Effect of Shock-Induced Cavitation Bubble Collapse on …10.1038... · · 2017-07-071 Effect of...
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Effect of Shock-Induced Cavitation Bubble Collapse on thedamageintheSimulatedPerineuronalNetoftheBrain.Yuan-TingWuandAshfaqAdnan*
MechanicalandAerospaceEngineering,theUniversityofTexasatArlington,Arlington,76010,USA*[email protected]: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
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