917
Ind. Eng. Chem. Res. 1993,32,917-921
GENERAL RESEARCH New Hemodialysis Method Using Positively Charged Membrane Dialyzer and/or Polycation Dialysate Mitsuru Higa’ and Akira Kira The Institute of Physical and Chemical Research (RIKEN), Hirosawa 2-1, Wako-shi, Saitama, 351-01 Japan
Akihiko Tanioka and Keizo Miyasaka Department of Organic and Polymeric Materials, Tokyo Institute of Technology. Ookayama, Meguro-ku, Tokyo, 152 Japan
1. Introduction In the case of chronic renal disease, patients exhibit phosphate retention and, commonly, some degree of hyperphosphatemia. Many attempts to prevent these symptoms have been made (Hercz and Coburn, 1987). Although adsorbents, such as aluminum gels, are effective for removing phosphate (Clarkson et al., 1972). they have several adverse effects (Alfrey et al., 1976; Parkinson et al., 1981). Recently, attempts have been made to improve
complicated to describe in an analytical form, and there have been few theoretical studies. The simulations in the present study indicate systematically the dependenceof the ion permeability coefficient on both membrane charge density and the ionic composition of a dialysate solution. The simulations also lead to the proposal of new dialysis methods using a positively charged membrane dialyzer and/or polycation dialysate for high removal efficiency of serum phosphate. Ion permeability coefficients in the model system were preliminarily measured for membranes with various membranechhge densities in order to examine the prediction of the simulations. 2. Theory 2.1. System and Assumptions. Figure 1 shows a model system of hemodialysis. A charged membrane lies between two cella containing electrolyte solutions. The
ioniccomponentsofcellsIandIIarethesameasaddysate solution and human blood serum, respectively. Ionic *Towhom correspondence should he addressed.
Dialysuc solution
Blwd Serum
are always in a state of Donnan equilibrium with the same equilibrium constant for all ions. For simplicity of consideration, we also assume (0all electrolytes dissolve perfectly and ionic activity coefficients equal unity in both the solutions and the membrane and (g) the standard chemical potential of ions in the solutions is equal to that in the membrane. 2.2. The Permeability Coefficient of the ith Ion in the Model System. The permeability coefficient of the ith ion in the system is obtained from the following Drocedures (Hiaa et al., 1989, 1991). At one side of the membrane which is indicated by 8 (e = 1.11). the Donan equilibrium constant (K,) isa function of the ith ionic concentrations both at the membrane surface (q) and in the solution (C:) in the cell at sides:
= exp(-Fz,A&n/RT) =
c//c: = I, 11) (8
(1)
where zi is the valence of the ith ion; F, R,and Tare the Faraday constant, and the gascontstants, and the absolute temperature, respectively. A&,” is the Donnan potential differencebetween themembranesurfaceand thesolution in the cell at sides. The electroneutrality condition in the
08885885/93/2632-0917$04.00/0 0 1993 American Chemical Society
918 Ind. Eng. Chem. Res., Vol. 32, No. 5, 1993
membrane requires where zx and C, are the valence and the concentration of the membrane-fixed charge. Equation 3 is obtained by substituting eq 1 into eq 2: (3) K,is obtained by solving eq 3, and substitution of K,into eq 1 yields Cq. On the assumption of a constant electric field gradient in the membrane (Goldman, 1943), the permeability coefficient of the ith ion is given by
where d is membrane thickness; oi is the mobility of the ith ion; 0 = exp(-FA4diff/RT); A@diff is the diffusion potential difference between the two membrane surfaces. 0 is the solution of the following equation (Higa et al., 1990):
(B, + 4B2+ 9B3)O4+ (2B, + 4B2+ 9B3- A1)P3+ (2B, + 4B2- 2A1 - 4A2)P2- (2A1+ 4A2- B , + 9A3)P(A, + 4A, + 9A3)= 0 (5) where
and the superscripts z+ and z- mean z-valent cation and anion, respectively. Substitution of both Cy and C:' into eq 4 gives the permeability coefficient of the ith ion in the model system. Equation 4 implies that Pi is a function of both the membrane charge density and the ionic mobility in the membrane. For comparison of the dependence of ionic permeability on the membrane charge density, the membranes should possess not only different charge densities but also the same structure in order to have the same ionic mobility in the membranes. It is difficult, however, to prepare such membranes. Hence, we define PCR as PCR = Pi/Pu (6) where P, denotes the permeability coefficient of urea. We assume that P, is independent of membrane charge, because urea is an electroneutral solute. With this assumption, the normalization of Pi by P, will cancel out the dependence of Pi on membrane structure, and the PCR thus normalized expresses the ionic permeability only due to membrane charge. 3. Experiment 3.1. Samples. Membranes were cast from aqueous solutions of a mixture of PVA [poly(vinyl alcohol), Wako Pure Chemical Industries Ltd., DP = 20001 and PSSA [poly(styrenesulfonic acid), Asahi Chemical Industry Co. La.] for negatively charged membranes and from aqueous solutions of a mixture of PVA and PAAm [poly(allylamine), Nittobo Industries Inc.] for positively charged membranes, where the ratio of PVA to PSSA or to PAAm was changed for the control of the membrane charge density. In order to control the water content of the gel
Table I. Ion Component of Serum and the Three Dialysate Solutions: Acetate Dialysate, Bicarbonate Dialysate, and Polycation Dialysate acetate bicarbonate polycation ion blood serum dialysate species (mequiv/dm3) dialysate dialysate 130 140 50 Na+ 140 2 2 2 K+ 5 3 3 1 Ca2+ 2.5 1 1 1 Mg2+ 2 101 110 400 c1105 0 30 50 HCOx20 0 0 0 HP04'10 35 8 0 CH3COO0 400 polycation
membranes, these membranes were annealed at 160 "C for 20 min. The negatively charged membranes were crosslinked at 20 "C in an aqueous solution of 20% NazSOr, 1 % H2S04,and 0.1% glutarladehyde, and the positively charged membranes were cross-linked at 20 "C in an aqueous solution of 20% NaC1, 1% HC1, and 0.1% glutaraldehyde. PVA is a hydrophilic polymer, and its membranes have higher water content than commercially available ion-exchange membrames such as Selemion CMV. Consequently the conditions of assumptions c, e, and g are met better in the experiments using the PVA membranes than in those using the ion-exchange membranes. 3.2. Membrane Charge Density and Permeability Coefficient. Membrane potentials (A&) were measured as a function of KC1 concentrations in the two cells by using the same apparatus under the same conditions as described in the previous paper (Higa et al., 1990). From the measured membrane potentials, the membrane charge density (C,) was obtained in terms of (Teorell, 1935;Meyer and Sievers, 1936)
A4 = -y n [
C;' (C,2 + [2Cf12)1/2- C
,I-
cy (CX2+ [2Cf'I2p2- c, (C,2 y w l n [ (C,2
++ [2c:'12)'/2 - C,W [2Cf12)"2 - C,W ] (7)
where W = (WK - WCl)/(WK + ocl), and WK and w c 1 are the ionic mobility of potassium and chloride in a membrane, respectively. Parameters Wand C, were adjusted so that the left-hand side of eq 7 fits the experimental data of A$ at various KC1 concentrations. The permeation of ions and urea was measured by using the same apparatus and method as mentioned in a previous paper (Higa et al., 1990). The permeability coefficient was evaluated from the initial slope of the time-versusconcentration curve. 4. Results and Discussion 4.1. Simulations. 4.1.1. Positively Charged Membrane Dialyzer. Dialysis membranes in common use are neutral or charged slightly negative because a positively charged membrane adsorbs proteins in serum. Generally, ionic permeation across a membrane is affected by fixed charges in the membrane. In this section the ionic permeation in the model system for the bicarbonate dialysate is simulated as a function of membrane charge density. Parts a and b of Figure 2 show PCR as a function of the charge density for cations and anions, respectively. In these figures, a positive value of PCR means that the ion permeates from the dialysate solution side to the serum side, and vice versa. In Figure 2a, the permeation of cations across a negatively charged membrane is larger than across
J."
2.0 1.0
1
[,
I
(a)
I
I
Bicarbonate Dialysate (Cations)
I
-.-.-..._.
2'o I .o
-._
I
-0.25
I
0.0 Charge Density
(b)
- CI'
(a)
I
0.25
Acetate dialysate (Cations)
t
I
I
0.5
-0.25
[mol/dm3]
I
I
I
0.0
0.25
Charge Density
0.5
[moVdm']
Bicarbonate Dialysate (Anions) 2.0
1.o
1.o
0.0
ki 0.0
c2
I 1
).5
Charge Density
[moVdm']
-0.25
I
0.0
Charge Density
I
0.25
\
0.5
[mol/dm3]
Figure 2. Simulation of ion permeability coefficient ratio (PCR) as a function of the membrane charge density in the model system using the bicarbonatedialysate solution: (a)for cations; (b) for anions.
Figure 3. Simulation of PCR as a function of the membrane charge density in the model system using the acetate dialysate solution: (a) for cations; (b) for anions.
a positive charged one. In Figure 2b, both HC03- and CHaCOO- ions permeate to the serum side and their PCR increasewith increasingmembrane positive charge density. C1- permeates to the dialysate side, except for charge densities higher than 0.3 mol/dm3. This means that C1is transported against its concentration gradient because the concentration of this ion at the dialysate side is larger than that at the serum side. This uphill transport of C1occurs by the diffusion potential difference generating by the permeation of the other ions. The permeation of HPOd2-to the dialysate solution side increases with increasing membrane positive charge density. This result indicates that the removal property of serum phosphate in hemodialysis will be improved by using a positively charged membrane dialyzer. The problem of increased adsorption of proteins on a positively charged membrane can be avoided by a compositemembrane. The compositemembrane can be made by pasting a positively charged and a neutral membrane together or by coating a positively charged membrane with neutral polymer. 4.1.2. Polycation Dialysate. Developing a new dialyzer membrane consumes large cost and time. One of the simplest ways to enhance the removal property of serum phosphate is to change the ion component of a dialysate solution. Wathen et al. (1982) reported a theoretical advantage of bicarbonate compared with acetate in dialysate for the control of serum phosphate. In this section, the ion permeation is simulated in model systems with various dialysate solutions in order to compare removal properties of serum phosphate. Table I shows the ion components of the blood serum and the three dialysate solutions discussed in this section. Figures 2 and 3 show the simulation of PCR as a function of the membrane charge density for bicarbonate dialysate
and acetate dialysate, respectively. As seen from comparison between Figures 2b and 3b, the PCR of HP0d2for the bicarbonate dialysate is the same as that for the acetate dialysate in all regions of the membrane charge density even if the PCR of the other ions differ between the two dialysates. Miller et al. (1983) have also reported that there are no significant differences in the removal of phosphate utilizing the two different dialysate. solutions. The reason for the coincidence in PCR of HP0d2- is that the concentration of Na+ and C1- in the serum is much higher than that of HPOd2-;therefore, the PCR of HPOd2depends hardly on the small difference of the ion component of the two dialysate solutions. An effective way to remove phosphate is to drive this ion by electric force. It seems to be difficult to apply external voltage in a hemodialysis system with electrodes; therefore, the hemodialysis system where the phosphate is driven by the diffusion potential is considered. The removal mechanism of serum phosphate in this system is shown in Figure 4. In the system, the diffusion potential appears and accordingly the electric potential on the dialysate solution side is much higher than that on the serum side, because Na+ ions diffuse from the serum side to the dialysate solution side and C1- ions diffuse from the dialysis solution side to the serum side owing to their concentration gradients. A divalent anion, HP0d2-, is, therefore, easily transported from the blood side to the dialysate solution side by this electric potential difference. The dialysate solution contains polycation in order to compensatefor the concentration difference of the mobile cations and anions as shown in Table I. Figure 5 shows the simulation of HP0d2-concentration change with time at the dialysate side in the model system of hemodialysis with the usualdialysates and in the system
920 Ind. Eng. Chem. Res., Vol. 32, No. 6,1993 serum
Polyeatian dialysate solution
+I I
I POlyEalion
(a)
II -
CI
SO 0
0 A
c-l c-2 PVA
c1-
I Membrane
Figure 4. Schematic diagram of the phosphate removal mechanism of polycation dialysate.
-
0 (b)
0 1.5
--- Bicarbanale or AcetatcDialysate -Polycatian Dialysate
-10
0
1
A-I
x
I
I 10-2
I@'
with the polycation dialysate. The concentration of HP041-increaseswithtime,andthe slopeof the polyeation dialysate is steeper than that of the bicarbonate or the acetate dialysates. These simulations indicate that the polycation dialysate has higher removal efficiency of HP04%than the dialysates in common use. 4.2. Experimental Results. Parta a and b of Figure 6 show the results of the membrane potential measurements for negatively and positively charged membranes, respectively. The solidlines show theoreticalcalculations made by fitting the experimental data to eq 7. From this fitting, the membrane charge density is obtained experimentally. The membrane charge density and permeability coefficient of urea (PJof sample membrane are listed in Table 11. The ion permeation experiment for the bicarbonate dialysate was performed using these membranes. It was difficultto measure HPO2- concentrations by our apparatus of ion chromatography because of the high concentration of C1-. Hence, another divalent anion, SO4%, was used instead of HPO&. The effect of the membrane charge sites on these ions is seems to be the same, since the two ions have the same valence. Our simulations,whose results are not described here, revealed that the dependence of HP04%permeation on the membrane charge is the same as that of Sod2-. Figure 7 shows PCR of so& as a function of the membrane charge density. The experimental data agree quantitatively with the theoretical prediction. The removal efficiency of the bivalent anion for the positively charged membrane with 0.3 mol/dm3 charge density is about 10times larger than that for the neutral membrane. From this result, the removal efficiency of phosphate for positively charged membrane dialyzer will be higher than that for the dialyzer membranes in common use whose membrane charge is negative or neutral.
101
C,' [moWdm'l
Time [mi".]
Figure 5. Simulation of the HP0.Z ion concentration change with time at the dialynate solution side.
100
Fwure 6. Renulta of the membrane potential meenurement: (a) for negatively charged memhranen; (h) for a positively charged one. Table 11. Membrane Charge Density and Permeability Coelficient of Urea for the Membranes Used in the Experiments membr charge permeability meff of sample no. density (moldma) urea (ms-9
__
Cl
4.9
c2
4.14 0.0
PVA A1
"'!0.4
6.7 x 10-9
Elo x i v g
1.1 x 10-8 6.2 X 10-'O
0.3
'
-0.2
0.0
0.2
0.4
Charge Density [moWdm'] Figure 7. PCR of 902- ion an a function of the membrane charge density. Solid circles show experimental data, and the iolid line shown the simulation result.
5. Conclusions
In the present study, we simulated ionic permeation in hemodialysismodel systemsto fmd more efficientmethods to remove serum phosphate than those currently used. The simulations led to the two improved methods. One is the use of a positively charged membrane dialyzer, and
Ind. Eng. Chem. Res., Vol. 32, No. 5, 1993 921 the other is the use of the polycation dialysate. These two methods can be combined so that the removal efficiency will be maximized. In the present study, we focused on the simulations of the efficient removal of serum phosphate. In practical use of the new dialysis methods, the component of metal ions and anions in dialysate solutions must be adjusted in order to hold homeostasis, because the permeation of these ions differs between the new technique and the current dialysis methods. In this adjustment, it is difficult to find the most suitable ionic composition of the dialysate solution and the membrane charge density by experiment only. The simulation is a great help in finding the best condition. These methods of selective removal of a divalent ion in multicomponent ionic solution can be applied to purification of biological products and the treatment of industrial wastewater. Acknowledgment
This work was supported in part by the basic science program from the Agency of Science and Technology of Japan and was supported in part by a Special Grant for Promotion of Research from The Institute of Physical and Chemical Research. Nomenclature
0 = ion concentration in the membrane surface in the cell at side s, mol/dm3 Cs = ion concentration of the solution in the cell at side s,
m01/dm3
C, = membrane charge density, mol/dm3 d = membrane thickness, m
K = Donnan equilibrium constant
F = Faraday constant, C mol-' P = permeability coefficient, ms-1 PCR = permeability coefficient ratio(Pi/P,) R = gas constant, J mol-l K-l T = absolute temperature, K = (OK - WCl)/(wK + 0'21) z = valence of ion
w
Greek Symbols
0 = exp(-F%iff/Rn A&ff = diffusion potential differencebetween the membrane surfaces, V A&,,, = Donnan potential difference between the membrane surface and the solution in the cell at side s, V wi = mobility of the i species ion, m2 mol s-1 J-l Superscripts s = side of cell (s = I, 11) z f = z-valent cation 2- = z-valent anion
Subscripts i = i species ion x = membrane-fixed charge u = urea K = potassium ion C1 = chloride ion
Literature Cited Alfrey, A. C.; LeGendre, G. R.; Kaehny, W. D. The Dialysis Encephalopathy Syndrome: Possible Aluminum Intoxication. N . Engl. J . Med. 1976,294, 185-188. Clarkson, E. M.; Luck, V. A.; Hynson, W. V.; Bailey, R. R.; Eastwood, J. B.; Woodhead, J. S.; Clements, V. R.; O'Riordan, J. L. H.; DeWardener, H. E. The Effect of Aluminum Hydroxide on Calcium, Phosphorus, and Aluminum Balances, the Serum Parathyroid Hormone Concentrations, and the Aluminum Content of Bone in Patients with Chronic Renal Failure. Clin. Sci. 1972, 43, 519-531.
Goldman, D. E. Potential, Impedance and Rectification in Membranes. J . Gen. Physiol. 1943,26, 37-60. Hercz, G.; Coburn, J. W. Prevention of Phosphate Retention and Hyperphosphatemia in Uremia. Kidney Znt. 1987,32, S215-S220. Higa, M.; Tanioka, A.; Miyasaka, K. Simulation of the Transport of Ions Against Their Concentration Gradient Across Charged Membranes. J . Membr. Sci. 1988,37, 251-266. Higa, M.; Tanioka, A.; Miyasaka, K. Theoretical Analyses of Ion Transport in Hemodialysis Using a Charged Membrane. Polym. Prepr. Jpn. 1989, 38, 747. Higa, M.; Tanioka, A.; Miyasaka, K. A Study of Ion Permeation across a Charged Membrane in Multicomponent Ion Systems as a Function of Membrane Charge Density. J . Membr. Sci. 1990, 49,145-169.
Higa, M.; Tanioka, A.; Miyasaka, K. An Experimental Study of Ion Permeation in Multicomponent Ion Systems as a Function of Membrane Charge Density. J . Membr. Sci. 1991, 64, 255-262. Meyer, K. H.; Sievers, J.-F. La permbabilith des membranes. I. Th6orie de la permbabilith ionique. Helu. Chim. Acta 1936,19, 649-664.
Miller, J. H.; Gardner, P. W.; Heineken, F.; Samar, R.; Shinaberger, J. H. Studies of Inorganic Phosphate Removal during Acetate and Bicarbonate Dialysis. Proc. Am. SOC.Artif.Inter. Organs. Abstr. Book 1983,12, 57. Naito,A.; Oinuma,M.;Ozawa,K.;Yamashita,A.;Takesawa,S.;Sakai, K. Effects of Charge Density on Electrolyte Transport Through Dialysis Membranes. Jpn. J . Artif. Organs. 1987, 16, 703-706. Okada, M.; Watanabe, T.; Imamura, K.; Tsurumi, T.; Suma, Y .;Sakai, K. Ionic Strength Affects Diffusive Permeability to an Inorganic Phosphate Ion of Negatively Charged Dialysis Membranes. ASAIO Trans. 1990,36, M324-M327. Parkinson, I. S.; Ward, M. K.; Kerr,D. N. S. Dialysis Encephalopathy, Bone Disease and Anemia: the Aluminum Intoxication Syndrome During Regular Hemodialysis. J . Clin. Pathol. 1981, 34, 12851294.
Teorell, T. An attempt to formulate a quantitative theory of membrane permeability. Proc. SOC.Exp. Biol. Med. 1935, 33, 282-285.
Wathen, R. L.; Ward, R. A.; Harding, G. B.; Meyer, L. C. Acid-base and Metabolic Responses to Anion Infusion in the Anesthetized Dog. Kidney Znst. 1982,21,592-599. Receiued f o r reuiew July 13, 1992 Revised manuscript receiued February 16, 1993
