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Journal of Membrane Science 352 (2010) 116–125

Contents lists available at ScienceDirect

Journal of Membrane Science

journa l homepage: www.e lsev ier .com/ locate /memsci

nalysis of the mass transfers in an artificial kidney microchip

issa Ould-Drisb, Patrick Paulliera, Laurent Griscomc, Cécile Legallaisa, Eric Leclerca,∗

CNRS-UMR 6600, Laboratoire de biomécanique et de bio ingénierie, Université de Technologie de Compiègne, BP 20529, 60205 Compiègne Cedex, FranceEA: 4297, Laboratoire de transformation intégrée de la matière renouvelable, Université de Technologie de Compiègne, BP 20529, 60205 Compiègne Cedex, FranceSATIE CNRS UMR 8029, ENS Cachan - Bretagne, Campus de Ker Lann, 35170 Bruz, France

r t i c l e i n f o

rticle history:eceived 23 October 2009eceived in revised form 26 January 2010ccepted 1 February 2010vailable online 6 February 2010

eywords:rtificial kidneyolydimethylsiloxane (PDMS)olyethersulfone membrane (PES)

a b s t r a c t

In this communication we demonstrate a conception of an artificial microkidney using pertinentmicrotools that more accurately mimic organ functions in vitro. We present a technique to integratepolyethersulfone (PES) membranes usually used in hemodialysis inside a polydimethylsiloxane (PDMS)microchip. The purpose of the microchip is to model glomerular filtration “on-chip”. Mass transfer ofurea (60 Da), vitamin B12 (1355 Da) and albumin (70,000 Da) are investigated by using two types ofmembranes (cut-off at 500,000 Da and 40,000 Da) in co-current and counter-current flow conditions.The time of urea, vitamin B12 and albumin removal, and the mechanisms of mass transfer, are controlledeither by controlling the pore size of the membranes or by controlling the pressure profiles along themembrane via the flow conditions. An analytical model, which is supported by our data, is put forth. The

ass transferlearancesicrofluidicicrochip

model allows the extraction of the diffusion coefficients of each molecule through the various membranesstudied. Due to the downscaling, the model and the experiments demonstrate that the dialysance in themicrochip is expressed by the sum of the diffusion and convection mass transfer components. The resultsof this work support an analytical model which describes the mass transfer in a microchip modelling aglomerular unit. Coupled with the advantages of the microfluidic biochip (high surface/volume ratio,reduction of the fluid volumes), our data will complete the integration of further cellular functions for

ent m

the utilisation of the pres

. Introduction

In toxicity studies, the effects of a molecule or drug are oftenested directly with animals (in vivo studies) or by using the spe-ific cells targeted by the molecule (in vitro studies). However,ost in vitro studies cannot reproduce in vivo studies due to the

ack of the systemic interferences and interactions between tissuesnd organs of a live organism [1,2]. Advances in bioengineer-ng are allowing the development of various complex bioreactorshat can reproduce the interactions between the organs suchs the liver, kidney, intestine or the lung [3–5]. These bioreac-ors consist of cell culture chambers containing engineered tissuend cell cultures interconnected and irrigated by a fluidic net-ork that control the flows of culture medium. The irrigationsing a microfluidic architecture permits continuous cell feeding,nd waste removal in addition to chemical loading and regula-

ion. Using these types of bioreactors, the toxicity of metabolitesf naphthalene or of benzo[a]pyrene, both metabolized by theiver (in a liver cell culture chamber) and then transported to

targeted organ (to the lung or to the intestine respectively

∗ Corresponding author. Tel.: +33 03 44 23 79 43; fax: +33 03 44 23 79 42.E-mail address: eric.leclerc@utc.fr (E. Leclerc).

376-7388/$ – see front matter © 2010 Elsevier B.V. All rights reserved.oi:10.1016/j.memsci.2010.02.007

icrochip as a future in vitro model of a miniaturized bio artificial kidney.© 2010 Elsevier B.V. All rights reserved.

for naphthalene or of benzo[a]pyrene) has been investigated[3–5].

In order to refine cell culturing models and methods for toxico-logical studies, bioreactors are now being miniaturized from macroto micro scales [6–8]. The miniaturisation of the bioreactors allowsthe reduction of the quantity of fluids involved in cell culture and inturn the reduction of chemicals used [9]. In addition miniaturisa-tion technologies allow working with physiological time of contactbetween the investigated molecules and targeted tissues.

As the main organ of detoxification is the liver, there is a largepanel of studies working on the miniaturisation of liver bioreac-tor [10–12]. However, only a few works deal with artificial kidneybioreactors. The kidney is an organ of prime interest in toxicitystudies since it is involved in the process of filtration and excretionof toxic metabolites.

Kaazempur-Mofrad et al. investigated the integration of a mem-brane (with a 0.4 �m porosity) and the mass transfers of urea andcreatinine inside a microchip [13]. Combined with the progressin bioartificial kidney technology [14], nano porous ultrafiltration

membranes [15], and Micro Electro Mechanical Systems (MEMS)-based microchips [16], the works on renal microchips using adialysis membrane are hoped to be extended to miniaturizedportable renal replacement systems. However, to achieve thisgoal, the microchips must provide a greatly increased surface area

A. Ould-Dris et al. / Journal of Membrane Science 352 (2010) 116–125 117

nes: (A

ammp

cpatriatilsmfibo

2

2

paifnt5at1mtii

2

llEtn

brane is sandwiched between the two PDMS layers. The microchipintegrity and the prevention of leaks are guaranteed by a sampleholder with 8 screws. The total surface available for filtration was1.3 cm2. The microchip and the sample holder are shown in Fig. 2C.

Fig. 1. SEM images of the PES membra

nd a significant improvement in the clearance efficiency of ure-ic wastes over current hemodialysis technologies. Ideally, theiniaturisation would enable the microchip to be portable and

otentially wearable [15].In a recent study, Baudoin et al. demonstrated the feasibility of

ulturing Madin Darby Canine Kidney cells (MDCK cells) inside aolydimethylsiloxane (PDMS) microchip [17]. The microchip, useds a miniaturized bioreactor, has several advantages compared toraditional in vitro methods including a higher surface to volumeatio, and dynamic chemical loadings. The results of the culturesn the miniaturized bioreactor coupled with the effect of dynamicmmonium chloride loading on MDCK cell cultures have illustratedhe potential of using microchips for wider in vitro chronic toxicitynvestigations. In the present paper, we investigate a glomerularike filtration microchip based on the integration of a polyether-ulfone membrane (PES) inside a PDMS microsystem that includesicrochannel networks and filtration chambers. The glomerular

ltration and the mass transfers in the microchip are characterizedy investigating experimentally and theoretically the behavioursf urea, vitamin B12 and albumin molecules.

. Materials and methods

.1. Membranes

We used two types of flat polyethersulfone (PES) membranesrovided by Membrana GmbH (reference numbers: MicroPES 1FPHnd MicroPES 8F). The polyethersulfone material is chosen becauset is widely used in the hemodialysers. The manufacturer gives theollowing properties of the membranes. The 1FPH and 8F nomi-al pore sizes are 0.04 �m and 0.8 �m respectively, correspondingo a filtration cut-off of molecular weights near 40,000 Da and00,000 Da. SEM views of the membrane are shown in Fig. 1And B. The pure water transmembrane flow rates are respec-ively 4 mL/(min cm2 bar) and 245 mL/(min cm2 bar) at 25 ◦C for theFPH and 8F membranes according to the manufacturer. The 1FPHembrane is classified at the transition between the microfliltra-

ion and the ultrafiltration processes, whereas the 8F membranes a microfiltration membrane. The thickness of the membraness 100 �m.

.2. Microchip

The microchip is composed of three layers, including two PDMS

ayers in which a PES membrane is sandwiched. Fig. 2A shows theayered assembly of the parts composing the filtration microchip.ach PDMS layer includes an inlet and outlet network and a fil-ration chamber. The PDMS filtration chamber and inlet/outletetworks are fabricated by a photo lithographically defined replica

) 1FPH; (B) 8F. The scale bar is 10 �m.

moulding as described in the literature [18]. The filtration chambersare 200 �m deep, 11 mm large and 13 mm long. A microchannelarray of 100 �m in depth is located at the bottom of each cham-ber, as shown by Fig. 2B. This array is added in order to create asieve, which is designed to avoid blockage of the filtration by thedeformation of the membrane on the PDMS surface during the fluidperfusion. In each PDMS layer, inlet and outlet ports are drilled,resulting in two separate microfluidic circuits. An inlet and out-let microchannel network (100 �m deep) is used to connect thefiltration chamber and the inlet and outlet ports (Fig. 2A). The mem-

Fig. 2. (A and B) Principle of the microchip; (C) photography of the microchip.

118 A. Ould-Dris et al. / Journal of Membrane Science 352 (2010) 116–125

Faf

Fh

2

fuwtica

(3atctwwa

2

t(d

Table 1Nomenclature, parameters and experimental extracted values used in the model.

1 Retentate footnote2 Permeate footnotef Filtrate footnotei Inlet footnoteR Outlet footnoteL Length of the chamber 1 cmb Width of the chamber 1 cme Height of each compartment 150 �mQ Flow rate m3/sQf Filtration flow rate m3/s� Fluid velocity m/sP Pressure PaC Concentration g/LDL Dialysance m3/sx* Abscise where Qf = 0 m� Viscosity Pa sV Volume of each compartment 1.5 × 10−9 m3

Rm Membrane water resistance of the 1FPHmembrane

7.5 × 1010 m−1

Rm Membrane water resistance of the 8Fmembrane

7.5 × 109 m−1

C10 Solute initial concentration in the retentate Section 2.5C∝ Equilibrium concentration Section 2.5PH2O Experimental transmembrane water flux

(1FPH)8 mL/(min cm2 bar)

PH2O Experimental transmembrane water flux(8F)

80 mL/(min cm2 bar)

Dm Coefficient of diffusion of urea (1FPH) 2 × 10−12 m2/sDm Coefficient of diffusion of urea (8F) 2 × 10−11 m2/sDm Coefficient of diffusion of vitamin B12

(1FPH)4 × 10−13 m2/s

ig. 3. Experimental setup: (A) co-current (full arrow) and counter-current (dashedrrow) flow circuits used during the mass transfer experiments; (B) dead end modeor the transmembrane pure water flow rate determination.

or comparative purposes, a microchip without a sieve structureas been also built.

.3. Experimental setup

In order to analyse the mass transfer in the microchip, two per-usion circuits were used as shown in Fig. 3A. The first circuit wassed to flow the retentate solution in which the molecule to filteras loaded. The second circuit corresponded to the permeate solu-

ion in which the molecule to be filtered was extracted. Each circuitncluded a 10 mL fluid reservoir and a peristaltic pump. In order toontrol the pressure, four manometers were connected at the inletnd outlet ports of the microchip (ports defined in Fig. 2A).

The experimental value of the transmembrane pure water fluxPH2O) was measured in the microchip. For that purpose, ports 2 andwere closed (Figs. 2A and 3B). The water was fed through port 1

nd exited at port 4. The transmembrane pure water flux throughhe membrane was measured in dead end filtration mode. A pre-ision scale weighing the water collected at the port 4 was usedo calculate the flow rate. The membrane water resistance (Rm)as extracted from this flux by the relation: Rm = PTM/�JfH2O (inhich � is the viscosity, JfH2O the transmembrane pure water flux

nd PTM the transmembrane pressure P1–P2 defined in Table 1).

.4. Filtration experiments

Co-current flow conditions were achieved by a flow stream inhe retentate and in the permeate flowing in the same directionand therefore coming from respectively the ports 1 and 3). Weefined the counter-current flow conditions when the retentate

Dm Coefficient of diffusion of vitamin B12 (8F) 6 × 10−12 m2/sDm Coefficient of diffusion of albumin (1FPH) 9 × 10−14 m2/sDm Coefficient of diffusion of albumin (8F) 2 × 10−13 m2/sı Thickness of the membranes 100 �m

and permeate arrived in the microchip from opposite directions.This meant that the retentate arrived from port 1 and the perme-ate from port 4. The flow rates used in the study were 150 �L/minand 300 �L/min in co-current or counter-current conditions. Eachexperiment for each membranes and flow conditions was repeatedat least 2 times independently.

2.5. Solutes and measurements

The mass transfer was tested with a urea solution which has amolecular mass of 60 Da. This molecule was used as a low molecularweight marker in our experiments. The retentate solution was con-centrated at 36 mg/mL whereas initially the permeate solution waspure water. In order to sample the solution, the perfusion pumpswere stopped and 50 �L was sampled from the retentate and per-meate reservoirs. The urea concentration was measured using theBioassay QuantichromTM Urea Assay Kit. The equilibrium concen-tration was theoretically 18 mg/mL.

The mass transfer was also tested with a vitamin B12 solutionwhich has a molecular mass of 1355 Da. This molecule was used asa middle molecular weight marker. The retentate solution was con-centrated at 120 mg/L whereas initially the permeate solution waspure water. The vitamin B12 concentration was measured in theretentate and permeate reservoirs using a spectrophotometer at360 nm. The equilibrium concentration was theoretically 60 mg/L.

The mass transfer was finally tested with a bovine albumin solu-tion which has a molecular mass of 70,000 Da. This molecule wasused as a large molecular weight marker. The retentate solutionwas concentrated at 1000 mg/L in PBS solution (phosphate buffer

saline) whereas initially the permeate solution was PBS solution(phosphate buffer saline). The albumin concentration was mea-sured in the retentate and in the permeate reservoirs using aspectrophotometer at 280 nm. The equilibrium concentration wastheoretically 500 mg/L.

A. Ould-Dris et al. / Journal of Membrane Science 352 (2010) 116–125 119

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isa

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the membrane due to the very short length of the membrane (H6).

Fig. 4. Schematic of the modelled filtration chamber and the associated

.6. Theory

We propose a model to describe the transport of the moleculen the microchip and through the membrane. The nomenclature isummarized in Table 1. The model takes into account the followingssumptions:

the osmotic pressure is neglected (H1);the inlet and outlet effects are neglected in both compartments ofthe filtration chambers meaning that the flows were fully devel-oped (H2);hypothesis H2 leads that there is no boundary layer of fluid veloc-ity occurring along the membrane (H3);the main resistance to the diffusive transfer is located in the mem-brane (there is no diffusion boundary layer in the compartments)(H4);the volume of the fluid in each compartment is assumed to bethat of the reservoir (volume of the connections was neglected)(H5);the concentrations in each compartment were constant along themembrane due to the very short length of the membrane (H6);the viscosity in each compartment are equal due to high dilutionof the solutes (H7).

The objective of the model is to determine the concentrationsf the solutes vs. time in the retentate and permeate solution inrder to obtain a predictive method of the mass transfers. The pur-ose of the model is also to establish an analytical method to findhe dialysance and to characterize the efficiency of the microchips.he model is based on the solution of the mass balance equations,he convective and diffusive equations of mass transfer across the

embrane and the transmembrane pressure equations along theembrane. In the model, the retentate (that can be understood as

he plasma circuit in conventional hemodialyser) is denoted by thefluid 1”, whereas the permeate is denoted as the “fluid 2” as shownn Fig. 4.

The mass balance in the retentate and permeate is given by

dV1

dt+ dV2

dt= dV1

dt= dV2

dt= 0 (1)

This equation indicates that the initial volumes in both reser-oirs were completely filled and remained constant during the

sure profiles in (A) counter-current and (B) co-current flow conditions.

experiments. V1 is the initial volume of the retentate with a solutionhaving an initial concentration of solute C10.

This leads to the following mass conservation:

d(V1C1)dt

+ d(V2C2)dt

= 0 ⇒ V1dC1

dt+ V2

dC2

dt= 0

⇒∫ C1

C10

dC1 = −V2

V1

∫ C2

0

dC2

C10 − C1

C2= V2

V1⇒ C2 = (C10 − C1)

V1

V2(2)

If the volume of fluid in each compartment remains constantthen the average transmembrane pressure is equal to zero. Thus,the mass balance in the retentate compartment can be written as:

dV1

dt= −

∫ L

0

Jf b dx = − 1�Rm

∫ L

0

(P1 − P2)b dx = 0

⇒∫ L

0

P1 dx =∫ L

0

P2 dx (3)

in which Jf is the transmembrane flux defined by Jf = (P1 −P2)/�1Rm. In these equations we suppose that is no boundary layerof fluid velocity occurring along the membrane (H2 and H3).

We denoted x* the membrane abscissa in which the pressurein each compartment P1(x∗) = P2(x∗), which leads to the followingmass flux in the retentate:

V1dC1

dt= −b

∫ x∗

0

[Jf C1 + Dm

ı(C1 − C2)

]dx

− b

∫ L

x∗

[Jf C2 + Dm

ı(C1 − C2)

]dx (4)

In this equation, it is assumed that there is no boundary layer ofthe solute concentration along the membrane (H4). It is assumedthat the concentrations in each compartment were constant along

This leads to the following equation:

V1dC1

dt= −b

[C1

∫ x∗

0

Jf (x) dx + C2

∫ L

x∗Jf (x) dx + (C1−C2)Dm

ı

∫ L

0

dx

]

(5)

120 A. Ould-Dris et al. / Journal of Membrane Science 352 (2010) 116–125

Table 2Experimental dialysance in �L/min for the urea, the vitamin B12 and albumin for the 1FPH and 8F membranes.

Molecules

Urea Vitamin B12 Albumin

Co-currenta Counter-currenta Co-currenta Counter-currenta Co-currenta Counter-currenta

150/150-1FPH 0.12 �L/min 0.3 �L/min 0.03 �L/min 0.174 �L/min 0.0054 �L/min –300/300-1FPH 0.12 �L/min 0.48 �L/min 0.03 �L/min 0.34 �L/min 0.0054 �L/min –

L/minL/min

mebtaaSovptactde

ttIapdt

fl

Q

o

Q

i

w

150/150-8F 1.2 �L/min – 0.36 �300/300-8F 1.2 �L/min – 0.36 �

a Flow conditions.

To solve Eq. (5), we must calculate the pressure in each compart-ent. In the model, we have neglected the sieve and have modelled

ach compartment of the filtration chambers as a Hele Shaw cham-er (b � e, parameters defined in Table 2 and Fig. 4). To determinehe pressure profile, we assume a fully developed flow and neglectny lateral effects (H2). Indeed Beavers and Joseph [19] proposedmodel of the slip velocity along the membrane in laminar and

tokes flow conditions. This model has been extended in the casef a slow velocity of filtration when compared to the upper free flowelocity [20–22]. It is shown in these particular conditions that theorous media can be consider as an impermeable media leadingo a velocity of filtration in the order of (1/Rm)0.5. Thus, in a firstpproximation we assumed that the slip velocity is 0 in our flowonfiguration. In our case, this led to consider an adherence condi-ion at the membrane surface. The hypothesis will be validated andiscussed in the result section. Therefore, the pressure gradient inach compartment was given by the Hagen–Poiseuille law:

dP1

dx= −12

�1v1

e21

(6)

dP2

dx= −12

�2v2

e22

To solve the system of the set of equations (6) we suppose thathe fluids have the same viscosity (H7). We can also suppose thathe pressure profile is linear over the length of each compartment.f the filtrate flow rate Qf does not exceed 1% of the flow rates Q1nd Q2 in the two compartments then it can be considered that theressure profile in each compartment is linear, meaning that theifference of the transmembrane pressure is too weak to modifyhe velocity in each compartment.

The filtrate flow rate, Qf is then defined as the internal filtrationow rate calculated with the following equation:

f =∫ x∗

0

Jf b dx = b

�Rm

∫ L/2

0

(P1 − P2) dx (7)

In this equation, Jf is equal to 0 at the abscissa x* = L/2. In the casef the co-current flow conditions, Eq. (7) becomes:

f = b

�Rm

∫ L/2

0

(P1 − P2) dx = 6b

Rm

(v1

e2− v2

e2

)∫ L/2

0

(L − 2x) dx

= 3L2

2Rme3(Q1 − Q2) (8)

n which Q1 = v1be1 and Q2 = v2be2 with e1 = e2 = e in our case.

e defineQ2 = k then Qf = 3L2Q1

3(1 − k) (9)

Q1 LRme

From Eq. (9) we may notice that if Q1 and Q2 are equal then Qf = 0

Qf

Q1= 3L2

2Rme3(1 − k)

Qf

Q2= 3L2

2Rme3

1 − k

k(10)

– 0.012 �L/min –– 0.012 �L/min –

The following equations are satisfied if the pressure profiles arelinear and therefore if Qf/Q2 < 1%. This meant that we must checkthat the following relation between the geometrical and physicalparameters is valid:

Qf

Q2≺ 0.01 ⇒ k � 1

(1 + 0.02Rme3)/3L2(11)

A similar analysis for the counter-current flow conditions fromEq. (7) lead to an equation of Qf given by:

Qf = b

�Rm

∫ L/2

0

(P1 − P2) dx = 6b

Rm

(v1

e2+ v2

e2

)∫ L/2

0

(L − 2x) dx

= 3L2

2Rme3(Q1 + Q2) (12)

This leads to write

Qf = 3L2Q1

2Rme3(1 + k);

Qf

Q1= 3L2

2Rme3(1 + k);

Qf

Q2= 3L2

2Rme3

(1 + k)k

(13)

The linear pressure profile assumption is valid in counter-current flow condition only if

Qf

Q2≺ 0.01 ⇒ k � 1

0.02Rme3/3L2+ 1 (14)

Taking into account Eqs. (8) and (12), Eq. (5) can be rewritten asfollows:

V1dC1

dt= −

[Qf (C1 − C2) + LbDm

ı(C1 − C2)

]

= −[(

Qf + LbDm

ı

)(C1 − C2)

](15)

Using Eq. (2), and expression of equilibrium concentration C∞,C∞ = C10(V1/(V1 + V2)), the differential equation above can berewritten as follows:

dC1

dt= −

[(Qf + LbDm

ı

)(V1 + V2

V1V2

)(C1 − C∞)

](16)

The solution of Eq. (16) is:

C1(t) = C1∞ + (C10 − C∞) exp[−

(Qf + LbDm

ı

)(V1 + V2

V1V2

)t]

(17)

The average flux is given by the following equation:

J̄f = Qf

bL/2(18)

Then the Peclet number across the membrane comparing con-vective and diffusive mass transfer across the membrane can be

embra

e

P

t

C

oc

C

w

l

t

iQmtpa

D

rt

D

D

l

ss

D

3

3

mbasswttmot

A. Ould-Dris et al. / Journal of M

xpressed by:

e = J̄f ı

Dm= Qf

bL/2ı

Dm(19)

Therefore, the differential equation (17) can be expressed usinghe Pe number:

1(t) = C1∞ + (C10 − C∞) exp[−Qf

(1 + 2

Pe

)(V1 + V2

V1V2

)t]

(20)

In co-current flow with Q1 = Q2, Qf becomes equal to zero andnly diffusive transport takes place across the membrane. In thisase, Eq. (17) reduces to the following Eq. (21)

1(t) = C1∞ + (C10 − C∞) exp[− LbDm

ı

(V1 + V2

V1V2

)t]

(21)

The linearized form of Eq. (20) can be used to validate the modelith experimental results

nC1(t) − C∞C10 − C∞

= −Qf

(1 + 2

Pe

)(V1 + V2

V1V2

)t (22)

Thus, experimentally the Pe number can be determined fromhe slope and Dm deduced.

The dialysance, DL, expresses the mass transfer (between thenlet and outlet of the retentate compartment, via the relation:1i − Q1rC1r, the scales are defined in Table 1) per unit of time nor-alized by the concentration difference between the retentate and

he permeate. The dialysance, that takes into account the multiass flows via the concentration C2, is expressed by the relationccording to Winger and Weiner [23]:

L = Q1iC1i − Q1rC1r

C1i − C2i(23)

In the present model, we assume that the mass transfer in theetentate can be expressed simply by the term −V1(dC1/dt) leadingo rewrite Eq. (23) as follows:

L = −V1dC1

dt

(1

C1 − C2

)(24)

L = V2dC2

dt

(1

C1 − C2

)(25)

The solution of Eqs. (24) and (25) lead to

n [C1(t) − C2(t)] = −DL(

1V1

+ 1V2

)t (26)

Thus, the dialysance can be deduced experimentally from thelope of Eq. (26). Following the present theory, the modelled dialy-ance is given by Eq. (15), Eqs. (24), (25) and (26):

L =[

Qf + LbDm

ı

](27)

. Results and Discussion

.1. Microchip design and fabrication

In conventional PDMS microchip fabrication processes, theicrofluidic network can be sealed to a PDMS or glass surface

y exposing the surfaces to a RF generated oxygen plasma thatllows a strong bonding of the PDMS to other PDMS or glass sub-trates. This effect is assumed to be due to the oxidation of theurface by the plasma creating OH bonds. However, as is the caseith PES membranes, we were unable to bond PDMS to it using

he plasma bonding technique. To achieve hermetic seal betweenhe PES membrane and the PDMS structures, we have devised a

icrochip holder that allowed us to clamp and maintain pressuren the PDMS parts. The holder allowed working with pressures upo 1 m of water (corresponding to 100 mbar). In terms of flow rate,

ne Science 352 (2010) 116–125 121

this led to a maximal working flow rate of 700 �L/min. At higherflow rates (and pressures) there was a radial leakage of the fluidthrough the membrane (data not shown).

3.2. Determination of the membrane water resistance

The values of the membrane water resistance (Rm) are shownin Table 1. In the case of the 1FPH membrane, the calcu-lated resistance is equal to 7.5 × 1010 m−1 resulting from theexperimentally measured transmembrane water flux equal to8 ± 1 mL/(min cm2 bar) (n ≥ 10). This value is twice as high asclaimed in the manufacturer’s data (4 mL/(min cm2 bar)). In thecase of the measurements using the 8F membrane, the value ofthe transmembrane water flux decreased with the time due to themembrane clogging. Therefore the value of the transmembranewater flux was 160 mL/(min cm2 bar) at the first measurement(compared to 245 mL/(min cm2 bar) value given by the manu-facturer) and decreased to 80 mL/(min cm2 bar) at the secondmeasurement (n ≥ 10). A limit value down to 20 mL/(min cm2 bar)was reached after repeating the measurements consecutively. Forthat reason, the transmembrane water flux was characterizedbefore and after each filtration experiment for all membrane. Inaddition, the membrane was changed for every filtration test. Usingthis experimental procedure, a membrane water resistance (Rm) of7.5 × 109 m−1 was calculated, corresponding to a transmembranewater flux of 80 mL/(min cm2 bar).

For comparative purposes, in the microchip without sieve, wewere unable to flow water through the membrane. This led toan artificially low value of the transmembrane flow rate (0.1 and0.004 mL/(min cm2 bar) for the 8F and 1FPH membranes respec-tively). This result can be attributed to the deformation and thecontact of the membrane with the bottom surface of the filtrationchamber. In addition, with this type of microchip, we observed acorrugation of the membrane that locally increased the pressureprofile on the membrane. In this situation, we cannot assume a lin-ear pressure profile along the membrane. The use of the sieve was akey component in the design to achieve reproducible mass transferexperiments.

3.3. Dialysis mode

In the case of the 150/150 �L/min and 300/300 �L/min flow rateconditions in co-current situations, mass transfers of the urea, ofthe vitamin B12 and of the albumin were not affected by the vari-ation of the flow rate as shown in Fig. 5A–C. As similar pressureprofiles were obtained in both fluids along the membrane, it couldbe expected that the local transmembrane pressure was alwaysclose to zero leading to small convective effects. This suggestedthe absence of diffusion boundary layer that could influence themass transfers and to consider that all the resistance to the dif-fusion was located in the membrane itself. Should the blood ordialysate resistance be significant, they would be different accord-ing to the perfusion flow rate (i.e. the higher flow rate, the lowerdialysate resistance), which was not observed. This result was con-sistent with the assumption in the model where the expression ofthe diffusive flux (Eq. (4)) was not function of these additional resis-tances observed in conventional hemodialysers [24]. In the presentexperimental cases, the diffusion was theoretically the only processof mass transfer.

For the three molecules and all flow rate conditions, we foundthat the mass transfer kinetics depended on membranes pore size.

The equilibrium with urea was reached after 20 min with the 8Fmembranes whereas 150 min were needed with the 1FPH ones(Fig. 5A). This was attributed to the larger pore size leading to highercoefficient of diffusion through the membrane. The data obtainedwith the vitamin B12 showed the same tendencies as presented

122 A. Ould-Dris et al. / Journal of Membrane Science 352 (2010) 116–125

Fig. 5. Superimposition of the modelled and experimental values of the concentra-ti33

il(n(

toge(n2tmsfms

Fig. 6. Superimposition of the modelled and experimental values of the concentra-

ion of the urea (A), of the vitamin B12 (B) and of the albumin (C) in the retentaten co-current flow conditions with the 1FPH membranes (Exp: � 150/150; Exp: �00/300, Model: black line) and with the 8F membranes (Exp: * 150/150; Exp: ©00/300, Model: dashed line).

n Fig. 5B. In addition, the vitamin B12 mass transfer rate wasower compared to urea transfer due to its larger molecular weight1355 Da vs. 60 Da). Finally, the equilibrium with albumin couldot be reached after 6 h of perfusion using the 1FPH membranesFig. 5C).

The diffusion coefficient, Dm, in Eq. (21) was the only parame-er to adjust in the model in order to fit the experimental resultsbtained in the dialysis experiments in which there is no otheroverning mass transfer mechanism. The other equation param-ters were the geometrical parameters of the filtration chamberthe discussion of the parameter choice will be performed in aext section). The model led to a diffusion coefficient for urea of× 10−12 m2/s for the 1FPH membranes and of 2 × 10−11 m2/s for

he 8F membrane (Table 2). In the case of the vitamin B12, the

odel fitted the experiences well if the diffusion coefficients were

et to 4 × 10−13 m2/s for the 1FPH membranes and to 6 × 10−12 m2/sor the 8F membranes respectively. Finally, for the albumin, the

odel fitted the experiences if the coefficients of diffusion wereet to 9 × 10−14 m2/s for the 1FPH membranes and to 2 × 10−13 m2/s

tion of the urea (A) and of the vitamin B12 (B) in the retentate in co-current (Exp: �150/150; Exp: � 300/300; Model: black line) and counter-current (Exp: ♦ 300/300;Model: dotted line; Exp: © 150/150, Model: dashed line) flow conditions used withthe 1FPH membranes.

for the 8F membranes respectively. These data were in agreementwith the expected results; namely the obtained coefficients demon-strated that urea diffusion was faster than vitamin B12 which wasfaster than albumin diffusion. For both membranes and the threemolecules, the co-current flow conditions allowed working with aQf value equal to 0 �L/min as shown by Eq. (9). The model assump-tions of no slip velocity, Poiseuille profile and linear pressure profile(Qf/Q1 < 0.01) were therefore valid. In addition, this led to a Pecletnumber equal to zero, representing a fully diffusion mode of masstransfer. Finally, the dispersion between the theory and the exper-iments in dialysis was found below 10%.

3.4. Diffusion-convection modes

In counter-current flow conditions, the mass transfer was fasterdue to an additional convection process through the membrane.This was due to different transmembrane pressure. When com-pared to the co-current flow conditions, the transfer time wasreduced as shown in Fig. 6A and B in the case of the 1FPH mem-branes for the urea and vitamin B12. In counter-current flow

conditions, an increase in flow rates reduced the transfer time byincreasing the flow through the membrane (due to the local trans-membrane pressure). For urea, this time was reduced from 60 minto 20 min when the flow rates were increased from 150 �L/min to300 �L/min (120 min to 90 for the vitamin B12 respectively).

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A. Ould-Dris et al. / Journal of M

To model these experiments, we used Eq. (20), in which the Dm

alues were those previously extracted from the dialysis experi-ents. The model was dependent on the Peclet number, Pe, and the

ltration flow rate Qf. In our flow configurations, we had in Eqs. (12)nd (13) k = 1, that led to Qf ≈ 0.18 �L/min and 0.36 �L/min when1 was set to 150 �L/min and 300 �L/min respectively with the 1PH membrane. These values were in agreement with the assump-ion of a linear pressure profile in each compartment, defined byf/Q1 < 0.01 in the model. In addition these equations showed that

he augmentation of the flow rate (Q1 and Q2) lead to an increasen the value of Qf and therefore an increase of mass transfer via

onvection (ultrafiltration process).

The Peclet numbers were 3 and 6 at 150 �L/min and 300 �L/minespectively during the urea experiments. In counter-current flow,oth convection and diffusion appeared to play a role in the massransfer illustrated by a value of Pe equal to 3. This also explains

ig. 7. Sensibility of the model using the parameters of Table 2: (A) to the diffusion coeB) to the flow rates (�: Q1 = Q2 = 300 �L/min; �: Q1 = Q2 = 75 �L/min; ♦: Q1 = Q2 = 150 �5 �m); (D) to the flow rates if Dm = 4 × 10−12 cm2/s (�:Q1 = Q2 = 150 �L/min; �: Q1 = Q2 =m = 4 × 10−13 cm2/s (�: 80 mL/(min cm2 bar); �: 1 mL/(min cm2 bar); ♦: 8 mL/(min cm2 b

ne Science 352 (2010) 116–125 123

the faster transfer when compared to the co-current flow condi-tions due to the addition of both phenomena (Fig. 6A). Then, in ourmicrochip, when the flow rates Q1 and Q2 were increased, the con-vection of urea became more dominant (Pe = 6). This was illustratedby a faster mass transfer.

Due to the size of the molecules, the diffusion process wasweaker when we used the vitamin B12 when compared to the con-vection process. This tendency was illustrated with Peclet numbersequal to 15 and 30 at 150 �L/min and 300 �L/min respectively. Inthose cases, the transfer of the molecules mainly resulted fromconvection through the membrane. Thus for urea, both diffusion

and convection played an additional role in the mass transfer ofthe urea while the mass transfer of the vitamin B12 was mainlydue to the convection. It should be noted that the differencebetween the Peclet number between both experiments (urea andvitamin B12 filtration with the 1FPH membranes) is dependent

fficient of the solute (�: 4 × 10−12 cm2/s; �: 4 × 10−13 cm2/s; ♦: 4 × 10−14 cm2/s);L/min); (C) to the height of the modelled chamber (�: 300 �m; �: 150 �m; ♦:

300 �L/min; ♦: Q1 = Q2 = 75 �L/min); (E) to the transmembrane water flow rates atar)).

124 A. Ould-Dris et al. / Journal of Membrane Science 352 (2010) 116–125

Table 3Clearances (CL) for the urea and the vitamin B12 reported in the literatures in microchip and in conventional hemodialysers compared to our microchip dialysance (DL) whenwe used the 1FPH membranes in counter-current flow conditions.

CL or DL (mL/h) Q1/Q2 Q2 (mL/min) Surface (cm2) Q2/A (mL/(min cm2)) Membrane type

Present worka (urea) 0.018 1 0.15 1 0.15 PES (40 kDa)0.029 1 0.3 1 0.3 PES (40 kDa)

Present worka (vit B12) 0.01 1 0.15 1 0.15 PES (40 kDa)0.02 1 0.3 1 0.3 PES (40 kDa)

Kaazempur-Mofrada (urea) [13] 15 1 0.033 – 0.0013 PC (200 kDa)40 1 0.033 – 0.0042 PC (200 kDa)70 1 0.033 – 0.007 PC (200 kDa)

Brunet et al. (urea) (hollow fibers) [27] 1380 1 16 6000 0.0027 AN69 (40 kDa)32

500

om

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n the coefficients of diffusion of the molecules through theembrane.Finally, for the urea and vitamin B12 using the 1FPH membrane,

he dispersion between the theory in diffusion/convection modend the experiments was found at 10% without changing the valuef the coefficient of diffusion for each molecule in each membrane.

When the counter-current flow conditions were applied withhe 8F membrane, the retentate flowed directly in the permeate.he volume of fluids in each circuit could not be kept constantand the retentate flowing directly to the permeate, it did not per-

it sampling of the solutions for measurements). There was noore tangential flow inside the chamber. These observations were

n opposition with the model assumption of Eq. (1) in which theolumes in both reservoirs were initially completely filled andemained constant during the experiments. Locally, this can bexplained by a pressure difference through the membrane so highhat the retentate penetrated directly in the permeate circuit athe port locations. Thus, experimental and analytical results didot match. In these situations, we found that Qf ≈ 1.8 �L/min at50 �L/min and the ratio Qf/Q1 = 0.012 meaning that the Poiseuillerofile assumption began to be incorrect. It probably resulted fromhe apparition of a slip velocity showing the limitation of the model.

.5. Model sensitivity to parameters

To superimpose the analytical and experimental data, we hado introduce the geometrical and physical parameters in the

odel. The transmembrane flow rates used in the calculation werextracted from the experimental data. The model did not take intoccount the microchannels of the sieve and the microchannels ofhe inlet and outlet networks. The filtration model represents andeal situation with two parallel flat flow chambers separated byfixed, inflexible membrane. To reproduce the experimental datae used a value of 150 �m that corresponded to the mean value of

he height of each chamber (see Section 2.2). In Figs. 5 and 6, weresented the data obtained with 150 �m. The coefficient of diffu-ion for each membrane was determined by using the experimentsf each molecule in the diffusion modes.

In Fig. 7, we have shown the sensitivity of the model to the trans-embrane flow rate (filtration flow rate), the diffusion coefficient,

he chamber height and the flow rates. In the diffusion-convectionode (Eq. (20)), the convection is an important phenomenon when

he microchip included the 1FPH membranes for the intermedi-te size molecules (such as vitamin B12). This was illustrated by

small variation of the filtration time when the coefficient of dif-

usion ranged from 4 × 10−13 m2/s to 4 × 10−14 m2/s (Fig. 7A). Inddition, the filtration time was strongly influenced by the variationf the flow rates or the chamber height at 4 × 10−13 m2/s (Fig. 7Bnd C). On the contrary, at higher values of the coefficients of diffu-

6000 0.0053 AN69 (40 kDa)

11,500 0.043 AN69 (40 kDa)

sion (see at 4 × 10−12 m2/s in Fig. 7A), such as for the urea and thesmall molecules, the diffusion in the microchip was not neglige-able. In those cases both phenomena of convection and diffusionacted on the filtration times (Fig. 7D). Finally, the sensitivity to thetransmembrane flow rate was presented. An augmentation of thetransmembrane flow rate decreased the filtration time. This can beunderstood by a higher porosity of the membrane (Fig. 7E).

3.6. Clearance and dialysance in the microchip

In Table 2, we have reported the dialysance of urea, vitaminB12 and albumin studying the microchips. As it can be seen fromTable 3, the dialysance increased when the membrane porosity wasincreased in the dialysis modes whereas the augmentation of thesize of the molecules contributed to reduce the dyalisance. Fur-thermore, the augmentation of the flow rates did not increase thedialysance. However, in convection diffusion modes, the dialysanceincreased with the flow rate augmentation. In addition, the dialy-sance decreased when the molecule size increased. This was due toa predominance of the convection term in the equations in counter-current flows when compared to the diffusion term (Pe � 1). In ourmicrochip, the convection through the flat membrane was there-fore an important phenomenon of mass transfer even for the smallmolecules. The model shows that the dialysance is the sum of thediffusive term (via Dm) and the convective term (via Qf). This ten-dency is not usual in conventional hemodialysis in which the globalmass transfer is mainly due to the diffusive mass transfer [24,25].This is due to the “asymptotic” saturation of the mass transfer [24].This leads to the expression of the dialysance and the clearance inthe conventional hemodialysis which is not the simple sum of theconvective and diffusive terms [24–26]. We may notice that in themicrochip the membrane size is very small and we assumed thatthere is no boundary layer to take into account during the masstransfer. This results to a term Qf representing the convection thatis as much as important as the diffusion.

For comparative purposes, in Table 3, we have reported thedata described in the literature using conventional hemodyalisers[24,27] and another type PDMS microchip previously developedwith a polycarbonate membrane (PC) [12]. The clearances of thedata found for the urea and vitamin B12 in the conventionalhemodialyser were higher than our dialysance. Those works weredone with an AN 69 membrane that have a typical cut-off about30,000–40,000 Da (similar tp the 1FPH membrane in this study[28]). Due to a smaller flow rate in our microchip (150 �L/min

and 300 �L/min compared to 16 mL/min and 32 mL/min [27], and500 mL/min [24]), and a short length and a small membrane surfacearea (1 cm2, when compared to 6000 cm2 [27] and to 11,500 cm2

[24]) the dialysance in our microchip was lower than in opti-mized conventional hemodyaliser. In spite of the efficiency of the

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A. Ould-Dris et al. / Journal of M

icrochip appearing to be lower than those types of conventionalemodialysers at their best working conditions, the comparisonust be balanced by the potential of the microchip to work with

maller flow rates and smaller membrane surfaces. For the utili-ation of the microchip as a miniaturized model of a glomerularltration, the obtained dialysances (up to 0.029 mL/(h cm2)) illus-rated the potential of our microchip as a miniaturized unit.

Finally, the comparison with the study using the microchips pre-iously developed in the literature [13] must be balanced by theype of membrane introduced in those microchips. Our microchipeemed less efficient but those microchips using a polycarbonateicroflitration membrane that have typical pore size larger than

.2 �m corresponding to a cut-off above 106 Da. This explainedheir high clearance compared to the present microchip data usinghe 1FPH PES membranes (40,000 Da).

. Conclusions

We have introduced a microchip in which the mass trans-ers of urea, vitamin B12 and albumin solutes were characterized.he mass transfers with two types of membrane of polyethersul-one and for three types of molecules have been presented. The

icrochip could be used either in dialysis mode or in diffusion-onvection mode. The introduction inside the microchip of a sievellowed controlling the mass transfer processes either by control-ing the pressure inside in the filtration chamber or by controllinghe membrane porosity. This demonstrated that the mass trans-er could be discriminated with our microchip according to theargeted applications. In addition, the proposed analytical modelllowed fitting the experimental data with the same diffusion coef-cient value for both co-current and counter-current flow. Theodel adequacy with the experiments is demonstrated by the inde-

endence of the diffusion coefficient whatever the flow regimesor a given couple of membrane and molecule. This is an encour-ging result because it will permit to use the model as a predictivenalysis tool of our “glomerular like microchip”. Finally, in ordero propose a complete bio artificial kidney, the proximal tubule rebsorption has to be included and investigated in the microchip.

cknowledgments

This work was granted by the ANR Program PCV. We thank B.arten and Dr. H.D. Lemke from Membrana GmbH for the supply ofembranes used in this study and their fruitful discussions during

he microchip development. We also thank Pr. Michel Jaffrin for hisomments during the paper redaction.

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