ArJ研ぐ≠dJO′g（7〃∫13（5）：458−163，RavenPress，Ltd．，NewYork◎1989lnternationalSocietyforArtincia10rgans

ErythrocyteDestructionunderPeriodicallyFluctuatlng
ShearRate：ComparativeStudywithConstantShearRate
ShigehiroHashimoto∫c力00J（オ〃gd∫cf〃g，片血∫〟rO U〃ルピr∫恒1∫dgdmJ／打肌】，ノ叩d〃Abstract：Thehydrodynamiceffectofperiodicallynuctu−（evaLuated with hemolysis ratio；Plasma hemoglobin

rates・Uniformshearrates（＜l，000s▲1；COnStantOrSiりu−
izedcaminebloodcontainedintheconcavo−COnVeXtyPe

isinterspersedwithsmaller（＜300s】）shearrates．Key
Words：Erythrocytedestruction−Hydrodynamiceffect−
Shearrate−Pulsatileflow−Concavo−COnVeXteStlngma−

ofCouetteflowtestingmachinefor（1．8−9．0）×103satchine−Couetteflow．

atlngShearrateonervthrocytedestructionwasquantita− COunt Per Whole blood hemoglobin count）decreases
tivelystudiedinvitroincomparisonwithconstantshear whentheexposuretimeoflarger（＞500s1）shearrates
SOidallynuctuatingwithtime）were applied toheparln−
240C．Theresults showthattheerythrocyte destruction

Inpulsati】eflows（e．g．，inarteriesorinflowpaths （Tay】orvortex）（1）intheblood．Bothcones（Fig−2）

Ofthe extracorporealcirculation with a pulsatile

are made oftransparent polymethylmethacrylate，pump），bloodisexposedtoperiodicallyfluctuating Whichenablesthebloodsampletobeobserveddur−

Shear rates．To study quantitatively mechanicalerythrocytedestructioninthepulsatileflow，thehy−

drodynamic effect ofshearratesin a periodicallyfluctuating mode on erythrocyte destruction wasStudiedin comparison with thosein the constant

1ngteStS．Theirsurfaceroughnessesmeasuredbya
StylusareintheorderoflLLm．Inordertoevaluate
the effect of surface−tO−VOlume ratio（1．6−6．3mm▲1）on erythrocyte destruction，Variations（1．lO−3．90）weremadeintheanglebetweenthecon−
VeX and concave cones，nameLy，five convex

modein vitro．

COneS（apexangle，113．OO−115．OO）andthreeconcave

COneS（apexangle，117・2O−120・8O）werepePared・

MATERIALS AND METHODS

TopreventthebloodsamplefromevaporatlOndur−

Three sets ofthe concavo−COnVeX teSt SyStem
1ng teStS，the concavo−COnVeX teSt Part WaS COn−
（Fig．1）weremanufacturedin ordertoapply uni一
tainedin polymethylmethacrylate chamber，in払rmshearratestobloodinCouette−typeflow．A Whichtheaqueousvaporwassaturated．Inthiscon−
heparinized sample（hematocrit38−45％）ofbeagleCaVO−COnVeX tyPe teStlng maChine，the uniform
bloodwasnlledbetweenastationaryconvexcircu−

Shearrates（G），Whicharecalcu】atedbyEq．1，arelarcone（diameter，48mm）andarotatingconcaveappliedin a similarway to a cone−and−plate typeCircular cone（rotated by DC motor；Sawamura（Fig．3）（2）．

Denki，Japan），andwasshearedfor（l．8−9．0）×103

Sat24OC．Theconcave（Outer）partwas rotatedinorder to minimize the effect of secondary flow

G＝（6〃／￠）sin（α／2）（1）

wherenistherotatingspeed（min．1）ofthecon−
CaVeCOne，αisitsapexangle，and4）istheangle（O）

ReceivedDecember1987；reVisedNovember1988．
between the convex and concave cones．
Address correspondence and reprint requests to Shigehiro
In any combination of the convex and concave
Hashimoto．Bioenglneerlng，SchoolofMedicine，KitasatoUni−
VerSlty、15−1．Kitasatol−Chome，Sagamihara−Shi，228Kanagawa， COneS，these shear rates，Which are contro11edin
Japan．
proportiontotherotatingspeed（＜350minl）of
ThisworkwaspresentedinpartattheVIthWorldCongressof
theconcaveconebyafunctiongenerator（Nationa］，
theInternationalSocietyforArti丘clalOrgansandXIVthCon−
gressoftheEuropeanSocietyfbrArtincialOrgans．
Japan），Were Periodically nuctuated with various
45β459

且尺yr仔尺OCyrEβ且∫7月UCコ70」V V∫．∫〃EA月月A7E

（B）

（A）

FIG．3．Cone−Plate（A）and concavo−COnVeX（B）test equip−
ments．

RESULTS

For6hoursfromtheblooddrawlng，HRwithout

FIG．1．Testsystem．Left，COnCaVO−COnVeXteSting machine；
Shearintheconcavo−COnVeXtyPeteStlngmaChineis
rotating−SPeedcontroller；right，functiongenerator・＜5×10r4，WhichislgnOredinthefbllowlngre−
Su］ts．Datain sinusoidallyfluctuatlng Shear rates

fluctuating conditions；the maximum（Gmax）
areshowninFig：5A−E，andthoseinintermittently（＜1，000s−1）ortheminimum（Gmin）（＞Os￣1）offluctuating shear rates are shownin Fig．5F．The
Shearrates andthefrequencyoffluctuation（＜0．8 totalexposuretimeofshearis7・2×103sinFigHz）in a sinusoidalmode（Fig．4B）．To compare 5A−F．Figure5A shows HR as afunction oftheWith this sinusoidalmode，COnStant（Fig．4A）andfrequency，Wherethemaximumandminimumshearintermittent（Fig．4C）modeswerealsotested．The ratesarefixedat300andOs￣1，reSPeCtively．The

Variationofthe rotatlngSPeedwasmeasuredbya

tachometer．Withthesimultaneoususeofthreesets

Oftestsystems，eVerySerialtest（forwhichdatais
COmParedinFig．5A−F）was坑nishedwithin6hof
the blood drawlng．EvaJuation oferythrocyte de−
StruCtion was derived from the hemolysIS ratio（HR），Whichiscalculatedby
HR＝月PHb／WHb（2）Tjme

WhereRisthevolumetricratioofplasmatowhole
blood，PHbistheplasmahemoglobinconcentration，andWHbisthewholebloodhemoglobinconcentra−tion．ThevaluesofRandPHbWeremeaSuredafter
centrifugationofbloodforlOminbyl．6×103g（g：accelerationofgravity）．Whenallthehemoglobins
arere］easedfromerythrocytes，HRbecomesunity．
Tjme

jn品rvalTうme

FIG．2．Concave circular cone（left），and convex circular FIG．4．Modeoffluctuationofshearrate（G）．A：Constant．B：COne（right）．
Sinusoidal．C：lntermittent．

Ar／すOrg（lm㍉Vd．〃，〃仇5，ノ9β9460∫．〟A∫〟J〟OrOCBlO

二 う5∵≡×．∝エ（⊃

⊂亡
コ＝0．5

1．0

0

1051050Gmean，XlO2s−1【，HzGmax■XlOZs￣1DT≡※．呈O 5

⊂ピ
コ＝

5100

GmHいXlOZs￣11D

5Gmax−GmいいXlO2s￣l01

2

345

Tjmes of jnterval（60s）

FIG・5・Hemolysisratio（HR）asafunctiono＝requency（f）（A）・Ofmeanshea〔rate（Gmean）（B），Ofmaximumshearrate（G，。aX）（C），

Ofminimumshearrate（Gm．。）（D），OfdifferencebetweenmaximumandminlmumShearrates（Gmax−Gmin）（E）andoftimesof
60sintervals（F）．

datumpolntatOHzshowsHRattheconstantshear

imumshearratesof＞450s．1・Figure5FshowsHR

rateof300s1・ThisngureshowsthatHRincreases as afunction of60sintervals，When the constantwithafrequencyof＞0．5Hz．Thefo】1owingngures shearrateof500s1isintermittentlyappliedfor7．2（Fig．5B−E）showHRatthefrequencyof＜0．5Hz， ×103sintotal．lnthecaseof3timesa60sinterval，

to keepapartfromthe effectofthefrequencyon
HR．Figure5BshowsHRasafunctionofthemean
Shear rate，Where the differences between maxir

mumandminimumshearratesarefixedatlOOs1
andthefrequencyisaconstantofO．1Hz．Theng−forexample，theexposuretimeisdividedintofour
parts，andtheconstantshearrateisappliedforl．8
×103sineachpart・Thisngure shows thatHR
decreases withincreaseinintervaltimes．

ure shows that HR becomes large at mean shear

The hemolysis ratios as afunction ofthe shear
exposuretimeinconstantshearratesareshownin

ratesof＞500s．1・Figure5CshowsHRasafuncT

Fig．6A．ThisngureshowsthatHRincreasesmark−edlyabovethecriticalexposuretimeateachshear
mumshearrateis坑xedatOs1andthefrequency rate and that HRis very small（＜0．005）even at
is O．5Hz．This figure shows that HRincreases l，000s▲lwithin900s，Datainconstantshearrates
markedly with the maximum shear rate of＞600
aresummarizedinFig．6Basarelationshipbetween
s1・Figure5DshowsHRasafunctionofthemin−Shearrate and shear exposure time，Where HRistion ofthe maximum shear rate，Where the miniT

imumshearrate，Wherethemaximumshearrateis

datumpolntat600s1showsHRattheconstant

O．01．This坑gure shows that HR depends on the
Shearrateandexposuretime．Throughthesetests，HRvariationWith4）arewithintherangeofstatis−

shearrateof600s1・ThisngureshowsthatHRticaldisperslOn，and no apparent moIPhologlCaldecreases when the minimum shear rate decreases

Change［e．g．，fragmentation（3）］isobservedwiththenxedat600srlandthen・equenCyisO．1Hz・The

below300sJl・Figure5EshowsHRasafunctionof
OptlCalmicroscopeinerythrocytesevenwhenHR
the difference between maximum and minimum＞0．1．

Shearrates，Wherethemeanshearrateiskeptat350s▼1andthefrequencyisO・1Hz．Thedatumpolntat

Os．1shows HRatthe constantshearrate of350

DISCUSSION

sl，andthedatumpolntat700s．1showsHRwhen There have been extensive controlled studies oferythrocytedestructioninflowsofvariouskinemat−
Os，1，reSpeCtively・ThisngureshowsthatHRbe− icsfbrover20years．Theirdevicesareaconcentric
themaximumandminimumshearratesare700and

COmeSlarge at the differences between the maxi−Cylinder（1），adouble−gapCOnCentriccylinder（4），amumandminimumshearratesof＞200srl：atmaX− COnCentriccylinderwithconeandpLateatthebot−

Arげ0′g（川∫，VoJ．〃，〃仇J，ノ9β9

且尺yr〃尺OCy7官β且∫7RUCコ70」V V∫．且打且A月月ArE

46ノHR二、0．01＼ ▲N一∈U・＼iこく．

U÷．ss

0Thjs study ＼X＼t △ヽ

■】111てdmS●Sute「a X△Belssヾnger HRく0・01246010510T，XlOisT，XlOヨs102103

10u

丁．s

FIG．6．A：Hemolysisratio（HR）asafunctionofexposuretime（T）inconstantshearrates．B：Relationshipbetweenshearrate（G）
andexposuretime（T），WhereherヮoJysisratioisO・01inconstantshearrates・C：ReJationshipbetweenshearstress（SS）andexposuretime（T），WherehemorysISratioisO．01inconstantshearratesLDatatakenfromthisstudyandfrompreviousstudies
OfNevaril（13），Leverett（14），WiJliams（15），Sutera（3），Beissinger（16．5）［

tom（5），aCOne−and−plate system（6），a SyStemOf Whered＜0．13cm（thedistancebetweenthecon−
twoparallelhorizontaldiscs（7），aCaPillarysystem
VeXandconcavecones），f＜0．5Hz（frequency），P（8），and ajetiqjection system（9）．The concavo−

COnVeX teStlng maChine，Whichis usedin the＝1g／cm3（densityofblood），andトL＞0．05dyns
cm▲2（viscosityof blood at240C）inthepresent

tests（showninFig5B−E）．BecauseWiscalculated
PreSent Study，isadevicetofbrmaunifbrmshearne］d，anditsbasicprlnCIPalisthesameasthecone− asasmallervaluethanunitybyEq．3［whichindi−and−platesystem．
CateS thatinertialforces can beignored（17）］，theThis concavo−COnVeX tyPe，however，has some flowbetweentheconvexandconcaveconesisesti−

advantagesoverthecone（withanobtuseapexan− matedtofbllow the rotarymotionofthe concavegle）andplatetype；remOValofair（10）andcollec−

COne．

tionofthebloodsamplefromtheconcaveconeis

In the previous study，the author reported that
Clotgrowthatforeign surfacesisconsiderablyin−

easy，andthesameshearratecanbeexactlyapplied

tothewholebloodsampleevenattherim（11）ofthehibitedat ashearrateof＞400sLl（2）．Figure7
Cjrcular cone（Fig．3）．Shear rates appljedin the Showstherelationshipbetweeninterna］radiusandpresentstudy（＜1，000s．1）arechosenintherange flowrateinacylindricalpipe，Whereshearrateson
Of shear rates ofbloodflowin the human cardio−

VaSCular system（12）．This range corresponds tolowershearstresses（＜102dyncmL2）thanthoseof

itswallare400sL−1inPoiseuilleflow・InthispIPe，
shearratesof＜400s．1areappliedtoerythrocytes

prevlOuS Studies（3，5，13−16），in which the higher

shearstresses（＞102dyncm−2）wereappliedwithin
ashorttime（＜103s）（Fig・6C）・Theexpoミuretimejn

Fig5A−Fischosensothatthehemo】ysISratiobe−
COmeSlargerthanO．1attheconstantshearrateof

l，000s−1（Fig．6A）．Theanglebetweentheconvex
andconcavecones（d））hasbeensetsothatthero−tatlngSPeedofthe concaveconemaynotexceed
350minLltoapplytheshearrate（10）．1ntherange
oftherotatlngSPeedof＜350minLl，thecentrifugal

effectisfairlyneutralizedbytheslopeofthecon−
CaVeCOneSOthaterythrocytesdonotaggregatetotherim ofthe circular cone．

Toapplyperiodica11yfluctuatlngShearrates，therotatlngSPeedoftheconcaveconeischangedsinu−
SOidallyinthepresentstudy，Asausefu1dimension−
less parameter，the Womersley number（W）hasbeen proposed to estimate the ratio ofinertialto
Viscousfbrcesinperiodica11yfluctuatingflows：
W＝（d／2）＞2¶仲山（3）246Fl…−rate，ノ．mjn−1

FIG．7．Relationshipbetweeninternalradiusandf10Wratein
acyIindricalpIPe，Whereshearrateonitswallis400s1．小甘（ル小〃L†．l■り／、／J‥＼■l−．∫．／叫リ∫．βA∫〃甜OrO

4∂2

becauseoftheiraggregationtotheaxisofthepIPe．
Inthepresentstudy，theresultsshowthaterythro−
Cytedestructionisconsiderablyinhibitedfor7．2×

103satashearrateof＜400s」・ThusFig・7sug−

gests an approprlate dimension ofartincialbloodflow path to inhibit clot growth and mechanicalerythrocyte destruction simultaneously，e．g．，the（where the calculated pressure dropis4．5mmHgm1）．
Theprocess ofmechanicalerythrocytedestruc−tionin blood bulkflowhas beenconsideredasfol−

5throughwhich6eminJlbloodflows，isO・68cm

1．SもLX．U

appropriateinternalradius ofthe cylindricalplpe，lows（Fig．8）．Whenashearrate（Fig．8a）isapplied
toblood，erythrocytesinbloodstarttorotate（Fig．
8b）．Erythrocytesaredeformedfromabiconcaveto

anellipsoidalshape，andtheirlines ofapsides tilt

0Paralleltothedirectionofflow（Fig．8c）（18）．Their

1

2

3

GxT，XlO6

membranesarethenrepeatedlystretchedinatank

FIG．9．ReLationshipbetweenshearrate（G）and productof
tread−1ikemotion（Fig．8d）（19，20）．Whenthemem− Shearrate（G）andexposuretime（T），Wherehemolysisratiois

O．01in constantshear rates．
branes are destroyed by fatigue through that mo−tion，hemoglobins are released from erythrocytes（Fig．8e）．Thedestructionofmaterialsbyfatiguein

generalhasbeenexperimentallydeterminedbythe

temoftwoparallelhorizontaldiscs（7）andthecap−
illarysystem（8）aresuitable．Inthepresentstudy，

StreSS amPlitude（S）and the numberofthe stress
CyCles（N）．In erythrocyte destructionin blood

Only polymethylmethacrylate has been used be−

now，Sis governed by the extent oferythrocyte
deformation，Whichisrelatedtotheshearrate（G）；

N is governed by the rotating speed of the tank

CauSe Ofits transparency and machinability．An−
other method to evaluate surfaceinteractionsis to

givevariationsinsurface−tO−VOlumeratio（16）．The
Valuesofhemolysisratioindependentof￠（andsur−
face−tO−VOlumeratio）suggestthattheeffectofsur−

tread−1ike membrane motion and by the accumu−
1ated numberofrotations，Where thefbrmeris re− faceinteractionontheresultsofthepresentstudy
1atedtotheshearrate（G）andthelatterisrelatedto maybeminor．Themeasuredorder（＜4匹m）ofsur−

the exposure time（T）．Figure9（calculated h−Om

face−rOughnessoftheconessuggeststhatitseffectFig．6b）showstherelationshipbetweenGandGx on the blood flow adjacent to their surfaces may
T，WherehemolysISratioisO．Ol．Thisnguresuggestsalsobeminor（11）．

thaterythrocytemembraneisdestroyedinfatigue
as the above discussion．
Theprocess ofmechanicalerythrocyte destruC−
tionhasalsobeenconsideredinsurfaceinteractions（21），Whichinclude alteration or denaturation oferythrocyte membrane（by collision oradsorption
to the solid surface）and destruction ofthe mem−braneduringitsdebrmationintheshearneldaqja−
Cent tO the solid surface．One of the methods toevaluatesurfaceinteractionsistoglVeVariationsin

In the present study，the results show that thehemolysISratioincreasesmarkedlywhentheshear
ratefluctuateswiththemaximumof＞500s￣landdecreaseswhentheexposuretimeoflarger（＞500sl）shearratesisinterspersedwithsma11er（＜300sl）shearrates．Theseresultsindicatethattheef−

fectivepartoftheexposuretimeisgovernedbythethresholdoftheshearrateandbytheviscoelastlClty
Oftheerythrocytemembrane（22）．

materialsofsolidsurface．Forthispurpose，thesys−

Acknowledgment：The author wishes to express his
gratitude fbrtheguidance and encouragementreceived

7、仔⇒ク⇒ぴ⇒辞n・Om Prof．TadashiSasada．The author also wishes to（a）（b）（c）

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FIG．8．TheprocessofmechanicaIerythrocytedestructioninbIood bulkf10W．Seetext fordetai［s．

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