Robust Bayesian estimation of the hemodynamic response function in event-related BOLD fMRI using basic physiological information.
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(325) !^ AI A < N F -= l 'r) > q ) +8(R< H ;+
(326) 3Q !1!^ <u>
(327) . "!# %$ & . H`. !. P . 1V R b R g h R ( 7 R 3 4 , H 11V R b R gih R ( 7mH 4'1 3 H ( 7m1 3 4 ( 7 R V R b R gih R :4 S 1FL4 H ! ) V ' b ' g h ( 'J
(328) F"m >!<1
(329) c B) > !>W!K H 1. | F . . ; E. `. 43 ( 7m4. H 1. `. : s ) l &<. w6L+. 1F4 ' "
(330) ` . F -=. 5V R b R g h R ( 7 R 3g4L# H 11V R b R g h R ( 7m4) H 1 3 ( 7 R V R b R g h R :4 S 1^L4 TV 6+
(331) a l+ H > F >) I!< H 11V R b R gih R ( 7m4 ' !+ F ?) >!<1 ;+l +8= 7;>" !+ u +mIi
(332) 99
(333) -> H 143 ( 7 R V R b R gih R :4j l+ ?) Il<1 GF >) &*,+
(334) ;J + H 1.
(335)
(336)
(337) #. !+ +- 9 Q $H N <8 V ' b ' gih 'H 15V R b R gih R ( 7 R 3g4NGTV ` H IZ ; + ( N F J
(338)
(339) 2l+ B9 Q)
(340) = 8 ;J + l+ H N <8 ! H lW ;+
(341) F"G; F ?) s ) l&< ! +. +| l+
(342) F >) I!< Qb yA9 q x . . +
(343) / m !^ ) A[ H ! 1 . WF -= ! + i: .
(344) ! !. ' ! ^ H >W ; ),+. !I+ < 8=7 H Iz H. 5; IQ4 . b'gh. 1V R b R g h R ( 7m4 , H 11V ( 7 R g h R :4) H 1 b ( 7@4) H 1 g h ( 7@4) H 1 ( 7m4 R 1 x?4 Qq+ H 15V ( 7 R gih R :4 ; ! F *6+ 1 ! 4 H 14b ( m 7 4 'H 14gih ( 7m4 ' H 1 ( 7m4j.
(345) a !W
(346)
(347) F" )l +- 8F ?) >!<1 9 H I 1 H I ) I b ' $` A" VH I *) I gi)h
(348) 7 4# ( J H 14g h ( @7 4L # 5g h A / H 1 ( @7 4# A / S H 1 b (@ H 1. 5!I+ < F -=. j +JlW / H 1. Y4 F -=&F -=Xw6L+. . ' ! ^
(349) 99
(350) 8> 8 R . 3 ( 7 R V R b R g h 4L# g h A
(351) . A[ H 5Z Jg! h 3OZV Z ^b h S. J 1 x?4j 1 L4! = l+ F ! *6+. . 1vL4
(352) 7& ! 1l+ H . 1 L4. >. H )V) I. V ' b ' gih
(353) A h g h A M / S A[ H
(354) Z ! 3OZV Z ^ b h C h V V S H 15V R b R g h R ( 7 R 3g4_# g h 9 ' 1^eL4. ; + / l + t(I 7 ) + F ?) 'IF Z ; J Qb B;>" <1 -FH8+
(355) / H ! ! !W 8= TV `. V!. " 6L+ ( . 8F -= l+ H l &;+
(356) A<. <1 ' l8 +-= ' !+ H <8 U )F IK. +rW+
(357)
(358) F" V) 0 ! ` '
(359)
(360) V>!+ H <8 B
(361) F" >+8` H N <8 Qq8 . <1 m` >K 6+8 ' L
(362)
(363) ?) Il<1
(364) a 9 K! +V N !+ E<1 =&F
(365) H Iq ; + ) V '>H 11V ( 7 R 3g4NwTV gH ) ZF + ; z&;+ F ) l&< w6+ 1^eL4 ! . X. "!$# # % &(') "!$# +* # % &(,- .!$# % &. 0 t5.h.
(366) !%.
(367)
(368) = 8=X yQ l WH !1l+ BIl+ H N<t (' I(I ) I!< +
(369) /J h ;?" . F 8= ! m!+ Z<1 =& .
(370) c . 1V ( 7 R 3 4 ,H 15V R b R g h R ( 7 R 3 4 H b H g h H S. = N 8= b . H 1. gih q N F= ) I!Qq ' W+
(371) 8=U H 15V ( 7 R 3*4 , H 11V R ( 7 R 3 4 H , H 11V ( 7 R 3 R :4 H 1 ( 7 R 3g4 H S. 0 . . t3 Q4 A9 ' ! `VF . !+ H !&;^
(372) A< JI I"2;>". '. = N
(373) - I;
(374) a +
(375) a F
(376) F ) Il< (R<B<B Qqs"t!Z N + <Z9 VF M h+ ` ! )
(377) ' &%R%I>S 'J ! i <1 w;>" [ 1 H-H ! [ <1 !+ +8= . 5V ( 7 R 3*4 H 15V ( 7 R 3 R , :4 S TV H8H l [ <1 8I
(378) ` * ) H 1 ( 7 R g 3 4 wH 99 Z +-= ml +8 "#'N>
(379)
(380) F" ' C+ 7C9 F 8=y I
(381) I" ; H ) Il<8 U;>" A[^< ) H 1 ( 7 R 3 4 1 gh =&+ 5e ) Ib I+
(382) 7
(383) +L4N H 1 ( 7 R 3 4b l+ ; i H8H l [ <1 2;>"1 N> ),+8 H 15V ( 7 R 3 4p;>" 3 4 H 15V ( 7 R 3 R :4'?1 Z :4 H , H 15V ( 7 R 3 R , l4 S H 15V ( 7 R g H 1. TV+ . . . N = L " H8H
(384) X+ .
(385) 2; i
(386) a +
(387) / ) ! R< !+. . K
(388) a +
(389) a l+. H . I. H )p) IWl+ 7?" H. H N <8 . 1V R b R g h R ( 7 R 3 4 H V H b H g h R. <1!> 5 ) K ' l+ n' H8H l [ <1 H 11V ( 7 R 3*4;>" H 11V ( 7 R 3 R , :4 ' ! H 1. . ` ! . ( 7 R 3g4 , H . H 1. I. H ). . . 1V ( 7 R 3 R , l4 , H 1 ( 7 ! R 3 4. H 1. H8H l [ <1 Z) I)!^ < =RF
(390)
(391) F } W 8= ! `q :+ A<8 ' Qb 8 Q4 s 3 . % "!$# & '
(392) . ! # # % & # % . X. H . 1V R b R g h R ( 7 R 3g4 H b H g h S g h
(393) Z;
(394) a +
(395) a 8
(396) F 8=. H 1. > ) I M
(397) )
(398) ' &%R% ! Sl. l+ <8.
(399) !!.
(400)
(401) ) I
(402)
(403) F Q . =& 9 ;>". . . Qq- Z. H ) ! z ?9 3 >3;
(404) 8= ! t "9 Q m) <
(405) F" ' ; + 3. ; + . @. C A/ Ah C A R . h 3 Z 1 1 4 3 H 1 ( 7 R 3g4L# 9 11 h 4 e 1Wi&4 Qq+ . , e Z e / ^^ ` !+ H ! 7 <1 [u <1 F 8= A<B 8= !+ ?+- . . . . . . . . . . ) l&< !+ ] + yd + <t
(406)
(407) a + /
(408) ) ! ! K <8 JW
(409) H )w`5 N F= ! ) >WK Q): ' R < j ; F ?) '8W+ C m l + i[ < + < &*,+
(410) 1F # 4 . ,. N 8 IF 8= ! + @<8 F r M Y4 l8I '. gih ( 7 R 3 R , :4. 1 ). ! #R#IS. . s ?&< . <1!>V ). = 1 < [. 7& ) !+ .
(411) F 9 (KpC
(412) H N <8
(413) Bh , gih V=& 9 ;>" `3. (7 R 3 4 S. H 1. #
(414) R ! W <
(415) a I+. B`B 8 Qb F . C , A X / Z] = ) 3 e Z 11 h 4 3 x 3 . K !6+. U ; + s . .
(416) (' . ' Q !. . . g h , Z h S. 1^kL4.
(417). . 1V ( 7 R 3 R , :4 |9C + WKU ; + s mQ ! G = . )p) . >&< '
(418) !C H N <2K. V , 11 2h 4 A / 3
(419) 7<1 [ , \hA11 2h 4 A / S TV^. A[ H 7 N ) 11V ( 7 R 3 R , :4b ; N 99 < !> ) >ul+ Et5.3h C A/ h 4 3 S 1^#L4 M V ( 7 R 3 R , IS , V , 11 *6+ 1v#L47Q ! , %L(> WH ! l+ mQb
(420)
(421) K^9 Q [ < + <7K \J 99
(422) 8> <1. 1. . . . . 1F \. .
(423). . <1 &4_IqP: l" \ 3| 6L+ <1 51WP \ |i <1 &4(R<B<B
(424) F" ) +8 F !+.
(425) N + M : K
(426) ' ! #i #?f H i |< l ' ! #&k ! SUh8I , % ' l 3` !^ ) Il< ) =R+
(427) a c <1l I ' Q ! H
(428) /s" F -= !^ W!>
(429) 5 ) l+ W =&+
(430) / c BH <8 g0 I" H-
(431).
(432) !.
(433)
(434) . =R+
(435) a c7 Kv H < c mH l! l(' Z ! X< 8 < c K 6L+ I"Rl ` l + W+ < )
(436) 99
(437) -> ),+8 L| =&+
(438) / c AH
(439) c m) I lIZ1 l+ >!< ) ! + ( > 9 ) > <BIlXI J 4 . C h [V+Z 3 h h V a h S. 0 / Y)s"9 W ) N <8 AQpI!9 ' l + B>
(440) + X. ). H l &; ;+
(441) EI
(442) + . <B . i + !R<1
(443)
(444) F"/; 1 < s . . l!+. a UQHO4nQv_oTuQ cQzsJ cs]y _ \
(445) 2s. Y)A"9 I .
(446) F" W`
(447) "7; H8H
(448) Z!ZI > 7 B 2) /.30w +NZ
(449) K " I5M h+ ! )
(450) F ' R%&%>I?f_h+ ` ! q
(451) F ' R%&%I ;8SF 3 >!+ ) H-H !I: ` lN 99 K& >I = ) !+ K H N <8 ) N<t AQV>!9u A9
(452) H l VH H P |l+ 8 < ;. s + H A +J
(453) F" A[ H
(454) / F 'n y< = !5; B ) K Wl8 5 Qq+ ! + Y =R 9 X),+8 V = 6+
(455) Xt5.h B[!
(456) 5h8I J ' ) V = > =&F ) ! &< m ; IF
(457) =& p
(458) I H ?" W IF
(459) =& p
(460) <B>
(461) ' & ! 6L+ I("G ) l <B>
(462) pQ ! !+. A[ H <8
(463) ! I+
(464) ; W xw 0 ) 6+ ` ) N <8A QpI! 9 ' l ( > WH ! 8= = F J l + >+
(465)
(466) Kv?" H I! ^ W` 11V , V = 4Z 0 Il + y QV>: ' Qb | y Qq+ l + 8 V `5W =& 8
(467) " ` ) l &< V Q = V ; 8= | + I KFu ; + ' l + m ) V = ) ! &< <B> ! y
(468) 117@4 ' s . 1V = 4 , 15V = Z Vw4 A / 11V = Z VV4 R 8 +
(469) 7; )!+ )
(470) c ) U1 P Z ! 4 A / K ` ; + U> ;+
(471) 9 5H l H @M TD 8 ' K 9 ! #&# x&S ' Qb l+ ) I y l+ * ! Z = ) 15V , V = 4b Z = , A / K M 11V = 4^S R 1 ! %L4 ! 9 Qq+ A / !^ + < +
(472) a 9 ` ; + 2),+8 1FA ) 4p ) !^ A / ; + K K 9 9 F F 8= B ) >" H >!+ I F -= ! + Qq+ V E i!!h@TV+ 8 <1 = 1. t5.3h. l + &< H. !L . . ),+8 . . n'.
(473) F 8= m<B>
(474) *Qq^ 8l+ < +
(475) +J . U .
(476) !.
(477)
(478) . + 5 !+ y [
(479).
(480) ' Qq : l+ X >! 8= <uI ! U;
(481) F W =&
(482) w1^ ) ` &4wTV V` >! 8=
(483) K! > I 0 ! ` F 8=-'& + H !W ;+
(484) )lu <1 2!+ t5.3h +J 4l+ q9 Q)
(485) = = F s ! H ) Il<> I ! + <8z + wTV+ 599 " A[ H
(486) a B !V
(487) F"7 . V I KI ; + s 2Q l H N <8 V F ?) I +
(488)
(489) F"Z
(490) R ) ! &< ! ^ U ^N '8 <t F
(491) "l W L P i! ` ` 9 Q n' l + 6+ J ! + H 7. ) l + 7t5.hUZ 0 !+. + A<B> ?" < ) IH J W =& 8 T ;J>! m; i r Q4 x F . IF=R .
(492) !x.
(493)
(494) . gh. % O%R% % O%R% % % % %. Èmå[Å Ê Î ÷. h F=R+. ! . | < +.
(495) / J . d3 @. > . "
(496) . |>d5. e OR# !# xj% !e OR# KI! % Oe&%. ! ! !. (> WH. F 8=. |>d5. U) I8l+ /t5.h. . ! F . A G KNMi [QHOaêM RSsMv_ow Qi oy w2s @ . . . . !
(497) Q !L!+ H ) >!<1 7 ) !^ 8 ;o 9 Z <1 J ) ! +J !+. !+. ) >
(498)
(499) F Q 8= l H8 < H I m ) !+ A< H I
(500) H I '
(501) A> @ ) l+ LI +
(502) . < H
(503) 8= ; + + U ) !+ < +
(504) +J3 6+ I: ) 7 + 7Q)
(505) F" s ^N! ! ' %&%&% I xK H F < H
(506) Q4 I < +
(507) a ) !R< !+ <8 > =&F
(508) +JW 8= " ! + / t5.3hV 1$ 8
(509) tz.3h +J /;?"m!+ B| #2/#R# ) IQ) A4 ' < +
(510) +Jq 6L+ X1, =R 9 =
(511) c7 ) ?R< 9 I KF
(512) a < +
(513) +J 4 6+ & ) ) w
(514)
(515) +J N F h F=R+ . Tq. Q) 8l ! < TV+ G> /. ) ! + j +r!W gihBQ) ! .) H <8@. 0Nw h8I W+ !I 9
(516) " F % S %&% !JR % S %&% R % S % !JR % S %
(517) ' ( I IH 8= l |Ld5. =R 9 X TD ;^
(518) 7 !+ i F
(519) " W`(' P Q) 3 )! t& %Z 6L+ & y ) q Q) JI /11] , L4 0 9 F= ) tz.3h <1 2H ) I! < z. Q) ! ! +JIF 8= l + K( &< H
(520) A <t N! " X h ' ! + 6+ R N Z l I 2/:15VV4y ! ; /8 Q F
(521) 8l + 1: 8 <1l I ` ! !+ Z w
(522) t5.h4 |9 7( ' > ( I . h 15VV4Q) X <8 W+ 7. ) l + +8 N F W "m ! ! Q ! t!+ =& 9 <1l Ig d3 Q ' > W + Z U I ) 7 +
(523) " ) ! ^ KI + N>( " ) ! + <1l I J 6L+ F
(524) "9 z B <1 )w) I ' H Ii <1! IE 1 Q ! F= 6L+ R N ! I 4UQ !
(525) Q > <
(526) R F 8= F l > + ; ZF ! L! +. <1 X h8I F J N ' ! > + )5H > F >) I! < GF ! X<B> 3
(527) 157m4z / TV y. !#"$%'&(" !#)#*,+ #- *,+ #-/.0. 1 2 - % 3465 574 &8+:9 ;=< ' j > ? 0@ BA !BC$DEFCG H IKJ &.
(528) !.
(529)
(530) . R
(531) =&
(532) ~( J 6+ U ) ! 7 W 8= l+ U> 7 ) l+ H > H ) yYV"m( J + n' !+ 7 = + ' !^ 7 F= + Wl+ 7> + 7|9 F -= A9 m < H
(533) > 8 F 8= I 'I( ( % ' Qq+ !+ ZI WH F -= <1lI V ! Q): ),+8 n' Qq : ` &;> +J F
(534) "LB9 !"@;& L <1!Iz ) !^ | + ut5.h4nY <1 Q) !^ ) >. 6L+ s ;>" 1 V R G4 '! ^ <1
(535)
(536) 2l + y; (' !^ <uI Y( J !> 9 j!+ K < % + R N Y ! >3 Qq
(537) F W <
(538) / ) qF M~
(539) ' ! #&#&# S . 2/:1 Vp4 0p l + KA9 N =. V. , P !Z ! +V ZV = ah S. 1. , P !Z. 1 L 4. = 4 , 9 A / K M 11V = 4^S S. 1 L4. !! 4. K !> H 4 <8 < H
(540) ) !+ j <1!Iq(&< H l!+ K + ytz.3h = a I yQq 6L+ s 2;?" l6L+. h1. 53H +. . ! F
(541) = A1 4 S lc = N
(542) ` ' ! #&#ReS ' !^ Z !< 4. !. ? Gh 3 ) l+ 7> 7 ) ; + I < H
(543) H N 7F !< ) ?" H !>
(544) + <8 j +JlW H8H ! [ <1AK wTV+ K
(545) F = l8< ) l <8 7 W+ K !+ ; K
(546) / 8!Z ! H8 <8 I+ wh F
(547)
(548) F" ' !+ q; Qq <8 W+ +JW 8= !+ ! A V ) l+ )
(549) 8tz.3h V = ) !R<-!^ q<B>
(550) ! w6+ F M . +. ! . 1 %4. 11V ) ! ' %R%&% W < + /
(551)
(552)
(553) hl+ < H
(554) . h8>) I: . +
(555) a B. . r(' l + i(I IH 8=2H. !. ) Il<1 W <1!>*Qq
(556) K. r y O cMv_oTuQ yY oQ U Oaêy O L )(R< H Z. \J 99
(557) 8> . <B>
(558) 8Q l . <1 '
(559)
(560) s .
(561) F >) I!< (I IH. 57 e 4 ' 1. 8= ! U [ < + <7K. !^ B<B>
(562) }Q ! !+ 8 A< H I
(563) H I ' 157 *4mh8I.
(564) 1 5 5 2B K& ! & 4 + 2B #!62B ?+@0 5 ' % @! 5 $ .! & 4#5 2 ! &&% ' ( 2 1# + "(&8+ 5#) 2B1 5 * 4#5 ,+X " 1&, #@ 5 +- -/.10 V 2B .32 V ) 2 1 5 ! - j#" 5 K 4 V 4#5 @* 575 + 5 57574 - " 1&8 #@ 5 +-B I6087 2B I0 790 !:.;2 V &)<= + + 5 22 > ) &8 4 &8 > * - !# &8+K& 5:- 4 5$4 8& "7"7 # 4 #@0 @?BA &4 5 5 " 5 2:&8 ) j >0>kVDC .
(565) !e.
(566)
(567) . W" H8
(568) W < +
(569) / J' h =&+ 2I) H + b <1 3tz.3h # ) >!<1 D <1!> Q4
(570) a +
(571) / ) >W!+ ! ' %R%&% `
(572) c Jq+JW 8=@*6+ J 1 !! 4 ' 1 ! 4j 1 ! L4UTV^. I+
(573) I+ <B<1 c F h =&+ ; mII h F=&+ t;n1 4K
(574)
(575) F" F l ' =
(576) l ) !^ ` Z
(577) A9
(578) ' <1 ) gih Qb . I + N ) >U ;JIl <B>
(579) (' 8 Q F 8= !^ 8!R; +J l ) l <1lI Zh =&+ 8 ;n1 4 -Q !|l + 1
(580) / 9 IH 7& ) F l+ @Y)s"9 W <B>
(581) F GQ ! 7 W 8= |>d5.K 5 t5.hk < n' ; W+
(582) 8= ) l &< l + F l> + ) A< H I
(583) H IBQb . ) I@ ! +. ) I`
(584) xG h ' ;o>! $<B>
(585) [? ; F IF 8= 6L+ & 8 l I7 Q l F W 8=m . 1^h =&+ KI& 1 4l4 ' ; + b <1! I V 1F( > WH F 8= l U<B>
(586) 157 4l4gQq < + C E<BI ul &; +r )!
(587) 157 e 4!4 |9 ' B N <1 y U ) F IF 8=Z l V e 1F( > WH F 8= ! u<B> w I Z. Q) I: A 9s Qq+ ! ^ H >5 Q) ( JW s = F n' ! +
(588) Qb Wl + |Ld5. ' ! +.
(589) a = Kl + Z ` X. 1vh F=R+ Z>& 1 4l4N7 Y + j! ` > Z + Qq 5 Ii! + + Z. ) ; F ! ^ 8 <1 n'nIF |l + B !A IF=& - Z. ) <B> ! q
(590) 117 45Qq
(591) < H ! 9 ( &< H s |! F 8
(592) <u> g
(593) 157 e 4 ' ; . h =&+ iI& 1 FF 4N. gQHRSQ UM`_HTiQ yY oQW_Hy`aês[Q s[M" vRSab_zn w2aêsJ EOa 2h [aêy _. . (I F -= l M Y4 l8I ' ! #R#&# S ' l+ |j +r!W + + E ) !^ ` l+ U<B> !
(594) ` ( J 6+ z ) !^ [ < + < K g ! H " H F FH
(595) '& Qq :B
(596) F"8l+ 5<8 7 8!^ > . ) !^ 8> +
(597) ` 1 t !I+ <8 !@; B9 Q
(598) A> K!Rl+ t
(599) F" W 5yW+ : ' !+. <1 8 +
(600) IX ! H !+ < H
(601) F 8=/) 6L+ ) !+ ` 9 TV ` Qq
(602) &; ! 9 BM
(603) D
(604) F ' & %R% ! Sw T j( !<! `(' Q4 I < +
(605) a ` < H
(606) 8) !R<> +J h ' F I I: ^ p Q l !^ V<B>
(607) ?" H I!^ W`(' j +r!W Z ` pQ) < H
(608) 8= ; + J }. %!O % ! w 0 >: Vl U<8 7 W+ )! ^ ul &; +J ! ) ! + z<B>
(609) 8Q ! +J 7Q l B<8 % 2> 5 = : ! `l + H /. ) < H IN
(610) W I
(611) a F ! ^ '5 .y1 x>47Q l [ H
(612) F
(613) " IF 8=2) > ! > Qq
(614) I < +
(615) a y h F
(616)
(617) " 'JH ?" W I
(618) =&
(619) 7. Qq JI R ! +. Y3P \_ ) / .30 IF=R _
(620) ) ! ^ W _
(621) + +J F ! + ) >
(622)
(623) Q 8=E n'8
(624) 7 =& J Qq^ . . 7 2 1 5 !&,2B '
(625) > t . 2
(626) > V tt % 2 > > Y .
(627) 2 > >×V t
(628) 3 2 &8 4 ! k> X >
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