Effects
of Different Parameters on Dialysis Performance
Md Shihamul Islam*, Jerzy Szpunar
Department of Mechanical Engineering, University of Saskatchewan, Saskatoon, Canada
Received May 22, 2013; revised June 20, 2013; accepted July 13, 2013
Copyright © 2013 Md Shihamul Islam, Jerzy Szpunar. This is an open access article distributed under the Creative Commons Attri-
bution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly
cited.
ABSTRACT
Problems frequently encountered in kidney malfunction include abnormal fluid levels in the body, increased acid levels,
abnormal levels of Urea, Glucose, Endothelin, β2-Microglobulin and Complement Factor D. Parameters characterizing
the structure of dialyzers are very important because they decide overall clearance of toxin molecules and at the same
time should allow retaining useful molecules in the blood. In this paper, a cross sectional image of the dialyzer mem-
brane with details of the porosity is presented. A multilayered membrane model with different porosity for each layer,
describes the actual structure of Polyflux 210H membrane. This model is developed using Finite Element Software—
COMSOL Multiphysics 4.3. A blood flow with substances like—Urea, Glucose, Endothelin, β2-Microglobulin, Com-
plement Factor D and Albumin is introduced. For a certain blood flow rate, the toxins diffuse through the membrane
and on the other side of the membrane a dialysate flow removes the toxins. Here, different parameters, such as flow rate
of blood and dialysate, length and radius of the fiber are changed to simulate how these changes affect toxin clearance
and the removal of useful molecules.
Keywords: Simulation, Dialysis; Axisymmetric Model; 3-Layered Membrane; Effective Diffusivity; Parameters;
COMSOL Multiphysics 4.3
1. Introduction
A substantial amount of research has been performed
regarding homogeneous dialyzer membranes. These ho-
mogeneous dialyzer membranes are mostly made of cel-
lulose. These membranes have a uniform pore structure
from the inner to the outer side of the membrane. The
surface of such membranes was not very biocompatible,
because exposed hydroxyl groups would activate com-
plement in the blood passing by the membrane. There-
fore, these days dialyzer membranes are made from syn-
thetic materials, using polymers such as polyarylether-
sulfone, polyamide, polyvinylpyrrolidone, polycarbonate
and polyacrylonitrile. These synthetic membranes acti-
vate complement to a lesser degree than cellulose mem-
branes [1]. They have a structure which is known as
asymmetric. This actually means that the shape of a pore
gradually changes from inner to outer surface of the
membrane. Synthetic membranes can be made in either
low- or high-flux configuration, but most are high-flux.
Polyflux 210H is an example of such high flux asymmet-
ric polymer membrane. Sakai et al. [2] studied and cap-
tured the images of inner and outer surface images of
such an asymmetric membrane. They calculated the sur-
face porosity based on those photomicrographs. These
give an idea of the surface porosity. But to what extend
that porosity continues from one surface to another is not
sure. Taking cross sectional image of the membrane and
calculating the porosity from that image allow a better
description of it. Experimental studies [3,4] have been
done to determine whether increasing the dialysate or
blood flow rate leads to better clearance or not. But these
studies did not consider the structure of the membrane.
Also these studies were limited to clearance of Urea only.
A reasonable concern for doctors, in these days, is
whether the necessary elements like Albumin are dif-
fused through the membrane during the dialysis or not.
Most of the experimental studies are done with dialyzers
which are commercially available. So they actually give
a comparison between different dialyzers. But which
parameters of dialysis process are really important to
have a better overall clearance of toxin molecules and at
the same time retain useful molecules is not clear. Also
*Corresponding author.
C
opyright © 2013 SciRes. OJNeph

M. S. ISLAM, J. SZPUNAR 162
how the change of those parameters will affect the clear-
ance is important and will be investigated in this work.
2. Polyflux 210H Dialyzer Membrane
In one dialyzer of Polyflux 210H, there are approxi-
mately 12,000 fibers. These fibers are made of Polyamix
which is a blend of Polyarylethersulfone, Polyvinylpyr-
rolidone and Polyamide [5]. Polyflux 210H fiber has a
porous structure. A single fiber has a length of 270 mm.
The fibers used in this research were fixed using a
mixture of 2.5% glutaraldehyde and 2% paraformalde-
hyde in a 0.1 M phosphate buffer. A series of mixtures of
pure ethanol and distilled water in different ratios were
used to dehydrate the fibers. To investigate the internal
surface of the fibers, some fibers were placed on a carbon
double sided adhesive scanning electron microscopy
(SEM) tape glued from the other side to an SEM stub.
The SEM stub with the fibers glued to its surface was
transferred for viewing under the stereoscopic optical
microscope. The fiber walls were dissected longitudi-
nally using a surgical scalpel. Then a 250 Å layer of gold
(purity 99.991%) is applied to render the surfaces of the
capillaries conductive for observation under the Scanning
Electron Microscope (SEM) and the Field Emission
Scanning Electron Microscope (FESEM). The SEM used
here is a Joel-6010LV and the FESEM is a SU6600 Hitachi.
Figure 1. Longitudinal image of a fiber.
At first the longitudinal image (Figure 1) of the fiber
is taken from the outside.
A cross section of the fiber is showed in Figure 2.
Then images of the outer and inner side of the mem-
brane are taken to get an idea of the pore size and poros-
ity. The outer surface has a range of pore size which var-
ies between 0.45 μm to 20.40 μm (Figure 3).
But for the inner surface the range is between 34 nm
and 45 nm (Figure 4). Then to get a better idea of the
porosity changes, cross sectional images of the mem-
brane are taken. This gives a clear idea of the porosity
changes across the thickness.
Figure 2. Cross section of the fiber.
In Figure 5, a dialyzer membrane having a total thick-
ness of 45 μm is divided into three different layers to
calculate the porosity for each of the layer. The first layer
(thickness of 8 μm) has a porosity of around 0.1, second
layer (thickness of 12 μm) has a porosity of around 0.27
and third layer (thickness of 25 μm) has a porosity of
around 0.4. Several photomicrographs from each of the
layers are taken to calculate the porosity and then an av-
erage value of porosity is introduced for each layer.
3. Method of Developing Model
The configuration of a modern hollow fiber dialysis as-
sembly can be seen in Figure 6 . The blood flows through
the fibers while the dialysate flows over the capillaries in
a counter-current manner similar to a shell and tube heat
exchanger. In this application the flow is laminar. Figure 3. Outer surface of the dialyzer membrane.

M. S. ISLAM, J. SZPUNAR 163
Figure 4. Inner surface of the dialyzer membrane.
Figure 6. Diagram of dialysis hollow-fiber dialyzer.
Figure 5. Cross section of the membrane.
Figure 7 shows the three sections of the axisymmetri-
cal domain: the domain on the left represents the blood
flow in the fiber, the small domain in the middle with
three layers represents the membrane, and the domain on
the right represents the outer dialysate flow in the shell.
4. Equations
The following simplified PDE (Partial Differential Equa-
tion) describes the convective and diffusion processes in
the blood and the dialysate [6].

0
ii i
Dc cu 

(1)
where ci denotes the concentration of the toxin (mol/m3)
in the respective phase, D denotes the diffusion coeffi-
cient (m2/s) in the liquid phases and u denotes the veloc-
ity (m/s) in the respective liquid phase.
For different toxins the diffusion coefficient is differ-
ent and it can be calculated from [7] Figure 7. Model Geometry with R1, R2, R3.

M. S. ISLAM, J. SZPUNAR 164
Table 1. Six molecules with their molecular weight, diame-

0.552
4
1.62 10DMW


 (2) ter and diffusion coefficient.
where MW is the molecular weight of the respective
toxin. Molecule Molecular Diameter (nm) Diffusion
(
Both the blood and dialysate flow is considered fully
developed laminar flow. For an inlet velocity of blood
along the axial direction [8],
2
2
1 1
21
B
B
Qr
vR
Rn 











 



,0 ei i
Dc 
Dk
(3)
where QB is the volume flow rate of blood, R1 is the in-
ner radius of the hollow fiber, r is the radial coordinate
and n is the number of fibers in a dialyzer which is
12,000 for Polyflux 210H dialyzer.
For the phenomenon of diffusion through the mem-
brane, the following equation has been used-

(4)
where ci denotes the concentration of the molecules
(mol/m3) in the respective phase, D denotes the diffusion
coefficient (m2/s) of the molecules and De denotes the
effective diffusion coefficient of the molecules in the
porous media.
The term effective diffusivity is defined [9] as

e
DDfqSA (5)
s
p
r
qr  (6)

35
5
1 2.10502.08651.70680.72603
1 0.758
57
qq q
fq q
 

6
q

q
(7)

2
1
D
S (8)
Where D is the diffusion coefficient of molecule, f(q) the
friction coefficient, SD the steric hindrance factor at the
pore inlet in diffusion, Ak the membrane porosity, q is the
ratio of solute radius rs to pore radius rp. Here, the poros-
ity values of the three layers of the membrane are used
for Ak.
The six molecules that are considered in this paper are
listed in Table 1 with their molecular weight [10], di-
ameter [11] and diffusion coefficient.
5. COMSOL Multiphysics 4.3
weight (Da) coefficient
x 10-8 cm2/s)
Urea 60 0.48 1690.35
Glucose 180 1.0 921.73
E 4
β2- in
ndothelin282.8 2.60 160.25
Microglobul11800 3.88 91.59
Complement
Factor D
Albumin
24000 5.12 61.89
66000 7.8 35.41
and boundary conditions, simulations are done for chang-
e rate of Urea at different blood flow
be concluded that the clearance
ra
7. Results
of Blood Flow Rate on Clearance
For d flow rate of QB = 300, 400 and 500 ml/min
, with the increasing
bl
7.2. Effects of Dialysate Flow Rate on Clearance
The flow rate, QB= 400 ml/min is kept constant
n-
st
7.3. Effects of Length of the Dialyzer Fiber on
The er fiber is varied from 270 to 540
es of different parameters. A post processing result is
showed in Figure 8.
6. Validation
ncAt first, the cleara
rate is compared with the experimental results provided
by the manufacturer [5].
From Figure 9, it can
te of Urea at different blood flow rate is in good
agreement with the data provided by the Polyflux 210H
manufacturer.
7.1. Effects
Rate
the bloo
and dialysate flow rate of QD = 500ml/min, the clearance
rate for six molecules is calculated.
As it can be seen from Figure 10
ood flow rate, the clearance rate of both Urea and Glu-
cose increase rapidly. Specially, for Urea, when the
blood flow rate increases from 300 to 500 ml/min, the
clearance rate almost gets doubled. And from Figure 11,
it is evident that the clearance rate of Albumin remains
almost constant.
Rate
blood
and the dialysate flow rate, QD is gradually increased.
From Figures 12 and 13, it can be said that at a co
ant blood flow rate, the increasing dialysate flow rate
ensures further clearance of Urea and Glucose.
COMSOL Multiphysics 4.3 is used for developing and
simulating the model of Polyflux 210H dialyzer. COM-
SOL Multiphysics is a finite element analysis, solver and
simulation software / FEA Software package for various
physics and engineering applications, especially coupled
phenomena or multiphysics.
Clearance Rate
length of the dialyz
mm when QB = 300 ml/min and QD = 500 ml/min. After developing the model with necessary inlet, outlet

M. S. ISLAM, J. SZPUNAR 165
Figure 8. Concentration of Urea at both blood and dialysate
side along the membrane (axisymmetric).
Figure 9. Clearance of Urea for both experimental and
simulation cases at blood flow rate, QB = 300, 400 and 500
ml/min whereas dialysate flow rate, QD = 500 ml/min.
Figure 11. Clearance rate of Endothelin, β2-Microglobulin,
Complement Factor D and Albumin at different blood flow
rates when QD = 500 ml/min.
Figure 12. Clearance of Urea and Glucose at different
Dialysate flow rates when QB = 400ml/min.
Figure 13. Clearance of Endothelin, β2-Microglobulin, Com-
plement Factor D and Albumin at different Dialysate flow
rates when QB = 400 ml/min.
Figure 10. Clearance rate of Urea and Glucose at different
blood flow rates when QD = 500 ml/min.

M. S. ISLAM, J. SZPUNAR 166
From Figure 14, it can be seen that if the length of the
di
7.4. Effects of Radius of the Dialyzer Fiber on
The r fiber is increased from 0.1 mm
in
cl
alyzer fiber is increased, the clearance rate of Glucose
increases more rapidly than the clearance rate of Urea.
For Endothelin and β2-Microglobulin (Figure 15) the
clearance rate increases twice compared to the initial
condition. Meanwhile, the clearance rate of Albumin
does not change that much.
Clearance Rate
radius of the dialyze
to 0.2 mm when QB = 300 ml/min and QD = 500 ml/min.
From Figures 16 and 17 it is evident that the effect of
creasing radius of dialyzer fiber is similar to that of
increasing the length of the dialyzer fiber. However, if a
case is considered where the clearance rate of Albumin is
similar for length of 450 mm with a radius of 0.1 mm and
radius of 0.17 mm with a length of 270 mm dialyzer fiber.
From Table 2, it is evident that for the same level of
earance rate of Albumin (or loss of Albumin), the dia-
Figure 14. Clearance rate of Urea and Glucose at QB =
300ml/min and QD = 500 ml/min.
Figure 16. Clearance rate of Urea and Glucose at QB = 300
ml/min and QD = 500 ml/min.
Figure 17. Clearance of Endothelin, β2-Microglobulin, Com
able 2. Clearance rate of different molecules for two dia-
Length = 270 mm,
-
plement Factor D and Albumin at QB = 300 ml/min and QD
= 500 ml/min.
T
lyzer fibers consisting length = 450 mm, radius = 0.1 mm
and length = 270 mm, radius = 0.17 mm.
Length = 450 mm,
Radius = 0.1 mm Radius = 0.17 mm
Ura e281.1 271.3
G
E
β2-in
C
lucose 234.1 221
ndothelin 67.21 61.8
Microglobul37.97 35.05
omplement Factor D24.04 22.92
Albumin 10.67 10.7
zer fiber with relatively higher length and lower radius ly
shows better clearance of Urea, Glucose, Endothelin,
β2-Microglobulin and Complement Factor D than the
dialyzer fiber with relatively higher radius and lower
length.
Figure 15. Clearance of Endothelin, β2-Microglobulin, Com-
plement Factor D and Albumin at QB = 300 ml/min and QD
= 500 ml/min.

M. S. ISLAM, J. SZPUNAR 167
clusion
of Urea at different blood flow rate is
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