An Electromechanical Model of the Myocardium for Cardiac Image Analysis and Medical Simulation
29
0
0
Texte intégral
(2) INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET EN AUTOMATIQUE. An Electromechanical Model of the Myocardium for Cardiac Image Analysis and Medical Simulation Maxime Sermesant — Hervé Delingette — Nicholas Ayache. N° 5395 26 Novembre 2004. ISSN 0249-6399. ISRN INRIA/RR--5395--FR+ENG. Thème BIO. apport de recherche.
(3)
(4)
(5) ! "#%$ & (') !*+ -,.+ ( 0/12345$ 6"(67 ( 8:9 ;'(< " =?>A@"BDCFEHG"EJIKC EMLN>PO1QNR*ST
(6) UEMIKVPWYXEMZDB[O\]EMQKQNE^S_T
(7) `BDa*b&c]Zd>PLfe<g1>Pa*bEhS ikjmlKnpoqrts?uwvyx{z}|tlnpo~zkmMM JmoKz
(8) o|
(9) mmmo mP t|{o+to~jmojmoP
(10) J^uwp *¡Mon¢mto+£M£¤uw ¢A oKz. _¥ ¦&§K¨©*ªm« ¨ ¬ ikjmz_oKztoK j:oP t|moKztoJ|zmoK®- ¯°o±oK(|t npoKjA mnf{{oK² ³+|tjmoh|®8F { )¡MoJ|t(±oKz {³
(11) o~z}|t±± npAofoKhzto´ o~|tzj ³µ³¹ <np|oKjm{o¶zt "n¢±n m± |t±o~ zYº<»&³|tz}jm|KoK¸]®o¢oKmo~5oK|tztoJ |¼
(12) _Anfho|tnpjmoK{^jA |tm±Kmm
(13) ±±MH5|t¡ ± ¡y±·m|xMnp¸o(|´tH+³µmM±< np|tjmo~o¶jAJAm J|t |*np|{¡M{o oz¼AA x{ztztoK± z MoKHM5{|t±½P oKmtÁdoK{M|¼½]Amz}±³µ npo~J|tA± *^|MztA zmº (iko~zjmº²oiknjmox ¾{K|jmop{ A5n3|M¾ J´|t |t oK(M|t|± ± "AztMnpA{{Jo*±|t±±oK )|jmz²zt ±mnMmjF*^|oK)jmoAMztMA p»&·±|N¿K®ÃÀm±A j{ÁÂA m m Ymnp oKo~5|t npo~jAm J mA±mAºvy±nm*|M¢ ³´²K{ 8(x{(±o ¸*® |tjf´MmAm tx Am·|MAz&toKmto~z}oKJ|t±mm±y{moKzztmto A)¡ Mmnpo Az}|t±J|zK¸{o~ mzk|p|tjmo¢( oK5|o~z|n |t± )³ ± A ´±{ ÄAnpo|tozk³|jmo { ¼³µAA5|Mĺ ikjmz8npymo]oA m±oKzÅ|jmo¼J|t{{A(|t± _ ³ÄA*|jm ± Mo~z¹ Ap|tjAo¼ztn¢m*|t± _³oKo~5|t AjJx{ztMM x±J|toKt¡MoJ|t± AzKºikjmo <moK®:mt ÁdM5|¡Mo8{o³µ n m±o npymom ³´|jmojmo~t|
(14) ±zűJ|t{{A(o~¢|t<|t Æ|tjmo |®8+¡ oKJ|t±o~zf|t±npoztoo~z³Ä { ±Kn { ±o~Mzº
(15) A*|o ±±nnfx^±A Atx ^MoKHztm|·|z+z{±xyAA{ np|t±Ko_|tjA´oK|¢jA|Njm¡y±zpMmA~t¸] KÁdMh5|t±¡ npo mnp*{¡ {ooK|t[jm¸
(16) o ® jAK±(j m J|tx¾oK A*H|oKztMHmAmz}|tmMo~tzt8z¼Æym³¹*® |tjmopo~{o( Èyo_| MÇ5|t|± jm o ³Å³µmA5|MA&A nfo|toKzk³µ nÉK{±M+±np o~z o¡Mo^±¾|tjAomoKztoAo³
(17) A z}x) ¼z}´z}om|Aº¼vyAjh npymoz} ±*®zÅ|jmo¼zt±nm*|M ³ m*¡* z(A± ÅA*|jm ± Mo~z
(18) ±¶ {o¹|t|toKz}|8|tjmoK Jxpz}|t*|toK ±oKz
(19) Ap|¢m_J|toKt¡MoJ|t± ´zº ʾËJÌ]ÍtÎ¢Ï ©*Ð&§ ¬ Ñ m±MfÒ^ymo±±mA¸ Ñ { frÂn MopÓA±x{z}zK¸&¯²o(³µMtn Ao¶Ò¾{{oK[¸&
(20) ±oK(|t npoKjA m Ñ Mmm±AA¸ vy±nA±|t± )³ Ñ {±MÅ|tjmMM ±oKz. ó ÞßÜNÔkøÅàNùÕô Ú"Ö5ÛN×Øî]Þß×[Ý*Ö5ÙáÚ[êßêßÛ â~Ù}×[Ö5à5Ù¹Ü~ÙÅÝNðÄõJÞßÜNÙ}Ö5Ú[à²ÜNÙ}ÝNááÖ5×[â~ÕdÜJãDä<ò ä~ñ&Ö5ú´×}âK×ØåÄÖöMû[æô ÙÚ"ÕÂá÷"ã}çKò*ÞßÖ5æ üµÚ[ý&ÛNÙ5ðÄÞ è ãdÚDáüÿÙþ ê×[èæ ìÙÖ5ÚDÛNáäNÜãdÞïáké&þ&ÕÙ}Ü(Ü(ã[ã[Þß×DÛ áÖ5êßÞßêßÙÞßÚ}ÜNò Ú}è ÜNÙÂãtèÄðÄë+Ö5áâ~çKã[ÞßÙ
(21) æ ÝNÙ
(22) ÙÚ"ìKÙõy×Øâ~æ Õ}ÙÞßÖ5ÚdáêßÙÜ(Ú}ã&ò Þß1Úú ÜNÖtí^~ò íÞ ã[ä¼ãD ìä~Ù8Ö5î1ÛNáäN×ØÞïÝNákÞïáþ&ÕÜ(ë+ã[ÞßÛ ðHÖ5êßðÄÞßÚ}Ùò ÚD*Ù}á×[á×ØÕdÜNäÕÙ ñ&×[Ö5â~ÛJò .
(23) . Unité de recherche INRIA Sophia Antipolis 2004, route des Lucioles, BP 93, 06902 Sophia Antipolis Cedex (France) Téléphone : +33 4 92 38 77 77 — Télécopie : +33 4 92 38 77 65. .
(24) ( ( ¹ &¢ p'; ' #$ & h' 5$ 6"3 K2 6Ã 8+ & ( p' 6 8 7( 6";'(< "( ( 8(
(25) § ¬HÑ opmP t|¼A ~z}oKM|o¢AYnp{{lKop{xyAnpJmo {op (|t±¡J|Ko~5|t n~A±Jmof{+m<P m< A±x{z}o {oz~MAoAoKz¼|toKnp´MtoK±oKz ±n o~z<o(|¾z}±nA±|t± nK{ oMº_iM{| P 1¸Amt{oKzz}Az+mo¶( ´z|tA(|t± {o np{{l±oKz<AM n ~ m±Jmo~z¼¡ ±mnpMAoKz<{Ynx {K{ o {o {opn ±MoKz| |t KmtJmoKz²oKz}|+nfz<oYm o º¹m±z± mA }|´oKM±oK|tzk± {^o¼${KY (P|t± |t{oKJÁÂ{|t±o½PÅ´ z}± _5|mMo²h|xymP Ao¼z²»&of|t¿~nÀxMmyMKj{Ád ²{oMo~mznp|+Azt¸{n¢Jmm]! K´o oK¸]tonp o(zt|to|toK³µM | ´ m ±AJ|+Az}ztm± +{o~m"z o²KAJA|t*jm|MMMA z¼±oKz{o(È^| # ¢Ktzt± ¡ n¢K{oKzÁ *|M_ J|toKt¡MoJ|t± ´zº&
(26) Aztm|to ¸y J|t (|t± {_n¢x { mo oKz}|np{# ±±z o¼z}A¹m(x{(±o m±MMAo & % 'o +mmo²M {o np´M}|onpoJ|<´(±AJ|<mY mA± (o Ko~5|tM n ~ m±Jmofo(|+{o~z+( ´{·|MAz¼±np·|oKz<±J| M J|² ±J|to (|t± YN¡ oK ±ozt mAº Ñ o+nf{{lKo+o~z| ´z}1¡*±# f|tN¡ oKzk(oK}|±AzkA nfl|toKz8 ± ´{È_o|{K{Èmo+±f³µMA5|M¡MoJ|t(m±to |KM {±AMJ mpo nf*º {){mlKoo¾³µ# z¢³µ o_n npm{±Ño{lm±+o o)KzKo~J5m|toKMA n (o~~zp m ±±n Jmo_MoKnfz¢z¢n o~F{A±±MoK(zKo ¸¸Å ±,A8 oKz}|f oK{ |±oz Èy|tm±tAoz¢{moKmzfoAn ( |nfjm{l{|tooKzf{o)JAzto Jnp|t|oKM|t|*³ØzÁ {o)^³µMA5|M K{±MJmo º o|}|to)mMm¡ oK±o_- . K|t± Fmonp{{lKo~zf. (³µ n m±oKz¢mÁ (|t³ØzPonpo(|¶ J| K op{o ±{³µMtn *|M¶+mMtAm ¶ztom±onpoKM|8z}m¹ A|tMnf±oo|¹o²( npP t|toKnfoKJ|¹n K mMAon z
(27) Azzt´ztm¹ M5|¡y| /Ko~5Á |tJmo²o| o¼np m¡MonpoJ|K1º 0o¼ mmMo² zto± m_n 2Knfo<np{{l±o< ±{³µMtn *|MAz8A|t npJmoKzK¸ymMn K mMAoKzo(| m±oKjyz x{±ztn MMM oKz8Mn AoKKz8{( J|o~tzk±mo(|m3o A p¡Jno+{±oK±zk PoM8z±ztfm± ±·m$| AKz z}|tzto~mztmzto¼m5 o(| np±foJm|$K±to~±ztzk± o)³Øz} ±n(3o m f*{|oKMz{n m~4{±KoKz8±o mº m| KoKzko(/| KAztoKz8( npnpo 6 Ï ¨K§ Í -« 7 §)¬ np{# ±±z*|M^ { JmoM¸mA x{zto+ ±n MoKzK{±MJmoKzK¸mnp{{l±oKz. (³µ n m±oKzK¸A mmM8o 5 K5|tMn (Á KmJmo ¸mztn¢m*|t± ){o+A|tjmMM ±oKzk m±MMAoKz.
(28)
(29) !"#%$& '( *)! '+,-$
(30) /.0 ! &12"34(56)87 97:5 / ; =<5'>+, ?. . P/ ¢ ' ¹ "( r |jm±zto~z}o~jHoP t|K¸®8o ±M|t{{´(o¶)moK® ±J|toM|to~YM¯Ãnp{{o
(31) ³k|tjmo ±o(³ÿ|¢ AYt± jJ|¡MoJ|t±o~z<³8|tjmo_jmoK }| ® jmj)´o<AztoK_³µ 8|jm'Co+z}72±'nD m *|M A¶|jmo+A x{zt±z³ { A*|jm ± Mo~zºikjmo<*¡ oK ´mAAo<z8moKz(PoK ±oKho~5»&|t± mAjJBo x{AMzt¸PM® MjA ox¾o´ hA AMnfo~jAAnf±K{z{º¶oKikjmAo ´´{oKz¼npÆyo(m|*o® z²±oK {³Mo|jm(Mz+nfnp±my_mo³µ¹tMKn4Y¡*|t jmtoK± A´z²o¶{zt npmA±±moKoKz¼H±A|t^(±A{±±mm
(32) Am**|| )n¢x ¸ M{oK|tMNAz}|Å|tjmonf{{oKm|<|tjmoMAzto¡N|t± AzKºikjmo² NAz}|to~fnf{{oK´KptoK¡ o~m<ymnPo¹³]Anpo(|ozAzto(³µmA³µ |Mjm¹o|jmo²A o½Px{o~zt5±z&| ³A³1|t|jAjmooP{om |t¹²³µmMA5|t(±|t ± ´Äz ºEØo rd|
(33) º Aº fM{ ±±zt<ÁD³µt´o~okMAAztooKA¢xf|t+ ztm±n¢|tm± * |tF(o ¸y¼Jxpym¡*nPxyoAÅ¢ ³´Aym|tjmn¢M´MoK k±oKz³Ä±EµyoMKº ´º"]±A{ {nf±zo|tjmoKonpz
(34) ³µ G F ±Az}|´(o(MA{A(|t±¡y·|x¶M(MM|M5|±·|xMº @. in silico. Clinical Data. Heart Model Electrocardiogram. Anatomy. Pathology Simulation Medical Images Test Strategies Plan Interventions. Electrophysiology. Cardiac Function Interventional Measures Ejection Fraction Biomechanics. Wall Thickness Strain, Stress. »&± moHA!Is²¡ oKt¡y±o®&I^oKo~5|t npo~jAm npymo ³<|tjmo^jAoKt| Az}|tA5|Mĸ8J|toKM5|M ® |tj A*|oKM|m*|A mm±±K*|t± ´"z IÅztn¢m±|t± ³Å { ¼ (|t±¡y·|x ³µM A*|jm ± Mx¶z}±nA±|t± )A(±A±Km|p´±xyztzº Ò¾{{oK±±m³1|jmojymn ´{{xpjAMz
(35) Poo_³Ä±A(oKMz}±m+±M|ooKz}|¹± |tjmo²±Mz|k{oKK {o~Kz J ¤ Ld¸yMz
(36) m Mto~ztztoKz&±¶m± ± Mx ¸ mjyx{zt±Kz² AH npm'{ |o72<'Dzt oKA(o¢npM{of·|+(MA(oK¡*AoMº²rd|<±z¼m*®PMzztm±o| n¢mAo 'NM 'M8 ´z}oKt¡**|Mĸ 'NMO' oÈyPo±nfoKJ|z ´ z}±nA±|t± AzKº k i m j K o t o f z H y j m o t | K o t | o(³µoKtoKA(o~z m*¡J{o+oÈ{ npmo~mz o_³M|Çjmo|jmnpooKM³µmz}mA5o|npMoKAM|k ±n ³Åo± oK±5m|Yt AF (nf|t±{¡y{·|oKxM±¸´±m{ho³µ ³np|jm|to± jAÄoKR¸ QAtP|*®J Mz£{4¸ ¸,Am¤J o+LdºF ikoKjmJo|*³µ| ±M*S ® J ±¤ mA ¸ AN³²y¸1|jm¤M{o¸1³µJmyA¸Ä5| 8£ MLdA¸Ä´nfH{ {³
(37) oK|t±jmzpop np³|{jm{o¾o±jm±oKm }| ³¹|tjmo)op{o±oKoK((|t|_±(KMnfAA{h|np|t± oKAjA 8mnp{{oK ±zK(¸8|t±m¡y·oK|ztx¾M m³
(38) oKÇ|tjm|topjmo~omt>| {J {¤ A¤´(¸1o {± ¸Y LDºoKÒH±z|y±x n Amo+|jmo¶ m±M¢M5|t±¡y·|xM¸ ³ÿ|to oKJm±t±m)jm± j(Mnpm{||t± A
(39) (Jz|z+Ah|tjAo np yA|mm±m¾³ )¡ oKtx^ o y mnpn¢m´{oK|¹m³]A|t ±nf o~nfz¹o |tAoKfzKºy¡ rÂpM ¡yA±m¹++mA±tnpJ |toKjÄp¸*®8ymon¢z}jA´ oKm
(40) p³1A |tjm oKnp
(41) z}o(oK|toKo~5zK|¹¸*|<jJ±´oz¹¡Mom±± *³]® npm{¼{|oKjm±oAP(|t oKnpJ|tA{|t³µ±m{±|o m® o·|±mj otJo~|t !,´zt A |t±m o ³m|tjmonpymoyAnpo|toz]³µ n(±±m±KJnpoK ztmonpoJ|zÄ ¢yx+z}PoK ,´¹A*|oKJT| Eµyxzt ±¡ym|tjmo8( oKzt´MA{±m±J¡Moz}o m AoKn F(º
(42) »&z| ®8 Æ |jm±z{oK(|t± ®8MzkmoKztoJ|to~_±¾fztxynp´Jz}±mn npoo|t±m* J ¤ Ldº Ñ Ó±zt®8o®8 m¶±±Æ oMm8nf{{oKP|tjAo±¶|tjAo²±J|tomo(|*|t± _³ m±M±np o¼z}o~MAoAoKzKº { n Mo²ztoMnfoK{Á |i *Ò¾|t± Vr JWAK z¹LDz}º|tr± ±´|jm¶o²M{5o|³µ¡M o n to~z}mo~±onpjf{ {too~´¼³µM zÅnpooP®8 t|tBÆ oKpJ ¤J± pLd¸M|tn jAo z}mA±tx ¡Mo{xo(³µyMxftn »m mmo²Mz}m
(43) t 0³Ø U oKJzÅANj´ L1N¡ oA¢Po|toKjA¶o²Azt´ztoKo~p(±_mz}ztoKzt mnpoo J³1|rÂ*
(44) |t
(45) ± npo(|jm{m>z J 4¤ X8LDºÓ (Mnm±A*|M)³
(46) z}´*|t&A|npof( ´z| J|z^ztAj¾np{{oz®k z AtM´Jz}o~)N \]J Z¤ 2YOLd 2Vº [ jmoKto~ z| oK±JA|tz}Aytmo~Az8(¢o~^Po( |}H|o|t jmop mnp´z||mMoK^zz| Mjm oKAHz}||tjmAo ztz}oo<MnfAoKJ|* |_M±AÄ(º±Ai"{_o² |t*³µmo~t5|t|jm oKKxp¸Ä_ A|tjAz}|ttoKo(±ÁÂJ{|zKnp¸ oK|Ajmoz}± o<´±z8m{ o(³µMtn AofÆyz}mm*t® ³Ø o~o{ oz nAmo~H® |tj _³µ mtÁdmnpo´z}± A Åz|*|tz}|tjmo~t|¼np |t± Ynf{{oK
(47) (MnfA{|to~^³µ n0ztoo~z¼³
(48) | MoKhÒ^.±n MoKz ±±^n JWA8 Y oMLD¸1ºÅ|tikjyjmAz+zknpPo(|t|}± |onpztoyMmnfo1oKJ±|**|®Mz8H¢ ´³¹o|t|}jA|toKopkztoKmJ|tmoKA±(ztoMº¢|t± Ó_m±|jm|tojm+o<o{ÈJ|½PooKAtmoKMoKY| ±n mm o~Mz
(49) M³µj^ nmoKfztoztJo|t o~np^oK±M_ |*J |R A
(50) ML¹¶( ³Än¢|mjm±o m,AoKz+z} | ±J|8¯²±z}|t±m{|t± ¶Ò^ymo` Eµ¹¯¼ Ò FAf|®8(Mmm±oKf|tmMm±|to~ z}mt³Ø oKz|zto npoKM|¹|tjmo±o(³ÿ|8¡ oKM|t(±o ¸MAztm¢z} ð"ð Üab 2b .
(51) ¤. U#<]" 2
(52) 7" U "D'434
(53) :U=)!G . ±HAz}nf| ´|t±( o+nnpA{·|{·ÁÂoztK³µ ±o³µ|tAjm¿o¿xJAÁÂ(·|±A± z}|tozt±|tm± PÄJ ºhM8¯LDº o³µ np m±o_z}A}³ØM(oKz¢ Çz}^Po mAo~® ·|jÇmMzto npoKM|*|Mĸ&³µ A^Å|Èyjm|o oAÓ zt5M|A¡Mz¶of Ó³+m|t´jmo~oh¹¯¼AÒ^ofzÒ^Ayz}mo~o z ± E[Óz}Ó²oK Ò npF5oºJÓ |*|t{±o~ zt:tnp±{o(||Mjmh{mz´ho^ Anp AztoK:z}MM^|tjA³
(54) oh|jmÓ oKzt5of|¡M|®oYvynpj´{P{ohoÒ¾z+{ {HoK±P^z o¢EØÓ²³µMvmm Ò A F ± JWAK8£ Ldº+ikjmoKztonp{{oK±z¼om*® {oK¡ oKM´o~)³µ <z}´*|t±ÁD|toKnp´M "m|mº²r Jß, A2Ld¸P|tjmopÓ²vmÒ zoÈJ|oAmoK¾| ¯ |npo yx¾±M|t{{´(±mztA*| Á[|onpP "ztjA ´o~>z EDv{i8ÁdztjA ´o~z F(º¼r J J LD¸]|jmopÓÓÒ ³µ npo®8 Æz¼o(Èy|toKA{oK¾|t¾ ¯ |t±nfo¢yx Azt±mom<|jmo±n oztoKJmoKA(oMz
(55) +ztmMo²z}jA ´ o
(56) N±J|to´z}|xznpm±o ¸ M¡y±m<|tjAoÓ 5|¡MoÓmPoK A(oÒ^|t± Ò¾{{oK E[ÓÓÒH Ò F5ºikjAoKztonp{{oz<H´o¢|tjmoK o(|±K±x)o(Èy|oA{o~¾|M¯¸]m{|¼|tjAofzt¿Ko¢ ³
(57) |tjAo¢np{{oz¼A^|tjmop{ m|x)|t M{| Ó8|¢)|t jmyo{_zt nf o¶to~|tz}±nfP oM´¸
(58) {{oo(A³µMoKtz8n ± )mMop¯ |on np m oK*zk|oKn z¢ oÆ ¡ o¼M·¡M|oKz}h|t±|t"*®k (m tz}oKMJm|8jmoKz|ztoK±K *|oKjAoKmmº tJ jmo~z¸³µ ¢Az}| A(o(Mnm±moK |® M|tjÇÆJ±qkm;Nx Jßo~ z}XLDº+Yq8({ |¼zz}³µ!o,´® K* |t³Å± |t jmo~z}´opYmÒHAtJÆ *¡)jmo~z AJ{|Mon *,A|oo+m|tjABz o¢J ¤J¡M8 LD±¸"m npo(|t mA ±ztmP¾oK5z}|¼j´P³
(59) o(jyÁÂmz}An M(ho ´M A+z n ´¾ {|tÁ jA,´o¢·|{otxyÁDAA Mnfz}o~ A|tmo ³k|jmo jmoK }|~º¯²mo |)|tjmo_ npm±o(È{|xH³8|tjAo_{o¡Mo± PoKYnpo(|jm{mz¸&|±znfJz|xY{ Ao JxYm A M|t±m_|jmo oKztmÅ|M m{np|o±|tm±oK¢np)ymMmoo<z²j´n N¡ Moo npEµ J z|Mx¾mo+Pz}o±oKH(o F¹±M||pt{|t{jm´o+(moKHoÈy|kYMm o {Jß 8 Ldº ³µmA(|t± A x{zt±z³µ ¼J|omto||t± HJß{¸4YOLd¸Ä z |jmoxf½]oűjAoÅnpoKjA m{´npo(|ozºikjAox®8oo z}<±J|tymA(o~¢± {o(³µMtn |t± pA x{zt±z&³µMÅmjyxyzt±±xMÁd\]A 2Mz}o~ 2 ±J|toP *|t± JWAK{`¸ YZA¸ LDº [Yo ´oK±o¡Mo |tjA|¡ Mmnpo|t±pnp{{oz ±zt¾±*® mop|¾J|t{{Ao nAj np o Æym*® ±oK{Mo¾ |tjAo^ M {±oK5|x :|jmoHztoMnfoKJ|*|M At{(o~ztzKº rd|:PoH´*|tMnp±K±{³µ n *|Mĸ±±Æ o ,Amo Mrd| t±oJ Ç||t± z}Ä^¸yPMo nfAz}o~o~ jA|tA_±K ]±J´|toK±xYjANo~¡yz|Mn m~¸M|t|o_pÆy±½]moo n np|t o<zt oKAmnp±o¼oKoKj´z}|t±mnp |t¹± mAzk P³"otjm|to~±oKzt| ÆJ³ ±m|tjAoKo_npn|txM{(z Jß y{¸A±m! n X{5¸ YJ Z £{YO¸mLD ºY{Ò¾¸´! MX8z}Ld| º ³|tjmo~z}o)AmtJ jmo~z+AztojAo(Èmjmo~{¹M|o(| jmoK{npoKztjmoKzK¸
(60) m{|f|tjAooo ±zth ·|oA*|¡Mo¶npoKztj{ÁD³µtoKo_npo(|jm{mz m PikMjmzto~oKz}^ o Jnp 8 {Ld{º oK±zEµ oK npo(|t mA
(61) N ÅAMnfo~jAA±K'F" to ´ zz}±¡ oknp{{oz¸M[º o º&|jmoxp{+m |J|t(±A|tok|tjAo { np|MĸJ|tjmoKxp m±xpo¡ M¡MomAmo|tjmo< (|t± ¶ 0³ A FÅoÈy|toA A±np o³µ (oKzA! F¹J|toKt´m³µMoKz¹® jm±j(MAz| p|jmo EØmoMMmnp± oKt|jAxp m±³ÄK|jm1o<npnp{{|to± z CF5º EµMo npo|t±KPnf{{oK± z F 8| Æ o²J|t M(MmJ|¹|jm"o ,Amo²Mt±oJ||t± Az8´f(MAz|·|{|t±¡ o¼N® ikjmoÆ ox¢±moK+±p|tjmz
(62) oP t|¹zÅ|+mm±±¶
(63) ÁÂÓ 5|¡Mo ¯o³µ np m±oÒ¾{{o ³]|tjmo²jmoK }|ųµM
(64) ±np o A±x{z}zKºrd|¹z ¡M ±mnpo(|t+{o(³µMtn mo+np{{oK³|jmojmo~t|J|o *|A \] 2 2 Æym*® ±oK{Mo< )|tjAonp|t± ¾±)|tjAoz}oK npoJ|*|t± m{(o~ztz|tjm A j+|jmo z}
(65) ±n mWU*|M³A|tjmoko±oK(|t±KJm A M*|MA|tjmo8npoKjA my(MJ|t 5|MĺÄrÂ|tjmo ( zzt ,´K*|M m±M ztPzKMºBztoK[YYo¶yPx o±»moK¡ mopM|t j´*|+|tjA±ztoKm¡yo® oK® oKJWmA~oLd¸&*||tjmMo_Hm t³ko~z}AoKjJJx{|tztoKYMMnp o(xJ|ÁdjmA{ ztoK®^Mmmo(³µ* ,mn |±m ±o |tjmnpo {t{(oMJz+|t ±JPAo ´Az+z+m¡Mo ® ±mPnpMo(z|z}t±mf±nf|t±{oK{zoK K{±M³µAA5|M^A x{zt±zKº |jmoik|®8jm+o²m¡ oKMÁÂ| t5(|±oK¡MzÅoztnpxyA{{jmoP ®mo¼ztoK±M¢|® t{·{|j ´(|tojmojAo Ñom¸oK|ztjmooJ|o(z³µMt¶ok±|Jjm|tooKtoAÈJ |´ooKmAom ³µxf ® (oKjmzMjm±x¢to~jA*N|t¡Mo~o8z¹|t¢( tnpo~*m|t±o o(|±o²{ AJ(|tMt (oK|t(± |t± Az³ |¶ NAz}| |tjAo+nf{{oK]|tp|jmo+´MmAm t±oKz8MAz}oKt¡MoK_|tjAo{ ²n oKzKº ¡* z()²Az}±± m"<A|tnpjmM{{Mo {±oK® z&|tjfAmjyJx{|z}oz}¡ Á1oJ|AMAmzjyº"xy»mzt ± &± ±A zxJ|ÁdAA zto oK¸N<|´jm±zÅ npmo(|ojAzÄo±n ¢{ÆMoKoK¡Jz&zt·|Åo¹|oKzt²jmmPMJzmz}±oKmz"±o¹|²|¼n zt±ÆMno¹moK*o~|5o8|tzt AnpjJokx{ztM{M± x Á z}|tAmo~zk|t (MtoK(|mmMtn PjAoKt| tjyxJ|tjAnpz ztjmM}|o~¸J±oKzzk±J¡*Mz}±¡ o<Anp o+z}´(o~ztz}³µmDº ikjmo<oKo~5|t npo~jAm ´np{{oKij"|tjmo+jmo~t|8Ato~z}oKM|oK±zk´ ztoK np|tjmoKn *|t 1z}x{z}|ton zk ³"mM{ÁD±±moK 8´t|t {½]ooJ|tÄo~JA*|MAz¸{zto(|M¢|tjAtoKo{npoKAz}± ´Ä{Mnp ¸m( ´z}{o±m|jmo+¡ oKJ|t±o~z8Mz p( J|ymmn)º ztn¢m[Y*o |tm± oKzt¸Mo|Jjm| ,AmMz}|j|tjmo o±AoK*(||t npnpoKyjAnp moKztj P(M(MAmz|mt±´m5´|t±ºÅ ik¸Njm|t±jmz8oKpz8¡N|tjm okmo±oK|t(oK|t mJjyx{±AztzM|8Mnp oKx< npztmymoKz¹o±³µt±mMnÃ+´A ¢|tj_|jm|tojm(o<M±M·||oM*5|t|AMt o Anpo~{±Ky±np o~zº&»"±A ±x+|®8²Am|t± Az to8moKztoJ|to~ IÄA|tjmMM x+z}±nA±|t± ¢ AztoMnpoJ||t± ³´< { ±n o+ztoKJmoKA(oMº < &( 8 ,.61 " &'
(66) &( |ikjmmokmn¢±x ¶{z}´ j¶{±+mn npyz"mooAAz8to~{z}o(oK|M|±oKo~pMz;J | o(|tLDºÅikjAoKjm{o²npJ ¡ M¶m npA*o||t np±¹nfo~Az}jf{³µ±MAt(n ±A{|t±±m < ®8Ao|tA ztnpo±z
(67) |tMjm±o²{³µn xMn yK*|M{ımº"n.ikjmMo8o mnp{o(|toKzx z ¸ |zm¡yz}± J|pm·½]ooJ|´*|tMnp±K]At|z A|tjmo<±{1Mt±oJ|*|t± ³"|tjmo+n¢Az(±o ,´mto~zº . !#"%$'&(*),+.-0/'1324)65.798#-:)6;<+:/'"%=. ikjmo)Mo npo|txÇ ´o¾oÈy|t 5|oKdzµtMn {·½]ooJ| npoK{ n ±mhnp{m |t±oKzKº »AtMn ¯4n o)³|jmo¾jmo~t|K¸ |jmon¢x { mmn3z¢ztoMnfoKJ|toKĸ&´z}±mh±Mztztn o¶m{(o~ztztA^npo(|tjAyAz¢±±Æ o |jmto~z}jA {Ah´n *|tjAon *|±K np mjmMM xMº"ikjmoKĸM²|tmMm±|to~¢ztmt³Ø (ok ³´|jmo nxMyK{±mn zÅ {|±moK¢AztA<|tjmo n jm±m<(mPoKz¹nfo|tjm{ J 8 Ld¸ üµý"ðüÿþ.
(68)
(69) !"#%$& '( *)! '+,-$
(70) /.0 ! &12"34(56)87 97:5 / ; =<5'>+, ?. . ztoAM:nf±oKz_J|{*oK|Mn * |³oK K|{ |tjm²oHn to~MMAoKz F5oKº
(71) »&±z}A±¿o_±xMEÿ¸A|xyfm¡ Mm±±npx o|t£M£ ±²£Y|tmo|t{{o~jmzpo~{³µ _]MnpoKmztj|tzo^ztto~n¢*|tmo~¶*|t³µ± n ¸8M|t*jmo<AK£M|t£ £YmmM{m{*oK|tz¶o~³µ ztjm|oKjmDo ¸ Azt±mp|tjmo<r ² rÓ zt³ÿ|®ko À²vm ¯ EØ»&±Aº´GF5º. »&± mo,I
(72) i"o(|tjAoK{]npoKztj ³"|jmo+mÁD¡MoJ|t(mknxM{{±mn µE ¤J£p£ £ £¢o±onpoKM|zF(º . . = ; +." ( / 1 ; $ ; )6$ $'/ =. i"HPo(|t|top(MJ|t A´±xyzto |jmo_np{{ok{m±m^|jmoztn¢m*|t± ¸&®8o_Po|tjAo´*|tMnp±K¹npo~z}j±J|thm·½]ooJ| oMMAzº8ikjmoKzto+o ± ´zk®oKtoztoMnfoKJ|toK±)|tjmonx {K{AnóµtMn |jmo ztm±oÀmn ¾
(73) o~5|yx¹Kº+·ÁÂÀoKm¿ À jmmo mĸMÀn¢mm3)m±¡ oKzt·|xBJ Ldº&ikjmzÅPo±±mz
(74) {Mmo yxoM±z}|toKt±m¼|tjmo npo~z}j ® |tjp|jmo*|±MzÅn o ¸MA |jmof zz}± m±m |o~ j+|o(|tjAoK{ <|jmo8±Mztz"(MtoKzt´MA{±mk|t²|tjAo¹¡ NÈ{oK±z® jmMztooJ|toKz"o
(75) ´z}{o|tjmzÄ|o(| jmoK{ Eµ|tjmo~z}o+¡MNÈyoK±zk to< m|±mo~_yx¶ z}|toKt±¿K|t± ĸJ|tjAo+® jm ±o<mt{oK{mo¼±zmo(| ±oK±C »&±AºmpmoKztoJ|z|jmo+to~z}A·| ³&|tjAoA|t np PoMMAzk*|t|tmm|t± ³µtMn |tjAo* |tJ z L'|F(pº |tjmo+npoKztjĺ C. E A. A. B. B. D. C. F G. D. F E G. &» ± mo¶RI+Ó´*|tMnp±K
(76) oMMAz¼ {|±moKH³µtMn0|jmo z}±m±o¶ÀÑ mn |t zOIqk z10Äo³ÿ|
(77) A{{K{± ÅoJ|t(±oPE[ÓF(¸ qk zÅvyoK{|tmn E[qVF5¸1¯Mzt ´ z 0o(³ÿ|<
(78) m{ ÅoJ|t(±o E F(¸1q8Mzt " ± jJ| ÅoJ|t(±o Eد(F5¸ÄqkMzt 0Äo³ÿ|¼¹m±K{ ÅoKM|t(±o/EµTF5¸AÓm±KMjM| ÅoKM|t(±o/EØ» F(¸AÓm 0Äo³ÿ|
(79) m {ÅoKJ|t±oE F(º
(80) . 2 %" 1 ; - / ; $ /-:) - /')6= + ;<+:/'"%= 5. ki jmonAz(±o1,AAto
(81) Mt±oJ|*|t± ´zÄ +´o {|±moK<³µ n {ztztoK(|t± +npoKMz}Ato~z1 &{·½]AztM<|toKAz}M"Ò^Çn MoKz0E[¯²ikr%F Jß8Ldº |jmo<{±zztoK5|M_npoKMz}Ato~z¹Pot³µ npoK¶Mf mAo²jmo~t|±_|jmo<m±Á oKm ±mooKt±m+P *| x³1|jmoÓ´ÆJ´ )m±¡ oKzt·|xM¸J o®Ñ Po~AºikjA±zm*| zto(|¹®k z¹J|toKtP *|oKp´ z}npy|jmoK yx¶|ikjmjmo+o mÆy±ymo*m® M±oKmmoK oo8A³P¢|tjmoPn¢ x *{| xfm ± ³"- |,´jmm o t)okAMt¡M±ooJz}|||tx ± A³ Vz E[»&±·´³µMºt4¤ AF"±mA¸{Nvmx{zÅ)p¯±onpMP tJß| MLd|
(82) º ±okf|jmo to~±±z}|t8npymo±±m ³8|jmo¶oKo~5|tA npoKj´m
(83) 5|¡y|xH ³8|jmo¶jmo~t|KºrÂA{oKoK1¸&|tjAo_(MA{A(|t±¡J|xHz+|xym ±x^³µMm+|npoKz± tMo ä(ãØãDÛJå tíÄíÄí ÿ×ØÖKÕ !è ÞßÜN×[Þïá~è "
(84) × à(áæ æ#á à5äNÚ $Ý à5ä~Útè ä(ãDæ ê % ä(ãØãDÛJå tíÄíÄí
(85) è &NÞßÖÙ}Ü~àNè áâNÕ('êïáÜNÝJè áÕ5è Ü*)+ äNÖ5æ Ù+ äNÖ5æ Ù5è ÛNäNÛ , ä(ãØãDÛJå Õæ ×ØàNè âNÕÚDÝJè ÙÝN-â ð"ð Üab 2b [Yo<mto~z}oKJ|8±¶|jm±zkoP t|¹|jmo<npymo1mm±|8³µ n. .
(86) . U#<]" 2
(87) 7" U "D'434
(88) :U=)!G . &» ± mo<¤IÅ»&Ato+Mt±oJ||t± Az8 zztMmoK_|tf|tjAo+nx {K{AnÃnfo~z}j³µ nÃ|jmom|fJ|o´M±|toK± ) Ñ v{¯¢º Mm|jmo",AmoKz8|jA|tjAo<|tAzt¡ oKzto{±to~5|Mĸy|tjmo<Mt±oJ||t± ³|jmo",AmoKz to~*|to~zpz}|t mpA±zt|tMJxp±_|jmo Az}|t|t{|¡Mo+±N® ³"|tjmo+n *|o± [¸m Az} (MAz}|t±Az|tjmo{±oK5|M ³|jmo(MM|M5|Mz}|toKzzº ( ¹ 3 f$ 6(2+$ .Ã
(89) " < " ¢ "( 9p '(+ "( n Ò^ ±y¾x{mA½]toJ oJjm|o~npz"I {{ozjAN¡Mo+´oKo^AtM´Jz}o~_|_ztn¢m±|to+|jmo¢K{ <o±oK(|t mjyx{ztMM x º8ikjmox)o{±¡y±{o~)^|® \R,)87 np{{oOz I&o±m8±o¡ oKPzt±nm*|MĸM´z}±m¢Mz¹¡* tm±oKz
(90) |tjmo¼(MA(oKM||t± Az¹³1|jmo¼m·½]ooJ| |xy´o~zk³MAz¸m AJ|toK *|m {½]ooJ| M)j´mmoK±z8AMz}o~_M¾À{{ Æy±{ÁÂÀ{È{±ox¶o~M´*|t± ´z Jß {¸A{¸m¤J£{¸´*¤ LDº \R
(91) ]
(92) ]3 np{{o"z Inp o+npM(Mz(Mm±¼np{{oz Azt±m¶¶ztnpm±oztx{z|on ³ÅoKJA|t± Azk|¶(MnfA{|to+|jmo (oKJ´ |toKM|± M® |tjA {|&o(È{m±±·|x+(Mnpm{|t±m|tjmoMAz AoJ|t*|MAzºrd|& Po mÁÂ{ n ±np{{oD¸N® jmoo
(93) |jmo ¡*±z8|±jm om±o~{z ½]oo<o|tAjmo+o o¸yÈy|tjA|to*Á (5o|±±Mm± P|AoJ|t±J|tDºÅ*rdÁÂ|(ozk±±mA± zt oK´ |t¾oKM»&|·±| ¿K±zKÀ¸mmM j{pÁ np mm npÁd{pMz}n x{z}|t±oKn npJW{A{¤mo¸=A ® ¸A jm8oLdº o<|tjmo¡N tAo Ó²z®8o+nf{{oKÄ|jmoo±oK(|t mjyx{ztMM x npMz}|t±x¶|_(MM|tM]|tjmof(MM|M5|Mĸ{®oAz}o<|jmoztoK A)AmtJ jĸA´o~´z}o |Pjmo¾|o(J |tJ|&M5|t)± P o±npzfoKn Mz}m±m±oKxÇĸmom*| |to~|jmo|H{|½]jmoo^o J(||t±M AFzP |AoJo|tJ|tDº *|Ò^MA z¸mo*zt ¡ oK®8K¸&o³µ(M ¶A(±)±mm |k ANz}´oM¸¹z|M|mjmxoA|jm o) o(npÈyo(|t|toK*ÁÂz8(oK ³&±m|jmo ± m+AmtJ j ³µ n (±m m|mº . . 1+:/ "%= " +.)<=%+:/'; $. ik mjmmo²M 5 |jMpxy´oK ±m|tz8oJ³Ø|M±z |AM®k¯N¡ (okMmnfA {A| M|t*±| AMz z¹A)ztn¢±m**®|tzo~f|t AKz}±m{|mto¼ztx{|zjm|oo+n mAA ztoK´f 1¶m±»& ±|t ¿~MÀ±KmM]j{mÁdjm ²oKmM mnpnpo+´RoKIJA*|MAzKº"ikjmz p(o±Äz (|t±¡N|to~_Mmx_³µ pz}|t±nm±Azk o8|jA¾p(oK}|±_|jmto~z}jA . |tjmoztjA ´o<³&|tjAo 5|MP|oJ|tÄmJo~zkm|moPoA |tjAoz|n¢m´z
(94). |tjmoKto<zfto³µM5| xfPo±y){At±mp® jmj_|jmo(oKKmA| ´o+oÈm(|toK . yx_o±Ä) (| z fAM(on Æ o~º Ó±o¡¾´¾Å# ,A±*¡){o¡Mo± PoK¾ np{{! ,AoK¾¡Moz}± ) ³Å|tjmof»"|t¿~ÀmMj{Á Mmnp¶oKJA|t± Az² m {|to~|t_|tjmof{xyAnpz ³"|jmo { ²o±oK(|t±K1P|oJ|t JWA
(95) L I {±¡ "!# %$'& &)( & * E%A F +*, &-/. 168037 250:4 9 !# &)(,&;$ <*# 5 ±zpHm n ±±ztoKM5|t± F´ |toJ|± 8 A * ±zfHztoK Am txY¡*± m±o ³µ ¢|tjmooP ±z*|Mĺ ! A= .^(MJ|t
(96) |jmo ±, oQAPm oKA(±oz*|³MAÄ ¸Äm´p> ³µ(¾oK|tJjmmo oKA(oKx_M5 |t± Y|tjmmo¢jm oK5m| Mnp)oKm´ Ä|toº¶J|ik± jA±z<{mnp{*|{oM¹±z Azt±nf|tAjm! z,AoKmY jmPoKottGo |I¼x¶|tz jmo m 68|0 7 2 m0 4 o9 o~{|ooK)n-*|o|tmjmo+oKztnpoJ |npzoK|Mjm|~o ¸ ztf|tjmzk|toKtn ±zkAo ±oK(|to~1ºÅÅnpo(|ok¡*±moKz to<{o±¡ oK_³µ n JWA
(97) L I?. @BA @ $ ¸ !C D B¸ ( E@BA $GFmº ikjmo<Mt±oJ||t± ³"|tjm8o ,AAto~zk±zmoKz(PoKyx |tjm-o HJIHp{½PAzt± |toKAz}MK *I $ @R@ MLONPQ @TST@ @U@ S<VW. üµý"ðüÿþ.
(98)
(99) !"#%$& '( *)! '+,-$
(100) /.0 ! &12"34(56)87 97:5 / ; =<5'>+, ? Y. ± A {´5 |tt±¡y|tjm·|Mx¾m ±¾n |jmo(,´´m ztt±ofz{® ±tjmo~M5zt|to± H,´±z}z²||xy¡MoKm5| ±±x±z³µMm ²|t|tjm±nfoYo~±yzK ,AoKm|oHjAM¾t±o|Jjm|op|t(± ´Ä{º A5Ó|z¡ym|x)o¡yHM|tAjmzto¢x |tnpAoztJ¡ |toK± ztmo+o~1m¸|mjmoMo ¸ ||xyjmmoo( ³µM±tx o)|¾®8|xy|mnp oKz 8¡*³Ø z}|tmook±³ |tS jm±o"z ,AS m o< @ A oKF{Jº|*ik|Mjm¶z¢|xyjA±omzpH|jm¡Mo¼o±|t{(A|xYzt¡ oK ³zt|tojAmoAAto MAE[ z8J*||tjm±o< mt M³A|tjAJo)*|MM5_|Mz}PÇo´o~ |toK³M||±jm o M5|t± P|toKJ|tÄzkm P t|t± A ´|f|tjmozJAo<ty|k³&|tjAo( ´{A5|¡y|Rx F5º [ |tjf±m|tJo(Èm(||t± ´*¡MoÅ|tjmo¹|tjmoKztjmM±1¸~|jmo8zt±nm*|oKM5|t± +P|oJ|tJ® |tj|jmz"ztx{z|on ±z&JA±|*|¡Mo±x ztnp±± k|tp|jmo+ 5|MP|oJ|tnfo~ ztmoK ){ ¼(oK&z EØ»&±Aº´G F5º 20. Action potential. 0 −20 −40 −60 −80 −100 0. »&± mo²,Ivy±nm*|M ³Ä (|t± p´ |toKM|± A® |tj_zt±nfA!,AoK Ó±o¡p´p #,A±*¡np{{oDºÅiknpoz
(101) A np ztoK¢|tM{| )M5|MP|oJ|tÄ{A|t± oKJA]|P A<|t±nfo+Am·|~º . . 0.5. /'( &$ ; +:/ "%= " +:7 ). . 1.0. 1.5. 2.0. 2.5 Time. - " ; ; +:/ "%=. Pikokjmo~toKz}o+mto~o~Jz}AoKJ*|t|oKMAJz x¢{o<±ztmJ|tNoKxy m*¼|oK¶¢M±ztMzt|tmjmto³Ø M(¯o¡ ³mM|jmmo np o(|t|t±± ¼npPoKzt|j¾oJ{|to,AyA¡*oK±m¾oMº&ztikoK(jm|tok± (¾Mnp{º¹mikojm|toko+m{xy AA npM±<|t±m ´ MP|to ± z}jm*® ® |tj|tjAo+±zt{jmtMmoKzK¸y® jmoo+(MMmz8omoKztoJ|8|tjmom·½]ooJ|{oK´M± tzt|t± _|t±nfo~z EØ»&±Aºm4 F5º 65 60 55 50 45 40 35 30 25 20 15 10 5. ±»&A±z} |mJof| I ³|tE 0jAoo(³ÿ |F²r{ztM zt¼mt(³Øx{ ((±o¢o ºK³ÅE[ |jm± o jJ| z}Fk±n mo~z}*A|·oK|^mMp5|z}M{^jm´ A|toKoKMzk|*± ³ÿ|o¡N (AMnpo ¸1moom|to+oKn¢ztox J{|t±m {|±jmmofn m{tMoK´AM±J *t|zM*)|t± ³µtMº M|~¸1*|< mo 0 ms.
(102) . & ( ),-0/'1 ; $ =%+ ) %-:; + /'"%=. ®ikjm|toj¾|t|oKjmnfoP»& ±m·|oJ
(103) |toK±o np*oK|MM|<Ò¾zo(|mjm {m1o¸P® Az}|t±mj^ ±³µA oKmt|tj¾|toM|t{jmoKo~{ m ÄA o±o(oÁ np<oK{M|t||z º zikjmjmoo¢np(o np Amm||t*jm|o¢Mz})A|t|t±npo"zJ||tooK¾ *z-|$ M@
(104) z{AM¾mo M¯ z}±nA±|t± H ³|jmo¶ (|t± h´ |toJ|± ¹{mA_|jmo¶ { f(x{*o EØ£Aº XJ_ z F²| Æ o~z¼ tMmA nfY )z|AAH Ñ ® |tj¾p¤M£f£ £M£oKoKnpoJ|zk|o(| jmoK{]npoKztjĺ ð"ð Üab. 2b.
(105) U#<]" 2
(106) 7" U "D'434
(107) :U=)!G X . . . 8"%( $ ) 24)61 7 ; = /'1 ; $ 24". . . ( 86 (
(108) " & ( ,.61 "5 "'¶ & ,. &(6. . . ' + "$. )<$. ¢nikjmAo¢z|fn´xMy(±KA{o{± mÇn7 (z|t ±¡ ^o¶ oK5|oKnf¡Mo+oKJm| m³µ ÁD±fA(oKMM²|Mm5|z} M|tÄ ¸&m <J|t¡y± z(±± oKÁDYoK±Myzxh|±|¼jmn o*M|5o|±M [ºk´rd ||tz²oJ |A± z}8|t|t {np|¡Mmo{|oKN® ±z²|t jmnpomm±o(oÈ)¡yMAA z ztoK(|t± ĸ¼A ÇAMztzt¡Mo^o±onpoKM|)omoKztoJ|t±m|jmoYnfo~jAA±K¼o z}|t(|x º vyo¡Mo¼( ´z|·|{|t±¡ oh±N®zjAN¡ oh´oKo m m mP±±MKzt*oK|tH± ´Yz¸{|±jm)op |t{oKo8|t|tm oKPo AJ4 AYJ¸o<*¡*¤m¸ ±±AKA{*¸|t±M y)¸, JA¸&±A£{z}| =¸ X8Ld±º mik jm op' mM op'M8m oKnpztoo~J |ztoKmhto~zhºrd|t|jmz+z AoMPz} o~t_|¼M_z+{|jmo~z}o± q8moKo~z}^|to³µMÁ Ñ +!(K±nfmoKJ |}Á vyMt±mo<np{{o0 JDYOLd¸m® jmj)J|toK *|oKz8|jmoÀ±ÁÂÒ^*È{®8o±´³µnpoK®Mt]Æ I Es. Ec. non linear non linear non linear. Ep. »&± mo:YZIÅÀ±ÁÂÒ^*È{®8o±]³µ nfoK®MtÆ ´z}o~¶³µMqo~z|oÁ Ñ 5npoKM|tÁÂv{ mo<(MAz}|t|t{|¡Mo¼N®+º A_® |toKzOI
(109) NG @ &Ym ¡ N . ! %$ &$ $ '$ ($ )$ * ( +$ &$ $ ,$ -$ )$ . * " 0/ 1. .
(110)
(111)
(112)
(113) . & BN 7 7 &
(114) N 8 & . . . #". . ED!F. ® |tj |tjmo PMzt·|Mĸ 4|jmoz|·½]mo~ztzK¸ |tjmom npmAA¸ |jmoz| ¸ |jmoz}|toKzz¸ |jmo mMtn ±z}o~ (|t± f´ |toKM|± A^ztmAz({| +to³µot±mp|¶|tjAo¢(MJ|t 5|±o+o±onpoKM| ¸PztmAz(±{| ¾|¶|jmoA ±oo±onpoJ| A^ztmAz({| |¢|jmo+z}oKt±oKz8oKoKnfoKJ| Nº
Documents relatifs
cosinus (en bleu à gauche) et d’une droite (en noir à droite) sur les données simulées pour 4 années à une température de 45°C, avec un bruit de fond interne réduit de 100,
Florence CARRÉ ~ Réoccupations funéraires de sépultures collectives néolithiques dans la boucle du
2 Vue plus en détails dans le chapitre 1... 2 phénomène d’agrégation des protéines amyloïdes en fibres et d’autres facteurs impor- tants doivent être pris en compte comme
In this chapter, we prove an a posteriori error estimates for the generalized overlapping domain decomposition method with Dirichlet boundary conditions on the boundaries for
Revue française d’héraldique et de sigillographie – Études en ligne – 2020-10 © Société française d’héraldique et de sigillographie, Paris,
Dans ce cas, comme les coulées du Bras de Sainte-Suzanne appartiennent au massif de La Montagne daté à plus de 2 Ma (McDougall, 1971), l’ensemble des coulées pahoehoe
In infantile Pompe disease patients, the glycogen storage diffusely affects brainstem motor and sensory neurons, and the whole spinal cord sensory neurons, interneurons, and
De ce point de vue, il est possible d’affirmer que la mission est accomplie : les projets de renouvellement urbain (GPV et ORU) élaborés depuis 1998 dans une centaine de villes
