modeling centrifugal cell washers using computational fluid dynamics

Artificial Organs28(11):1026–1034, Blackwell Publishing, Inc.© 2004 International Center for Artificial Organs and Transplantation

1026

Blackwell Science, LtdOxford, UKAORArtificial Organs0160-564X2004 International Society for Artificial Organs281110261034Original ArticleCFD SIMULATION OF BLOOD CENTRIFUGESB.E. KELLET ET AL.

Received June 2003; revised October 2003.Address correspondence and reprint requests to Dr. S. Ranil

Wickramasinghe, Department of Chemical Engineering, Colo-rado State University, Fort Collins, CO 80523, U.S.A. E-mail:[email protected]

Modeling Centrifugal Cell Washers Using Computational Fluid Dynamics

Beth E. Kellet, Binbing Han, David S. Dandy, and S. Ranil Wickramasinghe

Department of Chemical Engineering, Colorado State University, Fort Collins, CO, U.S.A.

Abstract: Reinfusion of shed blood during surgery couldavoid the need for blood transfusions. Prior to reinfusionof the red blood cells, the shed blood must be washed inorder to remove leukocytes, platelets, and other contami-nants. Further, the hematocrit of the washed blood mustbe increased. The feasibility of using computational fluiddynamics (CFD) to guide the design of better centrifugesfor processing shed blood is explored here. The velocityfield within a centrifuge bowl and the rate of proteinremoval from the shed blood has been studied. The results

obtained indicate that CFD could help screen preliminarycentrifuge bowl designs, thus reducing the number of initialexperimental tests required when developing new centri-fuge bowls. Although the focus of this work is on washingshed blood, the methods developed here are applicable tothe design of centrifuge bowls for other blood-processingapplications. Key Words: Centrifugal cells washers—Computational fluid dynamics—Blood—Velocity field—Protein removal.

Centrifuges are widely used to process humanblood. Whole blood is routinely fractionated by cen-trifugation into components such as plasma, redblood cells, platelets, and leukocytes. The name givento the centrifugation-based separation depends onthe specific application. Therapeutic apheresis is usedfor the treatment of a variety of diseases and disor-ders characterized by the presence of abnormal pro-teins or blood cells in the circulation, which arebelieved to be involved in the propagation of thatcondition (1). When the blood component to betreated is the plasma, the apheresis technique istermed plasmapheresis. Plasmapheresis is used in thetreatment of a number of diseases such as Walden-strom’s syndrome, glomerulonephritis, and myasthe-nia gravis. When the component of the blood to betreated is cellular, the process is termed cytapheresis.Examples of cytapheresis techniques include treat-ment of diseases such as leukemia (cytapheresis, usedto remove leukocytes) and sickle cell anemia (eryth-rocytapheresis, used to remove red blood cells) (2).In all of these apheresis techniques, the fractionation

of blood into its basic components is frequentlyachieved by centrifugation.

Today, blood-banking practice is moving awayfrom the transfusion of whole blood (3). Donatedblood is first separated into relatively pure fractions.Plastic bag systems are available, which enable thepreparation by centrifugation of units of red bloodcell concentrates, platelets, and plasma from wholeblood in a closed system thus, avoiding the possibilityof contamination. Further, donor apheresis tech-niques, such as donor plasmapheresis, are also usedto collect only the desired components from thedonor. Thus, centrifugation is frequently used inblood banks for blood processing.

Due to the risk of hemolytic reactions, immuneresponses, and the transmission of blood-bornepathogens, there is a great need to minimize thenumber of transfusions required during major sur-gery. Frequently, the patient’s own blood (shedblood) is collected during surgery, processed, andreinfused thus, minimizing the requirements fortransfusion of red blood cells (4–7). Because irriga-tion fluids are used during surgery, the shed bloodhas a very low hematocrit. Leukocytes and plateletsare often activated in shed blood, thus it is undesir-able to reinfuse them. Processing shed bloodinvolves centrifugation to concentrate and purify thered blood cells present.

CFD SIMULATION OF BLOOD CENTRIFUGES 1027

Artif Organs, Vol. 28, No. 11, 2004

Designing optimized centrifuges for blood pro-cessing is a complicated process. Here, we considerthe use of computational fluid dynamics (CFD) as atool for designing centrifuges. We focus on centri-fuges for processing shed blood. An optimized cen-trifuge is one that maximizes the recovery of highlypurified concentrated red blood cells. Further, it isdesirable that small volumes (about 100 mL) of shedblood be processed as quickly as possible for rapidreinfusion. The CFD analysis developed here may beused as a tool when designing centrifuges for otherblood-processing applications.

Previous studies have investigated the use of CFDas a design tool for biomedical devices. For example,CFD models have been used in the development ofnew blood oxygenator designs by several researchers(8–10). These investigators found that CFD modelscould help guide new blood oxygenator designs.

Numerous studies have considered the design ofblood pumps. Miyazoe et al. (11,12) and Tsukamotoet al. (13) investigated the use of CFD as a designtool for centrifugal blood pumps. They found that athree-dimensional CFD model was a useful designtool when combined with flow visualization resultsand hemolysis tests. Apel et al. (14) quantified shear-induced hemolysis in a microaxial blood pump usingCFD. They found that CFD was a convenient designtool for the general assessment of shear-inducedhemolysis. Burgreen et al. (15) present a detailedassessment of the value of CFD in the design of arotary blood pump. The blood-contacting surfaces ofthe pump were designed based on their CFD ana-lysis. They found that their CFD model eliminatedthe need to build a prototype after each geometricrefinement, resulting in savings of time and money.

We have developed and applied an axisymmetricCFD model of the centrifuge bowl used in the COBEBRAT 2 (COBE Cardiovascular, Arvada, CO,U.S.A.). The CFD model is used to compute the liq-uid velocity and pressure fields in the bowl and theremoval of plasma proteins from the shed blood asfunctions of the inlet fluid flow rate and centrifuga-tion rate.

MATERIALS AND METHODS

The COBE BRAT 2 is an autologous transfusionsystem that is designed to provide washed red bloodcells. The key component of the BRAT 2 is the cen-trifuge bowl known as a Baylor Bowl (16). Figure 1is a photograph of the centrifuge bowl while Fig. 2shows cross-sectional and plane views. Blood entersvia a central inlet tube and flows to the bottom of thebowl. Next, the blood is forced radially along the

bottom toward the outer wall of the bowl. As shownin Fig. 2, the blood flows around a fin that protrudesfrom the bottom of the inside spacer. The blood thenflows upward between the inside spacer and theouter casing to the outlet located at the top of thecentrifuge bowl. The outer casing of the bowl andthe inside spacer are connected and rotate at approx-imately 4400 rpm. The densities of the cellular bloodcomponents are: 1090–1100 kg/m3 for red blood cells;1050–1085 kg/m3 for leukocytes; and 1040–1060 kg/m3 for platelets (17–19). Consequently, the red bloodcells deposit on the outer wall of the centrifuge bowlwhile the leukocytes and platelets tend to deposit ontop of the red blood cells. The plasma flows upwardbetween the deposited cells and the inside spacertoward the exit located at the top of the bowl. Bloodto be processed is loaded into the centrifuge bowluntil the red blood cells are detected by a sensorlocated at the top of the bowl. Next, wash solution isadded. The aim of the washing process is to removeplasma proteins and to ensure minimal contaminantof the deposited red blood cells by trapped leuko-cytes and platelets. The bottom edge of the insidespacer contains the fin (see Fig. 2). The fin ensuresthat the wash solution is forced through the depos-ited red blood cells, thus enhancing the removal ofplasma proteins and trapped leukocytes and plate-lets. Finally, the red blood cells are concentrated. Theprocessed red blood cells are discharged by reversingthe direction of liquid flow. A CFD model of thecentrifuge bowl was developed to determine the liq-uid flow field within the bowl and the rate of removalof plasma proteins.

CFD MODEL

The continuity and Navier–Stokes equations for anincompressible liquid are used in this study,

FIG. 1. Centrifuge bowl modeled in this study.

1028 B.E. KELLET ET AL.


(1)

(2)

where V is the velocity, r is the liquid density, P isthe pressure, t is the time, g is the gravitational con-stant, and m is the liquid viscosity. Cylindrical coor-dinates (r, q, z) are used. Although there is anappreciable velocity component in the q directiondue to the axisymmetric geometry of the centrifugebowl (see Fig. 2), velocity and pressure are indepen-dent of this coordinate. At all liquid solid interfaces,the Navier no-slip boundary condition is assumed. Inaddition, a flat inlet velocity profile is used as aboundary condition because numerical experimentsshowed that the velocity profile was fully developedat the fin tip, regardless of the specific inlet condition.

A model of the bowl was built using ProEngineer(Parametric Technology Corporation, MA, U.S.A.).The model was converted to an initial graphicsexchange specification (IGES) format and thenimported into a preprocessor called Gambit (Fluent,Lebanon, NH, U.S.A.). Within Gambit, the flowdomain was discretized into cells. The resulting

— ◊ =V 0

r r mDVDt

P g V= -— + + —2

meshed geometry contained over 43 000 cells. It wasfound that using a smaller number of cells (a coarsermesh) led to a grid-dependent solution. Figure 3shows the meshed flow domain. The meshed flowdomain was then imported into Fluent (Fluent, Leb-anon, NH, U.S.A.).

Two simulations were carried out. In the first sim-ulation, water flowed through a centrifuge bowl spin-ning at 4400 rpm. This simulation gives the velocityfield within the centrifuge bowl. In the second simu-lation, it was assumed that the bowl was filled withblood. The washing process, using saline, was thensimulated. This simulation gives the rate of proteinremoval. For both simulations, it was assumed thatthe inlet fluid velocity profile was flat (i.e., plug flow).A liquid flow rate of 200 mL/min was used as this istypical of the values encountered in practice. The no-slip boundary condition for all tangential velocitieswas applied at all solid liquid interfaces. The densityand viscosity of the liquid (water and saline) wasassumed to be that of water at 25∞C: 998 kg/m3 and0.001 Pa s, respectively. Because the first simulationgives the steady state velocity field in the bowl, it istime-independent. The second simulation gives thechange of protein concentration within the bowl as afunction of time for a 5-minute washing cycle.

In addition, for the second simulation, it wasassumed that the bowl was filled with liquid. The inlethematocrit was taken as 10%, a typical value in prac-tice. The plasma proteins were modeled usingalbumin. The diffusivity of albumin was taken as1 ¥ 10-11 m2/s, which was calculated from theEinstein–Stokes equation (20) at the experimental

FIG. 3. Part of the meshed section of the bowl and locations ofradial and axial velocity profiles.

Liquid flow direction

Radial direction

Axi

al d

irec

tion

FIG. 2. Cross-sectional and plane view of centrifuge bowl.

Liquid inlet

Liquid outlet

Spacer RBC layer

WBC/Platelet layer

Plasma layer

Spacer

Tip of fin

z

r

Plasma layer

WBC/Platelet layer

Tip of fin

RBC layer Spacer

Liquid inlet

Liquid outlet

q



conditions. The inlet protein concentration was 174 g/L in the plasma. Finally, it was necessary to model-flow through the region of deposited red blood cells.This was achieved using the porous flow model,based on Darcy’s law, built into the Fluent software.Because the commercial Fluent software used herecannot account for the deformability of red bloodcells, the deposited red blood cells were assumed toconsist of rigid particles. Clinical data indicate thatthe pressure drop for flow through the bowl isbetween 6.89 and 13.8 kPa (1–2 psi). If a porosity of20% is assumed for the deposited red blood cells, apressure drop of 10.3 kPa (1.5 psi) is obtained. Fur-ther, by defining a porosity for the layer for depositedcells, the thickness of the deposited layer is specifiedbecause the inlet hematocrit of the blood was 10%.Thus, the deposited layer of red blood cells was mod-elled as a region of 20% porosity such that the resis-tance to liquid flow was the same as observed inpractice. In this study, the presence and the removalof leukocytes and platelets were ignored.

RESULTS

CFD simulation results were obtained for thevelocity field within the bowl and the rate of proteinremoval.

Simulation 1 velocity field within the bowlFrom Fig. 3, it can be seen that large changes in

liquid velocity occur near the fin as the direction ofliquid flow changes from radial to axial. Conse-quently, velocity and pressure profiles were obtainedat various locations near the tip of the fin as well as

at various axial locations shown in Fig. 3. At location1, the fluid is flowing along the bottom of the bowltoward the outer edge of the bowl. The correspond-ing velocity and total pressure profiles are given inFigs. 4 and 5, respectively. Figure 4 indicates theexistence of two flow channels, one near each solidsurface. At the surface of the flow channel, the liquidvelocity is zero because the Navier no-slip boundarycondition was assumed. Figure 5 shows that a largepressure gradient exists very close to the upper andlower surfaces of the flow channel. This is due to thelarge velocity gradient that exists in the two flowchannels (see Fig. 4). Because the inlet fluid velocityprofile was assumed to be flat, the observed radialvelocity field develops over a very short distance.Importantly, the velocity near the center of the flowchannel is close to zero.

Axial velocity and total pressure profiles at variouslocations marked 2–4 in Fig. 3 are given in Figs. 6 and7, respectively. Near the fin (location 2), a single axialflow channel exists next to the outer surface of thefin. The velocity in this channel starts to decrease asone moves along the axis of the bowl toward the topof the bowl. However, two additional flow channelsdevelop as one moves toward the top of the bowl(locations 3 and 4): one near the inner surface of thebowl and one in between the other two flow channels.Regions of negative (downward) velocity also exist.The location of the first negative velocity is near thetip of the fin at a radial distance a little greater thanthe outermost flow channel. The magnitude ofthe negative velocity in this flow channel rapidlydecreases as one moves toward the top of the bowl.Two other regions of negative velocity occur oneither side of the centrally located flow channel atlocations 3 and 4 (Fig. 3). The existence of theseregions of negative velocity indicates that there isFIG. 4. Velocity profile at location 1 (see Fig. 3) in simulation 1.

FIG. 5. Pressure profile at location 1 (see Fig. 3) in simulation 1.



recirculation of liquid within the bowl. Figure 6 alsoindicates that most of the fluid between the outersurface of the bowl and the outermost negative flowchannel is stagnant. At the outer and inner surfacesof the bowl, the liquid velocity is zero as enforced bythe Navier no-slip boundary condition.

The corresponding total pressure profiles given inFig. 7 indicate that the total pressure varies approxi-mately linearly with radial position. By comparing

Figs. 5 and 7, it can be seen that the variation of thetotal pressure at each axial location (locations 2, 3,and 4 in Fig. 3) is much greater than the variation oftotal pressure across the radial location (location 1 inFig. 3). Consequently, slight variations in the totalpressure due to the axial liquid velocity are notobserved. In Fig. 5 on the other hand, the variationin total pressure is less than 3000 Pa, consequentlyvariations due to radial liquid flow are clearly visible.

Simulation 2 protein removalThe second simulation assumes that the bowl is

fully loaded and that cell washing has begun. Conse-quently, there is a layer of deposited red blood cellsat the outer surface of the bowl. Velocity and pres-sure profiles were determined at the same locationsas the first simulation (see Fig. 3). The radial velocityand total pressure variations at location 1 are givenin Figs. 8 and 9, respectively. By comparing Figs. 4

FIG. 6. Velocity profile at locations 2, 3, and 4 (see Fig. 3) insimulation 1. The inner surface of the casing and surface of theinner spacer define the region occupied by the blood. The innersurface of the casing and the surface of the inner spacer have aradial position of 6.55 and 5.675 cm, respectively, while the outersurface of the fin has a radial position of 6.025 cm.

FIG. 7. Pressure profile at locations 2, 3, and 4 (see Fig. 3) insimulation 1. The inner surface of the casing and surface of theinner spacer define the region occupied by the blood. The innersurface of the casing and the surface of the inner spacer have aradial position of 6.55 and 5.675 cm, respectively, while the outersurface of the fin has a radial position of 6.025 cm.

FIG. 8. Velocity profile at location 1 (see Fig. 3) in simulation 2.

FIG. 9. Pressure profile at location 1 (see Fig. 3) in simulation 2.



and 8, it can be seen that qualitatively, the figures aresimilar. However, the presence of a layer of depos-ited red blood cells in the centrifuge bowl results inthe radial velocity in the two flow channels beingapproximately the same, unlike in Fig. 4. By compar-ing Figs. 5 and 9, it can be seen that the presence ofdeposited red blood cells changes the pressure pro-file. The total pressure is higher at all points.

Axial velocity and total pressure profiles at variouslocations marked 2–4 in Fig. 3 are given in Figs. 10

and 11, respectively. The axial velocity fields given inFig. 10 are quite different to those in Fig. 6. The flowchannel near the outer edge of the fin is now withinthe deposited red blood cells. Consequently, it disap-pears very quickly as one move toward the top of thebowl. Two other flow channels develop: one near theinner wall of the bowl and one at the cell–liquidinterface. In between the two flow channels, there isa region of negative velocity indicating recirculationof the fluid. By comparing Figs. 6 and 10, it is seenthat the degree of recirculation is greater in Fig. 10.The liquid appears to be stagnant within the regionof deposited red blood cells.

By comparing Figs. 7 and 11, it can be seen that thecorresponding pressure profiles are similar. At loca-tion 2, a flow through the region of deposited redblood cells causes a deviation in the approximatelylinear pressure variation with radial position.

The variation of albumin concentration after 5 minis given in Fig. 12. As can be seen, the albuminpresent in the plasma has been completely removed.However, the removal of albumin in the layer ofdeposited red blood cells is incomplete. The CFDsoftware treats the region of deposited red bloodcells as a region of increased resistance to liquid flow.

FIG. 10. Velocity profile at locations 2, 3, and 4 (see Fig. 3) insimulation 2. The inner surface of the casing and surface of theinner spacer define the region occupied by the blood. The innersurface of the casing and the surface of the inner spacer have aradial position of 6.55 and 5.675 cm, respectively, while the outersurface of the fin has a radial position of 6.025 cm.

FIG. 11. Pressure profile at locations 2, 3, and 4 (see Fig. 3) insimulation 2. The inner surface of the casing and surface of theinner spacer define the region occupied by the blood. The innersurface of the casing and the surface of the inner spacer have aradial position of 6.55 and 5.675 cm, respectively, while the outersurface of the fin has a radial position of 6.025 cm.

FIG. 12. Mass fraction of albumin in bowl after 5-min washing.



However, the software does not account for the factthat 20% porosity implies that 80% by volume of theregion of deposited red blood cells is not availablefor plasma, and therefore albumin. Rather, the soft-ware assumes that the entire volume may be occu-pied by the plasma; however, the resistance to flowis much higher, as specified by a porosity of 20%.Therefore, the current CFD model describes theremoval of albumin qualitatively. Nevertheless, themodel may be used empirically to obtain a semiquan-titative prediction of the level of albumin removal asdescribed in the next section.

DISCUSSION

During centrifugation, the contents of the bowlmigrate to the outer wall. As liquid enters from thebottom of the bowl, it has to pass around the fin (seeFig. 2) before it can flow upward, parallel to the axisof rotation, and exit the bowl. In both simulations,a liquid flow rate of 200 mL/min was assumed.Figures 4 and 8 indicate the existence of two flowchannels as the liquid flows along the bottom of thebowl. The existence of the upper flow channel nextto the upper surface of the bowl (axial position of0.05 cm, Fig. 4) is easy to explain. When the fluidreaches the fin, it starts to move upward, parallel tothe axis of rotation. Thus, this flow channel repre-sents the path of least resistance for liquid flow.

The flow channel at the lower surface of the bowl(axial position of 0.21 cm, Fig. 4) is more difficult toexplain. It results from the diffusion of axial momen-tum. At the tip of the fin, as fluid moves upward alongthe axis of rotation, the fluid below it will be at aslightly higher pressure. This causes the fluid a littlebelow to also move upward. This repeats itself all theway to the bottom surface of the centrifuge. How-ever, because fluid is entering from the left (seeFig. 3), this leads to the creation of a second flowchannel at the bottom surface of the bowl. Figures 4and 8 indicate that, aside from these two flow chan-nels, there is little fluid motion. As a consequence ofthe centrifugal force on the fluid at the outer surfaceof the bowl, fluid that is closer to the axis (whichexperiences a lower centrifugal force) is preventedfrom displacing it. Thus, there is a net resistance offluid flow along the bottom channel, resulting in thefluid flow being restricted to two flow channels.

By comparing Figs. 4 and 8, it can be seen that theactual values of liquid velocities in the two flow chan-nels are different in the two simulations at the samevolumetric liquid flow rate. These differences arecaused by the fact that in the second simulation, theliquid in both flow channels must flow through a

region of deposited red blood cells. The correspond-ing pressure profiles, Figs. 5 and 9 are similar but alsoindicate the effect of the deposited red blood cells.Figure 9 shows that the presence of red blood cellsleads to a higher overall pressure.

Figures 6 and 10 give the axial velocity as a func-tion of radial position for the two simulations at posi-tions 2–4 (see Fig. 3). Both figures show a rather largeinitial axial velocity at a radial position correspond-ing to the outer surface of the tip. This represents theliquid as it flows around the fin. However, the axialvelocity in this flow channel decreases with increas-ing axial position (from the bottom of the bowl). Dueto the centrifugal force, the resistance to axial flow isleast at the surface of the inside spacer (lowest cen-trifugal force). Thus, as axial velocity in the initialaxial flow channel decreases, new flow channelsdevelop closer to the surface of the inside spacer. Thechanges in axial velocity in the various flow channelsare more dramatic in Fig. 10. The reason is that theinitial flow channel in this case lies completely insidethe layer of deposited red blood cells, thus the resis-tance to axial flow is significantly higher compared tothe first simulation. Figures 6 and 10 indicate regionsof negative velocity indicating the existence of recir-culation. This is significant because recirculation willcompromise the efficiency of protein removal, whichis an important design consideration. The corre-sponding pressure profiles indicate a rapid increasein pressure at the outer wall of the bowl. Further,variations in pressure due to axial fluid motion aremasked by the strong dependence of the pressure onradial position due to the centrifugal force.

Figures 7 and 11 show the pressure profile for thetwo simulations at locations 2, 3, and 4 as a functionof radial position (see Fig. 3). Both figures show that,as distance from the axis of rotation increases, thetotal pressure increases approximately linearly. Thetotal pressure is the sum of static pressure anddynamic pressure due to the axial and angular veloc-ity of the fluid. For a given axial location (2, 3, or 4),the static pressure is constant. Because the largestaxial velocity is less than 7 cm/s (see Fig. 6) while theangular velocity is about 4400 rpm, the total pressurewill be dominated by the dynamic pressure due tothe angular velocity of the fluid. Consequently thepressure gradient is given by,

(3)

where w is the angular velocity and r is the distancefrom axis of rotation. Integrating the above equation,

(4)

dPdr

r= rw2

P r c= +12

2 21rw



where c1 is an constant of integration.The total pressure varies with the square of the

radial position. However, because the radial dis-tances given in Figs. 7 and 11 are small, 5.7–6.6 cm,the variation of total pressure with radial positionappears linear.

The removal of albumin is shown qualitatively inFig. 12. As can be seen, a saline front develops in thedeposited red blood cells, which slowly movesupward toward the exit of the centrifuge. Figure 12shows the position of the front after 5 min. Table 1gives clinical data for the percentage of residual albu-min after cell washing for the conditions used in thissimulation (inlet hematocrit 10%, flow rates for filland wash cycles 200 mL/min, wash time 5 min).

The CFD model may be used to predict semi-quantitatively the percentage removal of albuminby dividing the centrifuge bowl into two zones. Thezone that contains the plasma is assumed to havean albumin concentration equivalent to the initialmeasured supernatant albumin concentration. Thealbumin concentration in the zone containingdeposited red blood cells is determined by first cal-culating the total mass of albumin present, that is,supernatant albumin concentration multiplied bythe porosity of the zone (20% in this study). Thecalculated mass of albumin is then divided by thetotal volume of the zone (including red bloodcells). Thus, the centrifuge bowl is divided into twozones with different initial albumin concentrations.Using this method, the predicted albumin removalis 90%, which is a little less than obtained in clini-cal studies (see Table 1).

The CFD method that is used to predict the resid-ual albumin in the washed blood is based on a num-ber of assumptions. Firstly, to account for the factthat the volume occupied by red blood cells is notavailable for supernatant albumin, the albumin con-centration in the zone containing deposited redblood cells is artificially adjusted. Further, the porousflow model employed by the CFD program does notrigorously account for the tortuous liquid flow pathwithin the zone of deposited red blood cells. Never-

theless, the current CFD model may be used to indi-cate the effect of varying processing parameters suchas the wash time and liquid flow rate on albuminremoval.

The results of the two simulations presented hereindicate that CFD may be a useful tool when design-ing more efficient centrifuges for blood processing.For example, the velocity fields indicate the presenceof recirculation within the bowl, which will compro-mise performance. Simulations of new bowl designscould be run to determine which ones indicatereduced recirculation. By only testing bowl designsthat appear promising, CFD simulations could beused to screen new bowl designs reducing the num-ber of initial experimental tests required. Similarly,more realistic CFD models for the zone of depositedred blood cells could be developed, which in turncould provide initial estimates of protein removal.However, prediction of leukocyte and plateletremoval will be more difficult as this involves theremoval of interacting particles.

The results presented here focus on the use ofCFD for washing shed blood. However, centrifugesare used throughout the blood banking industry formany blood-processing applications. The CFD meth-ods described here may be used to determine thevelocity field in centrifuge bowls for other blood-processing applications. Consequently, CFD could bea useful tool in designing centrifuges for other blood-processing applications.

Although semiquantitative agreement is obtainedbetween numerical and experimental results foralbumin removal, the predicted velocity and pressureprofiles within the centrifugal cell washer have notbeen validated directly by experiment. Because albu-min removal is dependent upon the velocity profile,which in turn depends on the pressure distributionwithin the centrifuge, the numerically determinedvelocity and pressure profiles appear accurate. How-ever, before using CFD to design centrifuges, thisshould be verified.

CONCLUSION

A CFD model of the Baylor bowl used in theCOBE Cardiovascular, BRAT 2 has been developed.Two simulations have been run, one representing thecentrifuge bowl filled with water, and the second rep-resenting the bowl filled with blood. The first simula-tion was focused on determining the velocity andpressure fields within the bowl, while the secondexamined the predicted rate of protein removal.Both simulations indicate that zones of liquid recir-culation exist within the bowl. However, the degree

TABLE 1. Clinical data for albumin removal using the BRAT 2 (Data provided by COBE Cardiovascular, Arvada,

CO, U.S.A.)

RunInlet albumin

concentration (g/L)Outlet albumin

concentration (g/L)

Removalpercent

(%)

1 20.7 1.02 952 20.7 0.895 963 20.7 0.872 964 20.7 0.851 96



of recirculation is greater when the centrifuge bowlis filled with blood. The model provides semiquanti-tative predictions of protein removal during cellwashing. The result obtained here indicates thatdevelopment of CFD models could be a valuable toolwhen designing more efficient centrifuges.

Acknowledgments: Financial support was pro-vided by COBE Cardiovascular, Arvada, Colorado,and the Colorado Institute for Research in Biotech-nology. The authors would like to acknowledge Dr.Steve Hunley for his many helpful suggestions.

REFERENCES

1. Zydney AL. Therapeutic apheresis and blood fractionation.In: Bronzino JD, ed. The Biomedical Engineering Handbook.Boca Raton: CRC Press, 1995;1936–51.

2. Sawada K, Malchesky PS, Nosé Y. Available removal systems:state of the art. In: Nydegger UE, ed. Therapeutic Hemapher-esis in the 1990s. New York: Karger, 1990;51–113. (Currentstudies in hematology and blood transfusion, Vol. 57).

3. Wickramasinghe SR. Washing cryopreserved blood productsusing hollow fibres. Trans Icheme 1999;77:287–92.

4. Kongsgaard UE, Hovig T, Brosstad F, Geiran O. Platelets inshed mediastinal blood used for postoperative autotransfu-sion. Acta Anaesthesiol Scand 1993;37:265–8.

5. Schmidt H, Kongsgaard UE, Kofstad J, Geiran O, RefsumHE. Autotransfusion after open heart surgery: the oxygendelivery capacity of shed mediastinal blood is maintained.Acta Anaesthesiol Scand 1995;39:754–8.

6. Vertrees RA, Conti VR, Lick SD, Zwischenberger JB,McDaniel LB, Shulman G. Adverse effects of postoperativeinfusion of shed mediastinal blood. Ann Thorac Surg 1996;62:717–23.

7. Schönberger JPAM, Bredée J, Speekenbrink RG, EvertsPAM, Wildevuur CRH. Autotransfusion of shed blood con-tributes additionally to blood saving in patients receivingaprotinin (2 millino KIU). Eur J Cardiothorac Surg 1993;7:474–7.

8. Gartner MJ, Wilhelm CR, Gage KL, Fabrizio MC, WagnerWR. Modeling flow effects on thrombotic deposition in amembrane oxygenator. Artif Organs 2000;24:29–36.

9. Goodin MS, Thor EJ, Haworth WS. Use of computationalfluid dynamics in the design of the avecor affinity oxygenator.Perfusion 1994;9:217–22.

10. Bludszuweit C. Evaluation and optimization of artificialorgans by computational fluid dynamics. Proceedings of the1997 ASME Fluids Engineering Division Summer Meeting.Vancouver, British Columbia, Canada, June 22–26, 1997.

11. Miyazoe Y, Sawairi T, Ito K, et al. Computational fluiddynamic analyses to establish design process of centrifugalblood pumps. Artif Organs 1998;22:381–5.

12. Miyazoe Y, Sawairi T, Ito K, et al. Computational fluiddynamics analysis to establish the design process of a centrif-ugal blood pump: second report. Artif Organs 1999;23:762–8.

13. Tsukamoto Y, Ito K, Sawairi T, et al. Computational fluiddynamics analysis of a centrifugal blood pump with washoutholes. Artif Organs 2000;24:648–52.

14. Apel J, Paul R, Klaus S, Siess T, Reul H. Assessment ofhemolysis related quantities in a microaxial blood pump bycomputational fluid dynamics. Artif Organs 2001;25:341–7.

15. Burgreen GW, Antaki JF, Wu ZJ, Holmes AJ. Computationalfluid dynamics as a development tool for rotary blood pumps.Artif Organs 2001;25:336–40.

16. Carson GA. Method and apparatus for autologous bloodsalvage. US Patent 5 976 388, 1999.

17. Campbell N. Biology. Menlo Park: Benjamin/CummingsPublishing Co, 1996.

18. Bronzino J. Introduction to Biomedical Engineering. SanDiego: Academic Press, 2000.

19. Zucker-Franklin D. Atlas of blood cells—function and pathol-ogy. Milano: EdiEremes, Italy, 1981.

20. Freitas RA Jr. Nanomedicine, Vol. 1: Basic Capabilities.Austin: Landes Bioscience, 1999.

modeling centrifugal cell washers using computational fluid dynamics

Documents