Pediatric Mechanical Circulatory Support

Thermal Analysis of the PediaFlow Pediatric VentricularAssist Device

JEFFREY M. GARDINER,* JINGCHUN WU,* MYOUNGGYU D. NOH,** JAMES F. ANTAKI,† TREVOR A. SNYDER,‡ DAVID B. PADEN,*AND BRAD E. PADEN§

Accurate modeling of heat dissipation in pediatric intracorporealdevices is crucial in avoiding tissue and blood thermotrauma. Ther-mal models of new Maglev ventricular assist device (VAD) con-cepts for the PediaFlow VAD are developed by incorporating em-pirical heat transfer equations with thermal finite element analysis(FEA). The models assume three main sources of waste heat gen-eration: copper motor windings, active magnetic thrust bearingwindings, and eddy currents generated within the titanium housingdue to the two-pole motor. Waste heat leaves the pump by con-vection into blood passing through the pump and conductionthrough surrounding tissue. Coefficients of convection are calcu-lated and assigned locally along fluid path surfaces of the three-dimensional pump housing model. FEA thermal analysis yields athree-dimensional temperature distribution for each of the threecandidate pump models. Thermal impedances from the motor andthrust bearing windings to tissue and blood contacting surfaces areestimated based on maximum temperature rise at respective sur-faces. A new updated model for the chosen pump topology iscreated incorporating computational fluid dynamics with empiricalfluid and heat transfer equations. This model represents the finalgeometry of the first generation prototype, incorporates eddy cur-rent heating, and has 60 discrete convection regions. Thermalanalysis is performed at nominal and maximum flow rates, andtemperature distributions are plotted. Results suggest that the pumpwill not exceed a temperature rise of 2°C during normal operation.ASAIO Journal 2007; 53:65-73.

Implantable ventricular assist devices (VADs) chronically trans-mit heat to surrounding tissue and pumped blood. Pediatric ther-

mal design is particularly important because of the miniaturizedsize of the pump with less heat transfer surface area and lowerefficiencies compared with adult-sized VADs. The PediaFlowdevice would be located in the left upper quadrant, in the anteriorabdominal wall behind the left rectus abdominus muscle. Previ-ous studies have shown implants operating at temperatures be-tween 41°C and 44°C can cause damage to tissues, and impairvarious cellular functions relating to wound healing and immuneresponse.1–3 Tissue necrosis typically occurs at temperaturesabove 42°C.4 Denaturation of blood proteins can occur at surfacetemperatures above 40°C.5 During a severe fever, the patient’sthermoregulatory set point is elevated and the temperature ofblood passing through the pump, T�, can be higher than 40°C,further increasing the risk of cell damage. As a safeguard, ourgroup set the target maximum blood and tissue contacting surfacetemperature as 2°C (or less) above body temperature during thesystem design and optimization process.

The preliminary design stage of the PediaFlow projectdevelopment focuses on detailed investigation of threepump topology candidates, distinguished by their fluid pathdesigns: a symmetric, dual-impeller centrifugal pump(SDC); an asymmetric, dual-impeller centrifugal configura-tion (ADC); and a single gap mixed-flow impeller configu-ration (SGM). A primary objective in the evaluation of thethree configurations is determining the thermal impedancesfrom heat sources within the pump to blood and tissuecontacting surfaces, which are used to size motor and thrustbearing components. Another main objective is to identify“hot spots” within the pump and ensure that surface tem-peratures are � 2°C above the inlet blood temperature.Previous investigations of heat dissipation in VADs and totalartificial hearts were typically performed later in the designprocess, after a prototype device and mock loop werebuilt,6 – 8 or using CFD with a detailed geometry model.9 Inpreliminary design and analysis of blood pumps, wheremultiple concepts are in evaluation, detailed CFD modelsand bench top prototypes are prohibitively expensive. Thus,a need for a simplified heat dissipation model arose.

The geometry of the candidate models is driven by therequired flow rate and pressure which are based on the cardiacoutput needs of the intended infant patient population thatincludes newborns. To accommodate intracorporeal use in thesmallest of patients, the overall size has to be minimized. It isalso imperative that the pump operates at a speed below thefirst unstable mode of the magnetic suspension to ensureproper rotor stability and help reduce blood damage. General

From *LaunchPoint Technologies, Inc., Goleta, California, USA;†Department of Biomedical Engineering & Computer Science, Carne-gie Mellon University, Pittsburgh, Pennsylvania, USA; ‡Departmentsof Bioengineering and Surgery, University of Pittsburgh, andMcGowan Institute for Regenerative Medicine, Pittsburgh, Pennsylva-nia, USA; §Department of Mechanical Engineering, University of Cal-ifornia, Santa Barbara, California, USA, and **Chungnam NationalUniversity, Daejeon, Korea.

Submitted for consideration May 2005; accepted for publication inrevised form August 2006.

Supported in part by NIH Contract HHSN268200448192C (NO1-HV-48192), “Pediatric Circulatory Support,” to the University of Pitts-burgh.

Presented in part at the First International Conference on PediatricMechanical Circulatory Support Systems and Pediatric Cardiopulmo-nary Perfusion; Hershey, PA, USA; May 19–22, 2006.

Reprint requests: Jingchun Wu, LaunchPoint Technologies, LLC,5735 Hollister Avenue, Goleta, CA 93117.

DOI: 10.1097/01.mat.0000247156.94587.6c

ASAIO Journal 2007

65

pump layout is based upon our group’s experience with pre-vious adult VADs, namely WorldHeart’s HeartQuest andStreamliner. Wall thicknesses and seam locations are deter-mined by manufacturing capabilities and structural integrityrequirements. Thermal data from the initial models and thesurface temperature constraint are used to set an upper limit onthe maximum power of the optimized models. A weightedobjective analysis is performed on the three optimized modelsand each candidate is rated based on several main categoriesincluding manufacturability, anatomic fit, hydrodynamic per-formance and biocompatibility, with heat dissipation effi-ciency as a subcategory of the biocompatibility objective. Aftera topology is selected, a more sophisticated thermal model iscreated with a suspension geometry based on detailed elec-tromagnetic analysis and CFD optimized blade geometry andfluid path. At this design stage, additional sources of waste heatare identified and off-design flow rates are considered. Theupdated model incorporates CFD-derived fluid velocities, em-pirical heat transfer correlations, and the as-built geometry ofthe first generation implant. Upon completion of fabrication ofthe first generation prototype, an in vitro thermal study will beconducted using thermal sensors to map temperature distribu-tion and verify empirical and CFD results.

Materials and Methods

Device Specifications

All three candidate pump topologies have a nominal flowrate, Qn, of 0.5 l/min, a minimum flow rate, Ql, of 0.3 l/min,and a maximum flow rate of 1.5 l/min. Fluid entrance and exitregion dimensions are constrained to fit a cannula with adiameter of 5 mm for feasible implantation and reduction ofhemodynamic losses. Titanium (Ti6Al4V), kh � 6.7 W/m-K, ischosen for the pump housings for its biocompatibility and highstrength to weight ratio. The copper windings of the activethrust bearing and motor are assumed the significant sources ofheat loss. Master Bond EP21ANLV thermal epoxy, kep � 0.61W/m-K, is used as a potting compound to enhance thermal

conduction throughout the pump and to promote heat dissi-pation to the tissue contacting surfaces.

Suspension for the SDC impeller (Figure 1) is provided by afully magnetically levitated system, including two sets of radialpermanent magnet bearings and two active axial thrust bear-ings. Impeller rotation is provided by a brushless DC motorwith toroidally wound motor coils, which is compact andreduces radial negative stiffness. The nominal operating speed,�sdc, is 9,000 rpm. A split fluid entrance volute promotes equalflow rates across the blades on each side of the impeller. Theoutlet volute’s function is to collect fluid from the impeller andto convert some of the kinetic energy of the flow into pressureenergy.

The ADC impeller (Figure 2) suspension consists of a radialpermanent magnet bearing, a permanent magnet momentbearing and an active axial thrust bearing. Rotation is alsoprovided by a toroidally wound, brushless DC motor with anominal operating speed, �adc, of 9000 rpm. An inlet volutefunctions to guide fluid uniformly into the annular cross sec-tion of the impeller entrance region. The main fluid path in thispump is across the impeller main blades; a smaller amount ofsecondary flow travels through the back clearance gap be-tween the impeller and housing. Secondary blades on the backclearance side induce antegrade flow within the gap andeliminate undesirable back flow and vortices.10 The outletvolute functions similarly to the volute of the SDC pump,collecting fluid and recovering kinetic energy.

The SGM impeller (Figure 3) is supported by a fully levitated

Figure 1. Symmetric, dual-impeller centrifugal pump (SDC).

Figure 2. Asymmetric, dual-impeller centrifugal pump (ADC).

Figure 3. Single gap mixed-flow impeller pump (SGM).

66 GARDINER ET AL.

magnetic suspension,11 consisting of two sets of permanentmagnet radial bearings and an active axial thrust bearing.Impeller rotation is actuated by a toroidally wound, brushlessDC motor, with a nominal operating speed, �amf, of 9000 rpm.Stationary guide vanes located in the diffuser wall function torecover some of the kinetic energy of the fluid flow and createa predominantly axial fluid velocity.

Fluid Characteristics

Blood passing through the pump is modeled as a Newtonianfluid with a density, �b, of 1050 kg/m3, a viscosity, �b, of0.0035 Pa-s, a thermal conductivity, kb, of 0.5 W/m-K, and aspecific heat, cb, of 3.65 kJ/kg-K.12 Because blood temperaturevariation is relatively small in this model, viscosity and thermalconductivity are assumed constant. The pump’s rotary bladedesign generates a continuous, constant flow rate Q, rangingfrom 0.3 l/min to 1.5 l/min, with a nominal flow rate, Qn, of0.5 l/min. In the entrance and exit regions of all three topologycandidates, the mean fluid velocity is determined by the pumpflow rate and cross sectional flow area, and Reynolds numberis defined by:

ReD ��bumD

�b(1)

where D represents the entrance region diameter and um is themean fluid velocity over the regional cross section and issimply calculated by:

um �4Qn

�D2 (2)

The Reynolds numbers within the entry/exit regions of threepump types are about 600 at the nominal flow rate. Therefore,the flow in both the entrance and exit regions is assumed to belaminar. The Prandtl number is a ratio of the momentumdiffusivity to the thermal diffusivity of fluid and is assumedconstant throughout the pump. It is calculated by:

Pr �cb�b

kb(3)

The thermal entry length for a laminar flow is the distancefrom the inlet that thermal boundary layer is fully developedand is defined as13:

xfd � 0.05 ReD Pr D (4)

For each candidate �fd �� �e (the actual entry lengths of thepumps) which characterizes a developing flow. The averagelocal Nusselt numbers for developing laminar flow are foundby the Hausen correlation14:

NuD � 3.66 �0.0668(D/L)ReDPr

1 � 0.04[(D/L)ReD Pr]2/3 (5)

This correlation assumes constant surface temperature andthermal entry region length, L. An alternative correlation dueto Sieder and Tate15 is of the form:

NuD � 1.86�ReDPrL/D � 1/3� �

�s� 0.14

(6)

where �s is the viscosity at the surface, which is assumed to be

the same as �b. Results from each formula match within 7%difference. For our model, we will use the more widely usedSieder-Tate correlation. Finally, the local coefficient of con-vection is determined by:

hentry �NuDkb

D(7)

Accurate solutions for thermal entry problems are difficult toobtain because temperature and velocity are dependent on thedistance from the inlet as well as the internal diameter.

The internal flow through the impeller is three-dimensionaland complex due to the effects of rotation, curvature, andturbulence. In order to simplify the heat transfer analysis,Reynolds number in the impeller region is calculated at severalpoints along the fluid path based on the absolute velocity ub atthe corresponding diameter of the impeller by:

ReD ��bubDb

�b(8)

where, Db is the corresponding diameter of the impeller, andthe fluid velocities are given by:

ub � �Vm2 � V�

2 (9)

V� � �rb � Vm cot() (10)

Vm �Qn

Aw(11)

Where ub is the absolute fluid velocity and V�, represents thecircumferential component of the velocity at the blade tip. Vm

is the meridional component of the velocity, rb is the radius ofthe blades at a given point, is the blade angle, and Aw is theflow cross-sectional area. For the preliminary pumps, the bladeangle varies from 24° to 31° along the flow path. Fluid flowin this region transitions from laminar (ReD � 2000) to turbu-lent (ReD � 20000) at the nominal flow rate. The Nusseltnumbers for regions with ReD � 10000 are defined by theDittus-Boelter16 equation:

NuD � 0.027 ReD4/5Pr0.4 (12)

A more complex and generally more accurate13 correlationby Gnielinski17 is of the form:

NuD �( f/8)(ReD � 1000)Pr

1 � 12.7( f/8)1/2(Pr2/3 � 1)(13)

where, f is the Moody friction factor. Assuming a smoothsurface the Petuhov18 correlation is expressed as:

f � �0.790 ln ReD � 1.64)�2 (14)

Nusselt numbers from the two correlations match within a4% difference. The more sophisticated Gnielinski formula,which is valid for regions with ReD � 3000 versus ReD �10000 for the Dittus-Boelter correlation, is used for the model.The local coefficient of convection is then represented by:

hblade �NuDkb

Db(15)

67THERMAL ANALYSIS OF THE PEDIAFLOW

In the SGM design, the fluid path region, located down-stream from the blade area and before the outlet guide vanearea, is the most critical area of heat dissipation in the pump.In this area, the majority of the dissipated heat from the motorwindings and thrust bearings is transferred into passing blood.Heat generated from fluid friction losses in this region is as-sumed negligible. In the SDC pump, fluid passes through thethrust bearing area prior to entering the blade region, resultingin a flow similar to the annular region in SGM pump with anouter diameter, ro, and inner diameter, ri. The circumferentialvelocity induced by the rotation can be derived as:

V� ��ri

2

ro2 � ri

2� ro2

r� r� (16)

The absolute and meridional velocities are found using theprevious equations used in the blade region equations 9 and11. Flow in this region is transitionally turbulent with a Reyn-olds number of 3200 for the SDC pump and fully turbulent inthe SGM pump (14000) and the Nusselt number, Nu, is foundusing Eq. (13). The local coefficient of convection in this regionis found by:

ho �Nuok

2r(17)

The outlet stationary guide vanes located at the outlet regionof the SGM candidate function to recover fluid energy andprevent swirling. Here we assume the circumferential compo-nent of the fluid velocity, V�, linearly decreases from a maxi-mum value prior to entering the guide vanes (characterized byequation 16) to zero at the exit of the guide vanes. Themeridional velocity and absolute velocities are determinedusing equations 9 and 11. The guide vanes have been speciallyoptimized to smoothly transition a predominantly circular flowto axial flow, without creating undesired vortices in the region.

Tissue Characteristics

Tissue surrounding the candidate PediaFlow device is mod-eled as an isotropic solid material, with thermal properties ofmuscle tissue: a thermal conductivity, k, of 0.5 W/m-K, adensity, �, of 1000 kg/m3, and a specific heat, c, of 3.7kJ/kg-K.19,20 Heat is dissipated from the surrounding tissueprimarily through tissue capillary perfusion21 and is modeledusing Penne’s bio-heat equation22:

�cTt

� �k�T � qp � qm (18)

where, T, �, and c represent the tissue temperature, density,and specific heat, respectively; qp is the heat of perfusion; andqm is the metabolic heat generation term. Metabolic heatgeneration within the tissue model is assumed negligible.

Studies by Okazaki et al.21 and Liu et al.23 have shown thatmuscle tissue chronically heated by a constant heat flux de-creases in temperature over several days after implant due toincreased angiogenesis. In the study by Liu et al., muscle tissuewas subjected to chronic heat fluxes of 0.04 W/cm2, 0.06W/cm2, and 0.08 W/cm2 resulting in initial tissue temperatureincreases of approximately 1.5°C, 3.5°C, and 6°C, respec-tively, at a distance of 0 mm from the heated surface. From

these, an approximate average perfusion convection coeffi-cient for our model can be found by:

htissue �q pT

(19)

where, qp is the heat flux and T is the increase in tissuetemperature. Liu et al. found that perfusion changes little overtime when heated to 40.5°C. Tissue perfusion is assumed to betime independent in our model because tissue temperaturesare expected to be � 40°C. Also, heat dissipation throughtissue perfusion is assumed uniform among the tissue sur-rounding the pump. Due to the complexity of accurately mod-eling tissue perfusion, the model convection coefficients areconsidered approximate and a more complete model will beimplemented in the future.

Preliminary Thermal Models

Simplified three-dimensional thermal models of the pumpsare created using SolidWorks (SolidWorks Inc., Concord, MA)solid modeling software and then imported into CosmosWorks(SolidWorks) FEA software. Based on the preliminary pumprequirements, motor waste heat values can be estimated by:

qm � � QH�f�km

� 2

(20)

where the pump head, H, the nominal flow rate, Q, and pump

Figure 4. SDC thermal model.

Figure 5. ADC thermal model.

68 GARDINER ET AL.

speed are estimated based on pump requirements. The motorconstant, km, and pump fluid efficiency, �f, are estimatedbased on preliminary motor and pump parameters. Heat in-duced by eddy currents in the motor also contributes to qm andis investigated later in the design process, once a particulartopology candidate is chosen. Motor efficiency can be definedas:

�m ���

�� � qm(21)

where � is the rotor torque. From this, the overall pump effi-ciency is determined by:

� � �m�f �QH

�� � qm(22)

Estimated preliminary hydraulic efficiencies are 0.80 formotor efficiency and 0.08 for efficiency for SGM model atnominal flow rate and nominal operating speed. The virtual

zero force (VZP) design of the thrust bearing minimizes stabi-lization energy and dissipated heat. This heat is related to thethrust bearing circuit noise force, Fnoise, and the voice coilconstant, kv:

qv � �Fnoise

kv� 2

(23)

The nominal dissipation values for the motor and thrustbearing are estimated at 1.0 W and 0.75 W, respectively, foreach pump. Localized average coefficients of convection arethen assigned to several surface area regions along the fluidcontacting surfaces of the pump housing geometry (Figures4–6), with an assumed ambient inlet blood temperature, T�, of37°C. Heat transfer coefficients and Reynolds number at thenominal flow rate are shown in Table 1. The average coeffi-cient of convection due to perfusion, htissue, is assigned to theentire outer surface of the pump. The largest perfusion istypically near the heated surface.20 Pump geometry is dis-cretized with tetrahedral type mesh, with an average globalelement size of 0.020 inches and a tolerance of 0.001 inches.The analysis is set up for a steady state solution.

Figure 6. SGM thermal model.

Figure 7. Temperature distribution for SDC at nominal flow rateand nominal operating speed.

Figure 8. Temperature distribution for ADC at nominal flow rateand nominal operating speed.

Table 1. Convection Values

Convection Region Reynolds # h (W/mˆ2*K)

SDC entrance/exit 630 1500SDC voice coil 3200 2900SDC blades 1 18000 10000SDC blades 2 31000 13000SDC blades 3 48000 16000SDC blades 4 62000 18000ADC entrance/exit 630 1500ADC voice coil 98000 19000ADC blades 1 6700 6400ADC blades 2 23000 11000ADC blades 3 49000 15000ADC blades 4 83000 18000ADC annulus 1300 690SGM VC/MW 14000 6200SGM blades 1 2200 2100SGM blades 2 4300 4300SGM blades 3 11000 7600SGM blades 4 19000 10000SGM entrance/exit 630 1500SGM guide vanes 1 9200 5100SGM guide vanes 2 5300 3900SGM guide vanes 3 2700 2400SGM guide vanes 4 1500 1000Surrounding tissue N/A 1300

69THERMAL ANALYSIS OF THE PEDIAFLOW

The models are limited in that fluid convection coefficientsare assumed constant over relatively large areas along the fluidpath and are based on a nominal continuous flow rate. How-ever, the actual fluid behavior of blood pumps is complex withunsteady three-dimensional velocities and convection coeffi-cients varying continuously along the fluid path. The empiricalcorrelations used to determine the Nusselt number can resultin errors as large as 25%.13 Also, thermal contact resistancesbetween pump components were not included in the pumpmodels. Ideally the contact resistance between the titaniumhousings and thermal epoxy should be minimized. However,imperfections in the bond lines potentially will result in re-duced heat flow and higher critical surface temperatures.

Preliminary Results and Discussion

Four independent mean thermal impedances are deter-mined for each pump candidate topology using the FEA-gen-erated, three-dimensional temperature distributions (Figures7–9). The mean thermal impedances for each topology andheat transfer path are determined from the highest local surfacetemperature for a given waste heat value and are summarizedin Table 2.

Next, the simulations were run with simultaneous motor andthrust bearing waste heat values of 1.0 W for each motor and0.75W for each thrust bearing winding, which are the esti-mated preliminary maximum heating values. Maximum pre-dicted tissue and blood contacting surface temperatures atnominal flow conditions are shown in Table 3.

Differences among impedance values and surface tempera-tures of the three topologies can primarily be attributed topump geometry and fluid path. For instance, the thermal im-pedances and surface temperatures of the SDC pump aresubstantially higher than the other impedances in the study.The thrust bearings in this pump are located upstream from

impeller blades where the fluid velocity is lower and flowmore laminar, thus less heat transfer to passing blood. TheADC had the lowest overall thermal impedances and surfacetemperatures due to the proximity of the motor and thrustbearing windings to the secondary impeller blades, whichincreased local convection. The SGM design benefits fromwaste heat locations downstream from the impeller blades,where large circumferential fluid velocities increase heat trans-fer. The larger heat transfer surface areas of the thrust bearingwindings of the SGM resulted in lower thermal impedancesthan the motor coil. The thermal impedances and maximumsurface temperatures of the three candidate pump topologieswere used as part of the comparison matrix in selection of theSGM as the leading design topology of the PediaFlow first-generation pump. The suspension and fluid path geometry isthen optimized to create the first-generation pump geometryused for in-vitro and in-vivo studies.

To test the validity of the empirical formulas used in prelim-inary analysis, the velocity profile along the first-generationpump axis is found using empirical and CFD methods. TheCFD velocity profile of the first-generation SGM model isfound by tracking the streamline absolute velocity of 10 par-ticles released at the inlet region using CFX (ANSYS Inc, Can-onsburg, PA) software. The empirical profiles represent themean velocity within the gap between the rotor and stator,while the CFD particles are free to move from the high velocityrotor surfaces to the zero velocity stator surfaces. This results inempirical profiles that fall near the middle of the CFD velocitydistribution range at a given axial position (Figures 10and 11).The empirical data fall almost entirely near the middle of theCFD velocity range, with a slight overestimation within theblade region.

Eddy Current Losses

Eddy currents in the PediaFlow device are created in thestationary titanium housing by a rotating motor magnet as

Figure 9. Temperature distribution for SGM at nominal flow rateand nominal operating speed.

Figure 10. Velocity comparison, 0.5 l/min.

Table 2. Thermal Impedances

Impedance SGM ADC DBC

Motor winding to blood surface (°C/W) 0.263 0.222 0.270Motor winding to tissue surface (°C/W) 0.188 0.260 0.309Thrust bearing to blood surface (°C/W) 0.185 0.137 0.684Thrust bearing to tissue surface (°C/W) 0.170 0.154 0.500

Table 3. Maximum Surface Temperatures

SGM ADC SDC

Max blood surface temp (°C) 37.5 37.3 37.6Max tissue surface temp (°C) 37.5 37.3 37.4

70 GARDINER ET AL.

shown in Figure 12. We approximate the radial (eddy-currentproducing) B-field by:

Br � Bo

mR

cos(� � ) (24)

The average loss per unit area in a thin shell (T��R) isequivalent to the average loss in a planar system with themotor is rotating

Ey

x� �

Bz

t� Bo

mR

sin� xR

� � ̇ (25)

and E-field is induced perpendicular to the current sheet. FromMaxwell’s equations:

Ey � �0

xEy

x� C � �Bo

mR

cos� xR

� �R� � C (26)

Where we have assumed � �t, where � is the rotationalvelocity of the rotor:

Ey � �Bom�cos� xR

� �t� (27)

Choosing the constant of integration such that the average ofEy is 0 (i.e. C � 0) and simplifying yields:

The power loss is proportional to the conductivity of thetitanium shell, �, so we have that the time-average power lossis:

P � �0

T

dz�0

2�R

dx�0

L

d y�Ey2 � �TLR�Bo

2m2�2 (28)

The SolidWorks model is then updated to account for eddycurrent heating, which in our case p � 0.6W at nominal flowrate (9000 RPM) and p � 1.0W at maximum flow rate (12000RPM).

The Updated Thermal Model

The pressure rise versus flow rate curve, H-Q, and theefficiency versus flow rate curve, �-Q, of the first-generationprototype are determined by CFD using an optimized fluidpath and pump geometry with SST turbulence model (Figures13 and 14). Using equation 21, we can calculate the motor

Figure 11. Velocity comparison, 1.5 l/min.

Figure 12. SGM motor and shell arrangement.

Figure 13. Head vs. flow rate curves predicted by CFD.

Figure 14. Pump hydraulic efficiency vs. flow rate curves pre-dicted by CFD.

71THERMAL ANALYSIS OF THE PEDIAFLOW

waste heat at several off-design points (Figure 15). The motorheat dissipation gradually increases with greater flow rate andpump speeds; however, this is counteracted by increased con-vective heat transfer due to the larger fluid velocities (Figures10 and 11). From these data many operating points can beanalyzed in detail. This study focuses on the nominal flow rateof 0.5 l/min at 9000 RPM and the high flow rate of 1.5 l/min at12000 RPM. Internal flow surfaces of the updated first-gener-ation PVAD model are divided into equally spaced convectionregions 1 mm in axial length (Figure 16). This provides for agreater sensitivity to sudden fluctuations in heat transfer alongthe flow path over the preliminary models and an overall moreaccurate model. Figure 17 shows the distribution of convec-tion values along the pump’s axis at the nominal and maxi-mum flow rates. These profiles are based on an average path-line absolute velocity profile from CFD analysis, the geometryof the updated model and the empirical convection formulasof Sieder-Tate and Gnielinski (equations 6 and 13). The tissueperfusion model of the preliminary models is again utilized inthis model. A layer of 0.003-inch-thick polyimide tape isplaced between the copper coils and titanium housing toprovide a second insulation layer in addition to the insulationof wire. Double insulation reduces the safety risk of shortingthe electrical circuit to the housing components. However, thetape is not an ideal thermal conductor and potentially canincrease the operating temperature of the pump. The section ofthe titanium housing where eddy currents are generated ismodeled and meshed as a separate piece.

At nominal flow rate, the maximum blood contacting sur-face temperature is 37.5°C, while the maximum tissue con-tacting surface temperature is 37.4°C (Figure 18) essentiallythe same temperatures predicted by the preliminary model.The high flow rate maximum surface temperatures are 37.8°Cand 37.7°C, respectively (Figure 19). The higher surface tem-peratures can be attributed to the increased impeller speed andreduced motor efficiency resulting in larger motor and eddycurrent losses.

Conclusion

In this study, preliminary thermal models are created forcandidate PediaFlow pump topologies using empirical heattransfer and fluid flow equations along with solid modelingand FEA software. The models demonstrate that useful VADheat dissipation information can be procured without timeintensive prototyping or CFD studies. By simulating waste heattransfer out of the device as localized areas of convection onthe blood and tissue contacting surfaces of the pump, thecomplex behaviors of blood flow and tissue perfusion can beevaluated using a steady state FEA solver. The study alsodemonstrates that thermal impedances and temperature distri-butions were mainly affected by the proximity of the wasteheat sources to various regions of the fluid path, such as theimpeller blades and guide vanes.

Thermal impedances and surface temperatures of the threecandidate pump topologies were as part of the selection cri-teria in the choice of SGM as the final topology of the Pedia-

Figure 15. Motor heat dissipation vs. flow rate.

Figure 16. SGM first-generation thermal model.

Figure 17. SGM first-generation convection distribution.

Figure 18. PediaFlow first-generation temperature distribution,0.5 l/min and 9,000 rpm.

72 GARDINER ET AL.

Flow first-generation pump. This study suggests that the currentpump design will not thermally damage blood or tissue duringnormal operating conditions. Preliminary validation of thethermal model by CFD shows strong agreement between theempirically derived fluid velocity profiles and CFD based pro-files.

References

1. Utoh J, Harasaki H: Effects of temperature on phagocytosis ofhuman and calf polymorphonuclear leukocytes. Artif Organs16: 377–381, 1992.

2. Pasha R, Benavides M, Kottke-Marchant K, Harasaki H: Reducedexpression of platelet surface glycoprotein receptor IIb/IIIa athyperthermic temperatures. Lab Invest 73: 403–408, 1995.

3. Hershkoviz R, Alon R, Mekori Y: Heat-stressed CD4� T lympho-cytes: differential modulations of adhesiveness to extracellularmatrix glycoproteins, proliferative responses and tumour necro-sis factor-� secretion. Immunology 79: 241–247, 1993.

4. Seese T, Harasaki H, Saidel G, Davies C: Characterization of tissuemorphology, angiogenesis, and temperature in the adaptiveresponse to muscle tissue to chronic heating. Lab Invest 78:1553–1562, 1998.

5. Yamakazi K, Litwak P, Kormos RL, Mori T: An implantable cen-

trifugal blood pump for long term circulatory support. ASAIO J43: 686–691, 1997.

6. Endo S, Masuzawa T, Tatsumi E: In vitro and in vivo heat dissi-pation of an electrohydraulic totally implantable artificial heart.ASAIO J 43: 592–597, 1997.

7. Navarro RR, Kiraly RJ, Harasaki H, et al: Heat dissipation throughthe blood contacting surface of a thermally driven LVAS. Int JArtif Organs 11: 381–386, 1988.

8. Tasai K, Takatani S, Orime Y: Successful thermal management ofa totally implantable ventricular assist system. Artif Organs 18:49–53, 1994.

9. Song X, Wood HG: Computational fluid dynamics (CFD) of the 4th

generation prototype of a continuous flow ventricular assistdevice (VAD). J Biomech Eng 126: 180–186, 2004.

10. Wu J, Antaki JF, Wagner WR, Snyder TA: Elimination of adverseleakage flow in a miniature pediatric centrifugal blood pump bycomputational fluid dynamics-based design optimization.ASAIO J 51: 636–643, 2005.

11. Noh MD, Antaki JF, Ricci M, Gardiner J: Magnetic levitationdesign for the PediaFlow™ ventricular assist device. Proceed-ings of 2005 IEEE/ASME International Conference on AdvancedIntelligent Mechatronics: 1077–1082, 2005.

12. Fiala D, Lomas KJ, Stohrer: A computer model of human thermo-regulation for a wide range of environmental conditions: Thepassive system. J App Physiol 87: 1957–1972, 1999.

13. Incropera FP, Dewitt DP: Fundamentals of Heat and Mass Trans-fer. New York, John Wiley & Sons, 1996.

14. Hausen H: Z. VDI Beih. Verfahrenstech 4: 91, 1943.15. Sieder EN, Tate GE: Ind Eng Chem 28: 1429, 1936.16. Dittus FW, Boelter LMK: University of California, Berkley, Publi-

cations on Engineering 2: 443, 1930.17. Gnielinski V: Int Chem Eng 16: 359, 1976.18. Petuhov BS: Advances in Heat Transfer. New York, Academic

Press, 1970.19. Goto A, Nohmi M, Sakurai T, Sogawa Y: Hydrodynamic design

system for pumps based on 3-D CAD, CFD, and inverse designmethod. ASME J Fluids Eng 124: 329–335, 2002.

20. Duck FA: Physical Properties of Tissues: A Comprehensive Refer-ence Book. San Diego, Academic Press, 1990.

21. Okazaki Y, Davies CR, Matsuyoshi T, et al: Heat from an im-planted power source is mainly dissipated by blood perfusion.ASAIO J 43: 585–588, 1997.

22. Pennes H: Analysis of tissue and arterial blood temperatures in theresting human forearm. J App Physiol 1: 93–122, 1948.

23. Liu E, Saidel G, Harasaki H: Model analysis of tissue to transientand chronic heating. Ann Biomed Eng 31: 1007–1014, 2003.

Figure 19. PediaFlow first-generation temperature distribution,1.5 l/min.

73THERMAL ANALYSIS OF THE PEDIAFLOW