Urea separation in flat-plate microchannel hemodialyzer;experiment and modeling

Alana R. Tuhy & Eric K. Anderson & Goran N. Jovanovic

Published online: 29 February 2012# Springer Science+Business Media, LLC 2012

Abstract Two flat-plate microchannel hemodialyzers wereconstructed consisting of two identical laminae separated bya 20[m] thick ultrafiltration membrane (Gambro AN69).Each lamina contains a parallel array of microchannels 100[m] deep, 200[m] wide, and 5.6[cm] or 9.9[cm] in lengthrespectively. Urea was removed from the aqueous streamcontaining 1.0[g] urea per liter de-ionized water in the bloodside, by countercurrent contact with pure de-ionized waterin the dialysate side of the flat-plate hemodialyzer. In allcases volumetric flow rate of water in the dialysate side wasequal or less than the volumetric flow rate in the blood side,which is in large contrast to commercial applications ofhollow-fiber hemodialyzers where dialysate flow is several-fold larger than blood flow rate. A three-dimensional finitevolume mass transport model, built entirely from the firstprinciples with no adjustable parameters, was written inFORTRAN. The results of the mathematical model excel-lently predict experimental results. The fractional removalsof urea predicted by the model are within 2.7%11% ofexperimentally obtained values for different blood and dial-ysate velocities/flow rates in microchannels, and for differ-ent transmembrane pressures. The overall mass transfercoefficient was calculated using the urea outlet concentra-tions obtained at various average velocities (1.05.0[cm/s])in the blood and dialysate, and two nominal transmembranepressures (Ptm00 and 10,000.[Pa]). Overall mass transfercoefficients obtained experimentally ranged from 0.068 to0.14 [cm/min]. The numerical model predicted an averageoverall mass transfer coefficient of 0.08 [cm/min]. Thisvalue is 60% higher than those found in commercial dia-lyzers (~0.05[cm/min]).

Keywords Mass transfer .Microchannels . Flat-membranehemodialyzer . Urea . Hemodialysis . Dialysis

1 Introduction

The hollow fiber based hemodialyzer made an extremelyimportant impact in hemodialysis practice in the last threedecades. Patients with renal diseases were able to improvetheir life expectancy and maintain a somewhat improvedquality of life. In 2006 more than 1.6 million patientsworldwide (Kalorama Information 2007) were receivingdialysis treatment for end stage renal disease and the numberof patients requiring treatment is growing at a rate of 7% peryear worldwide (Grassmann et al. 2005). At the present ratethe number of patients requiring dialysis will exceed 2million by 2011. With the current growth rate and expectedimprovement of health care in developing nations, currentdialysis treatment models and practices need newapproaches and above all new technical solutions to providehigher quality patient care. It appears that hollow fibertechnology has met technical limitations in further develop-ment of dialysis practices and is limited to advancements inmembrane quality and production technology. The mainlimitation in the conventional hollow fiber approach is thenon-uniformity of the dialysate flow path. The packing offibers within the dialyzer is not uniform, which leads to non-uniform dialysate flow. It has been shown that the mostsignificant hindrance on mass transfer is the stagnantregions that can develop in the flow paths (Colton andLowrie 1981) and the path length for diffusion. In order tocompensate for this current designs typically increase thedialysate flowrate, which is not practical for home dialysis.The current practice of short, intensive hemodialysis ses-sions lead to significant fluctuations in blood chemistry andelicit immune system responses from blood membrane con-tact (Goerke et al. 2002). The morbidity of patients has been

A. R. Tuhy : E. K. Anderson :G. N. Jovanovic (*)Department of Chemical Engineering, Oregon State University,103 Gleeson Hall,Corvallis, OR 97331, USAe-mail: goran.jovanovic@oregonstate.edu

Biomed Microdevices (2012) 14:595602DOI 10.1007/s10544-012-9638-7

shown to be directly correlated with dialysis intensity(Brunelli et al. 2010). Microchannel hemodialyzers with flatmembranes hold many promises that are pertinent to theneeds of renal patients and healthcare providers.

This research effort was focused on the development of amulti-microchannel flat-plate hemodialyzer utilizing an ul-trafiltration membrane (Gambro AN69). This microfluidic-based hemodialyzer has markedly improved all mass trans-fer characteristics, i.e. mass transfer coefficient, mass flux,fractional removal and clearance. This results in higheroverall mass transfer efficiency. Enhanced mass transfercharacteristics were obtained as a result of uniform diffusionpath lengths on both sides of the hemodialyzer membrane:blood side and dialysate side. The consistency of diffusionpath-lengths throughout the dialyzer was achieved by uni-form design, and accurate microfabrication of microchan-nels (100200 [m] in cross section) in 1 [mm] polysulfonelaminae. The enhanced mass transfer efficiency creates op-portunities for alternate design approaches, which couldeasily result in: smaller dialyzer units, less membrane used,less expensive devices, reduced dialysate to blood flowratio, or improvements in other functional characteristicssuch as lower blood flow rates and pressure drops that arecompletely unattainable in commercially available hollowfiber hemodialyzers. An important characteristic of the flat-plate microchannel-based hemodialyzer is extremely lowblood damage, measured by the change of hematocrit, andplasma free hemoglobin. Experimental data related to blooddamage is reported elsewhere (Warner-Tuhy 2009).

2 Methods

2.1 Experimental setup

The dialyzers under consideration were of a parallel channelconfiguration in a flat-plate design. Two flat plates areassembled with channels aligned and separated with a 20[m] Gambro AN69 ultrafiltration membrane. All data pre-sented in this study is for the device operated in countercur-rent flow. For these experiments a fluid with zeroconcentration of the solute is pumped on one side of thedevice, while on the other side a solution of known concen-tration is pumped through the opposing set of microchan-nels. The output for each side of the lamina was collected,weighted, and the solute concentration measured. A detaileddescription of the experimental methods and setup has beenpreviously reported (Warner-Tuhy 2009).

Two dialyzers were tested. One design consisted of 26parallel channels which are 5.6 [cm] in length, with a crosssection of 100 [m] x 200 [m] (h x w) and was manufacturedby direct micro-machining of a polysulfone substrate using ahigh RPM CNC. Figure 1 is a rendering of a single laminae

and Fig. 2 is a photograph of the 26 channel assembled laminawithout a membrane. The second laminae design (not shown)consisted of 128 channels that are 9.9 [cm] long with a crosssection of 100 [m] x 200 [m] (h x w) and was manufacturedby thermo-embossing a polycarbonate substrate with a micro-machined stainless steel negative.

Various micromachining techniques could be used in themanufacturing of microchannels and other microscale fea-tures on a polymer (polysulfone) plate/substrate. In thisstudy the smaller 26-channel/5.6 [cm] long device wasmanufactured by directly machining the structures on apolysulfone substrate. Direct micromachining produces ac-curate features, and in this case results in a device withconsistent microchannel cross-section. Uniformly producedmicrochannels and other accurate microscale features pro-vide a device that can be used as an excellent benchmark forthe presented experimental, modeling and numerical work.Direct micromachining is a method of choice that providesconvenient and fast manufacturing of research scale devices.The 128-channel/9.9 [cm] long, device was manufacturedusing thermal embossing method. This method produces asomewhat less reliable spatial uniformity of microstructures,but is much better suited for high volume manufacturing. Inparticular, embossing process variations tend to cause themicrochannels to be somewhat shallower closer to the centerof the device. These variations result in a device with ashorter than expected characteristic diffusion path length insome microchannels, and non-uniformity in fluid residencetime distribution. After devices were successfully producedusing a direct machining approach, it was important todemonstrate the feasibility of producing devices with a highvolume manufacturing approach. Further optimization ofthe micro-embossing process is required before it will be

Fig. 1 26 rendered microchannel lamina

Fig. 2 26 microchannel lamina

596 Biomed Microdevices (2012) 14:595602

able to produce a device with increased accuracy in micro-channel dimensions.

Fluid was delivered to the dialyzer at a constant volumetricflow rate by syringe pumps. For the two dialyzers used in thisstudy the characteristic diffusion path length was 100 [m]with a total mass transfer area of 2.91 [cm2] and 25.34 [cm2]respectively. In mass transfer experiments fluid mean residencetime in the microchannel was varied between 1 [s] and 6 [s] inthe device with a channel length of 5.6 [cm], and from 2 [s] to10 [s] in the device with a 9.9 [cm] channel length. Dataobtained from numerical simulation represent the residencetime in a greater range to demonstrate the performance charac-teristics at residence time extrema that are not experimentallyfeasible. For the 5.6 [cm] device in the numerical simulationresidence timewas varied from 1.02 [s] to 11.2 [s], while for the9.9 [cm] device the numerical residence time was varied be-tween 1.8[s] and 19.8[s].

For mass transfer measurements de-ionized water wasused as the carrier fluid with urea (Sigma-Aldrich#U5128) as the analyte. The initial concentration of ureawas 1 [g/L]. The urea was analyzed using a Quantichromecolorimetric assay (DIUR-550) from Bioassay Systems(Hayword, CA). This test kit has a linear calibration up toa urea concentration of 1 [g/L]. Figure 3 is a schematic ofthe experimental test loop. Pressure was monitored at inletsand outlets using blood pressure transducers from UtahMedical Products Inc. (Midvale, UT). Three samples werecollected at each outlet, and for each flow rate, in 15 [cm3]centrifuge tubes. The samples were then weighed to checkthe mass balance. For the experimental runs requiring ultra-filtration pressure, a needle valve was connected to theblood outlet to increase backpressure, and to regulate thepressure drop across the membrane.

2.2 Analysis

Mass transfer results were evaluated at five different bloodflow rates corresponding to average fluid velocities be-tween 1.0 [cm/s] and 5.0 [cm/s] with equal dialysate flowrates and two nominal ultrafiltration pressures across themembrane (Ptm00.0 [Pa] and 10 000. [Pa]). One experi-ment was conducted with the dialysate flow rate being 75%that of the blood flow rate and no nominal transmembranepressure.

2.3 Mathematical model for urea transport

To accurately analyze, and predict the mass transfer perfor-mance of the microchannel dialyzer a three-dimensionalnumerical simulation algorithm was developed. Numericalsimulations are based on the mathematical model (Eqs. 1a,1b, and 2), which is entirely built on the conservationequations for mass and momentum transport with no adjust-able parameters. Since each microchannel pair operatesidentically to other parallel channels, only one channel pairneeds to be simulated to predict the performance of theentire device.

The computational domain is comprised of three sub-domains illustrated in Fig. 4. The two fluid domains areseparated by a porous membrane. The numerical solution ofthe differential equations is third order accurate and weresolved using GMRES and preconditioned conjugategradients.

The steady state NavierStokes equations for isothermal andincompressible fluid (Eq. 1a) were solved using the SIMPLEmethod to generate the three-dimensional flow field within apair of microchannels. The boundary conditions for the Navier

Fig. 3 Test loop

Biomed Microdevices (2012) 14:595602 597

Stokes equations are provided in Table 1, where ub,o and ud,o areaverage inlet blood and dialysate velocities respectively.

@u@t

u r u

rp r2u 1a

r u 0 1bWater was the carrier fluid used in the experiments and

the flow was assumed to be Newtonian and incompressible.The viscosity and density of water at 30C was used in thesimulations as this closely matched the ambient temperatureduring the experiments. Dilute solution assumptions wereinvoked since the concentration of the solute (urea) wassmall and was assumed to have no impact on the flow field.The general steady state convection diffusion equation for adilute solution (Eq. 2) was solved to evaluate the masstransfer in the microchannel pair. The boundary conditionsand diffusivities are provided in Table 2, where Dab is thediffusivity of urea in water and Deff is the effective diffusiv-ity of urea in water in the membrane. The effective

diffusivity (Deff) used for diffusion in the membrane wasevaluated from the literature values given below.

u@C

@x v @C

@y w @C

@z

D @

2C

@x2 @

2C

@y2 @

2C

@z2

2

Convective transport through the membrane is importantfor solute clearance and is also necessary for water removalfrom the bloodstream. Darcys law was used to model theporous flow through the ultrafiltration membrane domain.Literature values were used for membrane characteristics(Collins and Ramirez 1979), and were scaled for membranethickness using Ficks Law. In the membrane the effectivediffusivity for urea in water (Deff) is 5.5*10

6 [cm2/sec] andthe hydraulic permeability is 42 [ml/h m2mmHg].

Numerical simulations corresponding to experimentalconditions for each hemodialyzer device were run in orderto accurately compare the simulation results with the exper-imental results. The simulation results were in excellentagreement with experimental data and are discussed inSection 3, below.

Fig. 4 Computational domainfor model

Table 1 Boundary conditions for navierstokes equations

Inletujx0;htm

2.4 Mass transfer coefficient, K

The overall mass transfer coefficient (Eq. 3a) and fractionalremoval (Eq. 4) of urea were also calculated using the ureaoutlet concentrations. The overall mass transfer coefficientwas chosen as a performance metric to allow readers easyassessment of these findings with other published works andcommercial dialyzer data.

Ko N

CinletCoutletln

CinletCoutlet

0@

1A

3a

N mtransA t 3b

In Eq. 3a and 3b,N is the average mass flux and mtrans isthe urea transferred to the dialysate in [mg], t is the meanresidence time of the fluid in a microchannel [min], A is thesurface area available for transfer in [cm2], C is the concen-tration of urea in [mg/cm3], and Ko is the overall masstransfer coefficient with units of [cm/min]. The fractionalremoval of urea in the flat-plate hemodialyzer device wascalculated using Eq. 4 where Fr is the fractional removal,QD,O is the fluid flow rate out of the dialysate side, CD,O isthe concentration of urea in the dialysate outlet, QB,I is thefluid flow rate in on the blood side, CB,I is the initialconcentration of urea in blood inlet 1.0 [mg/cm3].

Fr QD;OCD;OQB;ICB;I 4

3 Results

The major objective of this work was to demonstrate that aflat-plate microchannel-based dialyzer could provide im-proved mass transfer characteristics (such as fractional re-moval of urea, and overall mass transfer coefficient) incomparison to the same mass transfer characteristics pub-lished for commercially available hollow fiber dialyzers. Allexperimental mass transfer data is obtained in the test loopschematic shown in Fig. 3.

A parametric study was conducted using the numericalsimulation to determine solute concentration along thelength of the channel. The final outlet concentration wasintegrated across the microchannel to determine the frac-tional removal and overall mass transfer coefficient.Figure 5 illustrates the concentration in the top (blood)channel with respect to the longitudinal (x) position in thechannel. The concentration profiles are for a channel length

of 5.6 [cm] at various average fluid velocities (at equalblood and dialysate flow) and no imposed pressure offset.

Fractional removal of urea at the five fluid velocitieswere calculated from experimental data and comparedagainst the simulation results. The experimental and modelcomparison with and without an imposed pressure offset,between blood and dialysate side of the hemodialyzer, isshown in Fig. 6. The model results are within 2.7% ofexperimental results indicating fractional removals of urearanging from 0.14[/] to 0.47[/]. The experimental data setshown in Fig. 6 is for the dialyzer shown in Figs. 1 and 2(laminae with 26 parallel microchannels, 5.6 [cm] in length)

Figure 7 shows the fractional removal comparison forurea with two blood-to-dialysate flow rate ratios (1:1 and1:0.75 [blood : dialysate]). The results show the experimen-tal data is within 11% of the simulation predicted fractionalremovals for urea. The experimental data set shown in Fig. 7

0.0

0.2

0.4

0.6

0.8

1.0

0.1 0.8 1.5 2.1 2.8 3.5 4.1 4.8 5.5

Conc

entra

tion

(g/L)

X Position in Top Channel (cm)Fig. 5 Simulated urea concentration along the length of the channel.Fluid velocities from bottom line to top line: 0.5, 1.0, 2.0, 3.0, 4.0, 5.0,and 5.5 (cm/s)

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 1 2 3 4 5 6

Frac

tiona

l Rem

oval

Fluid Velocity in Top (Blood) Channels (cm/s)Fig. 6 Urea fractional removal at varying fluid velocities for 5.6 [cm]channel. Simulation result for Ptm00.0 [Pa], Simulationresult for Ptm010 000 [Pa], () represents experimental data forPtm00 [Pa], and () represents experimental data for Ptm010 000[Pa]

Biomed Microdevices (2012) 14:595602 599

is for a dialyzer laminae with 128 parallel microchannels,9.9 [cm] in length.

In Fig. 7 there is an increasing difference between thesimulation results and experimentally obtained data for thefractional removal that is not observed with the smaller 5.6[cm] device. This is a clear demonstration of the effect ofunder-imprinting that was occasionally observed inembossed devices. Great care was exercised to use onlyembossed, 9.9 [cm], devices with minimal variations incharacteristic dimensions. Due to the nature of the thermalembossing process, variations in microchannel depth werefound to be one-sided; i.e. under-imprinting causes thephysical device to be shallower than the design depth micro-channels. Since the computational model assumes designedmicrochannel dimensions, it could be expected that simula-tion results under-predict the fractional removal achieved bythe device. This effect is not observed in the 5.6 [cm]channel device because direct micromachining does notcause this systematic process variation.

Fractional removal is rarely reported in open literature,thus it is difficult to find this mass transfer characteristic forcommercially available hollow fiber hemodialyzers.Fractional removal is also an extensive mass transfer char-acteristic, which depends on the length of microchannels/hollow fibers, and cannot be readily used for direct compar-ison of mass transfer performances of dissimilar (in con-struction architecture) hemodialyzer devices. Contrary tofractional removal, overall mass transfer coefficient, Ko, ismore often reported in open literature, and it is largelyinsensitive to the length of microchannels/follow fibersand initial solute concentrations. Thus, it can be used tocompare mass transfer efficiencies of dissimilar (in size,type, and architecture) hemodialyzer devices.

Below, are the experimentally obtained overall masstransfer coefficients, Ko, at characteristic operating veloci-ties in microchannels. The experimental results comparevery favorably with the overall mass transfer coefficientsreported in open literature for commercially availablehemodialyzers.

Figure 8 shows overall mass transfer coefficientsobtained at different blood and dialysate flow rates (veloc-ities in the microchannels) through a dialyzer lamina, whichwas assembled from two microchannel plates, separated byan ultrafiltration membrane. The average fluid velocities in amicrochannel are also shown in Fig. 8, in addition to therange of blood flow velocities typically encountered incommercial hollow fiber dialyzers. Overall mass transfercoefficients were calculated from experimental dataobtained in the test loop, schematically illustrated inFig. 3. Numerical values for the obtained experiential datapresented along with additional experimental results for theremoval of urea in a microchannel hemodialyzer can befound elsewhere (Warner-Tuhy 2009). The overall masstransfer coefficients for two blood-to-dialysate flow rateratios (1:1 and 1:0.75 [blood : dialysate]) are shown inFig. 8 for a lamina with 128 microchannels and a length of9.9 [cm]. Each data point represented in Fig. 8 is the averageof six independent measurements. The solid line is theoverall mass transfer coefficient predicted from the simula-tion. The corresponding pressure drops for each side of thelamina are given in Fig. 9. Overall mass transfer coefficientswere in the range of 0.07 [cm/min] to 0.14 [cm/min], theaverage simulation result was 0.08 [cm/min].

Increasing the nominal pressure on the blood side of thelamina increases convective transport through the mem-brane. Figure 10 shows the overall mass transfer coefficientsobtained at two nominal ultrafiltration pressure differencesacross membrane: Ptm00.0 [Pa] and 10 000 [Pa], at 1:1

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 1 2 3 4 5 6

Frac

tiona

l Rem

oval

Fluid Velocity in Top (Blood) Channel (cm/s)Fig. 7 Urea fractional removal at varying channel velocities for 9.9[cm] channel. Simulation result for equivalent fluid velocities,

Simulation result for (1:0.75) velocity ratio, () experimentaldata for equivalent fluid velocities and () experimental data for(1:0.75) velocity ratio

0.00

0.04

0.08

0.12

0.16

0.20

0 1 2 3 4 5 6

Ko (cm

/min)

Fluid Velocity in Top (Blood )Channels (cm/s)Fig. 8 Mass transfer coefficient at varying blood flowrates for 9.9[cm] channel. () 1:1 blood-to-dialysate flow ratio and () 1:0.75blood-to-dialysate flow ratio. () Simulation results ( ) Commercialhollow fiber

600 Biomed Microdevices (2012) 14:595602

blood-to-dialysate velocity ratio using a lamina containing26 microchannels with a length of 5.6 [cm]. Thecorresponding pressure drops for each side of the lamina aregiven in Fig. 11. The experimental overall mass transfer coef-ficients were between of 0.075 [cm/min] and 0.091 [cm/min],and the simulation results were between 0.079 [cm/min] and0.088 [cm/min].

Simulation results for the overall mass transfer coeffi-cient indicate a slight velocity dependence and are in agree-ment with the experimental results for the smaller 5.6 [cm]device. The mass transfer coefficient in the 9.9[cm] devicehas larger velocity dependence than is predicted by themodel. The authors hypothesize that this is largely due totwo factors. The first is that the manufacturing method isdifferent between the two devices. The 5.6 [cm] device wasdirectly machined while the 9.9 [cm] device was thermallyembossed, which may lead to larger manufacturing varian-ces in the embossed device. The second cause is pressuredependent flow misdistribution in the large device. It is

challenging to design an optimal header space that willuniformly feed larger number of microchannels, especiallyin the presence of occasional gas bubbles found in bothblood and dialysate side of the device. A simple plenumthat was used in laminae with 128 channels may not havebeen sufficient to guarantee uniform distribution of fluid ineach microchannel.

Issues related to variances in microchannel dimensionsemerging from thermal embossing are challenges that com-mercial manufacturers of microscale structures have alreadysuccessfully resolved. The appearance of gas bubbles isubiquitous for all microchannel structures, in which bubblescause unexpected and seemingly random variations in pres-sure and flow distributions. This particular phenomenon andsearch for a viable solution is currently explored by theauthors research group under NIH-RO1 grant.

The overall mass transfer coefficients obtained from allexperiments were in the range of 0.068 [cm/min] to 0.14[cm/min]. The range for commercial hollow fiber dialyzers:CT110GST, Nephral ST 200, and Nephral ST 500 is from0.049 to 0.051 [cm/min] (Morti and Zydney 1998; Warner-Tuhy 2009). The model predicts an overall mass transfercoefficient of 0.08 [cm/min] in the blood velocity operatingrange for commercial hollow fiber dialyzers.

A statistical analysis was performed on the experimentaldata sets to determine if there is a significant statisticaldifference in overall mass transfer coefficients for the caseof reduced dialysate flow, and the case of increased pressureoffset between blood and dialysate side. Based on a paired t-test the difference in mass transfer coefficients caused byreducing the dialysate flow rate by 25% was not significant(shown in Figs. 7 and 8). There is also no statistical differ-ence in the urea transport when a 10 000 [Pa] pressure offsetis imposed (Figs. 6 and 10). These results support theconclusion that flat-plate microchannel-based hemodialyz-ers may use substantially smaller quantities of dialysate,

0

5000

10000

15000

20000

25000

0 1 2 3 4 5 6

Pres

sure

(Pa)

Fluid Velocity in Top (Blood) Channels (cm/s)Fig. 9 Pressure drop (p) for each side (inletoutlet) for 9.9 [cm]channel. () 1:1 blood-to-dialysate flow ratio, () 1:0.75 blood-to-dialysate flow ratio. (white) dialysate side (black) blood side

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0 1 2 3 4 5 6

Ko

(cm/m

in)

Fluid Velocity in Top (Blood) Channels (cm/s)Fig. 10 Overall mass transfer coefficient for 5.6 [cm] channel. ()P00 [Pa], and () P010,000 [Pa]. () Simulation results ( )commercial hollow fiber dialyzer

0

2000

4000

6000

8000

10000

12000

0 1 2 3 4 5 6

Pres

sure

Dro

p (P

a)

Fluid Velocity in Top (Blood) Channels (cm/s)Fig. 11 Pressure drop for each side (inletoutlet) for 5.6 [cm] channel.() Ptm00 [Pa], () Ptm010 000 [Pa], (black) blood side and (white)dialysate side

Biomed Microdevices (2012) 14:595602 601

compared to hollow fiber dialyzers, without a penalty in theoverall mass transfer efficiency. It was somewhat surprisingthat the imposed pressure offset of P010,000 [Pa] did notyield significant gains in urea removal. The convective flowthrough a thin ultrafiltration membrane is still small enoughnot to contribute substantially to mass transfer of urea,which is dominated by diffusional transport phenomena.However, in a clinical setting it is still necessary to impose apressure difference to facilitate overall net transport for re-moval of fluids from the blood stream.

4 Discussion

The mass transfer coefficient of a dialyzer characterizes thedevices ability to transfer a given solute from the blood-stream. By isolating the boundary layers in microfluidicdevices the mass transfer coefficient can be greatlyenhanced.

The results found indicate that flat-plate microchannelhemodialyzers have the potential for overcoming some ofthe current limitations in commercial hollow fiber dialyzertechnology. The large increase in mass transfer efficiencymakes it possible to produce physically smaller and possiblymore economical dialyzers than are currently available. Asmaller device will both require a lower blood primingvolume and reduce the blood membrane contact time. Thisincrease in efficiency also lowers the dialysate requirementsfor a typical renal failure treatment, which both lowers the

cost of treatment and is the next step in the development of awearable dialyzer.

Acknowledgements Source of Support: This work was supported inpart by the National Institute of Biomedical Imaging and Bioengineering(grant no. R01EB011567). The content is solely the responsibility of theauthors and does not necessarily represent the official views of theNational Institute of Biomedical Imaging and Bioengineering, or theNational Institutes of Health. We, also, gratefully acknowledge the fund-ing obtained from: ONAMI (Oregon Nanoscience andMicrotechnologiesInstitute), John C. Erkkila Endowment, Murdock Charitable TrustOregon, and Oregon State University College of Engineering.

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602 Biomed Microdevices (2012) 14:595602

Urea separation in flat-plate microchannel hemodialyzer; experiment and modelingAbstractIntroductionMethodsExperimental setupAnalysisMathematical model for urea transportMass transfer coefficient, K

ResultsDiscussionReferences