In vivo interactions between tungsten microneedles and peripheral nerves.

ContentslistsavailableatSciVerseScienceDirect

Medical

Engineering

&

Physics

j o ur n a l ho m e p age : w w w . e l s e v i e r . c o m / l o c a t e / m e d e n g p h y

In

vivo

interactions

between

tungsten

microneedles

and

peripheral

nerves

Pier

Nicola

Sergi

a,∗

, Winnie

Jensen

b

_{, Silvestro}

_Micera

a,c

_{, Ken}

_Yoshida

d

a_{BioRoboticsInstitute,ScuolaSuperioreSant’Anna,Italy}

b_{DepartmentofHealthScienceandTechnology,AalborgUniversity,Denmark} c_{InstituteforAutomation,SwissFederalInstituteofTechnology,CH,Switzerland}

d_{BiomedicalEngineeringDepartment,IndianaUniversity-PurdueUniversityIndianapolis,USA}

a

r

t

i

c

l

e

i

n

f

o

Articlehistory:

Received13December2010 Receivedinrevisedform28July2011 Accepted19September2011 Keywords:

Biomechanics

Peripheralnervoustissue Neuralinterfaces Indentation

Microneedle/livingnervedynamical frictioncoefficient

a

b

s

t

r

a

c

t

Tungstenmicroneedlesarecurrentlyusedtoinsertneuralelectrodesintolivingperipheralnerves. How-ever,thebiomechanicsunderlyingtheseproceduresisnotyetwellcharacterized.Forthisreason,the aimofthisworkwastomodeltheinteractionsbetweenthesemicroneedlesandlivingperipheralnerves. Asimplemathematicalframeworkwasespeciallyprovidedtomodelbothcompressionoftheexternal layerofthenerve(epineurium)andtheinteractionsresultingfrompenetrationofthemainshaftof themicroneedleinsidethelivingnerves.TheinstantaneousYoung’smodulus,compressionforce,the workneededtopiercethetissue,puncturingpressure,andthedynamicfrictioncoefficientbetweenthe tungstenmicroneedlesandlivingnerveswerequantifiedstartingfromacuteexperiments,aimingto reproducethephysicalenvironmentofrealimplantations.Indeed,abetterknowledgeofthe interac-tionsbetweenmicroneedlesandperipheralnervesmaybeusefultoimprovetheeffectivenessofthese insertiontechniques,andcouldrepresentakeyfactorfordesigningrobot-assistedprocedurestailored forperipheralnerveinsertion.

© 2011 IPEM. Published by Elsevier Ltd. All rights reserved.

1. Introduction

Thereareseveralmedicalproceduresthatinvolvetheinsertion ofneedlesintobiologicaltissues:needlesareusedtoplace radioac-tiveseedsclosetoclustersoftumourcells(brachytherapy)[1],to reachlessaccessiblesitesandextractbiologicalspecimens(biopsy) [2,3],andtoinoculatedrugswithhighaccuracyinsidethebody (severaltypesofinjections)[4].Theyarealsocommonlyusedin microneurography[5,6].

Since thesekinds of procedures canbe intrinsically difficult andcansometimescausecomplications,alsoafterintense train-ingbysurgeons,severalstudieswereconductedtoinvestigatethe behaviourofneedlesduringinsertioninsofttissues.Inthese stud-ies,theneedlesweremodelledas linearelasticwithgeometric nonlinearities[7–9],andsimulationswerevalidatedusing numer-icalmodelsor phantomtissues.Theworknot onlycontributed tounderstandingtheseinsertionprocedures,butalsoprovideda generalizationtoautomatethem. Aparticularclass ofinsertion involvestheuseofmicroneedleswhichareusedforplacingneural interfacesintoperipheralnerves.Inparticular,exvivoinsertionof

∗ Correspondingauthorat:ScuolaSuperioreSant’Anna,piazzaMartiridella Libertà,33,56127Pisa,Italy.Tel.:+39050883135;fax:+39050883101.

E-mailaddress:[email protected](P.N.Sergi).

theseneedleshavebeenexperimentallydescribedinporcine[10] andrabbit[11]nerves.

Althoughthebehaviourofperipheralnerveshasalreadybeen studiedinradialcompressionexperimentsaimingtosimulatethe applicationofcuffelectrodes[12],thebiomechanicsofinteraction betweentungstenmicroneedlesandlivingperipheralnerveshas notbeensufficientlycharacterizedyet.

Indeed,thisknowledgecouldbeusefultoimprovethequality ofstandardinsertionprocedures,andcouldrepresentakeyfactor forphysicallybasedfeedbackaimedatmonitoringrobot-assisted procedures[4,13]inperipheralnervepunctureandinsertion tech-niques.

Therefore,theaimoftheworkwastoprovideasimple theo-reticalframeworkforanalysingtheexperimentalresultsachieved duringinvivoinsertionoftungstenmicroneedles.Theframework wasabletoaccountforthemainstepsoftheinsertion process, consideringontheonehandboththematerialofthemicroneedles andtheirtipgeometry,andontheotherthebiomechanical-based responseofthelivingnerves.Inparticular,themodelwasableto quantify notonlypiercingpressures,forces, andwork,but also physical parameters,suchas theinstantaneousYoungmodulus of livingperipheralnervesand thedynamic frictioncoefficient, characterizingtissueresponseandinteractionwiththetungsten microneedles.

Thiskindofdatacouldbeusefultoimproveinteractionmodels accountingforcomplexanddissipativeeffects.

1350-4533/$–seefrontmatter © 2011 IPEM. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.medengphy.2011.09.019

748 P.N.Sergietal./MedicalEngineering&Physics34 (2012) 747–755 2. Materialsandmethods

2.1. Animalpreparation

Insitu acuteexperimentswereperformedontheperipheral nervesofthreeDanishLandracepigs(∼8–9monthsold weigh-ingabout45kg).Allexperimentalprocedureswereapprovedby theAnimalExperimentsInspectorateundertheDanishMinistryof Justice.

The pigs were anesthetized using a mixture of Xylazine (Rompun®_{, 20ml/l), Ketamine (Ketaminol}®_{, 50mg/ml),}

Butor-phanol Tartrate (Turbugesic®_{, 10mg/ml) and a combination of}

Tiletamin and Zolazepam (combined in Zoletil, 50mg/ml). The animalswereintubatedand placedona veterinaryanaesthesia ventilator(model2000,HallowellEMC,USA) at15breaths/min. Anaesthesiawasmaintainedusinga50–50%air/oxygenmixture with 1–1.2% Isoflurane. The animals received 0.9% NaCl saline bycontinuousIVinfusionthroughearveintoprevent dehydra-tion,androcuroniumbromide(Esmeron®_{,10mg/ml)andFentanyl}

(“Hameln”50␮g/ml)toprovideanalgesiathroughouttheentire experiment.Theanimals’heartrateandoxygensaturationwere monitoredthroughouttheexperiment(Fig.1a).

2.2. Experimentalmethodsanddataacquisition

Surgical access was created in the upper forelimb to the ulnar and mediannerves, and thesite of insertion waschosen approximately50mmabovetheelbow.Preciseimplantationswere performedataconstantvelocity[14]of2mm/s,intheulnarnerves. Thecompressiveforcewasmeasuredusingaloadcell(Sensotec Inc.,Model31/1435-02,maxload0.1kg,resolution1.31mV/g).A malefittingontheloadcellwasusedtoacceptafemaleLuerlock ontowhichtheneedlesweremounted(Fig.1b).

The nerves were elevated using a plastic platform with a 4mmdiameterhole(seeFig.1b)centeredunderneaththem.The microneedletipswereperpendicularlyplacedslightlyabovethe externalsurfaceofthenerves,andwerethenadvancedintothem byamotor-controlled(MaxonDCMotor22-60-881,JVLIndustri ElektronikA/S,DK)hydraulicmicromanipulator(Narishige MMO-220)witharesultingmovementresolutionof0.25␮m.Aftereach insertion,theneedlewasrepositionedina differentpartofthe nervetoavoidmultipleinsertionpointsinthesamelocation.

Twogroupsofelectro-sharpenedtungstenmicroneedles,with differentshaftdiameters(∅)andconicaltipswereusedtoperform 32insertions:19and 13trialswereconductedusing micronee-dleswith∅=75␮mand∅=100␮m,respectively.Moreover,allof themwereassumedtohaveYoungmodulusandPoissonratioof En=411GPa,andn=0.28,respectively.

Round tungstenrods (no insulation, 75 and 100␮m diame-ters,A-MSystems)werecutinto2cmlengthsandthenmanually electro-sharpenedtocreateasharptip.Thetipsweresharpened byloweringoneendintoa2NKNO3 solution,placinga∼8VAC

potentialacrossit,andusingalargecarboncounterelectrodefor 20–40stoetchthem.Thetipswerevisuallyinspectedthrougha microscopeduringandaftertheelectrolysesprocedure.Finally,the openingangleofthetipwasmeasuredfollowingoptical photomi-crography(Fig.1c).Allelectrodeswerecleanedinde-ionizedwater beforeimplantationtoremoveanyresiduefrometchant.

The microneedles were inserted according to a ramp–hold–ramp profile (Fig. 1d), and the force and position signals(Fig.1e)werefilteredbeforesampling(1storderlowpass filter, sampling frequency=2.5kHz, NI DAQ card-6204E). The sampleddatawerealsofilteredoffline,tominimizesuperimposed physiologicalandinstrumentalnoise.Inparticular,therelaxation phase wasfilteredusinga 3rdorderButterworthlowpassfilter

(F3dB=0.325Hz),whilethecompressionandinsertionphaseswere

filteredwitha3rdorderButterworthlowpassfilter(F3dB=12.5Hz).

2.3. Modellingofcompressionandpuncture

Whenthetipof a microneedlecomesintocontact withthe outermostlayerofthenerve(epineurium),thepressureincreases (Fig.1e,phaseA)andthelayerdeforms:therelationbetweenthese setsofquantitiesisgovernedbyconstitutiveequations.

SinceanonlinearKelvinmodel[15]wasusedtoapproximate the generalbehaviour of the living nerves,and thevelocity of microneedleswasconstantforallphases(Fig.1e,phasesA–B–D), theinteractionforceswerewrittenas:

F(z,

v

s)=fs(z)+k(z)

v

s



1−exp



−

_v

z s



(1) wherezisthedimplingofthetissue(which,inthiscase,equals themicroneedletipdisplacement),

v

=dz/dtisthevelocityofthe needletip,fs(z)isanonlinearforce–displacementfunctionandk(z)

anonlinearspringconnectedwithanonlineardamperb(z),witha characteristicrelaxationtime_␶s=b(z)/k(z).Theexponentialtermof

Eq.(1)dependsonthedimplingofthetissuebeforethepuncture (z),aswellasonthecharacteristicrelaxationtimeofnerve(s)

andpiercingvelocity(

v

).Sinceinthisstudyvsz,theasymptotic

expansionofEq.(1)withrespecttovswasused:

F(z,

v

s)=fs(z)+k(z)

v

s



1−exp



−

_v

z_ s



=fs(z)+k(z)



z+O



₁

v

s



(1.1) andEq.(1)wasapproximatedwithEq.(1.2):

F(z) ∼_{= f}s(z)+k(z)z (1.2)

Eq.(1.2)showsthatthetotalforceisindependentoftheviscous characteristicsofthetissueforanychoiceoffs(z)andk(z).

Aboveall,duetothesmallsizeoftheneedletip(100␮m) withrespecttothenervediameter(3–5mm),thisproblemwas treatedasanindentationofanincompressibleelastictissue(i.e.the livingnerve)performedwithaconicalindenter(i.e.the micronee-dletip).Consequently,Eq.(1.2),whichimplicitlyrelatesforcesand dimpling,wasmadeexplicitbymergingthetwotermsandusing Sneddon’sapproach[16,17]togetherwiththechangesduetothe realgeometryoftheconicaltip[18].Furthermore,theliving periph-eralnerveswereconsideredanonlinearelasticmaterial,andthe measuredloadF(z)waswrittenas:

F(z)=8tg(˛)_3 M(E,z)z[z+ ¯ ()] (2) where E is the instantaneous Young’s modulus of the nerve, M(E,z)=Eexp(bz)modelsthenonlinearelasticityofthenerve[12] undergoingafinitedeformation(indentation)andassumed incom-pressible[19],˛isthehalfangleoftheneedletip,zisthedimpling ofthenerve(ortipdisplacement),and ¯ ()isafunctionofthe cur-vatureradiusofthetip,withthedimensionofalength.According to[18],forbothgroupsofmicroneedles,Eq.(2.1)canbewrittenas:

¯

()=c12+c2 (2.1)

wherec1=1.5×10−4m−1andc2=1.17×10−1.

Thehalfangles(˛)andthetipradii()ofthemicroneedletips weremeasuredfromdigitalpictures,andEq.(2)wasusedtofit experimentaldata(phaseA)throughnonlinearoptimizationwith parameteridentificationbasedonmeasuredcompressionforces (quasiNewtonianalgorithm,Scilab©INRIA).

Allexperimentsperformedwithmicroneedleswith∅=75␮m and∅=100␮mwereseparatelygroupedtoextractthemean val-uesofthequantities(E,b)characterizingthetissueresponse.

Fig.1.(a)Generalviewofexperimentalsetup.(b)Magnificationoftungstenmicroneedleandperipheralnervewithsupport.(c)Microneedletipgeometry,themeasures areindegreesandmicrometres.(d)Theramp-old-rampprofileofinsertion-rest-extractionofthemicroneedle.(e)Acharacteristiccurve(forcevs.time),inwhichdifferent phasesareunderlined.A:Compressionphase(frombeginningtopoint˛).˛:Pointofpuncture,wherecharacteristicdiscontinuityinthecompressionforcecanbeseen.B: Insertionphase.ˇ:Endoftheinsertionphase,wherethemovementofthemicroneedlecomestoastopinsidethetissue.C:Relaxationphase.:Retractionpoint,where theneedlebeginstoberetractedfromthetissue.D:Retractionphase.ı:Extractionofthemicroneedlefromthetissue.Thenegativevaluesoftheforces(traction)aredue tobindingofthetissueontheexternalsurfaceofthemicroneedle.

750 P.N.Sergietal./MedicalEngineering&Physics34 (2012) 747–755

Fig.2.Force–displacementcurvesduringthephaseofpiercing.Thisphasecanbe theoreticallydescribedasanindentation.(a)Experimental(lightgrey)indentations witha∅=75␮mtungstenmicroneedle,theoreticalfittingcurve(solidblack).(b) Experimental(lightgrey)indentationswitha∅=100␮mtungstenmicroneedle, theoreticalfittingcurve(solidblack).

Tointegratethisdirectbiomechanicalapproach,anindirect sen-sitivityanalysiswasperformedtofurtherinvestigatethedegreeof nonlinearityofthecompressionforce.Letq(z,n)beapolynomial functionofnorder,asshowninEq.(2.2):

q(z,n)=

n



j=1

nzn (2.2)

wherenaretheconstantcoefficientsofeachn-orderterm(the

0-ordertermissetidenticallytozerobecausetheforceof com-pressioniszeroforz=0).Thesetofexperimentalcurveswasfitted withthesephenomenologicalfunctionsbyvaryingthemaximum orderofpolynomialapproximation(n-index)inordertoevaluate boththeresidualsandR2 _index(R2_{isthesquareofthe}

correla-tionbetweentheresponsevaluesandthepredictedvalues).The orderofnforwhichtheimprovementofindicesstopsistheorder ofnonlinearityofEq.(2.2).

RecallingEq.(2),theglobalworkappliedtothenerveduring compressionuptothepuncturewaswrittenas:

W=



z0

0

F(z)dz (3)

where z0 is the coordinate where the tissue was pierced.The

nervewaspuncturedwhenacharacteristicmaximumpressurewas exceeded,thesurfaceofthenerveyieldedandacrackopenedin thetissue.Atthisstage,thecentralradiusofthecrackwasassessed withtheradiusofthemicroneedletip.Duringinsertion,thesizeof thecrackincreaseduptotheexternaldiameterofthemainshaftof themicroneedle:intheeventofyielding,thetheoreticalpressure atthemicroneedle-nerveinterfacewasroughlyassessedbyusing thefollowingequation[20]:

p(r)= 1−rt/r

(1−n) /En+3/[2Ets(εr)]

(4) where En and n are the Young and Poisson modules of the

needle, r and rt are the radii of the needle shaft and of the

needle tip, and Ets is the instantaneousYoung modulus of the

tissue.

Whentheinitialmicrocrackexpanded intoa hole,the non-linear behaviour of the tissue wasmodelled with thefunction Ets(r)=Eexp(ˇεr),whereεr=(rn−rt)/rt andˇ>0representan

exponentialconstantmodellingtheradialstrainhardeningofthe tissue[12].Eq.(4)isstrictlyvalidforapairofperfectlyelastic mate-rialsandusuallyprovideshighpressurevalueswhenther/rtratio

ishigh,asinthiscase.

Nevertheless,themaximumpressurethatcanbeobtainedat theinterfaceisyieldingpressure;viscousflowsarisebeyondthis thresholdwhichlowerthelocalfieldofcontactstresses.Eq.(4) showstheneedforyieldingattheinterfacebetweenthenerveand themicroneedlesbutisnotabletoquantifyit.Tothisaim,itcould beusefultorecallthebehaviourofthenerveunderthe micronee-dletip,beforeopeningofthehole:thetissueyieldsandviscous flowsarisebeforefracturingoftheoutermostlayer(viscoelastic fracture).

Asaconsequence,thesuperficialyieldingpressurewas reason-ablyapproximatedwiththepiercingpressure:

p(r)= ¯py=F(z0)

A (5)

whereA=[22_+(r+)



_(r−)2

+L12]andistheradiusof

curvatureofthemicroneedletip,risthenominaldiameterofthe mainshaft,andL1istheheightoftheconicalregionattheendofthe

needle[15,21].Toachieveameanvalueofthisparameter,digital picturesofmicroneedleswereanalysedandmeasured.Itshouldbe notedthatEq.(5)providesthesuperficialyieldingpressure,which differsfromthemeanpressureoverthemicroneedlecrosssectional areagivenby:

¯pc=

4F(z0)

d2 (5.1)

wheredisthenominaldiameterofthemicroneedle.

Atotalforceisappliedonthemicroneedlesafterpuncturingof thetissue,whichderivesfromthesumoffrictionandaconstant cuttingforce[14].Aboveall,thetotalinteractionforceincreases almostlinearlyduringinsertiontogetherwiththecontactsurface ofthemicroneedle.

Forthesakeofsimplicity,thefrictionwasmodelledas Coulom-bian,thenthemeandynamiccoefficientwaswrittenas:

¯ _d= ¯

¯py

sgn(

v

) (6)

where ¯=m/2risthemeanshearstressonthelateralsurfaceof theinsertedmicroneedle,misthederivativewithrespecttozof

Fig.3. (aandb)Polynomialfunctionsfittingexperimentalcurvesofcompressionwitha∅=75␮m(a)anda∅=100␮m(b)microneedle.Allfunctionswithn≥2perform thesamefitandareshownsuperimposedtothesolidblackcurve.(candd)Residualsofpolynomialfitsofexperimentaldataachievedwitha∅=75␮m(c)and∅=100␮m. (d)Forn≥2residualsareexactlysuperimposedtotheblackarea.(e)ChangesofR2_{indexvaryingthen-index(maxdegreeofpolynomialfunctionandorderofnonlinearity}

ofthecompression)forbothsetsofexperiments.Forn≥2R2_{indexremainsconstant,anddoesnotallowdirectassessmentofthen-orderofcompression.(f)Relevance}

analysisofconstantcoefficientsofallfittingfunctions:forbothsetsofexperimentsonlythelinear(1)andquadratic(2)termsaredifferentfromzero(lightgrey=0,dark

grey>grey>0,white=notallowed),revealingaquadraticcoreofthecompressionphenomenon.Forsakeofsimplicityonlyfourpowersareshown.

thestraightlinefittingthetotalforce,andsgn(

v

)isthesign func-tionofthemicroneedlevelocity

v

.Thepiercingpressureandthe slopeoftheinsertionforceareunivocallyrelatedforeachcurve. Asaconsequence,eachcurvewasseparatelyanalysed to quan-tifythefrictioncoefficientavoidingerrorscomingfromtheuseof meanvalues.Additionally,thisapproachallowedustoinvestigate thenatureofthedistributionofthedynamicalfrictioncoefficient amongexperiments.

3. Results

3.1. Anelasticframeworktodescribeinteractionbetweennerve andmicroneedles

For insertion experimentsperformedwiththe firstgroupof tungstenmicroneedles(∅=75␮m)meancharacteristicrelaxation timeand meandimplingwererespectively ¯s75=28.9558sand

752 P.N.Sergietal./MedicalEngineering&Physics34 (2012) 747–755 ¯z075=2.6456mm,whileforexperimentsperformedwiththe

sec-ondgrouptheywere(∅=100␮m), ¯s100=28.8158sand ¯z0100=

3.6369mm.Inbothcases,

v

¯s75 ¯z075and

v

¯s100>> ¯z0100,then

Eqs.(1.2)and(2)wereusedandtheelasticframeworkwasableto correctlydescribetheexperimentalresults.

3.2. Geometryofmicroneedlestipsandinstantaneousresponseof thenerve

Thehalf angles(˛) and thetip radii ()of the microneedle tipsforthefirstgroupwere˛=10.25±0.5◦and=1.7±0.577␮m, while for the second group they were ˛=7.875±0.478◦ and =2.48_±0.349_␮m:thesevalueswereinsertedinEqs.(2)and(2.1) tofitdataresultingfromexperimentalindentations(phaseA).

Fig.2shows bothexperimentsandfittingcurves:Eq.(2) fit-tedexperimentaldataof thefirst group(R2_{=0.8591) totheset}

{¯E75=22.2265kPa, b75=0, ¯ ()75=1.99×10−4mm}, and also

fittedexperimentaldataofthesecondgroup(R2_{=0.9649)tothe}

set{¯E100=32.9663kPa,b100=0, ¯ ()100=3×10−4mm}.

Furthermore,theindirectanalysisofthecompressionclearly showedaquadraticnatureofthephenomenon(seeFig.3a–f).The analysisofbothresidualsandR2_{indexesdidnotsupportthis}

con-clusion.Indeed,inbothcasesforn≥2therewasasuperimposition ofresidualsandaconstancyofR2_{asshowninFig.3c–e.}

However,therelevance analysisof thecoefficients offitting functions(Fig.3f)showedthatonlythelinearandquadraticterms weredifferentfromzeroforallpolynomialswithn≥2andforboth groupsofmicroneedles.

3.3. Piercingandinsertionfeatures

TissuedimplingandpiercingwasestimatedwithEq. (3).To this aim, thecontact areasfor both groups were calculated as A75=0.03304±0.0038mm2 andA100=0.0663±0.0130mm2,and

Eq.(3)ledto ¯W75=28.4912␮Jand ¯W100=60.8844␮J.Moreover,

Fig.4a showstheboxplotsofbothquantitiesW75andW100.In

particular,thelinesinsidethecentralboxesrepresentthe medi-ans ˜W75=22.9210␮Jand ˜W100=54.0432␮J,theupperandthe

lowerlinesoftheboxesshowtheupperandlowerquartiles,and the error bars include outliers. Fig. 4b shows thebox plots of thepiercingforces:themeanvalueswere ¯Fp75=27.4301mNand

¯Fp100=54.1736mN,whilethemediansofthesamequantitieswere

˜Fp75=24.094mNand ˜Fp100=51.4703mN.

Eq.(4)providesamuchlargertheoreticalinterfacialpressure thantheyieldingpressureofanysofttissue.Indeed,forˇ=0.145 and ¯E75or ¯E100,thepressureswerefoundtobe ¯p75≈110MPaand

¯p100≈162MPa,whilethetractionyieldstressfora 1002Asteel

was131MPa.Itshouldbenoticed,accordingto[12],thatavalue of ¯ˇ=4.03wasfoundforacircularcompressionofrabbitsciatic nerves.Therefore,Eqs.(5)and(6)wereusedtoapproximatethe yieldingpressureandthedynamicfrictioncoefficient.

Indeed, Fig. 5 shows the box plots of the piercing pres-sures and dynamic friction coefficients for each specimen and for each kind of microneedle. The mean and median values of yield contact pressure, pressure on the cross sectional area anddynamicfrictioncoefficientformicroneedleswith∅=75␮m were: ¯py75=0.8302MPa, ¯pc75=6.2121MPa,¯d75=0.1626,and

˜py75=0.7292MPa, ˜pc75=5.4565MPa, ˜d75=0.1748. Similarly,

for the ∅=100␮m group, the same quantities were ¯py100=

0.8171MPa, ¯pc100=6.9010MPa, ¯d100=0.1900 and ˜py100=

0.7763MPa, ˜pc100=6.5567MPa,˜d100=0.1726.

Finally,Fig.6showsthequantile–quantileplotsofdistribution ofthedynamicfrictioncoefficientamongexperimentaltrialsfor bothgroupsofmicroneedles.Inparticular,theShapiro–Wilktest wasperformedto assessthe degreeof “normality” of distribu-tion(R:Alanguageandenvironmentforstatisticalcomputing.R

Fig.4.(a)Boxplotsofworktoreachthenervepunctureforbothgroupsof exper-iments:thelinesinsidethecentralboxesrepresentthemedians ˜W75=22.9210␮J

and ˜W100=54.0432␮J,theupperandthelowerlinesofboxesshowtheupperand

thelowerquartiles,theerrorbarsincludeoutliers.(b)Boxplotsofforceforpiercing thenervesusingdifferentdiametersofmicroneedles:centrallinesrepresentthe medians ˜Fp75=24.094mNand ˜Fp100=51.4703mN.

FoundationforStatisticalComputing,UniversityofVienna).Forthe firstgroup,thistestresultedinW=0.9311,p-value=0.1623,while forthesecondgroup,W=0.9452,p-value=0.5278,whereWisthe squareofthecorrelationbetweenexperimentaldataandnormal distribution,whilethep-valueistheprobabilityofobtainingatest statisticatleastasextremeastheonethatwasactuallyobserved, assumingthat thenullhypothesis is true.Inthis case, thenull hypothesiswasthatexperimentaldata(d)camefromanormally

distributedpopulation. 4. Discussion

4.1. Asimpleframeworktomodelsuperficialinteractions

In this manuscript, the interactions between tungsten microneedles and the nerve were described using a simple mathematical framework. Specifically, the first phase of com-pression was modelled with an elastic indentation. The more theviscous effects were negligiblein a standard Kelvin model, the more this simplificationapproached theexact solution. As previously shown, the viscous effects slightly influenced the responseoftheperipheralnervesaccordingtothechosenvelocity of punctureand insertion, whichapproximated thatof surgical implants. In particular, viscous effects mainlyaffected the end

Fig.5.(a)Boxplotsofpiercingpressureatpuncturefordifferentdiameterof microneedles:centrallinesrepresentthemedians ˜py75=0.7292MPaand ˜py100=

0.7763MPa.(b)Dynamiccoefficientoffrictionduringinsertionintolivingnervesfor bothdiameterofmicroneedles:centrallinesrepresentthemedians˜d75=0.1748

and˜d100=0.1726.

part of indentation; furthermore, maximum difference with a fully elastic description was approximately 2% at the end of compression,whileatthebeginningitwasnegligible.

Moreover,theclassicalSneddon’s approach wasnot directly used,sincethisapproachisstrictlyvalidforaninfinitelysharp con-icalindenter,whiletherealneedleshadtipswithafiniteradiusof curvature.Therefore,amodificationoftheclassicaltheorywasused accordingto[12]toextracttheinstantaneousYoung’smodulusof thelivingperipheralnervoustissue.

In particular, the mean values of this parameter (22.2265–32.9663kPa) were comparable with mean data from othercompressionexperimentsonrabbitnerves.Indeed,aYoung modulus of41.6±5kPa [22] wasfoundfor in vitro unconfined compressions,andavalueof66.9±8kPa[12]wasfoundforinvivo circularcompressions.

Furthermore,theachievedvalueswerecomparablewith physi-calpropertiesofotherbiologicaltissuesandshowedthattheliving peripheralnervesofpigswereasstiffasdermis(35kPa).Again, theirstiffnesshadthesameorderofmagnitudeofmusclestiffness (80kPa)[23],andtheyweremorecompliantthanarticularcartilage [24].

In addition, although peripheral nerves were consid-ered as nonlinear elastic (Eq. (2)), the achieved values of b (1×10−2<b<1×10−3) showed a practically linear behaviour

Fig. 6.Quantile–quantile plotsof dynamicfriction coefficients achievedwith microneedlesof∅=75mm(a)and∅=100mm(b).Inbothcasesthenormal dis-tribution(straightboldline)ishighlyconsistentwithexperimentalvalues(dotted linesshow95%confidencebounds).

duringlocalizedcompressions(M(E75,100,z)≈ ¯E75,100)with

lim-itedvalues ofz.Asaconsequence,theYoungmodulusofliving nerves waspracticallyconstant and equal totheinstantaneous Young modulus,andforsakeofsimplicitytheparameterbwas settozero.Thisapproachledtoapolynomial(2◦order) indenta-tionlawconsistentwiththeindirectphenomenologicalanalysis (Fig.3a–f)andwiththeapproachgivenin[14].

Finally,thissimpleframeworkwasconsideredcorrectsincethe characteristicrelaxationtimeofthenervemultipliedbythe veloc-ityofindentationwasgreaterthanthecharacteristicdeflectionof thenervesurface.Sinceperipheralnervesmayexperiencealimited dimplingunderthemicroneedletip,thistheoreticalframeworkis still validandusableforalltissueshavingsimilarcharacteristic relaxationtimeandequalorhigherinsertionvelocities. Neverthe-less, viscoelasticeffects havetobeconsideredfor lowinsertion velocitiesorforshortercharacteristicrelaxationtime.

754 P.N.Sergietal./MedicalEngineering&Physics34 (2012) 747–755 4.2. Piercingandinsertionofmicroneedlesintoperipheral

nerves:interactionfeatures

Compressionforceswereusedtogaugeinteractionsbetween livingnervesandmicroneedles.Inparticular,theachieved pierc-ingforcesweregreaterthanthosefoundinsimilarexperiments withexvivoporcine[10]andrabbit[11]nerves.Thiscouldbedue todifferencesinexperimentalsetup.In[10],indeed,thenervewas keptunderaxialtensioninasalinebath,whereasinthese experi-mentsthenerveswerekeptintheair,andaperforatedsupportwas placedunderthemtoeasepiercingandtheinsertionof micronee-dles.However,inbothcases,thepartsofthenerveinteractingwith themicroneedleswerefreetodimpleunderthetipforces.

Anotherreasonforthiswasthegreaterstiffnessoftheliving nerveswithrespecttosimilarexvivospecimens.Indeed,adense microcirculationsysteminsidetheliving nervesprovides nour-ishmenttoallinternalsubstructures,andpressurizedbloodflows insmallveinsandcapillaries.Moreover,thenervousfasciclesare filledwithaphysiologicalfluidunderpressure.Asaconsequence, theglobaltissueresponsetolocalizedindentationisaffectedby thisinternalpressurization.Furthermore,inexvivospecimens,the lackofinternalpressureinfascicles,smallveinsandcapillaries, andpost-mortemautolysis,whichsoftenstheconnectivetissues, worktogethertolowertheglobalresponseofthenervesto exter-nalmechanicalstimuli.Thedifferencebetweeninvivoandexvivo piercingforceswasmostlikelyduetothecomplexinteractionof thesetwocauses,whichgenerallyseemstobevalidforothertissues also[25–27].

Again,itcouldbeworthpointingoutthedifferencesbetween themeanyieldingpressuresandthemeancross sectional pres-sures.Indeed,fortheanalysedgroupsofmicroneedlesthemean crosssectionalpressureswere∼7.4825and∼8.4458timesgreater thanthesuperficialyieldingpressure.Inparticular,since micronee-dleshavetobearthemaximumpiercingforcewithoutanybuckling effect[10,11,28],thecrosssectionalpressureisrelevantfor design-ingbothgeometryandmaterials.

Thepreviousdifferencewasduetotheprocedureusedfor esti-matingthecontactarea.Inthiscase,theareawastheconicalarea ofthetipincontactwiththedimpledtissue,accordingto[21].This choiceledtoamorecloseassessmentoftheforceforthesurface unitofthedimpledtissue.Sincethetipofthemicroneedlesank intothesurrounding(soft)tissuebeforecompression,thecontact areawasassumedtobeconstantforthewholecompression.

Eq.(4)wasusedtoassesstheinterfacialpressurebetweenthe mainshaftofthemicroneedlesandthelivingperipheralnerves. Since this approach exactly assesses the interference pressure betweentwo elasticmaterials,Young’smoduliof tungstenand nerveswereusedinthiswork.Aboveall,aspreviouslydiscussed, amicrocirculationsystemnourishestheinnerpartofthenerve and thefasciclesare filledwithendoneural fluid:sincethe tis-sueissoakedinbiologicalfluids,theincompressibility(≈0.5) [19]ofthewholenerve isacceptableandEqs.(2) and(4)were usedinthesesimplifiedforms.Furthermore,thestiffness ofthe microneedleswasassumedtobemagnitudeshigherthanthatof thelivingperipheralnerves:experimentsconfirmedthis assump-tion(En>> ¯E75,100)allowingEqs.(2)and(4)tobeindependent

fromthemicroneedlematerial.Inaddition,Eq.(4)onlyshowedthe needfortissueyieldingaroundthemainshaftofthemicroneedle. Asaconsequence,Eq.(5)wasusedtoassessthispressurebecause compressionandyieldingoccursimultaneouslyjustbefore pierc-ing.Therefore,thisprocedureallowedustoassessaquantitywhich isdifficulttoexplicitlyachieveinexperiments.

Finally, the interaction between peripheral nerves and microneedleswasroughlymodelledusingaCoulombiandynamic frictionmodel.Thiswasasimplificationofmorecomplex phenom-enathatarosebetweentheneedleshaftandthesurroundingtissue.

Nevertheless,thissimplemodelwasabletocatchthemain macro-scopicfeaturesofthisphenomenon,givingphysicallyreasonable valuesforthedynamicfrictioncoefficientbetweenbiologicaland conventionalmaterials,accordingto[29].Inaddition,astatistical analysisofdatawasprovidedtoinvestigatethecourseofthe dis-tributionofthedynamicfrictioncoefficients.First,aroughanalysis oftheabsolutedifferencesbetweenmeanandmedianvalueswas performedresultingin1.22×10−2(∼7.5%)forthefirstgroupand 1.74×10−2(∼10%)forthesecond.Althoughthesevaluesrevealed asimilarity,thiskindofanalysiswasnotabletoinvestigatethe globalcourseofthedistribution.Therefore,quantile–quantileplots werecreatedandtheShapiro–Wilksnormalitytestwasperformed. Theplotsshowedanalmostnormaldistribution,whilethetest pro-videdhighcorrelationindexes(W>0.9)andp-values>0.05forboth groups.Indeed,experimentaldatawereclosetothestraightline (normaldistribution)andthenullhypothesiswasacceptedinthe standardcaseof5%ofsignificancelevel.

5. Conclusionsandfutureworks

Insertion experiments together with a simple mathemati-cal framework wereprovided toinvestigate in vivo interaction between tungstenmicroneedles and ulnar porcine nerves. This approach allowedustoquantitatively assess themainphysical quantitiesfromwhichtheexperimentalcurvesdepend:the instan-taneousYoung’smodulus,compressionforce,theworkneededto piercethetissue,puncturingpressure,and thedynamic friction coefficientbetweentungstenmicroneedlesandlivingnerveswere quantified. Specifically,thedistribution of thedynamic friction coefficientwasfoundtobeapproximatelynormal.Thisstudycould provide usefulquantitiesfor modellingand automating [13,30] peripheralnerve insertion tasks. Aboveall,this framework can beextendedtoallcasesinwhichtissuedimplingissmallerthan theproductbetweencharacteristicrelaxationtimeand piercing velocity:forlongrelaxationtime coupledwithquitelow inser-tionvelocity,orshortrelaxationtimecoupledwithhighinsertion velocity.

Futureworkwillextendtheexperimentaltrialstootherliving nervesfeaturingdifferentkindsofneedlesanddiverse combina-tionsofrelaxationtimeandpiercingvelocity,toexplicitlyaccount forviscoelasticeffects.

Acknowledgements

TheauthorsthankDr.JacopoCarpanetoforhisvaluablehelp. ThisworkwassupportedinpartbytheEuropeanUnion(EU)within theTIMEProject(FP7-ICT–2007-224012,Transverse, Intrafascicu-larMultichannelElectrodesystemforinductionofsensationand treatmentofphantomlimbpaininamputees).

Conflictofinterest None.

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