Effect of Shock-Induced Cavitation Bubble Collapse on …10.1038... ·  · 2017-07-071 Effect of Shock-Induced Cavitation Bubble Collapse on the damage in the Simulated Perineuronal

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Effect of Shock-Induced Cavitation Bubble Collapse on thedamageintheSimulatedPerineuronalNetoftheBrain.Yuan-TingWuandAshfaqAdnan*

MechanicalandAerospaceEngineering,theUniversityofTexasatArlington,Arlington,76010,USA*aadnan@uta.eduAppendix1:SimulationSet-upThedetailofoursimulationset-upisdescribedinthissection.

1. Equilibration:Theinitialsizeofthesimulationboxis16nm,16nm,and25nmcontainingatotalof599,205atoms.We

haveequilibratedthewholesystemfor60ps. In the first10psofequilibration,wekept thehyaluronan“fixed”but

releasedthisconstraint for thenext50psofsimulation.TheequilibrationwasperformedwithNPTensemble (fixed

numberof atoms, fixedpressure, and fixed temperature) at 300K and101 kPa. The temperature andpressure are

controlledbyusing“fixnpt”commandinLAMMPS1.ThiscommandperformstimeintegrationonNose-Hooverbased

equationsofmotiontogeneratepositionsandvelocitiessampledfromtheisothermal-isobaricensemble.Moredetails

about the scheme and implementation can be found in LAMMPS website1 and the linked references therein2-6.

Specifically,thetemperatureiscontrolledbythethermostatthatisappliedtothetranslationaldegreesoffreedomfor

theatoms.Theexternalpressureiscontrolledbythebarostatasscalerhydrostaticpressure.Forprescribedvaluesfor

thermostatandbarostattimeconstants(weused1psforthebarostatand50fsforthethermostat),thetime-averaged

temperatureandpressureoftheatomsattainthetargetvalues(i.e300Kand101kPa,respectively).

2. ShockGeneration:Wehavegeneratedshockusing“reflective-boundary”method.First,wehavereplacedtheperiodic

boundariesnormaltoz-axistoreflectingboundaries.Wehavegeneratedvacuumbetweenbulkatomsand+zdirection

(3nm)/–zdirection(7nm).Wehavethensubjectedtheentireboxofatomstoavelocity,vp,alongpositivez-direction.

Theappliedvelocityvpcausestheentireboxofatomspropeltowardsandeventuallyimpactthereflectiveboundaryat

thesamevelocityvp.Suchimpactonthereflectingboundaryinducesashockwaveontheimpactingatoms.Itisevident

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frompriorliteraturesthatthephysicsofshockwaveformedbyreflectionissameasconventionalpiston-drivenshock

waveformation.Theshockvelocitygeneratedbyoursystemagreeswithexperimentalresultsandothersimulationwork.

Appendix2:CavitationFormationandNucleationSiteIn this section,we have investigated the distance between cavitation-induced bubble and hyaluronan to determine the

minimumdistanceatwhichhyaluronanexhibitstableconfiguration.Thesimulationboxcontainingwater,hyaluronan,and

ionsareslowlystretchedupto23%involume,whichenablesnanocavitationtoform.

Thissetofsimulationisaimedtoobtainthecharacteristicdistancebetweennanobubbleandhyaluronan(FigureA1).The

initialsizeofthesimulationboxis16nm,16nm,and25nmcontainingatotalof599,205atomswitha12foldhyaluronan

(~500atoms),whichisthesameequilibratedboxinthemainarticle.Westretchedtheentiresimulateddomain,includingall

oftheatoms,for10.78%involume(3.47%inlength)within10ps.Thenwecontinuuedthesimulationforanother40pswith

fixeddoaminsize.Duringtheentiresimulation,thetemperatureisfixedat300Kwiththedampingconstantof12.5fs.

FigureA1shows the results. It canbeobserved thatwhen thebox started to stretch,pressure starts togodownbelow

atmospheric(i.e.,buildingupofnegativepressureortensilepressure).Oncethenegativepressureisreachedthecritical

pressureforbubblenucleation(inourcaseitis~-170MPa,whichisclosetotheexperimentalresultfrom7),bubblesstart

toform,andthepressurestopstobuildfurtherevenwhentheboxiscontinuedtoexpand.Aftertheboxstopstretching(10

ps),thepressurestarttoriseup.Itcanalsobeobservedthatthenear-sphericalbubblesareformedfrommanynucleation

sites.Mostbubbles,withanaveragesizeof~2nm,areseentonucleateabout~3-5nmawayfromthehyaluronan-liquid

interface.Thenearestbubblenucleationsitewecapturedhasthedistance~0.5nmfrombubblesurfacetothehyaluronan.

Attheendofthesimulation(50ps),allthecavitation-bubbletendedtomergeintoone,whichisthelowestenergystateat

givenconstraint.

Byobservingthe interactionbetweenthenewlynucleatedbubbleandhyaluronan, it isclearthathydrophilichyaluronan

tendstorepelthebubbleaway.Thebubblesareonlystableataminimumdistanceof0.5nmfromthehyaluronanimplying

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thepresenceofatleastoneortwolayersofwaterbetweenthebubblesurfaceandthehyaluronan.Theminimumdistance

of0.5nmislaterusedinthemainarticle.

Appendix3:Visualcomparisonofthethreesetsofsimulation(withrotatedHAasinitialcondition)InFig.A2,resultsofallthreesetsofsimulationshavebeenshown.ThethresholdofHAbreakingarethesameinallthree

sets.SincetheHAofthethreesetsarerotatedby90degreeseach,thebrokensegmentoftheHAareatdifferentlocation

butfollowingthesamepatternofbreakingglyosidicbondandbreakingglucosestructure(mostlyfor7.2km/scases).

References1 http://lammps.sandia.gov/doc/fix_nh.html(lastaccessedon5-15-2017)2 Plimpton,S.Fastparallelalgorithmsforshort-rangemoleculardynamics.Journalofcomputationalphysics117,1-

19,doi:10.1006/jcph.1995.1039(1995).

3 Shinoda,W.,Shiga,M.&Mikami,M.Rapidestimationofelasticconstantsbymoleculardynamicssimulationunderconstantstress.PhysicalReviewB69,134103,doi:10.1103/PhysRevB.69.134103(2004).

4 Martyna,G.J.,Tobias,D.J.&Klein,M.L.Constantpressuremoleculardynamicsalgorithms.TheJournalofChemicalPhysics101,4177-4189,doi:10.1063/1.467468(1994).

5 Parrinello,M.&Rahman,A.Polymorphictransitionsinsinglecrystals:Anewmoleculardynamicsmethod.Journal

ofappliedphysics52,7182-7190,doi:10.1063/1.328693(1981).6 Tuckerman, M. E., Alejandre, J., López-Rendón, R., Jochim, A. L. & Martyna, G. J. A Liouville-operator derived

measure-preservingintegratorformoleculardynamicssimulationsintheisothermal–isobaricensemble.JournalofPhysicsA:MathematicalandGeneral39,5629,doi:10.1088/0305-4470/39/19/S18(2006).

7 Azouzi,M.E.M.,Ramboz,C.,Lenain,J.-F.&Caupin,F.Acoherentpictureofwateratextremenegativepressure.

NaturePhysics9,38-41,doi:10.1038/nphys2475(2013).

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FigureA1.(a,b)Cavitation-inducedbubbleformationandcoalescence.Allwateratomsexceptthoseonthebubblesurfacehavebeenremovedforclarity.Theblueshadesrepresentbubblesurface.(c)Accumulatedpressureinthesimulationcell.

t=22ps t=50ps

a b

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FigureA2.AtomisticsimulationsnapshotsshowingevolutionofHAimpactedbyWHjet,basedonresultsfromsimulationset(a)one(b)twoand(c)three.

a b c