PROOF COPY [BIO ] JBY

Save this PDF as:
 WORD  PNG  TXT  JPG

Size: px
Start display at page:

Download "PROOF COPY [BIO ] JBY"

Transcription

1 Tly P. Appelmn Joseph Mizrhi Dror Seliktr e-mil: Fulty of Biomeil Engineering, Tehnion - Isrel Institute of Tehnology, Hif 3, Isrel A Finite Element Moel of Cell-Mtrix Intertions to Stuy the Differentil Effet of Sffol Composition on Chonrogeni Response to Mehnil Stimultion Mehnilly inue ell eformtions hve een shown to influene honroyte response in 3D ulture. However, the reltionship etween the mehnil stimultion n ell response is not yet fully unerstoo. In this stuy finite element moel ws evelope to investigte ell-mtrix intertions uner unonfine ompression onitions, using tissue engineere enpsulting hyrogel seee with honroytes. Moel preitions of stress n strin istriutions within the ell n on the ell ounry were shown to exhiit spe-epenent responses tht vrie with sffol mehnil properties, the presene of periellulr mtrix (PCM), n the ell size. The simultions preite tht when the ells were initilly enpsulte into the hyrogel sffols, the ell size hrly ffete the mgnitue of the stresses n strins tht were rehing the enpsulte ells. However, with the inlusion of PCM lyer, lrger ells experiene enhne stresses n strins resulting from the mehnil stimultion. It ws lso note tht the PCM h stress shieling effet on the ells in tht the pek stresses experiene within the ells uring loing were signifintly reue. On the other hn, the PCM use the stresses t the ell-mtrix interfe to inrese. Bse on the moel preitions, the PCM moifie the sptil stress istriution within n roun the enpsulte ells y reireting the mximum stresses from the periphery of the ells to the ell nuleus. In tissue engineere rtilge expose to mehnil loing, the formtion of neo-pcm y enpsulte honroytes ppers to protet them from initilly exessive mehnil loing. Preitive moels n thus she importnt insight into how honroytes remoel their lol environment in orer to reistriute mehnil signls in tissue engineere onstruts. DOI: 0.5/ Keywors: finite element moel, rtilge tissue engineering, mehnil stimultion, hyrogel, poly(ethylene glyol), mehnotrnsution, honroyte Introution Crtilge ells re sensitive to their mehnil environment n ret iretly to mehnil stimultion. The ouple mehnil n iohemil ues t the ell surfe, where extrellulr signls re onverte to intrellulr ones, re the fol point of mehnotrnsution. Previous stuies hve shown tht the tivtion of mehnotrnsution pthwys use y ompressive strins n signifintly lter honroyte metolism 2 7. This tivtion, lthough still poorly unerstoo, ppers to inlue omintion of integrin-meite signling, strethtivte ion hnnel signling, n tin ytoskeleton eformtions 8. Other physil events pereive y enpsulte honroytes expose to mehnil loing my inlue whole ell eformtions, lol strin flututions, flui flows, osmoti hnges, n fixe hrge ensity ltertions. Theoretil moels of the honroyte miroenvironment re prtiulrly helpful in this ontext, s they enle quntittive preitions of events, Corresponing uthor. Mnusript reeive Mrh 30, 200; finl mnusript reeive Deemer 4, 200; epte mnusript poste Deemer 22, 200; pulishe online xxxxx-xxxxx-xxxxx. Asso. Eitor: Clrk T. Hung. whih re iffiult to mesure experimentlly. These moels require informtion on the onstitutive ehvior of the ells n the 9 8 sffols in whih they re emee or enpsulte. 20 In ntive rtiulr rtilge, the mehnilly loe honrotyes re enpsulte y periellulr mtrix PCM. The 22 2 PCM is istinguishe from the rest of the extrellulr mtrix 23 ECM y its unique omposition n mehnil properties. The 24 ell n PCM hve jointly een terme honron 2. The ECM 25 is omprise minly of type II ollgen n ggren proteoglyns while the PCM onsists of ollgen Types II, VI, n IX, fironetin, ggren, hyluronn, n eorin 2,3. When isolte honroytes re enpsulte in sffols, they synthesize tissue-speifi moleules tht initilly form PCM, whih therefter iffuses into the extrellulr spe to reinfore the sffol 3 30 n eomes prt of the eveloping ECM. 32 Our group hs previously reporte tht honroytes n respon ifferently when they re sujete to the sme ompres sive strin stimultion in ifferent enpsulting mteril To show this, we immoilize vrious proteins n proteoglyns 36 into poly ethylene glyol PEG se hyrogels to rete iosyntheti milieu for ultivting enpsulte honroytes uner ynmi mehnil stimultion. The honroyte-enpsulting 39 onstruts were sujete to 5% ynmi ompressive strin 40 Journl of Biomehnil Engineering Copyright 20 y ASME APRIL 20, Vol. 33 / -

2 " e Fig. Histologil ross-setions of hyrogel onstruts stine for proteoglyns with Sfrnin O: fter 24 h, n fter 28 ys with stimultion in two ifferent types of hyrogels, n n e exmples of setions inluing ifferent ells sujete to the sme mehnil stimultion ut resulting in ifferent quntities of PCM seretion. Sle rs: 0 m. 4 stimultion t Hz frequeny for 28 ys, n the ellulr response ws mesure. Our finings inite tht the mtrix prop erties i.e., iotivity n moulus signifintly influene the 44 metoli tivity of the ells, presumly through hnges in the 45 mehnotrnsution pthwys. We sought to pply finite element moel FEM to our experimentl system in orer to gin insight into how these smll hnges in the ECM properties n 48 result in ltertions to the mehnil stress n strin istriutions within n roun the enpsulte ells Finite element moeling of rtilge tissue ws previously pplie to simulte honroyte-mtrix intertions uner stey 5 52 stte 5,6, trnsient 7 9, n ynmi yli loing 53 20,2. Most of the work in this fiel hs een fouse on rtilge tissue explnts, either norml or osteorthriti, n hs s sume iphsi ehvior of the ifferent ell, PCM, n ECM 56 omponents. FEM simultions hve lso een use to lulte 57 the mehnil properties of either PCM or ell omponents y 58 inverse finite element pprohes omine with experimentl 59 t 5,22. Reently, FEM work reveling stresses n strins 60 for ifferent sffols use for rtilge tissue engineering ws 6 reporte y Blol n Bonssr 23. This work fouse on the 62 ifferenes in istriution n mgnitues of pressures, flui 63 flows, strins, n sher stresses in the entire onstrut, ut i not 64 ress istriutions of these fores t the ellulr level. In other 65 work reporte y Guilk n Mow 8, the iphsi simultion 66 prmeters were vrie to inlue grose n lginte hyrogels 67 sffols with enpsulte honroytes. Although ommonly 68 use for rtilge tissue engineering, oth lginte n grose re 69 very ifferent mterils when ompre with the PEG-protein hyrogels reporte y our group 4, n thus we pplie similr 70 7 FEM moeling pproh to our system in orer to etter unerstn our experimentl t The purpose of this stuy ws thus to evelop FEM pproh 74 to eluite the sequene of iomehnil n iohemil 75 events through whih pplie mehnil loing influenes 76 honroyte iotivity in tissue engineere rtilge in vitro. The 77 simultions were fouse on the pek mplitues uring ynmi 78 loing. We expet tht our results will provie further insight 79 into the omplex reltionship etween struture, iohemil 80 properties, metoli tivity, iomehnil performne, n tissue funtion; helping to gin etter unerstning of events 8 ssoite with tissue engineere rtilge evelopment in enpsulting PEG-se hyrogels Methos 2. Finite Element Simultions. A finite element nlysis 85 ws performe on hyrogel-enpsulte honroytes expose to 86 ompression using severl onstitutive moels. Speifilly, the 87 moeling ws se on honroytes enpsulte in four ifferent PEG-se hyrogel sffols, eh sujete to 5% y nmi ompressive strin stimultion t Hzfrequeny. The 90 mximum los t the pek 5% ompressive strin were ompre for the ifferent hyrogels 4. In other wors, the simul tions one were equivlent to the time point t the mximum 93 mplitue of 5%. The onstruts re initilly onsiere to e 94 ompose of sffol mteril n enpsulte rnomly istriute spheril honroytes. However, uring the ourse of their evelopment, the ells proue PCM roun their outer 97 periphery s eviene y our reporte experimentl finings 98 4,24 Figs.. The volume frtion of honroytes 99 ws pproximtely.6%, se on ell rius of 5 m n 00 seeing ensity ells per ui entimeter of hyrogel 0 mtrix. For our simultions volume frtion of 2% ws ssume. 02 The si unit ws tken s yliner with hrteristi height 03 of 32 m n rius 6 m, ssuming homogeneity of the 04 ells n the ove volume frtion. The enpsulte honroyte n its PCM n e moele s spheril inlusions with ell rius of 5 m n periellulr lyer of thikness of m 8. Due to xisymmetry roun the ell n symmetry 08 roun the r- plne refer to Fig. 2 for the oorinte system 09 the geometry use in the simultions ws reue to miroomin with rius of 6 m in the r iretion n height of 0 6 m in the z iretion Fig. 2. Vritions in the honroyte rius from the si 5 m were lso moele s follows: 3 2 rius of 7.5 m resulting in frtion volume of 6.8% Fig. 4 2, n rius of 0 m resulting in frtion volume of 5 6.3% Fig For ll simultions, the xil-symmetry stress-strin pplition 7 moe of the ommeril finite element softwre COMSOL MULT / Vol. 33, APRIL 20 Trnstions of the ASME

3 z r Fig. 2 2D meshes use in the xisymmetry simultion in the se of ell rii of 5 m, 7.5 m, n 0 m. The oorinte system use in the simultions n e foun in IPHYSICS CM version 3.5, COMSOL, In., Burlington, MA ws use. The mesh onsiste of tringulr elements with Lgrnge qurti sis funtions in ll ses. The mesh ws refine t the ell n PCM ounries, where higher stress grients were ntiipte. A mesh of 3750 elements ws foun suffiient for onvergene purposes for 5 m ell rius. A finer mesh with 5,000 elements resulte in less thn 0.25% ifferene in mximum von Mises stresses, n prinipl strins. In those ses where the mteril ws moele s isotropi with lrge eformtions, finer mesh of 794 elements ws require to hieve onvergene mesh not shown. A summry of the ifferent element numers for the simulte geometries is foun in Tle Governing Equtions n Constitutive Moels. Negleting the effet of oy fores, the governing eqution in eh of the suomins, the ell, the PCM, n the sffol ws given y 35 T = where T is the Cuhy stress. In ition to the xil-symmetry ounry onition roun the z xis n plne symmetry onition t z=0, onstnt presrie isplement equivlent to 5% ompressive strin ws pplie to the upper ege of the sffol suomin see Fig. 2 for oorinte system. Applying lulte ounry onitions from mrosopi moel to the miroomin Fig. 2, whih is known s the multisle pproh, ws foun unneessry ue to the efinition of the suomins s isotropi homogenous n monophsi mterils n the ssumption tht the ounry effets re negligile. With x enoting the present position n X the referene position, the eformtion grient F ws efine s F= x/ X. The Tle Mesh prmeters Cell imeter m No. of elements No. of egrees of freeom , , ,948 volume rtio ws efine s J=et F n the right n left 48 Cuhy Green eformtion tensors were given, respetively, y 49 C=F T F n B=FF T. The first eformtion invrint ws given s 50 I =C:I=B:I. To seprte volume effets the following sling 5 ws introue: C =J 2/3 C where the first invrint of C ws 52 then Ī =J 2/3 I. 53 For inompressile mterils, the inompressiility onstrint 54 on the volume rtio ws impose s follows: 55 J = et F = 2 56 while, in generl, the seon Piol Kirhhoff stress n e foun 57 y 58 S =2 W s C = W s 3 E 59 In this se, the seon Piol Kirhhoff stress ws foun y 60 S = pjc +2 W s C = pjc + W s 4 E 6 where the hyrostti pressure p is the Lgrnge multiplier rising 62 from the inompressiility onstrint n E= /2 C I is the 63 Green Lgrngin strin. 64 The Cuhy stress ws otine, fter the seon Piol 65 Kirhhoff stress ws foun, through the following inverse Piol 66 trnsformtion: 67 T = J FSF T 5 68 The strin energy of the inompressile isotropi neo-hooken 69 NH moel ws 70 W s = C I with the ition of Eq It n e shown tht the Cuhy stress in this se ws given s 73 T = pi +2C B B:I I The eformtion grient of n inompressile mteril sujete to unixil strin ws Journl of Biomehnil Engineering APRIL 20, Vol. 33 / -3

4 F = 0 0 where is the streth rtio. This resulte in left Cuhy Green eformtion tensor of B = E sffol =0kP 8 n Cuhy stress of 82 T = 2C p 0 0 p 0 2C p C Beuse T 22 =0, it n e shown tht T =2C 2 /. Beuse the time erivtive of the true strin ws efine 85 s = the true strin ws therefore efine s =ln ; i.e., =e. The xil stress eme T =2C e 2 e. The erivtive with respet to strin t smll strins yiele C =E 0 /6, whih for n inompressile mteril orrespone to C = 0 /2. Here, E 0 n 0 re Young n sher mouli t smll eformtions, respetively. Experimentl mesurements of the sffol properties emonstrte liner true stress n true strin reltionship up to streth rtio of 0.7. The ompressive moulus use for the hyrogel ws se on the liner est fit in the strin rnge To hieve etter pproximtion to the liner ehvior reporte in the experiments, moifition ws me to the NH moel y ing oeffiient A=.075, whih ws foun y minimizing the sum of squre error SSE in the rnge of streth =:0.8 Fig. 3. COMSOL simultions gve ientil results to these lultions. This enle us to vlite the implementtion of the ove NH moel moifition into COMSOL. The strin energy of the moifie NH moel MNH ws W s = A 0 2 I In COMSOL, the following mixe formultion ws implemente for the neo-hooken inompressile mteril: W s = 0 2 Ī 3 p J p where 0 = E 0 /2 2 n p ws the hyrostti pressure Lgrngin multiplier. Therefore the moifie NH strin energy ws implemente s W s = A 0 2 Ī 3 p J p The ompressile NH moel ws implemente in COMSOL y the following strin energy: Fig. 3 Moifition of the neo-hooken moel for the sffol suomin. The moifition of the neo-hooken moel squres versus irles proue etter fit to the experimentl ehvior plin line oserve in the ompression experiments. The experimentl tren line ws se on moulus vlues tken iretly from the true stress-strin urves of the sffol uner ompression, s mesure y n Instron testing mhine 4. W s = 0 2 Ī J n ws use to represent the ell n PCM ehvior. 25 In orer to hek the effet of this moifition on the overll 26 results, set of simultions ws lso run with ll the three suomins, ell, PCM, n sffol moele s NH To further investigte the effet of the onstitutive equtions on 29 the simultion results, the three suomins were lso moele s 220 isotropi elsti mterils, while ssuming smll eformtions, using the liner reltion etween the Cuhy stress n the liner strin through the liner elstiity tensor D. In ition, the three 223 suomins were lso moele s isotropi elsti mterils, 224 while ssuming lrge eformtions. In COMSOL, this ws implemente y ssuming tht the mteril ehves s Sint Vennt Kirhhoff hyperelsti mteril, whih mens tht the strin energy n e written s W s = 2 E:D:E This results in liner reltion etween the seon Piol 230 Kirhhoff stress n the Green Lgrngin strin, through the liner elstiity tensor D, whih for the inompressile se res S = pjc + W s E = pjc + D:E In generl, the Sint Vennt Kirhhoff onstitutive eqution is 234 useful for ses tht the strins re smll n the eformtions re 235 lrge, euse t smll strins the Lgrngin strin n the 236 Cuhy liner strin re lmost equivlent to eh other, s re the 237 seon Piol Kirhhoff stress n the Cuhy stress. The vntge is tht oth S n E re ojetive, n rottions ue to lrge eformtions re orretly tken into ount. One the seon 240 Piol Kirhhoff stress ws foun, the Cuhy stress ws lulte through the inverse Piol trnsformtion Eq Moel Prmeters. The PEG-se sffols were moele s inompressile monophsi isotropi mterils with ompressive moulus rnging from 2 kp to 0 kp s mesure 245 in previous experiments 4 Tle 2. The inompressiility ssumption 0.5 ws se on the reltion etween Young s moulus mesure using n Instron testing mhine, n the sher / Vol. 33, APRIL 20 Trnstions of the ASME

5 Tle 2 Simultion prmeters Suomin Size m Type E kp Chonroyte r=5 0 Hyperelsti-neo-Hooken Isotropi-smll eformtions Isotropi-lrge eformtions 3 Results n Disussion PCM h=2.5 Hyperelsti-neo-Hooken Isotropi-smll eformtions Isotropi-lrge eformtions Sffol L=6 Hyperelsti-moifie neo-hooken Hyperelsti-neo-Hooken Isotropi-smll eformtions Isotropi-lrge eformtions moulus of the mterils, whih ws mesure y strin-rte 250 ontrolle rheometer t not shown. These mesurements resulte in rtio of elsti moulus to sher moulus somewhere in the rnge 3, whih orrespone to Poisson s rtio of In ition, severl reports hve een pulishe with the 254 ssumption tht polymeri hyrogels, prtiulrly PEG-se hyrogels, ehve s inompressile solis 25,26. Chonroyte n PCM t were tken from the relevnt literture. The PCM 257 ws moele s n isotropi mteril with Young s moulus of kp n Poisson s rtio of Chonroyte moulus ws 259 tken s 3.2 kp se on ompression tests of ells enpsulte 260 in lginte onstruts 27. Chonroytes were moele s n isotropi mteril with Poisson s rtio of ,29. Even though honroytes re known to exhiit visoelsti properties, they 263 were moele s elsti mterils for simpliity. This ws not n 264 unresonle ssumption given tht mehnil loing ws performe t Hz, n the honroytes hve relxtion time of less thn 20 s 30. Furthermore, the sffols were sujete to h of ontinuous stimultion, n previous ynmi simultions 268 hve shown tht stey stte ws hieve in less thn 5 min Given the vrious ssumptions n euse we were intereste 27 in preiting the pek vlues of stress n strin, the mximum 272 mplitue of the ell, the PCM, n the sffol were moele in 273 the nlysis. The moel preite how the mehnil loing 274 ws trnsmitte to the ells, oth t the ell-mtrix interfe n 275 within the entire honroyte, given speifie hnges in the mehnil properties of the ifferent suomins, the ell size, n the presene or sene of the PCM Effets of Sffol Moulus. The sffol moulus ffete the stresses, eformtions, isplements, n prinipl strins in ll suomins in oth ses: with the PCM n without the PCM Fig. 4. In generl, with the PCM Figs. 4 n 4, stiffer sffol resulte in n inrese in stresses throughout the suomins n in higher strins in the PCM n ellulr suomins. In ition, stiffer sffol exhiite more homogenous stress n strin fiel in the sffol suomin while softer sffol trnsferre less stresses n reue the strins rehing the ell n PCM. With the PCM, fivefol inrese in the sffol moulus use the mximum von Mises stress in the PCM suomin to inrese y ftor of 3.4 n in the sffol y ftor of 4. Without the PCM Figs. 4 n 4, stresses throughout the suomins lso inrese ue to the stiffer moulus. In the se of the ltter, inresing the sffol moulus y ftor of 5 use the mximum von Mises stress in the sffol suomin to inrese y ftor of 6. When the sffol moulus ws higher thn the ell moulus e.g., 0 kp, the ell ws sujete to higher isplements resulting in n inrese in strin reltive to tht of the sffol, whih n reh up to 9.7% strin, wheres when the ell moulus ws higher thn the sffol moulus e.g., 2 kp, the isplement fiel ppere to wrp roun the ell, resulting in less strin to the ell t not 30 shown. The mximum von Mises stresses were preite to e in 302 the res immeitely outsie the ell ounry, lose to the ellmtrix interfe Figs. 4 n 4, irrespetive of the PCM Upon loser inspetion of the von Mises stresses t the ell 305 suomin, it ws evient tht the moulus of the sffol ffete oth the mgnitue n the istriution of the stresses Fig Our finings further reinfore the previously esrie oservtions tht the PCM introues stress shieling effet to the ells 6. Aoring to our simultions, the mximum stress vlues erese y 20% n 52% in the presene of PCM with 3 30 sffol moulus of 0 kp n 2 kp, respetively, in omprison 32 to no PCM. Without the PCM, the stress grient ws in the z 33 iretion Figs. 5 n 5, wheres with the PCM, the stress 34 grient ws moifie to grient in the ril iretion with 35 higher vlues t the ell enter n lower vlues t the ounry 36 of the ell Figs. 5 n 5. In ition, the stresses were 37 istriute over wier rnge when the PCM ws present: 00 P 38 versus 20 P for sffol moulus of 0 kp n 60 P versus 39 3P for sffol moulus of 2 kp. Without the PCM, the 320 lotion of the pek stresses in the ell hnge s funtion of 32 sffol moulus. When the sffol moulus ws higher, the 322 mximum von Mises stress ws ner the lterl sie of the ell, 323 wheres when the sffol moulus erese elow the ell 324 moulus, the mximum von Mises stress ws lote ner the 325 pex of the ell. Interestingly, fter the PCM ws introue, the 326 mximum stress move to the enter of the ell where the honroyte nuleus ws lote. With the PCM in ple, oth the mximum n minimum von Mises stresses inrese s the sffol moulus inrese. Beuse the moulus inrese i not eliit hnge in the sptil istriution of stress, ut i roen 33 the rnge of the von Mises stresses, this implie tht the stress 332 grients insie the ell lso inrese. 333 An inrese in sffol moulus use n inrese in the 334 mximum von Mises stress oth in the ell omin Figs. 6 n n t the ell-mtrix ounry Figs. 6 n 6, irrespetive of the PCM. Interestingly, with the PCM, this inrese epene on the ell size Figs. 6 n 6, wheres without 338 the PCM, the ell size i not ffet these vlues Figs. 6 n The simultions showe tht lrger ell with the sme 340 PCM thikness evelope higher stresses uner the sme presrie isplements uring loing. Therefore, thiker PCM woul e require to result in the sme effetive stress shieling 343 for lrger ell. This ws importnt euse the ell size, whih 344 ws ffete y the iotivity of the sffol 3, my pt in 345 response to its surrouning n therey nee to synthesize itionl PCM, even though it is sujete to the sme mehnil strin uner loing. Aoring to these simultions, ell emee insie sffol will initilly e sujete to stresses without eing ffete y the reltive ell size. However, one the 350 Journl of Biomehnil Engineering APRIL 20, Vol. 33 / -5

6 Simultions With PCM Von-Mises Stress, E Sffol = [2 kp] [P] Simultions Without PCM Von-Mises Stress, E Sffol = [2 kp] [P] ell egins to synthesize PCM, the stresses t the ell-mtrix ounry will inrese ue to the inrese stiffness of the PCM reltive to tht of the sffol. On the other hn, the stress shieling effet of the PCM will use the overll stresses in the ell to erese when the rius of the ell is 5 m or 7.5 m. These internl stresses epen on ell size; if the ell rius is 0 m the stresses without PCM re slightly lower thn with PCM, mening tht in this se, the PCM with thikness of 2.5 m is not suffiient to use stress shieling. Higher stresses in the ell my stimulte itionl PCM synthesis s to use higher stress shieling effets. Interestingly, our previous experimentl results onur tht ells hve ifferent PCM sizes, whih my e orrelte with the ell size 4,24 Figs. n e. 3.2 Cell Size n Cell Deformtion. Compression of the enpsulting mtrix evokes signifint ell eformtions, s quntifie y the reltive ell rius hnge RRC prmeter Fig. 7. RRC prmeter ws efine s the eforme rius ivie y the initil rius. Compressive eformtion inrese the RRC prmeter in the r iretion n erese it in the z iretion. The ell eformtion inrese inrese r-rrc n erese z-rrc with n inrese in the sffol moulus, irrespetive of the PCM. With the PCM, the initil ell rius ffete the RRC, oth in the z n r iretions Figs. 7 n 7. Aoring to these simultions, ell with smller initil rius unergoes Von-Mises Stress, E Sffol = [0 kp] [P] Von-Mises Stress, E Sffol = [0 kp] [P] Fig. 4 Sffol moulus effets on the von Mises stresses with eformtions: n with PCM n n without PCM, for sffol moulus of n 2 kp n n 0 kp. Eh set of mthing figures hve the sme sle n olor r to simplify omprison. PCM prmeters re E=40 kp, =0.04, ell prmeters re E=3.2 kp, = smller eformtions in oth iretions ompre with lrger 375 ell. Without PCM, the reltive ell rius in the z iretion erese s the sffol moulus inrese, though the influene of the initil ell rius ws more evient t higher sffol moulus Fig. 7. A lrger ell use less eformtion in the z iretion when mesure reltive to the originl rius. Without 380 the PCM, the ell rius in the r iretion inrese s the sffol 38 moulus inrese, ut hrly ny ifferene ws note etween 382 the ifferent initil ell rii Fig In ells with initil rii of 5 m n 7.5 m, the PCM 384 use strin shieling irrespetive of the sffol moulus. 385 Strin shieling ws note when the overll eformtion of the 386 ell ws reue, ompre with the se without the PCM Fig In the r iretion only, there ws lso strin shieling for ells 388 hving n initil rius of 0 m. Interestingly, t tht ell rius, 389 the presene of 2.5 m PCM lyer i not reue the reltive 390 eformtion in the z iretion, ut rther, slightly inrese it 39 when ompre with the equivlent sffols without PCM Constitutive Eqution Effets. The vrious onstitutive 393 equtions evlute showe tht the moel use in the simultion 394 n gretly ffet the preite stresses n strins within the 395 suomins. In generl there ws similr tren etween the 396 ifferent simultions in eh moel type; however, ifferenes in 397 the preite mximum vlues mong the moels were more thn / Vol. 33, APRIL 20 Trnstions of the ASME

7 With PCM Without PCM E Sffol = [0 kp] [P] E Sffol = [0 kp] [P] E Sffol = [2 kp] [P] 3.4 Effets of Cell Moulus. When etermining whih prmeters to use in our moels se on reent pulitions in the relevnt literture, we note tht rnge of more thn one orer of mgnitue hs een reporte for ell moulus, epening on the E Sffol = [2 kp] [P] Fig. 5 Von Mises stresses within the ell spe n with n n without PCM for the ses tht the sffol moulus ws n 0 kp n n 2 kp. Chnges n e note in oth sptil istriution n mgnitue % in some ses. The MNH moel preite the highest 400 stresses Figs. 8 n 9 n the lrgest RRC exept in the z 40 iretion without PCM Fig. 0. Assuming lrge eformtion 402 with smll strins n thus using isotropi onstitutive equtions 403 for lrge eformtions woul hve resulte in very lrge unerestimtion of the stresses n most of the ell eformtions. In terestingly in the z iretion without the PCM, this moel preite the smllest eformtions with the softer sffol mterils, ut ultimtely preite the lrgest eformtion for the stiffer mterils. In the MNH simultion only the sffol ws moele s MNH mteril, while the PCM n ell were ssume to e neo- 40 Hooken. This smll moifition resulte in notiele stress n 4 strin hnges throughout the ifferent suomins. Consequently, if we ssume isotropi mteril ehvior with smll e formtions, this woul result in loser preition to the MNH 44 thn with the isotropi lrge eformtion theory for the stresses 45 n strins ell origin n mesurement tehnique 22,27,28, For 420 most of the simultions, we hose ell moulus of 3.2 kp, 42 vlue estimte y Knight et l. 27 from ompression tests in 422 lginte. The effet of ell moulus on simultion ws lso onsiere, n simultions were thus performe with ifferent vl ues rnging from 0.35 kp to 4 kp Fig.. In the se where 425 PCM ws present, n low sffol moulus of 2 kp ws 426 hosen, hnging the ell moulus resulte in reltively liner 427 hnge in stresses n strins. The stresses in the sffol were 428 only slightly reue kp y the inrese in ell moulus. With the inrese in ell moulus, the stresses in the ell inrese, while the stresses in the PCM erese Figs., 43 f, n g. Deformtion in the z n r iretions erese 432 with the inrese in ell moulus Figs. n. The 433 mximum von Mises stress on the ell-pcm ounry lso erese with the inrese in ell moulus Fig. e. In this se, ll the mximum vlues hnge in ner-liner pttern Effets of the PCM. The effet of PCM synthesis ws 437 lso moele using FEM nlysis. This ws simulte y inresing the moulus of the PCM suomin 0 40 kp while reu ing Poisson s rtio Fig. 2. The stresses in the 440 Journl of Biomehnil Engineering APRIL 20, Vol. 33 / -7

8 Mx Von Mises Stress in Cell Domin [N/m 2 ] Mx Von Mises Stress on Cell-PCM Bounry [N/m 2 ] Simultions With PCM Cell Rius 5µm Cell Rius 7.5µm Cell Rius 0µm 200 E Sffol [KP] Mx Von Mises Stress in Cell Domin [N/m 2 ] Simultions Without PCM Cell Rius 5µm Cell Rius 7.5µm Cell Rius 0µm 400 E Sffol [KP] E Sffol [KP] Cell Rius 5µm Cell Rius 7.5µm Cell Rius 0µm Mx Von Mises Stress on Cell-Sffol Bounry [N/m 2 ] E Sffol [KP] Cell Rius 5µm Cell Rius 7.5µm Cell Rius 0µm AQ: # Fig. 6 Mximum von Mises stresses in the n ell suomin n n on the ell-mtrix ounry s funtion of sffol moulus in the se of three ifferent ell sizes, efore n fter the PCM ws rete Simultions With PCM Reltive Cell Rius Chnge Simultions Without PCM Reltive Cell Rius Chnge Fig. 7 The effet of sffol moulus on the reltive ell rius hnge RRC, efine s the eforme rius ivie y the initil rius, in the z n r iretions, with n without PCM, for three ell sizes -8 / Vol. 33, APRIL 20 Trnstions of the ASME

9 MxVonMisesStress[N/m 2 ] Simultions With PCM Sffol-Moife Neo-Hooken PCM-Moife Neo-Hooken Cell-Moife Neo-Hooken Sffol-Isotropi, Smll eformtion PCM-Isotropi, Smll eformtion Cell--Isotropi, Smll eformtion Sffol- Neo-Hooken PCM- Neo-Hooken Cell- Neo-Hooken Sffol-Isotropi, Lrge eformtion PCM-Isotropi, Lrge eformtion Cell-Isotropi, Lrge eformtion MxVonMisesStress[N/m 2 ] 2 Simultions Without PCM Sffol-Moife Neo-Hooken Cell-Moife Neo-Hooken Sffol-Isotropi, Smll eformtion Cell-Isotropi, Smll eformtion Sffol- Neo-Hooken Cell- Neo-Hooken Sffol-Isotropi, Lrge eformtion Cell-Isotropi, Lrge eformtion 0 E Sffol [KP] 0 E Sffol [KP] Fig. 8 The effet of ifferent moeling tehniques on the mximum von Mises stress in the ifferent suomins s funtion of sffol moulus, with n without PCM. Cell rius ws tken s 5 m PCM suomin inrese with the inrese in PCM moulus Fig. 2. This susequently use erese in the mximum stresses rehing the ell suomin. On the other hn, the inrese moulus of the PCM use n inrese in the stresses t the ell-pcm ounry, prtiulrly t the lterl sie of the ell Fig. 2 where the mximum stresses in the PCM lso our Implitions on Mehnotrnsution. Signling meite through integrin hesion reeptors regultes severl hon- royte funtions inluing ifferentition, viility, mtrix remoeling, n responses to mehnil stimuli 35. Integrins, primrily integrins, re responsile for honroyte tthment to the ECM. Iniviul integrin-firinogen ons hve imeter of 5 nm 36 n hve een evlute s hving rupture fore of f=00 pn 37,38. Clulting the verge single on rupture norml stress, 4f/ 2 =imeter, yiels vlue of 566 kp. 455 Integrin-fironetin on fores hve een evlute s 20 pn , therefore resulting in lulte norml rupture stress of kp. These evlute stresses re higher thn the simulte 458 mximum stresses t the ell-mtrix ounry, whih o not exee 5 kp for ll the simultions performe. It shoul e note tht ompressive stresses n rise up to 0 20 MP within the 46 joint 40, whih is orers of mgnitue higher thn the stresses 462 we report; however, ntive ult rtiulr rtilge lso hs 463 muh higher moulus when ompre with the PEG-se hyrogels use s sffol for the tissue engineere onstruts Reent experiments showe tht hrveste humn honroytes, whih were seee on rtilge tissue, ethe t sher stresses of 70 P, 80 h postseeing 4. In this se, integrin 468 Mx Von Mises Stress on Cell-PCM Bounry [N/m 2 ] Moife Neo-Hooken Simultions With PCM Isotropi, Smll eformtion Neo-Hooken Isotropi, Lrge eformtion E Sffol [KP] Mx Von Mises Stress on Cell-Sffol Bounry [N/m 2 ] Moife Neo-Hooken Simultions Without PCM Isotropi, Smll eformtion Neo-Hooken Isotropi, Lrge eformtion 200 E Sffol [KP] Fig. 9 The effet of ifferent onstitutive moels on the mximum von Mises stress t the ell-mtrix ounry s funtion of sffol moulus, with n without PCM. Cell rius ws tken s 5 m. Journl of Biomehnil Engineering APRIL 20, Vol. 33 / -9

10 z iretion Reltive Cell Cell Dimeter Rius Chnge Chnge - With PCM With PCM Moife Neo-Hooken Isotropi, Smll eformtion Neo-Hooken Isotropi, Lrge eformtion 0.8 ziretion Reltive Cell Cell Dimeter Rius Chnge Chnge - Without Without PCM PCM Moife Neo-Hooken Isotropi, Smll eformtion Neo-Hooken Isotropi, Lrge eformtion r iretion riretion ESffol[KP] ESffol[KP] Fig. 0 The effet of ifferent onstitutive moels on the reltive ell rius hnge RRC, efine s the eforme rius ivie y the initil rius, in the z n r iretions s funtion of sffol moulus, with n without PCM. The initil ell rius ws tken s 5 m. Suomin Type E [kp]! Chonroyte NH Sffol 2 PCM Cell f PCM NH Sffol MNH g MxVonMisesStress[N/m 2 ] e Mx Von Mises Stress on Cell-PCM ounry [N/m 2 ] ECell[KP] z iretion r iretion E Cell [KP] Reltive Cell Dimeter Cell Rius Chnge Chnge ECell[KP] Fig. The effet of ell moulus on mximum von Mises stresses in the suomins, reltive ell rius hnge, efine s the eforme rius ivie y the initil rius, in the z iretion, reltive ell rius hnge. In the r iretion, n e mximum von Mises stress t the ell-pcm ounry prmeters use re summrize in. The sptil von Mises stresses n eformtion re emonstrte for the se of ell moulus of f 0.35 kp n g 4 kp. -0 / Vol. 33, APRIL 20 Trnstions of the ASME

11 MxVonMisesStress[N/m 2 ] vpcm Sffol 8000 PCM Cell EPCM[KP] Von-Mises Stress on Cell-Mtrix Bounry [P] E PCM 0 [kp], v PCM E PCM 3 [kp], v PCM E PCM 6 [kp], v PCM E PCM 9 [kp], v PCM E PCM 22 [kp], v PCM 0.36 E PCM 25 [kp], v PCM 0.27 E PCM 28 [kp], v PCM E PCM 3 [kp], v PCM 0.78 E PCM 34 [kp], v PCM 0.32 E PCM 37 [kp], v PCM E PCM 40 [kp], v PCM Ar-length x0-6 Fig. 2 PCM seretion effets on the mximum von Mises stresses in the ifferent suomins n the von Mises stresses on the ell-mtrix ounry plotte oring to the r length ons re roken ue to high sher stress levels. In our simultions, ll von Mises stresses t the ell-mtrix interfe were preite to e in the rnge etween 330 P n 0 P, therefore exeeing the experimentl effetive sher stress reporte y Kurtis et l. 4, ut lower thn the lulte on rupture stress. Therefore, the possiility tht integrin on rupturing ws involve in the ifferenes in ell mehnotrnsution ws not supporte y the moel preitions. 3.7 Limittions n Other Consiertions. It shoul e note tht the present moels hve severl limittions ue, in prt, to simplifying ssumptions. In the experiments, honroytes emee in the hyrogels sometimes exhiite nonspheril geometry, off-xis lignment, lustering of ells surroune y single PCM, n uneven PCM thikness. The ssumption of perfet sphere ws me primrily to enle us to employ n xisymmetril simplifition. This is unlike mture helthy rtilge, where the ells re firly well ligne with the iretion of tissue epth 42 n where the ell s spet rtio n e tken into ount in the efinition of the xisymmetry simultions 43. Although, initilly, the sffol n e onsiere isotropi, with the inlusion of ells n synthesize PCM, the mteril eomes inresingly nisotropi. In ition, enzymes egre the sffol in iffusion epenent mnner wy from the ell ounry; wheres hyrolysis egres the sffol in ulk. For simpliity, we ssume isotropy euse of this highly omplite egrtion profile within the hyrogel. Unfortuntely, given the hosen omin size, whih ws itte y the seeing ensity, prt of the solutions exhiite presene of ounry lyers ner the omin eges. One of the inherent ssumptions ws tht perturtions in the eformtion ue to the inlusion of the ell vnish in the fr fiel ege of the omin. Therefore, when efining the suomin ounry onition, the presene of suh itionl ounry lyers my prelue this si ssumption. These ouple effets ner the ounries of the sffol omin were intensifie s the ell size ws inrese n the ell-to-sffol volume frtion inrese. Inresing the ury of the simultions woul neessitte in this se more omplex representtion of lrger omin inluing more ells, whih is eyon the sope of this stuy. As mentione efore, the visoelsti properties of the ell n PCM were neglete s were oy fores. Crtilge hs een previously moele s iphsi mteril 44. This present stuy iffers in two mjor respets from the work of Guilk n Mow 8 : first, the rpi moe of loing n, seon, the ft tht the meium simulte is loser to hyrogel thn to rtilge. In this respet our experimentl mesurements hve showe tht the mehnil ehvior of the hyrogels ws very 54 lose to tht of n elsti mteril n for this reson monophsi moel ws juge suffiient for this stuy. The moe of lo ing for whih the simultions were me in this stuy is onsiere in rtiulr rtilge to e short-term eformtion n is thought to e ssoite with rpi movement n rerrngements 59 of the tissue uner onstnt volume 45. This is onsierly 520 ifferent from long-term eformtion, whih involves the movement of flui reltive to the ollgen network through the very fine pores forme y the proteolgyln moleules 46. Due to the 523 ssumptions of homogenous monophsi mterils n negligile 524 ounry effets, multisle moel eme unneessry n ws 525 not implemente. Moreover, honroytes hve een reporte to 526 e sensitive to the type of loing onitions: Different loing 527 frequenies hve een shown to ffet glyominoglyns 528 GAGs synthesis wheres stti loing hs een shown to hve 529 negtive effet on GAG synthesis 3. It woul pper tht 530 more omplex FEM shoul e evelope for this type of system, 53 tking into ount the ove experimentl finings. The ell, 532 PCM, n sffol were efine not to llow ny slippge or 533 reltive movement, n onstnt tthment etween the suomins ws ssume. Cell tthment to its surrouning is elieve to our t istint fol ontt points. Thus, iotive n permissive sffols use in our experimentl stuy were elieve to hve evoke very ifferent fol hesion profiles. It woul e 538 interesting to investigte how ifferent ounry onitions etween the ell n its surrouning ffet the mehnil stimuli rehing the ell, ut this is eyon the sope of the urrent report. The PCM, while eing synthesize, hnges its mehnil properties n geometry. In this work we only resse the 543 hnge in mehnil properties. Further work shoul inlue the 544 investigtion of the effet of the hnge in the PCM thikness, 545 euse notiele hnges were oserve in experimentl finings Conlusions 548 A numeril FE moel ws evelope n use to simulte 549 tests tht were previously performe in unonfine ompression 550 uner vrious onfigurtions 4. The stresses n eformtions 55 of honroytes within ifferent sffol types were preite for 552 the pek phse of yli unonfine ompression loing. Four 553 ifferent moeling methos were ompre to evlute their effets on the preite vlues. The simultions presente in this stuy emonstrte epenene of the preite stresses in the 556 ellulr environment on the ifferent onstitutive moels use for 557 Journl of Biomehnil Engineering APRIL 20, Vol. 33 / -

12 the three ifferent suomins: ell, PCM, n sffol. In ition, it ws emonstrte tht the mteril properties of the sffol n PCM, s well s ell size influene stress n strin istriutions. The numeril simultions showe tht the PCM plys ritil role in regulting the iomehnil signls rehing the ell, oth in mgnitue n in sptil istriution. Interestingly, the effets of ell size prove signifint only one the 565 PCM ws intt. These simultion results provie further insight 566 into the vritions in the metoli responses previously reporte 567 y our group, foun with ifferent PEG-se ell-seee hyrogel onstruts sujete to the sme mehnil stimultion Aknowlegment 570 The uthors grtefully knowlege the finnil support of the 57 Unite Sttes-Isrel Bintionl Siene Fountion Grnt No n the Russell Berrie Nnotehnology Institute - Tehnion. The uthors grtefully knowlege the useful isussions with M. Ruin. Referenes Wng, N., Butler, J. P., n Inger, D. E., 993, Mehnotrnsution Aross the Cell Surfe n Through the Cytoskeleton, Siene, 260 5, pp Bushmnn, M. D., Gluzn, Y. A., Grozinsky, A. J., n Hunziker, E. B., , Mehnil Compression Moultes Mtrix Biosynthesis in Chonroyte/Agrose Culture, J. Cell Si., 08 4, pp Lee, D. A., n Ber, D. L., 997, Compressive Strins t Physiologil Frequenies Influene the Metolism of Chonroytes Seee in Agrose, J. Orthop. Res., 5 2, pp Free, L. E., Vunjk-Novkovi, G., n Lnger, R., 993, Cultivtion of Cell-Polymer Crtilge Implnts in Bioretors, J. Cell. Biohem., 5 3, pp Muk, R. L., Seyhn, S. L., Ateshin, G. A., n Hung, C. T., 2002, Influene of Seeing Density n Dynmi Deformtionl Loing on the Developing Struture/Funtion Reltionships of Chonroyte-Seee Agrose Hyrogels, Ann. Biome. Eng., 30 8, pp Muk, R. L., Soltz, M. A., Wng, C. C. B., Wong, D. D., Cho, P.-H. G., Vlhmu, W. B., Hung, C. T., n Ateshin, G. A.,, Funtionl Tissue Engineering of Artiulr Crtilge Through Dynmi Loing of Chonroyte- Seee Agrose Gels, ASME J. Biomeh. Eng., 22 3, pp Wlmn, S. D., Spiteri, C. G., Grynps, M. D., Pillir, R. M., n Knel, R. A., 2004, Long-Term Intermittent Compressive Stimultion Improves the Composition n Mehnil Properties of Tissue-Engineere Crtilge, Tissue Eng., 0 9 0, pp Lee, H. S., Millwr-Sler, S. J., Wright, M. O., Nuki, G., n Slter, D. M.,, Integrin n Mehnosensitive Ion Chnnel-Depenent Tyrosine Phosphoryltion of Fol Ahesion Proteins n Bet-Ctenin in Humn Artiulr Chonroytes After Mehnil Stimultion, J. Bone Miner. Res., 5 8, pp Wright, M. O., Nishi, K., Bvington, C., Goolphin, J. L., Dunne, E., Wlmsley, S., Jonputr, P., Nuki, G., n Slter, D. M., 997, Hyperpolristion of Culture Humn Chonroytes Following Cylil Pressure-Inue Strin: Eviene of Role for Alph 5 Bet Integrin s Chonroyte Mehnoreeptor, J. Orthop. Res., 5 5, pp Cmpell, J. J., Blin, E. J., Chowhury, T. T., n Knight, M. M., 2007, Loing Alters Atin Dynmis n Up-Regultes Cofilin Gene Expression in Chonroytes, Biohem. Biophys. Res. Commun., 36 2, pp Kok, L. M., Shulz, R. M., vn Donkelr, C. C., Thummler, C. B., Ber, A., n Ito, K., 2009, RGD-Depenent Integrins Are Mehnotrnsuers in Dynmilly Compresse Tissue-Engineere Crtilge Construts, J. Biomeh., 42 3, pp Poole, C. A., 997, Artiulr Crtilge Chonrons: Form, Funtion n Filure, J. Ant., 9, pp Mrous, A., 979, Physiohemil Properties of Artiulr Crtilge, Ault Artiulr Crtilge, M. A. R. Freemn, e., Pitmn Meil, Lonon, pp Appelmn, T. P., Mizrhi, J., Elisseeff, J. H., n Seliktr, D., 2009, The Differentil Effet of Sffol Composition n Arhiteture on Chonroyte Response to Mehnil Stimultion, Biomterils, 30 4, pp Mihlek, A. J., n Itriis, J. C., 2007, A Numeril Stuy to Determine Periellulr Mtrix Moulus n Evlute Its Effets on the Miromehnil Environment of Chonroytes, J. Biomeh., 40 6, pp Alexopoulos, L. G., Setton, L. A., n Guilk, F., 2005, The Biomehnil Role of the Chonroyte Periellulr Mtrix in Artiulr Crtilge, At Biomter., 3, pp Wu, J. Z., Herzog, W., n Epstein, M., 999, Moelling of Lotion- n Time-Depenent Deformtion of Chonroytes During Crtilge Loing, J. Biomeh., 32 6, pp Guilk, F., n Mow, V. C.,, The Mehnil Environment of the Chonroyte: A Biphsi Finite Element Moel of Cell-Mtrix Intertions in Artiulr Crtilge, J. Biomeh., 33 2, pp Chhine, N. O., Hung, C. T., n Ateshin, G. A., 2007, In-Situ Mesurements of Chonroyte Deformtion Uner Trnsient Loing, Eur. Cells 638 Mter, 3, pp Kim, E., Guilk, F., n Hier, M. A., 2008, The Dynmi Mehnil 640 Environment of the Chonroyte: A Biphsi Finite Element Moel of Cell- 64 Mtrix Intertions Uner Cyli Compressive Loing, ASME J. Biomeh. 642 Eng., 30 6, p Wu, J. Z., n Herzog, W., 2006, Anlysis of the Mehnil Behvior of 644 Chonroytes in Unonfine Compression Tests for Cyli Loing, J. Biomeh., 39 4, pp Ofek, G., Ntoli, R. M., n Athnsiou, K. A., 2009, In Situ Mehnil 647 Properties of the Chonroyte Cytoplsm n Nuleus, J. Biomeh., 42 7, 648 pp Blol, O. M., n Bonssr, L. J., 2009, Prmetri Finite Element Anlysis of Physil Stimuli Resulting From Mehnil Stimultion of Tissue En gineere Crtilge, ASME J. Biomeh. Eng., 3 6, p Appelmn T. P., Mizrhi J., Elisseeff, J. H., n Seliktr, D., 20, The 653 Influene of Biologil Motifs n Dynmi Mehnil Stimultion in Hyrogel Sffol Systems on the Phenotype of Chonroytes, Biomterils, , pp Elert, D. L., n Huell, J. A., 200, Conjugte Aition Retions Comine With Free-Ril Cross-Linking for the Design of Mterils for Tissue Engineering, Biomromoleules, 2 2, pp Lio, H., Munoz-Pinto, D., Qu, X., Hou, Y., Grunln, M. A., n Hhn, M. S., , Influene of Hyrogel Mehnil Properties n Mesh Size on Vol 66 Fol Firolst Extrellulr Mtrix Proution n Phenotype, At Biomter., 4 5, pp Knight, M. M., vn e Breevrt Brvenoer, J., Lee, D. A., vn Osh, G. J., 664 Weinns, H., n Ber, D. L., 2002, Cell n Nuleus Deformtion in Compresse Chonroyte-Alginte Construts: Temporl Chnges n Clultion of Cell Moulus, Biohim. Biophys. At, 570, pp Freemn, P. M., Ntrjn, R. N., Kimur, J. H., n Anrihi, T. P., 994, 668 Chonroyte Cells Respon Mehnilly to Compressive Los, J. Orthop. 669 Res., 2 3, pp Trikey, W. R., Bijens, F. P., Lursen, T. A., Alexopoulos, L. G., n Guilk, 67 F., 2006, Determintion of the Poisson s Rtio of the Cell: Reovery Properties of Chonroytes After Relese From Complete Miropipette Aspirtion, J. Biomeh., 39, pp Drling, E. M., Topel, M., Zusher, S., Vil, T. P., n Guilk, F., 2008, 675 Visoelsti Properties of Humn Mesenhymlly-Derive Stem Cells n 676 Primry Osteolsts, Chonroytes, n Aipoytes, J. Biomeh., 4 2, pp Dikovsky D., Bino-Pele H., n Seliktr, D., 2008, Defining the Role of 679 Mtrix Compline n Proteolysis in Three-Dimensionl Cell Spreing n 680 Remoeling, Biophysil Journl, 94 7, pp Zhng, Q. Y., Wng, X. H., Wei, X. C., n Chen, W. Y., 2008, Chrteriztion of Visoelsti Properties of Norml n Osteorthriti Chonroytes in Experimentl Rit Moel, Osteorthritis Crtilge, 6 7, pp Trikey, W. R., Lee, G. M., n Guilk, F.,, Visoelsti Properties of 685 Chonroytes From Norml n Osteorthriti Humn Crtilge, J. Orthop. 686 Res., 8 6, pp Ber, D. L., Ohshi, T., Knight, M. M., Lee, D. A., n Sto, M., 2002, 688 Deformtion Properties of Artiulr Chonroytes: A Critique of Three Seprte Tehniques, Biorheology, 39 2, pp Loeser, R. F., 2002, Integrins n Cell Signling in Chonroytes, Biorheology, 39 2, pp Gllnt, N. D., n Gri, A. J., 2007, Moel of Integrin-Meite Cell 693 Ahesion Strengthening, J. Biomeh., 40 6, pp Li, F., Reik, S. D., Erikson, H. P., n Moy, V. T., 2003, Fore Mesurements of the Alph5et Integrin-Fironetin Intertion, Biophys. J., , pp Litvinov, R. I., Shumn, H., Bennett, J. S., n Weisel, J. W., 2002, Bining 698 Strength n Ativtion Stte of Single Firinogen-Integrin Pirs on Living 699 Cells, Pro. Ntl. A. Si. U.S.A., 99, pp Thoumine, O., Koin, P., Kottelt, A., n Meister, J. J.,, Short-Term 70 Bining of Firolsts to Fironetin: Optil Tweezers Experiments n 702 Proilisti Anlysis, Eur. Biophys. J., 29 6, pp Ams, M. A., 2006, The Mehnil Environment of Chonroytes in Artiulr Crtilge, Biorheology, , pp Kurtis, M. S., Shmit, T. A., Bugee, W. D., Loeser, R. F., n Sh, R. L., , Integrin-Meite Ahesion of Humn Artiulr Chonroytes to Crtilge, Arthritis Rheum., 48, pp Clrk, A. L., Brly, L. D., Mtys, J. R., n Herzog, W., 2003, In Situ 709 Chonroyte Deformtion With Physiologil Compression of the Feline Ptellofemorl Joint, J. Biomeh., 36 4, pp Hn, S. K., Feerio, S., Grillo, A., Giquint, G., n Herzog, W., 2007, The 72 Mehnil Behviour of Chonroytes Preite With Miro-Struturl 73 Moel of Artiulr Crtilge, Biomeh. Moel. Mehnoiol., 6 3, pp Kwn, M. K., Li, W. M., n Mow, V. C., 990, A Finite Deformtion 76 Theory for Crtilge n Other Soft Hyrte Connetive Tissues I. Equilirium Results, J. Biomeh., 23 2, pp Mizrhi, J., Mrous, A., Lnir, Y., Ziv, I., n Weer, T. J., 986, The 79 Instntneous Deformtion of Crtilge: Effets of Collgen Fier Orienttion n Osmoti Stress, Biorheology, 23 4, pp Mizrhi, J., Mrous, A., n Benim, E., 990, Unonfine Compression 722 for Stuying Crtilge Creep, Methos in Crtilge Reserh, J.Mizrhi,A. 723 Mrous, n E. Benim, es., Aemi, Lonon, pp / Vol. 33, APRIL 20 Trnstions of the ASME

13 NOT FOR PRINT! FOR REVIEW BY AUTHOR NOT FOR PRINT! AUTHOR QUERIES 0080JBY # Author: When there is only one sentene in figure ption, ASME style is to hve no ening puntution.

Stress concentration in castellated I-beams under transverse bending

Stress concentration in castellated I-beams under transverse bending 466 ISSN 13921207. MECHANIKA. 2016 olume 22(6): 466473 Stress onentrtion in stellte I-ems uner trnsverse ening A. Pritykin Kliningr Stte Tehnil University (KGTU), Sovetsky v. 1, 236022, Kliningr, Russi,

More information

Stochastic Subsurface Data Integration Assessing Aquifer Parameter and Boundary Condition Uncertainty

Stochastic Subsurface Data Integration Assessing Aquifer Parameter and Boundary Condition Uncertainty Journl of Hyrology mnusript No. (will e inserte y the eitor) Stohsti Susurfe Dt Integrtion Assessing Aquifer Prmeter n Bounry Conition Unertinty Dongong Wng Ye Zhng Reeive: te / Aepte: te Astrt This reserh

More information

U Q W The First Law of Thermodynamics. Efficiency. Closed cycle steam power plant. First page of S. Carnot s paper. Sadi Carnot ( )

U Q W The First Law of Thermodynamics. Efficiency. Closed cycle steam power plant. First page of S. Carnot s paper. Sadi Carnot ( ) 0-9-0 he First Lw of hermoynmis Effiieny When severl lterntive proesses involving het n work re ville to hnge system from n initil stte hrterize y given vlues of the mrosopi prmeters (pressure p i, temperture

More information

Chapter 19: The Second Law of Thermodynamics

Chapter 19: The Second Law of Thermodynamics hpter 9: he Seon Lw of hermoynmis Diretions of thermoynmi proesses Irreversile n reversile proesses hermoynmi proesses tht our in nture re ll irreversile proesses whih proee spontneously in one iretion

More information

Ranking Generalized Fuzzy Numbers using centroid of centroids

Ranking Generalized Fuzzy Numbers using centroid of centroids Interntionl Journl of Fuzzy Logi Systems (IJFLS) Vol. No. July ning Generlize Fuzzy Numers using entroi of entrois S.Suresh u Y.L.P. Thorni N.vi Shnr Dept. of pplie Mthemtis GIS GITM University Vishptnm

More information

SECOND HARMONIC GENERATION OF Bi 4 Ti 3 O 12 FILMS

SECOND HARMONIC GENERATION OF Bi 4 Ti 3 O 12 FILMS SECOND HARMONIC GENERATION OF Bi 4 Ti 3 O 12 FILMS IN-SITU PROBING OF DOMAIN POLING IN Bi 4 Ti 3 O 12 THIN FILMS BY OPTICAL SECOND HARMONIC GENERATION YANIV BARAD, VENKATRAMAN GOPALAN Mterils Reserh Lortory

More information

Solutions to Problem Set #1

Solutions to Problem Set #1 CSE 233 Spring, 2016 Solutions to Prolem Set #1 1. The movie tse onsists of the following two reltions movie: title, iretor, tor sheule: theter, title The first reltion provies titles, iretors, n tors

More information

Lecture 27: Diffusion of Ions: Part 2: coupled diffusion of cations and

Lecture 27: Diffusion of Ions: Part 2: coupled diffusion of cations and Leture 7: iffusion of Ions: Prt : oupled diffusion of tions nd nions s desried y Nernst-Plnk Eqution Tody s topis Continue to understnd the fundmentl kinetis prmeters of diffusion of ions within n eletrilly

More information

mesuring ro referene points Trget point Pile Figure 1. Conventionl mesurement metho of the pile position In the pst reserh the uthors hve evelope Bum

mesuring ro referene points Trget point Pile Figure 1. Conventionl mesurement metho of the pile position In the pst reserh the uthors hve evelope Bum Development of New Metho for Mesurement of Centrl Ais of Clinril Strutures Using Totl Sttion Kzuhie Nkniw 1 Nouoshi Yuki Disuke Nishi 3 Proshhnk Dzinis 4 1 CEO KUMONOS Corportion Osk Jpn. Emil: nkniw09@knkou.o.jp

More information

H 4 H 8 N 2. Example 1 A compound is found to have an accurate relative formula mass of It is thought to be either CH 3.

H 4 H 8 N 2. Example 1 A compound is found to have an accurate relative formula mass of It is thought to be either CH 3. . Spetrosopy Mss spetrosopy igh resolution mss spetrometry n e used to determine the moleulr formul of ompound from the urte mss of the moleulr ion For exmple, the following moleulr formuls ll hve rough

More information

QUADRATIC EQUATION. Contents

QUADRATIC EQUATION. Contents QUADRATIC EQUATION Contents Topi Pge No. Theory 0-04 Exerise - 05-09 Exerise - 09-3 Exerise - 3 4-5 Exerise - 4 6 Answer Key 7-8 Syllus Qudrti equtions with rel oeffiients, reltions etween roots nd oeffiients,

More information

Available online at Procedia Computer Science 5 (2011)

Available online at  Procedia Computer Science 5 (2011) Aville online t www.sieneiret.om Proei Computer Siene 5 (20) 505 52 The 2n Interntionl Conferene on Amient Systems, Networks n Tehnologies Spe Vetor Moultion Diret Torque Spee Control Of Inution Motor

More information

Chapter Gauss Quadrature Rule of Integration

Chapter Gauss Quadrature Rule of Integration Chpter 7. Guss Qudrture Rule o Integrtion Ater reding this hpter, you should e le to:. derive the Guss qudrture method or integrtion nd e le to use it to solve prolems, nd. use Guss qudrture method to

More information

Thermodynamics. Question 1. Question 2. Question 3 3/10/2010. Practice Questions PV TR PV T R

Thermodynamics. Question 1. Question 2. Question 3 3/10/2010. Practice Questions PV TR PV T R /10/010 Question 1 1 mole of idel gs is rought to finl stte F y one of three proesses tht hve different initil sttes s shown in the figure. Wht is true for the temperture hnge etween initil nd finl sttes?

More information

CHAPTER 9 BASIC CONCEPTS OF DIFFERENTIAL AND INTEGRAL CALCULUS

CHAPTER 9 BASIC CONCEPTS OF DIFFERENTIAL AND INTEGRAL CALCULUS CHAPTER 9 BASIC CONCEPTS OF DIFFERENTIAL AND INTEGRAL CALCULUS BASIC CONCEPTS OF DIFFERENTIAL AND INTEGRAL CALCULUS LEARNING OBJECTIVES After stuying this chpter, you will be ble to: Unerstn the bsics

More information

Thermal Diffusivity. Paul Hughes. Department of Physics and Astronomy The University of Manchester Manchester M13 9PL. Second Year Laboratory Report

Thermal Diffusivity. Paul Hughes. Department of Physics and Astronomy The University of Manchester Manchester M13 9PL. Second Year Laboratory Report Therml iffusivity Pul Hughes eprtment of Physics nd Astronomy The University of nchester nchester 3 9PL Second Yer Lbortory Report Nov 4 Abstrct We investigted the therml diffusivity of cylindricl block

More information

Nanoscale heterogeneity promotes energy dissipation in bone

Nanoscale heterogeneity promotes energy dissipation in bone Nnosle heterogeneity promotes energy dissiption in one KUANGSHIN TAI 1 *,MINGDAO 1 *, SUBRA SURESH 1,2, AHMET PALAZOGLU 3 AND CHRISTINE ORTIZ 1 1 Deprtment of Mterils Siene nd Engineering, Msshusetts Institute

More information

5: The Definite Integral

5: The Definite Integral 5: The Definite Integrl 5.: Estimting with Finite Sums Consider moving oject its velocity (meters per second) t ny time (seconds) is given y v t = t+. Cn we use this informtion to determine the distnce

More information

Available online at ScienceDirect. Procedia Engineering 120 (2015 ) EUROSENSORS 2015

Available online at  ScienceDirect. Procedia Engineering 120 (2015 ) EUROSENSORS 2015 Aville online t www.sienediret.om SieneDiret Proedi Engineering 10 (015 ) 887 891 EUROSENSORS 015 A Fesiility Study for Self-Osillting Loop for Three Degreeof-Freedom Coupled MEMS Resontor Fore Sensor

More information

Graph Theory. Simple Graph G = (V, E). V={a,b,c,d,e,f,g,h,k} E={(a,b),(a,g),( a,h),(a,k),(b,c),(b,k),...,(h,k)}

Graph Theory. Simple Graph G = (V, E). V={a,b,c,d,e,f,g,h,k} E={(a,b),(a,g),( a,h),(a,k),(b,c),(b,k),...,(h,k)} Grph Theory Simple Grph G = (V, E). V ={verties}, E={eges}. h k g f e V={,,,,e,f,g,h,k} E={(,),(,g),(,h),(,k),(,),(,k),...,(h,k)} E =16. 1 Grph or Multi-Grph We llow loops n multiple eges. G = (V, E.ψ)

More information

NON-DETERMINISTIC FSA

NON-DETERMINISTIC FSA Tw o types of non-determinism: NON-DETERMINISTIC FS () Multiple strt-sttes; strt-sttes S Q. The lnguge L(M) ={x:x tkes M from some strt-stte to some finl-stte nd ll of x is proessed}. The string x = is

More information

The Emission-Absorption of Energy analyzed by Quantum-Relativity. Abstract

The Emission-Absorption of Energy analyzed by Quantum-Relativity. Abstract The mission-absorption of nergy nlyzed by Quntum-Reltivity Alfred Bennun* & Néstor Ledesm** Abstrt The uslity horizon llows progressive quntifition, from n initil nk prtile, whih yields its energy s blk

More information

(a) A partition P of [a, b] is a finite subset of [a, b] containing a and b. If Q is another partition and P Q, then Q is a refinement of P.

(a) A partition P of [a, b] is a finite subset of [a, b] containing a and b. If Q is another partition and P Q, then Q is a refinement of P. Chpter 7: The Riemnn Integrl When the derivtive is introdued, it is not hrd to see tht the it of the differene quotient should be equl to the slope of the tngent line, or when the horizontl xis is time

More information

This enables us to also express rational numbers other than natural numbers, for example:

This enables us to also express rational numbers other than natural numbers, for example: Overview Study Mteril Business Mthemtis 05-06 Alger The Rel Numers The si numers re,,3,4, these numers re nturl numers nd lso lled positive integers. The positive integers, together with the negtive integers

More information

Processes Using Advanced Physical and

Processes Using Advanced Physical and 156 IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. ED-32, NO. 2, FEBRUARY 1985 Simultion of C:llritil IC Fbrition Proesses Using Advned Physil nd Numeril Methods ERNER JUNGLING, PETER PICHLER, S : EGFRIED

More information

The master ring problem

The master ring problem 2005 Interntionl Conferene on Anlysis of Algorithms DMTCS pro. AD, 2005, 287 296 The mster ring problem Hs Shhni 1 n Lis Zhng 2 1 Computer Siene Dept., Tehnion, Hif 32000, Isrel. 2 Bell Lbs, Luent Tehnologies,

More information

CRISP-contourlets: a critically sampled directional multiresolution image representation

CRISP-contourlets: a critically sampled directional multiresolution image representation CRISP-ontourlets: ritilly smple iretionl multiresolution imge representtion Yue Lu n Minh N. Do Deprtment of Eletril n Computer Engineering University of Illinois t Urn-Chmpign, Urn IL 68, US STRCT Diretionl

More information

LIP. Laboratoire de l Informatique du Parallélisme. Ecole Normale Supérieure de Lyon

LIP. Laboratoire de l Informatique du Parallélisme. Ecole Normale Supérieure de Lyon LIP Lortoire de l Informtique du Prllélisme Eole Normle Supérieure de Lyon Institut IMAG Unité de reherhe ssoiée u CNRS n 1398 One-wy Cellulr Automt on Cyley Grphs Zsuzsnn Rok Mrs 1993 Reserh Report N

More information

Nondeterministic Finite Automata

Nondeterministic Finite Automata Nondeterministi Finite utomt The Power of Guessing Tuesdy, Otoer 4, 2 Reding: Sipser.2 (first prt); Stoughton 3.3 3.5 S235 Lnguges nd utomt eprtment of omputer Siene Wellesley ollege Finite utomton (F)

More information

arxiv: v1 [cond-mat.str-el] 22 Nov 2017

arxiv: v1 [cond-mat.str-el] 22 Nov 2017 Mgnetoeletri memory funtion with optil reout rxiv:1711.814v1 [on-mt.str-el] Nov 17 V. Kosis, 1, K. Pen,, 3 T. Rõõm, 4 U. Ngel, 4 J. Vít,, 5, 6 J. Romhányi, 7 Y. Tokung, 1, 8 Y. Tguhi, 1 Y. Tokur, 1, 9,

More information

Separable discrete functions: recognition and sufficient conditions

Separable discrete functions: recognition and sufficient conditions Seprle isrete funtions: reognition n suffiient onitions Enre Boros Onřej Čepek Vlimir Gurvih Novemer 21, 217 rxiv:1711.6772v1 [mth.co] 17 Nov 217 Astrt A isrete funtion of n vriles is mpping g : X 1...

More information

Iwao Nitta, Suvi Karvonen, Olli Himanen & Mikko Mikkola

Iwao Nitta, Suvi Karvonen, Olli Himanen & Mikko Mikkola Iwo Nitt uvi Krvonen lli imnen nd Mikko Mikkol 008 Modeling the effet of inhomogeneous ompression of GL on lol trnsport phenomen in PEM fuel ell Espoo Finlnd 3 pges elsinki University of ehnology Publitions

More information

Semantic Analysis. CSCI 3136 Principles of Programming Languages. Faculty of Computer Science Dalhousie University. Winter Reading: Chapter 4

Semantic Analysis. CSCI 3136 Principles of Programming Languages. Faculty of Computer Science Dalhousie University. Winter Reading: Chapter 4 Semnti nlysis SI 16 Priniples of Progrmming Lnguges Fulty of omputer Siene Dlhousie University Winter 2012 Reding: hpter 4 Motivtion Soure progrm (hrter strem) Snner (lexil nlysis) Front end Prse tree

More information

MAC-solutions of the nonexistent solutions of mathematical physics

MAC-solutions of the nonexistent solutions of mathematical physics Proceedings of the 4th WSEAS Interntionl Conference on Finite Differences - Finite Elements - Finite Volumes - Boundry Elements MAC-solutions of the nonexistent solutions of mthemticl physics IGO NEYGEBAUE

More information

expression simply by forming an OR of the ANDs of all input variables for which the output is

expression simply by forming an OR of the ANDs of all input variables for which the output is 2.4 Logic Minimiztion nd Krnugh Mps As we found ove, given truth tle, it is lwys possile to write down correct logic expression simply y forming n OR of the ANDs of ll input vriles for which the output

More information

63. Representation of functions as power series Consider a power series. ( 1) n x 2n for all 1 < x < 1

63. Representation of functions as power series Consider a power series. ( 1) n x 2n for all 1 < x < 1 3 9. SEQUENCES AND SERIES 63. Representtion of functions s power series Consider power series x 2 + x 4 x 6 + x 8 + = ( ) n x 2n It is geometric series with q = x 2 nd therefore it converges for ll q =

More information

MA123, Chapter 10: Formulas for integrals: integrals, antiderivatives, and the Fundamental Theorem of Calculus (pp.

MA123, Chapter 10: Formulas for integrals: integrals, antiderivatives, and the Fundamental Theorem of Calculus (pp. MA123, Chpter 1: Formuls for integrls: integrls, ntiderivtives, nd the Fundmentl Theorem of Clculus (pp. 27-233, Gootmn) Chpter Gols: Assignments: Understnd the sttement of the Fundmentl Theorem of Clculus.

More information

Mining Frequent Web Access Patterns with Partial Enumeration

Mining Frequent Web Access Patterns with Partial Enumeration Mining Frequent We Aess Ptterns with Prtil Enumertion Peiyi Tng Deprtment of Computer Siene University of Arknss t Little Rok 2801 S. University Ave. Little Rok, AR 72204 Mrkus P. Turki Deprtment of Computer

More information

Periodic string comparison

Periodic string comparison Periodi string omprison Alexnder Tiskin Deprtment of Computer Siene University of Wrwik http://www.ds.wrwik..uk/~tiskin Alexnder Tiskin (Wrwik) Periodi string omprison 1 / 51 1 Introdution 2 Semi-lol string

More information

arxiv: v1 [cond-mat.mes-hall] 3 Jun 2009

arxiv: v1 [cond-mat.mes-hall] 3 Jun 2009 Anisotropi Optil Spin Hll Effet in Semionutor Mirovities rxiv:0906.0746v1 [on-mt.mes-hll] 3 Jun 2009 A Amo, 1 T C H Liew, 2 C Aros, 1 E Gioino, 1 A V Kvokin, 3,4 n A Brmti 1 1 Lortoire Kstler Brossel,

More information

MEG6007: Advanced Dynamics -Principles and Computational Methods (Fall, 2017) Lecture 4: Euler-Lagrange Equations via Hamilton s Principle

MEG6007: Advanced Dynamics -Principles and Computational Methods (Fall, 2017) Lecture 4: Euler-Lagrange Equations via Hamilton s Principle MEG6007: Avnce Dynmics -Principles n Computtionl Methos (Fll, 2017) Lecture 4: Euler-Lgrnge Equtions vi Hmilton s Principle This lecture covers: Begin with Alembert s Principle. Cst the virtul work emnting

More information

AP Calculus BC Review Applications of Integration (Chapter 6) noting that one common instance of a force is weight

AP Calculus BC Review Applications of Integration (Chapter 6) noting that one common instance of a force is weight AP Clculus BC Review Applictions of Integrtion (Chpter Things to Know n Be Able to Do Fin the re between two curves by integrting with respect to x or y Fin volumes by pproximtions with cross sections:

More information

A027 Uncertainties in Local Anisotropy Estimation from Multi-offset VSP Data

A027 Uncertainties in Local Anisotropy Estimation from Multi-offset VSP Data A07 Uncertinties in Locl Anisotropy Estimtion from Multi-offset VSP Dt M. Asghrzdeh* (Curtin University), A. Bon (Curtin University), R. Pevzner (Curtin University), M. Urosevic (Curtin University) & B.

More information

Pre-Lie algebras, rooted trees and related algebraic structures

Pre-Lie algebras, rooted trees and related algebraic structures Pre-Lie lgers, rooted trees nd relted lgeri strutures Mrh 23, 2004 Definition 1 A pre-lie lger is vetor spe W with mp : W W W suh tht (x y) z x (y z) = (x z) y x (z y). (1) Exmple 2 All ssoitive lgers

More information

Common Voting Rules as Maximum Likelihood Estimators

Common Voting Rules as Maximum Likelihood Estimators Common Voting Rules s Mximum Likelihoo Estimtors Vinent Conitzer Computer Siene Deprtment Crnegie Mellon University 5000 Fores Avenue Pittsurgh, PA 1513 onitzer@s.mu.eu Astrt Voting is very generl metho

More information

INFLUENCE OF EVAPORATION ON CONTACT ANGLES ON HYDROLYZED PET FOILS

INFLUENCE OF EVAPORATION ON CONTACT ANGLES ON HYDROLYZED PET FOILS Mrtin NAGY,. Jiří ŠKVARLA INFLUENCE OF EVAPORATION ON CONTACT ANGLES ON HYDROLYZED PET FOILS ABSTRACT: Tis ontriution presents results from mesuring ontt ngles on moertely yrolyze PET foils immerse in

More information

McMaster University, 1280 Main St West, Hamilton, ON, Canada, L8S 4K1. *Author for correspondence

McMaster University, 1280 Main St West, Hamilton, ON, Canada, L8S 4K1. *Author for correspondence 3925 The Journl of Experimentl Biology 216, 3925-3936 213. Pulishe y The Compny of Biologists Lt oi:1.1242/je.84228 RESERCH RTICLE Uptke, hnling n exretion of N + n Cl from the iet in vivo in freshwter-

More information

Non-Linear & Logistic Regression

Non-Linear & Logistic Regression Non-Liner & Logistic Regression If the sttistics re boring, then you've got the wrong numbers. Edwrd R. Tufte (Sttistics Professor, Yle University) Regression Anlyses When do we use these? PART 1: find

More information

Transition systems (motivation)

Transition systems (motivation) Trnsition systems (motivtion) Course Modelling of Conurrent Systems ( Modellierung neenläufiger Systeme ) Winter Semester 2009/0 University of Duisurg-Essen Brr König Tehing ssistnt: Christoph Blume In

More information

Applied. Grade 9 Assessment of Mathematics. Released assessment Questions

Applied. Grade 9 Assessment of Mathematics. Released assessment Questions Applie Gre 9 Assessment of Mthemtics 21 Relese ssessment Questions Recor your nswers to the multiple-choice questions on the Stuent Answer Sheet (21, Applie). Plese note: The formt of this booklet is ifferent

More information

Plate Theory. Section 11: PLATE BENDING ELEMENTS

Plate Theory. Section 11: PLATE BENDING ELEMENTS Section : PLATE BENDING ELEMENTS Plte Theor A plte is structurl element hose mid surfce lies in flt plne. The dimension in the direction norml to the plne is referred to s the thickness of the plte. A

More information

NUMERICAL INTEGRATION. The inverse process to differentiation in calculus is integration. Mathematically, integration is represented by.

NUMERICAL INTEGRATION. The inverse process to differentiation in calculus is integration. Mathematically, integration is represented by. NUMERICAL INTEGRATION 1 Introduction The inverse process to differentition in clculus is integrtion. Mthemticlly, integrtion is represented by f(x) dx which stnds for the integrl of the function f(x) with

More information

On the application of explicit spatial filtering to the variables or fluxes of linear equations

On the application of explicit spatial filtering to the variables or fluxes of linear equations Journl of Computtionl Physics 225 (27) 2 27 www.elsevier.com/locte/jcp Short Note On the ppliction of explicit sptil filtering to the vriles or fluxes of liner equtions Christophe Bogey *, Christophe Billy

More information

Tree Pattern Aggregation for Scalable XML Data Dissemination

Tree Pattern Aggregation for Scalable XML Data Dissemination Tree Pttern Aggregtion for Slle XML Dt Dissemintion Chee-Yong Chn, Wenfei Fn Λ, Psl Feler y, Minos Groflkis, Rjeev Rstogi Bell Ls, Luent Tehnologies fyhn,wenfei,minos,rstogig@reserh.ell-ls.om, Psl.Feler@eureom.fr

More information

CSC2542 Representations for Classical Planning

CSC2542 Representations for Classical Planning 1 Aknowlegements CSC2542 Representtions for Clssil Plnning Sheil MIlrith Deprtment of Computer Siene University of Toronto Winter 2009 Some the slies use in this ourse re moifitions of Dn Nu s leture slies

More information

Continuous Random Variables Class 5, Jeremy Orloff and Jonathan Bloom

Continuous Random Variables Class 5, Jeremy Orloff and Jonathan Bloom Lerning Gols Continuous Rndom Vriles Clss 5, 8.05 Jeremy Orloff nd Jonthn Bloom. Know the definition of continuous rndom vrile. 2. Know the definition of the proility density function (pdf) nd cumultive

More information

Vibrational Relaxation of HF (v=3) + CO

Vibrational Relaxation of HF (v=3) + CO Journl of the Koren Chemicl Society 26, Vol. 6, No. 6 Printed in the Republic of Kore http://dx.doi.org/.52/jkcs.26.6.6.462 Notes Vibrtionl Relxtion of HF (v3) + CO Chng Soon Lee Deprtment of Chemistry,

More information

Conducting Ellipsoid and Circular Disk

Conducting Ellipsoid and Circular Disk 1 Problem Conducting Ellipsoid nd Circulr Disk Kirk T. McDonld Joseph Henry Lbortories, Princeton University, Princeton, NJ 08544 (September 1, 00) Show tht the surfce chrge density σ on conducting ellipsoid,

More information

6.5 Plate Problems in Rectangular Coordinates

6.5 Plate Problems in Rectangular Coordinates 6.5 lte rolems in Rectngulr Coordintes In this section numer of importnt plte prolems ill e emined ug Crte coordintes. 6.5. Uniform ressure producing Bending in One irection Consider first the cse of plte

More information

If only one fertilizer x is used, the dependence of yield z(x) on x first was given by Mitscherlich (1909) in form of the differential equation

If only one fertilizer x is used, the dependence of yield z(x) on x first was given by Mitscherlich (1909) in form of the differential equation Mitsherlih s Lw: Generliztion with severl Fertilizers Hns Shneeerger Institute of Sttistis, University of Erlngen-Nürnerg, Germny 00, 5 th August Astrt: It is shown, tht the rop-yield z in dependene on

More information

Polynomial Approximations for the Natural Logarithm and Arctangent Functions. Math 230

Polynomial Approximations for the Natural Logarithm and Arctangent Functions. Math 230 Polynomil Approimtions for the Nturl Logrithm nd Arctngent Functions Mth 23 You recll from first semester clculus how one cn use the derivtive to find n eqution for the tngent line to function t given

More information

AN020. a a a. cos. cos. cos. Orientations and Rotations. Introduction. Orientations

AN020. a a a. cos. cos. cos. Orientations and Rotations. Introduction. Orientations AN020 Orienttions nd Rottions Introduction The fct tht ccelerometers re sensitive to the grvittionl force on the device llows them to be used to determine the ttitude of the sensor with respect to the

More information

A Signal-Level Fusion Model for Image-Based Change Detection in DARPA's Dynamic Database System

A Signal-Level Fusion Model for Image-Based Change Detection in DARPA's Dynamic Database System SPIE Aerosense 001 Conference on Signl Processing, Sensor Fusion, nd Trget Recognition X, April 16-0, Orlndo FL. (Minor errors in published version corrected.) A Signl-Level Fusion Model for Imge-Bsed

More information

A NEW COMBINED BRACKETING METHOD FOR SOLVING NONLINEAR EQUATIONS

A NEW COMBINED BRACKETING METHOD FOR SOLVING NONLINEAR EQUATIONS Aville online t htt://ik.org J. Mth. Comut. Si. 3 (013), No. 1, 87-93 ISSN: 197-5307 A NEW COMBINED BRACKETING METHOD FOR SOLVING NONLINEAR EQUATIONS M.A. HAFIZ Dertment of mthemti, Fulty of Siene nd rt,

More information

Chapter 4. Additional Variational Concepts

Chapter 4. Additional Variational Concepts Chpter 4 Additionl Vritionl Concepts 137 In the previous chpter we considered clculus o vrition problems which hd ixed boundry conditions. Tht is, in one dimension the end point conditions were speciied.

More information

Génération aléatoire uniforme pour les réseaux d automates

Génération aléatoire uniforme pour les réseaux d automates Génértion létoire uniforme pour les réseux d utomtes Niols Bsset (Trvil ommun ve Mihèle Sori et Jen Miresse) Université lire de Bruxelles Journées Alé 2017 1/25 Motivtions (1/2) p q Automt re omni-present

More information

Measuring Electron Work Function in Metal

Measuring Electron Work Function in Metal n experiment of the Electron topic Mesuring Electron Work Function in Metl Instructor: 梁生 Office: 7-318 Emil: shling@bjtu.edu.cn Purposes 1. To understnd the concept of electron work function in metl nd

More information

Journal of Mathematical Analysis and Applications

Journal of Mathematical Analysis and Applications J. Math. Anal. Appl. 371 (010) 759 763 Contents lists available at SieneDiret Journal of Mathematial Analysis an Appliations www.elsevier.om/loate/jmaa Singular Sturm omparison theorems Dov Aharonov, Uri

More information

The Thermodynamics of Aqueous Electrolyte Solutions

The Thermodynamics of Aqueous Electrolyte Solutions 18 The Thermodynmics of Aqueous Electrolyte Solutions As discussed in Chpter 10, when slt is dissolved in wter or in other pproprite solvent, the molecules dissocite into ions. In queous solutions, strong

More information

f (x)dx = f(b) f(a). a b f (x)dx is the limit of sums

f (x)dx = f(b) f(a). a b f (x)dx is the limit of sums Green s Theorem If f is funtion of one vrible x with derivtive f x) or df dx to the Fundmentl Theorem of lulus, nd [, b] is given intervl then, ording This is not trivil result, onsidering tht b b f x)dx

More information

NUMERICAL SIMULATION OF FRONTAL MIXED CLOUD SYSTEMS AND CLOUD MICROSTRUCTURE EFFECT ON SATELLITE SIGNAL

NUMERICAL SIMULATION OF FRONTAL MIXED CLOUD SYSTEMS AND CLOUD MICROSTRUCTURE EFFECT ON SATELLITE SIGNAL NUMERICAL SIMULATION OF FRONTAL MIXED CLOUD SYSTEMS AND CLOUD MICROSTRUCTURE EFFECT ON SATELLITE SIGNAL V. Bkhnov, O. Kryvook, B. Dormn Ukrinin Hydrometeorologicl Reserch Institute, Avenue of Science 37,

More information

The Riemann-Stieltjes Integral

The Riemann-Stieltjes Integral Chpter 6 The Riemnn-Stieltjes Integrl 6.1. Definition nd Eistene of the Integrl Definition 6.1. Let, b R nd < b. ( A prtition P of intervl [, b] is finite set of points P = { 0, 1,..., n } suh tht = 0

More information

A Remark on Gauge Invariance in Wavelet-Based Quantum Field Theory

A Remark on Gauge Invariance in Wavelet-Based Quantum Field Theory New Avnces in Physics Vol. 5 No. Jnury-June 0 pp. -8 A Remrk on Gue Invrince in Wvelet-Bse Quntum Fiel Theory S. Albeverio & M. V. Altisky b c Wvelet trnsform hs been ttrctin ttention s tool for reulriztion

More information

PROPORTIONAL ELECTRO-HYDRAULIC CONTOROLS

PROPORTIONAL ELECTRO-HYDRAULIC CONTOROLS H RRINL ELECR-HDRULIC CNRLS -Hyrid Components...ge 656 roportionl Electro-Hydrulic Control s...ge 667 roportionl Electro-Hydrulic Controls 655 High-ccurcy, simple, convenient relizes your drems. Why simple?

More information

I N T R O D U C T I O N T O C O M P U T E R G R A P H I C S I N T R O D U C T I O N T O C O M P U T E R G R A P H I C S

I N T R O D U C T I O N T O C O M P U T E R G R A P H I C S I N T R O D U C T I O N T O C O M P U T E R G R A P H I C S How Are Trnsformtions Use in Computer Grphis? Ojet onstrution using ssemlies/ hierrh of prts l Skethp s msters n instnes; leves ontin primitives rolem: How to move n ojet We know how to move ojets in rel

More information

A Study of Ductile Damage and Failure of Pure Copper Part II: Analysis of the Deep Drawing Process of a Cylindrical Shell

A Study of Ductile Damage and Failure of Pure Copper Part II: Analysis of the Deep Drawing Process of a Cylindrical Shell TECHNISCHE MECHANIK, 3, 6, (1), 631-648 sumitte: Ferury, 11 A Stuy of Ductile Dmge n Filure of Pure Copper Prt II: Anlysis of the Deep Drwing Process of Cylinricl Shell M. Zpr, N. Tutyshkin, W.H. Müller,

More information

LOGARITHMIC INEQUALITIES FOR TWO POSITIVE NUMBERS VIA TAYLOR S EXPANSION WITH INTEGRAL REMAINDER

LOGARITHMIC INEQUALITIES FOR TWO POSITIVE NUMBERS VIA TAYLOR S EXPANSION WITH INTEGRAL REMAINDER LOGARITHMIC INEQUALITIES FOR TWO POSITIVE NUMBERS VIA TAYLOR S EXPANSION WITH INTEGRAL REMAINDER S. S. DRAGOMIR ;2 Astrct. In this pper we otin severl new logrithmic inequlities for two numers ; minly

More information

Role of Missing Carotenoid in Reducing the Fluorescence of Single Monomeric Photosystem II Core Complexes

Role of Missing Carotenoid in Reducing the Fluorescence of Single Monomeric Photosystem II Core Complexes Electronic Supplementry Mteril (ESI for Physicl Chemistry Chemicl Physics. This journl is the Owner Societies 017 Supporting Informtion Role of Missing Crotenoid in Reducing the Fluorescence of Single

More information

Taking Advantage of PostScript. John F. Sherman

Taking Advantage of PostScript. John F. Sherman Tking Avntge of PostSript John F. Shermn Tking Avntge of PostSript John F. Shermn University of Notre Dme Art, Art History & Design University of Notre Dme Notre Dme, IN 46556 5639 FRPEXX@IRISHMVS..n.eu

More information

Basic Angle Rules 5. A Short Hand Geometric Reasons. B Two Reasons. 1 Write in full the meaning of these short hand geometric reasons.

Basic Angle Rules 5. A Short Hand Geometric Reasons. B Two Reasons. 1 Write in full the meaning of these short hand geometric reasons. si ngle Rules 5 6 Short Hnd Geometri Resons 1 Write in full the mening of these short hnd geometri resons. Short Hnd Reson Full Mening ) se s isos Δ re =. ) orr s // lines re =. ) sum s t pt = 360. d)

More information

ON LEFT(RIGHT) SEMI-REGULAR AND g-reguar po-semigroups. Sang Keun Lee

ON LEFT(RIGHT) SEMI-REGULAR AND g-reguar po-semigroups. Sang Keun Lee Kngweon-Kyungki Mth. Jour. 10 (2002), No. 2, pp. 117 122 ON LEFT(RIGHT) SEMI-REGULAR AND g-reguar po-semigroups Sng Keun Lee Astrt. In this pper, we give some properties of left(right) semi-regulr nd g-regulr

More information

Data Assimilation. Alan O Neill Data Assimilation Research Centre University of Reading

Data Assimilation. Alan O Neill Data Assimilation Research Centre University of Reading Dt Assimiltion Aln O Neill Dt Assimiltion Reserch Centre University of Reding Contents Motivtion Univrite sclr dt ssimiltion Multivrite vector dt ssimiltion Optiml Interpoltion BLUE 3d-Vritionl Method

More information

Standard Trigonometric Functions

Standard Trigonometric Functions CRASH KINEMATICS For ngle A: opposite sine A = = hypotenuse djent osine A = = hypotenuse opposite tngent A = = djent For ngle B: opposite sine B = = hypotenuse djent osine B = = hypotenuse opposite tngent

More information

Semi-local string comparison

Semi-local string comparison Semi-lol string omprison Alexnder Tiskin http://www.ds.wrwik..uk/~tiskin Deprtment of Computer Siene University of Wrwik 1 The prolem 2 Effiient output representtion 3 The lgorithms 4 Conlusions nd future

More information

Polytechnic Institute of NYU MA 2122 Worksheet 4

Polytechnic Institute of NYU MA 2122 Worksheet 4 Polytechnic Institute of NYU MA 222 Worksheet 4 Print Nme: ignture: ID #: Instructor/ection: / Directions: how ll your work for every problem. Problem Possible Points 20 2 5 3 5 4 0 5 0 6 5 7 5 Totl 00

More information

Vectors. Chapter14. Syllabus reference: 4.1, 4.2, 4.5 Contents:

Vectors. Chapter14. Syllabus reference: 4.1, 4.2, 4.5 Contents: hpter Vetors Syllus referene:.,.,.5 ontents: D E F G H I J K Vetors nd slrs Geometri opertions with vetors Vetors in the plne The mgnitude of vetor Opertions with plne vetors The vetor etween two points

More information

Linear static analysis of perforated plates with round and staggered holes under their self-weights

Linear static analysis of perforated plates with round and staggered holes under their self-weights Liner sttic nlysis of perforted pltes with round nd stggered holes under their self-weights Mustf Hlûk Srçoğlu*, Uğur Albyrk Online Publiction Dte: 8 Nov 2015 URL: http://www.jresm.org/rchive/resm2015.25me0910.html

More information

Prefix-Free Regular-Expression Matching

Prefix-Free Regular-Expression Matching Prefix-Free Regulr-Expression Mthing Yo-Su Hn, Yjun Wng nd Derik Wood Deprtment of Computer Siene HKUST Prefix-Free Regulr-Expression Mthing p.1/15 Pttern Mthing Given pttern P nd text T, find ll sustrings

More information

3/8" Square (10 mm) Multi-Turn Cermet Trimmer

3/8 Square (10 mm) Multi-Turn Cermet Trimmer www.vishy.om 3/8" Squre ( mm) Multi-Turn Cermet Trimmer FEATURES Industril grde W t 70 C Vishy Spetrol Tests ording to CECC 400 or IEC 60393-1 Contt resistne vrition < 2 % Mteril tegoriztion: for definitions

More information

Entropy and Ergodic Theory Notes 10: Large Deviations I

Entropy and Ergodic Theory Notes 10: Large Deviations I Entropy nd Ergodic Theory Notes 10: Lrge Devitions I 1 A chnge of convention This is our first lecture on pplictions of entropy in probbility theory. In probbility theory, the convention is tht ll logrithms

More information

Available online at ScienceDirect. Procedia Engineering 190 (2017 )

Available online at  ScienceDirect. Procedia Engineering 190 (2017 ) Aville online t www.sciencedirect.com ScienceDirect Procedi Engineering 19 (217 ) 237 242 Structurl nd Physicl Aspects of Construction Engineering Numericl Anlysis of Steel Portl Frme Exposed to Fire Lenk

More information

320-fold luminescence enhancement of [Ru(dpp) 3 ]Cl 2 dispersed on PMMA opal photonic crystals and highly improved oxygen sensing performance

320-fold luminescence enhancement of [Ru(dpp) 3 ]Cl 2 dispersed on PMMA opal photonic crystals and highly improved oxygen sensing performance OPEN (214) 3, e29; ß 214 CIOMP. All rights reserved 247-7538/14 www.nture.om/ls ORIGINAL ARTICLE 32-fold luminesene enhnement of [Ru(dpp) 3 ]Cl 2 dispersed on PMMA opl photoni rystls nd highly improved

More information

METHODS OF APPROXIMATING THE RIEMANN INTEGRALS AND APPLICATIONS

METHODS OF APPROXIMATING THE RIEMANN INTEGRALS AND APPLICATIONS Journl of Young Scientist Volume III 5 ISSN 44-8; ISSN CD-ROM 44-9; ISSN Online 44-5; ISSN-L 44 8 METHODS OF APPROXIMATING THE RIEMANN INTEGRALS AND APPLICATIONS An ALEXANDRU Scientific Coordintor: Assist

More information

are coplanar. ˆ ˆ ˆ and iˆ

are coplanar. ˆ ˆ ˆ and iˆ SMLE QUESTION ER Clss XII Mthemtis Time llowed: hrs Mimum Mrks: Generl Instrutions: i ll questions re ompulsor. ii The question pper onsists of 6 questions divided into three Setions, B nd C. iii Question

More information

Pythagoras theorem and surds

Pythagoras theorem and surds HPTER Mesurement nd Geometry Pythgors theorem nd surds In IE-EM Mthemtis Yer 8, you lernt out the remrkle reltionship etween the lengths of the sides of right-ngled tringle. This result is known s Pythgors

More information

Revealing the molecular structure of single-molecule junctions in different conductance states by fishing-mode tip-enhanced Raman spectroscopy

Revealing the molecular structure of single-molecule junctions in different conductance states by fishing-mode tip-enhanced Raman spectroscopy Reeived 23 Nov 2010 Aepted 13 Apr 2011 Pulished 10 My 2011 DOI: 10.1038/nomms1310 Reveling the moleulr struture of single-moleule juntions in different ondutne sttes y fishing-mode tip-enhned Rmn spetrosopy

More information

1 Nondeterministic Finite Automata

1 Nondeterministic Finite Automata 1 Nondeterministic Finite Automt Suppose in life, whenever you hd choice, you could try oth possiilities nd live your life. At the end, you would go ck nd choose the one tht worked out the est. Then you

More information

Tool Support for Checking Railway Interlocking Designs

Tool Support for Checking Railway Interlocking Designs Tool Support for Cheking Rilwy Interloking Designs K. Winter W. Johnston P. Roinson P. Strooper L. vn en Berg Shool of Informtion Tehnology n Eletril Engineering University of Queensln Emil: kirsten@itee.uq.eu.u

More information

SEQUENTIAL MOVEMENT IN THE GREAT FISH WAR: A PRELIMINARY ANALYSIS

SEQUENTIAL MOVEMENT IN THE GREAT FISH WAR: A PRELIMINARY ANALYSIS Mjlh Bdn Pengkjin dn Penerpn Teknologi No. 79, Feruri 997 ISSN 06-6569 SEQUENTIAL MOVEMENT IN THE GREAT FISH WAR: A PRELIMINARY ANALYSIS Budy P. Resosudrmo Direktort Pengkjin Sistem Sosil, Ekonomi dn Pengemngn

More information

Analysis of Spatial Effects of Two-row Pile Structure of Foundation Pit Based on Elastic Resistance Method

Analysis of Spatial Effects of Two-row Pile Structure of Foundation Pit Based on Elastic Resistance Method Interntionl Journl o ivil & Environmentl Engineering IJEE-IJENS Vol: No: Anlsis o Sptil Eects o Two-row Pile Structure o Fountion Pit se on Elstic Resistnce Metho YUAN Mn ; DING Jihui b ; ZHANG Qin c ollege

More information