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ContentslistsavailableatScienceDirect

The Journal of Supercritical Fluids

jo u rn 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 u p f l u

New insights in the morphological characterization and modelling of poly( ␧ -caprolactone) bone scaffolds obtained by supercritical CO 2

foaming

Víctor Santos-Rosales

a,∗

, Marta Gallo

b,c

, Philip Jaeger

d

, Carmen Alvarez-Lorenzo

a

, José L. Gómez-Amoza

a

, Carlos A. García-González

a,∗

aDept.Farmacología,FarmaciayTecnologíaFarmacéutica,I+DFarmaGroup(GI-1645),FacultyofPharmacy,AgrupaciónEstratégicadeMateriales (AeMAT),andHealthResearchInstituteofSantiagodeCompostela(IDIS),UniversidadedeSantiagodeCompostela,E-15782,SantiagodeCompostela,Spain

bDepartmentofAppliedScienceandTechnology,PolitecnicodiTorino,CorsoDucadegliAbruzzi24,10129,Torino,Italy

cUniversityofLyon,INSAdeLyon,MATEISUMRCNRS5510,Bât.SaintExupery,23Av.JeanCapelle,F-69621,Villeurbanne,France

dHamburgUniversityofTechnology(TUHH),EißendorferStr.38,D-21073,Hamburg,Germany

h i g h l i g h t s

•Process-structure-functionalityrela- tionshipsofmanufacturedscaffolds wereelucidated.

•The combined ␮-CT/MIP analysis allowedafullmorphologicalcharac- terizationofscaffolds.

•CO2 soakingtimehadadramatical effectonthescaffoldarchitectures

•3Dmodelsof theporousstructure wereobtainedforthemanufactured scaffolds.

•Scaffoldswerescreenedfrominsilico cellinfiltrationandwaterpermeabil- itytests.

g r a p h i c a l a b s t r a c t

a r t i c l e i n f o

Articlehistory:

Received20April2020

Receivedinrevisedform8July2020 Accepted26July2020

Availableonline7August2020

Keywords:

Supercriticalfoaming 3D-biodegradablescaffolds X-raymicrotomography 3D-modelling Poreinterconnectivity Boneregeneration

a b s t r a c t

Hierarchicallyporoussyntheticbonegrafts(scaffolds)aregainingattentionintheclinicalarena.Scaffolds shouldcombinemorphological(macro-andmicroporosity,poreinterconnectivity),mechanicalandbio- logical(biocompatibility,degradationrate)propertiestofitthisspecificuse.Supercritical(sc-)foaming isaversatilescaffoldprocessingtechnology.However,theselectionoftheoptimumoperatingcondi- tionstoobtainadefinedscaffoldstructureishamperedbythelackofasinglecharacterizationtechnique abletofullyelucidatetheporousfeaturesoftheresultingscaffolds.Inthiswork,theeffectofsoaking time(1,3and5h)onthepreparationofpoly(␧-caprolactone)(PCL,50kDa)scaffoldsbysc-foaming wasevaluatedbyacombinedX-raymicrotomography(␮-CT)andmercuryintrusionporosimetry(MIP) 3D-morphologicalanalysis.Mechanicaltestsandinsilicomodellingforcellpenetrationandwaterper- meabilityofthescaffoldswerealsoconducted.Resultsevidencedtherelevanceof␮-CTandMIPasa synergisticanalyticalduotofullyelucidatethemorphologyofthesc-foamedscaffoldsandthesoaking timeeffect.

©2020TheAuthor(s).PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense (http://creativecommons.org/licenses/by/4.0/).

Abbreviations: ANOVA,analysisofvariance;BP,batchpressure;BT,batchtemperature;DR,depressurizationrate;FDA,FoodandDrugAdministration;MIP,mer- curyintrusionporosimetry;MSCs,mesenchymalstemcells;␮-CT,X-ray-basedmicrotomography;PCL,poly(␧-caprolactone);PLCL,poly(l-lactide-co-␧-caprolactone);PLA, poly(D,L-lacticacid);PLGA,poly(lactic-co-glycolicacid);ROI,regionofinterest;scCO2,supercriticalcarbondioxide;SEM,scanningelectronmicroscopy;SOP,standard operatingprocedures;ST,soakingtime.

Correspondingauthors.

E-mailaddresses:victor.santos.rosales@rai.usc.es(V.Santos-Rosales),carlos.garcia@usc.es(C.A.García-González).

https://doi.org/10.1016/j.supflu.2020.105012

0896-8446/©2020TheAuthor(s).PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense(http://creativecommons.org/licenses/by/4.0/).

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1. Introduction

Boneisthesecondmostcommontransplantationtissue and theharvesting of cancellous bone fromthe patient (allografts) is the current gold-standard surgical procedureto repair bone defectsinthelocomotorsystem.Nevertheless,theriskofinfections, theintervention-associateddamagesandthelimitedavailability of transplantable tissue evidence the need of new therapeu- ticapproaches. Thedevelopment ofinnovativesyntheticgrafts, theso-calledscaffolds,providesapromisingstrategytoregener- atedamaged tissuespromoting theself-healing capacity ofthe patients.Scaffoldsmustdisplaya3D-interconnectedandhierar- chicalporousstructureandamechanicalbehaviorthatareadapted totheanatomicaltargettogetanappropriateperformanceonce implanted[1].

Conventionalmethods for scaffold manufacturingfrequently involve the use of high temperatures and/or organic solvents andmayrequirelongandtedious downstreampathways[2–4].

Theseprocessingconditionsareusuallyincompatiblewithscaf- foldscontaining bioactive compounds (i.e. medicated scaffolds) whichdo notwithstandharsh treatmentsandmaybealsolost duringpurification.The useofmedicated scaffoldsis of partic- ularinteresttoimprovethescaffoldintegrationandtheprecise tissueregenerationortoalleviatepost-surgicalharms.Supercrit- ical(sc-)foamingisaversatilesolvent-freegreentechnologyfor theprocessingofbiodegradable polymericscaffolds.Sc-foaming isbasedonthesorptionanddissolutionofCO2 inthepolymeric matrix of the scaffold for a certain time period (soakingtime;

ST)undercertainpressure(batchpressure;BP)andtemperature (batchtemperature;BT),followedbyapressurerelease(depres- surizationrate;DR).Thelatterstepforcesthepolymerexpansion andCO2removalinordertoinducetheformationofporesinthe polymericmatrix.DuetotheplasticizingeffectofCO2,sc-foaming technologyoperatesundermoderateprocessingtemperatures,i.e.

compatiblewiththeincorporationofthermolabilebioactivecom- pounds such as growth factors [5–7], anti-inflammatory drugs [8–10]orantimicrobialagents[11–13]ofinterestforboneregen- eration.

Thefinecontrolofthemainoperatingvariablesofsc-foaming (BP,BT,ST,DR)allowedthemanufacturingoftunableporousand interconnectedarchitecturesforpolyester-basedscaffolds,suchas poly(D,L-lacticacid)(PLA)[14],poly(lactic-co-glycolicacid)(PLGA) [15,16],poly(␧-caprolactone)(PCL)[17,18]orpoly(L-lactide-co-␧- caprolactone)(PLCL)[19].Rationaldesignofpatient-personalized andquality-reproduciblescaffoldsdemands thedevelopmentof standardoperatingprocedures(SOP)forsc-foaming.Compilation ofprotocolsandprocessingparametersisofutmostimportanceto obtainscaffoldsfittedtothetargetgraftingsitedemands,partic- ularlyintermsofporesize,morphology,distribution,throatsize andinterconnectionthatarecriticalforcellcolonizationanddif- ferentiation[20].However,themodellingoftheporeformation mechanismduringsc-foamingprocessisstillchallengingbutabso- lutelyrequiredforthedefinitionofSOPs.

Thereare few studies reportingon theeffects of the foam- ing processing conditions on the resulting polymeric scaffold 3D-architectures[18,21–24].Commonly,morphologicalcharacter- izationiscarriedoutbyscanningelectronmicroscopy(SEM),which allowsfordirectmeasurementsofporesizesandvisualestima- tionsofporeinterconnectivityalthoughrestrictedtotheexposed surfacearea.TheevaluationofscaffoldsusingtheSEMapproach hasseverelimitationsmainlyrelatedtothesample preparation itselfandthemethodofdatatreatment.Aphysicalsectioningofthe scaffoldisrequiredasaprevioussteptoexposetheinnerregions.

Thispreparativestepisusuallyperformedmanuallyusingasur- gicalbladethatmakesthesampletobeundercompressionand shearforces. Theseforces maycausestructuraldamagestothe

structure,suchasporeocclusionanddeformation[25].Moreover, flawedcutsofthescaffoldsarefrequentdependingonthedimen- sionsandthedifficultyofhandlingofthescaffold;theobtained angled areasalsocompromise the qualityand reliability ofthe results. Finally,the datatreatmentof SEMimagestostudythe poresizedistributionconsidersthesizeofa poreequivalentto the cross-section diameter of thepore in theSEM-image. This assumptionusually results in anunderestimation of the actual poresizesinthecaseofsphericalpores.Forthecaseofelongated (cylindrical)pores,severalspecimenscutintheaxialandcoronal planeareneededtogetareliableporesizedistributionfromSEM images,requiringmoreamountofmaterialastheyaredestructive tests.

Mercuryintrusionporosimetry(MIP)isawell-establishedtech- niqueforthecharacterizationofporousmaterials,basedonthe profileofmercuryintrusionintoporeswhensubjectedtoincreas- ingpressures.Oncethemaximumpressureisreached,anextrusion profileisalsoobtainedfromthedepressurizationstep.Fromboth profiles,theporeandthroatsizesofthesamplecanbecalculated, andtheporetortuosity,compressibilityorpermeability maybe inferred[26,27].Despitetheadvantagesofthetechnique,MIPisnot asuitablecharacterizationmethodformaterialswithlargemacro- poresduetoitsupper-limitmeasurableporerange(uptoca.200

␮m)[28].Inaddition,MIPdoesnottakeintoaccountclosepores andassumesperfectlycylindricalporestocorrelatethevolumeof mercuryintrudedwiththeporesize,whichdonotalwaysrepresent therealityoftheanalyzedsamples[25,29].

X-ray-basedmicrotomography(␮-CT)isanon-invasivemethod thatprovidesquantitativeandqualitativeinformationregarding the 3D-morphology of samplesand is commonly used for the analysisoftrabecularbone [30,31].Theuseofthis techniqueis encouragingforscaffoldcharacterization[32–37],althoughthere aretwomainaspectstoconsiderwhenperforminga␮-CTscan:

thedurationoftheanalysisandthestorageoftheobtaineddata.

Indeed,thescanningoflow volumesamplescanlast over20 h andthegeneratedfileshavesizesintheorderofseveralterabytes dependingonthe␮-CTacquisitionparameters(e.g.voxelsize,rota- tionstep)[38]. Also,theselectedvoxelsizehasadirectimpact ontheimage resolutionfromthe␮-CTscan and,subsequently, onthelowestvalueofmeasurableporesizeoftheporousmate- rials.Therefore,atrade-offsolutionbetweentheimageresolution andthetime-costand datastoragespaceconsumptionmustbe met.

Overall,thestate-of-the-artofmorphologicalcharacterization ofscaffoldsindicatesthatthereisnotauniversaltechniqueableto fullycharacterizetheporousstructureofpolymericscaffoldsinthe micro-to-macroporousrangeregardingpore-throatdistributions andporeinterconnectivities.

Thecombinationofthesecomplementarytechniques(SEM,MIP and␮-CT)forthefullcharacterizationofscaffoldporestructure canovercometheindividualartifactsorpitfallsofeachindividual technique.Tothebestofourknowledge,itisthefirsttimethat thecombinationofthesecharacterizationtechniquesisexploited togenerateinformation onprocess-structure-functionalityrela- tionshipsofscaffoldsobtainedbysc-foaming,whichisofutmost interestforthedefinitionofSOPs.Thus,theeffectoftheCO2soaking timeduringthesupercriticalfoamingprocessonthescaffoldmor- phologywasevaluatedtogetthetargetscaffoldfeaturesrequired forsyntheticbonegrafts.Themorphologicalstudyoftheresulting scaffoldsofpoly(␧-caprolactone)(PCL),abioresorbablesemicrys- tallinepolymer[39–45],wasperformedbasedonthecombination ofSEM, MIP,heliumpycnometry and ␮-CTtechniques.Insilico studiesofcellinfiltrationcapacityandwaterpermeabilityaswell asinvitro mechanicaltests werecarriedout forthesc-foamed scaffoldstopredictthegraftperformanceonceimplanted.

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2. Materialsandmethods

2.1. Materials

Poly(␧-caprolactone)(PCL)inthepowderedform(50kDa,Tm

=61.4C,66.7%crystallinity)wassuppliedbyPolysciences(War- rington,PA,USA).CO2(purity>99.9%)wasemployedasfoaming andblowingagentandprovidedbyPraxair,Inc.(Madrid,Spain).

2.2. CO2sorptionkinetics

A thermostized magnetic suspension balance (Rubotherm GmbH,Bochum,Germany)wasusedtoevaluatetheCO2sorption kineticsonthePCLat140barand39C,i.e.conditionscloseto bodytemperatureandwherePCLwasmoltenaccordingtoprelim- inaryviewcelltests(notshown).Thepolymericpowderwasdosed (80mg)inaglasscontainerandattachedtothebalancethrougha metalhook.Priortothemeasurements,thepolymerwasmoltenat 80CinanoventoensureahomogeneousCO2sorptionalongthe material[46].

2.3. ProcessingofPCLscaffoldsbysc-foaming

PCLpowder was weighed (ca. 1 g) and dosed in cylindrical (length =24.6mm,internal diameter=17 mm)Teflonmoulds (BrandGmbH,Wertheim,Germany),followedbymanualcompres- sion.Mouldswerethenplacedina100mL-stainlesssteelautoclave (TharProcess,Pittsburg,PA,USA)andheatedto39C(BT).After- wards,thesystemwaspressurizedwithCO2(5g/min)until140 bar(BP)andmaintainedinthestaticmodeforacertainsoaking period(ST=1,3and5h).Thesystemwasstirredat700rpmdur- ingthewholeprocesstoenhancethemasstransferandtoensure ahomogeneousCO2environment.Theautoclavewasthendepres- surizedataconstantventingrate(DR=1.8g/min)untilatmospheric pressure.Priortotheirstorage,theouterskinofthescaffoldswas carefullyremovedusingasurgicalblade.Scaffoldsweredenoted as39STreferringtotheprocessingtemperature(BT=39oC)andthe subscriptaccordingtothesoakingtimeused(ST=1h,3hor5h).

2.4. Characterizationofscaffolds 2.4.1. Structuralcharacterization

Bulkdensities(␳bulk)wereobtainedfromtheratiobetweenthe weightandvolumeofeachscaffoldaftersc-foaming.Theskeletal density(␳skel)of thescaffoldswasdeterminedusing a helium- pycnometer (Quantachrome, Boynton Beach, FL, USA) at room temperature(25C)and1.01bar.Valueswereobtainedfromsix replicates.Overallporosity(ε)wascalculatedaccordingtoEq.(1).

ε(%)=

1−bulk skel

x100 (1)

The morphological properties of the scaffolds were investi- gatedbyscanningelectronmicroscopy(FESEM,ULTRAPLUS,Zeiss, Oberkochen,Germany)runningatavoltageof10kV.Priortotheir imaging, scaffoldswereslicedwitha scalpel and theniridium- sputtered(10nmthickness).

2.4.2. MIPanalysesandinsilicomodellingofPCLscaffolds

MIPanalysesofthePCLscaffoldswereperformed(AutoporeIV 9500model,Micromeritics,Norcross,GA,USA)atworkingpres- suresrangingfrom0.07−1800bartodeterminetheirporesize distributionsinthe0.01−180␮mrange.Porosityvalues(εMIP)and poresize(MIP-Meanporesize)weredeterminedfromtheintruded volumeofmercury(VpMIP)inthescaffoldswiththeincreaseofpres- sureusingtheWashburnequation[25].A3D-networkmodelwas

generatedfromtheMIP-cumulativecurveshavingidenticalperco- lationpropertiesasthoseofthemanufacturedPCL-scaffoldsusing PoreXpertv.1.6.567software(PoreXpertLtd,Plymouth,UK).Thisin silicomodelconsistsinacubicstructureformedby1,000pores(of cubicshape)connectedbyupto3,000throatsofarbitrarycylindri- calshape.ABoltzmann-annealedsimplexalgorithmwasusedto estimateandtosimultaneouslyoptimizetheconnectivity(mean numberofthroatsperpore),poreskew,throatskewandcorrela- tionlevelfromtheMIP-cumulativecurves.Waterpermeability(25

C,1.03bar)wasestimatedassumingthatPoiseuilleflow(water) occurredinthez-directionaccordingtoEq.(2)

kw=

cell(Farcs)lcell

Acell (2)

wherelcellandAcellrepresentthelengthandthecross-sectional areaoftheunitcell,respectively,andωcell(Farcs)isanaveraging operatoroverthewholeunitcelloperatingontheflowcapacitiesof theporethroat-porearcsparalleltothez-axis.PoreXpertcalculates thetermωcell(Farcs)bymeansoftheDinicnetworkanalysisalgo- rithm.Mesenchymalstemcells(MSCs)infiltrationinthescaffolds wassimulatedusingthefiltrationmodulefromthesoftwareand assumingacellsizeof26.5±5.0␮m,anaveragevalueforhuman MSCs[47–49].

2.4.3. MicroX-raycomputedtomographyimageacquisition, reconstructionandanalysis

MicroX-raycomputedtomography(␮-CT)scanswereacquired (in the local mode) using a Phoenix v|tome|x tomograph (GE, Boston,MA,USA)equippedwithaVarianPaxScandetector(1920

×1536pixels).Voxelresolutionwassetequalto12␮m.

3D images were reconstructed and analyzed using Avizo v.2019.1software(ThermoFisherScientific,Waltham,MA,USA).A generalschemeoftheworkflowfromtheimageacquisitiontocom- plete3DreconstructionandanalysisisdepictedinFig.1.Firstly,a specificregionofinterest(ROI)ofcubicshape(4.8×4.8×4.8mm3) andrepresentativeoftheentirescaffoldwasisolatedtoevaluate theinfluence of theworkingparameters ontheresulting mor- phologies.Afterwards,thecalibrationofthethresholdingofthe grey-scalewasperformedtodifferentiatethevoidfraction(pores andporeinterconnections,i.e.throats)fromthesolidmaterial.This imagethresholdingisconsideredacrucialsteppriorto3Dmod- ellingthatinfluencesthesubsequentanalysisandstructuralplots [50].Oncethevoidvolumewaspreciselyidentified,porosity(␧-CT) ofthescaffoldswascalculatedintheROIandexpressedasper- centageofvoidvoxelswithrespecttothetotalnumberofvoxels.

Connectedporosityofthescaffoldswascalculated(inpercentage) asthevolumefractionofthelargestgroupofinterconnectedpores withrespecttothetotalporevolumeintheROIofthematerial.

Tortuositywascalculatedfromthemeanpathwaydistanceofapar- ticlemovingfromonefaceoftheROItotheoppositeonedivided bythelengthoftheedgeofthecubicROI(i.e.theshortestpossible pathway).

A3D-networkmodelofballsandstrutswasalsoobtainedfrom the␮-CTdata,wheretheporesarerepresentedasballsandthe porethroatsascylindricalstruts.Thesizesofballsandstrutswere calibratedaccordingtoacolorscaletovisuallyidentifymorpholog- icaldifferencesbetweenscaffolds.Inaddition,poresizeandpore throatsdistributionsandtheirmeanvalueswereobtainedbasedon theformer3Dmodel.Finally,simulatedMIP-dataandporevolume distributionsofthePCL-scaffoldswereobtainedfromthe3Dmodel generatedfrom␮-CTusingXlibpluginfromFiji-ImageJsoftware [51,52].

2.4.4. Mechanicalproperties

PCLscaffolds (in triplicate)were subjectedto unidirectional compression tests in a tensile bench with a 30 kg load cell

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Fig.1.DataprocessingpathwayusedforthemicroX-raycomputedtomographyimageacquisition,reconstructionandanalysisofthesupercriticalCO2foamedscaffold.

Firstly,aspecificregionisisolatedfromtheentirescaffold.Throughtheimagethresholdingstep,thevoidfractionisconvertedtoa3D-networkmodelofballsandstruts, whosesizesarecalibratedaccordingtoacolorscale,andthesolidmaterialingray.Basedonthe3Dmodel,poresizeandthroatsdistributionplotsareobtained.

Fig.2. CO2sorptionkineticsinPCLatthesc-foamingconditions(140barand39C).Paralleldottedlinesindicatethethreesoakingtimes(60,180and300min)chosento evaluatetheinfluenceoftheamountofCO2absorbedontheresultingfoammorphologies.

(TA.XTPlus, Stable Micro Systems, Ltd., Godalming, UK) at a crossheadspeedof1mm/min.Alltheexperimentswereperformed atroomtemperature(25C),atmosphericpressureand45%rel- ativehumidity.Elasticdeformationwascalculatedfromtheratio betweentheinitialheightandtheheightofthesamplebearing thehighestappliedphysicalstress.TheYoung´smodulus(E)was calculatedfromthestress-strainplotspreviousconversiontoengi- neeringstressandengineeringstrain.

2.5. Statisticalanalysis

Allresultswereexpressedasmean±standarddeviation.Sta- tisticalanalysesof themechanical results(1-wayANOVA)were performedusingStatisticav8.0software(StatSoftInc.,Tulsa,OK, USA)followedbythepost-hocTukeyHSDmultiplecomparison test.

3. Resultsanddiscussion

3.1. ExperimentalCO2sorptionkineticsinPCL

SolubilityanddiffusivityofCO2withinapolymercanbemod- ulatedbytuningtheworkingtemperatureandpressureleadingto dramaticchangesintheresultingfoammorphologies[53].TheCO2

sorptionprofileinPCLunderanatmosphereofsc-CO2at140bar and39CisshowninFig.2.TheamountofCO2absorbedinPCL wasgreatlyinfluencedbythesoakingtimewithafastCO2sorp- tionkineticsfollowedbyaslowerstageafterca.60minofexposure withvaluesinthenear-saturationrange(0.23−0.27gramsofCO2 absorbedpergramofPCL).ThesolubilityvaluesofCO2 at35C and130bar,and40Cand150barwerepreviouslyreportedto reach0.22and0.40gCO2/gPCLatthesaturationstage,respec- tively[17,54].Thebroadrangebetweenthesetwovaluesindicates theproximityofthephasetransitionandshowsthatthereported

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Table1

MorphologicalandtexturalpropertiesofPCLscaffoldsobtainedbysc-foaming.Densityvaluesexpressedasmeanvalues±standarddeviation(n=6).

Scaffold bulk(g/cm3) skel(g/cm3) ε(%) εMIP(%) VpMIP(cm3/g) MIP-Meanpore size(␮m)

ε−CT(%) -CT-Meanpore sizea(␮m)

-CT-Meanpore sizeb(␮m)

391h 0.353±0.007 1.101±0.013 68.0±0.7 30.7 1.70 110.29 67.9 733.2±466.5 1340±341

393h 0.317±0.019 1.110±0.011 71.4±1.7 13.1 1.99 116.23 67.2 733.6±330.1 1096±527

395h 0.298±0.008 1.084±0.009 72.5±0.8 20.2 2.31 117.14 68.3 416.7±123.1 698±430

aValuesobtainedfromthe3D-modelreconstruction.Valuesfollowanormaldistribution(R2>0.99).

bValuesobtainedfromthe2D-imagesofthe␮-CTanalysisintheaxialplane.Valuesfollowanormaldistribution(R2>0.72).

Fig.3. SEMimagesofcoronalcross-sectionsofthefoamedPCLscaffoldsprocessedatincreasingsoakingtimes:(A,B)1h,(C,D)3hand(E,F)5h.Interconnectedporeswere obtainedinallcases(whitearrowsinB,D,F).Scalebar:200␮m.

valuesintheliterature[54,55]areinfairagreementwiththiswork, inspiteofthedifferencesinthemolecularweightandcrystallinity oftheusedPCLandinworkingpressures.ItisreportedthatCO2 dissolvestoahigherextentintheamorphousregionsofpolymers andinpolymersoflowermolecularweights[56,57].Finally,CO2

solubilityusuallyincreasesathigherpressures[17,54,58].Accord- ingtotheseresults,thesoakingtimesselectedforfurtherfoaming trialsweresetat1,3and5htoevaluatemorphologicaldifferences dependingontheincreasedamountofCO2 dissolvedinthePCL (0.238,0.261and0.270gCO2/gPCL,respectively)

3.2. Sc-foamingprocessdevelopmentandmorphological characterizationofthescaffolds

CylindricalandhighlyporousPCLscaffolds(␧=68–72%)were obtainedthroughsc-foaming,matchingthehumantrabecularbone porosityvalues[59,60].Adome-liketopendingwasobservedfor

scaffoldsprocessedwithsoakingtimesabove1hincontactwiththe CO2atthefoamingpressure(FigureS1).Allspecimenspresented anon-porousskinof100−140␮mthicknessduetotherapidCO2 diffusionupondepressurizationfromthesurfaceofthePCLmatrix [61].Longersoakingtimesfavoredthepolymericexpansionupon depressurization,slightlydecreasingthebulkdensityvalues(␳bulk) ofthemanufacturedscaffolds(Table1).

The morphological analysis of the scaffolds from SEM microscopyimagesunveiledsmoothsurfaceswithsubtlediffer- encesamongthemregarding theporegeometriesanddensities (Fig.3).391hscaffoldspresentedthelesshomogenousporemor- phologieswithsmallpores(<100␮m)combinedwithlargerones (Fig.3AandB).Enhancedcelladhesion,migration,proliferationand differentiationarereportedforpolymericscaffoldswithaporous populationinthe20–50␮mrange[62,63].LongerST(5h)favored thehomogeneity and sphericity ofthe pores(395h scaffoldsin Fig.3EandF).Qualitatively, scaffoldsprocessedduring3hpre-

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Table2

PorethroatandinterconnectivitiesofPCLscaffoldsprocessedbysc-foamingobtainedfromMIPand␮-CTdataanalysis.

MIP ␮-CT

Scaffold MIP-meanporethroatdiameter(␮m) Interconnectivity(%) Tortuosity -CT-meanporethroatdiameter(␮m) Connectedporosity(%) Tortuosity

391h 35.26 71.17 1.5 242.3±271.5 88.3 1.4

393h 36.86 79.00 1.2 285.8±198.4 99.2 1.5

395h 35.63 77.83 1.3 148.9±89.87 99.8 1.6

sentedmorevoidspacesalongtheanalyzedarea(393hscaffolds inFig.3C,D)than395hscaffolds.Allscaffoldshadinterconnected poresashighlightedbythepresenceofinnerporeswithinthelarge porecavities(whitearrowsinFig.3B,DandF).

Poreinterconnectivitystronglyinfluencestheperformanceof thescaffoldssincelowlevelscanhamperthecellcolonizationphe- nomenaandthediffusionofnutrientsandremovalofwasteprod- uctsfromthecells[1,4].Theporeinterconnectivitylevelofscaffolds obtainedbysc-foamingcanbemodulatedbymodificationsonthe depressurizationrate[18,64].MIPtechniqueallowedthestudyof openporepopulationsin the0.01−180␮mrangetocharacter- izethemesoporesandthesmallmacroporepopulationsaswell asdegreeofporeinterconnection.Theopenporosityobtainedby MIP(εMIP)ofthefoamedscaffoldrepresentedvaluesinthe13–30% range,clearlydivergingfromtheoverallporosityvalues(Table1).

Thisdivergenceinvaluescanbeattributedtothepresenceofpores eitherlargerthan180␮morclosed.Namely,thelowestoverall porositywasobtainedforthe393hscaffold.Themeanporesizecal- culatedfromMIPmeasurementsunveiledthatscaffoldsprocessed atlongerSTpresentedlargerporesincreasingupto6%for395hscaf- fold(Table1).Theporethroatdiameterswerevirtuallyidentical, althoughdifferencesinthedegreeofporeconnection(interconnec- tivity)wereobtained,mainlyrelatedtothedifferenttortuosityof thescaffolds(Table2).Overall,themanufacturedscaffoldspresent goodporeinterconnectivity(above70%)forregenerativemedicine purposes,regardlessoftheworkingparameters.

Fig.4. PoresizedistributionofthefoamedPCLscaffoldsprocessedatdifferentsoak- ingtimes(ST=1,3and5h)obtainedfrom2D-imageprocessingfrommicroX-ray computedtomographydata.LongerSTresultedinlowermeanporediameters.

3.3. -CTimagingofPCLscaffoldsobtainedbysc-foamingusing differentsoakingtimes

Thepresenceofnumerousporeswithdiameterslargerthan200

␮m(asobservedbySEM)encouragedtheuseof␮-CTinorder toeffectivelyassesstheeffectofCO2soakingtimeontheresult- ingmorphologies.Porosityvaluesdeterminedfrom␮-CTimages (ε−CT)wereinthe67–68%range,beingclosetotheoverallporos-

Fig.5.2Dhorizontalslices(top)ofthefoamedPCLscaffoldsprocessedafterincreasingsoakingtimes(fromlefttoright,ST=1,3and5h)withtheircorresponding3D reconstructions(bottom)obtainedfrommicroX-raycomputedtomographydata.Scalebars:2mm(top);arrowlength:2mm(bottom).

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Fig.6.CumulativeporevolumedistributionofPCLscaffoldsprocessedat39C and140barwithdifferentSTvalues.Distributionswereobtainedbycombination obtainedfromMIPexperimentaldataandfromMIPsimulateddatafrom␮-CT,with acut-offatadiameterof25␮m.

ityvaluescalculatedfromEq.(1)(Table1).Althoughallscaffolds hadsimilarporosityvalues,remarkabledifferencesintheirmor- phologywereobserved inthe2D␮-CTimagesasa functionof theprocessingtime(ST).Anincreaseinthenumberofporesand a reduction of thepore size was recorded asthe ST increased (Figs. 4 and 5). An overestimation of the mean pore size was obtainedfromtheanalysisofthe2Daxial planesectionswhen comparedtothebulkstructure,sincethefoamspresentelongated pores(Table1).Ontheotherhand,thetotalspecificporevolume ofthescaffoldscalculatedfrom␮-CTdataunderestimatedin5–10

%thevaluesobtainedfromMIPanalysis,sincethevolumecontri- butionofsmallmacroporesandmesoporescannotbeconsidered when␮-CTisusedduetoresolutionlimitations(Fig.6).

Thearchitectureofeachscaffoldwasfurtheranalyzedfromthe dataofthe3D-modelobtainedfromthelibraryof2Dslices(Fig.7).

Longersoakingtimesledtoa reductionin themeanpore sizes ofthescaffoldsandnarrowerporesizedistribution.Particularly, 395hscaffoldspresentedanarrowporesizedistributionwithvalues fallingintheidealsizerange(1−500␮m)forbonetissueengineer- ing[65,66].Theseresultsareinlinewithpreviousstudieswith neatPCLscaffoldsshowingaremarkablereductionoftheporesize withtheincreaseofthesoakingtime[18].Conversely,otherstudy [67]reportedtheoppositeeffectduringthesupercriticalfoaming ofpurePCLscaffolds,wherethelowestporediameters(11.75␮m) wereobtainedafterST=1h.Overall,thereductionoftheporesize ofthefoamedscaffoldsobtainedinthisworkfollowstheclassical nucleation-growththeoryofporeformation[68,69].Atlongerpro- cessingtimes,higherinitialamountsofCO2aredissolvedwithin thepolymer(Fig.2)loweringtheinterfacialtensionofthePCL-CO2 system.Thisreductionininterfacialtensionfacilitatestheforma- tionofmorenucleationsitessincetheinitialcritical nucleation radiusisreduced[70–72].Then,upondepressurization,scaffolds ofhighercelldensitieswithsmallerporesaretypicallyobtained whenprocessedatlongersoakingtimes[18,71].Thereductionin poresizeisaconsequenceofthespatiallimitationtothegrowth ofporesfromthesenucleationsitesduetotheirhighabundance.

Moreover,longersoakingtimesallowforamoreefficientCO2dis- tributionalongthepolymericmatrixresultinginmoreuniformand narrowerporedistributions[32].Botheffectsareeasilyappreciated inFig.7asthesoakingtimeincreased.

Scaffoldsallowingtheinfiltrationofcellswithintheirporous structuresandthetransportofnutrients,metabolitesandwastes through them are needed to match the demands of the bone regenerationprocess.Thesepropertiesarestronglydependenton themorphologicalpropertiesofthescaffoldsregardingporeand throatsizedistributionaswellastheporeinterconnectivity.The

Table3

InsilicopredictedvaluesofwaterpermeabilityandMSCsinfiltrationonsc-foamed PCLscaffolds.

Scaffold Waterpermeability(m2) Cellinfiltration(%)

391h 1.37·10−13 66

393h 1.42·10−13 77

395h 1.84·10−12 93

degreeofconnectedporosityinthescaffoldsandhowtheporesare interlinkedwerecharacterizedbytheporethroatanalysis.These featuresareofutmostimportancesinceinhibitioneffectsonthe tissuedifferentiationprocesswerereportedforporousimplantsof narrowporethroats[73].Theincreaseinthesoakingtimeresulted inscaffoldsshowingareductiononthemeanthroatdiametersand narrowerthroatsizedistribution,followingasimilartrendtothe poresizesdiscussedabove(Table2andFig.7).Furthermore,the decreaseinthemeanthroatsizeresultedinanincreaseonthetor- tuosityvalues,althoughthedegreeofconnectedvoidfractionwas almost100%forthelongersoakingtimetested(395hscaffold).

3.4. InsilicomodellingofwaterpermeabilityandhumanMSCs infiltration

Themicrostructureofscaffoldsplaysacriticalroleincellinfiltra- tionanddistributionofbiologicalfluids[74].Despitetheintrinsic limitationsofMIPtechniquepreviouslypresented,itwidelycovers porepopulationsbelow10␮m,unreachablebyboth␮-CT(with theselectedacquisitionparameters)andMIPinsilicosimulation basedon␮-CTdata(Fig.6).Therefore,thesimulationoftheper- meabilityandcellinfiltrationvaluesoftheobtainedscaffoldswas basedonexperimentalMIPdata.

Waterpermeabilityvaluesof391hand393hscaffolds(Table3) wereofthesameorderofmagnitudetothosereportedinsilicofor PCLscaffoldsobtainedbysc-foamingat37Candthesamepressure [75],andinvitroforlowmolecularweight-PLGAscaffolds(ca.10−13 m2)withsimilarporousstructures[76].Theincreaseofsoaking timeaugmentedwaterpermeabilityand395hscaffoldsdisplayed oneorderofmagnitudelargervalues.Overall,theobtainedinsilico permeabilityvaluesforthemanufacturedscaffoldswerecloseto thelowestexperimentaldatareportedforcancellousbone(10-12to 10-8m2)[77,78].Nevertheless,scaffoldpermeabilitywasbasedon awaterflowinasingleaxisdirectionanddifferencesareexpected asthestructureshaveanisotropicproperties.Forinstance,notonly directionalbutalsospatialdifferencesinpermeabilitycalculations werereportedforhuman[79],porcine[80]andbovine[81]cancel- lousbone.Despitetheabovementionedlimitationsoftheinsilico model,permeabilityvalueswereofthesameorderofmagnitudeto thosereportedfornaturalbonebyexperimentalperfusionmethods [78].

ThecellinfiltrationcapacityinthePCLscaffoldwasevaluated throughthespreadcapacityofparticleswithdefinedsizes(cor- respondingtohumanMSCs dimensions).395h scaffold hadcell infiltrationvaluesover 90%,suggestingthat thisstructure may havefullaccessibilityforcellsonceimplanted,allowingahomoge- neoustissueingrowthinsteadofrestrictingittotheoutersurface ofthescaffold.Lowercellinfiltrationvalueswereobtainedfor391h and393hscaffolds.Resultsshouldbesparinglyconsideredsincethe modelinthisworkwasbasedonindividualandnon-interacting particles.Forinstance,theformationofundesiredcellaggregates orclustersduringthecellseedingperiodmayoccur,beingasource ofvariabilityintheinvitrodeterminationofcellinfiltration[82].

Overall, 395h scaffold is the most promising candidate regarding its further biological performance as synthetic bone grafts in terms of water permeability and cell infiltration capacity.

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Fig.7.3Dnetworkmodels(left)ofballs(pores)andstruts(porethroats)representingthevoidfractionofthesc-foamedPCLscaffoldsunderincreasingsoakingtimes(from toptobottom,ST=1,3and5h),coupledwiththeircorrespondingsizedistributionsplots(right).ProlongedSTresultedinscaffoldswithlowermeanporeandthroatsizes andwithnarrowersizedistributions.

3.5. Mechanicalproperties

Mechanicalperformanceofscaffoldsdirectlycorrelatestothe structuralmodifications inducedby the variation of processing conditions. During the foaming process, the CO2 was vented in a singledirectionand thepolymer expansionwasforced to occur preferentially in the vertical axis, obtaining PCL foams with elongated pores mimicking the natural bone anisotropy (Fig. 3) [83]. Scaffolds presented an elastic deformation of ca.

25 % (Figure S2) and the obtained Young’s moduli were in the5−8 MPa range (Table4), being in the reported range for

Table4

Mechanicalcharacterizationofthesc-foamedPCLscaffolds.Meanvaluesandstan- darddeviation(n=3).Resultswerestatisticallyidentical(1-wayANOVA;p<0.05).

Scaffold Elasticdeformation(%) Young’sModulus(MPa)

391h 23.8±0.5 6.9±0.1

393h 23.9±1.8 6.3±0.9

395h 25.4±2.1 6.8±0.5

humancancellousbone(1–900MPa)[59]. Despitethemorpho- logicaldifferences andtheincrease incell density,theincrease ofthesoakingtimehadnosignificantimpactonthemechanical

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behaviorofthescaffoldswhensubjectedtouniaxialcompression stresses.

4. Conclusions

ThearchitectureofporousPCLscaffoldsproducedbysupercrit- icalCO2foamingcanbetailoredbymodificationsoftheprocessing conditionstoprovidehighlyadaptablescaffolds.Fromthe␮-CT analysis,realistic scaffold reconstructions were obtained, being particularlyusefultoanalyzetheeffectoftheprocessingcondi- tionsontheresultingmorphologies.Longersoakingtimespermit moreCO2tobedissolvedinthepolymericmatrix,leadingtohigher densityofporeswithlowersizes.Inaddition,morehomogeneous scaffoldsandhigherdegreeofporeinterconnectionwereobtained withlongersoakingtimes.Ontheotherhand,MIPallowedthechar- acterizationofthemeso-andlowmacro-porepopulationandofthe degreeofporeinterconnection.Thisisofparticularinterestsince thegraftperformanceafter implantationcanbehighlyaffected bytheseporepopulations.InthissenseandbasedonMIPmea- surements,theinsilicomodellingofcellinfiltrationcapacityand waterpermeabilityoftheobtainedscaffoldsconstitutedapoten- tialscreeningtoolforfurtherinvitro/invivobiologicaltests.The combinationofcomplementarycharacterizationtechniques(␮-CT andMIP)coupledtothemodellingofthegenerateddata,offersnot onlybroaderandmorerealisticinformationregardingthemanu- facturedscaffoldsbutalsoregardingtheirpotentialuseassynthetic bonegrafts.Overall,thehereinpresentedsupercriticalCO2foaming processallowsthemanufactureofPCLscaffoldsmeetingthestruc- turalandmechanical requirementsforbonetissue regeneration purposes.Thisworkrepresentsastepforwardtowardstheknowl- edgeonprocess-structure-functionalityrelationshipsinsynthetic bonegraftsforthedefinitionofstandardoperatingproceduresin themanufacturingofpoly(␧-caprolactone)scaffoldsbysupercriti- calCO2foaming.

DeclarationofCompetingInterest Authorsdeclarenoconflictofinterest.

Acknowledgments

Authorswould liketothankProf.EricMaire andDr. Jérôme Adrien for their fruitful advices on ␮-CT measurements. This research was funded by Xunta de Galicia [ED431F 2016/010], MCIUN[RTI2018-094131-A-I00],AgrupaciónEstratégicadeMate- riales [AeMAT-BIOMEDCO2, ED431E 2018/08], Agencia Estatal de Investigación [AEI] and FEDER funds. C.A. García-González acknowledges to MINECO for a Ramón y Cajal Fellowship [RYC2014-15239].V. Santos-Rosales acknowledgesto Xunta de Galicia(ConselleríadeCultura,Educaci ´oneOrdenaci ´onUniversi- taria)forapredoctoralresearchfellowship[ED481A-2018/014].V.

Santos-RosaleswantstoacknowledgetheCOSTActionCA18125

“AdvancedEngineeringandResearchofaeroGelsforEnvironment and Life Sciences” (AERoGELS), funded by the European Com- mission, for the granted Short Term Scientific Mission (STSM) to perform the magnetic suspension balance measurements in EurotechnicaGmbH.

AppendixA. Supplementarydata

Supplementarymaterial relatedto thisarticle canbe found, intheonlineversion,atdoi:https://doi.org/10.1016/j.supflu.2020.

105012.

References

[1]C.A.García-González,A.Concheiro,C.Alvarez-Lorenzo,Processingof materialsforregenerativemedicineusingsupercriticalfluidtechnology, Bioconjug.Chem.26(2015)1159–1171,http://dx.doi.org/10.1021/

bc5005922.

[2]S.Pina,V.P.Ribeiro,C.F.Marques,F.R.Maia,T.H.Silva,R.L.Reis,J.M.Oliveira, Scaffoldingstrategiesfortissueengineeringandregenerativemedicine applications,Materials12(2019)1824,http://dx.doi.org/10.3390/

ma12111824.

[3]A.Eltom,G.Zhong,A.Muhammad,Scaffoldtechniquesanddesignsintissue engineeringfunctionsandpurposes:areview,Adv.Mater.Sci.Eng.Int.J.2019 (2019)1–13,http://dx.doi.org/10.1155/2019/3429527.

[4]V.Santos-Rosales,A.Iglesias-Mejuto,C.A.García-González,Solvent-free approachesfortheprocessingofscaffoldsinregenerativemedicine,Polymers 12(2020)533,http://dx.doi.org/10.3390/polym12030533.

[5]M.H.Sheridan,L.D.Shea,M.C.Peters,D.J.Mooney,Bioabsorbablepolymer scaffoldsfortissueengineeringcapableofsustainedgrowthfactordelivery,J.

Control.Release64(2000)91–102,http://dx.doi.org/10.1016/S0168- 3659(99)00138-8.

[6]X.B.Yang,M.J.Whitaker,W.Sebald,N.Clarke,S.M.Howdle,K.M.Shakesheff, R.O.C.Oreffo,Humanosteoprogenitorboneformationusingencapsulated bonemorphogeneticprotein2inporouspolymerscaffolds,TissueEng.10 (2004)1037–1045,http://dx.doi.org/10.1089/ten.2004.10.1037.

[7]L.Diaz-Gomez,F.Yang,J.A.Jansen,A.Concheiro,C.Alvarez-Lorenzo,C.A.

García-González,Lowviscosity-PLGAscaffoldsbycompressedCO2foaming forgrowthfactordelivery,RSCAdv.6(2016)70510–70519,http://dx.doi.org/

10.1039/C6RA09369H.

[8]L.Goimil,V.Santos-Rosales,A.Delgado,C.Évora,R.Reyes,A.A.Lozano-Pérez, S.D.Aznar-Cervantes,J.L.Cenis,J.L.Gómez-Amoza,A.Concheiro,C.

Alvarez-Lorenzo,C.A.García-González,scCO2-foamedsilkfibroin aerogel/poly(␧-caprolactone)scaffoldscontainingdexamethasoneforbone regeneration,J.CO2Util.31(2019)51–64,http://dx.doi.org/10.1016/j.jcou.

2019.02.016.

[9]L.I.Cabezas,V.Fernández,R.Mazarro,I.Gracia,A.deLucas,J.F.Rodríguez, Productionofbiodegradableporousscaffoldsimpregnatedwith indomethacininsupercriticalCO2,J.Supercrit.Fluids63(2012)155–160, http://dx.doi.org/10.1016/j.supflu.2011.12.002.

[10]R.Boia,P.A.N.Dias,J.M.Martins,C.Galindo-Romero,I.D.Aires,M.Vidal-Sanz, M.Agudo-Barriuso,H.C.deSousa,A.F.Ambrósio,M.E.M.Braga,A.R.Santiago, Porouspoly(␧-caprolactone)implants:Anovelstrategyforefficient intraoculardrugdelivery,J.Control.Release316(2019)331–348,http://dx.

doi.org/10.1016/j.jconrel.2019.09.023.

[11]C.A.García-González,J.Barros,A.Rey-Rico,P.Redondo,J.L.Gómez-Amoza,A.

Concheiro,C.Alvarez-Lorenzo,F.J.Monteiro,AntimicrobialPropertiesand OsteogenicityofVancomycin-LoadedSyntheticScaffoldsObtainedby SupercriticalFoaming,ACSAppl.Mater.Interfaces10(2018)3349–3360, http://dx.doi.org/10.1021/acsami.7b17375.

[12]Y.X.J.Ong,L.Y.Lee,P.Davoodi,C.-H.Wang,Productionofdrug-releasing biodegradablemicroporousscaffoldusingatwo-step

micro-encapsulation/supercriticalfoamingprocess,J.Supercrit.Fluids133 (2018)263–269,http://dx.doi.org/10.1016/j.supflu.2017.10.018.

[13]K.Gong,M.Braden,M.P.Patel,I.U.Rehman,Z.Zhang,J.A.Darr,Controlled releaseofchlorhexidinediacetatefromaporousmethacrylatesystem:

supercriticalfluidassistedfoamingandimpregnation,J.Pharm.Sci.96(2007) 2048–2056,http://dx.doi.org/10.1002/jps.20850.

[14]Y.-M.Corre,A.Maazouz,J.Duchet,J.Reignier,Batchfoamingofchain extendedPLAwithsupercriticalCO2:influenceoftherheologicalproperties andtheprocessparametersonthecellularstructure,J.Supercrit.Fluids58 (2011)177–188,http://dx.doi.org/10.1016/j.supflu.2011.03.006.

[15]X.H.Zhu,L.Y.Lee,J.S.H.Jackson,Y.W.Tong,C.-H.Wang,Characterizationof porouspoly(D,L-lactic-co-glycolicacid)spongesfabricatedbysupercritical CO2gas-foamingmethodasascaffoldforthree-dimensionalgrowthof Hep3Bcells,Biotechnol.Bioeng.100(2008)998–1009,http://dx.doi.org/10.

1002/bit.21824.

[16]S.Milovanovic,D.Markovic,A.Mrakovic,R.Kuska,I.Zizovic,S.Frerich,J.

Ivanovic,SupercriticalCO2-assistedproductionofPLAandPLGAfoamsfor controlledthymolrelease,Mater.Sci.Eng.C.99(2019)394–404,http://dx.

doi.org/10.1016/j.msec.2019.01.106.

[17]M.A.Fanovich,P.Jaeger,Sorptionanddiffusionofcompressedcarbondioxide inpolycaprolactoneforthedevelopmentofporousscaffolds,Mater.Sci.Eng.

C32(2012)961–968,http://dx.doi.org/10.1016/j.msec.2012.02.021.

[18]C.-X.Chen,Q.-Q.Liu,X.Xin,Y.-X.Guan,S.-J.Yao,Poreformationof poly(␧-caprolactone)scaffoldswithmeltingpointreductioninsupercritical CO2foaming,J.Supercrit.Fluids117(2016)279–288,http://dx.doi.org/10.

1016/j.supflu.2016.07.006.

[19]S.H.Kim,Y.Jung,S.H.Kim,Abiocompatibletissuescaffoldproducedby supercriticalfluidprocessingforcartilagetissueengineering,TissueEng.Part CMethods19(2013)181–188,http://dx.doi.org/10.1089/ten.tec.2012.

0170.

[20]E.DiMaio,E.Kiran,Foamingofpolymerswithsupercriticalfluidsand perspectivesonthecurrentknowledgegapsandchallenges,J.Supercrit.

Fluids134(2018)157–166,http://dx.doi.org/10.1016/j.supflu.2017.11.013.

[21]C.-X.Chen,H.-H.Peng,Y.-X.Guan,S.-J.Yao,Morphologicalstudyonthepore growthprofileofpoly(␧-caprolactone)bi-modalporousfoamsusinga

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