Diamagnetic Effects of Blood in a Magnetically Levitated Blood Pump Arnold D. Gomez1 and Dr. Steven Day1

1Rochester Institute of Technology, Mechanical Engineering Department, Rochester, NY

1. Introduction Magne&cbearingsarebecomingan increasinglypopularop&onforventricularassistdevices. Inmostcases,bloodfills a

por&on of the gap between themagne&c actuators and rotor. Understanding the effects of the opera&ng fluid onmagne&c suspension becomes a necessity, par&cularly when the device geometry features a rela&vely large gap(typicallydefinedas>150µmandas largeas2mminsomepumps [1]).A largegapreducescelldamageandallowsunrestricted flow but, as a tradeoff, it increases the distance and amount of medium the magne&c fields mustpenetrate.

2. MethodsThisresearchfocusesoniden&fyingtheeffectsthatviscosityandthemagne&csuscep&bilityoftheopera&onfluidhaveontheperformanceofthemagne&cbearingsysteminaventricularassistdevice.The actual magne&c bearing system has mul&ple inputs and mul&ple outputs. Axial and radial symmetry enablessimplifica&on intocylindrical and conical responses. Though the resultsweresimilar forboth typesof response,only thecylindricalanalysisisdetailedhereforsimplicity.

5. Conclusions•Inselec&ngbloodanalogsforuseinmagne&cbearingtes&ngitisonlynecessarytomatchfluidicproper&es,themagne&csuscep&bilityisofliMleimportance.

•Thecontribu&onofviscosityinfrequencyandtransientresponsecanbeaMributedtoavaria&onintheiner&alelementofasecondordermodelandnotnecessarilytoitsdampingcoefficient.

4. DiscussionThe influenceofmagne/csuscep/bility:FluidSet#2wasdesignedto includeatypicalvaria&oninmagne&csuscep&bilitywithrespecttowaterandbloodasthesearethetargetopera&ngfluidsinventricularassistdevices.Intheextremecase,thepropertywasvariedbytwoordersofmagnitudeintheposi&vedirec&on.Anextremenega&vevaria&onwasnotstudied.

Naturalfrequency,dampingra/o,andmodeling:Fromamechanicalperspec&ve,itiseasytoexpecttheeffectofviscosityto be related to the system’s damping coefficient. However, none of the results can be explained as clear varia&ons indamping.Therise&meandbandwidthofasecondordersystemarerelatedinsteadtoitsnaturalfrequency[3](Equa&on5).

S&ffnessmeasurementsindicatethatitsmagnitude,k,remainsrela&velyconstantthroughout.Theiner&alcomponent,m,istheonlyvariablethatcanbeadjustedinordertomodelthisbehavior.Avaria&onintheiner&alelementcanalsoaffectthedampingra&o(Equa&on6).

Theaddi&onofaconven&onalfluidicbearingmodel[4]issufficienttoincreasetheroll‐offslopetomatchexperimentaldata.

3. ResultsS/ffnessMeasurements‐Steady‐StateResponseAllvaluesremainrela&velyconstantregardlessofvaria&onsinviscosityandmag.suscep&bility.

Acknowledgements•SpecialThanksto:StevenSnyderandJessicaWatkins,RochesterIns&tuteofTechnology•Na&onalHeart,Lung,andBloodIns&tuteGrant1RO1HL077085‐01A1

References1.HGWood,PEAllaire,PaulE.,DBOlsen,SWDay,XSong,AUntaroiu,AThrockmorton,Streamlinedunobstructedone‐passaxial‐flowpumpU.S.patent7,229,258.June20072.Shoemaker,D.P.Garland,C.W.,etal.ExperimentsinPhysicalChemistry,5thedMcGraw‐Hill1989.pp418‐429.3.Palm,WilliamJ.IIISystemDynamics.1sted.McGraw‐Hill2005.pp.495‐556.4.Muszynska,Agnieszka.Rotordynamics1sted.CRCPress,Taylor&FrancisGroup2005.pp227‐237.

Theneteffectoftheopera&ngfluidonthemagne&csuspensionsystemcanbecharacterized in terms of changes of the overall damping and s&ffness. Thesemaybecausedbytradi&onaltribologicalproper&es,suchas:

• density‐massperunitvolume• viscosity‐resistancetodeforma&onunderashearrate

orbymagne&cproper&esofthemedium,mainly:• magne&csuscep&bility‐netmagne&za&onunderanexternalfield.

Figure1:Ventricularassistdeviceprototype(right).Cross‐sec<onillustra<nggapfilledwithfluid.

Materialswithnega&vemagne&csuscep&bility,ordiamagne&c,willhaveanetmagne&za&onoppositetotheexternalfield.The opposite is true if the material has posi&ve suscep&bility (paramagne&c) i.e. the resultant field will align with theexternalfield.Waterisadiamagne&cfluid[2].

Table #1: Fluid SelectionRecipeRecipeRecipeRecipeRecipeRecipe Volume Density Viscosity Mass Susceptibility

Table #1: Fluid Selection H2O GlycerinGlycerin MnSO4

NaCL

Blood V ρ ν m χTable #1: Fluid Selection

% wt % wt% wt % wt % wt % wt l kg/l cP kg m3/kgSet #1: Moderate Viscosity Variation (+/- 3cP)Set #1: Moderate Viscosity Variation (+/- 3cP)Set #1: Moderate Viscosity Variation (+/- 3cP)Set #1: Moderate Viscosity Variation (+/- 3cP)Set #1: Moderate Viscosity Variation (+/- 3cP)Set #1: Moderate Viscosity Variation (+/- 3cP)Set #1: Moderate Viscosity Variation (+/- 3cP)Set #1: Moderate Viscosity Variation (+/- 3cP)Set #1: Moderate Viscosity Variation (+/- 3cP)Set #1: Moderate Viscosity Variation (+/- 3cP)Set #1: Moderate Viscosity Variation (+/- 3cP)Set #1: Moderate Viscosity Variation (+/- 3cP) bovine blood 0.0 0.00.0 0.0 0.0 100.0 0.075 1.022 3.84 0.0734 -8.82E-09 water-glycerin solution 58.0 42.042.0 0.0 0.0 0.0 0.075 1.122 6.22 0.0668 -1.00E-08 distilled water* 100.0 0.00.0 0.0 0.0 0.0 0.075 1.000 1.00 0.0750 -9.05E-09Set #2: Moderate Magnetic Susceptibility Variation (+/- 3e-8 m3/Kg)Set #2: Moderate Magnetic Susceptibility Variation (+/- 3e-8 m3/Kg)Set #2: Moderate Magnetic Susceptibility Variation (+/- 3e-8 m3/Kg)Set #2: Moderate Magnetic Susceptibility Variation (+/- 3e-8 m3/Kg)Set #2: Moderate Magnetic Susceptibility Variation (+/- 3e-8 m3/Kg)Set #2: Moderate Magnetic Susceptibility Variation (+/- 3e-8 m3/Kg)Set #2: Moderate Magnetic Susceptibility Variation (+/- 3e-8 m3/Kg)Set #2: Moderate Magnetic Susceptibility Variation (+/- 3e-8 m3/Kg)Set #2: Moderate Magnetic Susceptibility Variation (+/- 3e-8 m3/Kg)Set #2: Moderate Magnetic Susceptibility Variation (+/- 3e-8 m3/Kg)Set #2: Moderate Magnetic Susceptibility Variation (+/- 3e-8 m3/Kg)Set #2: Moderate Magnetic Susceptibility Variation (+/- 3e-8 m3/Kg) blood analog 5 – diamagnetic 32.0 68.068.0 0.0 0.0 0.0 0.075 1.090 3.76 0.0688 -9.07E-09 blood analog 6** – paramagnetic 31.5 67.567.5 1.0 0.0 0.0 0.075 1.112 3.78 0.0674 2.21E-08Set #3: Extreme Variation of One ParameterSet #3: Extreme Variation of One ParameterSet #3: Extreme Variation of One ParameterSet #3: Extreme Variation of One ParameterSet #3: Extreme Variation of One ParameterSet #3: Extreme Variation of One ParameterSet #3: Extreme Variation of One ParameterSet #3: Extreme Variation of One ParameterSet #3: Extreme Variation of One ParameterSet #3: Extreme Variation of One ParameterSet #3: Extreme Variation of One ParameterSet #3: Extreme Variation of One Parameter water-glycerin solution - high viscosity 27.0 73.073.0 0.0 0.0 0.0 0.075 1.171 32.00 0.0641 -9.11E-09 manganese sulfate solution - high susceptibility 80.0 0.00.0 20.0 0.0 0.0 0.075 1.178 3.36 0.0637 2.44E-07 blood analog 8** 29.0 61.961.9 0.1 9.0 0.0 0.075 1.153 3.35 0.0650 -8.98E-09

* Used as reference fluid for density, viscosity and magnetic susceptibility.* Used as reference fluid for density, viscosity and magnetic susceptibility.* Used as reference fluid for density, viscosity and magnetic susceptibility.* Used as reference fluid for density, viscosity and magnetic susceptibility.* Used as reference fluid for density, viscosity and magnetic susceptibility.** Recipe values are approximate.

Figure2:Theseexperimentsuseadesiredloca<ontodrivethesystem.Therela<onshipbetweentheinput(forces)andthemo<onthatfollows(posi<on)isdescribedmathema<callyusingdifferen<alequa<ons.

RiseTime‐TransientResponseFigure 4 shows a quan&fiable effect onthe rise &me due to fluidic resistance.This effect is related to viscosity and isappreciableanermoderate increments,but clearest in the highest viscosityvaria&on.Noeffectsduetomag.suscep&bilitycanbeobserved.

BandwidthandRoll‐offSlope‐FrequencyResponse.

Figure4:Responsetoastepinputusedtocalculate90%rise<mecategorizedbyfluidset.

Figure3:ResultsofapplyingEqua<on4usingastairinput

Figure5:MagnitudefrequencyresponseisobtainedbyapplyingaFastFourierTransformalgorithmtotheoutputsgeneratedbyachirpinput.

Experimental data suggests thatbandwidthitisinverselypropor&onaltoviscosity.Noeffectswereperceiveddueto changes in magne&c suscep&bility.Addi&onally, the roll‐off slope wasmeasured to be consistently higherthan that produced by a second ordersystem model, which suggests that athird or fourth order model could bemoreappropriateforthissystem.