8iorheolo訂，Volt31，No・ら，pp・521−532，1994
Copyrighl◎1994EIseYierSdenceLtd
PrinLedinLheUSA・A）IrighLsre＄erVedpe騨On

仰・3ら5X／94‡6．00＋．00

0008・355Ⅹ（94）EO0032−8

CLOT GROWTH UNDER PERIODICAI−LY FLUCTUATrNG
SHEAR RATES．HASHIMOTO
Biomedical−SystemsLaboratorY，DepartmentofElectronicEngineering，Osaka
InsdtuteofTechnology，5−16−10hmiya，Asahi，Osaka，535JAPANABSTRACT TocontrolthemorphologyofaClotformedonanartificialflow
Pathin pulsatile blood flow，the hydrodynamic effect of periodicallyfluctuating shear rate on clot growth has been quantitativelyinvestigatedin
Vitro・Uniform＄hearrateswere applied to a sample ofbeagle bloodin theCOnCaVe＜OnVeXCOneSSyStem・neSeShearratesweresinusOidal1yfluctuatedbetweenamaximumandaminlmuminonedirecdonatfrequenciesbetween
O・landO・6H2：・Evaluationofclotgrowthwasderivedfromaclotratio，Which

WaSeXPerimental1ydetermined ffomtherate ofincreaseoffrictionaltorquebetweenthe twocones・Ti1e reSultsshowthatclotgrowthiscontrolledsoas
not to occupy alarge space when theminimum shear rateis higher thanlOOs−1，OrWhenthe time ofapplication oflower（＜100s−1）shear ratesis

modifiedbytheintermittentapplicationofhigher（＞500s−1）shearratesas
longas血ef上equencyisless血anO・6Hz・

Introduction

ManyFactorscontrolthedynamicbalancebetweenthefbrmationandremoval
Ofclots・Throughthiscontrol，therupturedvesselwallisrepairedandtheflow

Pathmaintained．Thesefactorsarepresentin boththebloodandthevessel
Wall・TheylnClude platelets，COagulants and anti−COagulants．Many studies

havebeen perfbrmedin thisfield ffomthebiochemicalpolntOfview，Whichincludes山einteractionbetweenthebloodandthesurfhcematerials（Salzman，1981）・Ontheotherhand，theclothasbeenconsideredtogrowuparounda

Stagnationflow point．In a previous studY（Hashimoto elal．，1985），Clot
growthunder steady shearflow wasinvestlgated with a cone and plate。sa
Orintheflowpathsofextra−COrpOrealcirculationpoweredbYpulsatilepumps，
thiscase・TfthepeakshearrateofeachpulsecycleinterTuPtSthetermoflower

Shearrates（t）andwashesawaytheconditionsforclotgrowth・boththemaximum shear rate of each pulse and a shorter t for each pulse may be
efftctiveinpreventlngClotgrowth．Todiscoverthecondidonscontrollingthe

morphologyofclotsfbrmedintheardficialflowpathinpulsadlebloodflow，
EEYWORDS： Blood；Clot；Shear；Couetteflow；tOrque；Pulsatileflow
521

522

Cbf〟血ノ払血αお一瞥∫鮎αrVol．31，No．5

this studyinvestlgateS Clot growthunder sinusoidallyfluctuating shear ratequantitativelyinvilrouslngthe modified concave−COnVeX COneS teSt SyStem（Ha5himoto，1989）．

MaterialsandMethods
C州√ ・卜「棚tⅢTl，・ヾ／・や・ヾ／〃〃Inordertoapplyunifbrmshearratestotheblood，theconcave−COnVeXCOneS

testsystem was created（Fig・1）．The principle used bythe concave−COnVeX
COneSSyStemtOCreatethe unifbrmshearfieldisthesameasthatofthe coneand platesYStem（Hashimoto elal．，1985）．The concave−COnVeXCOneSSyStemdifftrsfromtheconeandplatesysteminthat：（i）Concaveandconvexcones

rFplacethe？Oneandplate；（ii）therotadonalspFedofthecoヮefluctuates
SlnuSOidal1Yln One−direction and（iii）the frictlOnaltorquelS meaSured

COntinuously．
The combinadon ofconcave andconvex cones hassomeadvaLntageSOVer

that ofcone and plate：（a）It neutralizes the tendency fbr erythrocytes toaggregateintherimofthecircularcone；（b）itequalizestheshearrateapplied
tothewholebloodsampleevenattherimofthecircularcone；（C）itsimpli丘es
theremovalofairfromthespacebetweentheconcaveandconvexcones；（d）itSimplifiesthe collecdon ofbloodfrom the concave cone afterthe test；and（e）it minimizes secondaryflowwiththe fbrce ofinertia bY Changing therotatingpartfromtheinnertotheoutercone・Amongtheseadvantages，both（b）and（c）havebeenpointedoutasdeftctsoftheconeaLndplatesysteminapreviousstudY（Monroeelal・，1981）．

Fig・2（A）showsthevelocitydisuibution（Couette−tyPeflow）inducedina
bloodsaLmpleplacedbetweenastadonarYCOnVeXCOne（diameter，4．8cm）anda rotadng（clockwise）concave cone．Theshearrate，γ，Calculated fromthe

Velocitydistribudon，is constant regardless ofthe value ofx（the distancebetweenPandSinFig・2），aCCOrdingtothefbllowingequation：＿γ＝一旦−＝（〃6X OO

Where uis the circumftrendalvelocityat S on the concave cone，8isthe
distancebe【weenSandQ（Fig．2），Oistheangularvelocity（rads￣1）ofthe
COnCaVe COne，Oisthe angle（0・056rad）be【ween the convex and concave

COneS：andβistheapexangleofthecone（2・10rad）・Notethatinderivingthis
equat10nandthosetofbllow，Oisassumedtobeverysmall・
Theseshearrates（γ）werecontrolledinproportiontotheangularvelocity

oftheconcaveconeinonedirection（3．2＜0＜52rads￣1；SeeEq．（1））bya
function草eneratOr（Fig・1），andwereperiodicallyfluctuatedwithvariationsin

thefbllowlngthreeindependentfactorsinasinusoidalヮode（exemplifiedin
Fig．3）：（i）Themaximum（γmax＜800s−1）；（ii）theminlmum（γmin＞25s−1）
OfshearratesaLnd（iii）thefrequencyoffluctuation（0．1＜f＜0．6Hz）・BothCOneSWere made oftransparentpolymethylmethacrylateto enablethe blood
SamPletobeobservedduringtests．

Vd．31，N0．5

C加〃 ゐrβ 血αガ，智∫おαr

Fig・1・Concave｛OnVeXCOneSteStSyStem．
Q（B）

ZFig・2・VelociFydistribudonbetweenSandq（A）・Shearrate

betweenastatlOnaryCOnVeX COne and arotatlngCOnCaVe COne（B）．

523

524

Cわ川 血β一血dめ智∫鮎肝Vol．31，No．5

The丘ichonaltorque，T（dyn／Cm），betweentheconvexandconcavecones
isglVenby（2ノ T＝

whereTl（dynscmT2）istheapparentviscosityoftheblood，andR（cm）istheradiusoftheshearingpordon ofwhich the blood sampleisa part（Fig．2）・
CombiningEqs・（1）and（2），WeObtain：（j） T ＝Eqs・（1），（2）and（3）areappliednotonlytosteadyflowbutalsotoquasi−Steadyflow，SuCh assinusoidally fluctuated flowat the frequency of＜0．6Hz（seeDiscussion）．

Thefricdonaltorque（T），Whichfluctuatesbetween themaximum（Tmax）
and theminimum（Tmi。）inpropordontotheshearrate（Y），is con也nuouslymeasuredbythestraingauge・
CわJ勉JわIneachtest，thebloodsample（1．5cm3）wasdrainedthroughastainlesssteel
needle from thejugularvein ofan anesthetized beagle，and collectedin a
POlypropylenesymngewithoutan山：Oagulants．Immediatelyafterthedrainage（withinlO seconds），1．O cm30fthebloodsamplewasplacedbetween theCOnVeX and concave cones，and was sheared for3−10minutes，While thetorqu？，T・WaSCOn血uouslymeasured（Fig・4）・Whenthetorque・T・increased

StePWISeWith clotfbrmadon，the rotation ofthe concave conewasstopped，andtheclotwasmacroscopICallyobserved．Whentheclotmakestheangle，0，tS1，乙Samplewas pouredinto aglass tube and thecoagula山）n dmewasmeasured
withoutshearas areftrence，Evaluadonofclotgrowthwasderived f［om the clotrado（Rc），Whichwas

experimentallydeterminedfromtherateofincreaseoftorque，T，Calculatedin
Eq・仔）・（4） Rc】怒〕十l】吾」−・．．：・：
torquetracings（Fig・4）・Whenthetorque，T，doesnotincrease（Tmax。＝Tmax．
andTmin。＝Tminl），Rcbecomeszero・Whenthetor9ue，T・increasesmarkedly（Tmax。くくTmaxlandTmin。

Tminl），Rcapproachesunlty・Tominimizethescatterofdataafftctedbyclotcapabilityfluctuationsuch
asthefluctuadonofcoagulants−COnCentrationinthe circulating blood day byVol．31，No．5

C加 血ノh血αめ瞥∫加αr525（s−1）†maX200†min

10Time（s）
Rg・3・Exユニ1pleofshearratefluctuationinsinusoidalmode・∈U
u音−日当b岩巨
0

2 4Time，min
Rg・4・Frictionaltorquetracings・

526

C如〃 血J‰血α正一官∫鮎αrVol．31，No．5

（A）

（B）

Fig・5・Clot ratio（A）before clot formation；（B）after clot
fbmation．

day・dataarrangedineachfigure（Figs・6−8）？OrreSpOnd toasetofdata
Obtained fromthesame beaglewithinsixhours，1n eaChcase．In the case of
COllectingdataffomalong−term teStSeries（Fig・9），Valuesofthe clotratioin

thesamefluctuateconditionofshearratewerecomparedasareference．
Result5

Fig・6presents clotratio（Rc）as afunction ofmaximum shear rate（γmax），

Whereγm享nisfixedat50sLlandwherefrequency（f）isfixedatO・1Hz・The
・、て、‥ミ＝750s−1indicatesRcattheconstantshearrate・ThefigureshowsthatRcis
Smaller than O．5andthat Rcincreases as the minimum shear rate decreasesin

therangeof†min＜100s−1・Fig・7BpresentsRcasafunction ofminimum

shearrate（†min），Where†maxisfixedat650s−1andwherefisfixedatO．1Hz．
Thedatumpolntat†min＝650s−1indicatesRcattheconstantshearrate・The

figureshowsthatRcincreasesas theminimumshearratedecreasesandthat
RcisbiggerthanO・5intherangeofYmin＜100s−1・Fig・8presentsRcasa
function of the difference between maximum and minimum shear rate（†max−†min），Where†meanisfixedat300s−1andwherefisfixedatO．1Hz．
Thedatumpolntat†max−Ymin＝Os−1indicatesRcattheconstantshearrateof
300s−1・ThefigureshowsthatRcislargewhenγmax−†min＝550s−1・Fig・9
presentsRc asafunction offfequency（0；Whereγmin＝50s，1（A），†max＝650s−1（B），γmean＝300s−1（C），†max−†min＝200s−1（D），reSpeCtively．The
figure showsthat Rc decreases asthefrequencylnCreaSeS，aSlong asthe

frequencylSlessthanO・6Hz・ThistendencylSmarkedwhen†min＝50s−］andVol．き1，No．5

Cbf〟血β一助αめ瞥∫鮎〃r527

γmax＝550s−1・Ontheotherhand，RcstillhasasmallvalueevenatO・1Hz，
when≠1in＝500s−1andYmax＝650s−1・The coagulation timeswithout shearinthe glass tube stayed around a
COntrOlvalueoftenminutesthroughoutdleteStS・1aDi5Cl椅5ion）s1100s−1becomeslongerandtha【RcissmallerthanO・5whentheintervalis
Shorterthan two seconds．

Reciprocatingconcave−COnVeXCOneSmadeofpolytetrafluoroethylenewere

used to shear dle bloodin a previous study（Dintenfass，1966），in which
frictionaltorque tracings were recorded by thromboelastograph（Har［ert，1951）・ThefeSultsshowedthatdleClotfbrmedinashortertermanddlerisingratiooffrictlOnaltorqueissmallatthehighershearrate，Inthepresentstudy，
the concave cone does not recIPrOCate，but rotatesin one direction・ThisOne−WaymOtionwaschosenfbrdlisstudytoimitatepulsatileflow．Theresults

ShownindlepreSentStudyarequalitativelyconsisten［withdlOSeOfdlepreVious
Study．

TheangularvelocltyOf山econcaveconeiscontrolled toapplyperiodicallyfluctuating shear ratesin the pres3nt Study・Asa usefuldimensionless

PaTameter・theWomersleynumber（W）hasbeenprpposedtoestimate theratlOOfinertialtoviscousforcesinperiodicallyfluctuatlngflows：

U銘

30000

γmaX（S・1）

Fig・6・Clotratio，Rc，aSafunctionofmaximumshearrate・

528

VoL31，No．5

C払f鋤血」伽肋α〟曙∫鮎Ⅳ

000

00

300

00

占009（川00900

Y m■ローs・l）

jOO

O／min（S・1）

Fig・7．clotrado，Rc，aS a function ofminiJllum Shear rate：†max＝750s−】（A）；†max＝650s−1（B）．

300

00

γmaX−†min（S・1）
ngL往r Clotratio，Rc，aS afunction ofthe difftrence bet（Ieell
rna：；imum and minimumshearrates．

Vol．31，No．5529

Cゎー肋血β〟血￠血g∫鮎￠r0（B）1■01（A）

7min＿7m狛−T min・￣r maX（S ）0．80 50．550

ム 50， 50﹂♀U

△ 50．200

0 ヱ00． 50● 50．65（l●△ △■■﹂
．44

き △ ○
●

∧U

J己△△。

e■﹂
′〇

○′hV△
●

● 500＿650

●

0 0○△

ヱ

∧U●

△○
●

三 2 ●

●

O

﹁▲OL

0．40，ヱ0．6

小0．40．ヱr（Hz）

0．60l■lH′l†min・†maX（S−1）
0△ 50．550
0 150・450■／min・Yれm‖（S● ヱ00．400○ ヱ00・4001△】l）0．J00● 400， 00

△△○

○

●

● i○

○

●！ ● △00．2

軋∩
0．4

ひ．ヱ

0．0

0．

0．Z

O．j

0．

l 1日■rlH乙）

mg・9・Clotralio，Rc，乙S afuncdonofffequency：γmirl＝50s−1γ二．，。arl＝3OC s−1（C）；γmax Lγmirl＝（A）；γmax＝650s￣1（B）；

200s−1（D）．

○●→Who】e term0．

08000 00●→○

0．4024t（S）

Fig・ le＞・Clotratio，Rc，aSafunction ofexpostlretimeofshear
mteof＜100s−1．

530Vol．31，No．5

CわI〟乃ぬJ‰血αガ一瞥∫鮎αr

Where d ＜ 0．15 cm（distance between the convex and concave cones），

f＜0．6Hz（frequency），P＝1g／cm3（densityofblood），andll＞0．05dymSCmT2（viscosityofbloodat240C）inthepresenttests（showninFigs．6−9）．Because
Wiscalculatedasasmallervaluethan unityinEq．（5）（whichindicatesthat

inertialfbrces can beignored（Caro et al．，1978）），theflow between theCOnCaVe and convex conesis estimated to fbllow the rotary motion ofthe
COnCaVeCOne・Tolimittheeffbctofinertialfbrce，thefrequencyoffluctuation

WaSCOntrOlledinthelowerrange（＜0・6Hz）inthepresentstudy・Ifamore
SOphisticatedsystemweredevelopedtoinvestlgatetheefftctoffluctuatingshear
Whe

（A）

（B）

Fig・11・Clotfbrmed atlowshear rate（A）；at high shear rate（B）．

Cわ川I血ルJ血融座両肌rVol．81，No．5

531

TablelSeveralEffects ofShear Flow on Clot Formation（a）Damageendothelium（b）Acdvateplatelets（c）PromoteEibri11inkagewith＋＋＋

molecularorientation（d）Activateprecursorofcoagulation＋fゝctors（e）DestroYCOa飢11ationfactors（f）Inhibitfibri11inkage（g）Inhibitadhesionoffactorsto

walls（h）DefbrmEibrinnetworkand

decreasethenumberofcaptured
eIYdlrOCYteS＋ ＝ Promotion ofclotfbrmation− ＝Inhibition ofclotformation

Minimizinglnertialfbrcewiththe ffequency ofthefluctuating now restricts
imitatlng Pulsadleflowsin arteries；theflow ratein pulsatile nows does notfluctuatein asimple sinusoidalmode，butina more complicated periodical
modewhichincludesharmoniccontentsofhigherfreqt！enCy（Hashimoto，1988）・Thepresentstudyrelatestotheperiodical1yfluctuatlngflowrateinthe

Simple sinusoidalmode．
There are somelimita也ons tothe testsystemin the presentstudy■ Clotratio satisfactorily corresponds totheamountofoptlCal1yobserved clots，but

the datarevealscatter（seeFigs．6−9）．One ofthe reasons fbr datascatteris
thatclotsdidnottakeunifbrmshape・ShowninFig・5（B），butt？Okirregular
ト■こ■こ．．‥
considered when the clot ratio evaluationis extended to thelow shear rate・m

rangeisthesamelevelasthatinthehumancardiovascularsystem（Whitmore，1968）．

SeveralefftctsofshearElow on clotfbrmation have been polnted outby
PreVious studies（Dintenfhss，1964；Hartert，1974；Hashimoto，1985；Spaeth，1973）・TheseeffectsarelistedinTablel・Efftct（a）isexcludedinthepreseヮtexperim∈nt，becausethe testsystemdoesnotincludeendothelium・Themaln
effect of shearflowin the present experiment might be（h），Whichis
SChematical1yillustratedinFig．11．
References

CARO，C．G．，PEDLEY，T．］．，SCHR6TER，R．C．
（1978）t me Mechanics qfthe Circulation・Oxfbrd University Press，Oxfbrd，PP．57−60・
DINTENFASS，L．（1964）．Viscosityand clotdngofbloodinvenous
山rombosisandcoronaryocclusions．Ci7T，Res．14，1−16，

Cbf〟，血」伽血α〟一瞥∫鮎αr

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DINTENFASS，L．（1966）．Efftctofvelocitygradienton the clotting
time ofblood and on the consistency ofclots fbrmedin tJitro，Circ・
月郎．Jβ，349−356．

HARrIERT，H．（1951）．DieThrombelastographie．EineMethodezur
physikalishenAnalyse des Blutgerinnungsvorganges・Zeitschrytf d・
併路面…叫知加齢加地ル知抜玩J〃189−203・

HARTERT，H．（1974）．Rheo−Simulation：Anewmethodfbrtheassay
OfclottingprocessandfactorXIII．Biorheologyll，355−360・

fWHIMOTO，S．，MAEDA，H．and SASADA，T．（1985）．Efftct o

Shearrateonclotgrowthatfbreignsurfaces・Arl￠OTganS具345−350・

fnSHIMOTO・S・andMORIm・H・（1988）・Efftctofrightventricular
bypasspeakflow−rateOnintrapulmonaryshuntrat10・Artif：OTganf12，
67−77．

fWHIMOTO，S・（1989）・ErythrocytedestruCtion underperiodicallynuctuated shear rate：Comparative studywith constant shear rate・A祀￠α那那Jj，458−16S．
MONROE，］．M・，TRUE，D・E・andWILLIAMS，M・C・（1981）．Surhce

roughnessandedgegeometriesinhemolysiswithrotatingdiskflow・J
月わwd．〟αf〝．月βJ．ノブ，923−939．

SALZMAN，E．W．（1981）．Interaction qfthe Blood with Naturaland
ArlyicialSu申CeS・MarcelDekker，NewYork・SPAETH，E．E．，ROBERTS，G．W．，VADWADKAR，SandJACKSON，C・M・（1973）・Theinfluence offluid shearon thekinetics ofblood coagulation reactions・Trans・Am・Soc・力付」血珊・
α那乃JJ具179−187．

WHITMORE，R・L・（1968）・Rheolog）QFthe Circulation・Pergamon
Press，Oxfbrd，pp・93−96・

Acknowledgment

ThisworkwassupportedinpartbyaGrant−inAidfrom theJapaneseMinis叩
OfEducadon，Scienceand Culture．
月βCdvβdJOOcわ∂〝JタガJαC呼fβdJ7ノお乃βJタタイ．