Real-time Elastic Deformations of Soft Tissues for Surgery Simulation
Texte intégral
(2) INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET EN AUTOMATIQUE. Real-time elastic deformations of soft tissues for surgery simulation Stéphane Cotin , Hervé Delingette, Nicholas Ayache. N˚ 3511 Octobre 1998. THÈME 3. ISSN 0249-6399. apport de recherche.
(3)
(4)
(5)
(6)
(7) !"# $
(8) %%&'()*%&+
(9) , % -& .
(10) /0 124365798;:=<?>A@B2#CD:FEHGJIK<MLNO3QPR<MSDCT:UV<W2X2#<YEZE[G]\KCT^_7@VSD8Z`bac"8;^_7<YEVEZE degfhbi0jk lnmpoqirqs_t/oquwvWmxegvWhbhyiznhys_t{eYuwmYi)| u}hys_~Wi|BYv_mYmYi|;tv_mYmBs_uws_mYti r v)ioYuwBs_Yr ibW_W s_YZvWr oYi.r it{eYirt{eYim0Wjp Wk t/oqvWgriy4WWk _Bs)~Wi R =/4#B_p lnm[oqeYuw'Bs_Zir|¡¢i?Yi tr u}Zi£s¤mYi/¡¥hbioqegv [¦§vWr'Yr ~Wir¨!uwh0g©ªs)ou}v_m«uwmYt©wYYuwmY~¬s YvWep©w¨6YhbuwtXis_o©;rhbuwtv hbgiv6©YYuwi]©OBYs_Yuwi©wbo¦§vWr mbvWh®i©}s_hb oiu}gtuwu}ont¨s_©"oeYu}hyivWs_r~_¨0i¡s_eYmYuwt{ e°s_ m'Yu±io{©ªs_s_Y©±oq¨uwt.©wu}hymg²6v6YoieY©}uwimY~beBv_s)¦%VoqieYv_i¦ZgYii/¦§¦§vWvWr rhKhyss_oqYuwvW©wimYV¯]v6dYuweYii s_mYQoqeYi¦§vWr tis)v6tu}s)oiQ¡uwoe?oeYibYi¦§vWr hys)oquwvWm¯b³´ris_©µz¶oquwhbibtvWhbYgoqs)oquwvWm?v_¦JoqeYibYi/¦§vWrhys)ou}vWm u}¢VvW uwY©wi·oqeBs_mg²6¸oqvbs0Yr i/z¶Yrv6tiuwmY~v_¦%i©}ihbimpo{s_r¨Yi/¦§vWrhys)ou}vWmg¹Yir u i¦§rv_h(sºBmYu±oqi·i©}ihyimpo hbioqegv ¯degu}¸hyi/oqeYv6ReBs)¸ZiimRu}hbY©wihbimMoi'uwms¨6 oqih®uwmYt©wYYuwmY~s.¦§vWrti¦§iiYYs_t{²Kgi u}tis_mY stvW©w©}uwuwvWm?Yioit/oquwvWm»s)©}~Wv_ru±oqeYh'¯0degiy u}hY©}s)oqvWr¡¸vWr²M.uwm¼r iXs_©µz¶ou}hbiA¡u±oqe?seYu}~_e?r i vW©} oquwvWm¼©wu ir hbv Yi©D¯ ½¿¾pÀOÁ ÂAà Ä) Å Yr ~Wir¨'uwh0Y©}s)ou}vWmO|BYi¦§vWr hys_Y©wihbv6Yi©w|Br iXs_©µz¶ou}hbi_|Y¦§v_rti¦§iiYBs)t{². Ò ÓYÔÖÕ×ØÚÙ}ÛZÜXÝDÞßà×á#ÞâäãVå/ÝDØÚá_æ=çDå/ß#à#Øè×#â ØÚá#éDØè×#â ê±é ÒÒÓYÔÖÕ×ØÚÙ}Û;ë
(11) Þéíì/Þâ îÞÙÚØïáð/ÞÊÝDÝDÞ{æ=çTåß#à#Øè×#â Øïá#éíØè×#â ê±é Ò/ÒÒ ÓYÔÖÕ×ØÚÙ}Û;ñ
(12) ØÚò¶àå/Ùè×/ç â óYô×/ò¶à#Þ{æ=çTåß#à#Øè×#â Øïá#éíØè×#â ê±é Ò/Ò/ÒÒ¹àÝTÝíßMÛöõ/õq÷"÷"÷â ØÚá#éDØè×#â ê±éÊõ{Ó;øù#ØÚß)Þç¶õÓ;úBû§î%ó"üý%ÓYÔÖÞá#ð)â àÝíÕ¢Ù Unité de recherche INRIA Sophia Antipolis 2004 route des Lucioles, BP 93, 06902 SOPHIA ANTIPOLIS Cedex (France) Téléphone : 04 93 65 77 77 – Télécopie : 04 93 65 77 65. ƱÇ
(13) ÈÊÉnË4̹È]ÍÎ}ÉnÏTÐÑ.
(14)
(15) "
(16) K&( % ¿Og¤
(17) %%&'® &' &' % -&'
(18) /=&
(19) +0 /.
(20) s_mYti rqs)YVv_r oYixrit{egirt{egi_|·mYv_YRYtru v_mY'YmYi mYvW i©w©wi hy/oqeYv6Yi Zir hyi/o z o{s_mpoYi° u}hY©wir0©}s¿t{egu}r Yr~Wuwi°giKoqrgtoqgriAs_mBs)ovWhbuMYioqr u}gu}hbimguwvWmYmYi©}©wihbv6Y©wu} i Ys_r ou}r u}hys_~WihbYuwtXs_©wi¯%i hyv6Yf©}i·geM¨6 uMYi.Yi·ti¹oqr YtoYris_mBs)ovWhbuMYii o¢¦§vWmYYYr¹©}s0oqegvWr u}i Yi©ï©ªs_oquwtu±oq©wu}mgXs_uwriMYu o{s)Y©}u±o©wi¹©wu}imyimpoqri©wi¦§vWrti]s_Yg©}uMYiJ Yr9titv_rY9hbvWgio©}s·Y¦§v_rz hys)oquwvWmRr g©woqs_mpoqi_¯mtXs_©wtY©ZimRoihbYÊznri©VYi·©}sY/¦§vWrhys)ou}vWm°i o¹VvW uwY©wi·~Wr)ti YmRYr /znts_©wtY© Yi0Y¦§vWr hys)oquwvWmY©whbimpo{s)u}r ivWgoimMYiBs_r©ªsxhb/oqeYv6Yi°giA©}hyimpoqAºBmYuw¯"!¢io oqiRhb/oqeYv6Yi
(21) oKhbuwibim?v i riyBs_mY.Ym?uwh0g©ªs)oiYrt{eYuwrYr ~WuwtXs_©uwmYt©wBs_mpoYm? ¨6 ofhbi
(22) ri/oqvWgr#ïi%$OvWros_uwmYu Mïgm s_©w~WvWr uwoeYhbiYi.Yoitou}v_mxYi.tv_©}©wu} u}v_mY¯'&vWggr impoqv_mYgii%( ihbY©wiYi.uwh0Y©}s)oquwvWm Yi.©ªs t{eYuwrYr ~Wu}ieYBs)oquMYi_¯ ) à 4 Á +* uwh0Y©}s)ou}vWm Yi.t{eYuwrYr ~Wuwi_|;hbv Yf©}ig¦§vWr hKs)Y©}i|B©}hyimpoqºYmYu}|Bu}hys_~_iruwihyYuwtXs_©wi_| ri/oqvWYr i$VvWroX|B©}s_oquwtu±oq©}uwmYXs)u}r i.
(23) b %
(24) y'& J
(25) &[uwoexoqegiYi i©}vWghyimpo.v_¦9©}s_Bs_r vWtvWYuwtoit{eYmYuMYi·¡egu}t{e r iYgtiAvWZirs)oquwmY~boquwhbiAs_mY¿hbvWrYuwYu±on¨W| Yr ~WuwtXs_©uwh0g©ªs)ou}v_m s_gVis_roqvQZi s_m i impoqu}s_©i©wihbimpoKv_¦oqvWhbvWr rv4¡ ïygr~Wir ¨W¯ lnmYgiiO|¹hbvW o YmYi (gZir u}imYti¬gr~WivWmYKs_mY oYYimpoKeBs i'ovQYrqs_t/oquwtioqegu}bmYv i©oqit{egmYuMYi)¯ &v4¡¹s)BsX¨ boqegi¨ Yrqs)toquwtixvWm[s_m¬imYYv_orqs_uwmYir|vWm¬©wu uwmY~ s_mYuwhys_©}KvWr°ts_Bs ir¯ deYi ©ªs)t{² v_¦·riXs)©}uwh u}m oeYixºBr o vW©wgou}vWm s_mY¿oeYiioqegu}ts_©grvWY©wihb©}uwmY²_i oqvyoqeYiv_oqegirvW©wgoquwvWmYeYv4¡ syriXs)©
(26) mgii¿¦§vWruwh0Y©}s)oqi Yr ~Wir¨W¯ degu} s_r ou}t©}iYriimMo·mYi/¡ u}Yis_¦§vWrgi i©}v_Yu}mg~sKr iXs_©µz¶ou}hbiYr ~Wir¨¿ u}hY©}s)oquwvWm ¨ oqih uwmYtvWrz Vv_rqs)ou}mY~oqeYi ¦§v_©}©wv4¡u}mY~t{eYs_rqs_t/oqiruw oquwt('¢s vW©wYhbioruwtgi¦§vWr hKs)Y©}i hyv6Yi©D|Bs¦§vWrti ¦§iiYBs_t{²KYi uwti_| s_mY ris_©±zíoquwhbigi¦§vWr hKsoquwvWmYBs_ i vWmxsMBs_ u"mYvWm z¶©}uwmYis_rYu}v_hyit{eBs_mYuwtXs)©
(27) ZieYs uwvWr¯ $. %. )+*,). -/.021435768.
(28) 9;:<.,:>=?14@8A+BC@ED. )+*JI. KLBM3
(29) 5768BCN<OP9+@8Q =. ·uwBs)©±z¶riXs)©}uwh¥s)mYQriXs)©±zíoquwhyiuwmpoqirqs_t/oquwvWmYs_rii impoqu}s_©uwm? Yr~_ir ¨ uwh0Y©}s)oquwvWm¯Ais_©±zíoquwhbiu}mpoqirz s_tou}v_m r i MYuwriboeBs)obs)mM¨£s_tou}v_m£¦§rvWhoqeYiRv_Virqs)ovWrA~WimYirs)oqibs_m u}mYo{s_mpoqs_mYiv_Ybri Vv_mYiR¦§r vWh oqeYi ou}hY©}s)oqi vWr~Ws_m|Y¡eBs)oi iroeYitvWhbY©wi%( u±on¨¿v)¦9u±oq~WivWhbi/oqr ¨_¯G¿v_riv ir|ZuwmYtiAs_©w©oqeYivWr ~ps_mY u}m¿oqeYieMYhys_m Zv g¨ s)rimYv_oruw~Wu}O|;oeYiuwr eBs_ZihysX¨ t{eBs_mY~_i0YYr u}mg~Rs_m¿vWVirqs)ou}v_m¯ !¢vWmY i MYimpo©w¨_| oqeYiyris_©wu} h¥v_¦¸oeYibYi¦§v_rhys)oquwvWmYuws)mYv_oqegir.²_i/¨¼ZvWuwmpouwm?Yr ~Wir¨Quwh0Y©}s)oquwvWm¯KdeYuwr iXs_©wu} h¥tXs_m ViimYeBs_mgti?p¨xoeYiu}mporv6YYtou}v_m?v)¦¸gi u}ti.¡eYuwt{e»s_©w©wv#¡ ¦§vWrsRZio oqiru}hbhbir uwvWm¼uwm oqeYi uwr oBs_© ¡¢v_r©w¯blnm? Yr~_ir ¨Q u}hY©}s)oquwvWm|%oqeYiuwmpoqi~W rqs)ou}v_m¼v_¦J¦§vWr tiA¦§iiYBs_t{² ¨6 oqihboqv'~WimYirs)oqib Yt{ e» im z qs)ou}v_mY0uw0v_¦¹Yruwhbi°uwhyZvWro{s_mYti_|=s_©}hbvWos_uwhyZvWro{s_mpos) uwBs_©J¦§iiYBs_t{²;H¯ &[eYim£tvWYY©wi¼¡uwoe YrituwitvWhbYgoqs)oquwvWmYv_¦
(30) oqegi.¦§v_rti|;u±ohKsX¨'Zi.VvW uwY©wi.¦§v_roeYi.Yr ~Wiv_m ovb¦§ii©"eBs)goquwt.imgqs)ou}vWmg t©wvWi.oqvbr iXs_©wuwon¨_¯ F. dirSRvWVv_Y©}v_UTVXWZY[]\ d+^ _=a`bD| &£soqir c\d&£so{pbí|s_mg¬©ªsoo°s_mYe^¢s_rrf\ï+^¹_gb eYs ix eYv4¡m¬oqeYi s_ s_mpo{s)~Wiv_¦¹Yep¨6uwtXs)©¢hbv gi©wv ir0²MuwmYihys)ou}tRhbv6Yi©w.¦§vWrtvWhbYgoirs_mYuwhKsoquwvWm¯³ hbvWmg~¿oqegii Yep¨6uwtXs_©;hbv gi©w|Mi©}s_ ou}it h9hbv6Yi©weB s iZiimKi ( oimY u i©±¨yYi truwZiyu}moqegi©}u±oqirqs)oYrij\ Å Vip | !kp | Å p |E^!!¹pbD¯deYiBs_r ou}tY©}s_r¸ eBs_Zi v_¦s_m°i©ªs) oquwt Zv6g¨bu}¢s.¦§gmYtou}vWm°v_¦Zv_oqeyoqeYiu}mpoirmYs_©; oqr i s_mYoqrqs)u}mA¡u±oqeYuwmAoqegi¹vW ito]s_mg0oqeYi¢i%(6oqirmBs_©6¦§vWrtis)YY©wu}ibov·u±oXm¯ limgirqs)©}©±¨W|W vWhbi¹hbv guwºBts)oquwvWmY vWr¢ u}hbY©wu±ºBtXs)ou}v_mYs_r i hys_Yi ovoeYi i©ªs_oquwtu±on¨°oeYivWr¨yu}mRv_rYir¸oqv0~Wu i·s0Ys_r ou}tY©ªs)r¢ZieBs u}v_r¸oqvoqeYi Yi¦§v_rhys_Y©wiZv6g¨W¯ ³hbvWmY~»oeYixr iYr iimpo{s)ou}vWmgYi¬¦§vWrKgi¦§vWr hKs)Y©}ixYr¦Ts_ti n vW©}ghyi|oqeYi¿hyv_ o°¡uwYi©w¨ Yi s_ripo8WZqSWZrsTVqtuvrsw xETY y·¡uwoez^]zng©}uwmYiRr iYr iimpo{s)ou}vWm s_mYc{+|t}V"T~TY TrsT|Vrsw xETY yuwmMorv6YYti¤¦§vWr tvWhbY oqir¸imY~_u}mYiir u}mYs~ \ kOuwi `Z`bZs_mY°s_YY©wu}iKovtvWhbYgoqir¹s_mgu}hys)ou}vWmyp¨bdiSr RvWVv_Y©}v_8| l.vWgrri/oX|Miot_¯ _BvWr¹i%(gs_hbY©wi_| l.vWgrri/ o TV;WZY[\#ljG¿ddWZ beYs iYi tr u}Zi¿sA ¨6 oih®¦§v_r¢hbv gi©wu}mY~AoeYieMYhys_m'eBs_mY ¡uwoe»sRºBmguwoiyi©}ihbimpo vW©wYhbiKhbi eYi»s_rv_YmYQVv_mYi¯deYi¨ ¦§v_rh0g©ªs)oiys_mYQvW© iKsi/ov)¦¢o{s)ou}t i MBs)ou}v_mY¦§vWr ²Mu}m gi¦§vWr hKsoquwvWm¿Ys_ixvWm Vv_mYi²MuwmYihys)ou}t·s_mg¿eBs)mY n)vW6itotv_mMoqs_toZvWu}mpouwmxs ~Wrqs)YuwmY~bo{s_ ²Z¯¸ oqegirZvW u}Y©wihyv6Yi©}s_r pi rpWyyy"oqt}| prsw xETY y¸¡u±oqe'oqegi.¡¸vWr ²6v_¦ G¿uw©}©wir \#G¿u}©}Wg bD| !¢eBs_g¡uwt{f² TVWZY[\ ! ]Wg bD|+&v_r oqv_fm TVWZY[\ &/d ^l.g( bD|+"Ytu}s_mYMu TVWZY[\ _!¹g bD| _vWg²6eYs_Bs_r \ _vWYp b s_mYU t}roYtut}V7y?q}(WEuTy¸¡uwoe|Y¦§vWri%(gs_hbY©wi_|BoeYi¡¢vWr ²Mv_¦ iYr Ym s_mgc l.s_tYi+© \ l.p bD¯ lnmHgr~Wir ¨[uwh0g©ªs)ou}v_m|tu}imMou}oq¿eBs i?hKs)u}mY©±¨!¦§v6tY'vWm[oqeYiQhys_ zn YruwmY~ hyi/oqeYv6Y YYi oqv oqeYiu}ruwhbY©}uwtu±on¨£v)¦u}hbY©wihbimMoqs)oquwvWm s_mg¼oqegiuwr0ri©ªsoqu i©±¨£©wv4¡tvWhbY o{s)ou}vWmYs_©]tvWhbY©wi%( u±on¨\^lZ | G !¹a `gZ| &Wgj bD7 ¯ _BvWr9i (gs_hbY©}i)8| YieYmBs_ ¦§i©Bs_mg &iuwuwY \# &Wgj bBYr i impo¸s·uwh0Y©}s)oquwvWmyv_¦ZimYgvWtvWYuwt " à#ØèçOÝDÞ éDÕ Øïá)òÊÙÚù 4Þ çÞ ÙÚ×ç§ÝíØÚò #ÙÚØïá#Þ×éÞÙè×/çTÝDØèò9×á ìXØèçDòåÔÖÞÙè×/çTÝDØèò
(31) Õ¹å 4ÞÙèç â ý%ý á (.
(32) Yr ~Wir¨bBs_ iyvWmys. Yr ¦Ts)tihys_ÊzngruwmY~hbv6Yi©T¯9³©woeYvWY~WebuwmyoeYuwtXs_ ioeYiu}mpoirqs)toquwvWmYJs_r iYru im p¨u}mg oqr Yhbimpoq¡u±oqe'imYvWr |;mYvA¦§vWr ti·¦§iiYBs)t{²u}Y i¯]deYi. u}hY©ªsoquwvWm¿im uwrv_mYhbimpo v)7¦ luwYvWm TVWZY[/\#l Å G _9a `b¹o{s)²_ibuwmpoqv?s_ttvWYmpoboqeYi vW©wYhbioqr u}t'mBsoqYr iv_¦oeYivWr ~ps_mY0¡u±oqe s Yi/¦§vWrhys)ou}vWm ©ªsX¡ Yiru i[¦§r vWh s¼hys_ z¶Yr u}mY~¤hbv6Yi©T¯ !¢v irUTVXWZY[\ !¹J._jgb eYs i s_©wv¼Yi i©wvWViHs¼hbv gi© Bs_ iQvWm oqegu}m Y©}s)oiAY©wuwmYi¦§vWr·©}s_Bs)rvW tvWYuwtA~ps)©}©Y©ªs)YYir Yr ~Wir¨ uwh0g©ªs)ou}v_mj¯ &¼iAts_mQs_©wvtu±oqi oqeYi¡¢vWr ²¿v)+¦ v6t{Le TV/WZY[\ l ! ^¹ Zb=s_mY ii i TV/WZY[\#.] gbvWmx¦Ts_tuªs)©
(33) ou} Yihbv6Yi©wu}mg~Y¯ _=uwmYu±oqi i©wihbimpo°hyv6Yi©}Ks_ri'©wi K¡uwYi©±¨ Yi¬YYiov?oeYi¿gu ytg©won¨ v_¦oqeYiu}ryuwhyg©}ihyimpo{s)ou}vWm s_mY oqeYiu}r ©ªs)r~WirRtvWhbY oquwmY~£oquwhbi_¯ &i iroqeYi©}i| Å s_~ps_r TV WZY[ \ Å ^Gf beBs iQYr vWVv_i[s¼hyi/oqeYv6!¦§vWr uwh0Y©}s)ou}mY~¦§is)oqYr i¹v)¦"oqeYi·eMYhys_mi/¨Wi·¡u±oqe's0tvWhbY©wi%(ZieYs uwvWr§©ªs_r ~Wi uwmYtvWhbYriuwY©wij i©}s_ ou}t Yi¦§v_rhys)oquwvWmY /¯ v4¡¸i ir|9mgv gio{s)u}©w0s)rib~Wu im»s_ZvWgooqegiKuwhbY©}ihbimpo{s)ou}v_m»v_¦JoqeYibºBmYu±oqibi©}ihyimpo hbioqegv ?Yi¼ov vW© iboqeYibi MBsoquwvWmY¯b³mYv_oqegir.i%(gs_hbY©wiKv)¦¢i/¨WiyYr ~Wir¨ ¡¹s)~_u im»p¨ "ibds_©}©wit TVWZY[\ "iWgj bD¯]lnm oeYu}¡¸vWr²;|BoqeYis_ oqeYvWr eBs is_t{eYuwi i s ir¨'Yrituwi oYg¨'v_¦oqeYi.Yi/¦§vWrhys)ou}vWm ©ªsX¡Hv_¦oeYi·i/¨Wi ¡eYimoqvWYt{egip¨RsoqriBs_m7¯ v4¡¢i ir|Y oqegi·tvW hbY oquwmY~0oquwhbi eYvWY©wRZis_tti©wirs)oqi p¨ s¦Ts)toqv_rv_¦¢_|g|0oqvys_©w©}v4¡«riXs)©±zíoquwhyi. u}hY©ªsoquwvWm¿¡u±oqe'¦§vWrti¦§iigBs_t{²;¯ !¢v_hyggoquwmY~¼ou}hbi riYYtou}v_m¬eBs_yViim¬oqYgu}i¬p¨ ^¢rv)z &uwi©wim!s_mY !¢v_oquwm \^ & !¹Z gbYuwmY~£s tvWmgYimYs)oquwvWm[oqit{eYmYu6gei \#kOu}i ``ibD¯ &[u±oqe!oqeYuwhbioeYv O|oqegi tvWhbYgoqs)oquwvWm[oquwhbi ri MYuwriH¦§v_rRoqeYi Yi¦§v_rhys)oquwvWm¼v_¦s vW©wYhbioruwtRhbv gi©tXs)m»ZiKr iYYti»ov oeYiytvWhbYgoqs)oquwvWm?oquwhyiyv_¦¹s¿hbv gi©]vWmY©±¨ u}m vW© uwmY~oeYiYr¦Ts_timYv6Yiv_¦VoeYihbieO¯ Å vWmY~s_mYyiY H¨ \ Å pi bBeBs iYitr u}Zi°s·oqit{egmYuMYi¦§vWr tgo oquwmY~©wu}mYis_r¹i©ªs_oquwt·vW itoYiºBmgi s_¸ºYmYuwoi·i©wihbimMohbv6Yi©w¯]deYuw¢oit{eYmYuMYi¡¹s)¹vWmY©±¨Rs)YY©wu}i oqv ir ¨»uwhbY©}iRon¡¸vQYuwhyimYuwvWmBs)©¹vW itoq¯ &»iRts_m s_©wv tuwois hbioqegv £¦§vWr¦§rii/z¶¦§v_rhtgo oquwmY~ u}m oqvWhbvW~_rqs_Yegu}t v_©}YhbiBs)oq~s \ /d pi b%Bs_i¿v_m v ( i©
(34) v_Virqs)ou}vWmg¦§v_rtgo oquwmY~°s)mY uwYs_©}u RXsoquwvWm¯ lnm?vWYrs_gYrvps)t{e|
(35) ¡¸iyeBs iboqruwiQoqv uwmMoi~Wrs)oqiKs_©w©9oqeYibr i MYuwrihbimMo0¦§vWr.s'ris_©}uw ou}tyuwh0g©ªs)ou}v_m TuT¯ïi)¯!ris_©±zíoquwhbi¿hbv6Yi©wu}mg~»v_¦ i©}s_ ou}t oquwgi_|ris_©µz¶oquwhbi uwBs)© s_mg eBs_ oquwt ¦§iiYBs)t{ ² ¯[deYixo{s)ou}t i MBs)ou}v_mYv_¦]oqeYi0i©}s_ ou}thbv6Yi©=s_riA vW© i?p¨ sRhbv6Yu±ºBi ºBmYu±oqi0i©wihbimpohbioqegv oeBs)o·oqs_²_iu}mpoqv s_ttvWYmpoyBs_roquwtY©}s_rZvWYmYBs)r ¨¤tvWmYYu±oquwvWmY¯¤deYi'vW©wgoquwvWm v_¦oqeYii'i MBsoquwvWmYy~Wu ibmYv_obv_mY©w¨»oqeYi Yi¦§v_rhbihbi eYgo¹s_©} v0oqegi¦§vWr tiJoqvAZi impo¹ovAs¦§v_rti¦§iiYBs_t{²KYi uwtis_ttvWr YuwmY~0oqvoqeYi s_toBs_© Yi¦§v_rhys)oquwvWm+¯ _u}mBs)©}©±¨W|Yr iXs_©µz¶ou}hbi·uwmpoqirqs_t/oquwvWmu}ZvW uwY©}i·oeBs_mY²M¹ovsAYriznYr v ti uwmY~bv_¦%i©wihbimpoqs_r ¨ Yi¦§v_rhys)oquwvWmY¢tvWYg©}i°¡uwoe's ViiYs)©}~Wv_ru±oqeYh'¯9deYi ©}uwmYiXs)r¢i©}s_oquwt·Yi¦§v_rhys)oquwvWmY|gtvWhbYgoqiu}m ris_©±zíoquwhbi_|O~_u isyºBr o·s_YYr v ( uwhys)oquwvWm v_¦r iXs_©wu±on¨ s_mgxoqeYuw eYs_·s_©w©wv#¡¸i oeYi0gi i©}v_Yhbimpov_¦]sKºBr o YiuwvWrhbuwvWim t{eBv_s_¦
(36) mgs0u}t s_u}©hr Yi ©ªsYoq©wvWor vW\ ! m¿ v_!¢¦ dooquwZbD ¯Ydi eYs_uwmY©}'uwmYmYiXv4s)¡ r¹hb~Wu v Yii ©OseBhbs)¹vWVr iiir m'iXs_i©wmguw eBoqs_uwt.mYtVii'eBs p¨Ku}vWoqrs_¯ ²Mu}mY~uwmpoqvbs_ttvWgmMo degi0¦§vW©w©}v4¡uwmY~itoquwvWmYgio{s)u}©
(37) oqeYiAhys_uwm tvWmYti goq.v_¦]v_Yr·s_gYrvps)t{e¯ Å it/ oquwvWm?KZvWuwmMo·vWgo oqeYi Yrv_Y©}ih(v)¦%i~_hyimpo{s)ou}vWm 'eYv4¡HovAYYuw©ws0hbv gi©Ov)¦oqeYi ©}u ir¢¦§rvWh$j hyiYuwtXs_©Vu}hys_~Wi¯ Å itou}vWm'j Yi tr u}Zi=on¡¸v·s)YYrv( uwhKsoquwvWmY §©}uwmYis_r=s)mY MBs_ uMmYvWm z¶©}uwmYiXs)rhbv6Yi©w "v_¦goeYiJYi¦§vWr hys)oquwvWm0©}sX¡¤v_¦gv_¦ o oquw Yi]s_mgAu}m0it/oquwvWm |_¡¸i¹Yr i impo]s hbioeYv6s_©w©}v4¡uwmY~ris_©±zíoquwhbi¢tv_hyggo{s)ou}v_mAv_¦Boqegi¢Yi/¦§vWrhys)ou}vWm s_mY oqegi0¦§vWrti¯deYitvW©w©}uwuwvWmQYioit/oquwvWm?s_©}~_vWru±oqeYh Y iQu}m oeYiAuwh0g©ªs)ovWruwYruwi Y¨xYi tr u}Zi?u}m itoquwvWm ¯ Å it/oquwvWcm Yr i impoqi%( Ziruwhbimpo{s)©r ig©wo s_mg it/oquwvWm `Atv_mYt©wYYi¡u±oqe VirZit/oqu i¯ ¸0' %=&'¸
(38) /0 ! deYibt{eYvWuwtiyv_¦¸sZitu±ºBty~Wiv_hyi/oqr u}tbriYriimMoqs)oquwvWm?u}.v_¦¸Yr u}hbibu}hbZvWr oqs_mYtiA¦§vWruwh0Y©}s)ovWr¯deYu} t{eYvWuwtiKeYvWg©}¼Vib~Wv irmYi£p¨ oqeYibr ig©wou}mY~ oqrs_Yi/z¶v $ Zion¡¸iim»riXs)©}uwh s_mg¼uwmpoqirs_tou}v_m¯°lnm?vWYr hbioqegv |oqeYiyris_©}uw ou}t°s_Zit/oAv_¦¢oqeYiyvWr~Ws_mYu}©}uwmY²_i|=ºBr o©w¨_|=oqvxs_m£s_ttYrs)oqiyi~Whbimpo{soquwvWm¤v_¦s vWvWr~W©wYs_hbm ior uwYt r ¦Thbs_tii_Y¯'uwtXlns)m»©ouwhyeYiys_~W¦§v_i¿©}©ws_v4mY¡u}mY|¸~g|it¡¸vWi°mYg¡©w¨_u}©w|¹©oq¦§v£v ts)Ym 0v_s_m¼gYoqregvWfi grYt#u}s)"ZoqTiq¯ridYeYriKi©}iu mpoqis)r0oquweBvWs_m¬0v_s ¦oqieYri ¨»uwihb~WVhbvWirmpo{oqs_imp o ¦§YmYt/oquwvWm¬uwm oqegi¿hbioqs_ZvW©}uwh s_mg u±oqyYr ~Wir¨ uwytvWhbY©wi%(V¯ G¿vWr iv ir|¹ oqegi¿Yi i©}vW ghyimpo'v_¦·mYi/¡ û§ñý"û§ó.
(39) ©ªs)Bs_rv_tv_Yu}toqit{eYmYuMYiJ¦§vWreYiYs)oquwt Yr~_ir ¨s_riv_¦V~Wrv4¡uwmY~u}mpoqiri oX¯d
(40) v.oqeYuw]imY|M¡¸is)ri¡¢v_r²Mu}mg~ u}m»tvW©w©ªs)VvWrs)oquwvWmQ¡uwoe»oqegi°hbiYuwtXs)©JoiXs_h v_¦¹]rf¯ Gxs_rits_ (£s)o0lÊ !¢³ |
(41) Zituªs_©wu Ri¤uwm»egiBs)ou}t Yr ~Wir¨W¯ CT scan, MRI, NLM database Construction of the surface 3D model of the organ Volumetric model. Geometric Modeling. Biomechanical Experiments Physical Model Finite Element Method Non-linear deformations. Non-linear forces. Physical Modeling. _=uw~WYri '
(42)
(43)
(44) "!$#&%'(
(45)
(46) ) * + ,-.+
(47) /) (0 1324&(+ ) 5 %'6! 7 8
(48)
(49) 9:;< ,=(>! I *,). ?U@8BC5768.9:>9A@v5:>5;:576890 .B 530 9NBM3j9A@ 6C4B 3.D+BC@. I *JI. -/.0ON 3
(50) BGP 0 BC=QC4BC=. lnm¤vWrgir0ov Yrv6YYtisxhbv6Yi©¸v_¦oqeYi°©}u irA¡uwoe s_mBs)ovWhbu}ts_©¢Yi/o{s_uw©w|]sxBso{s_ ioYr v uwYi p¨¼oqeYi E WZVtw|WZYGFtIH q,WZqKJvw
(51) ML TSxZtut}| TJ¡¹s_Y i¯JdeYuwBs)o{s)iotvWmYuw ov)¦9s ( u}s_©MGxl¢uwhys_~Wiv)¦oeYi.eYiXs_ s_mYRmgit{²Rs)mYR©wvWmY~Wu±oqYgu}mBs)©V itou}v_mYv_¦"oqegi ri ov)¦oqeYi Vv6g¨W¯=deYi !¢d[Bs)oqstv_mYuw ov_¦
(52) s ( uªs)©V tXs_mY v_¦=oeYi.impoquwriZv g¨Ko{s_²)imxs)ohbhuwmpoqir s_©w¯¢degi0s ( u}s_©"s_mYs)oqvWhbuwtXs_©"uwhys_~Wi s_r its_mYmYi Yuwtoqgri v_¦%tr¨WvW~_imYuwt.©wu}tiv_¦"oeYi·Zv g¨_¯deYi¨Rs_ri· Yu±o¹tvW©}v_r¹u}hys_~_i¹v_¦% u Ri M¨¿# 0Yu (gi©}¯]deYi i s_mBs)ovWhbu}ts_©%©wu}tis)ris_©} vs)o0hbh uwmMoir s)©=s_mgxtv_u}mYtu}gi¡u±oqexoeYi!¢d s ( u}s_©%u}hys_~_i¯deYiri0s_ri 4a `_trvW zn it/oquwvWmY¦§vWriXs_t{e¿hbv Bs)©}u±on¨W¯ d
(53) v i%(6oqrs_to oqeYi?eYs_Vi¼v_¦0oeYi?©}u ir ¦§r vWh oqeYuw Bs)o{s)io|·¡¢i?Y i«oeYi»s)mBs)oqv_hyuwtXs)© ©}uwti §t¦Ê¯ ºB~WYr i¿ /|¡eYuwt{e ~Wu iysQZio oqirytvWmp oqrs_ obZion¡¸iim oqegi ©wu irys_mg oeYiYr rvWgmYYuwmY~¼v_r~ps_mg¯£deYi Bs)oqs_i/otvWmgtir mYuwmY~oqeYiA©wu irts_m ZiAriYYti oqv's_ZvWgo04° ©}uwti¯³¦ oqir tvWmpoqrqs) o.imgeBs_mYtihbimpoX| ¡¢i s_gY©w¨¤s_m iY~Wigioqitou}vWm s_©w~WvWr uwoeYhov?i (6oqrqs)tooqegi tvWmpoqvWgrv_¦oqeYiuwhys_~Wi)|¢s_mg oeYim Y u}mg~ s? u}hbY©wi'oqeYr iegvW©}gu}mY~?oqit{eYmYu6gi_|¹¡¸i¿r io{s)u}m oqeYi'oqrv_mY~WirbvWmgi¯ &i (6oX|¢¡¸i¿gi'ihyuµzÊs)goqvWhys)ou}t Yi¦§v_rhys_Y©wihbv6Yi©w¸¦§v_r]on¡¸v)z¶Yu}hbimYuwvWmBs_©Ztv_mMovWYrJi%(6oqrs_tou}v_mKoqv~WimYirs)oqis io¸v_¦Oon¡¸v)z¶Yu}hbimYuwvWmBs_© YuwmBs_r ¨KuwhKs)~Wi §t¦Ê¯9ºB~_Yri· /¯deYi ©wu}ti~WimYirs)oqi's_rioqeYim o{s)t{²_i'oqv¦§vWrh$soeYrii/z¶Yu}hbimYuwvWmBs_© YuwmBs_r ¨Ru}hys_~Wpi \#G a `gb Tt¦Ê¯ºB~_Yrij ¯ nl m¬vWr Yirboqv¼tXs_goYri'oqegixeYs_Vi¿v_¦ oeYixi (6oqir mBs_©Yr¦Ts_ti¿v_¦·oeYi¿©wu iry¡¢i¿tvWg©}¬gi s?Y6z v( i© oqr uªs_mg~WY©}s)oquwvWm.Yrv uwYip¨·oqeYihys_r t{eYuwmY~tYZi
(54) s_©w~WvWru±oqegh \ !¹a`bD|)eYv4¡¸i ir%oqeYimMYhVir
(55) v)¦ oru}s_mY~W©wi ~Wimgirqsoqiuw¸ov v©ªs)r~Wi¦§vWrJ¦§gr oqegir¢grv6ti uwmY~Y¯;G¿vWr iv ir|Bshbv6v_oqeYuwmY~Av)¦"oqeYiYr¦Ts_tiu}¹mgitis_r ¨ R û áçTÝDØïÝDù#ÝDÞ9ê±å/é%ý%Þ çDÞ ×é¶ò¶àó
(56) ð×/ØïáçTÝãO×áòÞé¶çåê ÝDà#Þ]îØïðÞ çTÝDØÚì/Þ=ÝDé¶×/òÊÝ â ý%ý á (.
(57) _=uw~WYri¹?' %6 * /
(58)
(59) 5 ' 6,
(60) 5 )( ,
(61) 5 )(6! 7 5 5
(62) : / 0 > ,G 5%6 (,
(63)
(64) %6/ . M ) ,
(65) 5 )(
(66) M ! 7 5 5 %'0
(67) 5%6 3)(
(68) (, ,
(69) , %6 ( 5 ' ) 6,,I,()
(70) !. _=uw~WYri·j8'#=0 , %6 * /
(71)
(72) 3 5 5 %'(,=
(73) , /)'(0 %6 ' 24 5 5 %'6! ,(
(74) , I () =
(75) ,
(76) -
(77) 5 ' 0
(78) 5%6* ; +.
(79) /) (
(80) ,
(81) 5%
(82) ) 5%I)
(83) (, 5%'
(84) 5
(85) 9!. û§ñý"û§ó.
(86) oqv s v_u}[ oqs_uwrtXs)i i$Vit/oq §t¦Ê¯ ºB~WYr i j ¯ ³ VvW uwY©wi vW©wgoquwvWm[tv_mYuw ou}m!Yituwhys)oquwmY~ s_m!uwv)z Yr¦Ts_tiKhbv Yi©p¨¼guwmY~ s'hbie¼uwhbY©}u±ºBts)oquwvWm»ov vW©T¯ v4¡¢i ir|=¦§vWr.hbvWr i Bi ( u}Yuw©wuwon¨_|9Vv)oqe?u}m?oqeYi i~Whbimpo{s)ou}v_m s_mY uwhbY©wuwºBts)oquwvWm¿Yrv6tii|B¡¸ieBs iY iÊuwhbY©wi%('hbi eYi{¯ Å u}hbY©wi%( hbieYi°s_r i's_m vWruw~WuwmBs_©¸rigri impo{soquwvWm v_¦oeYrii/zngu}hbimguwvWmBs_©vW6itobYi i©wvWVi p¨ i©wuwmY~Wio oqi \ i©} sg| i©ª 8 bD¯J³ u}hbY©wi%( hbiexts_m'Vi. iimxs_s_m'i%(6oimY u}vWm¿v_¦=sb mBs_²)is \ &[dWgb u}m j s_mY»oeYir i¦§vWr iRuw¡¸i©w©¢guwoi¤¦§vWr~WimYirqs)ou}mg~ ~Wiv_hyi/oqr u}tRhbv6Yi©w0¦§r vWh vW©wYhbioruwtRBs)oqsg¯x³ uwhbY©}i (hbi etXs_m°ViYi¦§vWr hbiYmYgir¢oeYi·s_t/oquwvWmRv_¦ri~_Y©ªs)ru RuwmY~s_mY°i%(6oqirmBs_©Z¦§vWrti¯³YYu±oquwvWmBs_© Yrv_Vir oquwi©wuw²_isAtvWmg o{s)mMotvWmYmYitou u±on¨'Vi/on¡¢iim iroquwti s_mg'sAYBs_©wuwon¨K¡uwoeoqru}s_mY~_Y©ªsoquwvWmYeBs i Viim£giºBmYi¯ G¿vWriv ir|9uwhbY©wi%(»hyieYis_r i°s_Ys_goqu i)|=¦§vWr.i%(gs_hbY©wiRp¨?tvWmgtimporqs)ou}mY~ iroquwti u}mQs)riXs) v_¦egu}~We tYr s)oYri §oeYir ip¨ r iXs_©wu Ru}mg~s_m vW oquwhKs)© eBs_ZiAYi tr u}gou}v_m ¦§vWr·s°~_u im mMYh0Zir v_¦ ir ou}ti /¯deYi0hbi e hysX¨¿ZiriºYmYi vWrYituwhys)oqi YiZimYgu}mY~°vWm¿oeYigu}o{s_mYtiAv_¦oqeYi iroquwti ¦§rvWh oqegiBs)o{s)io¯9deYiYituwhys)oquwvWmbtXs_mys_©wvZiuwmMoirs_tou i©±¨btvWmpoqr vW©w©}i¯m_=uw~WYr i eYv4¡9oqegii$Vito v_¦9oeYihbie s_Ys_go{soquwvWmxs)mY¿¡¸i iioqeYi ir oquwtis_r imYuwti©w¨ tvWmYtimpoqrqsoqiQsoegu}~Weg©w¨'tYr i Bs_roq v_¦
(87) oqeYi.©wu ir¯ ^J¨¤u}mpoi~Wrs)oquwmY~QuwhbY©}i ( hyieYiKuwm oqeYi'i~Whbimpo{soquwvWm Yr v ti |¸¡¸i eBs i vWgo{s)u}mYi hbv v)oqeYi oqr uªs_mg~WY©}s)oqi¿ Yr ¦Ts_ti| ir¨¿t©}v_ioqvKs_m'u} v)zn Yr ¦Ts)tii%(6oqrs_tou}vWmO|BYgo¡uwoe¿¦§i/¡¢ir¦Ts)tioqvbr iYr iimpo oqeYi eBs_ZiAv_¦oeYivWr~Ws_mY¯lnm v_Yr·i%(gs_hbY©wi_|oeYiAhbv6Yi©9v)¦oqeYiA©wu ireYs_·ZiimQtriXsoqiQp¨ ºYoou}mY~'s uwhbY©}i (¿hyie'oqvoqegi.oruwYuwhyimYuwvWmBs)©
(88) gu}mBs)r ¨Ruwhys_~Wi.Yr i u}v_Y©±¨'Yi tr u}Zi¯JdeBs_mg²6oqvoeYis_Bs_goqsz oquwvWm?s_mY Yituwhys)oquwvWmQYrv_Vir oquwiv)¦JoeYiuwhbY©wi%(Qhbi eYi|
(89) oeYuwhyv6Yi©=uwtvWhbZvWi¼v_¦]v_mY©w¨» | oqr uªs_mg~W©}i|Y¡eYiris_oeYi.hys_rt{eYuwmY~KtYZis_©w~WvWru±oqegh®~ps i | oru}s_mY~W©wi §t¦Ê¯9ºB~Wgrijbs_mY /¯. =0uw~W Y r;i 5
(90) '43 )( )( *
(91) /
(92) ( , / '
(93)
(94)
(95) )(, (, 58
(96) %'(, G
(97)
(98) 5%6 ) 5) '
(99)
(100) "!
(101) 7
(102) M
(103) : ,
(104) 5%
(105) : .8 (8(,
(106) $,
(107)
(108)
(109) 5 %)(
(110) 0
(111) 5%6 / . _. .
(112) " ( A; 5
(113) M ) / 5,0% 5A:
(114) ) , & 6,)( ) ; 5* 0
(115) !. ³©woeYvWY~_e¿oqegu}s_YYr vps_t{e¿u} ir¨ Yi/¦§Y©
(116) ¦§v_rgYu}©wYuwmY~s Ê~WimYir u}t ©}u ir hbv6Yi©T|Vu±ou}i impouªs_©%oqv u}mpoi~Wrs)oqiÊBsoquwimpo z¶Bs_i bhbv6Yi ©w.u}m?oqeYibuwh0g©ªs)ovWr¯ylnmQoqeYi¦§rqs)hyi/¡¢v_ r² v_¦JoqeYuwri iXs_r t{e»Yr v)it/oX| G¿vWmpo{s)~WmBs)os_mg i©wu}mg~Wio oq~ i \ G a `gbs)riA¡¸vWr²MuwmY~'vWm?sRhyi/oqeYv6 ¦§vWr·i ( orqs_t/oquwmY~'©}u ir.hyv6Yi©}·¦§r vWh !¢dFts_m u}hys_~Wi¯]deYuwhbi/oqeYv6¿uwBs_ i vWm¿ u}hbY©wi%( hbieYi¡u±oqe¿s_YYu±oquwvWmBs_©OeBs_ZitvWmYoqrs_u}mpo¯ I *. ?U@8BC5768.,:A26C4B D+9310 B 6?@.B 0 9NBM3. Å uwmYti¼j i©}s_ ou}tuwon¨Hi MBsoquwvWmY tvWmY u}gir¿s vW©}uwHVv6g¨W|·s vW©}ghyi/oqr u}t?hbiegu}mY~ v_¦0oeYiQvW ito¿u} ri6gu}r i¯£degi vW©wYhbiYi©wuwhyu±oqi p¨¼oqeYiYr i uwvWY©±¨¤i ( orqs_t/oqi eBs_ZieBs_AoqvxViYu u}gi u}mpoqvQs i/oKv)¦ºYmYuwoi'i©wihbimpoqyv_¦uwhbu}©}s_ruRi)¯ Yioqv oeYi'eBs)Viuwrr i~WY©}s_r uwon¨¤v)¦ s)mBs)oqv_hyuwtXs)©¹hbv Yi©}|¢s Yý%iý tvWá hbV v_(u± oquwvWm¬v_¦·oeYi vW©wYhbixuwmpoqv»oioqrs_eYiYrqs_©i©}ihyimpoqRuwKoeYi¿ZioR vW©} oquwvWm¯!deBs_mg²6yoqv?oqeYi.
(117) YBs_©wu±on¨xYr vWZir on¨¿v_¦ u}hbY©wi%( hbiegi|V¡¢iAts_m is_uw©w¨¿tr iXs)oisyoru}s_mY~Wg©ªs)ou}v_m v_¦9oeYiA©wu ir · Yr ¦Ts_ti_¯ deYimO|
(118) oeYi vW©wYhbiyu}YitvWhbZvWi»uwmpoqv sio.v)¦¸oioqrs_eYiYrqsgt{e¼oqeYs)o·oqegiyv_ruw~Wu}mYs_©oru}s_mY~WY©}s)ou}vWm u} mYv_o·hbv6Yu±ºBi¯lnmxvWrYir oqvRs_t{eYuwi iAoeYuw|O¡¸iAY i?s°Yr v YgtoX|
(119) X|V¡egu}t{eQuw·Bs_ i vWm s i©}s_YmYs4¨pz F]vWrvWmgvWu%s_©w~WvWru±oqegh ¯ ! ,R% ¢¼ y' + ·Yr°hbv6Yi©u}KBs_ i¬vWm i©}s_ ou}tuwon¨ oqeYivWr ¨_|eYv4¡¢i irRvWYr°s_YYr vps_t{e gu$Vir °¦§rvWh-r i©}s)oqi¬gr~Wir ¨ uwh0Y©}s)ou}vWmy¡¢v_r²AvWmb i irqs_©;ZvWuwmMo¯m_u}r oX|poeYiu}mpoi~Wrs)oquwvWmyv_¦s·¦§vWr ti¹¦§iiYBs)t{² ¨6 oih´uwmyoeYiuwh0 z ©ªsoquwvWm¿©wv6vW¿r i MYuwri·s_Yguwou}vWmYs_©"tvWmg oqrs_uwmMo vWm'oqegihbv6Yi©T¯ Å itv_mY|ZYu}v_hyit{eBs_mYuwtXs)©oqYYuwi s_ZvWgo v_¦ o oquwgi.eBs ibZiim oqs_²_im?uwmpoqv's_ttvWgmMo.uwm oqegiYi¦§vWr hys)oquwvWm Yr v ti.s)©woeYvWY~We oeYiYmYgir©±¨6u}mg~ ©ªsX¡ rihKs)u}mY©wu}mgiXs_r¯Jdegu}r |goqegivW©wgoquwvWm'v_¦%oqegiYu$Vir impoqu}s_©"i6Ys)oquwvWmYuwvWgoquwhbu Ri'oqveBs)mYY©wi·¦Ts_ o Yi¦§v_rhys)oquwvWmYv_¦tv_hyg©}i ( hyv6Yi©}¯. /*,). 49+@QB B @ BCBCN5ABQ. /*JI. .
(120) 90 B B C45:.B 53jB 4 C 5 /D .
(121) 9@ 9A@v=E9A@S6 68.=E=81BC=. itimMoy¡¸vWr²\^ pbeBs)eYv4¡m oeBs)obuwm uwr oBs_©im uwrvWmghyimpoqKoeYi'imYi v_¦YriimYti¿u}eYuw~WeY©±¨ tvWr ri©ªs)oi?¡uwoe»oqeYiyYi~WriiKv_¦¢u}hbhbir uwvWm£uwm¼oeBs)oim u}r vWmYhbimpo¯ lnm¼Bs_roquwtY©}s_r|%oqegiK imYs)oquwvWm£v_¦ ¦§vWrti TeYs_goquwtA¦§iiYBs_t{² s_mY oeYibimgqs)ou}vWm?v_¦]oqi (6oqYr is_ri ir¨ u}hbZvWr oqs_mpo.u}mQhbigu}ts_©]s_YY©wuwtXsz oquwvWmY¯¸lnm hbu}mYuwhys_©w©w¨'uwm s)u i0 Yr~_ir ¨oeYiYr ~WivWm#ïeBs_mYgr ihys_uwmxvW oquwYi.v_¦oqeYi.Bs)ou}impo Zv ¨W| oqeMY.o{s_t/oquw©}iA¦§iiYYs_t{² u}.mYv)o.mYiiYi¯ Å uwmYtib¦§v_rti imY u}mg~xYiVimYYvWm oqeYiYi/¦§vWrhys_g©}ibmBs)oYribv_¦ oqeYi uwr oBs_©Zhbv Yi©D|6oqeYi riXs)©}uwh$v_¦oeYi ¦§vWr ti¦§iiYYs_t{²°uw¹eYuw~WeY©±¨ytvWr ri©}s)oiRoqvoqeYihyv6Yi© ¹Yep¨6uwtXs_© ris_©}uwh'¯ degi·u}m ¦§vWrhys)ou}vWm Bv4¡Hu}m°oeYi· u}hY©ªsoqvWr¹ eYvWY©w°¦§vWr h$s0t©wvWi©}v6vW \#Wpi b '=oqegi·hbv Yi©Vgi¦§vWr hy s_ttvWrgu}mY~¿oqv¿oeYi°hbv_ou}v_m»uwmYYYti¤p¨QoqeYiKYr ~WivWm¼¡uwoe¼oqegiK¦§vWr tiK¦§iiYYs_t{²¼gi u}ti_¯ deYuwAYi¦§v_rz hys)oquwvWm s_©w©}v4¡YoqvtvWhbYgoi·oqeYitvWmpo{s_t/o¦§vWrti.s_mYºBmBs_©w©±¨°oqegi©}v6vWuwt©wvWi¿p¨~WimYirs)oquwmY~AoeYu} ¦§vWrtioqeYr vWY~We'hbit{eBs)mYu}ts_©s_toBs)oqv_r¯ &[egim s_gYu}mg~K¦§vWr ti¦§iiYYs_t{²¿uwm syuwh0Y©}s)oquwvWm|ZoqeYihys_u}mxYu ytY©won¨¿uw ri©ªsoqi¿oqvKoeYi0r iXs_©µz¶ou}hbi tvWmg oqrs_uwmMo0u}hbZvWi£p¨» Yt{e¤s ¨6 oiHh 'oqvxr ihys_uwm»r iXs_©wu}oquwt_|=oeYiK¦§v_rti0hY o0ViytvWhbY oqi£s)oAs oquwir ¨yYiReYuw ~WoeKu$V¦§mYr iiMYis_mgmgt»¨W|goqs)eYoJiy©}i²Ms_u}mg o¸¤i v_M¦¹Bs)uwmp©;oqoiv0rs_j to u}v_4m¯R\# ^¢ig¦§rqvW r ghKbD¯9soqduwvWeYmYuw¸A¦§s)r imYM»Y~WimYrs_tY¨yeYtXuws)tmr is_mYr¨yYis_r tu}mgt~vWrYmYuwimYi~»oqoqv.v¿oqVeYii Vir ¦§vWr hbibs)o=s_ZvWgo] 4R)|_oqeYs)o9tvWrr iZvWmYg=oqvoqeYi¢¦§r i MYimYt¨0v_¦Yoqegi¹eMYhys_mAZir u}oqimYtiv_¦ uwuwvWm¯ _=uwmYuwoi0i©}ihyimpohbioqegv YvWrhKs)z¶Yr u}mg~Rhbv Yi©}·s_ritvWhbY o{s)ou}vWmYs_©}©±¨ Yrv_eYu}guwou i_¯dvR~_Bs_rqs)mMoii u}mpoirqs)toqu irqs)oi¡u±oqe ©ªs_r ~Wihbi eYi|Z¡¸igisZii6znYxs_©}~_vWru±oqeYh(YriimMoi uwm it/oquwvWm ¯ l¶ou}.eBs_r ?ov 6Ys_mpoqu±¦ ¨ oqeYibr iXs_©wu} h¥v_¦¢s'gi¦§vWr hKs)Y©}ibhbv6Yi© u}mYti ir¨Q©}u±oo©}ibuwmg¦§vWrhys)ou}v_m¼uws s_uµz ©ªs)Y©}i0ri~Ws_rYuwmY~°oeYi0gi¦§vWr hKs)Yu}©wu±on¨ v_¦eMYhys_m ou} Yi)¯.itimMo·YYY©wu}ts)oquwvWmY u}m oeYiºBi©} v)¦Yr ~WuwtXs_© uwh0Y©}s)ovWr]hys_²_iY iv_¦;oqeYuwm zng©ªs)oiYi¦§v_rhys_Y©wiYr¦Ts_ti|Mhys_ÊzngruwmY~hbv6Yi©w|MvWr vW©wYhbioruwt©wu}mgiXs_r i©}s_ ou}tuwon¨_¯ &[uwoexgt{e hbv Yi©}|ZoeYiriXs)©±zíoquwhyitv_mY orqs_uwmpo·uwYu ytY©±o ovRs_t{egu}i i¡u±oqegvWgo·gioqr u}hbimMo oqv»oeYixr iXs_©wuwh'¯ !¢v_m ir i©±¨W|riiXs)rt{e!uwm oqeYi ºBi©w¬v_¦·Yu}v_hyit{eBs_mYuwteYs_° eYv4¡m¬oqeBs)oyoqegi¿¦Ts_uwr©±¨ ris_©}uw ou}thbv gi©O¦§vWr v_¦ ooquw Yiu}Yr vWBs_g©w¨'s uwtvzni©}s_oquwtmYv_m zn©wu}mgiXs_rhbv6Yi©+\_BYmBWjibí¯]deYi.hysvWr Yuwqs_ s_mpoqs_~Wiv_¦= Yt{e shbv6Yi©"r ihys_uwmYuwoegu}~We tv_hyggo{s)ou}v_mBs_©"tv_hyg©}i (gu±on¨W¯ Ô 4éíù#Þ /×/Õ¹Þ ç /å/ù#ÙÚÞ=Ô !!"$#=ù#ô×/áòÊåù#éTÝãVSÞ 4&Þ %(Ô 'éí×/áòÊÞ ÜXØÚÕJùÙïåðÜpâ óJâ4M û§ñý"û§ó.
(122) /*. . 3,.:4BC5+@ BM3
(123) 5+=68.B .J6ZD 5+= 5 @?=6 5AN N@89 P.0 5m68.
(124) 9: 9=@ 6C4B<N4B @9+@0 576.
(125) 9: 35CO @9+@ =?A 9 @S668.
(126) =?=?14B. lnm'sAYri u}vWg¹¡¢vWr ² \ ! ³·ZbD| ¡¸ieBs i eYv4¡moqeYi·uwmpoqiriov_¦%©wu}mYis_r¹i©ªs_oquwtu±on¨s_¹s0ris_vWmYs_Y©wi.s_ z Yrv( uwhKsoquwvWm°¦§vWrJv_¦ oJoquw Yi gi¦§vWr hKsoquwvWm¯+iri¡¢i rits_©w©;oeYi o{s)oihbimpo¢v_¦oqegii©ªs_oquwtu±on¨°grvWY©wih'¯ "io Zi0oqeYi0tvWmgºY~WYrqsoquwvWm v_¦Js_m i©ªs) oquwtAZv ¨xZi¦§vWr i0Yi/¦§vWrhys)ou}v_m¯ mgYir·oeYiAs_t/oquwvWm v_¦JsKºYi©w v_¦ vW©wYhbioruwt¦§vWrti s_mg¤Yr¦Ts_tiR¦§vWr ti g|9oeYii©}s_oquwtVv6g¨¼u}Yi/¦§vWrhbi s)mY£o{s_²)ibs mYi/¡ tvWm ºB~WYrs)oquwvW m
(127) ¯deYiYrv_Y©}ih u}oqeYimxoqvyYioir hyuwmYi0oeYi0gu} Y©ªs)tihbimMoºYi©wx¡eYuwt{eQs_ v tuªsoqi ¡uwoe¿oeYiZvW uwou}vWm v_¦=s_mp¨¿Ys_r ou}t©}iv_¦
(128) oqeYiVv6g¨'Zi¦§vWr i.Yi¦§vWr hys)oquwvWm|;u±oqVv_u±oquwvWm ¤uwm¿oeYiºYmBs_© tvWm ºB~WYrs)oquwvWm¯]lnmvWr Yir¹ovvW© ioqegu}Yr vWY©wihmMYhbiruwtXs_©w©w¨_|Y¡¢i.Y i.st©}s_ u}ts_©ºBmYu±oqii©}ihyimpoqs_ z YrvWs_t{e|MuD¯ i_¯w|M¡uwoe %s_~Wrs_mY~Wii©}ihbimpoqJv_¦Zon¨ Zi \#^¹so{ ibí¯ uwmY~.oqeYuw]t©}s_Jv_¦Vi©wihbimpoq¸u}hbY©wuwi]oqeYi YitvWhbVv_u±oquwvWm v_¦oqeYiYvWhys_uwm Hu}mpoqv°sy io v_¦=oioqrs_eYiYrqs_©%i©}ihyimpoq·s)hbimpou}vWmgi uwmx itou}v_m ¯ïjg¯ deYrv_Y~We s_ru}s)ou}vWmYs_©%YruwmYtuwY©wi|oqeYii©}s_ ou}tuwon¨¿oqeYivWr ¨¿Yrv_Y©}ih ï· vW©wgoquwvWm ZitvWhbii MYu s_©wimpo·oqv oqeYi. vW©} oquwvWm¿v)¦9sb©}uwmYis_r ¨6 oiHh ' ! ¡eYir i "# uw°oqegi oqu $VmYi hys)oru ! (!s)mY!u}¨6hyhbi/oqruwt_| VvW uwou i YiºYmYuwoi_| s_mY!Ys_r %i $ uwRoqeYi YmY²MmYv4¡mxgu} Y©ªs)tihbimMoºBi©}¿s_mY oqegii%(6oqirmBs_©¦§v_rti¯]deYi.uRi.v_¦%oeYu}hys)oru ( uw'&()&( ¡eYir *i ( uw oeYiQmMYh0Zir v_¦hyie iroquwti Tv_rmYv gi ¯ &¼iQu}hbhbiguªs)oi©±¨HiiQoqeYs)ooqeYiQhbi e u Ri §riYriimpoi[p¨ oeYixmMYhVirRv_¦hbie!mYv6Yi yuwRs_m u}hbZvWr oqs_mpoRBs)rqs_hbioirKu}m YYimYtu}mg~£oqeYi tvWhbY o{s)ou}vWmAou}hbi)¯=deYi¹gi¹v_¦Bs ~Wv6v ~WivWhbi/oqruwt¢r iYr i impo{s)ou}v_mKs)mY0oqegi¢ZvW u}Yuw©wuwon¨0v_¦;uwhbY©}u±¦ ¨6u}mg~ uwop¨ Yitu}hys)ou}vWm Tt/¦Ê¯¹itoquwvWmQ6¯è s_r itvWmY i MYimpo©w¨¿v_¦Yr u}hbiu}hbZvWr oqs_mYti_|;i im u±¦=oqegu}tvWmYguwou}vWm u}mYv)o ytuwimpooqvyu}mY Yri.r iXs_©µz¶ou}hbi.u}mpoirqs)toqu uwon¨ §t¦Ê¯itou}vWm /¯ lnm sK~WimYirs_©9s_gYrvps)t{e|OsKio v_¦]i%(6oirmYs_©¦§vWr ti·s_r iAs_Yg©}uwi ovKoqegi0gr ¦Ts_tiAv_¦9oeYiAv_©}uwx¡eYuw©}i vWhbi¸hyieAmgv Yi=s)riº ( i §v_oqegir ¡uwi¢sorqs_mY ©ªsoquwvWm|)s_mY0mgv_osYi/¦§vWrhys)ou}vWmO|¡¸vWY©wAv6ttgr /M¯ &[eYim YuwmY~ s¦§vWr tib¦§iigBs_t{²QYi uwtiy¦§vWroqeYiyu}mpoirqs)toquwvWmY¡uwoe¼oeYi°Yi/¦§vWrhys_g©}iyhbv Yi©]uwouwuwhbVvW uwY©wi oqv hbiXs_ YriQoqegi ¦§vWrti'i%( iroqi«p¨¬oqegi?v_Virqs)ovWr¯ deYiQimYYv_tv_Vi ï i%(6oqr ihbu±on¨ ZvW uwou}vWm[uwoqeYi vWmY©±¨¤uwmg¦§vWrhys)ou}v_m orqs_mghbuwo oqi p¨¤oqegiYi uwti_¯ !¢vWmY i MYimMo©w¨_|¹oqeYigi¦§vWr hKsoquwvWm hY oyZi'Yru im p¨QZitu±ºBtytvWmg oqrs_uwmMo t}|xZt y"oYWEuTrsT|V9s_mY | wVt}|s wq uT/X¯ imYti)|v_Yr.VvWgmYBs_r¨ tvWmgYuwou}v_mYs_ri hys_u}mg©w¨RoeYi.tvWmpoqs_toZvWu}mpogu} Y©ªs)tihbimMo Zion¡¸iim¿oqegi Yr~_u}ts_©oqv6vW©s)mYoqeYi.Zv g¨_7¯ &»i.ts_moqeYim YigYtiyVv)oqe oqeYiA¦§v_rti.i%( iroqi¼vWm oqeYiimY?i$VitovWr.v_¦JoqeYiAov vW©=s_mYQoqeYi~_©}vWYs_©9Yi/¦§vWrhys)ou}vWmQp¨ s_YY©±¨6u}mg~°oqeYi©wu}mYis_ri©}s_ ou}tuwon¨ i MBsoquwvWmY §t¦Ê¯¢ºY~WYri0 ¯¹deYitvWhbYgoix¦§v_rti s)ri.ºBmBs_©w©w¨' io u}mpoqv oqeYi¦§vWrti0¦§iiYBs_t{²¿ ¨6 oih uwm vWr YiroqvYr v uwYis°hbit{eBs_mYuwtXs_©=ri u}o{s_mgtioqv°oeYiA Yr~WivWm ·eBs_mgY ' oqeYi.©wv v_ uwt©wvWi¯ lnm?vWr Yiroqv uwmYt©wYYiboqeYibmYi/¡´tv_mY orqs_uwmpoq|
(129) ¡¢iyriY©}s_tiboqeYib©wu}mgiXs_r. ¨6oqih + ! p¨ oqeYi mYi¡F ¨6 oih Tt/¦Ê¯]³ YZimYgu ( ³ ' , , 2 , ! í 43 0 .- /10 0 ¡eYir 6i 5 7 u}¢shys)oqr u (ytvWhbVv_iv)¦ itoqv_r9 8;:V¡uwoe=s <u}myoqeY2 i Doqe°VvW uwou}v_mRs_mY Rirv6i¹i©} i¡eYiri_¯ deYuw· ¨6 oih ri Y©±oq·¦§rv_hoqeYi8F W q,WZ| ?TrX?YVt oYtTq yhbioeYv ¿ ¡ eYu}t{eQuw Y i ¦§vWroqeYiu}hbZvWu±oquwvWm v_¦ ZituwºBi s_©wYi9¦§vWroeYi¹v_©}gou}v_m s_r uªs)Y©}i¯9degi s_©}gi? >:Bv_¦ vWgoqs_uwmYiys)¦ oir= vW© uwmY~oqegi¹ ¨6 oih í ¹s)ri·i6Ys_©oqvAoeYivWYZvWu±oqiv)¦
(130) oeYi·¦§vWr ti·oqeYs)omYiiYoqvbZis_Yg©}uwi¿s)o¹oeYiYi~_rii.v_¦%¦§r iigvWAh @B: u}m vWr YiroqvbuwhbVvW ioqeYi.YuwY©}s_tihbimpCo B: B:ED¯ ìÞ ònFÝíå/û á.éâ åù#éò ×/çDÞ _÷VÞ¸à×qì/ÞJå/á#ÙÚô ÝDà#éíÞ Þ 4ÞðéDÞ Þ ç"å/ê;ê±éDÞ ,Þ 4åÕ _òå/éíéDÞçTß_å/á #Øïá#ð¹ÝíåÝíà#Þ¸òå/Õ¹ß)åá#Þáݶç
(131) å/êBÝDà# Þ 4ØèçTß#Ùè×/òÞÕ¹ÞáÝ ý%ý á (.
(132) lnm ©wuwmYiXs_r·oeYiv_r ¨W|oeYiAZieBs uwvWrv_¦]oqeYigi¦§vWr hKs)Y©}ihbv6Yi©=u}·geM¨6 u}ts_©}©±¨Qtv_rrito.vWmg©w¨¿¦§vWr hKs)©}© Y uwY©}s_tihbimpoq Ts_ZvWgo v_¦ oeYi'hyie uRi |¹u±oKuwy©}iyriXs)©}uw ou}t'¦§vWr©}s_r~WirbYi¦§vWr hys)oquwvWmY¯ ³©±z oqeYv_Y~We?uwo.uws'hysv_rYu}s_ s_mpo{s)~Wibv_¦¢©wuwmYiXs_ri©ªs) oquwtu±on¨W|
(133) oqeYiuwmpoqi~Wrqs)ou}v_m¼v_¦J¦§vWr tiA¦§iiYBs_t{² uwmQoqeYi uwh0Y©}s)ou}vWm'©wu}hbu±oq¹oeYirqs_mg~Wi·v_¦
(134) Yi/¦§vWrhys)ou}vWmg¢oqv hKs)©}©gi¦§vWr hKsoquwvWmY¯degu}uwVitXs_gi·oqegi·¦§vWrti·u}m oqeYi Yr~_ivWm .eBs_mY ¡uw©w©u}mYtris_ibs_egiu}mYtris_i.oeYiYi/¦§vWrhys)ou}vWmO|OoqeMY.Yr i impoquwmY~¿©}s_r ~WiYi¦§v_rz hys)oquwvWmY¯ !¢vWmgi MYimpoq©±¨W|%oqeYiAgi¦§vWr hKsoquwvWm rihKs)u}mYr iXs_ vWmBs_g©w¨xhys_©w©D¯.³ mgv_oqeYiru}mpoiri o.v_¦J©wu}mgiXs_r i©}s_ ou}tuwon¨Kuw¸oqegiZvW u}gu}©wuwon¨yoqvtvWhbY oqi·s)mM¨yhbi eRYi/¦§vWrhys)ou}vWmK¦§rvWh oeYi ²MmYv4¡©wiY~_i·v_¦%s.ºBmYu±oqiio v_¦i©wihbimpo{s)r ¨ Yi¦§v_rhys)oquwvWmY¯]deYu}ZvWuwmMo¡uw©}©"Zi.Yioqs_uw©}ixuwm it/oquwvWm ¯. =uw,
(135) ~W 5Yr i 3?)(' 43 / )
(136) 0
(137) ! $' / : )(6 ! 7,
(138)
(139) / = 5 *,A (, )( )(
(140) 5 (, =%6
(141) 5'%63 +
(142) .+(> >! 7
(143) :
(144) = , 0
(145) 5%6
(146) (
(147)
(148) ,
(149) 5 % _.
(150) ,
(151) 6,
(152) 5
(153)
(154) 5) 6!. /*. a0ON@?9. D+BM0 BM:6L9A@~6C4B N CD=8.B 53 0 9NBM3 6?9<=?.,0]13
(155) 576?B145+=?.v:49:3,.:4BC5+@. BM35+=a68./B ."6gD. itimMo]gYY©wu}ts)oquwvWmYuwmYuwvWhbit{eBs_mgu}t]oimYAoveYv4¡ oqeBsos·ris_v_mBs_Y©wi¹hbv gi© ¦§v_r=v)¦ o9oquw Yiu}=mYvWm z ©}uwmYis_r uwtv)zni©ªs_oquwtu±on¨\_BYmBWjibí¯itimpoAi ( Viruwhyimpoqris_©wuRi»p¨ !¢eYuwmYiu \ !Gxa`bJvWm¼t¨6©wu}mYgruwtXs_© qs_hbY©wiv)¦oqeYiRgrqs_uwm ir ¨»v_¦ ooquw YiR¡uwoe sxuwhbu}©}s_rAZieBs uwvWr0oqv¿oqeYiR©wu irggoA¡u±oqe¤Yu $OirimMo Bs_rs_hbioqireYs iio{s_Y©wuweYiKoqegi¹¦§vW©}©wv4¡u}mg~YrvWZiroquwi('oqegiri Vv_mYiYmYgirtv_hygri uwvWmyYiZimYg vWm¤oqeYi©wvps_gu}mY~Q Vii §oqegiriuwbs orvWmY~Qoqri n) orqs_uwm rs)oqigiZimYYimYti ys)mY u}mYv_m zn©wu}mgiXs_r §t¦Ê¯ ºB~WYr i /¯ degi¿r iZiXs)oqs_Yuw©}u±on¨ oqioqyeBs i¿eYv4¡m oeBs)oboqeYi riZvWmY i¿r ihys_uwmYRs_gYrv( u}hys)oi©±¨ oqeYi qs_hbiYmYYiru}YimpoquwtXs_©%tv_mYYu±oquwvWmY¯ _Br vWh oeYi iKi (gZir u}hbimMoqs_©Jri Y©±oq|uwo.uwVvW uwY©wiyov¿Y©wv_ooeYiKtYr i
(156) s_mY /|
(157) uD¯ i_¯w|%oqeYi Y w WaxZt}| wq uT s_mYQoqeYH i q,WaxZtWZY+xZt y"oYWEuTrsT|Vs_¦§YmYtou}v_mY.v_¦¸oeYfi WtWZY+xZt y"oYWEuTrsT|V§t¦Ê¯AºB~_Yri ` s_mY ¯QdeYi i guªs_~_rqs_hbs_r iRvWmY©±¨¼ri©}s)oi¤oqv oeYiR©wvps_YuwmY~ YeBs)i's_mY¤mgv_oAoqegiR ori bri©}s (gs)ou}vWm YeBs_ i_¯ ³ Yhbu}mY~¿oqeBs)ogt{e¤tYr iAs_riKs s)u}©}s_Y©wiK¦§vWroeYi°vWr ~ps_mQ¡¢iKtvWmguwYir §uwouwmYv)o¨_ioAoeYiKts_i ¦§vWr.oqeYiK©}u ir /|]s ©}is_ o0 MBs_r i hbuwmYu}hbu RXs)ou}v_m£u}Yi£oqv ºBmY»oeYi°ZvW©±¨ mgvWhbuªs_©]¦§YmYt/oquwvWm
(158) s_ z Yrv( uwhKsoquwmY~
(159) ·s_mYQoqegiVvW©±¨6mYvWhbu}s_©9¦§YmYt/oquwvWm
(160) ·s)YYrv( uwhKsoquwmY~
(161) /¯ iZimYYuwmY~ vWmQoqeYi YrituwuwvWmQri6gu}r i ¦§vWroeYis_gYrv( u}hys)ou}v_m¼s)mYxoqegiAeBs)Viv_¦oeYiAi (gZir u}hbimMoqs_©9tYr i_|oqegiAYi~_rii v_¦
(162) oqeYi.ZvW©w¨6mYv_hyu}s_©¦§YmgtoquwvWmYrqs)mY~Wi¦§r vWh oqv' ¯ û§ñý"û§ó.
(163) controlled displacement and speed measured loading force. measured radial deformation. =uw~WYriv8'b³®qs)hyg©}iv_¦ v_¦ o0ou} YiuwAtvWhbYrii sos¿º ( i Vii£¡eYuw©wiRoqeYis (gu}s_©]¦§vWrti_|]s ( u}s_© YuwY©}s_tihbimpoX|Vs_mY rqs_guªs_©OYi¦§vWr hys)oquwvWm¿s_rihbiXs)Yr i¯ _. Loading speed = 500 mm/min 6.0. Axial displ. (mm) Radial displ. (mm) Force (N). 4.0. 2.0. 0.0 0.0. =uw~WYrij`E' 7 _. ý%ý á (. 0.5. 1.0. 1.5. 2.0. time (s). )
(164) '(,A / 5(9
(165) G
(166) .
(167) 5 =)( (,,
(168) 9, (( M M 5 !.
(169) d
(170) vAi ( oimYoeYi iri Y©±oq¹oqvAj ¡eYuw©}i·gri ir uwmY~Ks0Yi/¦§vWrhys)ou}vWm°©ªsX¡ Bs_ivWmR©wu}mgiXs_r¹i©ªs) oquwtu±on¨W| ¡¢i.hys_²)i·oqeYi·¦§vW©w©wv#¡uwmY~ys_ Yhbgou}vWmg¯;_=u}r o| oqegi tvWhbYgoqs)oquwvWm'v_¦s MBs_ umYvWm z¶©}uwmYis_rYi¦§v_rhys)oquwvWm ¡u}©w©]VibBs)i¼vWm¼s'©wuwmYiXs_rYi/¦§vWrhys)ou}vWmQr ig©woYuwmY~ oqeYibqs)hyiyhbi e¼¡u±oqe¼oeYibqs_hbiytvWmg oqrs_uwmMo¯ !¢vWmY i MYimpo©w¨_|
(171) §ri ¯
(172) eBs_oqvRZiAi%( Yr i i¼s_sy¦§YmYtou}v_m v_¦]oqeYiA©wuwmYiXs_r Yu} Y©}s_tihyimpo §ri ¯J©}uwmYiXs)r¦§vWr ti
(173) /¯ Å itvWmY|;oqeYi s_r uªs)ou}v_m¿uwm WZroYt}V8xETv_¦
(174) oqeYirqs)Yuªs)©"Yu} Y©}s_tihyimpo vWr·rs_Yu}s_©
(175) ¦§v_rti it/oqvWr u}tvWmYoqrqs)u}mYi oqvRZiAuwhbu}©}s_r·ov°oqeYi0i%( Viruwhbimpo{s_©tYr i¯deYiri/¦§vWr i)|oqeYi YuwY©}s_tihbimpo itovWrys_ v6tu}s)oqi ovysymYv6Yi £uwYitvWhbVvW i¿u}mpoqvbon¡¸v itovWr
(176) s_mY |BvWmYi tvW©w©wu}mYis_rs_mY»v_mYiKv_r oqegvW~WvWmBs)©=oqv'oqeYiyYuwritoquwvWm¼v_¦¢oeYiKtvWmYoqrqs)u}mpoX¯ Å Yt{e¤s'YitvWhbVv_u±oquwvWm£v_¦¸oqeYi hbv_oquwvWmAuw=r i MYuwribZits_Yi¢i%( Viruwhbimpo{s_© riY©±oq9grv u}Yi¢vWmY©±¨0uwmg¦§vWr hKsoquwvWm0vWmoqeYi¸rqs_Yu}s_©6Yi¦§v_rhysz oquwvWms_ttvWr YuwmY~ovAs0s (gu}s_©;tv_mY orqs_uwmpos_Yg©}uwiRv_m°oqeYioq v_°v_¦oeYi t/¨6©}uwmYYr u}ts_©Os_hbY©}i)¯!¢vWmY i MYimpo©w¨_| vWmY©±¨QoqeYiKmYvWm z¶©}uwmYiXs)r s_r uªs)ou}v_m»v_¦¸oqeYi°s_hbY©}u±oqgYi°v_¦¢oqeYiKvWr oeYvW~WvWmYs_©tvWhbZvWmYimMo0u}²MmYv4¡m¯¿deMY oqeYi's)hyg©}u±oqYgiRv_¦ u}0hyv6Yu±ºBi¤ovx¦§vW©w©}v4¡oqeYi°tYr i /|=¡egu}©wi tvWmpou}mMYibov eBs i©wu}mgiXs_r s_ru}lns)mQoquwvWvWr mY¯ irov i ( YrioeYibtYr i §ri=¯ s_.s¦§YmYtou}v_m?v)¦¢oqegitvWr ri Vv_mYYuwmY~x©wu}mgiXs_r Yi¦§v_rhys)oquwvWm
(177) §ri ¯
Documents relatifs
2) Le développement local c'est-à-dire les expériences d'intervention en développement économique communautaire, en économie sociale et en économie solidaire mises
La définition générale du concept d'évaluation formative des apprentissages retenue pour cette recherche constitue une synthèse découlant de la recension d'un ensemble
Effets et pouvoirs de la voix dans la philosophie et la littérature antiques Paris, Classiques Garnier, 2021 (Kaïnon - Anthropologie de la pensée ancienne, 19), ISBN :
relève de traités, et que les États membres sont des États au sens du droit international public, c’est à ce juste titre que J. Fischer peut qualifier l’Union actuelle de
Afin de saisir le déploiement de ce discours, j'analyserai dans un premier temps les représentations liées au temps dans le roman, en m'arrêtant d'abord sur toutes celles qui,
Cette recherche, de type qualitatif, consiste en une exploration de la littérature dont les buts sont de décrire selon divers auteurs, différe ntes expériences
For each sam- pling point is also given the value output of the merging process with the difference between the SH degree 100 expansions subtracted, the index corresponding to the
L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des