Parametric design, fabrication and validation of one-way polymeric valves for artificial sphincters

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ContentslistsavailableatScienceDirect

Sensors

and

Actuators

A:

Physical

jo u r n al h om ep a g e :w w w . e l s e v i e r . c o m / l o c a t e / s n a

Parametric

design,

fabrication

and

validation

of

one-way

polymeric

valves

for

artiﬁcial

sphincters

Tommaso

Mazzocchi

a,∗

_,

_Leonardo

_Ricotti

a

_,

_Novello

_Pinzi

b

_,

_Arianna

_Menciassi

a a_The_BioRobotics_Institute,_Scuola_Superiore_Sant’Anna,_Viale_R._Piaggio,_34,_56025,_Pontedera,_PI,_Italy

b_Dipartimento_di_Urologia,_Università_degli_Studi_di_Siena,_Via_Banchi_di_Sotto,_55,₅₃₁₀₀_Siena,_SI,_Italy

a

r

t

i

c

l

e

i

n

f

o

Articlehistory: Received5January2015

Receivedinrevisedform22June2015 Accepted7July2015

Availableonline15July2015

a

b

s

t

r

a

c

t

Thedesignofartiﬁcialsphinctersrequiresanaccuratedimensioningofdedicatedvalves,normallymade

ofpolymericmaterials.Thiseffortisalsointerestingfordevelopingﬂuidandpressureregulatingsolutions

relatedtootherbiomedicalandnon-biomedicalﬁelds.Inthisarticlewefocusedontheparametricdesign

ofpolymericvalves,bytakinginspirationfromcommerciallyexploitedsolutionsusedinthefoodindustry

andperformingappropriatescalinginordertomakethemsuitableforartiﬁcialorgansandcomponents.

Inaddition,differentmaterialswithdiversemechanicalpropertieswereconsidered,focusingona

low-costfabricationapproach.Finiteelementmodelanalyseswereconductedtosimulatethebehaviorof

differentvalveproﬁlesandtopredictthevalveopeningpressure.Simulationresultswerevalidatedby

comparingthemwithexperimentalresults,obtainedbyfabricatingandtestingdifferentvalvetypes.This

polymericvalveparametricanalysismaybeexploitedforthedesignofartiﬁcialsphincters,havingthe

potentialtotackleurinaryincontinence,adiseasethataffectsabout350millionpeopleworldwide.

1. Introduction

Approximately350millionindividualsworldwideexperienced

urinaryincontinence (UI) in2008 andthis number is expected

toincrease upto423millionby 2018[1].UI isa disorder that

produces an involuntary urine loss caused by an uncontrolled

overactivebladderorapelviperinealmuscledeﬁcitthatcanarise

as a surgery complication in male subjects (e.g. after prostate

surgery), while in female subjects it may occur after

child-birthorafterurogenitalorganssurgery.Inhospitals,UIdiseases

arenormallymanagedbyusingabsorbent materialsorurethral

cathetersprovided witha bag (tiedtothepatient’s leg).

Extra-luminal sphincters (ES) are devices able to control ﬂuid ﬂow

throughan elasticduct, by modulating thecompressionof the

elastic duct wall itself. They need to be implanted via.

surgi-cal procedures,so theyare rather invasive. The mostcommon

ESthat are commercially available totackle UI are the ProAct

system(Uromedica,MN,USA)andtheAMS800(American

Med-icalSystems, Minnetonka, MN, USA). These solutions require a

surgicalprocedurefortheirinstallationand theyareonly

avail-ableformales[2,3].ProActandAMS800areexpensiveandcan

lead to complications such as erosion, infection and

mechani-∗ Correspondingauthor.Fax:+3950883101. E-mailaddress:t.mazzocchi@sssup.it(T.Mazzocchi).

cal failure. Therefore, periodic revisions(rather complicated to

be performed) are mandatory. In addition, if replacement is

needed, a second invasive surgicalprocedure needstobe

per-formed.

Ontheotherhand,intraluminalsphincters(IS)donotrequire

asurgeryproceduretobeimplanted:theyareusuallyinstalledby

usingtheductoriﬁceandbroughttothesiteofinterestthrough

apushingcatheter.Atpresent,few commercialISareavailable,

suchastheFemSoft (RochesterMedical Corporation,MN,USA)

ortheInFlowdevice(Vesiﬂo,Inc,WA,USA)[4].ISarenot

com-pletelyinternaldevices:asmallportionofthesystemisinevitably

visible, thus raising psychological discomfort in certain

situa-tions.

Recently,advancedandrathercomplexmechatronicsolutions

havebeenproposedtotackleUI.Lamraouietal.reportedthedesign,

developmentand in vivotesting ongoats of a 60cm3 _artiﬁcial

sphincter(AS)prototypecomposedof standardmechanical and

electricalcomponents[5].Morerecently,aretro-compatibledevice

wasproposedbyHachedandcolleagues.Thesystemwasbased

onahydraulicmoduleandacontrolunitandshowedgood

efﬁ-cacyinbothbenchtestsandexvivotests[6].Thesameauthors

alsorecentlydevelopedawirelesslycontrolledandadaptiveAS,

capableofpostoperativeocclusivecuffpressuremodiﬁcation[7].

Alltheabove-mentionedmechatronicsolutionsareratherinvasive

andtheirlong-termsafety andefﬁcacystill havetobe

demon-strated.

http://dx.doi.org/10.1016/j.sna.2015.07.005

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Fig.1.Commercialvalveusedinmanywaterbottles.Thewholestructureandasection,arereported(A),togetherwithitsparameterization(B).Thevalveaxisandtheload distributionareshowninCandD,respectively.

Theauthorsalsorecentlyhighlightedapossiblenewdesignfor

IS,basedonmagneticallyresponsivemechanismsabletoengagea

unidirectionalvalveandthusmodulateitsstiffness[8].Atpresent,

aUIsolutionsuitableforbothsexesfeaturinghighstabilityandlow

invasiveness(withoutalteringthebodyscheme)isnotavailable.

Passiveunidirectionalpolymericvalvesareakeycomponentof

devicesdesignedtotackleUIdiseases.Theyareusefultocontrol

theliquidpressurebetweentwocompartments,thusensuringa

unidirectionalﬂowwhenacertainpressurethresholdisovercome.

Biocompatiblepolymersareobviouslyneededandindependence

fromenergysourceswouldreducetheintrinsichazardsrelatedto

theuseofsuchsystems.

The achievement of an artiﬁcial IS suitable for both sexes

requires an accurate dimensioning of ad hoc one-way passive

valves.Tothispurpose,theanalysisofavailablesolutionsforother

biomedicalor non-biomedicalﬁelds canprovidesome

interest-inghints.Manyliteraturestudieshavefocusedonthecorrelation

betweengeometryandvalveperformance,highlightingthe

impor-tanceofnumericalsimulationssuchasnon-linearﬁniteelement

models(FEM)inordertooptimizethedesignand thesizing of

valveproﬁles.Inthebiomedicalﬁeld,thisapproachhasbeen

exten-sivelyusedtodesign heart valves.Differentvalve proﬁleshave

beenreviewed by Mohammadiand Mequanint [9],in terms of

bothmodellinganddesignstrategies.Recently,Burriesciand

col-leaguesfocused ona noveldesign strategy for polymericheart

valves(supportedbynumericalsimulations),inordertoincrease

valveperformancesandreducestresslevels[10].Another

inter-estingstudywascarriedoutbyLabrosseetal.,whichdevelopeda

geometricmodelofanaortictrileaﬂetvalve,forthepurposeof

eval-uatinghowmuchthedimensionsoftheaorticvalvecomponents

couldbevaried,whilestillmaintainingpropertargetperformances

[11]. More recent studiesfocused onapplyingFEM analysesto

properlydesignleaﬂetmaterialsandtopredictthehydrodynamic

behaviorofnanocomposite-basedpolymericaorticvalves[12,13].

However,theaforementionedstudiescannotbeeasilygeneralized

andappliedtothedesignofaurinarysystemvalve.Thisismainly

duetotherathercomplicateddesignandmanufacturingprocesses,

neededtobuildheartvalveswhichrequireseveralstepsinorder

tocombineametallicstentwiththepolymericleaﬂets.

A differentapproach mustbe adopted when facingscalable

manufacturinginthepresenceofhighpressurerangesandsmall

ﬂowrates(␮l/min).Althoughtheseconditionsarenottypicalof

theurinarysystem,thisapproachhasbeenwidelyadoptedforthe

designofmicro-valvestobeusedinmicroﬂuidicsystems.The

geo-metricalparametersofthevalve,includingshape,ﬂuidchannel

widthandmembranethicknessareusuallyexamined.Snakenborg

et al. designed a polydimethylsiloxane (PDMS) membrane

pro-videdwithanincisioninordertofabricateacheckvalveableto

controltheﬂowrate[14].Mohanetal.reportedinteresting

consid-erationsconcerningthedesignandtheapplicationofelastomeric

microvalves,focusingonactuationpressureminimization,reliable

operationandconvenient integrationinto complexmicroﬂuidic

devices[15].Jahanshahietal.focusedonthedesignofamicro-valve

characterizedbyahighpressurerangeandarelativelyhigh

seal-ingcapability(noﬂowupto0.6MPareversepressure)[16].Hilbert

andcolleaguesintroducedaninnovativemicro-valve

manufactur-ingtechniquebyusingPDMSloadedwithneodymiumparticles,to

adjusttheswitchingpointofeachsinglevalve[17].

Hickersonand colleaguesdeveloped a valve design strategy

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tech-niquesthatallowthedevelopmentoflow-costdisposablesystems.

Thereportedresultsmaybeexploitedformanyapplicationsthat

requirespeciﬁcvalveperformance.However,theyarenotusableas

componentsforartiﬁcialurinarysphincters,duetothehigh

pres-surerange(12kPa–120kPa)andtothesmallﬂowrates[18].

Uohashiand colleaguestookintoaccount differentone-way

valve proﬁles, achievable by exploiting standard molding

pro-cesses.Theyensuredhighﬂowrates(ml/min).Interestingresults,

concerning the inﬂuence of material stiffness on valve

perfor-mance,werereported.However,anaccuraterelationshipbetween

valve geometrical parameters and performance was not

high-lighted[19].

Inthisarticle,wediscusstheparametricdesign,fabricationand

validationofaone-waypolymericvalveascomponentofAS,

tak-ingasamodelacommonvalveproﬁleavailableinwaterbottles.

Low-costfabricationtechniquesandabiocompatibleand

stiffness-tunablematerialwereconsideredforvalvedesignandfabrication.

Simulationresultsevidencedthemostsuitableproﬁlesin

corre-spondencetocertaindesiredopeningpressures.Forapplicationin

theurinarysystem,hermeticclosureshouldbeassured:sudden

coughsandinvoluntaryabdominalmusclecontractionscan

gener-atepressuresupto12kPa.However,thisphysiologicalparameter

dependsonthepatient’sanatomicalfeatures,thereforeatunable

openingpressure(OP)isdesirable[20–22].Ashighlightedbelow,

thiscanbeachievedbymakingsmallchangestothevalveproﬁle

geometryorbyslightlychangingmaterialstiffness.

2. Experimental

2.1. Valveproﬁleanditsparameterization

Toselectthevalveproﬁle,wetookinspirationfromthefood

industry,especiallyfromthevalvesintegratedinmanywater

bot-tles.Normally,theyareusedtoguaranteehermeticsealingupto

acertainpressure,afeaturethatmakesiteasiertodrinkliquids

duringsportactivities,forexample.Weconsideredacommercial

valvethathadavaultshapeandasurfacefeaturingasix-pointed

stardiecut.Thenotchesallowthevalvetoopenwhenthepressure

appliedonthetopsurfaceisaboveacertainthreshold.Weanalyzed

thevalveproﬁleandextracted9parametersabletodescribeit,as

showninFig.1.

The nine parameters that allow reproduction of the

com-mercial valve were: P1c=3.7mm, P2c=50◦, P3c=0.20mm,

P4c=83◦, P5c=1.28mm, P6c=0.37mm, P7c=97◦, P8c=1.00mm

andP9c=1.70mm(whereC=commercial).

We aimedat fabricatingone-way valveswitha speciﬁcOP,

bytaking into accountthe fabricationconstraints. Theanalysis

ofthenineparametersledtoaredundantproblem.However,all

parameterswerevaried,inordertohighlighthowtheirdifferent

valuesinﬂuencedoverallvalveperformance.Foreachparameter,

ﬁveequidistantvalueswereidentiﬁed(Table1).Moreover,they

werecombinedwithsixdifferenttypesofmaterialstiffness.

Theﬁrstanalysisaimedat assessinghowvalve performance

changedwhenapplyinganisotropicscaling(increasingor

decreas-ingvalvesizebyascalefactorthatwasthesameinalldirections).

Tothisaim,P1wasconsideredbecauseitisrelatedtotheradiusof

thevaultvalve.Avalveradiussuitableforurologicalapplications

mustbesmallerthan6mm[23].Thescalingfactors(SF)analyzed

inthisworkwere0.35,0.67,1.00,1.32and1.64.Theycorresponded

toP1valuesof1.3,2.5,3.7,4.9and6.1mm,respectively.Differently

scaledvalvesmayﬁndapplicationsindifferentﬁelds.

Anotherimportantaspectoftheanalysisconcernedhowvalve

performancechangedinfunctionoftheothereightparameters,

onceacertainvalvesizewasselected.Thisallowedustoidentify

themostrelevantparametersforvalveperformance.

2.2. FiniteElementModel(FEM)simulations

Matlab®_R2013a_(MathWorks)_and_Abaqus_6.13_(Dassault

Sys-temes)wereusedtomanagedataandtoperformFEMsimulations,

respectively.

Matlab®_environment_was_used_to_manage_the_different

param-eters. Once the desired valve proﬁle was generated, Matlab®

generatedanappropriateﬁle,readablebyAbaqus,whichloaded

thedesiredvalvegeometry,fordetectingtheOPoftherespective

proﬁle.Thisallowedustohandlealargenumberofsimulationsin

asimplemanner.ThevalvemodelwasimplementedusingPython

language.

WhenAbaqushadprocessedthesimulation,itgeneratedaﬁle

inwhichalltheresultswerereported.Analgorithmwas

devel-opedtocompareeachsimulationandtoidentifythevalveOP.The

algorithmtrackedalltheextremepoints(A8andA7inFig.1)for

eachvalvestrip:whenthedistancebetweensuchextremepoints

wasdoublethanthevalvethickness(P3),thevalvewasconsidered

open.Oncethesimulationwascompleted,theextremepointsof

thevalvestripreachedduringthesimulationwerestoredinaﬁle,

fromwhichMatlab®_was_able_to_indentify_the_valve_OP.

AftercreatingthevalveintheAbaqusenvironment,

experimen-taldata(stress-straincurves)ofthematerialusedwereimportedby

exploitingtheHyperplasticmodulesupportedbytheprogram.In

theAbaqusStepmodule,anexplicitdynamicbehaviorwasdeﬁned,

byimposingamassscalingequalto100.Appropriatetieconstraints

betweenthedescribedelementswereimplemented,thus

repro-ducingthecommercialvalveofFig.1A.

Thevalvemodelwasprovidedwithaﬁxedconstraintas

bound-arycondition,appliedonthesurfaceobtainedfromthesegment

(A5A6)revolutionaroundthevalve(A7A8)axis.Thetopsurfaceof

thevalvewasloadedwithapressure(normaltothevalvesurface)

whichlinearlyincreased,untilreachingthecrackingpressure.

Thevalve design wascomposedofthree elements. Theﬁrst

onerepresentedthevalvebasement,obtainedfromthe

revolu-tion(360◦)aroundthevalveaxisoftheareadelimitedbysegments

A6A5,A5A4,A4A2,A2A1,A1A3andA3A6(Fig.1B).Thesecondvalve

elementwasobtainedfromthecompleterevolution(360◦)around

thevalveaxisoftheareadelimitedbysectionsA1A2,A2A9,A9A10

andA10A11.Thethirdelementreferredtothevalvestripsobtained

whenthediecutwasappliedonthetopsurfaceofthepolymeric

valve.Asinglestripwasobtainedfromarevolutionof60◦around

thevalveaxisoftheareadelimitedbysectionsA10A8,A8A7,A7A11

andA11A10.

Theﬁrstelement(valvebasement)wasmeshedwith2160cells,

thesecond(valvehead)wasmeshedwith1224cells.Thethird

ele-ment(valvestrip)wasmeshedwith81cells.AstructuredHexmesh

wasusedforthethreebodies.Todemonstratethatthemeshwas

suitableforthetargetapplication,wecarriedoutmeshreﬁnement

tests(Supplementarymaterials,TableS1). Thementionedmesh

sizevaluewasidentiﬁedasagoodcompromisebetweenadherence

ofthepredictedOPvaluestotherealonesandthetimeneededto

completeeachsimulation.Oncethemeshgridofthevalvemodel

wasdeﬁned,a setofnodeswasgeneratedinordertostorethe

segment(A8A7)displacementvaluesforeachvalvestrip,during

theentiresimulation.Therefore,12meshnodeswereselectedto

detectvalveopening.VonMisesstresseswerealsorecordedfor

eachsimulation.

2.3. Polymersynthesisandmechanicaltesting

The material selected for valve fabrication was PDMS

(Syl-gard184,DowCorning).Thismaterialisparticularlysuitablefor

biomedicalapplications,duetoitshighbiocompatibility,its

tun-ablemechanical properties, and itsgood thermal and chemical

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oxy-Table1

ParametervaluesconsideredduringFEMsimulations.

genplasma,formodifyingsurfacepropertiesandmechanicaland chemicalperformances[24],[25].

PDMSstiffnesscanbemodulatedbyvaryingtheratiobetween

the monomer and its curing agent. In this work, 6 different

monomer/curingagentratioswereanalyzed:5:1,10:1,20:1,30:1,

40:1and50:1(w/w).

SamplemechanicalpropertieswereevaluatedwithanINSTRON

(5)

performingtractiontests.Sampleswerecutinto20×5×2mm3

slicesandallocatedbetweentwoaluminiumclamps.Allsamples

werepulled atthe constantspeed of 5mm/min, untilreaching

samplefailure.Datawererecordedatafrequencyof100Hz,the

stresswascalculatedastheloaddividedbythecross-sectionarea

oftensilespecimens,whilethestrainwascalculatedastheratio

betweentheextensionandtheinitiallengthoftensilespecimens.

Thetensilemodulusforeachtestedsamplewascalculated

start-ingfromthestress/straincurve,accordingtoastandardprocedure

[26].Mechanicaltestswererepeatedonthreedifferentsamples,

foreachsampletype.

2.4. Valvefabrication

Inorder tovalidate thesimulation results, polymericvalves

werefabricatedbyexploitingdedicatedmolds.Themoldswere

composedoftwoparts,providedwiththroughholes,neededfor

aligningthepartsandclosingthemold(usingM3screwsandnuts).

Toachievethediecutonthevalvesurface,aproperframe(designed

toconstrainthepolymericvalve)andacustombladewereused.

Bothcuttingframeandmoldswerefabricatedbyusinga3D

printer(HD3000,ProJet).Thecustombladewasobtainedby

mod-ifyingthecuttingedgeofanoff-the-shelfsurgicalblade(CHIMO,

size22).

Thevalvefabricationprocesswasbasedonthefollowingsteps:

(1)PDMSpreparation:monomerandcuringagentweremixedwith

thedesiredratio,thenthemixturewasdegassedfor20minina

vacuumchamber.(2)Moldsurfacetreatment:a thinteﬂonﬁlm

(LOCTITE8192) wasdeposited byspraying it onthe mold

sur-face,tofacilitatesubsequentPDMSremoval fromthemold.(3)

PDMScasting:oncethemixturewaswelldegassed,itwascasted

intotheteﬂon-coatedmold.(4)Polymerization:afterPDMS

cast-ing,themoldwasclosedandthermallytreatedat90◦Cfor3h,to

allowfullvalvepolymerization.(5)Valveextractionandcutting:

themoldwasopenedand thepolymericvalveremoved.Itwas

thensubjectedtodiecuttingbythededicatedframeandcustom

blade.

2.5. Valvetesting

Totestthepolymericvalvefunctionality,adedicated

experi-mentalset-upwasdeveloped(Fig.2).

Theset-up consistedof a motorized pistonprovided with a

ﬁnecontrolofboth horizontalstrokeand speed.Thehorizontal

strokekeptconstanttheheightofthewatercolumndownstream

of thevalve during the tests,which wasneeded to detectthe

valveOP.Speedcontrolwascompiledintoadevelopmentboard

(STM32F407,ST)exploitingSimulink(MathWorks)environment

withasamplingfrequencyof1kHz.

TomonitortheOP,thedevelopmentboardwasconnectedtoa

pressuresensor(HCX001D6V,purchasedfromSensorTechnics)for

wetenvironments,capableofmeasuringpressuresupto100kPa.

Themechanicalparts ofthetesting set-upincludeda Screw

Ball(BSSC1510-300-SC10,diameter15mm,stride:10mm,stroke:

300mm)andappropriatetoolsforsupportingit(BSW12,BUN12,

BNFB1505C-30 produced by MISUMI company). These

com-ponents were assembled on a derlin-polycarbonate frame. A

DC-micromotor(Series2342012CR,Faulhaber) providedwitha

PlanetaryGearheadtoincreasethemotor torquewitha

reduc-tionratioof43:1(Series30/1S3,Faulhaber),ahighperformance,

low-cost,three-channelopticalincrementalencoder(HEDS-5540,

AvagoTechnologies)andafullH-Bridge(L298,ST)weremounted

onthesystem.

Thetestingset-upallowedasyringe(5ml)anditsplunger,

con-nectedwiththepistonpusher,tobemounted.Athree-wayT-joint

Table2

showsthedifferentPDMSmonomer/curingagentratiosandthecorresponding Young’smoduli,obtainedbywayoflinearﬁttingofthestress–straincurvesinthe initial(linear)region.

Monomer/curingagentratio Young’smodulus[MPa]

5:1 4.95±0.33 10:1 3.55±0.35 20:1 1.26±0.16 30:1 0.41±0.06 40:1 0.14±0.02 50:1 0.08±0.01

connectedthevalveseat,thepressuresensorandthesyringe out-put.Thevalveopeningdirectionwashorizontal,toavoidgravity effects.

Six polymeric valve types (four valves for each type) were fabricatedby using three different molds (thus,three different geometries)andtwodifferentmaterialtypes(10:1and20:1PDMS). Theﬁrstvalvegeometrytobefabricatedfeatured aP1valueof 3.7mmandaP3valueof0.2mm.Thesecondvalvegeometry fea-turedaP1valueof2.5mmandaP3valueof0.25mm.Thethird valvegeometryfeaturedaP1valueof2.5mmandaP3valueof 0.3mm. The otherparameters, common for thedifferent valve geometries,were: P2=50◦, P4=83◦, P5=0.86mm, P6=0.25mm, P7=97◦,P8=0.67mmandP9=0.13mm.

Oncethe twenty-fourpolymericvalveshad been fabricated, theyweretestedinordertomeasuretheirOP(detectedusingthe dedicatedsensortomeasurepressuredrop).Thesyringewasﬁlled withairordistilledwater(d-H2O)andthepistonspeedwassetat 5mm/s.Eachvalvewastestedthreetimes,andsixcyclesof open-ing/closurewereperformed,withineachtest.Thus,eighteenOP valueswererecordedforeachtestedvalve.

Anadditionaltestwascarriedout,inordertoevaluatethe tight-nessofthefabricatedvalves.Duringthistest,thepistonspeedwas setat0.25mm/sanditwasstoppedbeforereachingthevalveOP. Differentconstantpressurevalueswerekeptfor10s.Thisallowed thevalvepressurelosstobemeasuredwhenrelativelyhigh pres-sureswereappliedandkeptconstant.

3. Resultsanddiscussion

3.1. PDMSmechanicalproperties

Thestress–straincurvesexperimentallyobtainedforthePDMS sampleswithdifferentmechanicalpropertiesasshowninFig.3.

ThesecurveswereimportedintheAbaqusenvironment,inorder

toproperlysimulatematerialmechanicalbehavior.

Table2Young’smoduliofthePDMSsamplestested,fordifferent

monomer/curingagentratios.Threesamplesweretested,foreach

sampletype.

3.2. Simulationresults

Fig.4showssomeframescapturedfromvalveFEMsimulations,

inwhichprogressivevalvevaultcompressionandopeningphases

arereported.Adynamicsimulationofvalveopeninganda

compar-isonbetweentherealandthesimulatedvalveareshowninVideo

S1(seeSupplementarymaterials).

Theanalysisofthe9parametersgenerated9datasets.Ineach

dataset,the5parametervaluesofTable1werecombinedwith

6materialstiffnessvalues,thusgenerating30simulationresults.

Asimpleapproachthatimmediatelyhighlightsmacroscopic

dif-ferencesbetweentheobtaineddatasets isdesirable. We ﬁtthe

simulationresultsandcomparedthecoefﬁcientsobtainedfromthe

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Fig.2.Valvetestingset-upanditscomponents.

Fig.3.Representativestress-straincurvesofPDMSsamplesshowingdifferentstiffness.

Fig.4.FEMsimulationframes(toppictures:topview,bottompictures:bottomview),showingvalvebehaviorwhenanincreasingpressurewasappliedonthetopvalve surface.DifferentcolorsstandfordifferentvonMisesstressvalues.

thevalveperformance.Themathematicalexpressionusedfordata

ﬁttingwasanexponentialfunction:

P(x,y)=a×xb×yc (1)

wherexwasthematerialstiffnessandywastheparametertobe

evaluated(fromP1toP9).Thecoefﬁcientsa,bandcwereobtained

byusingcftool(Matlabtoolbox),andﬁttingtheopeningpressure

P(x,y),obtainedfromFEMsimulations,asafunctionofthe

mate-rialstiffnessandtheparameteranalyzed.Theresultsareshownin

Table3.

Byfocusingontheobtainedcoefﬁcientvalues,especiallywith

regardtotheexponentialcoefﬁcientc,animmediatecomparison

betweenparameters(P1andP9)ispossible.Thevalvethickness

(P3)isthemostsensitiveparameter,beingcharacterizedbya c

valueof1.6920.AnotherparticularlysensitiveparameterisP4(c

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Fig.5.Valveperformances(intermsofopeningpressure)incorrespondencetodifferentmaterialstiffnessanddifferentP1values.Alltheotherparameterswerethoseofthe commercialvalve.Angularparameters(P2,P4andP7)werekeptconstant(Pi=Pic),whilelength-relatedparameters(P3,P5,P6,P8andP9)wereproperlyscaledaccording tothehomothetictransformation(Pi=Pic×SF).

Fig.6.Valveperformances(intermsofopeningpressure)incorrespondencetodifferentmaterialstiffnessanddifferentP3values.Alltheotherparameterswerethoseofthe commercialvalve,properlyscaledaccordingtothehomothetictransformationinordertohaveaP1equalto2.5mm(P2=50◦,P4=83◦,P5=0.86mm,P6=0.25mm,P7=97◦, P8=0.67mmandP9=0.13mm).

previouslymentioned,thedesignofapolymericvalveshowinga

speciﬁcOPisaredundanttask.Therefore,itcanbeusefultoselect

adesignprotocolaimingatreducingtheoverallsimulationeffort.

Byvaryingvalvethicknessandmaterialstiffness,alargerangeof

OPvaluesisachievable.Anefﬁcientdesignprotocolmayinclude:

(1)thedeﬁnitionofthevalvesizeandtheidentiﬁcationofa

suit-ablescalingfactor;(2)thetuningofvalvethicknessand/ormaterial

stiffness.Alltheotherparameters(P2,P5,P6,P7,P8andP9)playa

minorrole,ashighlightedbythesmallcoefﬁcientvaluesreported

inTable3.

Fig.5showsthesimulationresultsobtainedbyapplyinga

homo-thetictransformation(i.e.byvaryingP1).Fig.6showsthevalve

performanceswhenvalvethickness(P3)varied.

Asmentioned,theotherparametersarenotcrucialfor

deter-miningvalvebehaviour.Inanycase,thecorrespondentsimulation

resultsarereportedinFig.7.

Table3

Coefﬁcientsa,bandcderivingfromtheﬁttingofFEMdata,byusingEq.(1).

Parameteranalyzed Coefﬁcientvaluesderivedfromdataﬁtting R2_value

a b c P1 0.0052 0.6956 0.0517 0.9858 P2 0.0055 0.7273 0.0114 0.9898 P3 0.1363 0.8298 1.6920 0.9961 P4 0.0009 0.6991 0.4127 0.9878 P5 0.00786 0.7716 −0.1892 0.9926 P6 0.0050 0.7319 −0.0183 0.9887 P7 0.0043 0.7481 0.0471 0.9942 P8 0.0057 0.7274 0.0057 0.9890 P9 0.0054 0.7039 −0.0052 0.9871

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Fig.7. Valveperformances(intermsofopeningpressure)incorrespondencetodifferentmaterialstiffnessanddifferentparametervalues.Whenaparameterwasvaried, alltheotherangularparameterswerekeptconstantandequaltothoseofthecommercialvalve(Pi=Pic),whilelength-relatedparameterswerekeptequaltothoseofthe

commercialvalve,properlyscaledaccordingtothehomothetictransformationthatallowedP1=2.5mm(Pi=Pic×0.67).

Fig.8.(1)Closedmold,castedwithPDMSandthermallytreated;(2)moldopening;(3)valveextraction;(4)frameusedtopunchthetopsurfaceofthevalve;(5)valve positioningintotheframeusedfordiecutting;(6)bladeinsertionintotheframe;(7–9)valveprototypeandinsertionintoavalveseat,toconstrainthepolymericvalve withinthetestingset-up.

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Fig.9.OPvaluesexperimentallyobtainedfromthetestingoffour10:1valvesandfour20:1valvesforeachgeometryproﬁle(dataareexpressedasmeanvaluesandstandard deviations)andcomparisonwithFEMpredictions.Themeanabsoluteerror(MEA)valuesarereportedforeachsampletype.

3.3. Fabricationandvalidation

Fig.8showsapolymericvalveobtainedbyusingthededicated

moldandcuttingframe.

Thevalveproﬁlesselectedtovalidatethesimulationshadthe

followingparametersincommon:P2=50◦,P4=83◦,P5=0.86mm,

P6=0.25mm, P7=97◦,P8=0.67mm and P9=0.13mm. The ﬁrst

testedvalvegeometryfeaturedP1=3.7mmandP3=0.2mm.The

secondtestedvalvegeometryfeaturedP1=2.5mm(suitablefor

urinarysystems)andP3=0.25mm.Thethirdtestedvalvegeometry

featuredP1=2.5mmandP3=0.3mm.

Foreachvalvegeometry,fourPDMSvalvesmadeof10:1PDMS

andfourvalvesmadeof20:1PDMSwerefabricatedandtestedby

usingtheset-upofFig.2.

ThetargetOPscanbeextrapolatedfromEq.(1).FEM

simula-tionspredictedthattheﬁrstvalvegeometryshouldhaveanOPof

13.6kPaifmadeof10:1PDMSandanOPof6.6kPaifmadeof20:1

PDMS.ThesecondvalvegeometryshouldhaveanOPof37.4kPaif

Fig.10.(A)Pressureproﬁlesovertime(sixopeningcycles)fora10:1polymericvalve(P1=2.5mm,P3=0.30mm)testedwithad-H2Oﬂowproducingacontinuously

increasingpressure.(B)Pressureproﬁleovertimeforthesamevalve,obtainedbyraisingthepressureuntilreachingthevalveOP.Differentconstantpressurevalueswere keptfor10s.Thesetestsallowedustoevaluatevalveleakage.

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madeof10:1PDMSandanOPof15.7kPaifmadeof20:1PDMS.

ThethirdvalvegeometryshouldhaveanOPof50.9kPaifmadeof

10:1PDMSandanOPof21.4kPaifmadeof20:1PDMS.

Inagreementwiththeconditionssetinthesimulations,the

fab-ricatedvalvesweresolicitedbyahomogeneouspressurenormalto

thevalvesurface.Thiswasachievedbyloadingthemwithaliquid

ﬂow.Thepistonadvancedwithaconstantspeedof5mm/sandthe

pressuredetectedbythepressuresensorincreaseduntilthe

open-ingpressurewasreached.Afterwards,thepressureimmediately

fell.Theactualperformancesofthefabricatedvalvesarereported

inFig.9.

Theresultsobtaineddemonstratethattheperformancesofthe

fabricatedunidirectionalvalves,intermsofOP,areingood

agree-mentwiththepredictionsderivedfromFEMsimulations,witha

maximumerrorof23%.ThisallowsustouseEq.(1)asanefﬁcient

toolforthedesignofunidirectionalvalvesfordifferentapplications,

byplayingonthegeometricandmechanicalfeatures.Concerning

thedesignofanAScapableoftacklingUIdiseases,thesecondvalve

geometrytested(P1=2.5mmandP3=0.25mm)anda20:1PDMS

monomer/curingagentratioseemparticularlysuitable.

Fig.10Ashowspressureloading/unloadingcyclesperformedon

avalveprototype.Fig.10Bdemonstratesthatthevalveshowsa

goodtightness:thevalvewasloadedwithrelativelyhigh

pres-surevalues,keptconstantonthevalvefor10s,withsmallpressure

losses.ForpressurevaluesuptoabouthalfofthevalveOP,almost

no losses were detected(max pressure loss: 0.7% in 10s). For

higherpressurevalues,upto90%ofvalveOP,thepressureloss

increased,butitdidnotovercomeinanycase2.4%in10s.This

fur-therdemonstratesthesuitabilityofthistechnologicalsolutionfor

thedevelopmentofanAS,aswellasforotherapplications.

Thisresearchworkcanbeconsideredworthyofattentionfor

differentreasons.Themain purposeofthis article istolaythe

groundworkforthedesignandmanufacturingofanASthatcan

tackleUI[27](seeSupplementarymaterials,Fig.S1).Theresults

reportedinthispaperpermitthedesignofapolymericvalve

show-ingspeciﬁcperformancesintermsofOP.Thevalveproﬁlehasbeen

described by univocallydeﬁning the correspondent parameters

(thesedetails,inmanyarticles,arepartial,omitted,ordescribed

inanonparametricmanner)[9,10,16,18,19].Anotherimportant

noveltycomparedtothestate-of-the-artistheaccurateparameter

analysis,conductedwiththeaimofhighlightingwhichparameters

weremoresigniﬁcantforvalveperformance.Finally,the

valida-tionresultsdemonstrate that relativelysimple and widespread

manufacturingtechniques[28]canbeusedtofabricate—ina

reli-ablewayandwithrelativelysmalldeviationsfromthesimulation

results—one-wayvalvesthatareabletoensureatightseal-up

pres-sureintheorderof10kPamagnitude.

4. Conclusion

Thispaper aims at describing thesteps needed todesign a

polymericvalvesuitableforapplicationinartiﬁcialsphincter

sys-temsemployedfortacklingurinaryincontinencediseases.Aftera

preliminaryanalysis,acommercialvalveproﬁleusedinthefood

industrywaschosen asreference.Byanalyzing thecommercial

valvecrosssection,nineparameterswereextracted,whichdeﬁned

thevalvedesign. Then, aparametricanalysiswasconductedto

identifywhichfactorsweremoresuitableforachievinga

signif-icanttuningofthevalveperformance.Thisapproachallowedusto

deﬁneadesignstrategyaimedatminimizingdesignefforts.After

settingthevalvediameter,themostinﬂuentialparameterswere

valvestiffnessandthickness.Byvaryingtheseparameters,opening

pressuretuninginthephysiologicalrangewaseasilyachievable.

Appropriatemoldsandframesformanufacturingandtesting

polymericvalvesweredesignedandfabricated.Twenty-four

poly-mericvalves(dividedinsixdifferentexperimentalgroups)were

testedinordertovalidatethesimulations.ExperimentalResults

revealedamaximumerrorof23%comparedtosimulation

predic-tionswithageneralgoodagreementbetweentheenvisionedand

theactualvalveperformance.Thisworkwillconstitutetheground

forfutureadvancementsonthedevelopmentofbothpassiveand

controllableartiﬁcialurinarysphincters.

Acknowledgment

The authors would like to thank the Fondazione Cassa di

RisparmiodiLucca(Lucca,Italy),forprovidingﬁnancialsupport

forthisstudy,intheframeworkoftheSUAVESproject(Artiﬁcial

UrinarySystembasedonbladderandsphincterendoprostheses).

AppendixA. Supplementarydata

Supplementarydataassociatedwiththisarticlecanbefound,in

theonlineversion,athttp://dx.doi.org/10.1016/j.sna.2015.07.005

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Biographies

Tommaso Mazzocchi obtained a M.Sc.in Biomedical EngineeringinApril2013atUniversityofPisa(Italy)with athesisentitled:“Developmentandvalidationofsafety systemsformagneticallyactuatedendoluminalrobots”. HeiscurrentlyResearchAssistantatTheBioRobotics Insti-tuteofScuolaSuperioreSant’Anna,wherehecarriesout researcheffortsinthefieldofbiomedicaldevices,witha particularfocusonsystemsaimedtofaceurinary inconti-nenceandbladdercancer.Heisinventorof2international patentsrelatedtoartificialsphinctersandartificial blad-ders.

LeonardoRicottiisAssistantProfessorandheadofthe “Micro-Nano-BioSystemsandTargetedTherapy”Labat TheBioRoboticsInstituteofScuolaSuperioreSant’Anna. Hisresearchinterestsincludebiomechatronics,bionics, biomaterials,regenerativemedicineandbiohybrid sys-tems.Heisauthorofabout50scientiﬁcpapers(Source: Scopus),withmorethan30onISIJournalsand3book chapters.Heisalsoinventorof4patents,relatedtosmart mechatronicdevicesformedicalapplications.

NovelloPinziobtainedaM.Sc.inMedicineandSurgeryat theUniversityofPisa(Italy)in1976.In1980heobtained the specializationinUrology atthe UrologyClinicof Florence(Italy),andin1985heobtainedasecond special-izationingeneralsurgeryattheUniversityofPisa.Over thepast25years,heperformedatotalof800 interven-tions.Hismainfieldsofinterestarebladderreconstruction afterradicalcystectomyandtreatmentofurinary incon-tinencebymeansofartificialsphincters.Heisinventorof 2internationalpatentsrelatedtoartificialsphinctersand artificialbladders.

Arianna Menciassi is Full Professor of Biomedical Roboticsandleaderofthe“SurgicalRoboticsandAllied Technologies”Area,attheBioRoboticsInstituteofScuola Superiore Sant’Anna.Hermain research interests are inthe ﬁeldsofmedical mechatronics,bio-hybrid sys-tems,biomedicalmicro-andnano-devicesandrobotic surgery.Shepossessesanextensiveexperiencein Euro-pean Projectsand internationalcollaborative projects ontopicsrelatedtoroboticandmicroroboticdiagnosis, surgeryandtherapy.Sheisauthorofabout300 interna-tionalpapers(Source:Scopus),withmorethan150onISI journals,1editedbookand6bookchaptersonmedical devicesandmicro-technologies.