Design and Transient Computational Fluid Dynamics Study ofa Continuous Axial Flow Ventricular Assist Device

XINWEI SONG,* ALEXANDRINA UNTAROIU,* HOUSTON G. WOOD,* PAUL E. ALLAIRE,* AMY L. THROCKMORTON,† STEVEN W. DAY,*AND DONALD B. OLSEN‡

A ventricular assist device (VAD), which is a miniaturizedaxial flow pump from the point of view of mechanism, hasbeen designed and studied in this report. It consists of aninducer, an impeller, and a diffuser. The main design objec-tive of this VAD is to produce an axial pump with a stream-lined, idealized, and nonobstructing blood flow path. Themagnetic bearings are adapted so that the impeller is com-pletely magnetically levitated. The VAD operates under tran-sient conditions because of the spinning movement of theimpeller and the pulsatile inlet flow rate. The design method,procedure, and iterations are presented. The VAD’s perfor-mance under transient conditions is investigated by means ofcomputational fluid dynamics (CFD). Two reference frames,rotational and stationary, are implemented in the CFD simu-lations. The inlet and outlet surfaces of the impeller, whichare connected to the inducer and diffuser respectively, areallowed to rotate and slide during the calculation to simulatethe realistic spinning motion of the impeller. The flow headcurves are determined, and the variation of pressure distri-bution during a cardiac cycle (including systole and diastole)is given. The axial oscillation of impeller is also estimated forthe magnetic bearing design. The transient CFD simulation,which requires more computer resources and calculationefforts than the steady simulation, provides a range ratherthan only a point for the VAD’s performance. Because ofpulsatile flow phenomena and virtual spinning movement ofthe impeller, the transient simulation, which is realisticallycorrelated with the in vivo implant scenarios of a VAD, isessential to ensure an effective and reliable VAD design.ASAIO Journal 2004; 50:215–224.

Claiming approximately 945,836 lives in the year 2000,cardiovascular disease (CVD) is the number one killer in theworld. It is estimated that approximately 4.8 million people inthe United States have congestive heart failure (CHF), a clinicalsyndrome that involves severe ventricular dysfunction andultimately leads to a reduction in cardiac output. Approxi-

mately 40,000 patients with CHF die each year, and as manyas 250,000 deaths are a result of CHF related illnesses. Ac-cording to statistical estimations, approximately 400,000 newCHF cases are diagnosed each year in the United States.1

These patients with cardiac failure follow a significant regimenof cardiac medications and often require heart transplantation.Because there is a limited number of donor hearts availableeach year (approximately 2,500), many such patients withCHF may not survive the lengthy waiting period for a donorheart. Patients with CHF often need mechanical circulatorysupport (MCS) as a bridge to transplantation and even as along-term destination therapy.

MCSs have been researched and developed for decades andfall into three main categories: total artificial heart (TAH),volume displacement blood pump (DBP), and rotary bloodpump (RBP).2–6 The TAH aims to completely replace the na-tive heart with a pulsatile MCS. DBP and RBP are the ventric-ular assist devices (VAD) that merely assist the native ventricleto pump blood through the body and, therefore, reduce itsworkload. DBPs are typically pulsatile blood flow supportdevices with flexible membranes or pusher plate design in-cluding a multitude of valves. In contrast, RBPs provide con-tinuous blood flow via a centrifugal or axial flow design withno membranes or valves. Up to 2003, there were three MCSsthat had received U.S. Food and Drug Administration (FDA)approval and could be used for a designated therapy: ThoratecVAD, HeartMate LVAS (left ventricular assist system), andNovacor LVAS. Several MCSs were undergoing clinical trials.VADs have been proven to provide effective supplementalcirculatory support to patients with cardiac failure. An esti-mated 35,000–70,000 people in the United States could ben-efit from long-term MCSs each year.7 To provide a viable MCSoption as long-term therapy for these patients with cardiacfailure and an improvement over currently available devices,the present authors designed a fully implantable axial flow RBPwith a magnetically levitated impeller for the adult population.

The Virginia Artificial Heart Institute (VAHI) has developedseveral prototypes of continuous flow centrifugal left ventric-ular assist devices (LVADs) with magnetically levitated impel-lers for long-term use for patients with CHF.8–19 The mostrecent and successful prototype, the HeartQuest CF4b, is cur-rently undergoing animal testing at the Utah Artificial HeartInstitute.20–24 The CF4b pump has been implanted in a seriesof four calves for 30–60 days and in one calf for approximately110 days. The calves performed well on the treadmill with thepump support; they did not show an increase in plasma freehemoglobin over the support duration, and they had no fibrinsplit products or d-dimers in the circulating blood (indicativeof thrombosis) that had been broken down with the fibrolysin

From the *Mechanical and Aerospace Engineering Department,Virginia Artificial Heart Institute, University of Virginia, Charlottesville,VA; †Biomedical Engineering Department, Virginia Artificial HeartInstitute, University of Virginia, Charlottesville, VA; and the ‡UtahArtificial Heart Institute, Salt Lake City, UT.

Presented in part at ASAIO-ISAO Joint Conference, June 19–21,2003, Washington, DC.

Correspondence: Xinwei Song, 122 Engineer’s Way, Mechanical &Aerospace Department, University of Virginia, Charlottesville, VA22903.

DOI: 10.1097/01.MAT.0000124954.69612.83

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enzymes. The experiences gained from this successful centrif-ugal design effort were helpful in developing an axial flowblood pump.

Even though the advantages and disadvantages of axial ver-sus centrifugal VADs are still in dispute, the present authorsbelieve that there are a number of advantages of the axial flowdesign as compared with the centrifugal configuration, espe-cially for a totally magnetically suspended impeller. The cen-trifugal pump presents a geometry that is not easily implantedto a calf or a human because of its inflow and outflow portlocations. The magnetically levitated impeller design for acentrifugal RBP generates a secondary blood flow path throughthe clearances between the pump housing and the rotatingimpeller.24 This secondary flow path may create possibilities offlow stagnation and high shear stresses, which could lead tohemolysis and possible thrombosis. In contrast to centrifugalVADs, the magnetically levitated impeller design for thepresent authors’ axial flow pump does not include a secondaryblood flow path. Furthermore, axial pumps have better ana-tomic fit because of their compact sizes and tubular configu-rations. As a result, axial flow pumps require less time toimplant, thereby decreasing the cost and invasiveness of theprocedure.25,26

The main design objective of the present authors’ axial flowpump, named the LEV-VAD, is to produce a pump with astreamlined, idealized, one pass, nonobstructing blood flowpath that can deliver 100 mm Hg pressure rise at 6 L/minvolume flow rate. As previously mentioned, the LEV-VADincludes an impeller that is suspended entirely by magneticbearings (MBs). This suspension design allows the impeller toavoid any contact with the pump’s internal housing. Thisdesign also reduces regions of stagnant and high shear flowthat normally surround a fluid or pivot bearing by allowing forlarger clearances between the rotor and housing. Unlike tra-ditional mechanical bearings, MBs have no moving parts incontact; thus they do not wear over time and consequentlyhave a longer operational lifetime. The bearing Hall sensorsprovide information that aids in the control of the impeller’sposition and movement. Novel algorithms that have beendeveloped and tested over years will be implemented to de-duce the pump operating flow rate and pressure rise by mon-itoring the electrical power to the bearings.27–29 Figure 1 illus-

trates the LEV-VAD design including magnetic bearings andmotor components.

Materials and Methods

Pump Design Theory

Turbo machines involve an energy transfer between therotor and the flowing fluid. In the axial pump, the impellerreceives energy from an external electric motor and impartsthe energy to the fluid. Basic design expression for an axialpump is a form of Newton’s law of motion applied to the fluidtraversing the rotor, which states that the torque on the impel-ler is equal to the changing rate of the angular momentum offluid.30–32

Equation 1 defines the torque (T) as a function of mass flowrate (m), the radii (r1 and r2), and the tangential absolutevelocities (Vu1 and Vu2).

T � m�Vu1r1 � Vu2r2� (1)

Equation 2 is the vector expression of the velocity triangle.The relative velocity of fluid (W) with respect to the movingblade is added to the blade velocity (U) to obtain the absolutefluid velocity (V).

V � W � U (2)

The corresponding velocity triangles at the inlet and outletare shown in Figure 2. From the definition that the pumppower (P) is the product of torque (T) and rotational speed (�)in radians per second, P can be written as (Equation 3)

P � m�Vu1U1 � Vu2U2� (3)

where the blade speed Ui substitutes for �ri. By dividingEquation 3 by the mass flow rate (m) and gravity (g), we obtainthe head expression (Equation 4):

H �1g

�U2Vu2 � U1Vu1� (4)

Equation 4 represents the well known Euler’s head equation,where H is a theoretical head because all hydraulic losses havebeen disregarded. Euler’s velocity triangles are used for graph-ical determination of the impeller blade shape. If the fluid

Figure 1. Sketch of configuration of LEV-VAD. VAD, ventricularassist device. Figure 2. Velocity triangles at inlet and outlet.

216 SONG ET AL.

enters the rotor axially (without a tangential component ofvelocity or Vu1 � 0), Euler’s equation reduces to:

H �U2Vu2

g(5)

The mass flow rate (m) through the impeller is calculated bymultiplying the axial velocity (Va) by the normal area of flowpassage and the fluid density (�).

m � �VaA (6)

This relation represents the conservation of mass.In a pump working with incompressible fluid, the important

parameters are the volume flow rate (Q) and the total pressurerise (�gH). They are often combined to two dimensionlessvariables to characterize the pump performance

Head coefficient: � �gH

�2�2r�2 (7)

Flow coefficient: � �Q

��2r�3 (8)

Specific speed �s and specific diameter Ds can be definedby the head coefficient � and the flow coefficient �

Specific speed: �s ��1/ 2

�3/4 ��1/ 2

�gH�3/4 (9)

Specific diameter: Ds ��1/4

�1/ 2 �D�gH�1/4

Q1/ 2 (10)

Performance curves are frequently plotted using a pair ofdimensionless variables described above, such as curve orcurve. Additionally, dimensionless variables are commonlyused to select the type of machine and to determine theimpeller size and geometry according to the operating require-ments. For example, Figure 3 displays the copy of empiricaldiagrams for selection of machine and initial guess of pump

dimension based upon the specific speed �s.30 High efficiencyaxial pumps correspond to the range of specific speed of2.5–5.5. The particular speed specific diameter plot (Cordierdiagram) shows the optimum relation between the operatingspeed and pump dimensions, allowing for high efficiencies.The impeller geometry, including impeller tip and root diam-eters, annular flow area, blade number, and inlet and outletblade angles (�1,�2) can be determined by the specific diam-eter based upon some other empirical charts and formulas.31

An axial pump so selected and designed would be expected tohave a high efficiency. Generally, the blades have shapes orprofiles similar to those of airfoils: they are thin, cambered, andstreamlined.

The conventional design theories and approaches may onlyproduce a rough geometric estimation for an axial flow bloodpump because the characteristic dimensions of a blood pumpare much smaller than the applicable limits of those empiricalformulas and diagrams. Therefore, computational fluid dynam-ics (CFD) must be used as an important tool for optimizing thesize and geometry and finalizing the design of the pump beforemanufacturing to satisfy all blood pump requirements.

Design Objectives and Criteria

The design process of an axial flow RBP is far more complexthan that of a typical industrial axial flow pump. Blood pumpdesigners must consider a number of specific design require-ments besides pump performance, such as implantability,blood compatibility, durability, and MBs feasibility.33 Toachieve an implantable pump, the overall size of the devicebecomes the central focus and the most important constraintduring the design phase. Designing a pump with high effi-ciency and lower power consumption helps to minimize thesize of the motor, thereby reducing the overall size of the RBP.Also, a miniaturized blood pump would reduce device relatedinfections and could eliminate the need for an abdominalsurgical pocket.

Because, for the same head and capacity requirements, thepump operational speed is inversely proportional to thepump’s size, a smaller pump corresponds to a higher rotationalspeed of the rotor. Unfortunately, a higher rotor speed impliesa higher value of shear stress, which could have a traumaticeffect on blood. Therefore, the second important constraintbecomes the rotor rotational speed and the clearance gapsbetween the rotor and the stationary housing. The larger theclearance gaps, the smaller the shear stress value under a givenrotational speed. However, wider clearance gaps create morechallenges to the MB designs.

The blood pump should be a nonthrombogenic device.Fundamentally, blood needs to be constantly in motion toavoid clotting and thrombosis. The smooth, nonobstructingflow path through the pump should be ideal to maintain acontinuous wash over all surfaces and to avoid recirculation orstagnant flow regions that would encourage deposition ofplatelets. Additionally, platelet activation is far more sensitiveto high shear flow conditions. A combination of smooth flowpath and proper flow pattern near surfaces can reduce poten-tial deposition and activation of the coagulation cascade.

Durability is the main motive for using MBs in the presentauthors’ LEV-VAD designs. MBs have an expected lifetime of15–20 years and are more reliable than mechanical bearings.

Figure 3. Conventional pump design approach. Top, specificspeed chart; bottom , specific speed-specific diameter plots(Cordier Diagram).

217CONTINUOUS AXIAL FLOW VAD

Another advantage over mechanical bearings is that blood canwash over surfaces to avoid stagnation. In addition, mechan-ical bearings generate more shear stress near the touch points.On the other hand, MBs need extra space to locate the per-manent magnets and coils. The fluid forces and moments onthe impeller and more detailed information on the fluid fieldare required to design the stiffness and control capability ofMBs. Also, the VADs with MBs need more percutaneous wiresas compared with those with pivot or fluid bearings.

Depending upon the diversity of patients and the level oftheir physical exertion, the axial RBP must be able to operateover a wide range of flow conditions. Designed to operate at asingle, best efficiency operating point, blood pumps quitefrequently are required to perform at off design conditions. Therobust motor and suspension system and its control systemmust be able to successfully and quickly respond to these flowcondition adjustments by varying pump rotational speed. Thedesign of the LEV-VAD requires a multidisciplinary consider-ation of traditional hydraulic analyses, MB design and itscontrol system, and hematologic performance criteria. Com-promises must be explored among those design elements toobtain the best overall performance. Table 1 gives the insightof design objectives and considerations.

Design Iterations

The flowchart illustrated in Figure 4 presents the generaldesign procedure of an axial blood pump with magneticallysuspended impeller. A baseline analysis was completed first bymeans of classic pump design formulas and empirical dia-grams to obtain an initial pump geometry. Based upon that, aCFD model was generated, and an initial MB design wasexecuted. The detailed information of fluid field exposed thedeficiencies of the initial design and provided the fluid forcesand moments for optimizing MB design. The CFD fluid pathand MB designs will greatly affect the overall pump geometricparameters. A number of design iterations have been per-formed to reach the prototype stage for manufacture andbench tests. It should be noted that a proper mechanical designdoes not necessarily create an ideal VAD prototype. Unfeasi-bility or extremely high cost of manufacture, coverage byexisting patents, or absence of innovation could abort a desir-able design.

Table 2 elaborates the design iterations that the presentauthors experienced before the final design. A configurationwith inducer, impeller, and diffuser has been adopted. The

inducer straightens the flow and removes prerotation of thefluid before the fluid reaches the impeller region, which makesthe design of the impeller much easier. The simple geometry ofinducer provides the possibility to optimally locate the activemagnetic bearings (AMBs) without increasing the VAD’s over-all size. The impeller accelerates speed of the fluid and trans-forms the rotational energy imparted by the motor to thekinetic energy of the fluid. The stagger angle of the bladeshould gradually increase along the flow direction; otherwise,flow separation would likely occur. Unlike the simple velocitydistribution at the discharge of inducer, the existing angularvelocity and nonuniformity of axial velocity at the trailing edgeof the impeller blades make the design of the diffuser ex-tremely challenging. The diffuser converts the kinetic energy ofthe fluid to the desired pressure energy and thus must bedesigned to avoid recirculation, minimize resistance to flow,and allow for manufacturability. Because of the great curva-

Table 1. Axial Blood Pump Design Objectives and Considerations

Design Objectives Considerations

Fluid System Provide the required range of flow andhead

● Size● Smooth, nonobstructing flow path● Impeller to housing clearance● Fluid forces● High efficiency● Impeller position

Suspension/Motor System ● Keep the impeller suspended● Provide the required mechanical power

● Size● Stiffness● Body force and fluid force● Magnetic gaps● Sensor and control system

Figure 4. The design flowchart of axial blood pump with magneticbearings.

218 SONG ET AL.

ture, three diffuser blades are finally adopted in the LEV-VADfor ease of manufacturing.

Figure 5 shows the design and development history of thepresent authors axial blood pumps. It displays the main phases(UAP-1 to UAP-4) before the final version (LEV-VAD).

Last Version: LEV-VAD

The last version, named LEV-VAD, reached desirable fluid,magnetic, and hematologic performances. The LEV-VAD mea-sures approximately 100 mm in length and 30 mm in diameter.Figure 6 shows the blade angle (Beta on the ordinate) distri-butions along the axis in impeller section at different spans.The blade angle is measured from the axial to the tangentialdirection. The M-Prime on the abscissa represents the radiusnormalized distance along the meridional curve. The bladeangle is designed to change gradually. Figure 7 shows thepump’s configuration and the CFD model of the LEV-VAD. Thefluid enters the inducer, the impeller, and the diffuser sequen-tially. The axial gaps between inducer and impeller and theimpeller and diffuser are both 1 mm. The main geometricparameters for inducer, impeller, and diffuser blades are givenin Table 3. The inducer’s fluid dynamic function is to feed theimpeller straightly, so both its inlet and outlet blade angles arezero degree, which means that the inducer blades are parallelto the axis. The inlet angles of impeller and diffuser blades are

designed to be tangent to the fluid incident angle to avoid thevortex and reduce the friction and energy loss. They are rela-tively large because of the high rotational speed of the impel-ler. Counter-clockwise is specified as positive; clockwise isspecified as negative. The diffuser blade outlet angle is desig-nated as zero degree to minimize the angular component offluid speed and, thereby, eliminate the swirl at the pump

Table 2. Design Iterations of LEV-VAD Series

Prototype Geometric Feature and Update Performance Main Problems

UAP-1 ● 6 front straighteners, 4 blades, 6 diffuser vanes● 62 mm long, 35 mm OD● Blade height: 2.3 mm● Blade tip to housing gap: 0.3 mm● Housing ID: 21.6 mm● Leading edge angle: 60°● Trailing edge angle: 25°● Stagger angle: 45°

● 10,000 RPM—108 mm Hg● Shear stress:—450 Pa● Efficiency: 13%

● Vortex occurred between impellerand diffuser;

● Pressure lost in diffuser was too high;● Hemolysis or/and thrombosis due to

high shear stresses.

UAP-2 ● Diffuser inlet blade angle: 60°● Diffuser length: 25 mm

Efficiency: 23% Magnetic bearings needed more space

UAP-3 ● 3 impeller blades and 3 splitters● 81 mm long, 30 mm OD● Rotor electromagnet buried in impeller blades● Inducer combined with active bearing● The gap between the rotor and stator: 0.2 mm● Housing ID: 19.6 mm

● 8,000 RPM—199 mm Hg● 6,000 RPM—94 mm Hg● Shear reduced

● The procedure to bury the magnetinside impeller blade was extremelydifficult.

● The cost was too high.● This technology has been covered by

existing patents.UAP-4 ● Remove the straight section of impeller blade

● Trailing edge angle: 40°Good fluid performance ● Manufacture difficulties of diffuser

● High power consumption

OD, outer diameter; ID, inner diameter; RPM, revolutions per minute; VAD, ventricular assist device.

Figure 5. Design history and iterations.

Figure 6. Blade angle distribution of impeller at different spans.The span: 0.0 is the hub, and span: 1.0 is the shroud.

Figure 7. CFD Model of LEV-VAD. CFD, computational fluid dy-namics; VAD, ventricular assist device.

219CONTINUOUS AXIAL FLOW VAD

discharge. The length and height of blades are largely depen-dent upon the design and requirements of MBs.

CFD Analysis

CFD Software. This study used four software programs:BladeGen, TurboGrid, Build, and TASCflow, which are com-mercial software available through ANSYS Corp. Inc. (Can-onsburg, PA, U.S.A.) BladeGen is an interactive turbomachin-ery design program for Windows platform, which allows easygraphical manipulation of the complicated impeller or diffuserdesign parameters and configurations. It easily isolates one ormore parameters, which helps to create complicated bladeconfigurations. For example, it is able to change the bladeheight while keeping the hub and shroud profiles constant, ormodify the stagger angle without changing the blade angle.With an impeller or diffuser design, BladeGen exports theproper data files defining the hub, shroud, and blade profiles toTurboGrid. TurboGrid is an interactive hexahedral grid gener-ation system, specifically designed for turbomachinery. It ispreprogrammed with several templates tailored to the complexcurvatures of various types of turbines, compressors, andpumps. TurboGrid provides a graphical user interface (GUI) formanipulating the total number and distribution law of meshseeds. This functionality allows for optimization of the gridthrough iterations, such as the grid amount within the bound-ary layer, and the location of nearest grid to wall surface. Fromthis, TurboGrid generates a well distributed grid for computa-tion in the final program, TASCflow, which is the fluid Navier-Stokes CFD solver and postprocessor. Build, which is a genericgrid generator, is used to define and generate mesh for allregions in the pump except the blade regions. The entirecomputational grid must include no negative volumes ortwisted elements. It must have acceptable skew angles (gener-ally �15° and �165°) for each region of the pump. TASCflowis a finite volume method based upon a finite element ap-proach of representing the geometry. It uses the computationalgrid and a prescribed set of boundary conditions to character-ize the flow field. It has strong computational capabilities, such

as conjugate heat transfer (CHT),24 different turbulence mod-els,34 transient or steady simulations, Lagrangian particle track-ing,35 and so on. These programs are consistent and robustsoftware code, through which the slight or large changes couldbe quickly progressed for the iterations of pump design.

Computational Efforts for Transient Simulations. Becauseof the complex blade curvatures, the CFD model of LEV-VADinvolves a rather dense and complicated mesh algorithm. Tas-cflow provides some beneficial recommendations for gridquality based upon a substantial number of computationalexperiences and experimental test comparisons for varioustypes of turbo machines. For instance, it suggests the y� valueof first grid near to walls as 2, and the number of grids withinthe boundary layer as 10–15 for the low Reynold numberregions in blade passages. To satisfy these grid generationcriteria and thereby reach acceptable computation accuracy,the inducer, impeller, and diffuser have 74,700, 200,000, and77,800 grids, respectively. The LEV-VAD CFD model, whichhas approximately 352,500 total grids, requires at least 370 MRAM for running a steady flow simulation. Table 4 illustrates aquantitative insight for the computational cost and resource.

As compared with the steady state flow simulations, thetransient calculations entail far more in computational re-sources. The memory allocation for a transient computation,with the same CFD model, requires three to eight times that fora steady computation, depending upon the iterative strategyselected. These additional computational requirements for thetransient study coupled with the already large CFD model ingeneral leads to an extremely computationally intensive set ofsimulations.

Because of the high rotational speed and the small dimen-sion of the pump, the computational time step must be verysmall. For example, if the rotational speed of the four bladeimpeller is 7,000 RPM, it takes approximately 2.1 ms for theimpeller to spin one pitch. To capture more information aboutthe flow field from the movement of the blades, the presentauthors selected an incremental time step of 0.42 ms. This timestep allows for 200 time-points to be computed, recorded, andprocessed for a single heartbeat with normal period of 0.8seconds. The postprocess, which reads the information fromeach transient result file, is time consuming, as well.

Results

Pump Performance

Two transient components are examined simultaneously inthis report. One component relates to the time varying bound-ary conditions (TVBC): the pulsed inlet flow rate. The otheraspect is related to the transient rotational sliding interfaces

Table 3. Main Parameters of LEV-VAD

Inducer Impeller Diffuser

Inlet blade angle 0° 71° �62°Outlet blade angle 0° 24° 0°Stagger angle 0° 37° �30°Blade length 19 mm 63 mm 18 mmBlade height 2.8 mm 1.5 mm 1.4 mm

VAD, ventricular assist device.

Table 4. CFD Model Information and Computational Resource

Region Sub-block # Total Grid # Interface #Memory

Allocation

Inducer 6 74.7 K 39 77 MImpeller 4 200 K 27 210 MDiffuser 3 77.8 K 21 83 MFull Pump 13 352.5 K 89 370 M

CFD, computational fluid dynamics.

220 SONG ET AL.

(TRSI) between the rotational and stationary reference frames.They have different mechanisms that bring about the subse-quent transient effects. The period of TVBC is 0.8 secondscorresponding to the native heartbeat, and flow rate variationis selected from simulative data of representative patients withCHF who would be considered prime LVAD candidates. Theperiod of TRSI case is directly decided by the rotational speed,such as 2.1 ms for 7,000 RPM. The time step was set as 0.42ms for a total of 250 time-points to complete one heartbeatwithout any effects of initial conditions. For each time step, theimpeller rotates approximately 18°.

Figure 8 demonstrates the static pressure distribution acrossthe pump at five sequential time steps during a single periodfor a constant rotational speed of 7,000 RPM and a periodicinflow rate with the average volume flow rate of 6 L/min. Thepressure is increasing spatially smoothly and temporally grad-ually, which indicates that the designs of blades and flow pathare desirable. The pressure field, especially around the inter-face between impeller and diffuser, changes obviously at dif-ferent time-points.

Figure 9 illustrates the correlation of volume flow rate andhead rise of LEV-VAD, i.e., the Q-P curve, during a heartbeat.The relation of pressure rise and flow rate demonstrates hys-teresis, as expected, to form a closed loop curve. The maxi-mum difference of pressure rises is approximately 55 mm Hg.The static pressure rises ranged from approximately 80–180mm Hg, depending upon the absolute flow rate and its gradi-ent. The peak head rise occurred at the end of native heart

diastole, when the volume flow rate of blood through the VADis at a minimum and when this peak would be expected.

The forces exerted on the impeller are essential to the mag-netic suspension designs. After the fluid dynamics simulationwas completed, three vector components of fluid forces can bedetermined by summing the individual contributions at allelement surfaces on the impeller’s walls. Because of the axiallysymmetrical configuration of the impeller, the radial force isrelatively small and below 0.15 N. The axial force, however,which could be as large as 5.5 N, is a critical parameter for a

Figure 8. The pressure distribution changes during a period.

Figure 9. Q-P curve of LEV-VAD. VAD, ventricular assist device.

221CONTINUOUS AXIAL FLOW VAD

successful magnetic suspension design. Figure 10 displays theaxial forces on the impeller. The direction of the axial force isthe conventional negative z direction because the pressure inthe back clearance is larger than the pressure in the passages.The axial force increased as expected theoretically with adecrease in flow rate or an increase in rotational speed. Os-cillations of the axial force with even transient intervals canalso be observed in Figure 10. This oscillation phenomenonresulted from the TRSI simulations allowing the impellerblades to virtually rotate. After each rotation, the interfacecomponents between two reference frames are updated withrespect to the location of the impeller at that time. This detailedtransient simulation is more similar to in vivo operating con-ditions and thereby more realistic than the steady state simu-lation. Furthermore, it can provide more information to vali-date the level of shear stress in the pump and to predict thelevel of blood trauma. The maximum shear stress of approxi-mately 350 Pa occurred when the impeller blades encounteredthe diffuser blades angularly. The loci are around the tip ofimpeller blades at pressure side and the root of diffuser bladesat the suction side. Dynamic investigation of the shear stresslevel makes the pump design more reliable and effective.

Comparison With Experiments

Once the CFD design is finished, a Solidworks file is createdfor the manufacturer to build a physical model to test the pumpperformance. A plastic model is used to conduct particle im-age velocimetry (PIV) tests, and the velocity and pressuredistributions and fluid forces can be measured in laboratory.With the plastic materials, MBs are replaced by mechanicalbearings. The tolerance of measurement of the flow rate iswithin 1% based upon the manufacturer’s certification andcalibration experiments conducted before the formal tests withthe same working fluid. The tolerance of pressure measure-ment is within 2 mm Hg. Because the spinning speed of theimpeller is too fast for comparing the response time of themeasuring machine, it is impossible to conduct correspondingmeasurements for TRSI cases. The measurements for TVBCcases hopefully can be performed with the help of a heartsimulator in the future.

The steady numerical CFD results agree well with the mea-surements over the entire range of operational conditions

tested. The maximum discrepancy between CFD simulationsand PIV measurements is less than 20% and occurs at a flowrate of 4 L/min and 6,000 RPM. Generally, the discrepancy isless than 10%.

Axial Oscillation of Impeller

The transient CFD simulation of the fluid field in the LEV-VAD provides information regarding the pressure differenceacross the whole pump as it varies with time. The time varyingaxial fluid force, which is approximately equal to the productof pressure difference and axial cross section area, can becalculated and estimated. Under the action of this force, theimpeller moves forward until the MBs produce a restoringforce that could overcome the axial fluid force. The fluid forceand counter-restoring force may create an axial oscillation orvibration of impeller in the internal cavity of VAD. The ampli-tude of this vibration is also variable, whereas the maximumdisplacement of the vibration caused by the extreme fluidforces would be critical for the magnetic suspension design.Note that blood is a viscous fluid whose viscosity is approxi-mately 3.5 times higher than that of water; therefore the oscil-latory motion of the impeller experiences a damping influencefrom the fluid’s presence.

The force analysis is drawn in Figure 11. When the impellermoves toward the inlet, the magnetic force and damping forcefrom blood are opposite to the fluid force. The total forceexerted on the rotor is equal to the product of the mass and theacceleration of impeller.

mD � D � Sf � P � A � C � D (11)

Here, A: axial cross section area of impellerC: damping coefficient of blood, 0.5 N · s/mD: displacement of impellerSf: Stiffness of magnetic bearing, 12 N/mm in this designP: pressure difference between the impeller, calculated by

transient CFD simulations.The velocity and acceleration of impeller are obtained by

solving Equation 11. The balance location during the opera-tion is moved toward the inlet by 0.4 mm. The maximumamplitude of vibration is approximately 0.2 mm, which re-quires the axial gap between the leading edges of the impellerblades and the stationary trailing edges of inducer blades atleast 0.2 mm to prevent the impeller from hitting the inducer.

The TASCflow has the capability to run a moving grid case.The mesh topology and number of grids remain constantwhereas the volume of elements and coordination of grids varyduring the calculations. With the movement of the impeller,the grids at one end are compressed and those at the other end

Figure 10. Axial force change with time in a heartbeat.

Figure 11. Force analysis on impeller. P, pressure differencebetween two ends of impeller; A, impeller’s axial cross section area;V, oscillating velocity of impeller; C, damping coefficient of blood(0.5 N · s/m); D, displacement of impeller; Sf, stiffness of magneticbearing (12 N/mm).

222 SONG ET AL.

are expanded. However, the large amount of memory requireddisables the moving grid computation. Fortunately, we canevaluate the effect of the impeller’s axial oscillation on thepump performance by bench tests. The experimental results bythe plastic pump described previously showed that there islittle difference in pump performance for different axial loca-tions of the impeller. This indicates that the pump performanceis not sensitive to the location of the impeller.

Discussion

The LEV-VAD design history and iterations have been de-scribed in this report. Conventional pump design approachand empirical formulas helped to establish the initial bloodpump model. Detailed CFD simulations are followed to inves-tigate the fluid field and pump performance and to finalize thepump design. The general blood pump design procedure andstrategy presented in this report are found helpful.

A transient simulation study of the LEV-VAD, includingTVBC and TRSI, was implemented by means of CFD technol-ogy. The variations in pressure rise and forces on the impellerunder transient conditions were determined. The relation ofpressure rise and flow rate demonstrates hysteresis. The vari-ations of pump performance caused by the rotating position ofimpeller have been observed. Transient results indicated thatthe shear stress level was underestimated in steady studies.TRSI is highly recommended in the CFD simulation of bloodpump for blood compatibility studies. The transient simula-tions, which require more computational efforts and sources,give more detailed information for pump performances andprove to be essential to ensure a reliable and effective design.

The axial oscillation of the impeller in the magnetic field hasbeen described and investigated. Results indicate that the os-cillated motion of the impeller is less important to pumpperformance but is critical for MBs design.

The approaches introduced in this report enable a completecomputational evaluation of the VAD’s performance undertransient flow conditions. This analysis provides insight intothe pump’s performance under dynamic flow conditions,which are realistic when considering in vivo implant scenariosand can generally be applied in the design process of VADs.Future research efforts will focus on PIV measurements for theLEV-VAD prototype and comparisons of such measurements tothe transient flow computational predictions.

Acknowledgment

Supported by the Utah Artificial Heart Institute, Department ofHealth and Human Services, National Institutes of Health and theNational Heart, Lung, and Blood Institute: Grant number R01HL64378–01.

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