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
!"#%$&(')
!*+-,.+(0/12345$6"(67
(8:9;'(<"
=?>A@"BDCFEHG"EJIKCEMLN>PO1QNR*STUEMIKVPWYXEMZDB[O\]EMQKQNE^S_T`BDa*b&c]Zd>PLfe<g1>Pa*bEhS
ikjmlKnpoqrts?uwvyx{z}|tlnpo~zkmMM
JmoKz
o|
mmmo
mP
t|{o+to~jmojmoP
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
{³o~z}|t±±
npAofoKhzto´
o~|tzj
³µ³¹
<np|oKjm{o¶zt
"n¢±nm±
|t±o~
zYº<»&³|tz}jm|KoK¸]®o¢oKmo~5oK|tztoJ
|¼_Anfho|tnpjmoK{^jA
|tm±Kmm±±MH5|t¡
±
¡y±·m|xMnp¸o(|´tH+³µmM±<
np|tjmo~o¶jAJAm
J|t
|*np|{¡M{ooz¼AA
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
nm±o
npymom
³´|jmojmo~t|±zűJ|t{{A(o~¢|t<|t
Æ|tjmo
|®8+¡
oKJ|t±o~zf|t±npoztoo~z³Ä
{
±Kn{
±o~Mzº
A*|o
±±nnfx^±A
Atx ^MoKHztm|·|z+z{±xyAA{
np|t±Ko_|tjA´oK|¢jA|Njm¡y±zpMmA~t¸]
KÁdMh5|t±¡
npomnp*{¡
{ooK|t[jm¸o®
jAK±(jm
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|tjAomoKztoAo³A
z}x)
¼z}´z}om|Aº¼vyAjhnpymoz}
±*®zÅ|jmo¼zt±nm*|M³
m*¡*
z(A±
ÅA*|jm
±
Mo~z±¶
{o¹|t|toKz}|8|tjmoK
Jxpz}|t*|toK
±oKz
Ap|¢m_J|toKt¡MoJ|t±
´zº
ʾËJÌ]ÍtÎ¢Ï ©*Ð&§
¬ Ñ
m±MfÒ^ymo±±mA¸ Ñ {
frÂnMopÓA±x{z}zK¸&¯²o(³µMtnAo¶Ò¾{{oK[¸&±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[ÞßÙæ
ÝNÙÙÚ"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
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
(
(
¹&¢
p';' #$&h'
5$6"3
K2
6Ã8+&(p'
6 87( 6";'(<"( (8(
§ ¬HÑ opmP
t|¼A ~z}oKM|o¢AYnp{{lKop{xyAnpJmo{op
(|t±¡J|Ko~5|t
n~A±Jmof{+m<P
m<
A±x{z}o
{oz~MAoAoKz¼|toKnp´MtoK±oKz ±n
o~z<o(|¾z}±nA±|t±
nK{
oMº_iM{| P
1¸Amt{oKzz}Az+mo¶(
´z|tA(|t±
{o
np{{l±oKz<AMn ~
m±Jmo~z¼¡
±mnpMAoKz<{Ynx
{K{o {o{opn±MoKz| |t KmtJmoKz²oKz}|+nfz<oYm
o
º¹m±z±
mA
}|´oKM±oK|tzk±
{^o¼${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&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|tMn ~
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_nnpm{±Ño{lm±+o o)KzKo~J5m|toKMAn (o~~zp
m ±±nJmo_MoKnfz¢z¢no~F{A±±MoK(zKo
¸¸Å ±,A8oKz}|f oK{ |±oz Èy|tm±tAoz¢{moKmzfoAn
(
|nfjm{l{|tooKzf{o)JAzto
Jnp|t|oKM|t|*³ØzÁ
{o)^³µMA5|MK{±MJmo
º o|}|to)mMm¡
oK±o_- . K|t±
Fmonp{{lKo~zf. (³µ
nm±oKz¢mÁÂ
(|t³ØzPonpo(|¶ J| K
op{o
±{³µMtn*|M¶+mMtAm
¶ztom±onpoKM|8z}m¹ A|tMnf±oo|¹o²(
npP
t|toKnfoKJ|¹n K
mMAonzAzzt´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{±ztnMMM
oKz8Mn AoKKz8{(
J|o~tzk±mo(|m3o
Ap¡Jno+{±oK±zk
PoM8z±ztfm±
±·m$| AKz
z}|tzto~mztmzto¼m5 o(|
np±foJm|$K±to~±ztzk±
o)³Øz}
±n(3o mf*{|oKMz{n
m~4{±KoKz8±o
mº m| KoKzko(/| KAztoKz8(
npnpo
6 Ï ¨K§ Í -« 7 §)¬ np{# ±±z*|M^
{
JmoM¸mA
x{zto+ ±nMoKzK{±MJmoKzK¸mnp{{l±oKz. (³µ
nm±oKzK¸A
mmM8o 5 K5|tMn (Á
KmJmo
¸mztn¢m*|t±
){o+A|tjmMM
±oKzk
m±MMAoKz
!"#%$&'(*)! '+,-$/.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
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
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|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|tjmoKonpz³µ
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·|x³µM
A*|jm
±
Mx¶z}±nA±|t±
)A(±A±Km|p´±xyztzº
Ò¾{{oK±±m³1|jmojymn
´{{xpjAMzPoo_³Ä±A(oKMz}±m+±M|ooKz}|¹±|tjmo²±Mz|k{oKK
{o~Kz J ¤ Ld¸yMzm
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
±n³Åo±
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{
{³oK|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
m³oKÇ|tjm|topjmo~omt>| {J {¤
A¤´(¸1o
{± ¸Y LDºoKÒH±z|y±x
nAmo+|jmo¶
m±M¢M5|t±¡y·|xM¸
³ÿ|to oKJm±t±m)jm±
j(Mnpm{||t±
A
(Jz|z+Ah|tjAonp
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´
oKmp³1A
|tjm
oKnpz}o(oK|toKo~5zK|¹¸*|<jJ±´oz¹¡Mom±±
*³]®
npm{¼{|oKjm±oAP(|t
oKnpJ|tA{|t³µ±m{±|o
m®
o·|±mjotJo~|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»&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
{
nMo²ztoMnfoK{Á
|i
*Ò¾|t±
Vr JWAK z¹LDz}º|tr±±´|jm¶o²M{5o|³µ¡M
o
nto~z}mo~±onpjf{
{too~´¼³µM
zÅnpooP®8
t|tBÆ oKpJ ¤J± pLd¸M|tnjAo
z}mA±tx¡Mo{xo(³µyMxftn»m
mmo²Mz}mt0³Ø
U oKJzÅANj´ L1N¡
oA¢Po|toKjA¶o²Azt´ztoKo~p(±_mz}ztoKzt
mnpoo
J³1|rÂ*|t±
npo(|jm{m>z J 4¤ X8LDºÓ (Mnm±A*|M)³z}´*|t&A|npof(
´z|
J|z^ztAj¾np{{oz®k
z
AtM´Jz}o~)N \]J Z¤ 2YOLd2Vº [ 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(³µMtnAofÆyz}mm*t®
³Ø
o~o{
oz
nAmo~H®
|tj _³µ
mtÁdmnpo´z}±
A
Åz|*|tz}|tjmo~t|¼np
|t±
Ynf{{oK(MnfA{|to~^³µ
n0ztoo~z¼³|
MoKhÒ^.±nMoKz
±±^nJWA8
Y oMLD¸1ºÅ|tikjyjmAz+zknpPo(|t|}±
|onpztoyMmnfo1oKJ±|**|®Mz8H¢
´³¹o|t|}jA|toKopkztoKmJ|tmoKA±(ztoMº¢|t±
Ó_m±|jm|tojm+o<o{ÈJ|½PooKAtmoKMoKY|
±nmm
o~MzM³µj^
nmoKfztoztJo|t
o~np^oK±M_ |*J |R AML¹¶(
³Än¢|mjm±o m,AoKz+z} |
±J|8¯²±z}|t±m{|t±
¶Ò^ymo` Eµ¹¯¼Ò 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
¤
U#<]"2 7" U "D'434 :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|ooAÓ
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^|tjA³oh|jmÓ
oKzt5of|¡M|®oYvynpj´{P{ohoÒ¾z+{
{HoK±P^z o¢EØÓ²³µMvmmÒ 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+ztmMo²z}jA
´o 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|tjAo¢np{{oz¼A^|tjmop{ m|x)|t
M{|
Ó8|¢)|t
jmyo{_zt
nf
o¶to~|tz}±nfP
oM´¸{{oo(A³µMoKtz8n±
)mMop¯ |onnp
m
oK*zk|oKnz¢
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´P³o(jyÁÂmz}AnM(ho
´M
A+z
n´¾
{|tÁ jA,´o¢·|{otxyÁDAA
Mnfz}o~
A|tmo³k|jmojmoK
}|~º¯²mo|)|tjmo_
npm±o(È{|xH³8|tjAo_{o¡Mo±
PoKYnpo(|jm{mz¸&|±znfJz|xY{
AoJxYm
A
M|t±m_|jmo
oKztmÅ|M
m{np|o±|tm±oK¢np)ymMmoo<z²j´nN¡
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\]A2Mz}o~2 ±J|toP
*|t±
JWAK{`¸ YZA¸ LDº [Yo´oK±o¡Mo|tjA|¡
Mmnpo|t±pnp{{oz
±zt¾±*®
mop|¾J|t{{AonAj np
o
Æym*®
±oK{Mo¾
|tjAo^
M
{±oK5|x:|jmoHztoMnfoKJ|*|MAt{(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|Mnm~¸M|t|o_pÆy±½]moo
nnp|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¸m{|f|tjAooo
±zth
·|oA*|¡Mo¶npoKztj{ÁD³µtoKo_npo(|jm{mz
m
PikMjmzto~oKz}^ o
Jnp
8 {Ld{º oK±zEµ
oK
npo(|t
mAN
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|tM(MmJ|¹|jm"o ,Amo²Mt±oJ||t±
Az8´f(MAz|·|{|t±¡
o¼N®
ikjmoÆ
ox¢±moK+±p|tjmzoP
t|¹zÅ|+mm±±¶ ÁÂÓ
5|¡Mo
¯o³µ
np
m±oÒ¾{{o ³]|tjmo²jmoK
}|ųµM±np
o
A±x{z}zKºrd|¹z
¡M
±mnpo(|t+{o(³µMtn
mo+np{{oK³|jmojmo~t|J|o
*|A \]22 Æym*®
±oK{Mo<
)|tjAonp|t±
¾±)|tjAoz}oK
npoJ|*|t±
m{(o~ztz|tjm
A
j+|jmo
z}±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|¼nzt±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}|tonzk
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
moKztjP(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"&'&(
|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
|tMjm±o²{³µn
xMnyK*|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
!#"%$'&(*),+.-0/'1324)65.798#-:)6;<+:/'"%=
ikjmo)Mo
npo|txÇ´o¾oÈy|t
5|oKdzµtMn {·½]ooJ|npoK{
n
±mhnp{m
|t±oKzKº »AtMn
¯4n
o)³|jmo¾jmo~t|K¸
|jmon¢x
{
mmn3z¢ztoMnfoKJ|toKĸ&´z}±mh±Mztztn
o¶m{(o~ztztA^npo(|tjAyAz¢±±Æ
o|jmto~z}jA
{Ah´n*|tjAon*|±K
np
mjmMM
xMº"ikjmoKĸM²|tmMm±|to~¢ztmt³Ø
(ok
³´|jmo
nxMyK{±mn zÅ
{|±moK¢AztA<|tjmo
njm±m<(mPoKz¹nfo|tjm{ J
8 Ld¸
üµý"ðüÿþ
!"#%$&'(*)! '+,-$/.0!&12"34(56)87
97:5/;
=<5'>+,?
ztoAM:nf±oKz_J|{*oK|Mn*
|³oK K|{
|tjm²oHnto~MMAoKz
F5oKº »&±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,Ii"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±oÀmn¾o~5|yx¹Kº+·ÁÂÀoKm¿
À
jmmo
mĸMÀn¢mm3)m±¡
oKzt·|xBJ
Ldº&ikjmzÅPo±±mz{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´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±KoMMAz¼
{|±moKH³µtMn0|jmo z}±m±o¶ÀÑ mn
|t
zOIqk
z10Äo³ÿ|A{{K{±
ÅoJ|t(±oPE[ÓF(¸
qk
zÅvyoK{|tmn E[qVF5¸1¯Mzt
´
z 0o(³ÿ|<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|m
{ÅoKJ|t±oE F(º
2%" 1 ; - / ; $ /-:) - /')6= + ;<+:/'"%= 5
ki jmonAz(±o1,AAtoMt±oJ|*|t±
´zÄ
+´o
{|±moK<³µ
n {ztztoK(|t±
+npoKMz}Ato~z1
&{·½]AztM<|toKAz}M"Ò^ÇnMoKz0E[¯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"- |,´jmmo t)okAMt¡M±ooJz}|||tx±
A³ Vz E[»&±·´³µMºt4¤ AF"±mA¸{Nvmx{zÅ)p¯±onpMP
tJß|
MLd|º
±okf|jmo
to~±±z}|t8npymo±±m
³8|jmo¶oKo~5|tA npoKj´m
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 "× à(áæ
æ#á à5äNÚ $Ý à5ä~Útè ä(ãDæ
ê
% ä(ãØãDÛJå tíÄíÄíè &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
U#<]"2 7" U "D'434 :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
(
¹3 f$6(2+$ .Ã"
<"
¢"( 9p '(+"(
nÒ^
±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|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]]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|jmo
¡*±z8|±jm
om±o~{z
½]oo<o|tAjmo+o
o¸yÈy|tjA|to*ÁÂ
(5o|±±Mm±
P|AoJ|t±J|tDºÅ*rdÁÂ|(ozk±±mA±
zt
oK´
|t¾oKM»&|·±|
¿K±zKÀ¸mmM
j{pÁÂ np
mm
npÁd{pMz}nx{z}|t±oKn npJW{A{¤mo¸=A
®
¸A
jm8oLdº o<|tjmo¡N
tAo
Ó²z®8o+nf{{oKÄ|jmoo±oK(|t
mjyx{ztMM
xnpMz}|t±x¶|_(MM|tM]|tjmof(MM|M5|Mĸ{®oAz}o<|jmoztoK
A)AmtJ
jĸA´o~´z}o
|Pjmo¾|o(J
|tJ|&M5|t)±
Po±npzfoKnMz}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
j³µ
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|tAKz}±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
|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±
PoK¾np{{! ,AoK¾¡Moz}±
)
³Å|tjmof»"|t¿~ÀmMj{Á Mmnp¶oKJA|t±
Az²
m
{|to~|t_|tjmof{xyAnpz
³"|jmo
{
²o±oK(|t±K1P|oJ|t JWAL I
{±¡ "!# %$'& &)( & *
E%A F
+*, &-/. 168037 250:4 9 !# &)(,&;$ <*#5
±zpHm
n±±ztoKM5|t±
F´
|toJ|±
8
A * ±zfHztoK
Am
txY¡*±
m±o³µ
¢|tjmooP
±z*|Mĺ !
A=
.^(MJ|t
|jmo
±, oQAPm
oKA(±oz*|³MAÄ
¸Äm´p> ³µ(¾oK|tJjmmooKA(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 JWAL I?. @BA @ $
¸ !CD 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
!"#%$&'(*)! '+,-$/.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±txo)|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*|M³Ä
(|t±
p´
|toKM|±
A®
|tj_zt±nfA!,AoKÓ±o¡p´p
#,A±*¡np{{oDºÅiknpozA
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±
ojJ|
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
& ( ),-0/'1 ; $
=%+ ) %-:; + /'"%=
®ikjm|toj¾|t|oKjmnfoP»&
±m·|oJ|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||zº
zikjmjmoo¢np(o
np
Amm||t*jm|o¢Mz})A|t|t±npo"zJ||tooK¾
*z-|$ M@ 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
U#<]"2 7" U "D'434 :U=)!G
X
8"%( $ )
24)61 7 ; = /'1 ; $ 24"
(86 (
"&
( ,.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|±|¼jmno*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|tmoKPo AJ4 AYJ¸o<*¡*¤m¸ ±±AKA{*¸|t±M
y)¸, JA¸&±A£{z}|
=¸ X8Ld±ºmik
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
NG @
&Ym¡ N ! %$ &$
$ '$ ($ )$ * ( +$ &$
$ ,$ -$ )$ .*
"
0/ 1
& BN 7 7 & 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| NºÓ {o(|±o~z}|tAmx¶³"|tjmz
(MnfAo|to<npymoı
A®
|tjSA(ÁÂ{±nfoKAztMA]z}±nA±|t±
Azk
Po
³µMmAS J Ldº
2
3
3
76 54
98
56 7:
;6</
/'( $ />= ) 24)<1 7 ; =/'1 ; $ 24" )6$
ikjmo¢o±oK(|t
npoKjA
mnf{{oKmtM´Jz}o~jmooz²ztPoK(! ,´K±x){oKzt±
mo~)³µ
¼{
+±nMoA
x{zt±z²AHz}±nm*|Mĺ
drik|+jmopz²A{moK|+zh|
{
o²to~|t5|²P|tofjmop
z}np±npmm{±| ,´*K|t±*
|´MH±x)oo ¶
zoKyMx¾|~¸ÄAz}ztm®8of|tjAjmopJNz}¡*o
|t)mz}±±o¢npm±±·m³µx)
|jm&o±{(³µ
M´tnz|*·||{M|tı¡
º+ofr±hN®|tjm
z²³¹oK³µJ
Anf|toK±®
MtÆ]{º¸
|jmo¢np{{oKK^Po¢moK(|t±x^(
npA
to~)®
·|j 'SM 'M8 npoKMz}moKz|tjm
A
j¾npoK{
nMoKzK¸A|jyAzn
ÆJ±m¶¡*±±A*|t±
PMzz}±m±o
º¯o~z}m|to|z¢z}±npm±±·|xY(
npA
to~^|¾|jmo
Az}|t|tm|t±¡
oN®z<mtM´Jz}o~H±Y|tjmo_|toK|tmo
¸"·|oAt{{AoKz
Jm|to+®8o±]|tjmo+MMAÄ
A{
1´oKjAN¡yMmk³&|tjmo+n¢x
{
mmn)º
ikjmo+ztnpm±! ,AoKnpoKjA
m1np{{oKÄjA
z8|jmo<³µ
±±*®
mp(Mnp´MmoJ|Oz I
p(
J|M5|t±±o²oKoKnfoKJ|®
jm±j¾to~*|to~zkfz}|toKzz8|toKAzt
¸m
J|t
±o~_yx|jmo
(|t±
´
|toKM|±
fA±oK]o±onpoJ|®
jmj)±z
m±zt|tMm±AoK
¡yztÁdo
z}|t
A)(oK*|oKzkpz|to~ztz8|oAzt
º
»A
p|tjAo¾o±oK5|tMnpoKjA
m±K
(Mmm±AA¸m·½]ooJ|¶N®zpjAN¡
o)z} PooK AtM´Jz}o~ JßG YJ¸8, A2Ldº [ho^jAMzto) ztnpm±o
MM5{|t±±
Ah
t´x
|t{oK½PM|oK±t
oK[Mº(|±[Y
o¢o~PJoA±*±o|¡
Mo¢|tj´|t*|<(·M|<M±|z¼tM±np|´jmMo}|
Jm|²A|_±mAÆMo¸omH|toKjm(of|t±x np{
{npoÅmzt{np|Am^±of|tMjAzoA
|<J|tnp
(y|tx)±
±m±M|o
A&ztnp|o~x
zt³µtmMtn°o~z|
jmtoo
N¡*±m±o|fMNAz}|k|tjmzk±N®+ºÅikjmo<(MJ|t
5|±o¼o±onpoJ|k±z
J|t
±o~yx|tjAo¼oKo~5|t
PM5|t±
´
|toKM|±
]|tjm
A
j¶|jmo
s¼¯²KI
N 7 & ®
jmoKto 7 ±z8|jmo+´Jz}|t±¡
o<¡*±mo+
³ I 7 ³ ;@ ¸{|jmo®
±zto 7 E@ º
? %$ &$
$ )$
$ &$
A@
$ &$ *
$ &$
üµý"ðüÿþ
!"#%$&'(*)! '+,-$/.0!&12"34(56)87
97:5/;
=<5'>+,?
Ec
piecewise linear
Ep
&» Mmto&XI¹v{jmonpo<³&|tjAoz}±npm!,Ao~jmoK
±
´np{{oK[º
o~M´Ó²*|tzk±
m
®
|t(j|t±|t
jmo<´³µ
M|t±o*J®
|±±
m1±z8(
mAMmtn±mp±z}npo~¶{{Poo(|I ®8oo)£fA^A
¸y®8o<KA
xJ|t
±x¶AmtNÈ{±n*|to|tjmo+zt
±{|t±
³"|tjmz
N $ & {{AAtt±±mm¶{ooKP´
M±
t±zzt*||t±M
= = I I
E[GF
8( S S :L
®
|tj |tjAo¼ {oK´M±
tz*|t±
p|npoM¸ |jmo¼toK´M±
tzt|t±
f|t±npo
¸ |jmo<(
J|M5|t±
p*|o
¸ |tjmo¼toK±Èm*|t±
p*|o
¸yA
º [Yo
Ah(MAz|J|<|t A ± ¹P0º EØ4 F|)nf{{oK|tjmop|npo{oK±Nx^Po(|®8ooKH|jmopo±oK(|t±K
{oK´M±
tz*|t±
A|jmo+npoKjA
m±K1(MJ|t
5|Mĺ
ikjmo|t±mnpo´z}±
A
´
J|t
(|t±
z|to~ztzÅ|to´z}M¹z¹M{|
mo~p®
·|j¶|jmo³µMtn¢m±
¸
®
jmoKto {om
|to~zÅ|tjA/o ,Amo
M±Jt|t±ooJM||t|t±o~
_^*
¡MAo
|tojm±oo¢np|tooKJA|~zt¸m
·|AtoK{ztm{A|(zk| ±_Eµ³µ
|jm<o<¶³µ(
M(mo<np¡M^oK5|¡M
oK(I|t
´¸ A F(º²rÂ^|tjmop{xyAnpzoKJA*|MĸP®
jmo
*
) !"#$
* *
,+
. %
.
&('
-+ / *1032/0
2
34
2
4
4
4
0
4-
{¡ L L
³µ
n ÑooK{Ás¼z}|t
MMmztÆJJ³µMtn¢m±A¸M®
|tj |tjAo¼ztmt³Ø
(o²m
nD¸ A |tjAo²oKoKnfoKJ|8¡M
±mnpo²´¶z}A}³ØM(o
¸JoKzt´o~5Á
|¡Moik±x
jmº z
ztJnp|mM±5 ,´|t±oK
_(³µ
´(zo<|·|z8{|t|tjy±¡
Ao)z
o~NM®7A¡*zp±tooKJm|kto~|t¶z}oKfJ|tmoKFoKzyztxFmtho<AAmnp±moK±m ±
npA¢|t|·jmÈ o8,Am³µ
o<p
|jmoKo)J|J*||oMÄAº
¡yztMzt·|xA
}|~¸
z}|t½PAoKzzknp|t·È 0³µM|jmo<|t´z}¡Moz}o
mz}
|t
moK±Mz|±²A
}| Eµ´±oKPoKoKnpoJ
| F8´³µ
(o¼¡
o~5|tM
npm{|oK
³µ
n4s²A(
o<J|JM|t5oK|t
±
*C|oKEض
±JJ|t|tp
(||tjm±oo¼{oxy±oAnpnpoJ2| zkF5º o~M´*|t±
¸{·|®
·|oKzOI
5
0:20
7698
-;
*>0?20
<6,=
@
;
-@
*A
A
B5
C
L
L
L L ,E
DE
D
E
5
5
Eؤ4F
®
|tj |tjmo¼{±ztm
onpoJ|¡MoK(|t
~¸ |jmo¼m±
´mn
zzn|t·È*Eµn
zz±mnpm±m4F(¸ |tjmo<NxyoKMjmnpm±mn|t·È1¸
|tjAo¶mz}
|t
m¢±moK
+o
z}|tpz|·½]moKzz<n*|tÈ1¸ |jmo¶{½PoKtoKJ|<oÈy|toA
ÅJ
mz²³µ
nÉ|jmo´MmAm
txh(
´{·|MAz
A |tjmo<³µMo²¡MoK5|
k³µ
nÃ|jmo(MJ|t
5|Mĺ
|jmo ik0"jmon ´_oK(jAMNA¡yz}M|mJ|z
³jmz}´Jz}jÇoK H|t^(MAA
z}|t}||t{xY|¡Moo_moKNzt® oJ|+zf|tz}jAjmo_*®
±A(MMnfFAHto~ztmztmA¶±·|¡MxY
±nmnpÆMo¶op|tjmo»"±(
mAPtoom{º±*[Y|too¡
KoK}|DZKMA±ztxho®
¡
opjmo|tÇj´*||
npmoKzz}o~zjA
¿K
J|
±x
º
E
*C
F5
.5
G
" & =
; -
8#" =
/ +:/ "%=5IH +:7 )*8#; - / ; 17 ; 5 )65
®i"jyxz}±|njmAo
±{|t½PooKtoKMoK|JA|t±jAt
oztKoKz
{³A±M|tkjAo(x{(±o
{¸
|t
jm8o
(±x{J(|t±ookjA
(N|t¡
±o8
p|¼P³Po
|tjA±oM|nt{xM{y´K(oKÄ{¸±m®
n jm®
jf|t±jpnp|tmjA±oo~mzű{J·{½]fozoJ¡
|oKtPx
mnp´mP
tx|(JM|~Aº&{ik|tjm±
zÅAzKz º
ikjmojmoK
}|f(x{(±o_
ÇPo{±¡y±{o~±³µ
m¢mjAMz}o~"z I,A±±mA¸z}*¡M
±mnpo(|t(MM|M5|Mĸ"o}oK(|t±
ĸ
A ±zt*¡
MAnfo|t±
o*Èm*|Mĺ
»A
m{½]ooJ|´MmAm
tx¶
Am·|MAz
o<Az}o~_M|tjmo+npoKj´m
Pnp{{oK? I
''D'43 IÅmoKzztmto8zÅmm±±oK|t¼|tjmok¡Mot|t(oKz&
³A|tjAo
oA{{K{Anº"rd|z±J|to´z}|xzoKJAJ|²|jmo
npoK
¢moKzztmto
³"|tjmo|tmn)ºÅrd|K´o
m
npoJ|oK{mmf|jmo+:®8N¡Mo|f±J|t{{A(o|t±
1(
J|M5|t±
1
7"M6+, "?2 ?!"? IpPo´|x(MAz}|t±M|
zAm±oK|p|tjmo¡
ot|t(o~zk³&|tjmooA{{K{An |tÆMooK|jmo
¡
oKM|t(±o¼¡
±mnpo+(MAz|J| "J
ð"ð Üab
2b
A~£
U#<]"2 7" U "D'434 :U=)!G
»&±
moRI Ñ
J|t
(|t±
NE ,Az}|t*® Fk
A)toK±Èm*|t±
SEØztoK
A*® Fkz}±nAÑ ±|t±
)
^m´oMº
»"±moKz
to+jA
¿K
J|
ÄA
E[m^Aƶ·|m±
±m"!o
IÅ(P|t±
¾Pz}o~|1o¸{J|t±
jJ&|
±z²oK mIA{±oKoK´M|±¶
t|tztjAoKo±F(o(º ³ÿ|³ØM(o|³Å|jmo¢m´oMº
±
AtoKmoKztoJ|zk|jmo¢M5|M¾´
|toJ|±
¡*±mo
"
IhmoKzz}Ato±zpAm±oKÇ|th|tjmo¡
oK}|±oKz¢³|jmo)oAmyK{±mn)ºrd|zfJ|oAzt·|xzfoKJA
|H|jmonfo~
m´o+oKnpzz}m{{om
*³|oK|tjmop®
|tMj¾}|; [ Eÿ³µM¼Am|tÆ
jmoKofzztoo³ÿ1|¼np¡M{oJ{|to1(|p±o FJ
|tA{¾{|Ajmofo<m
}m|±onfx¶MA(Mnfx¾At|toKAtSx o+Eÿ³µAM²|jmoKofzt±z}t|±
AjJ|²(Oo ¡M
oJ|t(±o F5º¼rd|+(
A±
1
7"M6+, "?2 Z I¶´oKA|x
Az}|t±J|±z¼Am±oK||tjAo¡
oK}|±oKz³|tjmo¢oAmyK{±mn)¸AÆ
oKom±m|jmo
¡
Mmnpo+(MAz}|J|~º
i"HjmM±|tjmonpoKztjÇz}AM(oM¸Å®oz}±nm*|o¶|jmo ,AAtMAz¢z}|tA(|tmo_
AA |tjAo_¡*±¡
o~z®
|tjFztmAMzj´N¡J±mh
mo
oÈJ|trÂoK_np·|,Ax_z|8|}|¡
ojmzto~M¶Ä|¸¶|jm¢o²´zt
Az]oKzmz}{±
{o
³1´|t¶jm|o¼jm{o+½P|oKjmtoKoM
|8omÈJjA|tMoKz}npo~z¹·|®kx_
z|}||t
Mjm
o~o¶oK|f¶y( x,AÈyo~ztxJ´´MjmtJM|Kmº zt|t±
pnpoKjA
m±ztn A
ztoK
M^z|Am
Ñ ºPqm||tjmz±oKMmzk|m
{ÁÂ(MJ|t±JA
AzknpoKj´m
(MAz|
J|zk®
jm±j¾K¾(oK|to+±Az|m±±·|o~z¸P
z
m±{³µMtn*|M
´M{|
|tjmo+npo~jAm
1z|*|to+
³|jmo+npymoÄzkAztoK|tjA
m
o¼³µ
n Mmo<mjA
zto¼|t¶
m|jmo~º
rÂ|tjAo(mtoKJ|8¡Moz}±
ĸJ|jmo+mjAMz}o+jA
m
o<z
{|
n*|±K±x¶
J|t
±o~_±|tjmo¼³µM±*®
Af®kN]x I
{mA' ,A±±m´¸M²moKzz}mo8±zÅ
mm±o~|²|jmo
o´{{{±mn)º [ jmoKf|tjmo
(MJ|t
5|M¢z}|
}|z¸N|jmo
(
J|M5|t±
³µ
(o
®
±&|toKA¾|_oo~5|<m±J{1¸1zt_®
jmoK¾|tjA±z²³µ
(o¢±z²np
o±np´M}|J||jA¾|jmopmm±±oK^Ato~ztztmo
¸´|tjmo¢my{* Q´*®
¡*EØzt±np¡
oKmzk±x
AoK)z}|t±zn|*t||8oK|¶jmMo+zz}|*jm¡Mo²
¡M±m
np±mo(np|to|np(Mo<J|t{o
5|¡*M|tı¡
º o F¹jAA
oKzz}±
ºikjA±z±z8AztoK|tp(±Mzto
|tjmo<*|tÁd¡
oJ|t(m
{mA|jmo
±zt*¡
MAnfo|t±¹(
J|M5|t±
¸N|tjmo
Am±oK¢PoA
·|x
Az}|t±J|
mJ|oAAoKzÄ|tjmo
J|t
(|t±
+³µMo
¸
z}f|8z
{±to~5|t±xoKJm±¡*±oJ|8|t¢|tjmo<±M|ÁD¡MoJ|t(mAto~ztztmo
#º [ jmo|tjmo<±J|to´z}|x³"|tjmz8´oKA|x¶(MAz|
J|
±zz|npt|
zKº o+npP
t|J|
|jA)|jmot|toKt1Ato~ztztmo
¸{|jmo¡
oKJ|t±m±
}ÁÂt|toKtP¡*±¡
o~z
PoĸPA|jmoo}oK5|M¾mjAMz}o
{mAo}oK(|t±
ĸ(MM|M5|M^³µ
(o¶moK(oKMz}o~z<*³ÿ|toKoP
±z*|MĸÄz})®
jmoK ·|z+±oKzz<npP
t|
M|+|jA
}|o(Á
ttoK±8Èmm*|toK±z
z}AtmoMjA¸"M|z}jmoMo º QA*® jA
m
o~zztMFAÇ|tjmo¡
oKJ|t±m±
}ÁÂt|toKtÅ¡*
¡MoKzf(±Mzto
¸z}|t|t±mH|tjmo±zt*¡
MAnfo|t±
{mAz}*¡M
±mnpo(|to*Èm*|Mĸ|jmok´oKA|x(MAz}|t±M|&toKmoKztoJ|zÄ|tjmokmoKzz}AtoM¸Nzt®
jAo|űz&±oKzz&npP
t|J|
|tjA
¾*|t]moKzz}mo
¸J|jmo*|tÁD¡MoJ|t(m8¡*±¡
oKz8M´oKĸAz}|t|t±m¢|tjm8o ,´±AmjA
zto
º
¡Mo¢®
·|j|tjAoKzto8
npm±o(|toKx+±A{oK´oKA{oKM|
A{|t±
´zijµM"|jmo8o³ÿ|Å
A+MjJ|&A
}|z
³m|tjAojmo~t|K¸N|jmo¹|®8¡MoJ|t(±oKz
z}M|NNx¾Az}®8|fo(±MÅJz}|txyA
5jm|±
|AxH±ztoKA1
¸]
®
nfjmo|tjhoKz¼ztjm³µ*
®n°z²|t|tj´jm*o|¼³µoK
m(|opj{o³k¡Mo|t±jA
omnp{o½PJoK|<toK±z<J|
mjmjAoKMtz}oKo~Mz|<¸±HA|jm
o¢±ztnp){³µ{oK
[n°º¢rd|t|<jmon
*Æ
|toKz²¹|<
PAMzzttm|t±oKo¢t|t
moKzztmto~zº
rd|¹z±J|toKto~z|m<|m
|t(o
|jA*||jmoKztomj´
zto
|tAzt|t±
Az
to
npm{|oKp±A{oK´oKA{oJ|x¢³µtMn.|jmojmJz}oK(
´z|·|{Á
|¡Mo+±N®+¸mztf|tjmo+m±
npo~jAmz8np{{o"o¡M
±¡
o¼®
·|jm
m|jAN¡ym¢|toKmoKztM¶|tjAo+´MmAm
tx_
Am·|MAzko¡M
±{|t±
ĺ
üµý"ðüÿþ
!"#%$&'(*)! '+,-$/.0!&12"34(56)87
97:5/;
=<5'>+,?
A!A
& ( ),-0/'1 ; $
=%+ ) %-:; + /'"%=
ki jmo¼np{{o]z±J|toK
*|to~p_|t±npo²Azt±m|jmo<À
A´M·|
z}oKnp·Ádnpm±(|kzjmonpoM¸J
A¶±ztA
oAzt±m|jmo¼»&±m|to<±onpoJ|
Ò¾o|tjm{p®
|tjf|to|tjmo~{{±mo~oKoKnpoJ|zK¸
{o|±zųP|tjmo~z}o
npo|tjm{mzfPo
³µ
m´¢±nyx±Mztzt±K{Py
Æ{z¸Mz}oKo&J Y8L
³µM²±Az}|´(o
º<»mM|jmo±npm±onpoJ||t±
^®8o´z}o~¾|tjAo¹ivm p±mx_³µM²±±moK
²±
oKm
Po*|MAz¸A|tjyAz<±±*®
m
{z}|ti"^mm
|toKjm±on¡Mo*||tjmÈzz}o|t±MoK(
|t
o
np¸yAoK
j´
m±o]
moKzt±n
Amm*·||MMmĸA®8pop
AjAN¡
Aof|t¾±±oKJ]|t·oK|
o**|t|tof±¡
|o+®8zt¾
±{¡y·½]mo´º oJ|AjmomMnpoA I+o±oK5|tMmjyx{zÁ
±
±
MxYL
A m±
npoKjA
mzK¸
Ao~
j³
|jmo_np{{oK±z¢jA
z¢^{z|´5|f|t±nfoz|oĺhrd³®8o_
L ¢|jmoo±oK5|t
|npo
z}zt|t´oKÄ(o¶¸ |jmo_P|tjAooMnpAmoKAjA^
m±³
K|jm]o|npztn¢omz}|to*|t±¸´
´¸ |oKMEµoKjztÄ´º z|(JF8| |jm+o(³
m|jmooJK|
o±{oK5
|t(
x{0 Eµo¶oK®8ztÄo¶º±Jnp|toKoMj´|tmo|
jm9 F8o_±±JoK|tMozM|f
|t{o~¡*¶´|(npoK o
mjAomMnfoKm
I
IÅ®o<±J|toM|to¼|tjAo+o±oK5|t
]mjmoA
npomMĸA
A¶|jmo <L ¸ L ·³
<L ¸ <L IÅ®o<±J|toM|to¼|tjAo+nfo~jAA±K]mjmoKm
npoA
ĸA
A_|tjmoK
·³
Aztoikjm)of
zA|{m|±±¡M·|o²x¾|(npMAoz}|tz}|toKıM¸{|®
z
·³µ|j^
n4¢|t|t±jAnfo¢oPz}
|tmoK´ m$ @ x|t±
npAoKmz·|ztnMAz²±oK
to¢{mMA·A|¢of|{jm½]o+oz}o*J¡M|¼
±{mAnpt±o(m|t¶|jmmo¢jAmMz}·½]o~zoºoJ|<mjA
ztoKzKº [Yo
ikjmo®
jmMoo±oK5|tMnpoKjA
m±K8{
(x{(±oztn¢m*|t±
®
·|jÇ|jmoKztoP
AAmx(MA{|t±
Az¢|
Æ
o~z±oKzz|jA
£
np
±npJmm|t{oK|z¼*|tM±h
z³k||tAjmmo
±zt^*¡
MÑ mnpEµ¤Jo£|t£M±f£
£mjAoKMoKz}npo~zoJoK|¡
z²o|to|t³k|tjmjmo~oK{x t&oKmnfto~o~z}z}oK5j JF5|º
Àm
±·xY³
³tM|mjmAo z}±A~n m*
|³
M|t¾jm|to¶±npjAoKop±tz<|¢{oKxy¡
oM|oK¸)´o~|_|´jmz}oo
|jmoxto~MAo+¢n¢Aj)z}n±±o
npoKjA
mP|npoz}|to|pMjm±o¡
o+z}|
m±|x
º
((<"() ,. )+(6 ! " 9;'(<"
3
+" , $ &
6'&
6
"
.
9
,
D
!#; $ / <
; +:/'"%= " + 7 )
1+:/ "%= " + )6= + /'; $- - " ; ; +:/ "%=
i"hztn¢m*|to¾to~±±z}|t
¯ m
A
M|t±
Y³
|tjAo
(|t±
P|oJ|t|jmo_n¢x
{
mmn°®o_moo~ |tHmo(|toKtnp±mo¶|jmo
oKo~5|tkMAz}o|p³µ
f|tjmo)±m|t(MA{|t±
AzKº:ikjmozt±mM|t±
8Aymoz¢|tjmo¾´*|tA
8´
(oKnÆ
oKK¸Å±{|toKF®
·|jm±|jmo
®k±³8|tjAot±
jJ|*|t±mn)º¶rd|MomoK|toKz¼oKo~5|tűnpmmz}o~z<|tj´*|o
to~HyxYz}PoK±
(
´{A5|A)|tztztmop|t)|jmo
oK|to~5*|t¡MoJ|t"±npmmA¼±ztmo¢{M{yo
oKº¶zÓm*³ÿ|t®
o^t_o~
(MjmA±{mA(|t|t±jmmo¶||t±zz}*A¡Mo oJEÿ||tjm±ofmmmA¼{m±{of{o
³¹¸"À{z
Fk|t|to~j´H*|²Po(A|®8
AooKhjmoK|zjmo¶J|*_|tA)|tjyA®8hNx{¡
zkoKJ||tjA*±|<o~z}Az¸1m|mjm±x o
|jmoMjJ|¹Ap±o(³ÿ|¹¡MoJ|t(±oKzKº&ikjmo~z}o
´*|tj´z¹o
±oK¢|jmoMjJ|mmA{±om´jp
Ap±o(³ÿ|AmA{±omAjpoKzt´o~5|¡Mo±x
º
ik
tjmo¼o|tjAoo+³ÿ|mmm´ÆJ{±*oo+mm
oA|®jfMt³µÆ]m¸{t|t(jmoKoK¹|t{±m±¡J¢{|to~jmzok±Mm|´<5||t®±
)ztPmo(|®8mooK´|jmjmoKKz zE[z}P
oK±oK±¢
ijØ
(Mz(A{(±AoK(
z |tF5±ºmikjmz}ox{z}o|tÈyo|tn4onpA·_|o~|tzÅjAo+³]n|jmx
oK{ztKom{m´A{no~º z
My»Ax
np&
oKm{z}
±mn±Anp±
|t
±±
mÄA¸*#º ®8[Yo¹o
moKAoKz}o~f|t¼|tjm{o
np|to~o¹
|tztjmmo~to~z}o8z³µm
nÆy¯²*mokmtoKo |®M0tƼU o(JÈyAG|A2tL´oK®
nfjm|t±oKjpzK¸*mmoK{zt|oJ||Åz"|tjmjAo±zt{{±x¼jm¡ytMz}m±moK±z&o±y¶x{pzz}z}Mo~±5|t|t±
oK
jymn:jmo~t|K¸A
oK³µtMn;|tjAo^z}PoK±
(
´{A5|AÇz}x{z}|ton)ºikjmo ,Az}|¶±zt{jmtMmoKzf±±*® |t±{|to|tjmo¾¹mtÆy±*o
mmooK|®ztoMJt|ÆHoKo(Èy¾|to»&np´º=|t±AKoK£¢z<
zYN¡*|jmo±±
omAmo¼y
K|t{jAo+rÂ
M³|oPm|o(j| OF(oº ³ÿ|AYMjM|+¡MoJ|t±o~z Eÿ|jmo¶(MMm+¡
oKztMH
³|jmoKztonpoK
ztmoKz
Ó ,´z}|¡*±±m|t±
p³]|jmo
¯ (MnfA{||t±
(MAz}z}|zÅ
³]
npA±m¼|tjmooKztm|t±m
(|t±
pP|toKJ|tAztyjAtMmoKz®
|tj
|jmonpo~
ztmto~z<³µ
n#¯mo " U º Óz¢®8o_
Fz}oKo¶±F»&´º A~£m¸
mfz}±nA±|t±
z¢JA
||t±¡
o±xY¡
oxhJz}o¶|t^|jmo
oP
t|to~_npoKMz}Ato~zº
[Yoz}<AztoKf±y¡NMz}±¡
oknpoKMz}Ato~z"MAmo
jAoKt|z&³µ
n.|tjm/o 0"P
*|
x¼
³ Ñ
m±M¹mo
o|tzK¸
|t±
A
AÀo~t|K¸
0mmA¸Aq±y{ÇrÂAz}|t|t{|o
¸8 *|MA8rÂAz}|t|t{|oKzp
³ÀoK
·|j E[ rÀ F|h¡*
m*|o¶|jm±zpnp{{oK[¸Å|jmo)z}±nm*|MAzfA
npoKMz}Ato~z
Po<³µ
mA±^ J M8 LD¸A
A)J±_o(Èmo±oKM|JA
||t±¡
o+(MtoKzt´MA{oKA(o~z¹®8oo+
jm±o¡MoK1º
!#; $ / <
; +:/'"%= " + 7 ) 2
%"
1 ; -
/& (
8#"%= + -:; 1+:/ "%=
s²mo+ztjm*®z|tjA±z
ztoK(|t±
¶|jA*|
Mmknf{{oKÄ
om{{Ao²fto~±±z}|t²nf
|t±
³|jmo¼|®f¡
oKJ|t±o~z¹³µ
n foK{´(oK
tz o(o|km{³{o~A
ztoK±fx¶|t(jAMoJnp|t
|t±±o~
pA
³]|tjmnpo²o(jm|oKo
}z|º#M[ Az}|toKj)t¡MoKfn±py|tA±
nf]o¼MNz}oKtA±z}oK|tznpo³ÄJ
|k¯³Ä||Mjm
o¼o~AfÒHnp
o(A|o(o|tz
N o~¸ z}MA¸yA
Ao
rÂnEØ
zto~ozKo¼EعÒHP
ºmr%GFVF¹Jß®8Ldo ¸
moKztoJ|oKF³µ
f|tjmo^
m(ÁdAMzt
|*|t±
EØ»&´ºKA¤ZF5¸8AF³µ
f|tjAo¾M{±
8
J|t
(|t±
EØ»&´ºVAK4F5º [ho¾o¾z} Ao
|ÇmymA(oHm¡
oKzf³µM¶|jmo^±o(³ÿ|¡MoJ|t(±So E0 (F¡M
±mnpo^M´±·|*|t±¡
oKx z}±np¶|t|jmoH(At¡MoKzoÈJ|M5|oK³µtMn |jmo
ztoMnfoKJ|*|M
³&Ò^r E[»"±Aº A~! F(º
ä(ä(ãØãØãDãDÛJÛJåå t íÄ&~â~íÄãDíêßÙÿ×âNè ÕÜNÕ(Þ èç
ã[â~è æ
ã}è ÕÚt è á&ÜNæêè à5áÖêßæ
-Þ KÛâNÙÂã[Ö ÚD +Õ &Ù}Û
æ Ùã[ ÚD&Õ Ù#æ &ÞßÜ~ÖÝNÖ ÙÂ'*çM è ä(ãDæ
ê
ð"ð Üab 2b
9+
+
AN
U#<]"2 7" U "D'434 :U=)!G
65
60
55
50
45
40
35
30
25
20
15
10
5
0 ms
»&±
mo A~R£ IÄÓ
(|t±
P|oJ|tyz}{jm
AoKz EØfnzFnpoKMz}moKJx¯²mtoK " U Eÿ|
¢t*® F(
npA
to~+®
|tj|jmokz}±nm*|oK
MmoKz&EØ´
|}|tMn7*® F5º
ikjmo+ztn¢m*|t±
to~z}A·|z®8o<moKztoJ|k
to¼m±|t|toK*³ÿ|o8|®8fztn¢m*|to~x{(±oKzK¸J±
{o8|tf
m|± A|tm±m·|±
A{|t±
´z8³µtMn7Po{{(|x
º
Ï 7 Ë)Ï ¨ Ë Ë ¨K© Ø« 7 Ë §
[Yo{o ,Amopz}o|³&|t±
m
±oKz8omoKztoJ|m¢|tjAooAmyK{±mn ³&oKMj¡MoJ|t(±o¼
A®o¼|tjAo^(±Mzto¼|tjmzztmt³Ø
(o<®
|tj
|jmoA
tx{(oKJ|to8
³P|zoK{Mok|t(Mnpm{|tok|jmo±mmoK¡
Mmnpo
³´|jmo
¡
oKM|t(±oKVz EØto~pz}mt³Ø
oKz
Af
ooK¢±AoKzű¶»&´Rº A!A8F5º
ikjmo+oK¡
M{|M
³"|jmo+¡
oKJ|t±o<¡
MAnfo+{At±mp|tjAoz}±nm*|M)³&|tjmoK{±M²x{(±/o EØ»&´=º A~G F8±zk¡Mox_ztnp±±
k|t
|jmo²m|+N¡*±m±o
p|jmo±·|o*|mt'o ^E[z}MOoK'Mo J
8 L´³µ
¹±Az}|
A(8o F5ºÓz®8o®kJ|Å|tAz}o|tjmznp{{oA³µ
¹±m
´Am|t±
AzK¸
®8oz}fjAN¡Mo|¶(
npA
to¼|®
·|j
MAz}oKt¡*|t±
AzK¸y[º o
ºÅnpoKm±K1±np
±mAº
Ó{|tMnp|t
{
¢±np
ozto
npoKM|*|MHzz|±¹¡
oKtx^j´±oKm
±m|
ztÆ]¸"
AHn
J´zto
npoKM|*|Mh
³8³µm±
¤JztoK¯Jmz}oKo~AM(Ao<oA³Åo²fz8¡
MMmmJ¢|
ooAk¶jm|o~oK{t±|
´®
z·`º |j[Y|o¼jmoAtzto~oz}npoKM·ÁÂ|8jmmo|t
o<n¢|t
²npnpAo|tjmz}{M)¶{®
o(|·|j±o~¢_¡
±MSAJ nfLDºo¼(m¡
o¼o(Èy|M5|to~³µ
n f
¯ Ò^
r
üµý"ðüÿþ
!"#%$&'(*)! '+,-$/.0!&12"34(56)87
97:5/;
=<5'>+,?
AK
»&zto(±|
zmo o²A!´A!z}IÅo~i"_t|A(
±±MoKztz8o²z}|ojm|zko+A¡
ztoKoKJ_|t|t±o~{zo ,A±mo<|tjm|to+jAo¼¡M
oK±Am{np{o+
(
mnp±¢mm³&|*oK|
Mjĺ ¡
oKJ|t±oMº&ikjmo+´xyoJ|toKz³"|tjmo+o~{
o~z8³|jmoKzto
Measured and Simulated Left Ventricle Volume
130
Simulated
Left Ventricle Volume (in mL)
120
Measured
110
100
90
80
70
60
50
40
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
Time (in s)
*¡»&±
±mmo~z
o/A~ARI8|tÒ^jAoKo+
oztmoK(oK|t)±
±o(³ÿ³µ|¼M¡
5o|JM|Ct(E[±
o£ ¡
MFkA
nfto<o<z}³µ±np
nÉÒ^k|prk|tjm
o<npMAm
oKzkto~npoK|tMz}A|jmto~o¢_zt±n¢)m¡
*±|tmo~J¾|toK(ox{
(m±o
º²|PikjmEØMo¢ ztn¢F5º m*|to~)¡
Mmnpo
ikjmoz}±nA±|toK ¡MoJ|t(±o¶¡
Mmnpo_m¡
o¶z¢JA
||t±¡
oKxY¡
oKtx z}±np|tH|tjmonfo~
ztmoK
Ao
¸®
·|j
ooK(|t±
³µ
t
o¼(|t|t±±
npHoKz
³®
jA£ o_¸]|tjm
o+np±JA|t
t*o~Ád¡
)o|tJ)|t
( m8±^¡
M|jmAopnfnpo+oK{
o zt,AmmoK|tzK±º+
)ikjmzko¢mn|
|Yt±¡y{±·
½]1oo´|t(jAoKo¼z¼±no¢MmoKmzKtº ±mmjAMz}o|tAzt·|MAzK¸P®
jA±j
oKzt±[Yz}|
o²A
(to oJ Mm{t]¸ Yo8JLD|¸Px¢*|
J|t|tjAo{{
A{| QAm*¢®?& [ ³|tjm´o{Æ
¡
o~oztJzt|ot´nf(±oK{zK{ºoKik[¸Jjm®
ojm
}j|o±z±
1(m
oKzzztz}±mKmoKzknp®8{
{AoP±³]|tjA|jmo^o²zt±x{Az(|ooKnpMz}±o+{(
Anpt±mm±oAo~5o|MAÄ ¸
|jJ´znÆy±m|jmo¡M
±mnpo(m¡
ozt±
Po¢ztjA±*®8o~ºkikjm±z²z¶npMto+oK
z|±nf{{oK"
³|tjmof*³ÿ|toK}Ád±M
ĸA®
jmj¾±z¼Jm|to
±np´ikM}jm|o¼Jo¡M|
±){|t±
m±M³Ä|³µjmmoK´zt5o<|t¡
±
Mm¸´np´o~z¹nztjm
ÆMAoK±z·|
±P¡
Mo<zz}oK±mztm±o·||z
(
±MNztoA8z}|8|tp|tjm|o+jmo+(MnpJoK|tM
z}m5|oK±zK|º xf´npo(|ozEØnpÈ{n¢mn (MM|M5Á
|MĸA(MJ|t
5|Mzt´oKoK1¸AtoK±È{|t±
z}Poo~ F³µtMnÃ|tjAo+ooK(|t±
³µM5|M
A|tjmo+mj´
zto<mm|t±
AzKº
Ï «M.ª 7k¥ Ø« ÏAÍ ªm§~.ª 7 _Ï ¨Kª{¨ Ï »AtMn |jmo<{o ,AA·|M_³1|jmo¼o³ÿ|8¡MoJ|t±o²oAmyK{±mn)¸M®8o²K_
npm{|o|jmo±mot|tÈ{±z³1|jmo²±o(³ÿ|k¡
oKJ|t±o Eµm±mo
±ÈyAo²zK¸y±|tjm»&
±Am5º MA!jmA
F(m`º |8[h|jmo²oAz}
o²|tmjA±M±z8²*È{xyzoM|¢º (Mnpm{|to²|tjAo²±{]A±ÁdA
zm|*|M³1|tjAtoKo²P
±J|z EØ»&´]º AKG F¹
m´f|tjmz
|jmoikjmA
zx{zzt±npz8ok
³"t
||
|tM±oK
fÒ^®8M
zrnfz&Jßo~8
Ldztº moK³µ
{½PoKtoKJ|´MJ|z³P|tjmo
n¢x
{
{±mn yx¢jm±±Az
o~z}o~jf»A
A(o8|jmtMm
j
ikjmoh¡*±moKz_³µtMn |tjmo z}±nA±|t±
oH¡Mox zt±nf±¶|Ç|jmohnpo~
ztmto~z¶P|j JA±|*|¡Mo±x
AJA
M|·|*|¡Mo±x
º
¹ztPoK(±±x)|tjmof
mPMzt|top{oK(|t±
^
³¹||t±
¾Po(|®8ooK^|tjAo¢AMz}ofA^|tjmopPo(È^z²mto~z}oKJ|²P|tjY±^|tjAofztn¢m*|t±
ð"ð Üab
2b
AK¤
U#<]"2 7" U "D'434 :U=)!G
»&±
moAKIq8Mzt
[¸{o~JA*|
±
ÄA)A±K1P
±M|zM|jmo+oA±K{An7AztoK|tMAzto¡
o¼|tjmo+±{
Ät
||t±
){mmp|jmo
ztn¢m*|to~){
¼(x{(±o
º
14
Base Epicardial Rotation
Equator Epicardial Rotation
Apex Epicardial Rotation
12
10
Rotation (in degrees)
8
6
4
2
0
−2
−4
0.2
0.3
0.4
Time (in s)
0.5
0.6
0.7
»&±
m&o A¤ I E 0o(³ÿ2| Fi"®
±z}|t±mA
±o{mm<|jmoztn¢m*|to~p(x{(±o
¸
³µ
¹{½]ooJ|¹P
±M|z
³´|jmooA±K{AnI"A
zto EµA±MÆ,F(¸
o~»AM´
A*|t(Mo¼ ³µ
EØmMmz}·jA½]oKoomJ|APo Fk
±M´|zk
³&´|tojmÈ^o+Eµn¢oKx
{F5ºK
EØmMmjMn)|2Fkº i®
z}|t±m¶mMo<oÈJ|M5|oK³µ
n7|
o~_Ò^ryx¶jA±´z
o~z}o~j
m
Aj´p
zto¼p
|Ajm¶onp|jmoKo+M
z}A(|tt±o~¡Nzº&|tik±
jm±zz}o~|M®
A±z}o|tA±mo
+ºÅnpikjm|o+Mz}±n
A±M|t´±
*_|to~
z&³Ä³µt|tMjAn o<M|5jm|o M,A_mPo|tMoKtJ±o|tJ|1|tm±
AAz
AM{||t±
¶zt<´³µt¶Mn |jmo<|tjAoA±zt´*¡
z}±M
Anf³o|t|jm±o
{½]ooJ|mjAMz}o~zk³|jmo
m±M²xyo+z8|tjyAznpP
t|J|k|tpoK*¡
o8±yK1A
npo(|toKz8
³"|jmo+{
¼np|Mĺ
Ï «M.ª 7 ªmÐ Ø.ª 7 Ï ¨K©*ªm«¨ Ï Óm|jmo"npP
t|J|±{
A
nfo|toKijy|tjAo
m±M&³µmA5|Mz1|tjAo¹
{
J|t
(|t±
ĸK®
jmjnpoK
ztmoKz]|jmo¡**|t±
³"||*jm|to±
{Yz|z<AAz}o~o<h³µt|tM¾n (Mfnf´AM{J|t|
op||pjmo|tjmoM{oJÅ|t(MÄM|ÈyM5zK|¸y|tMjmH
m³8M|tjmjA
tmoK|8of|Pjm
o±JK|z+{
±³¹M|²jmox{(o±o
³ÿ|º¡
ikoKjmJo|tz±npofo+oA±mmoytK|tp{*±È{m±n z
MEØz8»&³µ±
A
º0|ANjm!o F
{At±ikmjmfo
|tzjmonpzto8±nMm{*±
|oKJ)
(Jx{|t(±
o
(º |t±
®k
z&npoKMz}Ato~<³µ
Å{½PoKtoKJ|P
±J|z&³´|tjmokn¢x
{
{±mn yxjm±±AzÅoKztoKj»A
A(o
|jmtMm
j|tjAoA
x{zt±z8³&|
MoK_ÒH
r&z Jß LDº
ikjmo(Mnf´±zt
³
|jmo)z}±nm*|oK
m±
(MJ|t
5|M ®
·|jÇ|tjAo_npoKMz}moK Mmo_M¡MoKz¢z}HH
y{(Mto*|M
E[»"±AºTAK4F5¸&®
jmjÇ(
.,Atnz|tjmo³ØM5|¢|tjA||tjmoz}±nA±|toK o}oK(|t±
³µ
5|M±z¢(±Mztop|tH|tjmo¶oK
¹MmoKz
AY|tj´*||jmo
np{{ojA
zkf
y{_±{
1´oKjAN¡yMmKºikjmzkM{1(MM|M5|M_zkto~z}P
Azt±mo¼³µM|jmo+o¡M
±{|t±
³&|tjmo<®k±]|tjmÆymoKzz
{At±mf|tjmoK{
¼(x{(±o
¸m®
jA±j±zz}pp(±m
ıA{o(ȳ&|tjmoK{±M³µAA5|Mĺ
üµý"ðüÿþ
!"#%$&'(*)! '+,-$/.0!&12"34(56)87
97:5/;
=<5'>+,?
A~
»&±
mo>AN,Iqk
zD¸Mo~M´*|tMtPAm
]´MJ|z8
³Ä|tjmo¼±o(³ÿ|
¡
oKM|t(±ooKA{{
mmn AztoK¶|tf
Azto¡
o|tjmo<±yKPM{
J|t
(|t±
mmt±mf|tjAoz}±nm*|oK)
m±M²xyoMº
1.1
1.05
Base Endocardial Contraction
Equator Endocardial Contraction
Apex Endocardial Contraction
1
1
0.95
0.9
Radial Contraction
Relative Radial Contraction
Base endo
Base epi
Equat. endo
Equat. epi
Apex endo
Apex epi
0.8
0.7
0.9
0.85
0.8
0.75
0.7
0.6
0.65
0
100
200
300
400
500
600
»&±
mo A~RI E0Äo(³ÿ|2F¼
{Å
J|t
(|t±
^{m±m_|jmopz}±nm*|oKh(x{(±o³µM<m·½]ooJ|<´MJ|z¼
³Å|tjmopo´{{{±mnPIAMz}o
EØm±MRÆ F5¸1oKJA|tM EØmAo¢Á
Á F²AhPo(È EµoKF5º E[
±
jJ|
F²
m±
J|t
(|t±
^oÈy|t
5|oK^³µtMn|M
o~^Ò^
ryx¾jA±´z
o~z}o~j»A
A(o¼³µ
m·½]ooJ|P
±M|zk³&|tjmo+n¢x
{
mmn)º
)((8<"( " <"(2+$ 9;'(<"( /]¢"k &(1(2
vy´j)pnp{{oKÄoA
m±oKz8|tjAoz}±nA±|t±
³Å{·½]ooJ|K{*¡*Mztm±
¹A|tjmMM
±oKzK¸m*|
|jmo+o±oK(|t
mjyx{z}±
±
M±KPoK¡
oK1
npoKj´m
&±o¡MoDºikjmof
Azto¡**|t±
H³|jmo(
´z}o~MAoAoKz
³¹|jmoKzto¢´*|tjA
±
±oKz
H|tjmoztn¢m±|to~H
m±M+³µmA(|t±
mjmo±)mA{oKz}|
A¶|jmo+mjmoKm
npoKAm¸y|oKz}|{·½]ooJ|k|tjAoyx_z}|t*|toK
±oKzk´_m)±J|to¡
oKJ|t±
AzKº
0
0.2
0.4
Time (in s)
0.6
0.8
Time (ms)
1+ " /'1
/
" 1& 5 ; =
G
& =
$')7G -:; =1 7
G
$ " 1
¯²·½]ooJ|<o±oK(|t
mjyx{z}±
±
M±KÄ{zt
{oz
^Pofztn¢m*|to~1º<Ó^o~5|tMm+³µ{(Az<K^Po±J|tymA(o~¾yx±AAmm
Mm{|t±
A
Äo(Èm(||t±
)P
±M||t|jmomMtn1¹mtÆy±*ooÈJ|toKnp·|o~z¸´®
·|j¾·|z*®
)o(Èm(||t±
¾ztoKJmo´(/o EØ»&±A=º AY¢o³ÿ
| F(º
Ó mmAmo<mAj_m{Æ
¶Po<zt±nm*|oKyxonp*¡ym|tjmo¼mÆy*o¼mo|®MtÆfo(Èy|tonp|t±oKz8±_
Ao³|tjmo¼¡
oKM|t(±oKzK¸
A
Azto¡
o²|tjmo<oKztm|t±m{oP
±z*|M^ E[»"±Aº A8Yt±
jJ2| F5º
- / $'$';<+:/'"%=
rd|jAMz&´oKoz}jA*®
|tj´*|z}MnpokK
ztoKz&³]
{
,Am±*|t±
po|tjmokoKztm·|Å
³P¼z}m±{³]{oP
zt|t±
npoK
A{oKt±m¼
||jmjmo²o®kn¢Nx
¡
{o(Ád
mmoK
mÆ+n)nfºÅovy|tAjm{j_*ztE[m»"±±A
º±z8AOX4
FT¶J
P¤o¼LDºztvJn¢|Am{*±oK|tz¹o~³]®
|tjm|to~j¶z}o²|jmz}o<m±jmMzÅzto(
Anp±p{{jmooKD¸y¶AmztoKmztfMfmnpAMtMto
mto *|ooK±mJ|·|±{
o1,´(m
t´±±{±·||t
MAzzJWAO±X8Æ
Ldo ¸
yx_´z}±mf´o|}|toK{o ,Am±±|t±
|t±npm¶
A_|tjyAz
±oKzzkomoKtMx
º
ð"ð Üab
2b
A~
U#<]"2 7" U "D'434 :U=)!G
65
60
55
50
45
40
35
30
25
20
15
10
5
»&EØA±
mt|o³AYZ>IÄ[Y¹
o~5½P|tÁDÅ
AjJÆyx{zt´z}MMM{
Á[
jA
·A|o<|tztjmxyMA{M
±oKnpzo<z}±z}n±nAm±|t*±|
ÄM¸*mF5ºKoKE[zt
o±J
|jJoK|
Fk®
±|t
jfjJ|
oKmztm·|AAj²mz}±{{jmÆ_
z}A±noKzKAº ±E |t0±o(
³ÿÄ|
ºF&5|tMm¹³µ{Az
0 ms
Normal
Action
Tissue
Potential
Non-conducting
Tissue
Time
&» ±
mo/AOXIvyn¢m*|t±
¾
³¹¶ooKM|txz}A"Az}±m_N®kN¡
o(Ñ ÁdmoK
ÆMº&EØi"
5F¯²oKz({|M¾³Å|jmo®kN¡
oÁDmoK
ƶnpo(|jm{1º
E[q
|}|
n/F
vy±nm*|MMp(A´o<³nxM{{±mnÃnp{{oDº
±
mkomoKztoJ|z|jmo
(|t±
´
|toJ|±
0Eµ±MjM|
oK IÅ{oK´
Á
±ztoKĸmmƶm±mo!IÅo<´M±
tztoKF(º
; /'"* -:)&
= ; - 1+ ) -:),;
)6=1
$';
+ /'"%=
mÒ¾J{z(|ko~{m³1|o²jmo¼zk¡
o³ÿJ||ot)(moKm|jyo±x
oK¸{(®
|tjm
mjyjx{z}oK±
ztm±
M|z8±K±){A
A|tjmztM{oM
±oKmz±o
omN
x|8{o~M
ztztoK±zkx{|oKto~±*¡
|oKoKt1o~¸{
´A|t®
jAo²·|j
{±mÁD³µ´oK(Jotm|o
´(x¢
mm|(*M|tnp±
o
º
vy±nA±|t±m_|jmofA*|jm
±
Mx)
A)|jmo¢M{|
npof³{½]ooJ|¼
m±|t±
Yz||toMo~z
m^jmoKH³µ
²|tjmofmmAm³8z}Aj
±i"JoK|tojm¡
AoK
J±
|t
±
±oKAz
zKF5ºfºikrd|²jA
o±m*t®o~z8z}oK
Jm|to¼oKH|np´yMmoJ|®k±y
Kz<*|(MMmAmzk±oK¾hM®
¯·|j
_|t³µjAMo+nfo(ÁD{³µ{oo~oK{A
´Æ^MjA¯
m
Jo<|o±)t³Ø
t(o~*o ]EØ|t±npjAo<J|t|jm
n0
o¢(³µ
´
{n3A5vy|o¡yAz|x¶Ao ³
|jmoKzto+{K*|t±
´z¸{®
jm±z|k|tjAoz}±nm*|Mz
mmm±m* EØ»&±A=º A~G F(º
vyMnpo|tztztmo¶´*|tjA
±
±oKzK¸Ä±ÆMo¶±{³Ø5|oK oKMz¸& Po_±J|tymA(o~h± |tjAo¶´
|toKM|±
¹m
´M|t±
AY± |tjmo_nfoÁ
jA
m
J|t
(|t±
ĺikjmo~z}opoMMAz< Po
Azto¡
o~^®
|tj *|toÁDoKmjA
A(oKnfoKJ|+ÒH+¸1|tjyAz{
ztoKhY|tjAonf{{oK
MnpooK
npj´o|tmx
º:
rÂm{³Ø
P5o|toK|t±FoKz|tzt³Åztm|to~jAzpo¢jAn¢Nx
¡
{o¾
{±±mnfn)´º
5ik|jmMo~z}of|{jm·o¾½]o±yoKJ|¼
o((½]MAoK5{|Az²(K|t±¡y^·|xMP¸8oM±yzp¡
®o~zoK|JM*zp|to~
|tjm|tjm
o)A
Aj^Mztztzt±n¢¡
o¾m±A|t±
A
zK(¸´|t±³µ¡
o
üµý"ðüÿþ
!"#%$&'(*)! '+,-$/.0!&12"34(56)87
97:5/;
=<5'>+,?
A8Y
m»&±*
|mMo*ĸ
AKyI/xE np0Äo{³ÿ{|
F<³µxy¹mjAÇJ|t|tjmMoHn°M
¯ÃAmAJ5||otm³Ø
(´oM¸Ä³µ
npn#o(|ovyozAz³¼A|tojmohi"oKnpjmymmMoM®
±jAoKozKº;o¾EØ
·|±
jAjJ
|2zF+Po
oKm
Á[ ³µoK(J
mJ|oK
A5(|¶x^®
m|t±j:|t|±
jm o¾z}|±JnfMÁ
EØjm
np
MomoK
Az8MtoKx_oKMz F(º
oÈ{
npmok|jmo
±, QAmoKA(oM|jmoo}oK5|Mf³µM5|t±
¸®
jmjpmoK(oKMz}o~z&³µtMn.M ?|
f|tjAoz}±nA±|toKfMz}o E[»&´ºM4£ F5º
140
Volume (in mL)
130
120
110
100
90
80
70
60
50
0
0.2
0.4
Time (in s)
0.6
0.8
&» ±
mo£I"qk
zm±o(³ÿ|om
{{±{³Ø
(|toKp¿K
mo EØm±mo FÅzt±nm*|Mĺ& (MA{A(|t±
´¢A(MM|M5|M¢±p|tjmz¹
to~mº
E[
MjJ|
F Ñ
to~z}P
Amm)¡M
±mnpo_(m¡
o~z®
|tjmM{|E[m
ztjmo~F
A®
|tj E[z}MF+±{³Ø
(|Kº^1o~5|Mdzµ
5|MÇ{oKto~
ztoKz
³µ
n4M .|_
¶º
m*|Mdz|tjmo)z}±nA±|t±
Ç
³|tjmo~z}oA|tjmMM
±oKzzfm
oKzz+®
|tjm±|tjmo Ñ {
¶Ò^
oKztoK
j tMmĸ
<±m4 z Ñ
±±o
3
i"¾
jm±o¡Moo |0jm
±Az{M±nĸ ¸"mmox® znpÀo(M|ztjmm{m|
z+[jA.¸ 0N¡M
oA{|¾M ´o¶J Z {YOo~Ldz}º ±
AoKH|t¾Po¶m±of|t){K±xHMNAz}|+|tjmo´npo(|oz²
³|jmo
np{{oJ||tjAo8N¡*±m±om|A,º Åox+m
np±zt±moKztm·|zj´N¡
oPooK
m|±mo~+
|tjmo8Anpo|to&
N´z|nfoKJ|"³Pztm}³ØM(o
npnp{oK{j´o´m³]|t
jA1oAomnp
o(m|omz8n o³±|oKjm(o|t
¯mjynfx{z}{±
{±oK
]M³µx tMJ
n 8£ Ld¸J
±mA(ÄmA*o|JA|º o(½]
t|±z{±to~5|to~p*|¹r ²
rÓ |+±{oKJ|t³µx¢oKo~5|t´A
)((8<"(
" /1235$6(6 & mù" 0
!*+Å°
s²mo¼³"|tjmo¼
Jz¹
³mm±{A¢|jmzknf{{oK]±z|tpAmx_·|8|t
m±M
n
o<z}oK
npoJ||t±
ĺikjmo<Æ
oKxp±{o~z|tpmm±
}ÁÂÓ
5|t±¡
o²¯o³µ
np
m±oÒ¾{{o ³1|jmojAoKt|³µM±n
o²A
x{zt±zK¸
Dº oMºÅ+¡
Mmnpo|t±mo(³µ
nm±onp{{oK´
³P|jmo¼jmoK
}|
±±JJ|t|tooMA
|tJ±oKmm oV
\5x+2oM2mÆym*±zt®
A±oK
m|t
jmo
o
{fo³µ|
jmonnp*|t±|
M¢Ä±z¸|jm
tnpMmm
{jf|oK|jm³µotMztn n¢m|tjm±ok|to±
±oKp(|t³]
|npjmooKoj´±oK(m|t
npMnpoK{j´{om{A
toKy¡J±
J´|tz}±
x<(|tm±t
o~Äz}º&oKJik|tjmoK o
ä(ãØãDÛJå tíÄíÄí ÿÞßÛNàNè âNæ
Ý~Útè áÕ5è *â ' æ<è ÚDÙ×[æ
ÙÚDáÜ(ã ÞßÜNÝNÙÂç
è ÛNäNÛ
ð"ð Üab
2b
U#<]"2 7" U "D'434 :U=)!G
AX
|
jmAoKpzto+|tjAoomoKo(tÈyM|oo~z8A®
mtoK|tmooM
z¹xf³µMz¹(oKMzOnpI m{|to~p³µ
n L |tjmo²nML o
³µoK|tmoKzKº#[ho|tjyAz8z}M¡Mok|tjmo²mo®{xyA
np±KzoKJA|t±
ĸJ®
jmoKto
ED! F
L L ®
|tj |tjAo(
J|M5|t±
_³µ
(o~z¸ |tjAo¼±nMo²³µMoKzK¸mA |jmo+®oKMjJ|t±mpAnpo(|o8³µ
k|jmo+±np
o¼³µ
(o~zº
C
5
95
= +.)6- = ; $ " - 1 )65
+ ),- = ; $ " -01 )65
DE
D
,E
E
5
+ 5
+
ki jmo¼±M|oA´³µ
(o~z
to²(
npmm|toK¶³µtMn |tjmo<o±oK(|t
npoKj´m
mtjAo
±
M±Kmnp{{oK[¸y|jJ´z¹±J|tymA(±m|jmo<z}±nm*|oK
³ÅJzt|toK(
|t(±
|t±)
ĤAººß¢[h|to
A(
zto8np|tmjmmo
|tnpo<|t{jA{ooKmnpmoKoKjAzto
Jm|t±o~K¢ztoK
(|tJ±|t
p
(m|tºW±A
Ä|+º8(»m
Mnp
m|tjmmo|tok|t|t±nfjAoo¢
z}5xy|AM¢jmP
A|±oz*J||tMÄ{A¸{tmM³µA
Jnp*|t±|t
±
f)
A|t|jAjmo
onf±np{
{
oKo
ztoKJmoKA(o¶MJmz}|t±
±*®z<´z+|t¾Æym*®.|tjmo_jmoK
}|+PoK*|f{m*|t±
¸Ä|tjAo¶ ®8N¡MofPMzt|t±
Ah|jmop|t±npmH³koK
j
±n
o_|jmox{(±o
ºHikjmz¢±zAz}o~ |t^|tM
o|tjmo
(|t±
P|toKJ|t¹AtMAJ*|t±
A
N´z|¢|tjmo
5|M´
|toKM|±
{A|t±
ĸmMzk®oKÄMz8|t¶(Mnpm{|to¼|jmo+o(Èy|toKt´]³µ
(o~zº
»A
+|jm±z¢z}oK
npoJ|*|t±
MMD¸"zt
npo¶P
AAmxh
Am·|MAz¸&±ÆMomto~ztztmo¶AYz}*¡M
±mnpo(|tfmjA
ztoKzK¸oAt|t±x
±±A{³µ(
±An{o~* |M ĺ¶|tjAiko¾jmnz<±z<Mo)|jmo{³µMoKt
nzt
h|t±
®
Äjyº x^ikm)jmo^npMoKm{jAoK
m±Kz}|tŽPPm
o~mztz´m|tx^toKm(MoKAzt{oJ|t±|p
A|tjmz+o¾
|t¡*jmoK±¡
<o~|tzfjA
±z¶h
±±nzt Mho¢´³µMt|poK
z+³²
|tjmopo¾m±npA
±oK
o
®
jmoK|tjmo+np{{o±zkAztoK±|tjmzkn
o+A
x{zt±z³µnpo®8
Æ]º
±n)²
o(z}A,A
A±
x
"¸mPztoMMztnp·|oMJÄ|º |t[Y±
o¶Pnpoo(±±|ojm¡
{o¢m·zk|¼A±z²zto<±nf
mPo¼
tt|o~
zJ|k|²PmM
zt·|||tMt
o~³Äz}o|t|jmo<|tjAnpof{z}{|to1±P^o
A±nHz|Mto
o~¸{zt(z²M*t|²oKo~zt
´Mj)A{|±npmo¢|³µ
|nfjmo<omho
¡yM{Aoz
|H
{|tmo¶±Å|jmo_jA
M5|toKtz}|tz¼³8|tjmo{o(³µMtn*|Mh
³k|tjmo¶n¢x
{
mmn)º_ikjyAz®o®kJ|+|t¾´z}o¶Mm±xH
Aoto~z|
PMzt·|M)³|jmo+jmo~t|8³µMk|tjmo
npm±o(|oz}o~MAoAo
º
¯²mo+||tjmo±
tMo{·½]oo´(o+±Hz}j´Po+´o|®oKo)|tjAo+|toKoÁd{
z}|tM<PMzt·|M^A|tjAo|toKoÁdztx{z|
±±<PMzt|t±
ĸ´Az}±m
\522 Æym*®
±oK{Mo+
¾|jmonp
|t±
¾jmoKAz²oK(*¡Mok|jm±z¼{o³µ
np|t±
ĸP
z|tjmofn
o<³µ
(o~zMmxjAN¡Mo+|t(
oK5|
|jmo
moKm±(|toK){o³µ
n*|t±
¸{m|(oK|to<|
³µtMnÃ|tjmo<|o±o(ÁÂ{
z}|t
±¼ztjA
´oMº
ikjmo_o(Èy|toKtA
ųµ
(o~z+oJ|t{{AoK
z)J
mA±oKh|t^|tjmo¶npo~jAm
ÅnpymoDº»A
o~
jz}A}³ØM(om{{o
³8|jmo
npoKztjĸM®o
±y
Æ+³µM¹<(
oKzt´MA{±m²P
AAmxP
±J|p|jmo
n
ok¡
NÈ{oz&xy±m±
A²|jmoztm}³ØM(okmMtnD¸
+±Mztzt±K
mmM
j³µM¼{o³µ
nm±onp{{oz±H
npm{|o¼¡JztMĺikjmo¢´MmAm
tx´MJ|<±z¼zto±oK5|oK¾
nfMm|jmoKzto¡MNÈyoK±z³µtMn
|±Jp|to|tjm´oz}|{x
¸´z}|
´
({o¼±o|tJf||t{jA±±tz
o~5P|t
±
A¾Am
Ax¶
¡MN
Èy{oK±1oJ|
A¡*
±m±ooJ(|to~·|¶o±± |J ¤Mz {LDº8ikoK(jm|to±
¾Äfº ³µ
(o+z
mm±o~|tp|tjA±z
Aymo
¸AAtM´M}|MA
INTENSITY
REGION 1
n
P
REGION 2
BOUNDARY
n
DISTANCE
P
BOUNDARY
»&4±
m±
ofmRA!|tIkjAofÅÈyA|t
oKtnpA
³µ M|oKz²|jm(op
npnpmoKmzt|j *|ztmMtijØ
º>Eo
0ĺPo³ÿEØ|
F¼±
v{jJ|
F¼{ÁD
±±oKm
o¢±
M
A·h|jmPn7
m|A_AoÈJ|xHM(5|·||ojm±of
nhM|tjAoof¡
NoÈ{ÈyoK|t±z
5³µ|toKMhn4¡
_NÈ{¡
ootz|to|tÈ
{o|toKtnp±mo<|tjmo+P
AAmx¶P
±J|
to~z}P
´{A|¢|jmoztm}³ØM(o<¡
oK}|o(È pº
ikjmo~z}o³µ
(o~z
HPo¢{½]ooJ|¼M^oKMj^³Å|jmop{·½]ooJ|+A|tMnf
oMMAz
³Å|tjmofnpymoD¸]moPoA{±m
^®
j´*|
zk¡y±ztAo<±_|jmo{½PoKtoKM|
A
}|z8³|jmo<n
o<A
|tjmo<±n
o<±J|to´z}|x¶jA
(|toKtz|±Kz¹±|tjmo~z}o<o
±
´zº&rd³zt
npo
@
0
üµý"ðüÿþ
!"#%$&'(*)! '+,-$/.0!&12"34(56)87
97:5/;
=<5'>+,?
AK
AMm
}x¶|z
|tjm³&o+|t±jAJo|tonAxM
y]K³µ
{(±oKmzkn7®
±±Äo<nmÆ
|²o²¡J|tjAztoKmzt±o+o
¸m¡
o|tjmt|to(oo~Èyz8|too¡
AM
¡M]o
³µº
(oKz
K)PotoKnp*¡
oK_³µ
|tjmo
to~z}P
AmmpoMMAzkA
$"
; $
.&
5 +:( )6= + + "
; +:/ )6= +
= ; + "%(
pnikjmoKoztj¾(
||toKjmzt´o¢MAA*{|ooK´J(|²oKz<APo(|t|M®8nooKx
Yº
Ó|tjm³ÿo_|tozt¼mt³Ø
moMmj^{{±oKz¢MmnpAhoJ|t|jAo_³ÅP|jm
moA¡
AoKJ|txH±¡
No~È{z¸´oK±®z+oK
np´mo_{A|oz}o~Y|to|t¾*|M¡MMo±Ax¶±|jmxYo
PNoKz}´|²z||Mjm± o
|
Az³µMtn|t±
Po(|®8oo¶|tjmo²nfo~z}jAp|jmo±nMo
ºÓ
³ÿ|toK
(
y¡Mo
o´(o
¸
®o¼(
npmm|to|jmoPoKz}|
z}±np·|xp´,AA±±x
|jmo+´o~z| mo<|tAz}³µ
n)º [Yo+Aztofmo®?(·|oMm
PMztoK_yx ºA&oKmmo~¼
AmoKztoJ|to~_±^J
LDº
)& )6=1 ) ) %( )6= + ; +:/ "%= H #/ (*) 1 "%= +:/'=& " & 5 (
; ) " - 1 ) / )<$ Ó²z²®8oAzto¢
^o±oK(|t
npoKj´m
Änpymo&³µ
|tjmofJ|oA"omoKtMx
¸P®o¢moo~)|tJ|toK
*|o·|<
K(
{±m|¶|t±npo¢z}|toKAz
M ¡Mo¾yx¾z|m±|x)(
´z|
J|zK¸A®
jA±jH
to+±A{oK´oKA{oKM|¼³µ
n |tjmo¢nMo
KJm±zt|t±
)|t±npooKzt
±{|t±
ºK[hof(oK|to
|t±npo(ÁÂ(
J|ymMAz¹±nMo³µMo',AoK±.²yxAz}±m¢|tjmo¼|®8±n
o~z¹
³|jmo¼ztoKJmoKA(o<ztmt
AA{±m|jmo+(mtoKJ|±M|oM|toK
|npofH|tjmop(x{(±o|_±J|toP
*|to|tjmo¢³µ
(o|t)mm±x³µtMn4|tjmo¢|®_³µ
(o~z(Mnpm{|to~^®
|tjm±Ho~
j¾
³|tjmo~z}o¢n
oKzKº
mikjm{(z&o~oztAzKztº moKz"ztnfy
|tjoK¡
±{|M³{|jmonpo~jAm
P
m´mx+(
´{·|MAzK¸K|jyAz"´o|}|oÅz|m±±·|x+´z}oK
npoJ|*|t±
rd³&®o¼jAN¡
o<n
o ²*|
´z|J| ²
A¶|jmo<mo(Èy|
A
o zk*|
±Az|J| ¸m´¶|jmo+z}oK
npoJ||t±
¶At{(o~ztz8zk*|
|npo 8|tjAo{
¼(x{(±o
¸{Po(|®8ooK ¼A ¸{|jmo|jmomA±oKn
o¼³µ
(o<"z I
.
5
)
D
&
$
D
D
D
& 2 ?& 9 D
5
/
5
»&±
moH
RIHvyoMnfoKJ|*|M
³{
n
o^ztoKJmo´(o)®
·|j:|tjmoHmt
ÁdM5|¡Monp{{o³¼|tjmo^jAoKt|Kº ikjmo¾npymoz
{ztm±NxMoK®
·|jzt±±oKzk³&
mo<±n
o<
³|tjAoz}o~MAoAo
¸{m{|
|jmo<o(Èy|toKt´]³µ
(o~zko<
npm{|oK®
·|j|®fn
oKzKºÅikjmo
MM5|t±|
jm)oPztm}|³ØoMJ(|to¼¡
"oK¡N}
|±AoKoz8±|tz*(®k
±
A}|ÁÂjm({o{(o~M_tMoKztP|
jmAo{np±m{¢{oKnz}MAoK}zk³ØM¡M(NoÈyoK´±zKº |tjmooK)ztoMnfoKJ|z
omoKztoJ|k|tjAoo(Èy|toKt´1³µMoKz
)65.&$ +:5
vy Ñ i ±np
oz}o~MAoAo®
|tj
A
zzt¡Mom±
npoKj´m
mo(³µ
nm±onp{{oKAH®
·|jH|jmopmt
ÁdM5|¡Mo{o(³µMtn
mofnp{{oDºikjmoKxHo¢
npAoK¾|t
}
m´|t{|tj.¡*
mo~zM{|
AoK¾®
|tjYm
|tjmoK²zto
npoKM|*|M¾nfo|tjm{hA)|¶|jmooKo~5|t
npo~jAm
np{{o±
Ao
º
i"²Ato~z}oKM|&|tjA±z&my³A
³´(MA(oK{|K¸®8o8Az}o
vy Ñ iDZnp
±m®
jAooP
m´mx+{o,AA·|M¢zMA·|oko~"|t<{onpMAz||to
|jmo+iko(½]jmoKo(|
A³&zt|toKjmJomoKMA5(|top±¡
o<³±J|tjm|tooA±J
|t´³µ{M{AoK5zK|¸{M®
h·|
jm³
m |
\5|t2pn2 AÆymj)*±®
, QA±oKm{oKMAo¢(o+MH
³|jm|jmoonpjm
|M(ho<
±Y³"o(|tÈyjm|ooztAo
]np³µMoKM|oK*zK|ºMhz+´o|}|toK
o~z|n*|M¶³]|jmo¡M
±mnpo
¸JoKzt´o~(±xf³]|tjAo|toKoÁdztx{z|
±±´Jz}|t±
; E[z}oKo²»&´ºJ
A_»"±Aºy*Z¤ F5ºikjmoo}oK5|M³µ
5|Mĸ
³µ®
jm(|tjH±
^z+(Mhnpmnp{P|to~
)t|³µ
M
|<n (±|tjmAo±K}
´A{Ao(ÈH|t
³{|t|tjAj.ofKzM{ ±_M+ºV³µ[Ym´o5|t
±{
|¸Ä±^±z²|¾jmoo}YoKnp5|
M¾o¢³µ
K
(5m|M*¾|o±x¾³(!
X npÃm®
m|t|toKj)ĺ|jmikojmAoft
oÁdoKM(5|t|t±±
¡
o
np{{o Eµ|tjmo²o±oK5|tMnpoKjA
m±K´nf{{oKP
MmojAMz
¶oo~5|M³µM5|M³M FÅ®
jmoKto~
zÅ|jmo´
zz}±¡
onp{{oK´oKztm|z
Mmx º
[Yo)mto~z}oKJ|fjmoKto_|tjmo)±o(³ÿ|¡
oKJ|t±o¡
±mnpo)(m¡
o~zM{|
mo~Ç®
jmoKztoMnfoKJ|t±mh
ð"ð Üab
2b
£
U#<]"2 7" U "D'434 :U=)!G
M 5|t±»A¡
mo}nf|jm{o{oKnp[¸y
Po
oK¸]K|jmAopztomo|o~
{AoKhxf®jA
oKzM|tjJf|¼(
³¹|toKjA5o|Å|njmoMAoto~³µ{M±(|toKo~zK¸ :np |t±
o~M¸M´m*
|t±|
|t fE[(G F5oK¸Ä|tz¼ok|t|toKjAHo²|®
npjmMoKzo²z}{no(³µM±t±on<*®
|·M|pjH³µ|tjmMopn.m|jmo Á
|o±o(ÁÂ{±Mz|
±±¼PMzt·|Mĺ
$+
130
"Ground−Truth"
Image Forces only
Simulated Contraction only
Image Forces and Simulated Contraction
120
110
Volume (in mL)
100
90
80
70
60
50
40
30
0
0.2
0.4
Time (in s)
0.6
0.8
Ñ
m»&±
mÁÂ
(o¶|t±¡
RofI npyMmnfo´EØto~±zth
h±±m´o oF(|º_®oKikojmYo |t}jm
o¶
ztmoAMnpHo|tJ{|||tj.±
Hzto´Mz}np±mo)J||tjA|to±
AH
zz<z}±|¡
jmofo¶mm±
±mnpo¶oKzMj´´moK
zK¸Ä&npA{h{oK|tjA oEµmm±m±MoÆh±Amo MF<z}jAoK´hH|±mjmoo
ztjm*®z"|tjmokoKo~5|t
npo~jAm
Mnp{{oKm±
moMº"ikjmok(Mnm±moK¢Azto
³´oKo~5|t
npo~jAm
Mnp{{oK{®
·|j¢±n
o8±{³µ
n*|t±
±*®zkp´o|}|toKzto
npoKM|*|M_³&|tjAo¼±nMo<ztoKJmoKA(oMº
rd|<ik±*jm®okz8np|{¶{oJA|oo¡
M´Mm±|t±|t
oKzMn¡MoKzÅMo+<(mM³µJ
|t±npJA
|t±A
z&oK|tz}|t±n(
*|oKMzt¢´M
A³A_|tjAPo
oKnz}|²x
{|KoKM{jAn|np´Joz}®
|t±jA
o¢H|t
jm
±An
jmMMo+{|±z²|tjmNo¡N
KA{±oM¹
Axy|toM º
J|t±ym
Azt±x_{o(³µMtn7)Po(|®8ooº
Ò¾MtoK*¡
oKK¸Ä´z}±m)|tjA±z¢mÁÂ
5|¡Mopnf{{oK¹M¡MoKz \522 m³µ
np|t±
|jmo¶±{¹|
m
oKM|±
np|M Eÿ|tMzt±
F
®
jmj^zj´{x¡y±zt±moHmtoKM|²nfo~{&±np
o~z Eµ®
|tjmM{|<Az}±m|Jz F(ºikjmzÆy±A¾³Ånp{{o(Mm¾jmo±^oK*¡
o
|jm±znf
|t±
ĸA®
jm±jz
z}Jm|to+±nfP
t|
J|k±¾
{
³µmA(|t±
ĺ
»&±
mo*¤I Ñ Mnf´±zt
³|jmozto
npoKM|*|M_³vy Ñ i?±np
o<z}o~JmoAo
¸{±|tjmoo<
t|tjA
MA]zt(o~zk³&|tjmo¼|toKoÁ
ztz}|x{Nzx{|
z<±±(f±MPztMo²zt·||tM |tjmEØopto~±nI<
Aof
zPz}±
¡
mo¢AmA±
npx
¸]oKoKjAzt´
o~m(±x¾npA{oK{o¼D¸|jmxMoo¢±´*
&® ztI²o mE[*È{Á±
Å5|(
¡MJo¢|npM{5{|t±oK
9 5F(ºpFik´jA^of®8oKofo~5K|tHMnfMo~AztjAo¡
Ao±K|jm&opnft{±
{jJoK|
¡MoJ|t±o
J|t
(|t±
¢³]|tjmo
np{{oK[¸Jo¡Mop·³P|tjAot±
jJ|¡MoJ|t±okzÅm
|¡Jztm±o±f|tjmo±nM(o E[{mo
|<mo¡yMAzÅoMM
³&±J|tooKz}|
o(Èy|t
(|t±
F(º
ikjmofz}oK
npoJ|*|t±
H³¹³µA±np
ofz}o~MAoAo®
|tj¾|jmo¢At
ÁdM5|t±¡
onf{{oK|ÆMoKz²o~ztz|tjA
hnp±y{|to~z²MH_z}|
{Á
m
Y Ñ º [ho_Az}o¾(M
zto<npoKztj E A~£¾£
£
£oKoKnfoKJ|
z F<®
jmj±z+Po(|t|toK¢
A{|oKh|t)|jmo¶±np|toKÇnMopto~z}M{|Mĺ
üµý"ðüÿþ
,A
!"#%$&'(*)! '+,-$/.0!&12"34(56)87
97:5/;
=<5'>+,?
kiztojmMo_nf±oKztJ*|¡
*M|mMnp¶o||tnp±fo<m{jAyMoKz8z}o~mz|{ooKm´
oK|¢Az}±
n¶A|±jm|to²oKY|t±nf± o<|tjmoKztz
±K{
|tzt±o
¸_ztN³¡y|±mjm¾o<^nzt
Mo²m zt,PoKJmJoK|A(o<
np
z8m{M|m*xf|t±
|´jmo<¹o±oKM5z}||Ktº)MnpikoKjmo¶jA
®
mjm±MKo
|mjAnpoomMz}nf|tooK´Azfº (
J|tMA|jmo<J|toK
*|M|t±npo¼z}|toKAz¸m
A|jmo±np
o³µ
(oKzk
to¼(
npmm|toK¶³µ
koKMj_
³Ä|tjmo~z}o¼±M|oM|toK
., ('66
npikjmoKo¢m±{KoK¹ztM±n¾M³o_(MAnp
mx{{zt|±z|t±
AAY
Ä|npjmo{{oyxhz
zt±³njymmn*|
M¾=
IM|jm´zzk±ozP¶
tm|o®moKztoKoztJoK|to~j),AJoA)n®
Pjmoj¾
³
zP|ooAAzzm|to*®®kPM^zz}|±jmm±z|tM±MoKz¹³µ
K{±M±nMox
¸m´_n¢Az|Po+mAmoz|J{
z
fmo±np±Axmy³"
³
Ao{|
±|tjmz
oKztoKj_{±oK5|Mĺ
®
jmikj^jmo+z}|tnp±{{±oK*®8®8oKo+)mpto~z}oKoK
J|toKz|±®k{
zoK{(o~|²z}±zt
n¢AoKm±*|t|²±
f)n³
|jmtJoztjm
o~mt¼|npoK¡
o|1M®
|t®
j^jAp±o¢±±nf
±|t*o~®
)Aymnto~P
ozt
A
³&m±Jo+|toKt
Anp
ÄmA{|
m
¶nf|to±|tnfoKoMz º
[Yoztz}jm*®8oK|tj´*|¹Mm6 At
ÁdM5|t±¡
o 8{o³µ
np
m±o
nf{{oKAAzt±m+·|zűM|oA´(
J|M5|t±
¢³µ
(o~zztxJ´jmtMmz}o~M¢|jmo
Ñ
| jA¾f®8npMz<
o<m±o±M|ztztPo(:|t|t}oKA¼
zztoK¡M*o ¡
²oK{o|t³µjA
opnpzto
Mmnp±o¼onpJ|{{|t±oK
Ä^®
jm³|tjjmop®8jm
mo~t|²{¡Mo(o³µMJt|tn±mo~Az{³µoKk
n0|tjmo_M|t5±np|t±
oz}oKt³±oK±npz²
³o²K³µ
{(
o~zk
±nm±x
Mº oKz
A
»&np±Ao(|t±oKxMz
¸¹³µMtmMpnnf¶{J{AoK
n®8PMo¼z¢m³oKzt(±MAm±oKKÇ&|tnfo~
±zt*m® onp|jmooJ|³µzK{¸A|tA±^to¾Mz}{|tAoK{xF|_(³oK|jm|to¾oA{||t
±noJ*|}|Á±zt´o~{(!o,´J+|t! jm,´o~K*t|t|²±
np{{³¼o·|zzpº ÑJm|toKtto´J|
®8
Æ|jm±z{oK(|t±
±z±to~
{x¡MoxmtMnp±ztA Jߣm¸mR A¸AG X8Ldº
à (
2
¢"6
ikjmoÑ
{|tjmMz¼®8
m^±±Æ
o¢|t|tjA
mÆ¾Ñ ³µM²|jmo±(MP
*|M^¯~ºf¹{®kHÀzth³µtMn0¯mÆMo )m±¡
oKzt·|x ĹKºfÓA{o®
Ò^ m±{j:³µ
n )m±¡
oKzt·|x³ ±·³µMtA±A¸
vm¯²oK
²~º +
tÁÂÀo±m¿¾À MjmmoH
A:jmz¶MtMm ³µtMn À
nmAt
)m¡Moz}|x ´¯²Kºs²±¡y±o K
)
A)jm±±Az¼Ò¾oKm±K&v{xyz}|toKnz
oKztoK
j)Åz A|tjmo Ñ
m±M+Ò^
oKztoK
j
m
± mx z¢ÀJz}m|
[¸ 0ÄMA{M
A ±|jmo_(
ÁD®8
Æ
oKz²³8|tjAo¶r Ñ ¹Ò^Ó (
±P
*|t±¡
ofoKztoKj
5|MAzp³µmA{o~ yx
r ²
rÓ¸±pAt|t(A±
&»8º Ñ 5 npoJ|~¸
ÒºMvyMt±moM¸ ¢º Ñ MA{±lÑ o
¸¯¢º Ñ jAPo±±o
Ñ ¸ ´º
v{±J|toÁdÒ^
t±o
¸º Ñ npnp
ĸMv]º 0"J| KtD¸
Anp np&ºoJ0Ä|DzKºÅ¸Aikjm´o<{M|{jm
ÓzA®8m
tmJ|±ztÆM±nfo|N¡
|MjAA+m³µÆ¶M
ik±onp³ÿ|¡
|jJoKxM|t
(±}o<|o¡
~M¸ys²mnp±¡yo+±ozt o
np±oK|tM¿²|*
|A¶M¶¹³µjm
±n7±m´Ko+Ò¾{±MM²oKÒH
p
³µr5
º |tjmMm
jJ|t³µm
Ñ MMmk¡
oztM_³&|tjAo+mto~z}oKJ|toK+ ,AMmto~zkA¡y±{oKm±n*|t±
´z
o<N¡*
m±o¼
|tjmo+±J|tomo| º
!*k&
8
6
JA"L+ºPÓ±o¡)A¾Óº´Å
# ,A±*¡Pº
Ó z}±npmo|®
ÁD¡*
tm±o<npymo
³¹
{
<oÈm(|*|Mĺ .R!7 < D' 7 !" 7 ¸
YREØ4 F2Iß
yMR£ A
¸ AKM
mº
J L Ñ º"Ó±MAjmo
¸v]º"ÒHÆy
n)¸ ºÓxJ
jmoM¸"
A Àº¯²o±A
o(|t|toMºÓ moK® Æy±mo(|±pnp{{oK±m^zjmonpof³µ
+|jmojymn
± o(³ÿ|p1
¡
oKJ|t±o®8
8np|t±
®
·|jÒ^
Á[|
MA^nÑ
±mAº r +,5"5`Ñ 1 O3'Z3H]^OGD'Z3 %$B R 2
*¸´JAnPo
£¢ 0oK5|mo< |oKzk± Mnpm{|toKv{(±o´(/
o E 0" Rv F(¸mA
oKz
A{! Xmº{vym±m
oKK¸A
£
R£ AMº
J L+ºPÓA{±
M|z}±np±N¡M
AA4¸ 0º ĸ]¯º]À±±[¸1´^+º]¿~N¡JDºvy±nfAop
{
+ÒH
rz}oK
npoJ|*|t±
º
r 12 "25
] < O""?) $("3!5"? 7"]5
';
"'5><]"" (
"?'Z3 ¸´¡
±mnpo<m¸mA
o<MR A
¸A£M£
Aº
J !¤ L+ º*ÓxM
jAo
¸NoK{|tMKº .0 \5+, ], !" 7 $V R +, ) ºmÀ²A{Py
Æ+
³A mnpo{ÓA±x{z}z Eغ Ñ ±
t±o(|
zto±oKz8oK{|tM
F(ºmz}oK¡yoKK¸A
£
£¤´º
J L+»8ºÄÓ¿K~¸Ä¯¢ºÄÒ¾o(|*Èm
zK¸ÄAYÒºv{jAA±[º¢Ò¾o(|jm{mz¼³µ
+np{{o±±m
Ahmto~{5|t±mnpoKjA
m±KÅ{o³µ
np|t±
Az²³
|jmo+moKMz|
mAmo
o(Èy|oA1Pot|tmA|t±
AzKº ;
51 O3G(5D)87297 ¸P E%A F2IWAmG Y{¸y
£
£Mmº
J L º [º*q8oo±o´ÀºN
om|to~ºy
oK
Az}|tA5|M+³{|jmo8M5|M´
|toKM|±
M
³m¡
oKM|t(A±
nxM{{ ,´´oKzKº +,2]
%$"!0,)87
3) ¸1G XRIWA8Y!Y#{R AK£m¸ AK4 YGYyº
J Y8L$
´ºq8oKz}|toK[¸»8º Ñ 5 npoJ|~¸&
AÒº"vyMt±moMºÓÃm±
npo~jAm
Ånpymo¹
³
nAz(±o¶(MM|M5|Mĺ¶r 12"34
.0K\]+,?'Z3/]. K\]+, "? 7
72972 ' "2M8" B1..K1 N¸A¡
±mnpo²M!£ X³ % "+,: 7'N.0 \5+, < "5
% .#< N¸{´
o~(
z A!AN ]A!A~R A
ºJvymmMo~¸A£MR£ A
º
& ä(ãØãDÛJå tíÄíÄí ÿ×ØÖKÕ !è ÞßÜN×[Þïá~è "× tí"ä~Ö *×[ÙÝNÙ×ØÞ !KâNÙ5è î]êßÙæ
ÙÜ(ã ÞßÕÙ}æá~è ä(ã[æ
ê
' ä(ãØãDÛJå tíÄíÄí ÿ×ØÖKÕ!è ÞßÜN×[Þïá~è "×ÚDÖ5ÚDÚ[Ö ÞßÕÙ}æá #ÞßÕÙæá ~è ä(ãDæ
ê
( ä(ãØãDÛJå tíÄíÄí ÿÚDÖ5ÛMè ÞßÜN×[Þïá~è "× Ù}Û~ÞßÝ*áâN×ØÙ ÛÙ×ØÚDÖ5ÜNÜNÙê ë+áçKÞßæ
Ù5è ìKÙ×[æ
ÙÚdáÜ((ã à(áêßêßÙ}×µö(è ÛNäNÛ
ð"ð Üab 2b
J
J
J
M
U#<]"2 7" U "D'434 :U=)!G
J XL+¯¢º Ñ ±±oKt±o
¸ÄÓºÄÒ¾
m
ĸ]
AY
m|Kºi"*®kmz+,Amo(ÁdA
ztoKh(MAz|·|{|t±¡
ofN®³µ
¼|tjAofn¢x
{
mmn)º+rÂ
! "'D'43 <5'>+,? $ .0 \5+, %!
:']&]&<5+,?3G"2) P<=.#P< *¸y¡
Mmnpo(A~m¸A
oKzM#{
£mº
8 v{ÓrÒ#{(oKoK{±mMzK¸m£M£M{º
J L+¯¢º Ñ jAPo±oM¸J»8º Ñ !KnfoKJ|K¸y»º A|K¸Jº-0oi"
±oK
¸JÒǺJvyMt±mo
¸JA ´º-)Jm±¿KAº1Ó mjyx{z}±
±
M±K±xJÁdA
ztoKnf{{oK
³µM¼|tjmo¶M5|t±¡
op
m±Mn¢Aztop(MJ|tÑ
5|Mĺr +,5"?5Ñ 1 O3'Z3^5 !"D'43C $ R 2 12 *¸
ymn¢´oK
£¢ 0Äo~5|mto+ |to~zk MnfA{|toKv{(±oAo/E 0" vRF(¸mAMoKz(ANX]AKMmºJv{mt±mMo~¸{
£
£A
º
JWAK£ L+i<º Ñ y|to~z´ Ñ ºMi&NxJ±
~º1vJ||tz|±KAnp{{oK±z¹³ÄmPoK
A(o8³µM¹npoK{
m±np
o
A±x{z}zÅ´(
npmm|to¡y±ztMĺ
rÂ
h£
£ ÒA
º ºPvyMmÆ*¶´ pº´À²Azt
ĸ´oK{|tMzK¸ !O
'Z37 %$ < ! 1 12"3!'43 ¸P¡
±mnpo¤JM
m¸mA
oKz¼M {G¤ XA¸
JWA!A"L+¯¢ºM¯²mtoKK¸M+º
¡*¯¼n)¸ ºJ»moAĸMÒº M
Az}oM¸
»8º
Ò¾oK ±o~¸J
Ap+º
Ót¿KAo~jmo~ºAi"|
mo(Èm·|*|t±
p
³´|jmoz}M±|toK
jymn
jmo~t|Kº .`'"+, ¸A¤ A4EØ4 F2I X
y A~{¸ AKZ Y*£mº
JWA~ Ls¢º´»Az¸A»8º´¡*AzK¸´¯¢ºAAm±zK¸P&ºPÀoKn)¸ ´ºAi&NxyMK¸AÓº Ñ jmo~z}mÆ]¸´Òº {|}|np
ĸ Ñ º]s²¿(|mÆP¸´AºPÒ^ ÅoKMjĺ
*¡
oK|oKjmmJmo¢³µ
<{
+oKo~5|tMnfo~jAA±Kn
mm±m®
|tjhn
Ao(|toKzt
´Ao±np
±m|
MA´^
oKm{]o±oK(|t{{o+z}{Æ]º 5 7 $"K
=T43!'5
"2'43 ¸´ AGEµZ¤ F2I ¤MM£ J¤M¤M£A¸M£M£
mº
JWAK L+ÒǺA»moKtJ|K¸mÓºA
AN¡y[¸mq¼ºAÒH
P¸m»8º M
±oKzt¿
¸m+0º <Æy±m±zK¸m´)v1Rº [Y
,´o1º
oM±z}|t*|M
³M¯ J|
Po*|t±¡
o
ÒH nMoKz³y|tjmo¹m
+´z}±m ,´m·|oo±onpoKM|&m±
npoKjA
m
nf{{oK[º 100R7"!"?R7T>
!12"3!'43 ¸
R£ IWAKG X¤ ]AKM4 Yy¸
£
£ A
º
JWA!¤ L+º»"|t¿~ÀmMjĺ:rÂnpmmz}o~zAmjyx{z}±
±
M±Kkz|*|to~zf |tjAo
o(|±Kknp{{ozp³¼mo¡
onponA
mo
º V
\R,)87
+,25 =¸ A!I ¤
¤y# J¤J
AR¸ AKMR A
º
JWA~ L+ӺĻmmM[¸ [ºÄ o~ztzto¸AhÒº ±o
oK¡
oKKºikjmooÁdmnpo´z}±
A
"np{{oK±m³µ
¼³µmA(|t±
A
A
x{zt±z²³k
{
±nMoKOz IÓ o¡y±o®+º 1 0R7G7:;
]1 O3'Z3 =¸ A4E[
G£ F2Iß# m
m¸y
£
R£ AMº
JWAK L+Óº*»mmM[¸*¯¢º
moKÆMot|K¸*´ ´º~¯²mAKĸo~{|t
zKº >,]87 '
5,
:'7
5=.0!T12"34T]D)87297 ¸
¡M
±mnpo, AGE[G F(º&r¹i´ztM5|t±
´zMÒ^oK{
1rÂnp
±mA¸A
£
£Mmº
JWA8Y8Ls¢º K
1¸²Óº Ñ
±±o(|¾q±±Mĸ ´º ÁdÒºk
Mmo(|~¸¼Òº J
ĸ²Òº»m
{Æy±Ä¸²
A Ñ º
Ó±
AjAo
ºÃ ¶(±oJ|¾np{{oÁ
´
ztoK^JA
M| ,P*|M¾³±o(³ÿ|<¡
oKM|t(±o+³µm´5|t±
hh
¯ oKjmM
mjyx
º 100R7"!"?R7 ^
12"3!'43 ¸
R AGE[G F2IWAK£J 5AK£M! XA¸
£
£J{º
JWAOXL º |t|®8
±Ä¸&Óº"Anf±~¸
A º <AztÆyx
º^vym±®kN¡
o¶{³ÿ|¢±A{AoKyx z|n¢m±|t±m^®kN¡
of|t±AzKº .=!7 ¸
AGAGE[GF2I ¤GXZY y¤M¤´¸M£M£RAMº
JWAK L$
´º ´(±
Ao_AFÓºÒ^ Ñ m±±yjº 5
2)C%$ 2 R27 \Z)87227 55D'])5 7 $
G=$
+,5" ¸j´{|o"»&±m|to¹oKoKnpoJ|"np{{o±±m
³m¡
oJ|t(mnfo~jAA±Kz¸~AMoKz A~, A 5AK¤
¤AºvyAt±m
oK}Á ÅoA¸
A~
A
º
Jߣ L$
´ºAÀ *³µmoKK¸P»º]v{
j´z}oM¸ Ñ ºPv{
Azt
m~¸ ºPv{oon
mĸ´
A^s¢º´¯ Mzz}oK[º8ÀxyPoo
z}|t+{oKz(m|t±
)³Åo
z}|tMnpoKjA
m±
AtM´oK}|o~z¹
³Ä|tjmo<jmo~tO| IÓ?mo®n|toP±N®
A¶|z
mm±±K*|t±
º V '97"
Z ¸{Z¤ YNÁ AR I YGY*£ Y!Ym¸
£
£J{º
Jß, A"L ºÀ²nmoKjAfi<º Az}|N¡{ztzt
ºy¯²o(³µMtn
mokztA*|
Á[|onp´M
JztjA
´o8npymo"z I"ÅÈy|to´{A<Ó¼v{Ò7|t+
¯ |t±nfoMº
+,25# $K12"34 5972 .0 \5+,'43 ¸´
EØ4F2I ¤MRA J¤,Y*£m¸y£M£¤Aº
Jß
L+ÓºJÀ{{
Æy±_A_ÓºyÀ{È{±ox
º"Ó JAJ|·|*|t±¡
o²{oKz(m|t±
³ÄnpoKnmmo²(mtoKJ|A¶·|z
mm±±K*|t±
p|¢
A{´5Á
|M¾Ao(Èm(||t±
)moKt¡Mo
º +,2] $ !0Z)872W3!) ¸ AY!Y,I
£
£ m*¤M¤AR¸ A~M
mº
Jß L<ºÄÀzth´ Ñ º1ÀoKmtJmo¿MºÒ¾x
{K{±
,APo<Mt±oJ||t±
^n
mm±m´z}±m_oKmA(o~^o´({{±mm·½]AztM^|toKAzt
±nMm´º +,25 $.0M87""+,:"3!5"? 7"]5
¸ARI MM#{
A¸M£M£RAMº
Jß*!¤ L$
´º1ÀmnpmjAtoKx
¸Ä+ºÄvJ|tmnp{³¸Ä
AH»8º ²±Äº¯²o(|onf±A|t±
H
³_
Az}|t|tm|t±¡
oftoK±|t±
¾³µM²AMztzt±¡
on¢x
{
mmP
nI
r5º´Ó mo® ³µmA5|MAijµ
nº (< +,2] %$ V R
T43!'5
"2'43 =¸ A!AN, I
M yM
AR¸ AKM
£mº
Jß
L<ºkÀmJ|o~¸Òº8 ²
ztjĸ
A º
v{
AmzKº .0K\]+, ?5 K3) $;' 2 ¸j´{|o
AN, I Ñ
npm{|*|t±
´
¹o~5|t
npo~jAmz8
³"|jmoÀo~t|K¸{A
oKzk
¤J#y¤M£ZYyº M
jA [ ±oKx vy
AzK¸ AKM4Y{º
Jß L<º1ÀAM|o~¸ÄÓº]m±Ä¸1´Hq¼º]v{np
±Dº<Ò^ymo±m_|t
|jmo~t|³µm´5|t±
º + "M - $ K
#TZ3 ]
2'Z3 ¸´R IAKZ¤ Y#5A8YGYy¸y£
£Mmº
üµý"ðüÿþ
J
J
!"#%$&'(*)! '+,-$/.0!&12"34(56)87
97:5/;
=<5'>+,?
JßGY8L<ºAÀmJ|toKAq¼º´vyn±±[ºikjmo
A±x{z}z8³Å
{
³µmA(|t±
=I
J|t±ymmn7
mmMMjĺ !3!7
7(' V
\R,)87
7
5;
+,W K3!) ¸]M,IWKA £RA 5~A ¤A¸KA !XGmX º
JßXL º MM(
¸ Aº Óº
m±o
¸ Ñ º¹q8ojAtoKJAtAj¸¹Óº%<oK±
¸´Óºq8
mm±mAº:ÓÉztjAPo(ÁÂz}´
(oÁD´
ztoKÇ
mmM
jÇ|t
|10M0Æy m,fnRx{7"!
"{±
R17:´M;mo
z8
A)]12JA"3!J'|t4³µ3 xyAtoK
±
A
P±o(³ÿ|tÁD¡MoJ|t(m8³µmA(|t±
^
mm±o~±)oKjm{K{M
mjyxMº
¸P,A4EØ4F2Iß
{
!Xm¸J£
£J{º
JßL+ÒǺ Ádº
M±x
¸ º¯²{|m¸
A ºÅ»AmmÆ**Á 0Äo~mºÇvyoMnpoJ||t±
F
³|tjAo±o(³ÿ|¡
oKJ|t±o {
Ò^ ±n
o~zº rÂ
!O
'Z37: $ '100 1 2]50.0 $"5
_.0 \5+, 97
1.. *¸1£
£A
º
J
£ L+i<º +|t±±A¸*r5ºÒ^Mm¸*&º Ñ x{ztzto
¸ ´º*Ò¾
J|
A|K¸
A ´º* oA
moKĸoKm·|
zº +,5"?5!1 O3'Z3>5 !"D'43
%$& R 2 12 N¸´ymnPoM
£¢± 0oK(|tmo+ |oKzk± Ñ
npm{|ov{oKA(/
o E0 Ñ v F5º´vyAt±m
oKK¸A
£
£ A
º
J R A"L+ÒÇ0º +´z¸ ´ºm¡M
¾q8oA¸ ´º [YooKzto
¸ [º´ ±oKzztoĸPA º´oÆ*~ºÓ{|tMnp|to~¾z}oK
npoJ||t±
)³&|tjAoo³ÿ|¡
oKJ|t±o
±¾
{
¼Ò^
r5º 512"34&5D)87297 ¸ XEØ4 F2Iß*¤y# {M*¤´¸J£M£¤´º
J M L<º <±mo~¸ º &º ¹m´¸"Óº [ ±Æ
o~z¸+º&Ò¾
jm
A{¸"¯¢º"»&np¸
A Òº ¹M(MmĺӲz}xynpnpo(|tpto~{±to~5|t±
Y³
Q´*®|tjAtMm
j|tjmo+jAoKt|Kº >+, ¸{¤J£¤I Y
Y*A
¸
£M£
£Aº
J
Lº <yAmztoĸyÓºyÀM±moĸyA AºJq±A{±ox
º A
||t±¡
onp{{oK±A³1npoKjA
mÁdo±oK(|t±K{³µoKoK{´
Æf¶+¡MoJ|t5Á
A±
(o±Dº V+,'"'C $ '
V3!) ¸] E[
G FIAGA~# ]AOXA
R¸ A~
4 Y{º
J !¤ L
¢º <t±AztÆJxMº v{mto~
³o(Èm·|*|t±
? mjA
np
MomoK
Az_nfo~{±mn EØz}||to z}±np|t:
{
,Am±±|t±
F(º
K "! ¸ AGA!I 4 Y* yG X
m¸ AK
Mmº
J M L+q¼.º 0o±oK¡
oy|~¸´v]ºAÒ¾|jAo±[¸ ´ºAq8Mzjĸ{+ºm¡*¾{oK oo~z|~¸mÒº´vyMmÆ*m¸m´ ´ºm
oKPo~ºiknpo
J|t±ym
AzkztoMnfoK{Á
|!*|OM
^7
7
'³¹Z3CK' {±M;+
±np
o12ztoK"J3!m'oK4A3 (o~ z1 !T´/z}±1mM5|¡MomPoK
A(onf
|t±
+,¾ np:{{ozK7/º²'r . !KO
\]
+,
"'/Z3< 7"$(512
O $ 2 /.#?< N¸¡
Mmnpo)!£ XJ³ %
%
*¸
´
o~z8¤
¤MJ¤y
{º{vym±m
oKK¸m£M£RAMº
J
L+À4º 0ı¾Aº´vyjA[º¹Ò^oKztj{³µtoKo<toKmto~z}oKJ|*|M
A
npm{|*|M= IÓmA|t±
Azk|{
¼np|M
A±x{z}zºrÂ
1O$2 ? !T 27
72'43 '
512"3!'43 1 !T/1 N¸A¡
±mnpo¼4 Y*J¼³ % "+, : 7 'N.0 \5+, <]""5
% .#< *ºAvym±m
oKK¸A
£
£
Aº
J 4 Y8L+˼ 0
A<º~vyjmDºMvy±nA·|moK
Az1o~z|n|t±
+³{±o(³ÿ|¡MoJ|t(m1np|MA¼n*|o±
m
Pot|t±oKz1®
|tj+nÈy±nAn
fPMz}|toKt±
1z||toMx
ºr 100 .0 \5+, 97
C5 !V "2 3'? ¸´
£
£Mmº
J ! XL<º 0Ä´¸mÀº 0ıĸA´º]vyjmDº¹
À ,A·|oA¶Amjyx{z}
Änpymo±mf³µMtMmAz}|
ÆJ±moKnp|tz
o~z|n|t±
ĺr 100
1 2]]0.0 $] P12"34$!T 7
72'43 ¸´£M£
mº
J
L([º 0Ä
o´z}oK´Àº Ñ ±moMºÒ^jm±mfmPoKOz I¢jAMjoKzt
±{|M
¯.z}mt³Ø
o²oK
Az}|tA(|t±
M
·|jmn)º . \]+, "\Z7 !T OU %$(<Z1 "! *¸AR AGEµZ¤ F2IWAKM 5A~
AR¸ AKG X4Yyº
J ¤M£ L Ñ º 0ÄA´ ¢º]
A{xMº¼Ó np{{o&³Å|jmo¡MoJ|t±m²K{
M5|t±
¾P|oJ|t I{oK´M±
t±¿K|t±
ĸ´toK´M±
t±¿K|t±
ĸ
A_|tjmoK±J|toKM5|t±
º .`'"+,? 7"
¸AG XRIWA~
R£ A]A~Mm¸ AK
A
º
J ¤ A"L+ºÒ^M 0ÄoK{1¸
q²º ²±n
¿
¸q¼ºi&
K{D¸
q²º¹mAztÆ
oM¸ ¢º
vyo´M
±Ä¸
A ¯¢º8q8JMÆ{zº?¯±to~5|
A:±J¡Moz}o
np
o|t,jm{m zp³µM¶
{
nmAm Azt±m nm|t±o±oK(|tymo)K*|jmo(|onpoKMz}monpoKM|zº +,2] $ K
"'97"
R
¸A¤JR Iß4£ Y#{
£
m¸J£
£ A
º
J ¤J L<r5ºÒH
Aĸ ´º*Ò¾
J|
´*|K¸Nº Ñ xyzzto
¸ ´ºN omMmo¸Afi<º +*|t±m¸*oKm·|
zº +,5"?5!1 O3'Z3>5 !"D'43
%$& R 2 12 N¸´ymnPo
4YN¤f± 0oK(|tmo+ |oKzk± Ñ
npm{|ov{oKA(o/E0 Ñ vF5º´vyAt±m
oKK¸A
£
£Mmº
J ¤M Lv1ºPÒ^Mz}y{1¸ º &º ¹m´¸´¯¢º´oKmmo±D¸P
A¾¯º]»&npº
rÂJ¡MoKz}|t±M|t±mJ|t±Azt±+n¢x
{
m±
1nfo~jAA±K"z I¹|tjmo¢tMo
³8Ò^ |
±m´¸1¡
o±{(|x)mjA
ztopnmm±m)Ah{½PAzt±
YnMAAº +,2]0 $ O3] 27"]]:12"3!'43 ¸
ANR E[G F2I X4Y ,X!X
A¸M£M£
£Aº
J ¤
!¤ L+Óº~ÒH Ñ m±{jĸ ´º q¼ºNqk
zz}±m|jy®8
MjM|o
¸K&º ´º~ÀmJ|to~¸*¯º*
m±o
¸*i<º 0ºNq±mAmo±[¸*´i<ºKÅN®zt
ĺ Ñ
npm{|*|t±
´
AMM
x
³´|jmo
jmoK
}| I&»AtMn.z}|tA5|mtok|<³µmA(|t±
ĺ !T327
7K' V
\RZ)8727 W"+, K3) ¸{M E[ *4 F2IWA~, A MA5¸ A~
G Xmº
J ¤J L+i<ºMÒ^(rÂmoKtAox
Ap¯ºJioKt¿K
P
m±MzKºm¯o³µ
nm±o
npymozÅpnpoKm±K{±np
o~zÅA
x{zt±Oz I"<ztmt¡MoxMº ,12"34
]D)87297 =¸ A4E[! FI A]AK!£ XA¸ A~
Mmº
ð"ð Ü ab 2b
J
J
J
J
¤
U#<]"2 7" U "D'434 :U=)!G
J ¤ML+ÒǺ´Ò¾±
m
|}|o
¸ ´ºAÒ¾oKmm±o~¸´´ ´º Á Ñ
M
mjm±n
o~z¹´z}±mp{o(³µMtnAo|toºAnpi&m*{|oK³zkº¹´´¶{n{Æ
{*¡f1P
A
m{M´nm,´x_oo~mzz|º n!V*|? M¾2 A]|tD)8
729Æy7 ±m]p )o~\!\]jmD{
{±7 Á ¸
¤5EµZ¤ F2Iß
{4 YZA
¸y£MR£ A
º
J ¤ZY8L$
´ºÒ¾MJ|MA*|+´YÀº¯²o±mMo(|t|to
º_v{A
o¶AH|t±npo_z}j´Pop
Az}|t±mo~h{o³µ
nm±oz}mt³Ø
oKz²³µ
¤M¯ npoK{
±nMo^z}oK
npoJ||t±
Ä+,º r > 2
7('
V.012K"\]34+, ".0(<] "\5+,]
'43 /].# < .0 \5+, "? 7
7297
^1 2M" B1..K1 N¸
¡M
±mnpo AK
J
³ %
%
*¸mA
oKz A~
m£J{ºJv{mt±mMo~¸A£
£M£mº
J ¤GXL$
´º1Ò¾
J|
´*|¼
AYÀºÄ¯²o±mMo(|t|to
ºfÓ toK¡J±o®
³8{o³µ
nm±ofztmt³Ø
oKOz I
|tM´MM
x
¸1MoMnfo|tx¾Ah{o(³µMtn*|Mĺ
1 O3G ] 972 .0K\]+,?'Z3 =¸ A~ E%A4¤ FIA~£M
5A~£¤J£m¸
£MR£ AMº
J ¤M L$
´ºMÒ^
J|
A|K¸
ÒºyvyonpoKzJ|K¸JÀºJ¯oK±m
o|}|o
¸ ºMÒ^
±
Am±Ä¸JA ºMÓxMMjmo
º]ÓA±zt|tMm± ,´·|om<³µMnp{{oÁ
´
ztoK¾zto
npoKM|*|M¾³¤M¯ (xy±´{t
o~jm{{±
M
mjm²±nMoKzKº !V "2 3!' % 7 ¸P¤ I XRAN# ZXJ XA¸
£
£Mmº
Jߣ L
¢ºAÒ¾Mto~{Á ±5 Mo~¸{Àº´¯²o±±m
o|}|toM¸´ÒºPvyonpoKzJ|K¸´s¢ºA»´±zK¸{ºPÒ^ ÅoKMjĸA´ º´ÓxJ
jmoMº MA
A{K
´npo(|okoKz}|t±n*|t±
³ÅfnpymoÄ
³|tjAo+o±oK5|t
Ä
(|t±¡J|x¶
³|tjAo+jmoK
}|~ºi"oKjAm±K1oP
t|K¸{r ²
rÓ¸´
£
£
¤Aº
Jß, A"L+ÒǺ] ²
ztjĺ ;
R75B 2!T
\R"2?7 %$: R 2V+Z72'43*5 'D)B
+, : R"
!" ºj´¯|tjAoKzt±zK.¸ )m±¡
oKzt|x¶³ÅÓAÆyAĸ AK
G Xmº
Jß
L<º{ ±oztoĸyr5#º 0Äo t(oM¸yq¼º{vyn±[¸{
Aº{ÀmJ|toKKº&Ò^*|jmon|t´npymo]³ÄMo
npo|txf
A ,AAtMAz¹z}|tA5|mo³
|jmo+jmo~t|Kº "2
+,25 $"!0,)8723) ¸1M£ EDG FIA~
J# 5A~4 YXm,¸ AKMR AMº
Jß L+¯¢ºA
m±o
ºÒ¾{{oK±mf|tjAo+jmoK
}|~º ! Z)8723!) #¸ A~R IWAK A5A~4 Y{¸M£M£¤Aº
Jß*!¤ L+¯¢ºm Mm±o
¸mÓº
jmo~z}oM¸Mº ²
jmD¸{Aºm MmoMºrÂnfAt*¡MoKMmAoK*Ádm±¢¡MoJ|t(mk(oK1np{{o1±A
´M|t±m¢
mAK¤±MIW{A~
±+5ztAA~M¤´(o
¸R¸ AKM !Xmº A ¸´´±oA|tj¾
A|to´z}±
¾{oK´oKA{oJ|At{(o~ztztoKzKº .0]! +,25 $/. 3) ¸
Jß
L ¢º
Å´
{oKnfo|t±zK¸
Óº ´ºMvy±J´ztMz¸J¯ººy¯±
Ao
¸M
A AºJv]ºM¯²mAKĺP¹z}|t±np|t±
³]M¯±o(³ÿ|¹¡MoJ|t±o
{o³µ
n*|t±
³µ
n7oKjm{
mM
mjyx
º ;
]1 O3G(5D)87297 ¸´RE%A F2IWA8Y#{!Xm¸{£
£A
º
Jß L$
´ºJ
tÆ]¸{¯¢ºyÒ^o(|Èm
zK¸J
A 0º{ÓÈyoK[º&ÓA
x{zt±z³Ä±o(³ÿ|
¡MoJ|t±m®k±´np
|t±
_´
ztoKM¶¡
Mmnpo|t±²{o(³µMtnAo
np{{oK±z
A)Ò^
rdÁvy1ÓÒ^Òº ;
51 O3G(5D)87297 ¸´AMoKz
RY,A
5¸ AK
Mmº
JßG Y8LpºMÅÆP¸J¯ºyÒ¾o|*ÈmMz¸JA 0¹ºJÓÈyoK[ºÄÓ ,Am|tooKoKnpoJ|np{{oA³µ
¹³µmA5|MA]´±xyztzų1¤M¯
{
(Á[|M
oKfÒ^
±n
M+,oKzKº8:r 7 '_
. 1K \]O+,3G "(.0<]"K"\]5+,
? 'Z 3*5.#< .0 \5+, ?(7
7
972 1 2M" B1..K1 N¸1¡M
±mnpo¢ XZYXf³
%
%
*¸{A
oKzk¤JR A J¤MG XmºyvymmMo~¸A£M£
mº
Jß XL º Ñ ºmj´n)¸´»8º ²´(oJ|~¸Aº Ñ x{ztzto
¸mº Ñ tM±zt±±o
¸m´)r5ºAÒ^Mm±ÄºÓ »&¹Ò¾ÁDAMz}o~¾{o(³µMtn
mo<np{{o³µ
|jmo
M 12¯.< ! ztoMnfoKJ|*|M¾A|MÆJ±mp³|jmojmo~t|^K{
<Ò^
r5º
r 1 O3G ]B<63!5 !T 27
72'43P55D)87297
*¸´
£
R£ AMº
Jß L+Óº
npnpot|K¸ pº ÁÂÀº
À
jmAo
¸Mq¼º0 QAoKzz}oKK¸
ºM
jJ|toKK¸
ÒǺM
±onpo~¸
i<ºMvmjmoKnmĸJ+ºMv{jymPot|K¸ )ºyv{jymn
jmoKK¸
A )ºPiko~{o
º Ñ oK|t±m¶pjm±
j{ÁdoKzt
±{|t±
¾ztA*|±
z}xynP
±²np{{oK³|jmo±mmoK
M
AzkAMz}o~M)|tjmo¡Jztm±o
jymn
ĺ 51 O3G(5D)87297 ¸PR E[G FI M, Am
! Xm¸M
£
R£ AMº
J
£ Lpºjm{{o
¸8¯º¹À±D¸º¹m®8
mzK¸ ´ºÀ±y®oKD¸8¯¢º
mo~Æ
oK}|~¸ º¹v{
Ajmo¿Ás²t|t±¿
¸8v]ºÀoKM{oM%¸ ºjymA|tjA
ĸ
RAYR+7"!ºÄ"?¿~RN7:¡y[ºf
oM±z}
|t*5|1 MHO3'AZH3 |t
Æy±m|tJ|toK
*|o ÁDNx^AYÒ^ n
oKz¼±Y
¼Ò^.³Ø
(±±·|xMº 100
¸]
E A!A8F2IWAKM
YXA¸M£M£
mº
J R A"Lpº´
jm{{o
¸]Òº]vyonpoKzJ|K¸ º]v{´jmo¿Ás²t|t±¿
¸´v1º´ÀoKM{oM¸´¯¢º´
AoKÆ
oK}|~¸A¯¢º´À±±[¸]A¾º´
¿KN¡y[º ²Ò^ Mm{oK
K
£
£
{¤Aº
oKo~5|tMmjyxyzt±
±
xfz|A{x_
A¶
m³µto~MAoAx¶m*|MĺrÂ)Óº{Ónp±mD¸moK{|tMK¸ < ! 1 512"3!'43 ¸
J M LpºNv{JN®8A¸+º 0ıo
¸NA$
´º~v{j´o(³µoKK º*i"E%AO
XMA
ztG ±F(º |t±
¼+,2³´]s|} |%$»&
mÆ
" z1+,´Po5¯.0±o'
6+,mA;{³µ.0
n{o~zÄ3!) t¸|toKMtR ±oEØ4±F2oKIß<
m m{4z}o~Y!z Y{¸
]o|zjmt³ÿ|+³µmfq±
±
MoZ YZI G¤ X
ÁÂM;
A~
M£mº
J
L º{v{
Ajmo¿Ás²t|t±¿
¸ Gº [YMjM|~¸J º Ñ Æ
oM¸ ´ºM¯²oKoKÆ]¸yÓºyq8
mm±mA¸y´ Aº Óºy MmoMºÄÓ{|
n*|oK¶M¯ o~jm{
}Á
m1 MO
3'Zm3 jyx<A
x{zt±z&(Mnf´oK<®
|tjfnp
yAy{o±±moK|t±
Az&Afvy Ñ iÒ ) Óº 10 ,R7"!"R7 ;
¸P, AGE[G FIA~£
5A~4£ Y*A¸M£M£Mmº
üµý"ðüÿþ
/
!"#%$&'(*)! '+,-$/.0!&12"34(56)87
97:5/;
=<5'>+,?
Ñ
Ñ
Ñ
ÇÒ º]vyMt±moMº
Mto~ztzkM|*A®8{
±lAo
z
¸k!np"À'yDº'm4¯²3ooÁDN±A±mM<5
z}'o~o>)|}|t+,oMoKW¸z}|t ±nºkV*Ó$|t±xM
M¾. jm
o
³ÅK¸ |t\]jm
A+,opºk v{"
%±Jm|t±GoM
Ád<Ò^o;
±oKt
5±o
|t¸kM¯¢'np]º KoKjA]jA
K
m´±<5KoK+,?±o
34M¸52»8|) º¡y P|x5 <.³µnp#
oKnM|~< ¸
ÑA
N¸
¡Mzt±
±Am
np±z1o
A~A{¼¸{¤M´¯Ç
±o~nz A~MoKzK5º~A~rÂRA
ºMv{ÓrÒ#t{ooKmmJz¸A
£
£J{º
J ML+ÒǺ1v{onfo~zt
J|K¸s¢º1»Az¸Ä»8º]¡*AzK¸1ºÄÒ^ Åo±
jĸ fº Ñ
AmlKtoM¸]Àº1¯oK±m
o|}|o
¸
AH º]ÓxJ
jmoMº+o±np±Ax
¡*
P<m+,*|?34M"+2):A<5zt'm> +,'?MO'M nf]o~
zt<]m%$
oK zÄ
9³A772+n&
;t J!zt"D
'Zm3 o1
±< oK(|t=± KMnf{{oKM
³{|tjmo8jmo~t|Kº
r 12 "25]4<Ñ) \872'+,
N¸AJAnPo
£+±
0oK5|mo¼ |to~z¹±
npm{|o
vm(±oAo E0 Ñ Rv F5º]vymmMo~¸m£
£Mmº
J
L+ÒǺvyoKtnpo~zt
M|~¸ Ñ º&»mMto~z|~¸ ¢º"oAmoK
¸Àº&¯²o±±m
o|}|toM¸A º&ÓxJ
jmoMº¯²o(³µMtn
mo_mMnpoKjA
m±Knp{{oK±Oz I
Ómm±±K*|M|p¤M¯ K{±M±nMo¼
A±x{z}zº ]12"34&56)87
97 5¸ YREµZ¤ F2I Z¤ Y J4¤ X!Xm¸y£M£
mº
J 4 Y8L+ÒǺAvyonpoKzJ|K.¸ pº{
jm{{o
¸mÓºmÓ*Mt±Ä¸mv]ºmÀoMmo
¸ ºAv{´jmo¿Ás²t|t±¿
¸y¯ºmmoKÆMot|K¸J&.º 0"n¢m±Mz}oM¸ Ñ ºyq8AÆyA
D¸
±¯¢nºyÀM±mD´¸J
ºkAr¶ +;ºJ
¿~N=¡y12[º1vy"±34nm. *|KM\]+,?'³1Z|t3*jAo]o±oK(.0|t
Knp\]oK+, jA"
?m7
72´972
5
| ¡y12|x"2
M8³1"|tjmojA oK t/|¹1A.zt±.=m 1 ² ÒH* ¸0ÄJo~|5o|tA¡
tooJ| MA|to~z
± Ñ
npm{|ov{oKA(o E0 Ñ v F5ºPv{mt±mMo~¸{
£
£
¤Aº"|t¶A´o~~º
J ! XL+ÒǺyvyoKtnpo~zt
M|~¸ pºy
jm{{oM¸mv]ºJÀoJ{o
¸ º{v{AjAo¿(Á}s²t|t±¿
¸M¯¢º{
mo~Æ
ot|K¸J#º 0n¢m
zto
¸ Ñ ºyq8AÆyA±D¸J¯¢º{À±D¸{A
®
º´|tj
Ò^¿KN+¡yºÄ[ºkr Ҿ12{{ oK"2±5A|tjm]of5<]
{"
¼)ToK$o~5|t
Onp3o~]jA m2
7"Ä
](|t]±¡J |x'³µ
±J|t"oK'
5 *|t<]±
"³Å? ToKo~5|t
"AjJ'4x{3 zt¸JM¡M
M±
mnp
o(]Y{z}|t¸M´A{
o~oz
A X
M£m¸m£M£¤Aº
J
Lv1º´vy±PoAMÄAÓº´¯o~z}P
P
m±MzKº .0 ?W87: $ !0,)8723) ºkikjm±onpoÒ¾o~{±K1Amztjmo~=¸ AKMR AMº
JDY*£ L+Óº&vy|toKÆ]¸ º <oKĸ º m±±´oKt´¸&
A+ºÀmoKztnĺ¯o³µ
np
m±onf{{oK¹
³8|jmojmo~t|®
·|
j ,A´oK¢z}|tA5|mo
º
100 ,R7"!"R7: &+"
< "5
¸m¤M EØG F(¸A£M£M{º
JDYZA"Ls¢º]vyÆyt±*}
K¸PÓº´ ²AN¡yD¸´
A AºP¯AA
ĺ
Ò¾{{oÁdmt±¡
oK¾m
¾ztjm³ÿ|¼(Mnp´oKAzt|t±
ĺ =1 O3G ]D)87297 ¸
EµZ¤ F2I
R A yZ Y*m¸y£M£M{º
JDY L+ ºvJ|toKtMMmm±MzK¸&q¼`º [ho~z|ojm³¸
AÇ #º [YoKz}|toKtjA³ºhi"|kt|toKtmoK}|Ao_
z|tjAo_³µMm}|jÇo±onpoKM|p³
|jmo
®
±A{ÆMoKzz}oK1npymoDº "2
+,2] %$ !0Z)8723!) ¸ÄG YR I À XRA ZXA¸ AKM
Aº
JDY* Ls¢º P±omÆy±o®
(¿¶´+º"i&NxyMKº ] '' TW "'O º^Ò^ N®kÁÂÀ±D¸ 0
Am
ĸ ) p¸Ä³µMmt|tjoKm·|Mĸ
A~
¤Aº
J ¤!L+ÒǺ8vyoKtnpoKzJ|~¸ fº
J
ð"ð Üab
2b
Unité de recherche INRIA Sophia Antipolis
2004, route des Lucioles - BP 93 - 06902 Sophia Antipolis Cedex (France)
Unité de recherche INRIA Futurs : Parc Club Orsay Université - ZAC des Vignes
4, rue Jacques Monod - 91893 ORSAY Cedex (France)
Unité de recherche INRIA Lorraine : LORIA, Technopôle de Nancy-Brabois - Campus scientifique
615, rue du Jardin Botanique - BP 101 - 54602 Villers-lès-Nancy Cedex (France)
Unité de recherche INRIA Rennes : IRISA, Campus universitaire de Beaulieu - 35042 Rennes Cedex (France)
Unité de recherche INRIA Rhône-Alpes : 655, avenue de l’Europe - 38334 Montbonnot Saint-Ismier (France)
Unité de recherche INRIA Rocquencourt : Domaine de Voluceau - Rocquencourt - BP 105 - 78153 Le Chesnay Cedex (France)
Éditeur
INRIA - Domaine de Voluceau - Rocquencourt, BP 105 - 78153 Le Chesnay Cedex (France)
ISSN 0249-6399
© Copyright 2026 Paperzz