んイ折c由JO堵♂〃∫9（4）：345−350，RavenPress，NewYork◎1985Internationa］SocietyfbrArtincialOrgans

EfftctofShearRateonClotGrowthatForelgnSurfaces
ShigehiroHashimoto，＊HiroyoshiMaeda，and†TadashiSasada∫c／王00Jq†〃gdfci乃g，g血∫αJoU〃ルピr∫〜Jy，∫αg（‡∽′んαrα／＊〃gdfcαJ∫c／！0∂J，〃βg（）γdCfけぴ〃ルビr∫砂，〃αg（）γd／α〝d
ナFdC〟Jけq′g〃g∫〃eピタ血g，7b桓oJ〝∫J〟〟Jeq「rec／‡㈲わg）′，れ）桓0，Jdpα〃

Abstract：Thehydrodynamicefftctonclotgrowthat払r−eign surfaces wasinvestlgated quantitativelyln Vitro．

WaSeXperimentallydeterminedn・Omtherateofincrease

Offrictionaltorqlle between the rotating cone and theShearrates丘・Om2tol，000s−1wereappliedtoablood

Stationaryplate．Theresultsshowthattheclottingratio

Sample containedinacone and plate viscometer．Four
difTbrentartincialmaterialswereusedfbrconeandplatedecreasesmarkedlyastheshearrateincreasesto400s−1，
regardlessofmaterialused．Thisstudydemonstratesthat

COmbination，namely，Stainlesssteel，pOlytetranuoroethy− atashearrateof＞400sLl，Clotgrowthatfbreignsurfaces
isconsiderablyinhibited．KeyWords：Blood coagula−
1ene，pOlycarbonate，andpolymethylmethacrylate．Eval−

uationofclotgrowthwasderivedfromtheclottingratiotion−Hydrodynamic effect−Clot growth−Shearrate−Coneandplateviscometer−Artincialmaterials．

（thevolumetricfractionofclotinthewholeblood），Whichequlpment，abloodsampleisshearedinaconstantBlood coagulates when it contacts foreign sur‑faces，SOthatclotgrowthatleasthastobeinhibited
topreventclogglngthebloodnowpathinartificial
OrganS．Theclottingprocessincludesmanystages

VelocltygradientfieldasshowninFig．2．Whena

COne Whose apexPis touchinga stationaryplate
andisrotatingontheaxisPZ（perpendiculartothe

thatinvoIveaseriesofenzymicreactions．Withre− plate）ataconstantspeed，aCOnStantShearrateis

applied to the blood sample throughout the space

gardtoclotfbrmationonartincialmaterials，many

betweentheconeandtheplate．Avelocitydistri−Studieshavebeenconductedonthebiochemicalin−bution，aSShowninFig．2b，isinducedbetweenS
teraction between blood and the material（1）．On
theotherhand，ClotR）rmationisalsogovernedbyandQ．TheshearrateG，Whichiscalculatedfrom
ahydrodynamicefftct；i．e．，Clotsdonotgrowon thevelocitydistribution，is constantregardless ofthevalueofr（distancebetweenPandQshowninmaterialswherebloodflowssmoothly（2）．
Fig．2）accordingtothefbllowingequation：
Inthisstudy，tOeValuatetheeffectofshearrate
OnClotgrowthatfbrelgnSurfaces，relationshipsbe−
G＝＝＝tweentheshearrate（befbrefbrmationofclot）andtheclottingratio（thevolumetric丘・aCtionofclotin（1）

the whole blood）were examined quantitativelyin

WherevisthecircumftrentialvelocityatSonthe

COneandplateviscometertests．

Circularcone，disthedistancebetweenSandQ，Wistheangularvelocityofthecone，andOistheangle
between the cone and the plate．Notethatin de−rivlng this equation and those to fbllow，Ois as−

MATERIALS AND METHODS

Testequlpment
The cone and plate viscometer（VisconicED；
Tbkyokeiki，Tbkyo，Japan）wasusedtoapplycon−
StantShearratestoabloodsample（Fig．1）．Inthis
ReceivedSeptember1984；reVisedMayl，1985，
AddresscorrespondenceandreprintrequeststoDr．S．Hash・
imotoatBioengineering，SchoolofMedicine，KitasatoUniver−Sity．15−1，Kitasatol−Chome，Sagamjhara−Shi，228Kanagawa，Japan．
j4！

Sumedtobeverysmall．
Inactualpractice，theshearrateiscalculatedas
G＝（2）

WhereNistherotationalspeed（rpm）oftheconeand4）is the angle（0）between the cone and the

Plate．
Four difftrent materials were used fbr the cone∫．〟A5 〟ナ財OrO且rA上．

ブイ6

J

to drivjng
motor

rotating rod
SPrlng盛莞COnespace fora sample bl。
r1ヽ■−−へstaいOnary

Plate

￠
to camera（Fig．4）

F］G．1．Test equipment・Left＝Schematic diagram ofthe cone and plateviscometer．Fljght：Externalappearance ofthetest
equipment．Thefrictionaltorqueismeasuredbythetorsionangle伸）inthespringattachedtotherotatjngrodintheviscometer（VM）（right）．Thevalueoftheangle中is picked upopticallyeveryrotation bythesensor（SE）andtransmittedtothe recorder（RE）（right）．

（radius2．4cm）and plate（shapedlike acuptobe tween the cone and the plate，the rotation ofthen11ed with a blood sample）：Stainless steel，pOly−
cone started and a constant rotational speed wastetrafluoroethylene，POlycarbonate，andpolyme− maintainedfbr30min．Duringthisperiod，thefric−thylmethacrylate（Fig．3）．Tbchecktheef托ctofthetionaltorque was measured everyrotation．Inthegeometry of the space between the cone and the
Plate，tWOOrthreevariationsweremadeaboutthe
apexangleoftheconefbreachmaterial．
Shearratesfrom2tol，000s1wereappliedto

CaSeOfthepolymethylmethacrylateconeandplate，
the clot fbrmation was observed macroscopICally
throughthetransparentstationaryplateatthesametime．

thesamplebloodbyvaryingN（fromO．5tolOOrpm） Thesetestswereperfbrmedfbrtheconeandplateand4）（fromO．6tol．60）．

ThefrictionaltorqueTbetweentherotatlngCOne
andthestationaryplateismeasuredbythetorsion

combinations of the fbur kinds of materials withvariations ofthe shearrate．

Duringthesetests，the bloodtemperaturewas

angle中（Fig．1，1eft）ofthe springattachedtothe

maintainedat240Cinthe room．Tbchecktheeffbct

rotatlng rOd．The value ofthis angleis recorded
OPtlCallyeveryrotationand transmittedtothere−

Ofthebloodtemperature，additionaltestswereper−
fbrmedin the case ofthe stainless−Steelcone andCOrder（Fig．1，right）．

Plate；thebloodtemperaturewasmaintainedat370C
by a constant temperature bath that was attached

Procedure

Humanbloodwas collectedfromaslngledonor

tothestainless−Steelplate．

intosodiumcitrate（1：6．6sodiumcitrate／blood；9．8 Determinationofclottingratio

mMfinalconcentrationinblood）andpreservedfbr
2weeksat50Cbefbre testlng．Tb check the effect
Ofpreservation，additionaltestswereperformed
Withfreshbloodin the case ofthe polymethyl−
methacrylateconeandplate；Caninebloodcollected
fromasingledonorintosodiumcitrate（1：9sodium

Evaluation ofclotgrowthwas derivedfromthe
Clottlngratio，thisbeingexperimentallydetermined
bythefollowlngmethod．Preliminaryexperiments
indicated thatmacroscopICClotfbrmationwas ob−
SerVedthroughthetransparentplate（Fig．4）within
lOmin（3mininthecaseofcanineblood）fromthe

Citrate／blood；13mMnnalconcentrationinblood） Start Ofthe blood coagulation process（from theStart Ofrotation），and that the frictionaltorqueWaS uSedimmediatelyinthis case．Theblood co−agulation process wasinitiatedby adding calcium

began toincrease at the same time（Fig．5）．This

Chloride（0．1：1calcium chloride／blood；0．25Mso− increase occurs whenbloodflowis obstructedby

1ution）betweentheconeandtheplate．

Immediatelyafterthebloodsamplewasfilledbe−
Ar】甘OrgdJはVoJ．9，〃0．4，ノ9β5

clot．

Thetorque T（dynes・Cm）isgivenby

j47

且FFECrOF∫肱4月月A7苫0〃C上OrG月OWr〃

FIG・3・Cone（bottom）and plate（top）combinationsoffour
differentartificialmaterials：Stainlesssteel（A）；POIytetrafluo−roethylene（B）；POlycarbonate（C）；POlymethylmethacrylate
（D）．

（b）

rotating cone⊥

CreaSeSfrom￠oto d）1aftertheformationofclot・（c）The apparent viscosity ofblood after the forL
mationofclot（BinFig．6b）isequaltothatofblood
befbrethefbrmationoftheclot（BinFig．6a）．That
lS，TTISCOnStantinEq．4．

Thus，reftrringto Eq・4，㌔（torquebefbrefbr−
mation ofclot）and T］（torque after formation ofClot）aregivenby

Stationary plate

FIG・2・Ve10CitygradientinabIoodsamplefilFedbetweena
rotating cone and astationary plateL a：Geometryofthe
SPaCe betweentheconeandtheplate，b：Ve10CitygradientT，
between Sand O．u，angUlarve10Cityofthecone：PZ，rOta−
tionalaxis：0，anglebetweentheconeandtheplate；d，dis−tancebetweenS（Onthecircularcone）andO（OnthepJate）；
γ1r，distance between P（POintwheretheapexofthe conejs
touching the plate）and Q（On the plate）；V，Circumferential
VelocityatSonthecircularcone．
CombiningEqs．5−7，

r＝恥骨¶月3G

4丁叩月5〃￠0

4丁叩月3〃（3）

whereTl（dynes・S・Cm▲2）istheapparentviscosity
Ofb】00d，R（cm）is the radius ofthe cone（2．4cm

inthisstudy），andG（s．1）istheshearrate．Com−
biningEqs．2and3，γ＝47T¶月jⅣ（4）

lb calculatetheclottlngratiobya simpleequa−tionrelatedtoarateofincreaseoftorque，thefbl−

lowingapproximations a−C Were aPPlied．（a）The

clot is spread over the whole space between theCOneandtheplateinashapelikeAinFig．6b．Then
Clottingratio（CR）isgivenby
C月

￠0一￠1

1一

（5）

FIG. 4. Macroscopic clot formation observed through atransparent plate in the polymethylmethacrylate cone andWhere￠oand（♭1areangles definedinFig・6・（b）

PrateteSt（10minfro

Theflowintheclot（AinFig．6b）canbeignored；tweentheconeandthepJate￠＝1．1O；Shearrate＝550s￣1；．

i．e．．theanglebetweentheconeandtheplatedeLPreSerVed humanb100d）・

ArげOrg（プ那，V（）J．夕，Ⅳ仇4，J9βJ

∫．〟A5 」打J〃OrO占■rA上．

examplesofthevisua］qua］ityoftheclotformedon

the polymethylmethacrylate cone and plate（nuidPartisremovedaftertestinthefigure）．Theclotting∈U ・ u 合 ． ト 聖 b L O ト

ratio，itis seen，decreases markedly as the shear

rateincreases to400s1，independently ofotherfactors，namely，material，4）（anglebetweenthe
COne and the plate），b］00d preservation，and thebloodtemperatureusedinthetests．
Intheshearraterangebetween2and50s−1，theValues ofthe clottlng ratio show scatter，but theyu

卜

二十了 l l l0

二￣＿rl＝二∴▲l「n ■：÷ u‖ u j u l ll◆

20

10are＞0．5，and the clot appears nlm−1ike（Fig．8A，
B；ClotformedontheconeinFig．8A）．Intheshear

口 n u ■

raterangebetween50and400s1，theclottlngratio

30

丁うme，mjn
FIG・5・Torque recording fromthesametestasthatshown
inFig・4（POlymethylmethacrylateconeandplate；anglebe−
tweentheconeandtheplate￠＝1．10；Shearrate＝550s1；
PreSerVedhumanb100d）・To，tOrqUebeforeformationofclot；
Tl，tOrqUeafterformationofclot．

（ 尺 ニ ー（8）decreasesmarkedlyasthe shearrateincreases．In
theshearraterangebetween400andl，000s−1，theValues ofthe clottlng ratio are＜0．5，and the clot
Showssmallplots（Fig．8C）．
Relativetothe artificialmaterials，the clottlng
ratioissomewhatsmalleronstainlesssteel（Fig．7，
topleft）thanonpolytetrafluoroethylene（Fig．7，tOP
right）at200s1．
In relation to4），the data do not show a clear

Thus，theclottlngratiocanbecalculatedbyEq．8relationship between the clotting ratio and4）．For

Where㌔and TlaredeterminedfromtorquedataPOlycarbonate，thedatashowthattheclottlngratio
likethoseexemplinedinFig．5．

isbiggeratl・4thanatO・70at430s1，butsmaller
atl．4thanatO．70at86s1（Fig．7，bottomleft）．

In relation to blood preservation，the values oftheclottlngratioinfreshcaninebloodarescattered
Figure7showstheclottlngratioasafunctionof
but are somewhatlarger than thosein preserved
Shearrateoneachmaterial，andFig．8showssome
humanbloodathighershearratesonpolymethyl−
RESULTSmethacrylate（Fig．7，bottomright）．

Relativetobloodtemperature，theclottlngratiois］argerat37thanat240Con stain］ess steel（Fig．
7，tOPleft）．

Theclottlngratiowaswellcorrelatedtotheform
Oftheclotobserved（Fig．8）．

DISCUSSION

Evaluation ofclotgrowth was derivedfromthe
Clottlngratiointhisstudy．Themeritofthismethod
isthatclotgrowthcanbeevaluatedwhiLeaconstant
Shearrateisappliedtothewholebloodsample．It
maybe alsoconvenienttoevaluateclotgrowthin
thattheclottlngratiodirectlyshowshowmuchthebloodflowis obstructed．

The methodto determine clottlng ratioin thisStudy，however，includes someapproximations，SOthere are some difftrences between the hypothe−
Sized and actualobservations．First，the clotis of
FIG．6．DeterminationofcIotting ratioinconeandplatevis−
a moreirregular shape than thatin Fig．6b，and
COmeterteStS before（a）and after（b）formation of clot・A，torquesometimesincreasesanddecreasestoreveal
Clot：B，blood；To，tOrquebeforeformationofc10t；Tl，tOrqUe
after formation of c10t．

ArJすOJ・g（川∫，† 0／．9，〃0．4，／9β5

amorecomp］icatedcurvethanthatinFig．5．Thus，

gFF且CrOF∫〃EAノ‡尺ArEO∧rC上OrG尺OW71仔

05︵5︶○ こ 2 ぎ こ ぢ ﹁ U

500

J・J9

500

shear rate G，SeC−1

Shear rate G，SeC−1

500

500
−1

Shear rate G，SeC−l
Shear rate G，SeC
FIG．7．Clotting ratioasafunctionofshearratein bl00d between coneand platemadeofstainlesssteel（topleft），POJytetra−
fluoroethylene（topright），P01ycarbonate（bottomleft），and polymethylmethacrylate（bottomright）．￠，anglebetweenthecone

andthepIate．

itis sometimes dimculttodetermine Tl（torqueto800s￣1fbrparabolicvelocityprofiles（5）．Sotheaf［erformationofclot）．Thisisthemainreasonfbr rangeofshearrateappliedtothebloodinthisstudy
thefluctuationsoftheclottlngratio（calculatedby

is typICally that applied at human vesselwalls．It

hasbeendeterminedthat200srlisatyplCalshearEq．8）inFig．7．Second，bloodisknowntobenon−
Newtonian；andwith reduction ofthe shear rate．
rateatthewallofgreatveins（5）．1nthisstudy，Only
theapparentviscosltylnCreaSeS SteePlyatashear

four different materials were tested，but Fig．7

rateof＜50s￣1（3）．Thisnon−Newtonianbehavior

showsthatnear200sltheclottlngratiodepends
greatlyonthe shearrateofeachmaterialused，SOa constant shear rate condition is preferred for a

explainsinpartthe scatterlngOftheclottlngratio（calculatedby Eq．8）atshearratesof＜50sLlin
Fig．7；i．e．，theapparentviscosltyOfbloodbe丘）re COmparison between materials．In this regard，thetheformationofclotwouldnotbeequaltothatof

testin the cone and plate viscometer has advan−

bloodafterformationoftheclot．Atashearrateof
tagesovertestsintubes．
＞50s￣1，thismethodtodeterminetheclottingratio Bloodisregardedashomogeneousinthistest．A
POSSible effect ofthe dimensions ofb】00d cells，
isapplicable，becausetheapparentviscosltyCanbee．g．，Can be eliminatedin the experimentaldeter−
treatedasaconstantvalue（Eqs．6and7）．

Flow patternsin human vessels have been ob−
SerVedin many studies where theinside diameter
OfthevesselandtheflowveJocltyOrflowrateareminationoftheclottlngratio．becausefluctuatjons
Ofclottlng ratios arewithin the range ofexperi−mentalerrorinthedeterminationofTl（torqueafter

measured（4）．From these data，Shearrates at the

わrmationofclot）inFig．7whentheanglebetween
theconeandtheplatechangesfromO．6tol．60．

＼＼ allin the circulation are calculated to befrom60

んイ√0／・よⅥ／TL−，V（フ／．9，〃0．4，ノpβ∫j50∫．〟A∫〟J凡才07「0上汀A上．

Thetimefromthestartofthecoagulationprocess
to clot fbrmation waslongerin preserved humanblood（Fig．5）thaninfreshcanineblood．Thissug−

gests that the ability ofplatelet aggregationmight
havebeenreducedinhumanbloodafter2weeksofpreservation，and the effectonplateletsmightex−

plainthescatteringofthecIottlngratioinfreshca−
ninebloodinFig．7（bottomright）．

Everytest was perfbrmedinvitrointhis study，butthe effectofshearrate onclotfbrmationmay
bedifferentinvivo；i．e．，Whenshearrateincreases
invivo，flowrate sometimesincreases，tOO．Thus，

Shearrate as wellas the entry rate ofcoagulation
factors should be examined at the same time invivo．Forexample，Grabowskietal．（6）reportedon

thedependenceofplateletaggregategrowthrateon
ADPentryrateandshearrate．Inthepresentstudy，

theefftctofshearrateonclotgrowthwasinvesti−
gatedunderconditionswithnoadditionofcoagu−
1ationfactors．

Acknowledgment：TheauthorsthankHiroshiIshikawa
and MasakiSohmafbrtheirtechnicalassistance．

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