28

6 - UHcanic/papers/hemodynamics/hemopaper.pdfÖÇÝ Ü ÖÇÚ Ý ê ì í ò bkxwx: n @

  • Upload
    others

  • View
    6

  • Download
    0

Embed Size (px)

Citation preview

Page 1: 6 - UHcanic/papers/hemodynamics/hemopaper.pdfÖÇÝ Ü ÖÇÚ Ý ê ì í ò bkxwx: n @

� �������������� ���� ������������������� �������� ����� �!���"����# �$�%��� ��"�&� � � �'�)($�$#"*����!��

�+��,��$� ��� *��-�)��, �%�-�/. ����#/� ��0 � '�)�+($�!�1���2���3)�546�7���+�+����#2�� 8)������$�!�

9;:=<�>? @A?�B >C B < @ED?�FG!H�I BKJMLON H < LQPSRUT�BKLWV H N�BKLW@A?�XY < @[Z H JWXW@[L]\'PSR_^`P : XMLOP <

^`P : XMLOP <"acbedfdfgKhSiKjlkKimdSn

o :=< ^ H : @7p-@AN�qG!H�I BSJrLON H < LsPSRUT�BKLOV H N�BKLO@t?�XC BKuA@tRvPSJ < @AB 9 LOBKL H%Y < @tZ H JWXM@tL]\w P <=xzy H BK?5V|{ C~}e�Shf�Si�h�jO��hfh��

�~�S�r���f���K��� ���$�������~���E�K�M�����s�����M� �r���¡�%¢£�5� ���r¢£�5����¤M�1¥6�E���1¥�¦��§�¨��©Eª�� ���!«�¬��E� ��¥­�����M�E��l®f�M¤l���|�1���¨�§����¯����`�¡��¦��K�M� °S©E¥���¤±�§¦��§� �M¢²©1ª³���E�§�����E¥S´��µ®f�r���r��� �¨�1¥f�W« ¬K�5� ��©E�K�¶¢c©�´��r¥�����¯¡°�¥­©�©�´· ©5�¸����� © ¬�¯E�z¥��E� ¯ �`¤l© ¢c��¥­�¨�1���~¹E�M��� �r¥¨�rº$»|���¼�M«�¬��1� ��©E���~�1���`´��M� ��¹E�W´$¬�� �­��¯�� �§¦�¢c��� ©E� �¨¤���M´�¬�¤l� ��©E�¼©1ª�� ��������¤r©E¢c�����M���§��°�¥��_½±�O¹����r� ¾v¿�� © ÀE�M���W« ¬K�5� ��©E�K�6���!���1����©5��Á�¥�©E��¯c¤Â�K�1�����M¥��Mº»;©s¯ ¬��1�Â�1��� �M���§� ����¤l�±��¦��K�M� °S©E¥���¤r�µ�v¦!����ÃK���§�_´��M� ��¹E��� ���~�M�§� ��¢£�5� �W�7© �Ä�����¡�����­���E¥��E��´°S©E¬���´��1��¦U´��5���±�����¨¤Â����¢c��¥­¦��§� ���¨¤]�=��¦��S�r��°K© ¥­�¨¤l�­�v¦������ ���6���r¯ �­© ��©1ªK� ¢c©�©1� � · ©5��º³Å���� ���M�����©5¹E���£¯ �r���M���E¥�� ���r©E���r¢Æ�����¨¤Â�-����©5¹���´��W�Ǥl© ��´��­� ��©E���±¬���´��r�7������¤Â�%�E�-�­���µ�����E¥µ¾È°K© ¬���´��E� ¦¹5�1¥�¬������ © °�¥­�M¢ÆªÉ©E�U�s«�¬�� �§��¥­�����W�1�7��¦��S�r��°K© ¥­�¨¤�� ¦��v���r¢Ê�E´�¢~�­���_�s� ¢c©�©1� ���§© ¥­¬�� ��©E�mºUË7� �­��¯� ���������M� ¬�¥­�Ì�6��� ��©5������5�Ì��¬�¥����5���­¥�� · ©5��°K© ¬���´��E� ¦�´��5�����E¥­�|�O¦��³¯ �­¹ �|� �¨�§�|��©��§��©�¤ÂÀ�ªÉ© � ¢£�1¾� ��©E�¼ÍÉ����¯E��¯E�Â�E´����r�����;����� ����¹E�M¥­©�¤r�µ�v¦��1�K´��������r��¹E�W� � �r¥��Â�E´���¬��ÂÎ]º³Å����M�§� ��¢c�1� �¶� ���6� ��¢c���E��´� ����¥­©�¤r�1� ��©E�¡©1ªS� ���|Ã��Â�§��� ��©�¤ÂÀUªÉ©E��¢£�5���­© �~�E��´¡� ��©5�$�����5�Ì���£�_���M�E¥µ����¦��­��´��­¹��¨´�¬��1¥AÁE� ��©�¤ÂÀ��ªÉ©E��¢²���r¥�¥K© ¬���� ��´��7�����U����¦�� ��©E¥�©E¯E�¨¤r�E¥­¥�¦~�­��� �M� �W�v���­��¯����r¯E��©E��ÍtÏ�º Ð�¢c�r� �r�Â�|´�©5�����§� ���M�E¢ÑªÉ��©E¢� ���±����¥��l�6°S©E¬���´��1��¦�Î]º=���£�����±�M��´£���7�����M� �r���6�¡�v��¬�´�¦c©1ª������_�­� · ¬��r��¤r�7©Eª³¹E�W� � �r¥����1�S�r������¯©E���§��©�¤ÂÀ`ªÉ©E��¢£�5� ��©E�³ºÇÅ��¡©E°��Â�1���%�s� ¬���������� �­��¯£� �W�§¬�¥­�MÒ�¹ �M���§�M¥m�Â�1�S�r���­��¯s�K©��v���K© ���M�_�§��©�¤ÂÀªÉ©E��¢£�5���­© �mº=Å�������©5¹���´��_�E�¼�rÓ���¥��E���5���­© �QªÉ© �Ç����¦£� ���¨���¨��� ����¤M�E� �Eº

Ô Õ5Ö�×�Ø�Ù±Ú±ÛÇÜ�×|Ý�Ù_Ö} XM@AN I u H P < H j]Þ @tN H < XW@tP < BSuÌNzP Þ H u6PKRÇß=uAP³P Þzà P�áÊLOV=JMP :=x V2B�â;@ j XM\³NzN H LOJM@A?Q?�PfN I ut@ÈB < L�Z H X jX H uAX)ã g;ä[��imå V=BSX/ß H�H <æ: X H Þ ß�\ÆN�B < \çB : LWV=PfJWX�LOP²XML :=Þ \èZKBSJW@tP : Xé@tXWX : H X'J H uÈB�L H Þ LOP¸LOV HZKBSXW? : uÈBKJ`Xr\;XrL H Nëê � { n { � { ��ì { ��d�í�ä`a V H XM@AN I uA@t?�@tL]\éPSRULWV H NzP Þ H u7NéBSî H X`@tL : X H R : u_@ < R§BSXrLJ H BSu j LO@tN H ?�PSN I : L5BKLW@AP < X�áQV H <'ï³: @A?5î�B < XMá H JMXQBSJ H < H�H Þ H Þ @ < LOV H ?�BSX H XcáQV H < LOV H x H PfN H jLOJr\éPKR�LOV H-I B�LO@ H < L�ðµX~Z H XWX H u�?�B < ß H B I�I JWP�â;@AN�BKL H Þ ß�\'B�XrLOJWBS@ x V�L�{ < BSJMJWP�áÄ{=? PfN I uA@ÈB < L�á~BSuAu?5V�B <�< H u ä'a V H NzP Þ H u�V�BSX%ß H H <¸: X H Þ {_RvPfJ H â�BSN I u H {±@ < LWV H ? PfN I : L5BKLW@AP < PSRcß=uAP³P Þ�à P�áLOV�JWP :=x V�LWV H BSPfJMLOBB <=Þ ?�P : I u H Þ LWPzLWV H k�j G B <=Þ u : N I¶H Þ NzP Þ H uAX~LWP�XM@AN : uÈBKL H LOV HÄH < LW@AJ HV : N�B < ZKBSXM? : uABSJQXM\³XML H Nñê �Kí�òÌ: XM@ <=x B�óMXMLWJ : ?EL : J H Þ LWJ H�H ô LWP�XM@AN : uÈBKL H LOV H óWBSJrL H JM@ÈBSu6LOJ H H�ô {LOV H P < H j]Þ @AN H < XM@AP < BKu£N�P Þ H u£@tX$LOV H ß�BSXW@tXzRvPSJLWV H <³: N H JW@A?�BSuQXW@tN : uÈB�LO@AP < X I J H X H < L H Þ @ <

õ1ö1÷�ø ø�ùMú�ûvü]ýÄþ5ÿ-û���ü����rû�� ù����6ö ���µü���Âü�� ùW÷��ý�lû��µù���÷���ý ü ú��Mú����1û����£ö����������� �!"�#����ý%þ1ÿ¼û���ü�$Sü&%��'�(��)��� ü�ú* ý ÷�+�rû�� ù���,;ù-�rú§ý/.1032345�6�lû���ü+7��lû��8��'�9:�rú����5û3���� �;-<�=>��� !�!>="�?=�����!�@

A ö1÷�ø ø�ùMú�ûvü]ý�þ1ÿ�û�� ü��B�lû��µù��C��fö��+� ü+��ÂüD� ùW÷��ý�lû��µù��~÷���ý ü úE�Mú����5ûF�D�£öG�H��!"�� �I-=�

Page 2: 6 - UHcanic/papers/hemodynamics/hemopaper.pdfÖÇÝ Ü ÖÇÚ Ý ê ì í ò bkxwx: n @

�������� ÖÇÝ�Ü � ÖÇÚ� ��� ��� Ý��

ê ��ì�í ò BKXWX : N�@ <=x ZKBSJM@ÈBSß�u H�� P :=<�x ð­XsNzP Þ=: u : X£LOV�@AXQN�P Þ H u�V�BSXsß H H <�: X H Þ @ < ê i { ì�í LWPéXrL :=Þ \I JMP I6H JMLW@ H X¡PSR�ß=utP;P Þà P�á B <=Þ LWV H P I LO@AN�BSu Þ H XW@ xf< PSRÇXrL H < LWXÄã I JWPfXrLOV H X H X å @ < LOV H`H <=Þ P�ZKBSX j? : uÈBSJLOJ H BKLWN H < LéPSRÄBSß Þ PfNz@ < BSuQB < H : JM\³XWN ò @ < ê nKí ZKBSJM@ÈBSß�u H�� P :=<=x ð­X�N�P Þ=: u : XéB <=Þ LOV HP < H j]Þ @tN H < XW@tP < BSu H ïm: B�LO@AP < X-V�B�Z H ß H�H < @tN I u H N H < L H Þ LOP'XrL :=Þ \ H <=Þ P�ZKBSXM? : uABSJ!LOJ H BKLWN H < LPSR±XML H < PfXM@AX ä� < X I @[L H PSRÄLWV H B I=I¶H BSJWB < ? H @ < B áQ@ Þ H uA@[L H JWBKL : J H {cá H V�B�Z H RvP :�<=Þ LOV�BKLéLOV H J H BSJ H

X H Z H JOBSu�@tXWX : H X-J H uÈBKL H Þ LWP/LOV H XrL5BSß�@AuA@[L]\�B <=Þ XM@ <=xf: uÈBSJM@tL]\'RvPfJMNéBKLW@AP < LOV�B�L-V�B�Z H$H @tLOV H J < PKLß H�H < î < P�á < PSJsLWV�BKL`V�B�Z H < PKL¼ß H�H < ?�PfN I u H L H ut\ :�<=Þ H JMXMLWP;P Þ|ä � < LOV�@AX I B I¶H J`á H�I J H X H < LB�? PfN I J H V H < XM@tZ H JW@ x PfJWP : X¡N�BKLOV H N�BKLO@t?�BSuÌB < BSut\³XW@tX¡PKR�LOV H :=<=Þ H JWut\³@ <=x ïm: BSXM@AuA@ < H BKJ I BSJMLW@ÈBSuÞ @�� H J H < LW@ÈBSu H ïm: B�LO@AP < X¡áQ@[LOV�LWV H @ < @tLW@ÈBSu=B <=Þ ß¶P :=<�Þ BSJM\ Þ B�L5B�LWV�BKL¡?�PfJMJ H X I P <=Þ LOP I : uAXWBKLO@tu Hß=utP;P Þ/à P�á@ < uABSJ x H Z H XWX H uAX ä~a V H J H X : u[LOXQPSR±LOV=@tX I B I¶H J£?�B < ß H X : NzNéBKJW@�� H Þ BSXcRvPfutuAP�áQX ä��� � H~I J H X H < L¡B!JW@ x PfJMP : X Þ H JW@[ZKBKLO@tP < PSR�LWV H£H ïm: BKLW@AP < X_áQV=@A?5VzBSJ H Pfß�LOBS@ < H Þ : XM@ <=x BKXM\³N I j

LWPSLO@t?�B < BSu[\³XW@AXéPSRÄLOV H @ < ?�PfN I J H XWXM@Aß=u H"! B�Z³@ H J jl9 LOPfî H X H ïm: B�LO@AP < X/@ <æ< BSJWJMP�áÄ{`uAP <�x?5V�B <=< H utX ò X H�H ê g�í RvPSJ£ß�BSXW@t?-J H R H J H < ? H ä

#$� � H Þ H JM@tZ H LOV H ? P <=Þ @[LO@tP < XéP < LOV H @ < @tLW@ÈBSuQB <=Þ ß6P :=<=Þ BSJr\ Þ BKL5B�LWV�BKL I JWP�Z³@ Þ H XMLOJM@A?ELV�\ I6H JW߶PfuA@t?�@[L]\�PSRcLWV HéH ï³: BKLO@tP < X%@ < LWV H J H x @AP < PSRcXMN�P³PSLOV à P�á ä ã } u[LOV=P :=x VÑXMLOJM@A?ELV�\ I6H JW߶PfuA@t?�@[L]\�PKR�LOV H-H ï³: BKLO@tP < Xc@tXcBSXMX : N H Þ H Z H Jr\³áQV H J H @ < LOV H ut@tL H JOB�L : J H {³@tLc@tX < PKLLWJ : H LWV�BKL-LOV H$I JWPfß�u H N áQ@Autu_ß H XMLOJM@A?ELOut\"V�\ I6H JW߶PfuA@t?�RvPfJÄB < \�@ < @tLW@ÈBSu7B <�Þ ß¶P :=<=Þ BSJM\Þ B�L5B ä�å

%$� � HéI JWP�Z H B x H < H JOBSu�LOV H PfJ H N"{UXrL5BKL H Þ @ < LOV H RvPSJWN�áQV=@A?5V ?�B < H BSXM@Au[\�ß H B I�I uA@ H Þ LWPLWV H :=<�Þ H JMut\³@ <=x H ïm: B�LO@AP < X�{máQV=@A?5V I JWP�Z³@ Þ H X¡LWV H ? P <=Þ @[LO@AP < X :=<=Þ H J¡áQV=@t?5V'B < @ < @tLW@ÈBSu j߶P :=<=Þ BSJM\�ZSBKu : H¡I JWPfß�u H N RvPfJ�B!V�\ I¶H JW߶Pfut@A?cXr\;XrL H N PSR I BSJrLO@ÈBKu Þ @�� H J H < LW@ÈBSu H ïm: BKLW@AP < XV�BKX`B$XMN�P³PSLOV2XMPfu : LW@AP <�ä

&'� � H : X H LOV=@tX LOV H PfJ H N LOP I JMP�Z H LOV�B�L I : uAXWBKLO@tu H ß6P :�<=Þ BSJr\ Þ BKLOB�áQ@AuAu~BSutá~B�\³Xzu H B Þ LWPXMV=P;?5îçRvPfJWN�BKLO@tP < @ < B < @ Þ H BSut@�� H Þ ß=utP;P Þ Z H XWX H u-LOV=BKL2@AXéZ H Jr\æuAP <�x B <=Þ XrLOJOBK@ x V�L ä� HéH XMLO@tNéB�L H LOV H LO@AN H B <=Þ utP;?�BKLO@tP < PSR)(�JWXrL XMV=P;?5î)RvPfJMNéBKLW@AP < @ < LOV H ß=uAP³P ÞÑà P�áI JMPfß=u H N B <=Þ XMV=P�á LWV�BKLc@ < B V H BSutLWVm\�@ <�Þ @tZ³@ Þ�: BSu�{�XMV=P³?5î³X Þ H Z H uAP I á H utu�P : LWXW@ Þ H LOV HI V�\³XW@tPfuAP x @A?�BSuAu[\J H u H ZKB < L Þ PfN�BS@ <�ä

*$� � H : X H <³: N H JW@A?�BSu|XM@AN : uABKLO@tP < X�LOP x H LOV H JcáQ@tLWV2LWV H Þ H JM@tZ H Þ H XMLW@AN�BKL H XcLOPXML :=Þ \2XMV=P;?5îRvPfJMNéB�LO@AP < @ < L5B I¶H JM@ <=x Z H XMX H utX ä � H PSß�L5BS@ < B/X : J I JM@AXW@ <=x J H X : u[L!áQV=@t?5V�XWV=P�áQX-LOV�B�LLOB I6H JW@ <=x ?�B : X H X Þ H uÈB�\�@ < LWV H (�JMXML-XMV=P³?5î�RvPfJMNéB�LO@AP <|ä � H�I JWP�Z³@ Þ H B < H â I uÈB < B�LO@AP <RvPfJcáQV�\'LWV=@AX£@tXcLOV H ?�BKX H ä

+ ,.-'/¸Ú0/ÌØ�Ý�1 � ×�Ý�Ù_ÖÆÙ32Ñ×$-0/4�!Ù_Ú0/657/68_Û � ×�Ý�Ù±Ö'9} u[LOV=P :=x V¸ZKBSJW@tP : X%Z H JMXW@tP < XPSRQLOV HéH ïm: BKLW@AP < X á H XML :=Þ \²@ < LOV�@AX I B I6H J$V�B�Z H ß H H < : X H Þß�\ÊNéB < \ B : LOV=PSJWX'LOPçN�P Þ H u¼ß=uAP³P Þæà P�á LWV=JWP :=x V ? PfN I uA@AB < L/Z H XWX H uAX {%á H V=B�Z H RvP :�<=ÞLOV=BKLQLOV H Þ H JM@tZKBKLW@AP < PSR±LOV H%H ïm: B�LO@AP < XQXML :�Þ @ H Þ V H J H V�BSX < PSL`BSutá~B�\³X`ß H�H <�Þ H XW?�JM@Aß H Þ @ < BXOB�LO@AXrR§BS? LWPfJM\ÄN�B <=< H J ä±} X_B¼?�P < X H ïm: H < ? H {�LOV H XWP : JM? H L H JMN�X Þ H XM?�JW@tß=@ <�x LOV H Z³@AXM?�P : X H � H ? LWX

g

Page 3: 6 - UHcanic/papers/hemodynamics/hemopaper.pdfÖÇÝ Ü ÖÇÚ Ý ê ì í ò bkxwx: n @

� /6�!Ù±Ú � Ö � �!Ý�Ü 9

@ < B�â;@AXr\³N�N H LWJW@A?K{ < BSJMJWP�á+B <=Þ uAP <=x Z H XWX H uAX {|V�B�Z H Þ @ � H J H < LsRvPfJWNzX`@ <"Þ @ � H J H < L¼ut@tL H JOBKL : J HXWP : JW? H X ä�� PfJ!LOV H XWBSî H PSR¡?�PfN I u H L H < H XMX�B <=Þ ?�PfJMJ H ?EL < H XWX {_á H @ < ?�u :=Þ H LOV H Þ H JW@[ZKBKLO@tP < PSRLOV H%H ïm: BKLO@tP < XQV H J H ä

a V H J H BSJ H B?�P : I u H PSR Þ @ � H J H < L!B I=I JWPfBS?5V H X`P < H ?�B < L5BSî H LWPéPfß;L5BS@ < LWV H :=<=Þ H JWut\³@ <=xH ïm: B�LO@AP < X : XW@ <=x BKXM\³N I LOPSLW@A?�J H Þ=: ? LW@AP < RvJWPSN LOV H R : utufX H L_PKR=@ < ?�PfN I J H XWXM@Aß=u H ! B�Z³@ H J jr9 LWPfî H XH ïm: B�LO@AP < @ <Ê< BKJWJWP�áÄ{ÄuAP <=x ?5V�B <=< H uAX ä��-< H @tX"ß�BKX H Þ P < B I JM@APfJM@ H XMLW@AN�BKL H X�{ÄB <�Þ LOV HPSLWV H J$P < LWV H < P <=Þ @tN H < XW@tP < BSut@���BKLO@tP < PKR`LWV H :=<=Þ H JWu[\;@ <=x H ïm: BKLW@AP < X ä � < LOV=@tX I B I¶H J á HL5BKî H LWV H uÈBKLML H J¼B I�I JWP�BK?5V ä � H áQ@tuAu I¶H JMRvPSJWN BSXM\³N I LOPSLW@A?�J H Þ�: ? LW@AP < PKR�LWV H H ï³: BKLO@tP < X!@ << P <�Þ @AN H < XM@AP < BSu;ZKBSJM@ÈBSß=u H XUß�\@ xf< PfJM@ <=x LWV H L H JWNzX�PSR�PSJ Þ H J���~B <�Þ XMNéBSutu H J�{KáQV H J H ��@AXULOV HJOB�LO@AP�PSR±LWV H áQ@ Þ LOV/Z³X ä LOV H u H <=x LOV'PSRÇLOV H ?5V=B <=< H u ä o XWX H < LO@ABSuAu[\éLOV�@AXc@tXcáQV�BKL£á~BSX Þ P < H @ <ê g�í�ä� H XMLOBSJMLQáQ@[LOV2LOV H @ < ? PfN I J H XWXW@tß=u H B�â�@tXM\³NzN H LOJW@t? ! B�Z³@ H J jr9 LOPfî H X H ïm: BKLW@AP < Xs@ < ?E\;ut@ <;jÞ JM@A?�BKu|?�P³PfJ Þ @ < BKL H XÄã� ������� å1ä�a V H �?�P³PfJ Þ @ < B�L H @tXQBSuA@ xf< H Þ áQ@[LOV/LWV H B�â;@AX£PSR±XM\³NzN H LOJM\éPSR

LOV H ?5V=B <=< H u ä G!H < PSL H LWV H Z H uAP³?�@tL]\�?�PfN I P < H < LOX%ß�\����&ã���������������� åEä � H (�JMXML�BSXMX : N HLOV=BKL£LOV H B <�xf: uÈBKJcZ H utP;? @tL]\é@AX£?�P < XMLOB < L`LWPzPSß�L5BS@ < LOV H RvPfutuAP�áQ@ <�x H ïm: BKLW@AP < XsPKR_NzPSLO@tP <� � �� !#" ��� � ���� � " � � � ���� " �$ �&%� � ' ( � � ���� � � " �� � ���� � " � � ���� �*) �� � �� !+" � � � ���� � " ��� � � �� " �$ �&%� � � ' ( � � ���� � � " �� � ���� �-, � �� � " � � � �� �.) �B <=Þ LOV H @ < ?�PSN I J H XMXW@Aß�@AuA@[L]\z?�P <=Þ @tLO@tP <� � �� " �� � ã/�0��� å� � � h21 ã g;ät��å

+ � Ô ,.-'/¸Ø /ÌÚ±ÛÇÜ$/ÌÚÆÖÇÙ±Ö7Ú7Ý�� /ÌÖ'9�Ý�Ù_Ö � 5"/ 8±Û � ×�Ý�Ù_Ö'9� < LOJMP Þ=: ? H LOV H RvPfutuAP�áQ@ <=x ?5V�BSJOBK? L H JW@tXMLO@t? ïm: B < LO@[LO@ H X35476 B <=Þ � 6 BSJ H LWV H ?5V�BSJWBS? L H JW@tXMLW@A?ÄJOB Þ @ÈBSu�B <=Þ B�â;@ÈBSu¶Z H utP;? @tLW@ H X {398 @tXcLOV H ?5V�BKJOBS?EL H JM@AXrLO@A?Äu H <=x LWV|{�B <�Þ;: 6 @AXcLWV H ?5V�BSJWBS? L H JW@tXMLW@A?-@ <�< H J£Z H XWX H u7JOB Þ @ : X�{B <=Þ LOV H ? PfJWJ H X I P <�Þ @ <=x< P <=Þ @AN H < XW@AP < BSu6ZKBSJM@ÈBSß�u H X�<3 �=� : 6&>�?�@A� 8B>C� ! � DE�F >! {G� �H�I� 6 >� �&��� �.� 476 >� �J� % � $ �=�6 >% ä! PKLO@A? H LOV�B�L : 68 � 476� 6 � ã g;ä¨gSå

áQV=@t?5V�@AXQLOV H XMNéBSutu I BSJWBSN H L H JK� ä ã � < LOV H à P�á J H x @AN H ?�PfJMJ H X I P <=Þ @ <=x LWP�LWV H BKß Þ PSN�@ < BSuBSPfJrL5B!ß H L]á H�H < LOV H J H < BKu�B <=Þ @Aut@ÈBS?¡BSJML H JM@ H X {fLOV H JWBKLO@tP!ß H L]á H H < LOV H JOB Þ @ : X�B <=Þ LOV H u H <=x LWV@AX£PKR_PfJ Þ H JML'ã ��hON � åEä�å

k

Page 4: 6 - UHcanic/papers/hemodynamics/hemopaper.pdfÖÇÝ Ü ÖÇÚ Ý ê ì í ò bkxwx: n @

�������� ÖÇÝ�Ü � ÖÇÚ� ��� ��� Ý��

a V H @ < ? PfN I J H XMXW@tß=@Aut@tL]\z?�P <�Þ @tLW@AP < @ <�< P <=Þ @tN H < XW@tP < BSu¶ZSBKJW@ÈBKß=u H XcJ H B Þ X�: 6 �� >��� : 6&>� 476 >����� " �8 �� >�� : 6&>�0� 6 >� ��� � h � PfJ�� >� � >� >� ��� " � 6 : 64 6 8 �� > � >� >� ��� � h21

! PKLO@ <�x LOV�BKL E�F��?F�F D � � á H PSß�L5BS@ <�� >�� >� >� � � " �� >�� >� >� � � � h21 ã g;ä�kfåa V H (�JWXrL`NzPfN H < L : N H ïm: B�LO@AP < @ <2< P <=Þ @tN H < XW@tP < BSu¶ZKBSJW@ABSß=u H X£ß H ?�PfN H X� 68 �� >! � � 6 >����� " 4 6 >� � �: 6 �� >��� � 6 >����� " � 6 >� � �8 �� >�� � 6 >����� " �$ � �6 $8 � >%� > �

'� �: �6 � 6 � � >� �� >� � " � 6: 6 � >� �: 6 � >���� >� " � 68 � � � >���� > ��� 1} R�L H J Þ @[Z;@ Þ @ <�x LOV=@tX H ïm: BKLW@AP < ß�\ � �6 B <=Þ N : u[LO@ I ut\³@ <=x ß�\ 8 á H Pfß;L5BS@ <� >� �� >! " 476: 6 8� 6 >� � >���� >� " >� � � >� �� > " � >%� > � ' 8� 6 : �6 � � >���� >� � " � >� � >���� >� " : �68 � � � >� �� > ��� 1a BSî H @ < LWP'BS? ?�P :=< L-LWV�BKL F� F DE F � �fä-a V H <�< PSLO@t? H LWV�BKL!LWV H uABSXML!L H JMN @tX¼PSR�PfJ Þ H JH���B <=Þ< H x u H ? L�@tL ä � PfJ�LOV HsI JMPfß=u H N Þ H XW?�JM@Aß=@ <=x ß=uAP³P Þ$à P�áæ@ < LOV H BSß Þ PfNz@ < BSu=BSPfJMLOB-ß H L]á H H < LOV HJ H < BSu6B <=Þ @AuA@ABS?QBSJrL H JM@ H X�{mLOV H ?5V�BSJOBK? L H JW@tXMLO@t?`ZKBSJM@ÈBSß=u H X�L]\ I @A?�BSuAu[\ L5BKî H LWV H RvPSuAuAP�áQ@ <=x ZSBKu : H X'�� k21¨g��¼��h N�� N ��� XJ� : 6 � h21­hfhf�fg N � 8 � h 1t� N B <=Þ � 6�� h21[� N � XXWP LWV�BKL¡LOV H ? P H�� ?�@ H < LQ@ < RvJMP < LcPSRÇLOV H JW@ x V�L~V�B <=Þ;j XM@ Þ H @AX~PKR±PSJ Þ H JKL'ã ��h N�� å B <=Þ á H î H H�I@tLQXM@ < ? H @tL£@tX£uÈBSJ x H JcLWV�B < ��ã§B <=Þ {�PKR_? P : JWX H { � � å1ä} R�L H J < H x u H ? LO@ <=x LWV H L H JWNePKR6PSJ Þ H J �@��á H N : u[LO@ I \ÄLWV H BS߶P�Z H£H ïm: BKLW@AP < ß�\ >�sLOP-Pfß;L5BS@ <

>� � >���� >! " >� >��� >���� >� " >� >��� � >� �� > " >� � >%� > � ' 8� 6 : �6 �� >��� >� � >���� >� � � 1� H J H áQJM@tL H LWV H u H R�LcV�B <=Þ;j XW@ Þ H @ < ?�P < X H JrZKBKLO@tP < RvPfJWN ßm\2?�BSuA? : uÈB�LO@ <�x!!#"� � >� >� � >� � � � >��� !!#"� � >� >� � � " >� >� � ! "E�$!%"�!!&"� � >� >� � � � � >��� !!&"� � >� >� � � " >� >��� ! "E�$!&"� ã g;ä­i�å

B <=Þ ß�\ : XW@ <�x LOV H @ < ?�PfN I J H XWXM@Aß=@tuA@tL]\"?�P <=Þ @tLW@AP < LOP�Pfß=X H JrZ H LWV�BKL%LOV H (�JWXrL�L H JWNzX%P < LOV HJW@ x V�L%V�B <=Þ;j XW@ Þ H BKJ H LOV H XOBSN H ß : L�áQ@[LOVÑP I=I PfXW@[L H XW@ xf<|ä Y XW@ <�x ã g;äµimå LOV H L H JWNzX�P < LOV H

i

Page 5: 6 - UHcanic/papers/hemodynamics/hemopaper.pdfÖÇÝ Ü ÖÇÚ Ý ê ì í ò bkxwx: n @

� /6�!Ù±Ú � Ö � �!Ý�Ü 9

u H R�LsV�B <=Þ;j XW@ Þ H PSR±LOV H (�JWXrL!NzPfN H < L : N H ïm: BKLW@AP < ?�B < ß H áQJW@tLML H < @ < LOV H ?�P < X H JrZ H Þ RvPfJWNLOPPfß;L5BS@ < LWV H J H Þ=: ? H Þ (�JMXMLsNzPfN H < L : N H ïm: BKLW@AP < @ <2< P <=Þ @AN H < XW@AP < BSu6ZKBSJM@ÈBSß�u H X�� >! � >� >� ��� " �� >��� >� >� � >� ��� " �� >�� >� >� � � � " �� > ã >� >% å � ' 8� 6 : �6 �� >��� >� � >� �� >� � � 1 ã g;ä¨ìSå

a V H X H ? P <=Þ N�PfN H < L : N H ï³: BKLO@tP < @ <2< P <=Þ @AN H < XM@AP < BKu6ZKBSJW@ABSß=u H X£J H B Þ X� 68 �� >! � 476 >� � � " 476 >� � �: 6 �� >��� 476 >� � � " � 6 >� � �8 �� >�� 476 >��� � " �$ �: 6 �� >��� $ � �6 >%�� �' �: �6 � �� >� � � 476 >��� � " �: �6 >� �� >��� 476 >��� � , 476 >� �: �6 >� � " �8 � � �� > � � 4 6 >� � � � 1G @tZ³@ Þ H LOV�@AX H ïm: B�LO@AP < ß�\ � �6 B <=Þ N : utLO@ I ut\�ß�\ : 6 LOPzPfß�LOBS@ <: 68 4 6� 6 �� >! � >����� " 4 �6� �6 >� � �� >! � >����� " : 68 476� 6 �� >�� >� ��� " � >%� >� �

' �: 6 476� �6 � � >���� >� � " �: 6 476� �6 �>� � �� >! � >��� � , 476� �6 >� �: 6&>� � " : 68 � 476� �6 � � >� �� > ��� 19 @ < ? H : 6 � 8 � 476 � � 6 �I�±BSuAufLWV H L H JMN�X7@ < LOV H BS߶P�Z H�H â I J H XWXM@AP < BSJ H PSR=PSJ Þ H J �@� H â;? H I L_RvPSJLOV H!I J H XWX : J H L H JWN�{=B <�Þ XMP={=B�R�L H J~@ xf< PSJW@ <�x LOV H L H JWNzXcPSR7PfJ Þ H J �@�£LWV H-H ïm: BKLW@AP < ß H ?�PfN H X {� >%� >� � h21 ã g;ä�nfå

a V H J H RvPSJ H {ÌLOV H J H Þ=: ? H Þ X H ? P <=Þ N�PfN H < L : N H ïm: B�LO@AP < @tN I ut@ H X~LOV�B�LsLWV HÄI J H XWX : J H @AXQ?�P <³jXMLOB < L`BS?�JMPfXWX£LOV H Z H XMX H u7?�JMPfXWX j X H ? LW@AP <�ä

+ � + ,.-'/ � 1�/ÌØ ��� /¶Ú / 8±Û � ×�Ý�Ù_Ö'9� H < H â³L H â I J H XWX£LOV H X H!H ïm: BKLO@tP < Xc@ < L H JWNzX~PSR�LWV H B�Z H JOB x H Þ'ïm: B < LO@[LO@ H XcBK?�JWPSXWXcLOV H ?�JMPfXWX jX H ? LW@AP < BKuÇBSJ H B ä w�H L >:+Þ H < PSL H LWV H @ <=< H JcZ H XWX H u7JOB Þ @ : X ä � H @ < LOJMP Þ�: ? H

>4 � �>: � � "�6 g >� � >��� >�O� � �>: � >4 � � "�6 g >� � � >��� >� 1

>4 @tX~LOV H B�Z H JOB x H Þ B�â;@ÈBSu�Z H utP;? @tL]\éB <=Þ @AXcLWV HÄô ?�PfJMJ H ? LO@tP < L H JWN ô PfJ~LOV H%ô C PfJW@tPfuA@tX¡? P H R j(�? @ H < L ô ê �Kí áQV=@A?5V�LOBSî H X!@ < LWPéBS? ?�P :�< L`LOV H R§BS? LsLOV=BKL`LWV H J H X : utLW@ <=x NzPfN H < L : N H ï³: BKLO@tP <áQ@Autu H â I J H XWXs?�P < X H JrZSB�LO@AP < PKR7LWV H B�Z H JOB x H Þ N�PfN H < L : N B <�Þ'< PSL£LOV H BS? L : BSu�NzPfN H < L : N ä� V H < LWV H Z H utP;? @tL]\ I JWP (�u H >���%@tX£@ <=Þ H I6H <=Þ H < L`PSRC�LWV H L H JMN @AX£? P < XrL5B < L ä

ì

Page 6: 6 - UHcanic/papers/hemodynamics/hemopaper.pdfÖÇÝ Ü ÖÇÚ Ý ê ì í ò bkxwx: n @

�������� ÖÇÝ�Ü � ÖÇÚ� ��� ��� Ý��

� H áQ@Autu�@ < L H x JWBKL H LWV H x P�Z H J < @ <�x H ï³: BKLO@tP < X£RvJWPfN >�=� h LOP >� � >: B <=Þ H â I J H XWX`LWV H N@ < L H JMN�X-PSR�LOV H B�Z H JWB x H ÞÑïm: B < LO@[LO@ H X ä�} LÄLOV=@tX I PS@ < L!á H < H�H Þ LOP2X I6H ?�@tR�\"LOV H ߶P :=<=Þ BSJM\?�P <=Þ @tLW@AP < B�L£LOV H á~BSuAu�áQV H J H >�=� >: ä � < LOV�@AX I B I¶H J£á H áQ@AuAu6ß H BSXMX : Nz@ <�x LWV H XMLWJ H BSN�ut@ < H?�P <=Þ @tLW@AP < � >� ��� "��� "� � � >:� >

� >����� "��� "� " � >:� >! ã g;ä¨dSå

áQV=@t?5V"XWB�\³XQLOV�B�L à�: @ Þ Z H uAP³?�@[L]\/@AXcLOB <=x H < LsLWP$LOV H á~BSuAu�X : JMR§BS? H ä

,.-'/¸Ý�ÖÇÜ|Ù3���ÌØ /69 9�Ý�6Ý�5³ÝÈ× � Ü|Ù±Ö7Ú7ÝÈ×�Ý�Ù±Ö� H @ < L H x JOBKL H-H ïm: BKLW@AP < ã g³ä�k�å LWP�PSß�L5BS@ <� >� >��� � "��� "� " �� > � "�6 � >� >� � � � >� , � >:� >

� >� >� � � "��� "� � h21y \/LOBSîm@ <=x @ < LWPzBS?�? P :=< LQLOV H Þ H ( < @tLW@AP < PSR >4 á H x H L

>: � >��� � "�� "� " �� > � >4 >: �g � , >: � >:� >

� >� � � "�� "� � h21 ã g;ä��få

a V H XMLWJ H BKN�ut@ < H ? P <=Þ @[LO@tP <'< P�á@tN I ut@ H X

>: � >:� >! " �� > � >4 >: �g � � h �

PfJ {�áQJW@[LWL H < @ < ?�P < X H JrZSB�LO@AP < RvPSJWN �� >! >: � " �� > � >: � >4 � � h21 ã g;ä��få

,.-'/ 2;Ý�Ø 9�× �¼Ù�� /ÌÖ�×�Û'� /68_Û � ×|Ý�Ù_Ö� < L H x JOBKL H LOV H J H Þ=: ? H Þ (=JWXMLsNzPfN H < L : N H ïm: BKLW@AP < LOPPfß;L5BS@ <�� >! � "�6 >� >� � � >� , >: � >����� "��� "� � >:� >! " >: � >� � >� ��� "��� "�

" �� > � "�6 >� >� � � � >� , >: >� � � � >:� > " � "�6 >� � >%� > � ' 8� 6 : �6 >: � >���� >� � "��� "� 1� H R§BK? LOPSJ P : L >: � >� ��� "��� "� RvJWPSNñLOV H LOV=J H�H L H JWNzX LOV�BKL? P < L5BS@ < LOV=@tX R§BS? LWPfJB <=Þ < PSLW@A? HLOV=BKL¡LWV H J H X : utLW@ <=x L H JWNzX¡? PfN I JW@tX H LOV H u H R�L�V�B <=Þ;j XW@ Þ H PKR�LOV H XMLWJ H BSN�ut@ < H ? P <=Þ @[LO@tP < ã g;ä�dfåEä} utXWP < PSLW@A? H LOV�B�L >% @tX$@ <=Þ H�I¶H <=Þ H < L�PKR >��B <=Þ LOV H @ < L H x JWBSu~@ < ZSPfutZ³@ <=x LOV H2I J H XMX : J H ?�B <

n

Page 7: 6 - UHcanic/papers/hemodynamics/hemopaper.pdfÖÇÝ Ü ÖÇÚ Ý ê ì í ò bkxwx: n @

� /6�!Ù±Ú � Ö � �!Ý�Ü 9

ß H ?�BSuA? : uÈB�L H Þ�ä ��: JMLWV H JMN�PfJ H {=@[R±á H J H ?�BSutu�LOV H Þ H ( < @[LO@AP < X£PSR7LOV H B�Z H JOB x H Þ�ïm: B < LW@tLO@ H Xcá H( < BKuAut\�Pfß�LOBS@ <�� >! � >: �

g >4 � " �� > � >: � >4 �g � " >: �

g� >%� > � ' 8� 6 : �6 >: � >� �� >� � "�� "� 1

� H X : NzNéBSJM@�� H LOV H < P <=Þ @AN H < XW@AP < BSuA@ � H Þ {=B�Z H JOB x H Þ {�J H Þ=: ? H Þ H ïm: BKLO@tP < X�� >! >: � " �� >�� >: � >4 � � h ��� >! � >: � >4 � " �� >�� >: � >4 � � " >: � � >%� > � g ' 8� 6 : �6 >: � >���� >� � "��� "� 1p H�H I @ < Nz@ <=Þ LOV�BKL_LOV H Z³@tXW?�P : X_L H JWN P < LOV H JW@ x VmL_V�B <=Þ³j XW@ Þ H PKR¶LWV H NzPfN H < L : N H ï³: BKLO@tP <@AX£P < H PfJ Þ H JQPSR_N�B xf< @tL :�Þ H XWN�BSutu H J¡LOV�B < BSutu�LOV H PKLOV H JcL H JMN�X ä

+ ��� ,.-'/¸Ø /ÌÚ±ÛÇÜ$/ÌÚ�� � 1�/ÌØ ��� /¶Ú / 8±Û � ×�Ý�Ù_Ö'9/Ý�Ö Ú±Ý�� /ÌÖ'9�Ý�Ù_Ö � 572mÙ_Ø �� H Þ H ( < H LOV H B�Z H JOB x H Þ ? JWPfXMX j X H ?ELO@AP < BSu�Z H uAP³?�@tL]\ 4 B <=Þ LOV H ?�PSJWJ H ? LW@AP < ?�P H � ?�@ H < L B <=Þ( <=Þ LOV H @AJ£J H uABKLO@tP < XWV�@ I áQ@tLWV'LOV H < P <�Þ @AN H < XM@AP < BSu ïm: B < LW@tLO@ H X ä

a V H B�Z H JOB x H Þ B�â;@ÈBSu�Z H uAP³?�@[L]\ >4 H â I J H XWX H Þ @ < L H JMN�X�PSR£LOV H Þ @AN H < XM@AP < BSu ï³: B < LO@tLW@ H XH ïm: BKuAX

>4 � : �6: � � �6 g �: 6 �� 6 ��� �: 6 ���=� g� 6 : � � �6 �&� � ���áQV H J H : @AX7LOV H @ <=< H J±Z H XWX H u�JOB Þ @ : X_@ <�Þ @AN H < XM@AP < BKu³ZKBSJM@ÈBSß=u H X ä � H Þ H ( < H LWV H Þ @tN H < XW@tP < BSuB�â;@ÈBKu�Z H uAP³?�@tL]\ 4 � �: � � �6 g �&� � ��� B <�Þ Pfß;L5BS@ < 4 �#� 6 >4 �áQV=@t?5V"@tX£?�P < XM@AXrL H < LsáQ@tLWV2LWV H B�â;@ÈBSu6Z H utP;? @tL]\é?�PfN I P < H < LQLOJWB < XMRvPSJWN�BKLO@tP <|ä

} XW@ANz@AuABSJ�?�BSut? : uABKLO@tP </x @[Z H X

� �: � 4 � � �6 g � � � ����� 1 ã g;ä[��h�å

Y XM@ <=x LWV H X H Þ H ( < @tLW@AP < Xsá H LOJWB < XrRvPfJWN LOV H J H Þ=: ? H Þ H ïm: BKLW@AP < X¼ß�BS?5î2LOP�LOV H @AJ Þ @AN H <;jXW@tP < BSu6RvPfJWN LOPPfß�LOBS@ < � : �� ! " �� � : � 4 � � h ��� ! � : � 4 � " �� � : � 4 � � " : �$ ��%� � g ' : ( � ���� � ) ��� � 1 ã g;ä[�f��å

d

Page 8: 6 - UHcanic/papers/hemodynamics/hemopaper.pdfÖÇÝ Ü ÖÇÚ Ý ê ì í ò bkxwx: n @

�������� ÖÇÝ�Ü � ÖÇÚ� ��� ��� Ý��

+ ��� ,.-'/41±Ý�9�Ü|Ù_Û'9�×$/¶Ø �a P-Pfß�L5BK@ < LWV HcH ïm: B�LO@AP < X_áQJW@[LWL H < @ < L H JMN�X_PSRÌLOV H B�Z H JOB x H Þïm: B < LO@[LO@ H X_á H < H�H Þ LOP-X I¶H ? @tR�\LOV H B�â;@ÈBSuQZ H uAP³?�@[L]\ I JMP (�u H ��� ä � R%á H BSXMX : N H LOV=BKL/LOV H�I JWP (�u H @tXé@ <=Þ H�I¶H <�Þ H < L2PSRÄLOV HI PfXW@[LO@AP < Ç{�LOV H < LWV H Z³@AXM?�P : X-L H JWN áQ@Autu_ß H V=PfNzP x H < H P : X {ÇB <=Þ LOV�@AX!áQ@AutuUBSutXWP/u H B Þ LWP ß H @ <�x B$? P < XMLOB < L ä} L]\ I @A?�BKuÇB I=I JMP�â;@tNéBKLW@AP < RvPfJcLOV H Z H uAP³?�@[L]\ I JMP (�u H @tX� �M��� " g

� 4 �� , � �: ��� � ã g;ä[��gfå

ã ^`B x H <;j�� Pf@AX H : @tuAu H à P�áÄ{ÌX H�HÄH ä­x=ä ê gSkKíÈåEä! PSLW@A? H LOV�BKL � � g ?�PfJMJ H X I P <=Þ X�LOP-LOV H !sH á£LOP < @ÈB <$à�: @ Þ|ä � � � @AX�? uAPfX H JULOP-LWV HQôfI u :�xà P�á ô�I JWP (�u H ò @tL Þ H XM?�JM@Aß H X�LWV H à P�á PSR£B < P <³j !`H á£LOP < @ÈB <Ñà�: @ Þ J H à H ?ELO@ <=x LWV H R§BK? LÄLOV�B�L

ß=utP;P Þ @tX!BzX : X I6H < XW@tP < PSR�? H uAu : uÈBSJ H u H N H < LWX$ã§NzPfXrLOut\2J H Þ ß�uAP³P Þ ? H uAuAX å @ < I uABSXWN�B ä � L!V�BKXß H�H < J H�I PfJrL H Þ @ < ê gSh { ���Kí LOV�BKL � � � @AX±B x P;P Þ ? PfN I JWPfNz@AX H (=L±LWP`LWV H~H â I¶H JM@AN H < L5BKu Þ BKL5B ä� � � u H B Þ X!LWP � �01t�fä ! BSN H ut\S{�ã g³ät��hfå B <=Þ ã g;ä[��gfå @tN I ut\2LOV H RvPfutuAP�áQ@ <�x J H uÈBKLW@AP < XMV=@ Iß H L]á H�H < LOV H XWV=B I6H PSR³LOV H Z H uAP³?�@[L]\ I JMP (�u H Þ H L H JWNz@ < H Þ ß�\ � B <=Þ LWV H ?�PfJMJ H ?ELO@tP < ?�P H � ?�@ H < L � � g ,

, � 1� H ?�B <é< P�á Þ @ � H J H < LO@ABKL H LOV H L H JWN P < LWV H JM@ x V�L¡V�B <=Þ³j XW@ Þ H PKR|LOV H N�PSN H < L : N H ïm: B j

LO@tP < @ < ã g;ät�S��å LOPPfß�LOBS@ < LWV�BKL£LOV H JM@ x V�LQV�B <=Þ;j XM@ Þ H-H ïm: BSuAX� � g ' :�� , ã � " gfå 4: � , g ã � " gSå ' 4 1 ã g;ä[��k�å

+ ��� ,.-'/ /68_Û � ×�Ý�Ù±Ö09 Ý�Ö�Ú7Ý�� /ÌÖ'9�Ý�Ù±Ö � 5 2mÙ_Ø � Ý�Ö�× /ÌØ � 9Ù�2 × -'/ Ü|Ù±Ö09 /ÌØ 13/¶Ú8_Û � ÖÇ×|ÝÈ×�Ý�/69

� < LOJMP Þ=: ? H LOV H ã§XM?�BSu H ÞÌå ?�JMPfXWX j X H ? LW@AP < BSu7BSJ H B�� � : �!B <�Þ LWV H NzPfN H < L : N ß�BSX H Þ P < LOV HB�Z H JOB x H Þ Z H uAP³?�@tL]\�� ��� 4 B <�Þ áQJW@[L H LWV HéH ïm: BKLO@tP < X%áQV=@A?5V Þ H XW? JW@tß H ? P < X H JMZKBKLW@AP < PSRN�BSXWXsB <=Þ NzPfN H < L : N � �� ! " � �� � h �� �� ! " �� � � �� " � $ �&%� � , g��� N�� '�� � 1 ã g;ä[��imå

a P%? uAPfX H LOV H XM\³XML H N�{mLWV H£I J H XWX : J H L H JWN < H�H Þ X�LOPÄß H X I¶H ? @ ( H Þ|ä�a V=@AX_@AX_áQV H J H LOV H Þ @AXrL H <³jXW@tß=@Aut@tL]\2PSR�LWV H ß=utP;P Þ Z H XWX H uAXÄ? PfN H X!@ < LWP I uÈB�\ ä � < LWV=@AX I B I6H J¼á H : X H LWV H$ô @ <�Þ H�I¶H <=Þ H < LJW@ <=x N�P Þ H u ô ãWê � { ��n { ����íÈåEäèa V=@AXzNzP Þ H uc?�B < ß H PSß�L5BS@ < H Þ RvJMPfN LOV H ! B�Z³@ H J H ïm: BKLW@AP < Xê ���Kí RvPSJ H uABSXMLW@A?�N H N�ß=JOB < H BKR�L H J-BSXWX : Nz@ <=x LWV�BKL-LWV H P < u[\"RvPSJW? H$H â H JML H Þ ß�\�LOV H à�: @ Þ LWPLOV H Z H XMX H uÇá~BSuAutX£@AXcLOV H%I J H XMX : J H PSR±ß=utP;P Þ ã§@ xf< PfJM@ <=x XMV H BSJQXrLOJ H XWX å B <�Þ LWV�BKLsuAP <�x @tL :=Þ @ < BSuÞ @tX I uABS? H N H < LWXsBSJ H < H x uA@ x @Aß�u H ä±a V H J H X : u[LO@ <�x ãvXMLOBKLO@t? å H ïm: B�LO@AP < @tX

% ã�� å ��� 6 � � �� 6 ��� � , � ��

Page 9: 6 - UHcanic/papers/hemodynamics/hemopaper.pdfÖÇÝ Ü ÖÇÚ Ý ê ì í ò bkxwx: n @

� /6�!Ù±Ú � Ö � �!Ý�Ü 9

áQV H J H � 6 @AX£LOV H :=< XMLOJ H XMX H Þ ã§?5V�BSJWBS? L H JM@AXMLW@A? å ? JWPfXMX j X H ?ELO@tP < BSuÇBSJ H BzB <=Þ � 6 @AXcLWV HÄH uABSXMLW@A? j@tL]\"?�P H � ? @ H < L�ã I JWP I PfJrLO@AP < BSu�LOP/LWV H � P :=<�x ð­X-NzP Þ=: u : X åEä-a V�@AX x @[Z H X!uA@ < H BSJ`J H uÈBKLW@AP < XMV=@ Iß H L]á H�H < LOV HI J H XMX : J H B <�Þ JWB Þ @ : X-PSR~B'Z H XMX H u äa P2@ < ?�u :�Þ H LOV H R§BK? L-LOV=BKL-LOV H Z H XWX H u�JOB jÞ @ : X�?5V�B <=x H X�XWuAP�á H J�BKL�V�@ x V H J I J H XMX : J H X�ã < P < ut@ < H BSJ�J H X I P < X H {�X H�H�H äµx=ä ê d�íÈå @ < LWJWP Þ=: ? HI BSJWBSN H L H J��¸B <�Þ"Þ H ( < H % ã � å � � 6 � � �� 6 � � � , � � ã g;ä[��ìfå

áQV H J H ��� �~Þ H XW? JW@Aß H X < P < ut@ < H BSJÇXMLOJ H XMX j XrLOJWBS@ < J H X I P < X H ä w BKJ x H �Ñã���� � å ? PfJWJ H X I P <�Þ XLOP XMLO@�� á~BSutuAX ä � L/ácBKX/J H I PfJrL H Þ @ < ê ��� { gShKí LOV�B�L� � g I JWP�Z³@ Þ H X'B ô x P;P Þ (=L ô áQ@tLWVH â I¶H JM@AN H < L5BSu Þ BKL5B ä

o BS?5V²PSRcLWV HéI BKJOBSN H L H JWX%@ < ã g;ä[��ìfå ?�B <¸Þ H�I¶H <�Þ P < èB <�Þ ! ä � < ê n { iKí LWV H � P :=<=x ðµXNzP Þ=: u : X Þ H I6H <=Þ X�P < ¸LWP�BS? ?�P :=< L%RvPfJ-LOV H ?5V�B <=x H @ < LOV H�H uÈBSXrLO@A? @tL]\ I JWP I¶H JrLO@ H X%PSRcLOV H?5V�B <�< H uÌácBKuAu�@ < ?�BKX H X�áQV H < B < H <=Þ P�ZKBSXM? : uABSJ I JWPfXrLOV H XW@AX�@AX�@ < XML H JML H Þ @ < LOV H Z H XWX H u ä � < ê kKíLOV H ? P H�� ? @ H < L � 6 Þ H I6H <=Þ X¡P < ߶PSLWV /B <=Þ ! LOP�BS?�? P :=< L�RvPfJULOV H R§BS?EL�LWV�BKL�LOV H XrLO@�� < H XWX�PSR? H JMLOBS@ < I JWPfXrLOV H X H Xzã§X H utR j H â I B <=Þ @ <=x XML H < LOX åsÞ H�I¶H <=Þ X!P < LWV H XrLOJWBS@ < B <=Þ @tX¼BR :=< ? LW@AP < PSRLO@tN H ê gSg�í�ä � < LWV=@AX I B I¶H Jcá H XWV�BSutu|BSXMX : N H LOV=BKL � 6 B <=Þ � BKJ H ? P < XMLOB < L ä�a V H :=< XMLOJ H XMX H Þ?�JMPfXWX j X H ? LW@AP < BSuÇBSJ H B � 6 áQ@AuAu6ß H BKXWX : N H Þ ? P < XMLOB < L H â;? H I L¼@ <"9 H ?ELO@AP <�ì áQV H J H á H XrL :=Þ \LOV H @ <�à�: H < ? H PKR±Z H XWX H u�L5B I6H JW@ <�x P < XWV=P³?5îéRvPfJMNéBKLW@AP <�ä_a V H J H � 6 áQ@Autu�ß H B$R :�< ? LW@AP < PSRCB <=Þ XM\³XrL H N ã g;ä[��imå @AXcLWV H <�< P <³j V=PfNzP x H < H P : X ä� H < P�á V�B�Z H B ? uAPfX H Þ XM\³XML H N PKR I BSJMLW@ÈBSu Þ @ � H J H < LO@ABSu H ïm: BKLW@AP < X x @tZ H < ßm\)ã g;ä[��imå B <=Þ

ã g³ät��ìSå1ä � H áQ@AuAu�X H H @ < 9 H ? LW@AP <²i�ät� LWV�BKL LWV=@AX Xr\³XML H N @AX�XMLOJM@A?ELOut\ÑV�\ I6H JW߶PfuA@t?�áQV H < H Z H JLOV H ? JWPfXMX j X H ?ELO@AP < BSu`BSJ H B�@AX I PfXW@[LO@[Z H ä � H áQ@AuAu I JWP�Z H LOV�BKLzLOV�@AX?�B < ß H xf: BSJWB < L H H Þ @ <LOV H J H x @tP < PSR¡XWNzP;PKLOV à P�áeáQV H < H Z H J%LOV H @ < @tLW@ÈBSu±B <=Þ ß¶P :=<=Þ BSJM\�? JWPfXMX j X H ?ELO@tP < BSu�BKJ H B'@tXx J H BKL H J�LWV�B < � H JWP)B <�Þ LOV H ߶P :=<�Þ BSJM\ÑZ H uAP³?�@[L]\æã I : uAXWBKLO@tu H Z H uAP³?�@tL]\ I JMP (�u H P < LWV H @ < u H Lã I JWP�â;@AN�BSu å ß6P :=<=Þ BSJr\ å XOBKLW@AX ( H X$? H JMLOBS@ < B I JM@APfJM@~߶P :=<=Þ X ä 9 H�H 9 H ? LO@tP <²i=ä[�fäÑ} utLWV=P :=x VLOV H J H BSJ H ZSBKJW@AP : XéL]\ I6H X"PKR�@ < @tLW@ÈBSu j ߶P :=<=Þ BKJM\²ZKBSu : H�I JWPSß=u H N�X/LWV�BKL�BSJ H PKR�@ < L H J H XML�@ <V H N�P Þ \ < BSNz@A? X�{Ç@ < LOV�@AX I B I¶H J-á H RvP³? : X%P < LOV HzI JMPfß=u H N áQV=@t?5V @tX I PfX H Þ P < LWV H X H Nz@ j@ < ( < @tL H Þ PSNéBS@ <� ���;ã� � ! å� h�� � � � !�� h�� áQ@tLOV�LWV H @ < @tLO@ABSu Þ BKLOB I J H XW?�JM@Aß=@ <=x LOV H?�JMPfXWX-X H ?ELO@AP < BSu�BSJ H B'B <�Þ N�PfN H < L : N ã§B�â;@ÈBSu7Z H uAP³?�@tL]\ å B <=Þ LOV H ߶P :=<�Þ BSJM\ Þ BKLOB)ã§P < LOV Hu H R�L H <=Þ PSR7LOV H Þ PSNéBS@ <Ìå I J H XM?�JW@tß=@ <�x LWV HÄI : utXOBKLW@Au H à P�áJOB�L H ä

a V=@AX I JWPfß=u H Nñ@AX�á H utu j I PfX H Þ B <=Þ á H áQ@Autu~XML :=Þ \¸LWV H ?�P <=Þ @tLW@AP < X�P < LOV H @ < @[LO@ÈBKu¡B <=Þ߶P :=<=Þ BKJM\ Þ BKL5B%LOV�BKL xf: BSJWB < L H H ß=utP;P Þ�à P�áÊáQ@tLWV=P : L~XWV=P³?5îácB�Z H RvPSJWN�BKLO@tP <|ä � < LOV H < H â³LX H ? LW@AP < á H (=JWXML I JMP�Z H B�LOV H PfJ H N áQV=@t?5V I JMP�Z;@ Þ H X$X : � ?�@ H < Lz?�P <=Þ @tLO@tP < X P < LWV H @ < @[LO@ABSuB <=Þ ß6P :�<=Þ BSJr\ Þ B�L5B"LWV�BKL @tN I ut\�LWV H/H â;@tXML H < ? H PKRsB�XWNzP;PKLOV XMPfu : LO@AP < RvPfJ�B�V�\ I¶H JMß6PSuA@A??�P < X H JMZKBKLO@tP < uÈB�á ä�a V HÄI JMP;PSR±J H Z H BSuAX£LOV H ?�P <=Þ @tLO@tP < XcáQV=@t?5V < H�H Þ LOPß H XOBKLW@AX ( H Þ RvPfJcLOV HH â;@tXML H < ? H PSR`B�XWNzP;PKLOV à P�á B <=Þ I JWP�Z³@ Þ H X$LOV H L H ?5V < @ ïm: H X < H ? H XMXOBSJr\èLWP H XrLO@AN�BKL H (�JWXrLXWV�P;?5î RvPfJMNéB�LO@AP < RvPfJULOV H Þ BKL5B-LOV�B�L Þ P < PSL�XOBKLW@AXrR�\ LOV H ? P <=Þ @[LO@AP < X_RvJWPSNeLOV H LWV H PfJ H N ä � HáQ@Autu6X H�H LOV=BKL£LOV H-I : uAXWBKLO@tu H à P�á JOB�L H ߶P :=<=Þ BKJM\ Þ BKL5B�L]\ I @t?�BSutut\�u H B Þ LOP$XWV�P;?5îéRvPSJWN�BKLO@tP <|ä^`P�á H Z H J�{�RvPfJ�LWV H Þ BKLOB�?�PSJWJ H X I P <=Þ @ <=x LOP)B�V H BSu[LOV�\ @ <=Þ @[Z;@ Þ=: BSu {3(�JMXML$XMV=P³?5î�RvPfJMNéBKLW@AP <P³?�? : JWX±á H utumP : LOXM@ Þ H LWV H Þ PSNéBS@ <ÄÞ H XM?�JW@tß=@ <�x B < \%X H ? LW@AP < PSR�LWV H V : N�B < ?�@AJM? : uABKLOPSJM\-Xr\;XrL H Nã g³ä�� N H L H JWX£RvJWPSN LOV H @ < u H L£ß¶P :=<=Þ BKJM\ åEä¡9 H H 9 H ? LW@AP <2i=ä

Page 10: 6 - UHcanic/papers/hemodynamics/hemopaper.pdfÖÇÝ Ü ÖÇÚ Ý ê ì í ò bkxwx: n @

�������� ÖÇÝ�Ü � ÖÇÚ� ��� ��� Ý��

� � �!Ù_Ù7× -�2 5mÙ����Ä× -'/ � /¶Ö'/ÌØ � 5�Ø /69�Û'5�×� < LOV=@tX£X H ? LO@tP < á HÄI JMP�Z H B LOV H PfJ H N áQV=@t?5V I JMP�Z;@ Þ H X£? P <=Þ @[LO@tP < X :=<�Þ H J£áQV=@t?5V"B < @ < @tLW@ÈBSu j߶P :=<=Þ BKJM\�ZKBSu : H�I JWPfß=u H N RvPfJ-B/Xr\;XrL H N PSR�L]á~P ïm: BSXM@Aut@ < H BSJ¼? P < X H JMZKBKLW@AP < uAB�áQX!B Þ Nz@tLOX¼B?�P < LW@ <m: P : X-XWPfu : LO@tP <|ä%a V H B I=I JMP�BS?5VÑ@AX!XM@ANz@AuABSJ£LOP/LOV=BKLÄPSR¼ê g³��í�ä�a V H$I JMP;PSR�@tX!ß�BSX H Þ P <LOV H XML :=Þ \�PSRULOV H ß H V�B�Z³@APfJsPSR�LOV H XWPSu : LW@AP < B <=Þ @[LOX Þ H JM@tZKBKLO@[Z H BSuAP <�x LWV H ?5V�BSJWBS? L H JM@AXMLW@A? Xê �f� { ��g�í�ä a V H NéBK@ < BSXMX : N I LO@tP < @AX$LOV=BKL$LOV H XM\³XrL H N ?�B < ß H áQJW@[LWL H < @ < L H JWNzXzPKR¼LOV H���������� �������� ������������������� {=PfJ! !����"#�$�$%�&$'�(�)*���)$+ �� ä� H XrL :=Þ \�B g-,)g XM\³XML H N PSR±?�P < X H JrZKBKLO@tP < uÈB�áQX4/. "10 ã 4 å �H� h � 32�4;� ! � h ã k�ät��å

áQV H J H 4 ã ! �@ å 254 �%B <=Þ 0 <+4 � � 4 �Ä@AX-B'XMN�P³PSLOV�R :�< ? LW@AP < PSR 4 ä � H XMV�BSutuUBSXMX : N HLOV=BKL LOV H XM\³XML H N @tX XMLWJW@A?ELOu[\�V�\ I¶H JW߶Pfut@A?S{ULWV�BKL$@tX�{ULWV H J H'H â;@AXrL L]á~P Þ @tXMLW@ < ?EL H @ x H < ZKBSu : H X�{8 �76_ä � H ?�P < XW@ Þ H J£LOV H BKß6P�Z H XM\³XrL H N @ < ?5V�BSJOBK? L H JW@tXMLO@t?!ZKBSJW@ABSß=u H X

89. " 8 ã 8 ��: å 8 � � h � ã k�ä¨gSå: . " 6 ã 8 ��: å : � � h � ã k�ä�kfå

áQV H J H 8 B <=Þ :�{ÌLWV H �������;�� <��*�&�� =���-���������)�����QPfJ> !����"#�$�$?��$'�������$' =� {ÌBSJ H LOV H :=< î < P�á <R :=< ?ELO@tP < X¡B <=Þ 8 B <=Þ#6 BSJ H XWNzP³PSLOVR :=< ?ELO@AP < X�PSR 8 B <=Þ : ä ã � H < PSL H LOV=BKL¡LWV=@AX�J H Þ=: ?ELO@tP <?�B < BSu[ácB�\³X�ß H Þ P < H uAP³?�BSutut\ ä�å �Ì: JMLOV H JWNzPfJ H {!á H XWV=BSuAuÄBSXMX : N H LWV�BKL�XM\³XrL H N ã k;ät��å @tXx H <³: @ < H ut\ < P < uA@ < H BSJ {;LWV�BKLQ@AX ! D!A@CB� h B <=Þ !�D!�EFB� h @ < LOV H Þ PfN�BS@ <':=<=Þ H J`? P < XW@ Þ H JWBKLO@tP <|äC P < XM@ Þ H J|LOV H RvPfutuAP�áQ@ <=x @ < @[LO@ABSu�ß6P :�<=Þ BSJr\ j ZKBSu : H_I JWPfß�u H N P < LOV H Þ PfN�BS@ <� � �;ã� � ! å� ! �h �@ � ã ! åHG � � �

B�L ! � h < 8 � 8J6 ã� å � : �F: 6 ã� å ã hIG � � åP < �+ � ã ! å < : �FJ�ã ! � 8 å ã k�ä­i�å

áQV H J H á H V�B�Z H BKXWX : N H Þ {=áQ@tLWV=P : L£LWV H uAPfXMX£PSR x H < H JOBKuA@tL]\S{;LWV�BKL � ã hfå � h�ä � H áQ@AuAu6XWV=P�áLOV=BKL :=<�Þ H JU? H JrL5BS@ < BSXWX : N I LO@tP < X_LWV=@AX±@ < @[LO@ÈBKu j ߶P :=<�Þ BSJM\sZKBSu : H~I JMPfß=u H N+B Þ Nz@tLOX±Bã :�< @ ïm: H å?�P < LW@ <m: P : XsXMPfu : LO@AP <|äUa V H ß�BSXM@A?-V�\ I PSLWV H X H X¼BSJ H LOV H RvPSuAuAP�áQ@ <=x=äK ��� ã 9 N�P³PSLWV < H XMX£PSR_LWV H Þ BKLOB å G BKL5BL: 6 � 8J6 B <=Þ J/BSJ HNM � B <=Þ LOV H ߶P :=<=Þ BKJM\ � 2 M � äK #$� ã } I JW@APSJW@ H XMLO@tNéB�L H X åéa V H ߶P :=<�Þ BSJM\ � @AX < P <;j ?5V�BKJOBS?EL H JM@AXrLO@A? ä T"PfJ HÑI J H ?�@tX H ut\f{8 ã 8 �*: å � PO � ã ! å �Q6 ã 8 ��: å P < �+ � ã ! å B <=Þ

6 ã 8 ��: å , O � ã ! å �SR ã�T 6 �AU �AV å ��W hLG ! G T 6 ��W 8 XG UK��W : ;G V��áQV H J H R ã�T 6 �AU ��V å � h�ä

K %$� ã � < @tLW@ÈBSu Þ BKLOB åZY ã 8J6 ��: 6 å�Y�[ F @AX£ß¶P :=<=Þ H Þ B <=Þ 8 O6 ã åHGÊh {P:>O6 ã� å � h RvPfJ hIG � � 1K &'� ã y P :=<=Þ BSJM\ Þ BKL5B å~a V H Þ H�I¶H <=Þ H < ? H PSR\J/P < 8 @tX£X : ?5V�LOV�B�L � J� 8 � h21

��h

Page 11: 6 - UHcanic/papers/hemodynamics/hemopaper.pdfÖÇÝ Ü ÖÇÚ Ý ê ì í ò bkxwx: n @

� /6�!Ù±Ú � Ö � �!Ý�Ü 9

K *$� ã o @ x H < ZKBSu : H X å~a V H�H @ x H < ZSBKu : H X£XOBKLW@AXMR�\ � 8� 8 �Æh � � 6� : � h21K�� � ã C PfN I BKLO@tß=@Aut@tL]\ å�a V H RvPSuAuAP�áQ@ <=x ?�PSN I B�LO@Aß�@AuA@[L]\?�P <�Þ @tLW@AP < X£V�Pfu Þ

: 6 ã h�å � J�ã h � 8J6 ã h�åMå O � ã h�å , 6 ã 8J6 ã hfå ��: 6 ã h�åWå : O6 ã h�å � � J� ! ã h � 8J6 ã h�åWå" � J� 8 ã h � 8J6 ã h�åWå ã O � ã h�å , 8 ã 8J6 ã hfå ��: 6 ã h�åMå 8 O6 ã hfå 1

� H XMLOBKL H LOV H LOV H PfJ H N @ < BzRvPfJMN áQV=@A?5V�áQ@Autu�ß H : X H R : u±@ < I JWP�Z³@ Þ @ <=x @ < RvPfJMNéBKLW@AP < BKß6P : LLOV H J H x @AN H Xz@ < áQV=@A?5VçLOV H à P�á PSRÄß=uAP³P Þ NzP Þ H u H Þ ß�\ ã g;ä[��imå$Þ P H X < PSL H â�V�@Aß=@[LéXMV=P;?5îá~B�Z H X ä

,.-'/ÌÙ_Ø /6� � � Ô����������� ������������������ ��� ����������! "��#%$�&('*) !�+! . G h ��� -,�.,��/,0��#213���.4$���53���6 ��#7� -�458�19#: 3; ã k;ä¨gfå=< ã k;ä­imå ��$�;>,����?�A@B�C.,0D9� FEHG�#:�1���# M � ���#7���/,��. ã 8 ã ! �@ å ��:$ã ! �@ åWå �.��� -$��;"��,�. &

I Ø6Ù_Ù�2+� wÇH L � ã ! å ß H LOV H RvPfJrácBKJ Þ ?5V�BSJWBS? L H JW@tXMLW@A? H N�B < B�LO@ <�x RvJWPfN LOV H�I Pf@ < L � h � ! � h�äa V H < V�\ I PKLOV H X H X`^ k B <=Þ ^ ì @AN I u[\zLWV�BKLcLWV H J H-H â;@AXrLOXsB2ã :�< @ ïm: H å~x uAPfß=BSu M � XWPfu : LO@tP < @ <LOV H Þ PfN�BS@ < � � �;ã ! �@ å� � � ã ! å � ! � h��mä¼9 H H ê g³��í�ä ��: JMLWV H JMN�PfJ H {ÌLOV H ß H V�B�Z³@APfJ`PSR 8BSutP <=x LOV H ?5V=BSJOBS?EL H JW@AXrLO@t?= � ã ! å I BSXMXW@ <�x LWV=JWP :�x V'LOV H PfJM@ x @ < @AXQX : ?5V"LOV=BKL

� 8� ! ã ! �@ � ã ! åWåHGÊh21 ã k�ä¨ìSå

� < LOV H J H XrLÄPSR�LOV H$I JWP³PSR�á H RvP³? : X!P < LOV H XWPfu : LO@tP < @ < LOV H Þ PfNéBK@ < � � �;ã ! �@ å !��h �@ � ã ! å G G � ã ! å �mä 9 H�H � @ xf: J H k�ä[�fä � H áQ@AutuQXWV=P�á LOV�BKL�RvPfJ/B < \ (�â H Þ T 6 � hB <=Þ�h � T G T 6 {ÌLOV H�M � < PfJMN PKRULOV H XWPSu : LW@AP < P�Z H J`LOV H Þ PfN�BS@ < "J � �;ã ! �@ å h#G ! GT*�@ � ã ! å G G � ã ! å � @AX7߶P :=<=Þ H Þ @ <=Þ H�I¶H <�Þ H < LOu[\ÄPSR T%{ < BSN H ut\S{ Y ã 8 ��: å�Y [LKBMONQP�R G M ã�T 6 å {áQV H J H-M ã�T 6 å � h @tX`@ <=Þ H�I¶H <�Þ H < L-PSR h � T G T 6 ä � R�LOV H J H�H â;@AXrLOX!B x uAPSß�BSu M � XWPfu : LO@tP < {@tLQV=BSX£LOPXOBKLW@AXrR�\éLOV�@AX M �¡H XMLO@tNéB�L H ä

w�H Lã ! �@ å 2 J ä£a PéXrL :=Þ \�LOV H ß H V�B�Z³@APSJ`PSR_LOV H XWPfu : LO@tP < BKL`LWV H%I Pf@ < L$ã ! �@ å á H áQ@tuAuLOJWBS?5î"LWV H V=@AXrLOPfJr\�PKR�LWV H XWPfu : LO@tP < B <�Þ @[LOX Þ H JW@[ZKBKLO@[Z H BSutP <=x LWV H RvPfJMá~BSJ Þ B <=Þ ß�BS?5î�á~BSJ Þ?5V�BSJWBS? L H JM@AXMLW@A? X I BSXMXW@ <=x LWV=JWP :�x Væã ! �@ åEä�y \)V�\ I PKLOV H XW@AX ^ g B < \)RvPfJrácBKJ Þ ?5V=BSJOBS?EL H JW@AXrLO@t?ãváQ@[LOV2XWutP I¶H 6 � h�å I BSXWXM@ <=x LOV=JMP :=x V ã ! � å N : XMLs@ < L H JWX H ?EL`LWV H ß6P :�<=Þ BSJr\ � BKLsP < H B <=ÞP < u[\ P < H'I PS@ < L ò¡Þ H < PKL H LOV=BKL I Pf@ < L$ß�\ ã ã ! � å �=S�ã ! �@ åMåEä 9 @ANz@AuABSJWu[\f{ÇXW@ < ? H 8 � 6 {�B < \ß�BS?5î�á~BSJ Þ ?5V�BSJWBS? L H JM@AXMLW@A?zã�áQ@tLOV'XMuAP I¶H 8 �æhfå N : XrLQ@ < L H JWX H ? LQLOV H ?5V�BSJOBK? L H JW@tXMLO@t?-? : JrZ H �BKL~P < H B <=Þ P < u[\P < H`I Pf@ < L ò³Þ H < PKL H LWV�BKL I Pf@ < L~ß�\�ã��¡ã ! �@ å �8T�ã ! �@ åMåEä G!H < PSL H ß�\ 8J6 ã ! å LOV HZKBSu : H PSR 8 BSutP <=x LOV H ?5V�BKJOBS?EL H JM@AXrLO@A?-߶P :=<�Þ BSJM\ � ä�a V H <

8 ã ! �@ å � 8J6 ã��¡ã ! � åWå � ã k�ä�nfå:$ã ! � å � J�ã ã ! �@ å � 8 ã ã ! �@ å �=SÌã ! �@ åWå�1 ã k�ä¨dSå

�f�

Page 12: 6 - UHcanic/papers/hemodynamics/hemopaper.pdfÖÇÝ Ü ÖÇÚ Ý ê ì í ò bkxwx: n @

�������� ÖÇÝ�Ü � ÖÇÚ� ��� ��� Ý��

X

(t,x)

2(t)

(α, ξ)( β, η )

x

t

1

2D

D

� Ý � ÛÇØ / � � ÔP� a V H X : ß Þ PfN�BS@ < X � B <=Þ� � PKR±LWV H Þ PfN�BS@ < �ä

9 @ < ? H �¡ã ! �@ å G ! á H V�B�Z HY 8 Y [ F M7N P R G M ã�T 6 å ��WUã ! � å 2 J áQ@[LOV h � T � T 6 1 ã k�ä��få

! P�á XW@ < ? H ã ! �@ åHG ! { H ïm: BKLW@AP < ã k;ä¨dfå B <=Þ H XMLW@AN�BKL H ã k�ä��få @AN I ut\Y : Y [ F MONQP�R G M ã�T 6 å �<WUã ! �@ å 2 J áQ@tLWV h � T � T 6 1 ã k�ä��få

a V=@tX I JWP�Z³@ Þ H X`B :=< @tRvPfJMN M 6 H XMLO@tNéB�L H X£PKR±LWV H XWPfu : LO@tP <|ä� HI JMP;? H�H Þ ß�\ x H LWLW@ <=x':=< @tRvPfJMN H XrLO@tNéBKL H X-PSR�LWV H XWPfu : LO@tP <�Þ H JM@tZKBKLW@tZ H X-ß�\ Þ H JM@tZ³@ <�x

LOV H PfJ Þ @ < BKJM\ Þ @�� H J H < LW@ÈBSu H ï³: BKLO@tP < X�LOV�BKLcBSJ H XOB�LO@AX ( H Þ ßm\LWV H Þ H JW@[ZSB�LO@tZ H X�PSR|LWV H XMPfu : LO@AP <BSutP <=x LOV H ?5V=BSJOBS?EL H JW@AXrLO@t?%? : JMZ H X�ê �S� { ��g { g³� í ä� H (�JMXML H XrLO@tNéBKL H !A@! � ä wÇH L

� �����M @�� E R � 8� ã k�ä[��h�å

áQV H J H� @tX Þ H ( < H Þ ßm\ � �� : � , �6 , 8 � 8� : 1 ã k�ä[�f��å

a V H < P < H ?�B <ÑÞ H JM@tZ H LWV H RvPfuAutP�áQ@ <=xA� G-o áQV�@A?5VÑ@AX-XOB�LO@AX ( H Þ ß�\ � BKuAP <=x LWV H ß�BS?5î�á~BSJ Þ?5V�BSJWBS? L H JM@AXMLW@A?MPO§ã ! å � 8 áQV H J H 8 @tX£?�P < XrL5B < L

� �� !� � �� ! " 8 ã 8 ��: å � �� � , � � M @�� E R � 8� 8 � � 1 ã k�ä[��gfå

a V H ? PfJWJ H X I P <=Þ @ <=x @ < @tLW@ÈBSu-? P <=Þ @[LO@AP < { x @tZ H < P < � ã ! å � 6 ã�: 6 � 8J6 ã ! åWå {�J H B Þ X � � � �� � !A@! � � � ä � H ?�B < XW@AN I ut@tR�\£LOV�@AX|ß�\ < PKLO@ <�x LOV�BKL|P < � LWV H RvPfuAutP�áQ@ <=x V=Pfu Þ X 8 O6 ã ! å � � 8� ! " 6 � 8� 19 @ < ? H � 8 � � ! � , 8 � 8 � � ²á H x H L-LOV�B�L � 8� � �

6 , 8 8 O6 ã ! å P < � äza V H J H RvPfJ H {7LWV H @ < @[LO@ABSu?�P <=Þ @tLW@AP < ?�B <�< P�áß H áQJM@tLML H < BSX

� � � � � �M E F � @ F M . R R

ã 6 , 8 å ã�: 6 � 8J6 ã ! åWå 8 O6 ã ! å 1 ã k�ä[��k�å

��g

Page 13: 6 - UHcanic/papers/hemodynamics/hemopaper.pdfÖÇÝ Ü ÖÇÚ Ý ê ì í ò bkxwx: n @

� /6�!Ù±Ú � Ö � �!Ý�Ü 9

a V H @ < @[LO@ABSu j ZSBKu : H£I JMPfß=u H N ã k�ät��gfå B <=Þ ã k;ät��kfå V�BSXsB$XWPfu : LO@tP < � áQV=@t?5V"@tX x @tZ H < ß�\

� ã ! �@ å � � �M E F � @ F M � R R 8 O6 ã�� å� ã ! � �¡ã ! �@ åWå �

áQV H J H� Í������;Î�)Í���� KÎrÍ���������� Í��;ΧÎ������� Í��;Î����� "!$#&% '�#( *),+�+.-0/)21

1� ����34��56 �37���;���������;��,89�: ;!< ;=&%;>? "=@% )�+�+A% '�#� *),+�+AB,34C

^ H J H -� >±ã�D2� � åzÞ H < PSL H X/LOV H ß�BS?5î�ácBKJ Þ ?5V�BSJOBK? L H JW@tXMLO@t? I BKXWXW@ <=x LOV�JWP :=x VÆLOV H�I Pf@ < Lã�� �8T åEä`y \"V�\ I PSLWV H XM@AXÄ^ g á H V=B�Z H LOV�B�L 6 , 8 @AX`ß6P :�<=Þ H Þ�:�< @tRvPfJMN�u[\2B�ácB�\�RvJWPfN � H JWP�{B <=Þ XW@ < ? H 8 O6 � 8 � � 8 � h ã§V�\ I PSLOV H X H Xc^ k B <=Þ ^ ìfå á H ? P < ?�u :=Þ H LOV�B�L � @AX < H Z H J � H JWP B <=Þá H Pfß;L5BS@ < B :�< @tRvPfJMN ߶P :=<=Þ PSR � B <�Þ LWV H < PSR � 8 � � <

EEEE� 8� ã ! �@ å EEEE G M ã�T 6 å � WUã ! �@ å 2 J � h � T G T 6 1

��: JMLWV H JMN�PSJ H {;á H x H L£LWV�BKLsXW@ xf< � 8� � XW@ xS< 8 O6 ã ! å � , �&1!`H â;Lsá H%H XMLW@AN�BKL H � :� ß�\ I6H JMRvPfJMN�@ <=x LOV H RvPSuAuAP�áQ@ <=x LOV�J H�H XrL H�I X ä

� × / �2Ô ã a V H XW@ xf< PSR !�E! � P < A� � ã ! åWå < G @ � H J H < LO@ÈB�L H LWV H ß6P :=<=Þ BSJr\!? P <=Þ @[LO@AP < : � J�ã ! � 8 åBSutP <=x A�5 � ã ! å B <=Þ ?�BKuA? : uÈBKL H� :� � � O � ã ! å , 6

( � J� ! " � J� 8 ã O � ã ! å , 8 å � 8� ) BKuAP <=x � � ã ! å�1 ã k�ä[��imå

! P�áÄ{�XW@ < ? H 8 � PO � ã ! å � 6 {�XW@ xf< ã !A@! � å � XW@ xf< ã 8 O6 ã ! åWå B <=Þ !�+!A@ � h {�B <=Þ ß�\ L5BKî³@ <=x @ < LWPBS? ?�P :=< LQLOV H BKXWX : N I LW@AP < � J��! GÊh {=á H x H LQLWV�BKL � :� � h P < � ã ! åEä� × / ��+ ã a V H XM@ xf< PSR !�E! � @ < J å < 9 @ < ? H : @AXÇ? P < XMLOB < L�BSutP <=x LOV H RvPfJrácBKJ Þ ?5V=BSJOBS?EL H JW@AXrLO@t?�á HV�B�Z H :$ã ! �@ å �S: ã ã ! �@ å � SÌã ! � åWå {;WUã ! �@ å 2 J {�áQV H J H S�ã ! �@ å �5 � ã ã ! �@ åWå1ä�a V H J H RvPfJ H� :� ã ! �@ å � � :� ! ã �=S å � � ã ! �@ å " � :� ã �=S å � S� ã ! �@ å � ã O � ã ! å , 6�å � :� ã �=S å � � ã ! �@ å 1a P Þ H L H JMN�@ < H LOV H XW@ xf< PKR � : � � @ < J á H (�JWXrL < PSLO@t? H LOV�BKL PO � , 6 �æh B <=Þ !�E! � ã � S å � h�ä��: JMLWV H JMN�PSJ H {KRvJWPfN+LOV H Þ H ( < @[LO@AP < PSR � ã ! �@ å á H X H�H LWV�BKL Þ H ?�J H BSX H X¡BSX é@ < ?�J H BSX H X {B <=Þ XWP � � � GÊh;ä�a V H J H RvPfJ H {Ì@ <� J á H V�B�Z H XW@ xf< � :� � h21� × / � � ã a V H#M 6 H XMLW@AN�BKL H PSR � : � � @ < J å < w�H LGF � ��H M @�� E R � :� áQV H J H ! H!A@ � �D N D !�D!�@ 1��:=< ?ELO@AP < F"XOBKLW@AX ( H X£LOV H RvPSuAuAP�áQ@ <=x � G-o BSutP <=x LWV H ?5V�BSJOBK? L H JW@tXMLO@t?H O � 6

�IF� ! � , � N H M @�� E R � 6� : F �

��k

Page 14: 6 - UHcanic/papers/hemodynamics/hemopaper.pdfÖÇÝ Ü ÖÇÚ Ý ê ì í ò bkxwx: n @

�������� ÖÇÝ�Ü � ÖÇÚ� ��� ��� Ý��

B <=Þ @ < @tLO@ABSu�?�P <=Þ @tLO@tP < F±ã � S å � � H M @ M � � � R � E M � � � R%R !AE! � ã �=S å�x @tZ H < P < � ã ! å B�Lcã ã ! �@ å �=S�ã ! �@ åMå 1y \'@ < L H x JOBKLW@AP < á H x H L

F±ã ! � å � � H M @ M � � � R � E M � � � R R !�E! � ã �=S å�$ã ! � å � ã k�ä[��ìfå

áQV H J H

������������� 1�1 6

�����E�� ;'& ��4% �+ % !< ��.% +�+ -�/� 1

1� Í��SÍ�37� 56 Í�34���=ΧÎ(����Í�� ���EΧÎ�� 8 ;'& ;=&% >? ;=&% � +�+ % !< ��.% +�+ B 37�QÍ���º�����Î

áQV H J H A� >±ã D � å @tX7LWV H RvPfJMá~BSJ Þ ?5V�BSJWBS? L H JW@tXMLW@A? I BSXWXM@ <=x LOV�JWP :=x V�LOV H~I Pf@ < L~ã �=S å1ä_9 @ < ? H� 6 � � : � h ã§V�\ I PSLOV H XW@tX!^ ìSå B <�Þ � : � � � h P < � ã ! å ã 9 L H�I ��å á H X H�H LOV�BKL �$ã ! � å @tX< H Z H J � H JWP ä�a V H :�< @tRvPfJMN H XMLW@AN�BKL H RvPSJ � : � � �P < J RvPSuAuAP�áQX~RvJMPfN Vm\ I PSLOV H XW@tXs^ g {�B <=ÞRvJWPSN LWV H :�< @tRvPfJMN H XrLO@AN�BKL H X~PKR 8 { : B <=Þ � 8 � � "@ < JÇä�a V=@AX¡?�PfN I u H L H X¡LWV H¼I JMP;PKR ä� < LWV H < H â³L�X H ?ELO@tP < á H XWV�BSutu : X H LWV H2H XMLW@AN�BKL H X I J H X H < L H Þ @ < LWV H BSß6P�Z H�I JWP³PSR`LWPÞ H L H JMN�@ < H LWV H LW@AN H B <�Þ LOV H uAP³?�BKLW@AP < PSR-LOV H (�JWXrL'XWV�P;?5î RvPfJWN�BKLW@AP < @ < LWV H NzP Þ H uQPSR

ß=utP;P Þ'à P�á ã g;ä[��imå áQ@[LOV I : uAXWBKLO@tu H ߶P :=<�Þ BSJM\2? P <=Þ @[LO@tP < P < LOV H u H R�LQß6P :�<=Þ BSJr\ ä~a V H N�BS@ <J H BSXWP < RvPfJ-áQV�\)LOV H XWPfu : LO@tP < ß=J H BSîmX Þ P�á < @AX I PSXW@tLW@tZ H @ <�à P�á JWBKL H BKLÄLWV H ß H x @ <=< @ <=x PSRH BK?5V�Xr\³XMLOPSu H áQV=@t?5V Þ P H X < PSLQXWBKLO@tXMR�\zLOV H N�BS@ < BSXWX : N I LO@tP < PSR�LOV H LOV H PfJ H N LOV=BKLcLOV H u H R�L߶P :=<=Þ BKJM\%?�P <�Þ @tLW@AP < JÄ@AX Þ H ? J H BKXW@ <�x @ < LO@AN H � J� ! G h;ä �!: J H XrLO@AN�BKL H XÇáQ@AuAumXMV=P�áÄ{fV=P�á H Z H J�{LOV=BKLÄ@ < B'V H BSutLWVm\�@ <=Þ @[Z³@ Þ=: BKu±XMV=P;?5î�á~B�Z H X < H Z H J%RvPfJMN&@ < B < \�X : ß�X H ?ELO@tP < PKR¡LWV H ß=uAP³P Þ?�@tJW? : uÈBKLWPfJM\�Xr\;XrL H N XW@ < ? H LWV H utP;?�BKLO@tP < PSR�LWV H (�JMXML-XMV=P;?5î�RvPfJWN�BKLW@AP < @AX`á H utuUP : LWXW@ Þ H LOV HI V�\³XW@tPfuAP x @A?�BKuAut\z@ < L H J H XMLW@ <=xÞ PSNéBS@ < ã g;ä­� N H L H JWX Þ P�á < XMLWJ H BSN RvJWPfN LOV H V H BSJML åEä

� Õ ���65mÝ�Ü � ×�Ý�Ù±Ö'9�2³Ù±Ø � 5³Ù±Ù_Ú�2 5³Ù��� < LWV=@AX¡X H ?ELO@tP < á H!I J H X H < L£B Þ H LOBS@Au H Þ B < BSu[\;XM@AX�PSR|LWV H!H ïm: B�LO@AP < X-ã g;ät��imå�Þ H XW? JW@tß=@ <=x ß=uAP³P Þà P�á @ < ?�PSN I ut@ÈB < L£Z H XWX H utX ä¼9 @ < ? H LWV H�H ïm: BKLO@tP < X¼BSJ H ïm: BSXW@tuA@ < H BSJ {�@tLs@AX < PSL`?�u H BSJsB I JW@tPfJW@LOV=BKL¼LWV H Xr\;XrL H N&@AX¼BSutá~B�\³X¼V�\ I6H JW߶PfuA@t? ä � <Ñ9;: ß=X H ? LW@AP <�i=ät� á H Þ H JW@[Z H LWV H ? P <=Þ @[LO@tP < XsP <LOV H @ < @tLW@ÈBSu~B <=Þ ß6P :�<=Þ BSJr\ Þ BKL5B�LOV=BKL xf: BSJWB < L H�H XMLWJW@t? LzV�\ I¶H JMß6PSuA@A? @tL]\ ä a V H ?�P <�Þ @tLW@AP < XBSJ H ïm: @tL H J H BSXWP < BSß=u H <LOV H ? JWPfXMX j X H ?ELO@tP < BSu~BSJ H B�PSR£LOV H Z H XWX H u£@ < @[LO@ABSuAu[\�B <=Þ P < LOV H u H R�L߶P :=<=Þ BKJM\'XMV=P : u Þ'< H Z H Jsß H-H ï³: BSu|LOP � H JWP�B <=Þ LOV H-I : uAXWBKLO@tu H Z H utP;? @tL]\ I JWP (�u H ã I J H XM?�JM@Aß H ÞP < LOV H u H R�L/ã I JWP�â;@AN�BSu å ß6P :�<=Þ BSJr\ å N : XrL�XWBKLO@tXMR�\�? H JrL5BS@ < B I JW@tPfJW@�߶P :=<=Þ X ä � H áQ@tuAu�X H HLOV=BKL�LWV=PfX H B I JW@tPfJW@�߶P :=<=Þ X�áQ@AuAu�ß H XOB�LO@AX ( H Þ @ < B�V H BSu[LOV�\ @ <=Þ @[Z;@ Þ=: BSu�XM@ < ? H LOV H ß=uAP³P Þà P�á Z H uAP³?�@[L]\ @AXL]\ I @A?�BKuAut\ N : ?5VÆXWN�BSutu H J LWV�B < LOV H X I¶H�H Þ B�L�áQV=@t?5VÆXW@ xf< BSutX I JWP I B x BKL HLOV�JWP :=x V¸LOV H BSß Þ Nz@ < BKu¡BKPfJMLOB ä !`H â;L$á H @ < Z H XMLW@ x B�L H LWV H à P�á J H x @AN H X @ < áQV=@A?5V XMV=P;?5îá~B�Z H X < H Z H J RvPfJMN ä � H'I J H X H < LzLWV=PfX H J H X : utLWX @ <è9³: ß=X H ? LW@AP < i=ä�g;ä � @ < BSuAu[\f{7@ <è9;: ß�X H ? jLO@tP < i=ä­k á H XMV=P�á LOV�BKL I : uAXOB�LO@Au H Þ BKLOB)áQ@tuAu~L]\ I @t?�BSutut\ x @[Z H JW@tX H LOPÑXWV=P³?5î²RvPfJWN�BKLW@AP < @ <B'X H N�@ j @ < ( < @tL H ? PfN I uA@ÈB < L¼Z H XMX H u¡ß : L-LOV H uAP³?�B�LO@AP < PSR�LOV H (�JMXML%XWV=P³?5î�RvPfJMNéBKLW@AP < @AX!á H uAuP : LWXW@ Þ H LWV H!I V�\³XW@tPfuAP x @A?�BKuAut\ @ < L H J H XrLO@ <=x Þ PfN�BS@ <|ä � H Þ H JW@tZ H B < H XMLW@AN�BKL H áQV=@A?5V I J H Þ @A? LWXXWV�P;?5î2RvPfJWN�BKLW@AP < uAP³?�B�LO@AP < B <=Þ LO@tN H {¶B <=Þ @ <�9 H ? LO@tP <)ì XWV=P�á LOV�B�L`LWV H \�BSJ H @ < H â;? H uAu H < LB x J H�H N H < LQáQ@[LOV'LOV H <m: N H JM@A?�BKu|XW@tN : uÈB�LO@AP < X ä

��i

Page 15: 6 - UHcanic/papers/hemodynamics/hemopaper.pdfÖÇÝ Ü ÖÇÚ Ý ê ì í ò bkxwx: n @

� /6�!Ù±Ú � Ö � �!Ý�Ü 9

9 @ < ? H @[L�á~BSX XMV=P�á < @ < 9 H ? LO@tP < g LWV�BKL�LOV H XMP : JM? H L H JWN @AX�PSR£P < H PfJ Þ H J�PKRQNéB xS< @ jL :�Þ H XWN�BSutu H JcLWV�B < LWV H H � H ? LOX¼PSR < P < uA@ < H BSJ`B Þ Z H ? LW@AP < {6LOV H�H XrLO@tNéBKL H X`PSRULOV H (�JMXML-XMV=P;?5îRvPfJMNéBKLW@AP < BSJ H PSß�L5BS@ < H Þ áQ@tLWV�LOV H � H JWP�XWP : JM? H L H JMN ã§@ < Z³@AXM?�@ Þzà P�á å1ä�a P XM@AN I uA@[R�\�LWV H ?�BSu j? : uÈBKLW@AP < X H Z H < R : JrLOV H J�{³á H BSuAXMP BSXMX : N H V H J H LWV�BKL�LOV H ?�P H � ?�@ H < L @ < H ïm: BKLW@AP < Xã g;ä[��imåH ïm: BKuAX � {�áQV=@A?5V�?�PSJWJ H X I P <=Þ XsLOPLOV HÄI u :=x$à P�á ã§PSJQLWV H à BKLQZ H uAP³?�@tL]\ I JWP (=u H å1ä � V�\³XW@t?�BSutut\LOV�@AX-@AX-J H BSXMP < BSß�u H XW@ < ? H Z³@AXM?�P : X H � H ? LWX�BSJ H N�PSXML I JMP < P :=< ? H Þ @ < LWV H RvPfJWN�BKLO@tP < PSR�LOV Há~BSuAu�߶P :=<=Þ BKJM\)uÈB�\ H J ä � < Z³@AXM?�@ Þ�à P�á áQ@tuAu�V�B�Z H < P�߶P :=<�Þ BSJM\)uAB�\ H J {UB <�Þ LOV H J H RvPfJ H�I u :�xà P�áÊ@AX¡B I=I JWP I JM@ÈBKL H @ < LWV�BKL¡?�BSX H ä � H¼I Pf@ < L¡P : L�LOV�BKL¡LOV H X H XW@AN I ut@tR�\³@ <=x BSXMX : N I LW@AP < X¡BSJ Hx Pf@ <=x LOPß H : X H Þ P < ut\/@ < LOV=@tX£X H ?ELO@tP < PSR±LWV HÄI B I¶H J ä � LsáQ@tuAu6ß H XWV�P�á < @ <"9 H ? LW@AP <"ì LOV�B�LLOV H XMV=P³?5î�RvPfJWN�BKLO@tP < H XrLO@tNéBKL H$I J H X H < L H Þ @ < LOV=@tX-X H ?ELO@tP < @tXÄ@ < B x P;P Þ B x J H�H N H < LÄáQ@tLWVLOV H <m: N H JM@A?�BSucXW@tN : uABKLO@tP < Pfß�LOBS@ < H Þ áQ@tLWVçB < P < � H JWP XMP : JM? H L H JWNëB <�Þ I V�\³XW@tPfuAP x @A?�BSuAu[\J H BSXWP < BSß=u H ZSBKu : H XsPKR '2B <=Þ ã ' � k21�gL,¸��h N�� � � ��� B <=Þ � �01t��å1ä� JM@tL H XM\³XML H Nñã g;ä[��imå áQ@[LOV � H JWPzXWP : JW? H L H JWN @ <2ïm: BSXW@tuA@ < H BSJ¡RvPfJWN

� � .� . " � h �, � �� � " �� � % O ã � å � �� � �K�� � � � hh 1 ã i=ät��å

a V H%H @ x H < ZKBSu : H XQBSJ H

8 � 4 , � �$ � % O ã�� å � 4 , � 6 �$ � 6 � 6 � 4 " � �$ � % O ã � å � 4 " � 6 �$ � 6 � ã i=ä¨gSå

áQV H J H 4 ��� � � @tXcLOV H B�â;@ÈBKu�Z H uAP³?�@tL]\ ä�a V H JW@ x VmL£B <=Þ u H R�L H @ x H < Z H ?ELOPfJMX¼BKJ H x @[Z H < ß�\

� D � � �8 � � D � � �6 � � D � � , 6 � � � D � � , 8 � 1 ã i=ä�kfå

a P : X H LWV H J H X : u[LOX¼RvJMPfN 9 H ?ELO@AP <)k á H Þ @ÈB x P < BSuA@ � H LOV H XM\³XML H N ß�\"?�BSut? : uABKLO@ <=x LWV H�� @ H jN�B <=< @ < ZSBKJW@ÈB < LWX ä w�H L 8 ß H LOV H�� @ H NéB <=< @ < ZSBKJW@ÈB < LsRvPfJQáQV=@A?5V�� 8 � D � h B <=Þ :+X : ?5VLOV=BKL�� : � D � h�ä�y \2@ < L H x JOBKLW@AP < P < H Pfß�LOBS@ < X

8 � g � � F� �� F , 4 ��: � g � � F� �� F " 4 1 ã i=ä­i�åa V H Þ @ÈB x P < BSut@�� H Þ Xr\;XrL H N J H B Þ X

89. " 8 ã 8 ��: å 8 � � h �: . " 6 ã 8 ��: å : � � h21 ã i=ä¨ìSå

� H XML :�Þ \-XWPSu : LW@AP < X�PSRmLOV H @ < @tLW@ÈBSu�߶P :=<=Þ BKJM\ j ZKBSu : HUI JMPfß=u H N P < LWV H Þ PfN�BS@ < � �;ã ! �@ å ! �h � h-G � � � áQ@[LOV'LOV H @ < @tLW@ÈBSu6B <=Þ ß¶P :=<=Þ BSJM\ Þ BKL5B x @tZ H < ß�\� < @tLW@ÈBSu Þ BKLOB < 8 � 8J6 ã å � : �F: 6 ã å �y P :=<=Þ BSJr\ Þ BKLOB < : �FJ�ã ! � 8 å � 8 " g 4������ ã ! å � ã i=ä�nfå

áQV H J H 4������ ã ! å @tXQLWV HÄI : utXOBKLW@Au H à P�á JOBKL H { 4������ 2 M � {ÌB <=Þ 8J6 ��: 6 2 M � ä � < P : J <m: N H JW@t?�BSuXW@tN : uABKLO@tP < X�{SX H�H 9 H ? LO@tP <éì {fá H : X H LWV H`I : uAXWBKLO@tu H à P�á JOBKL H PSß�L5BS@ < H Þz: XM@ <=x LOJM@ x P < PfN H LOJM@A?

��ì

Page 16: 6 - UHcanic/papers/hemodynamics/hemopaper.pdfÖÇÝ Ü ÖÇÚ Ý ê ì í ò bkxwx: n @

�������� ÖÇÝ�Ü � ÖÇÚ� ��� ��� Ý��

R :=< ?ELO@tP < X�ã � �_aså LOP (=LzLOV H"I V�\;XM@APfutP x @t?�BSu I : uAXOB�LO@Au H à P�á JOBKL H Þ BKL5B I J H X H < L H Þ @ < ê ��iSí�ä��: JMLWV H JMN�PSJ H á H XMV�BSuAu|BSXWX : N H LWV�BKL8 O6 ã åHGÊh � : O6 ã� å � h � 8J6 ã å � 8J6������ � h � : 6 ã åHG : 6���� 1 ã i=ä¨dSå

� /6� � Ø�� �'� Ô '3. �F 35�;-� )��*� � ��.��� 35 6 =$ D9����.�/,��0,� �� � ��.4$ � � � 4 ��.4$�,��/,��.�� ã i=ä¨dSå58 =��$

8 O6 ã� å � �� � � � � F � M 6 � � R� � F , 4 ã h �@ å � GÊh ��: O6 ã å � �

� � � � � F � M 6 � � R� � F " 4 ã h �@ å � � h �8J6 ã� å � � F � M 6 � � R� � F , 4 ã h � å � h ��: 6 ã� å � � F � M 6 � � R� � F " 4 ã h �@ åHG : 6���� 1

'*)���� -,�.,��/,0��# $������ ,:�� ��.��3����.� < � ã h � å � � 6 ��.4$ 4 ã h �@ å � h ) �5> �� ��; �4#: < �*� ��3,%G�. )8J6������ ,:�� ��.��3,:�3�F 3.��� ,��*� � F � M 6 � � R� � F � h &a P�B < BSut\ � H LOV H XMPfu : LW@AP < X PSRsLOV=@tX @ < @[LO@ABSu¡ß¶P :=<�Þ BSJM\ j ZSBKu : H/I JWPfß=u H N á H (�JMXMLXWV�P�á LOV�B�L:=<=Þ H J~? H JrL5BS@ < J H BSXMP < BSß=u H BSXWX : N I LO@AP < X¡P < LOV H @ < @tLW@ÈBSu�B <=Þ ß¶P :=<�Þ BSJM\ Þ BKL5BÄXM\³XML H N&ã g;ä[��imå@AX£XrLOJM@A? LWut\éVm\ I¶H JMß6Pfut@A? ä

�'� Ô � ×|Ø�Ý�Ü�× - � �6/ÌØ ��Ù35³Ý�Ü�ÝÈ× �� H @ < Z H XrLO@ x BKL H LWV H ?�P <=Þ @tLW@AP < X :=<=Þ H J-áQV=@A?5V)LOV H$H @ x H < ZSBKu : H X 8 B <=Þ 6 PSR�LOV H�� BS? Pfß=@ÈB <PSR�XM\³XrL H N ã g;ä[��imå XWBKLO@tXMR�\ 8 ã 8 ��: å � 6 ã 8 ��: å1ä � H RvP :=<=Þ LOV=BKL!LOV�@AX!Xr\;XrL H N�V�BSXÄB < @ < L H J jH XrLO@ <=x I JMP I¶H JML]\S{�XM@ANz@AuÈBKJcLOP/BzN�P Þ H u Þ H XW? JW@Aß�@ <=x ?�PfN I J H XWXM@Aß=u H @tX H < LWJWP I @t? x BSX Þ \ < BKN�@t?�X <@tR¡LOV H XM\³XML H N @AX%XMLWJW@A?ELOu[\)Vm\ I¶H JMß6Pfut@A?@ < @tLO@ABSuAu[\"B <=Þ P < LOV H u H R�L�߶P :=<�Þ BSJM\S{±LWV H < @[L�XrL5B�\³XXMLWJW@t? LOu[\�V�\ I6H JW߶PfuA@t? H Z H JM\máQV H J H @ < LOV H Þ PSNéBS@ < PSR�LOV HH â;@tXML H < ? H PSR~B'XWNzP;PSLWV�XWPfu : LO@tP <|ä��: JMLWV H JMN�PSJ H {³á H Þ H JW@[Z H LOV H ?�P <�Þ @tLW@AP < X~P < LOV H @ < @tLW@ÈBSu¶B <�Þ ß6P :�<=Þ BSJr\ Þ BKLOB�áQV=@A?5V2@tN I u[\XMLWJW@t? L$V�\ I6H JW߶PfuA@t?�@[L]\�P < LWV H u H R�L$߶P :=<=Þ BSJM\¸B <=Þ XWV�P�á LOV�B�L LOV H X H ? P <=Þ @[LO@AP < X$BSJ H ïm: @tL HJ H BSXWP < BSß=u H @tRl{�RvPfJ H â�BSN I u H {�?�P < XrL5B < L`@ < @[LO@ABSu Þ BKL5BzBSJ H ?�P < XM@ Þ H J H Þ|ä� @AJMXML < PKL H LOV�BKL H ï³: BKLO@tP < X�ã i=ä�gfå @tN I u[\ LWV�BKL2XM\³XrL H N ã g³ät��i�å ? H BKX H X�LOP ß H XrLOJW@t? LWut\V�\ I6H JW߶PfuA@t?/@tR � � h ã�LOV=@tX$?�PfJMJ H X I P <=Þ X$LOP�LWV H ZSBK? :=: N XML5B�L H @ < x BKX Þ \ < BSNz@A?�X åEä w�H L J � �;ã ! � å� h�G ! G T*� h G � � �éÞ H < PKL H LWV HH â;@AXrL H < ? H Þ PfN�BS@ < PSRcB�? P < LO@ <m: P : XB <=Þ I @ H ? H áQ@AX H�M � j XWPfu : LO@tP <|ä,.-'/ÌÙ_Ø /6� �'� + ���������� "������� ��� #: *)��(13��C.4$���5�� � ã ! å � h ,:� . �.�� �����5 �� 3� 35�,:�3�0, @B,0&0 9& <8 � PO � �76 E�& '*) �$ã h �@ å � h ,�.,��0,0��#�#7� < ��.4$ , ) �$ã ! �@ � ã ! åMå � h �. ��� #: *)�� 13��C.4$���5�� < ��� 3.�$ã ! �@ å � h � WUã ! �@ å 2 J < ��.4$>�� �3���3�F 3; ã g;ä[��imå ,:� �3�/5�, 3�0#7�"����� 35 13�#7, �,�. J &I Ø6Ù_Ù�2+� w�H L �+±ã ! å ß H BÄXWPSu : LW@AP < ? : JMZ H PSR6LOV H � G-o � �

� . � 4 ã ! �@ å�1ma V H (=JWXML H ï³: BKLO@tP <@ < ã g³ät��i�å @tN I uA@ H X¼LOV=BKL�BSuAP <�x � ±ã ! å LOV H ?�JMPfXWX j X H ? LW@AP < BSu~BKJ H B2XOB�LO@AX ( H X��

�� . � , � ! ! � �áQV H J H � � � � ! � � � � � ! " 4 � � � � Þ H < PSL H X LOV H Þ H JW@[ZKBKLO@[Z H BKuAP <=x ��±ã ! åEäÑ9;: I�I PfX H

LOV=BKL"ã ! FJ�@¶F å 2 J @tX$X : ?5VèLOV�B�L �$ã ! FJ�¶F å � h�ä a V=@tX$@AN I uA@ H X 8 � 6 � 4 ã ! FJ�@¶F å B�Lã ! FJ�¶F åEä � JWPfN LOV H Þ H ( < @tLW@AP < PKRsLWV H/H @ x H < ZKBSu : H X'ã i=ä�gfå á H X H H LOV�BKL : I LOP ã ! FJ�@¶F å LOV H@ < L H x JWBSu�? : JMZ H �5±ã ! å I BSXWXM@ <=x LWV=JWP :=x V�ã ! F �¶F å uA@ H Xcß H L]á H�H < LWV H ?5V�BSJWBS? L H JW@tXMLW@A?!? : JMZ H XLOV�JWP :=x V²ã ! F � F åEä£a V H J H RvPfJ H {�@tL H @tLOV H Js@ < L H JWX H ? LWX`LOV H ! � h B�â;@tX`PfJs@tLs@ < L H JMX H ?ELOXsLOV H u H R�L

��n

Page 17: 6 - UHcanic/papers/hemodynamics/hemopaper.pdfÖÇÝ Ü ÖÇÚ Ý ê ì í ò bkxwx: n @

� /6�!Ù±Ú � Ö � �!Ý�Ü 9

߶P :=<=Þ BKJM\ ä%9³: I=I PfX H LWV�BKL � ±ã ! å @ < L H JMX H ? LOX!LWV H @ < @tLW@ÈBSu�ut@ < H ! � h;ò|Þ H < PSL H LWV�BKL I Pf@ < Lß�\Êã h �@±ã ! F �@ F åWå � ã h �@ 6 åEä�a V H XWPfu : LO@tP < PKRsLWV H � G-o XOBKLW@AX ( H Þ ß�\ � BSuAP <=x 9��±ã ! å@AX x @tZ H < ß�\ �$ã ! F �@ F å � �$ã h �@ 6 å � N���� õF����� $ �� ��B <=Þ á H X H�H LOV=BKL �$ã ! F �@ F å � h @tR�B <=Þ P < ut\@tR �$ã h �@ 6 å � h áQV�@A?5V�?�P < LWJOB Þ @A? LWX`LWV H BSXMX : N I LO@tP < LWV�BKL!@ < @tLW@ÈBSutut\ �$ã h �@ å � h RvPfJ!BSutu äa V H XOBKN H J H BSXMP < @ <=x B I=I ut@ H X`LOP/LOV H ?�BSX H áQV H < �� ±ã ! å @ < L H JWX H ? LWX-LOV H u H R�L-߶P :=<=Þ BKJM\ äa V=@tXs? P < ? u :=Þ H X£LOV HÄI JMP;PSR ä

I Ø6Ù �ÌÙ�9�ÝÈ×�Ý�Ù±Ö �'� �� � ) �#�#:�� ,�.�G� ��.4$�,��0,��.�� �. 4 ã ! å� � K � 6 ��.4$ �. 8J6 ã å G�� ��5 ��.�F � �*�������� -�����3�C; �4�0,��.�� ) � ��58 3; �4&�� ��58 �9���0,:��� =$��

�01 , �� 8J6������ � 4 ã ! å � 8J6������ @tN I uA@ H X 8 � PO � �76 P < � � h 1 ã i=ä��fåg?1 4 ã ! å � , 8J6 ����� @tN I ut@ H X � ã ! � hfå � h21 ã i=ä��få

I Ø6Ù_Ù�2+� a P2XMV=P�áeLOV=BKL�ã i=ä­��å @tN I ut@ H X 8 � PO � � 6 á H (�JMXML < PSL H LOV�B�L�� � 6 � � ã � 6�$ å �ã�: " 8 å � i=ä�a V H J H RvPfJ H {

8 � K M . R � 6 � 4 ã ! å , �i ã�: " 8 å � K M . R � 6 � 4 ã ! å , �

i ã g 8 " g 4 ã ! åMå � 4 ã ! å , Nz@ < 8J6 ã� å 19 @ < ? H 4 ã ! å � 8J6������ á H Pfß;L5BS@ < 8 � K M . R � 6 � h�ä�9 @ANz@AuABSJWu[\f{6 � K M . R � 6 � 4 ã ! å " �

i ã�: " 8 å � K M . R � 6 � 4 ã ! å " �i ã g 8 " g 4 ã ! åWå � �

g ã k 4 ã ! å " Nz@ < 8J6 ã åWåáQV=@t?5V"@tX I PfXM@tLW@tZ H Þ�: H LOPLOV H (�JMXMLs@ < H ïm: BSuA@[L]\é@ < ã i=ä­��åEäa P2X H�H LOV=BKLzã i�ä���å @AN I uA@ H X �$ã ! � h�å � h á H (�JMXML < PSL H LWV�BKL � ã ! � h�å � h @[R�B <=Þ P < u[\�@[R: " 8 � h BKL= � ã ! å � h�äé9 @ < ? H : " 8 � g 8 ã ! � h�å " g 4 ã ! å P < � � h {Ç?�P <�Þ @tLW@AP < ã i=ä��få@AN I ut@ H X�LOV�B�L!: " 8 � h P < LWV H u H R�LQß6P :�<=Þ BSJr\ ä

� Ù±Ø�Ù35 5 � Ø � �'��� �����3� 3; ã g;ä[��imå ,:� �3�/5�, 3�0#7� ����� 35913�#7, ", )"��� ",�.,��/,0��#�$������ ã 8J6 ��: 6 å ��.4$��� -13��C.4$���5�� $����B� 4 ã ! å ��58 (�3� ��?�������

: 6 ã� å " 8J6 ã å � h ãvLOV�@AXs@AX H ïm: @tZKBSu H < L¼LWP �$ã h �@ å � hfå ã i=ä[��h�å

, �k 8J6������ � 4 ã ! å � 8J6������ 1 ã i=ä[�f��å

� /6� � Ø�� �'� � '3."� 35�;-� ) ��� ��.��� 35 6 =$�D9����.�/,��0,� �� � ��.4$ � < �����3��;>,�.�G < ) �5 �3,�; �4#7, 3,��/� < ��.��3����.�>,�.,��/,0��# $����B� < �$ã h �@ å � � 6 ��.4$ �Ñã h �@ å � h�< � � 35� � 6 ,:� ��� ��.��3�/58 ����� =$ 358����3���� 3�/,��.4��# ��58 =� < ��.4$�,��0,��. ã i=ä[�f��å 58 =D9�C,�58 �� ������� ��� 6 3#: 3,��0� 4 ã ! å �458 �� 35�,013 =$ �.��� -#: *)�� 13��C.4$���5��",:���3� �� ������� , �� � � F� � 4 ã ! å � � � F� 1�� �.��3,0$� 35�,�.�G �*�������*� �� � 3�F =$� 6 35 ��G� 6 3#: 3,��0��,:� ��. �5 $� 35 ) ;"��G�.,��0� $� ��3;"��#�#: 35 �*����. � � F� < �*��,:� ,:� 5=����� 35 58 =�����.4��19#: 9&@ � �����C.4$ �F� � =$ ,�. ����,:�-; 9$� 3# ,:��;>� ���#%��5/G� 35��*����. ��� ;"��G�.,��0� $� " )!�*� @ � 6 35 ��G� =$3E19#:�9$ 6 3#: 3,��0� & E�� �5(��� �4�C# �9���0,�#: �� �� 13���.4$���5�� $������ ��.��3,0$� 358 =$ ,�.��Q 3�0,��.�� < ��.4$ ) �5��� 6 ��#7� �� ) � 6 ��5�58 ��F��.4$�,�.�G �F � � =��#7�*��� ,�.4$�, 6 ,0$�� ��# < �� � �Q 3�0,��.�� ��.4$! F�"�"# < ����,:� ��.4$�,��0,��.�,:�-��# � ����� �9���/,:��� =$�&

��d

Page 18: 6 - UHcanic/papers/hemodynamics/hemopaper.pdfÖÇÝ Ü ÖÇÚ Ý ê ì í ò bkxwx: n @

�������� ÖÇÝ�Ü � ÖÇÚ� ��� ��� Ý��

�'� + ��±Ý�9�×$/¶ÖÇÜ$/ÑÙ�2 � � 5mÙ � � 579 �!Ù_Ù7× - 9�Ù�5mÛ�×�Ý�Ù±Ö� < LOV=@tX�X H ? LO@tP < á H : X H a V H PfJ H N k�ä[� LOP Þ H JW@[Z H LOV H ? P <=Þ @[LO@tP < X :=<�Þ H J�áQV=@t?5VzLWV H J H£H â;@AXrLOX�BXWNzP³PSLOVzXWPfu : LO@tP < PSR6LOV H @ < @[LO@ABSu�߶P :=<=Þ BSJM\ j ZKBSu : HQI JWPSß=u H N XML :=Þ @ H Þ @ < LWV=@AX I B I¶H J ä � < PKLOV H Já¡PfJ Þ X {Uá H J H I V=JOBKX H LWV HéH â�@tXML H < ? H LOV H PfJ H N"{ a V H PfJ H N k�ä[� {_@ < L H JWNzX�PSR~LOV H ï³: B < LO@tLW@ H XB <=Þ�Þ BKLOB�BSJM@AXW@ <=x @ < LOV H ß=uAP³P Þzà P�á I JMPfß=u H N NzP Þ H u H Þ ß�\�ã g;ä[��imå {³PSJ H ï³: @tZKBSu H < LOut\S{mßm\zLOV HH ïm: B�LO@AP < X�ã i=ä�ìfå5ä,.-'/ÌÙ_Ø /6� �'��� � �.��3,0$� 35 ��� ,�.,��/,0��#�13��C.4$���5���� 6 ��#7�� �458�19#: 3; ã i=ä�ìfå�< ã i=ä­n�å � � 358 �*� ,�.,���0,0��#��.4$!13��C.4$���5���$������(�9���0,:�*)�� ��.4$�,��/,��.�� ã i=ä�dfå�< ã i=ä[��h�å ��.4$(�*� ��; �����/,019,�#7,��0� ��.4$�,��0,��.��

: 6 ã h�å � 8J6 ã hfå " g 4 ã hfå, 6 ã 8J6 ã h�å ��: 6 ã h�åMå :>O6 ã h�å � g 4 O§ã h�å , 8 ã 8J6 ã hfå ��: 6 ã h�åMå 8 O6 ã hfå ã i=ä[��gfå

� �C5���� 353; �58 < #: 3� 4 ã ! å � , �i 8J6������ 1 ã i=ä[��k�å

� 3.�, ) 4 O ã ! åHGÊh � W ! � h ã i=ä[��imå��� �45��19#: 3; ��$�;>,��*����@B��.,0D9� FE �4,� � � ,:�� M � �����#7�C�0,��.4&I Ø6Ù_Ù�2+� � @tJWXrL < PSLW@A? H LOV�B�L-?�P <�Þ @tLW@AP < X ã i=ä[��h�å @AN I ut\2LWV�BKL!LWV H XM\³XrL H N&@AX!XrLOJW@t? LWut\�V�\ I¶H J j߶PfuA@t? ä � H < H â;L¡XWV�P�á LOV�BKL�BKuAu�LWV H Vm\ I PSLOV H X H X~PSR a V H PfJ H N k�ät� BSJ H XWBKLO@tX ( H Þ|ä ^Q\ I PSLWV H X H X^ � {�^ k {³^ i B <=Þ ^ n BSJ H B Þ @AJ H ?EL~? P < X H ïm: H < ? H PSR|LWV H Þ H ( < @[LO@tP < PKR|LOV H ß=utP;P Þzà P�á I JWPfß ju H N :=<=Þ H J¼? P < XM@ Þ H JOBKLW@AP <|ä ^s\ I PSLOV H XW@tX ^ g @tXsXWBKLO@tX ( H Þ ß H ?�B : X H ã i=ä[��h�å B <=Þ ã i=ä[��k�å V=PSu Þ|äT"PfJ HÄI J H ?�@AX H u[\f{�P < � ã ! å � h á H V�B�Z H

6 ã 8 ��: å , O � ã ! å � ki : , �

i 8 � ki ã 8 " g 4 ã ! åWå , �

i 8 � �g 8J6 ����� " k

g 4 ã ! å � �� 8J6������ � h21

^s\ I PSLOV H XW@tX ^ ì V=Pfu Þ X%BKR�L H JÄá HzH â I J H XWX%LOV HzH @ x H < ZKBSu : H XÄ@ < L H JWNzXÄPSR~LWV H � @ H N�B <=< @ <;jZKBSJW@AB < LOX 8 � �

i : , ki 8 � 6 � k

i : , �i 8 ã i=ä[��ìfå

LOP¼X H�H LWV�BKL � 8 � � 8 � , k � i �æh {fB <=Þ � 6 � � :I� k � i � h�ä � @ < BKuAut\S{KXM@ < ? H � J � � ! � 4 O§ã ! å Gh { a V H PfJ H N k�ä[� @AN I uA@ H X~LWV HÄH â;@AXrL H < ? H PSRUB x utPfß�BSu I @ H ? H áQ@AX H�M � j XMPfu : LW@AP <�ä� /6� � Ø�� �'����� �$�5 � � �(����5 ��#�#: 3# 13 3� � � 3. �*� �13 ���� 6 ,��5($� �� 35�,013 =$ ,�. � ��58 3; �4&0 ��.4$�>�458�19#: 3; ,�. ��; �458 ����3,019#: �G���� $�� .4��;>, ��9&-'3;"��G�,�. >� �4,:�3� �. < �53,%G�,�.4��#�#7� #: =��� =$ ��� ��� �5�,%G�,�. < ; 6 ,�.�G � ,���� �F� � =$ 4 ã ! å ,�.��"�0� 13 � ��, �� ,:�������3�C; =$>�F 13 ,�. � .,��F < ��.4$ �*����� ��� G����>�. ��� !53,%G���� �3,0$� > )���� �4,:�3� �. ,:�!,:�� 3.�058��4, 9&� ���3��;>,�.�G ������� ��� �4,:�3� �. ; 6 3; 3.�$�� ���. �� 358 =��� � 6 �� 3���C; �3�B���F < ��.4$������3��;>,�.�G �*�����Q��� 358 � ����. 6 �� 3���C; �3����� ,�.,��/,0��#�#7� <, )��*� �� � 3#: 35=���0,��. ) ��� �4,:�3�F�.",:� . �G����0, 6 < ��� � �� $�5�, 6 3. 19�(�*� �4,:�3�F�.�� ,�#�#�13 �3; �����) �5���#�#Q�0,�; 9&

���

Page 19: 6 - UHcanic/papers/hemodynamics/hemopaper.pdfÖÇÝ Ü ÖÇÚ Ý ê ì í ò bkxwx: n @

� /6�!Ù±Ú � Ö � �!Ý�Ü 9

�'��� � -ÇÙ±Ü �Q� � 13/ 2mÙ±Ø � � ×�Ý�Ù±Ö� < LWV H ?�BSX H áQV H < LOV H u H R�L%ß6P :=<=Þ BSJr\ Þ BKLOB�? PfJWJ H X I P <=Þ X�LOP2LOV H�I : uAXOB�LO@Au H à P�á JOB�L H {±BSX jX : N I LW@AP < ã i=ä[��imå PSR a V H PfJ H N i=ä�n @AX < PSL!XWBKLO@tX ( H Þ|ä¼9 V=P³?5î�á~B�Z H X!RvPSJWN ß H ?�B : X H LWV H à P�áJOB�L H V�BSXzB)uÈBSJ x H'I PSXW@tLW@tZ H x JOB Þ @ H < L äè} Xzá H XWV�BSutucX H H @ < LOV=@tXzX : ß=X H ? LW@AP < {¡LOV H LW@AN H PSRLOV H (�JWXrLXWV=P³?5î�RvPSJWN�BKLO@tP <�Þ H�I¶H <=Þ XP < LWV H � P :�<=x ðµX N�P Þ=: u : X�{UB <=Þ P < LWV H N�B xf< @[L :=Þ HPSR�LWV H Þ H JW@[ZSB�LO@tZ H PSR_LOV H I : uAXWBKLO@tu H à P�á+JOBKL H ä � < LOV=@tX¼X H ? LW@AP < á H H XMLO@tNéB�L H LWV H LW@AN H B <=ÞuAP³?�B�LO@AP < PKR~LOV H (�JMXML�XWV=P³?5î�RvPfJWN�BKLO@tP < B <=Þ ?�PfNzN H < L%P < LWV HéI V�\³XW@tPfuAP x @A?�BSuUN H B < @ <=x PSRP : J ( <=Þ @ <�x X ä9 @ < ? H LOV H%H < LW@AJ H à P�á @AX Þ JW@[Z H < ß�\'LOV H%I : uAXWBKLO@tu H à P�áá H ?�B < ?�P < XW@ Þ H JQXW@tN I u H @ < @[LO@ABSuÞ BKLOBáQV�@A?5V�BKJ H X : ?5V"LOV�BKLQLWV H ? P <=Þ @[LO@tP < XcRvJWPSN LOV H%I J H Z³@AP : X`X H ? LW@AP < ãvLWP xS: BSJOB < L H�H {ÌRvPSJH â�BSN I u H {�XrLOJM@A? LQV�\ I¶H JW߶Pfut@A?�@[L]\ å BSJ H XOBKLW@AX ( H Þ|ä � H ?�P < XW@ Þ H J£?�P < XMLOB < L ã :=< XrLOJ H XWX H ÞÌå @ < @[LO@ABSuÞ BKLOB �$ã h �@ å � � 6 � 4 ã h �@ å � h � ã i=ä[��n�åáQV=@t?5Vé@ < L H JWNzX�PSR�LWV H � @ H N�B <=< @ < ZKBSJM@ÈB < LOX�J H B Þ : 6 ã å � 8J6 ã å � g � � F� 1 � PfJULWV=@AX�X H L�PSR@ < @tLO@ABSu Þ BKLOB 8 @AXc? P < XMLOB < L H Z H JM\máQV H J H @ < LWV H J H x @AP < PSR7XWNzP;PKLOV à P�á ò LWV H ?5V�BSJWBS? L H JM@AXMLW@A? XBSJ H XMLOJWBS@ x VmL!uA@ < H X!@ <� � ���;ã ! �@ å ! � h �@ � ã ! å G � � � {6áQV H J H � ã ! å @AX¼LWV H RvPfJrácBSJ Þ?5V�BSJWBS? L H JM@AXMLW@A?= O � � 6 H N�B < BKLW@ <=x RvJMPfN ã h � h�åEä£a V H XWPfu : LO@tP < @ < J H x @AP < � � �;ã ! �@ å� ! �h � h-G G � ã ! å � {Kß6P :=<=Þ H Þ ßm\ÄLWV H u H R�L±ß6P :�<=Þ BSJr\ � � h B <=Þ LWV H RvPSJMá~BSJ Þ ?5V=BSJOBS?EL H JW@AXrLO@t? � {�@AX Þ JW@[Z H < ß�\ 4 ã ! å P < � B <=Þ áQ@tuAu Þ H Z H uAP I XMV=P;?5î"ácB�Z H X Þ�: H LOP'LOV H R§BS? L!LWV�BKL 4 O ã ! å?5V�B <�x H X±XW@ xS<|ä � < R§BS? L�{KLOV H¡I : uAX H ?�PSJWJ H X I P <=Þ @ <=x LWP`LWV H Xr\;XrLOPfu H XrL5BSJrLOX7áQ@tLOV�BsV�@ x V I PfXM@tLW@tZ Hx JWB Þ @ H < L 4 O§ã ! å � h {�áQV=@A?5V�áQ@AuAu x @tZ H JW@tX H LOPÄLOV H XWV=P³?5î$RvPfJWN�BKLW@AP < BKL�XWPSN H LO@tN H !�� {�BKL�LOV HuAP³?�B�LO@AP < � áQV H J H � � !�� � 6 ã 8J6 �*: 6 åEäa P H XMLW@AN�BKL H LOV H LO@tN H !�� á H < PSL H LOV=BKL B�L�LWV HéI Pf@ < L/ã !�� �@ � å LWV HéI BKJMLO@ABSu Þ H JW@tZKBKLW@tZ H� : � � ß=uAP�áQX : I ä%a V=@tX-P;? ? : JMXÄBKL!LOV H$I Pf@ < L¼áQV H J H LOV H Þ H < PfNz@ < BKLOPfJ �$ã ! � å @ < ã k�ä[��ìfåß H ?�PSN H X H ïm: BSu£LOP � H JWP ä a V H Þ H < PfNz@ < B�LOPfJ � ã ! � å ?�B < ß H ?�BSuA? : uÈB�L H Þ RvJMPfN H ï³: BKLO@tP <ã k;ät��nfå ßm\/J H ?�BSuAut@ <=x LWV�BKL � 6 � � :I� k � i B <=Þ LWV�BKL 8 � 8J6 H Z H JM\máQV H J H ä~a V=@AXQ@AN I ut@ H X�LOV�B�L@ < ã k;ät��nfå � H M @ M � � � R � E M � � � R%R N H M @ M � � "� M � � � R R � E M � � � R%R � � B <=Þ XWP � ã ! � å � � " �

�!�E! � ã �=S å ã ! , å 1� JWPfN H ïm: BKLW@AP < ã k�ät��imå á H X H H LWV�BKL !�E! � � K � 6 � , � �� M . RD " DD !A@! � 1¶9 @ < ? H !A@! � � h {�á H Pfß�L5BK@ <

� ã ! � å � � , kg4 O ã ! å6 ã ! , å�1 ã i=ä[��dfå

a V H J H RvPSJ H {�LWV H (�JWXrLsLW@AN H LOV H XMV=P³?5î/RvPfJWNzX£@AX H ï³: BSu|LOP

!�� � " 4 ã ! å " � � F �� � F�� 4 O����� ã ! å 1 ã i=ä[����å

I Ø6Ù �ÌÙ�9�ÝÈ×�Ý�Ù±Ö �'��� � ���3��;>,�.�G ��.��3�B��.��,�.,��/,0��#2$������ < �*� ��0,�; !�� )!�*� � 58�3� ��� �� ) �5��;"���0,��.�,:� G�, 6 3. 19� ã i=ä[����å &o ïm: BKLO@tP < ã i=ä[����å @ <=Þ @A?�B�L H X�LWV�BKL�LOV H XML H�H�I¶H J�LOV H`I : utX H {mLOV H XMP;P < H J¡B <=Þ ? uAPfX H J�LOV H XWV�P;?5îmXáQ@Autu�RvPfJWN ä p H�H < H J£B <=Þ29;< H \ Þ PSß�L5BS@ < H Þ B�XW@tN�@tuÈBSJ�J H X : utLc@ < ê ��h�í ã BSu[LOV=P :�x Véu H XWX x H < H JOBKu åEä

���

Page 20: 6 - UHcanic/papers/hemodynamics/hemopaper.pdfÖÇÝ Ü ÖÇÚ Ý ê ì í ò bkxwx: n @

�������� ÖÇÝ�Ü � ÖÇÚ� ��� ��� Ý��

a V H \ ?�PfNzN H < LzLWV�BKLLOV�@AX$ß H V�B�Z³@APfJN�B�\²ß H J H uÈB�L H Þ LOP�LWV H"I @AXMLWPfu j XWV=PKL áQV=@A?5Vè?�B < ß HV H BSJ Þ LOV�JWP :=x VçB�XrL H LOV=PfXM?�P I¶H @ < I BKLW@ H < LWX áQ@tLWV BSPfJMLW@A?/@ < X : � ? @ H < ? \S{¡ß : L < PSL@ < PKLOV H JI BKLW@ H < LWX ä�}`< PSLOV H Jc@tN I ut@A?�BKLO@tP < PSRÇP : J¡J H X : utLWXc@AX�LOV�B�L~LOV H XWV=P³?5îmX£áQ@AuAu�RvPfJMN XWP³P < H J~@tR�LOV Há~BSuAutXcPSR7LOV H Z H XWX H u±BSJ H u H XWX£JM@ x @ Þ|äUa V=@tXcáQ@Autu|BSutuAP�áÊR§BSXML H J Þ H ?�J H BSX H @ < LWV H ?�JMPfXWX j X H ? LW@AP < BKuBSJ H B �+BSXsBJ H X : utLsPSR7LOV H utP�á Þ @ABSXMLWPfuA@t? I J H XWX : J H ä� H ?�P < ?�u :=Þ H LOV=@tXsX H ?ELO@AP < ß�\2Pfß�LOBS@ < @ <=x B < H XMLW@AN�BKL H RvPfJ£LWV H utP;?�BKLO@tP < � PSR_LWV H (�JWXrL

XWV�P;?5î!RvPfJMNéB�LO@AP < @ < LWV H N�P Þ H uSPSR�ß�uAP³P Þ!à P�á�LOV=JMP :=x V-LOV H BKß Þ PSN�@ < BSufBKPfJMLOBcß H L]á H H < J H < BSuB <=Þ @Aut@ÈBS?£BKJML H JW@ H X ä_a V H`H uÈBSXrLO@t?�@tL]\ N�P Þ=: u : X � 6 N H BSX : J H Þ RvPfJ�LOV=@tX I PfJrLO@tP < PKR�LOV H BSPSJML5B-@tXPfß�LOBS@ < H Þ RvJWPfN ê ��i�í B <=Þ @tX H XMLW@AN�BKL H Þ LWPQß H � 6 � i/,!��h ��� � � � ä_y utP;P ÞÄÞ H < XW@tL]\Ä@tX�L5BSî H < LWPß H $ � ��h�ìSh � J � � � ä � H BSJ H : XM@ <=x I : utXOBKLW@Au H à P�á ߶P :=<�Þ BSJM\ Þ BKL5BQáQ@tLOV%LOV H N H BSX : J H N H < LWXPfß�LOBS@ < H Þ RvJMPfN ê ��iSí {�B I�I JWP�â;@AN�BKL H Þ ß�\�LWV H LOJM@ x P < PfN H LOJM@A?ÄR :=< ?ELO@AP < X : XM@ <=xA� BSXrL � P : JM@ H Ja JOB < XrRvPfJWN ä%} uAuÇLOV H ( xf: J H XÄ@ <)9 H ? LW@AP <�ì @ < ?�u :=Þ H LWV H ?�BSut? : uABKL H Þ B I=I JWP�â;@AN�BKLO@tP < PSR�LOV HI : utXOBKLW@Au H à P�á JWBKL H @ < P < H ?�BKJ Þ @ABS?�? \³? u H ä � H Pfß�LOBS@ < LWV�BKL2N�B�â 4 Ovã ! å P³?�? : JWX�BKL'LOV Hß H x @ <=< @ <�x PSR H BS?5V�Xr\³XMLOPSu H {ÌB <=Þ @tX H XrLO@AN�BKL H Þ LOPß HÄH ï³: BSu|LOP �fnI, ��h N�� � � � � ä�a V=@AX Þ BKLOBx @[Z H XsJW@tX H LOPLOV H ? JWPfXMX j X H ?ELO@tP < BSu7BSJ H B �$ã ! � å áQV=@t?5V�@tX£PSR_LWV H XWBSN H PSJ Þ H JsPKRUN�B xf< @[L :=Þ HBSX£LOV H :�< XMLWJ H XMX H Þ ?�JMPfXWX j X H ? LW@AP < BKuÇBSJ H B � 6 ä�a V H J H RvPfJ H { : XM@ <=x ã i=ä[����å á H Pfß�L5BK@ <

!�� � � i�hfhShfh � ��hfìSh�&1�ìL,��21­n � h21µimdS� � B <=Þ � � !�� 6 � h21µimdS��� � i�hfhfhSh � ��h�ìKh � g 1­��ì �&ã i=ä[����å

áQV=@t?5V�@AX�á H utu�P : LOXM@ Þ H B < \ I V�\³XW@tPfuAP x @A?�BSuAu[\¼J H u H ZKB < L±X : ß Þ PfN�BS@ < PSR;LOV H ?�@tJW? : uÈBKLWPfJM\¼XM\³XML H N ä� < I BKJMLO@t? : uABSJ�{�@[L�@AX�P : LOXM@ Þ H LOV H Þ PfN�BS@ < ? PfJWJ H X I P <=Þ @ <=x LOP�LWV H BKß Þ PSN�@ < BSu�BSPSJML5B%ß H L]á H H <J H < BSuÇB <�Þ @tuA@ÈBK?¼BSJrL H JW@ H X£áQV=PfX H u H <=x LWV�@tX£PSR7LOV H PfJ Þ H JQPSR ��h ?�N ä

� � Û'� /ÌØ�Ý�Ü � 5�Õ5Ö$1�/69�×�Ý ��� ×�Ý�Ù_Ö� < LWV=@AXsX H ? LO@tP < á H @ < Z H XMLW@ x B�L H XWV=P³?5î�RvPSJWN�BKLO@tP < @ < LWV H XMPfu : LO@AP < PSR�Xr\³XML H N ã g;ä[��imå£: XW@ <=x<m: N H JW@t?�BSu¼XW@AN : uÈBKLW@AP < X ä � H XWV=P�á&LWV�BKL�P : J/LWV H PSJ H LW@A?�BSu I J H Þ @A?ELO@tP < X2BSJ H @ < H â;? H uAu H < LB x J H�H N H < LsáQ@tLWV�LWV H J H X : utLWX¼Pfß;L5BS@ < H Þ�: XW@ <=xz<³: N H JW@A?�BSu�XW@tN : uABKLO@tP < X ä � < B Þ=Þ @tLW@AP < LWP�LOV H@AXMX : H XzB < BSu[\ � H Þ @ < LWV H2I J H Z³@AP : X$X H ?ELO@AP < XPSRQLOV H2I B I¶H J$@ < LOV=@tX$X H ? LO@tP < á H BSutXWP�XrL :=Þ \LOV H @ <�à�: H < ? H PSRQZ H XMX H uQLOB I¶H JW@ <=x P < XMV=P³?5î RvPfJWN�BKLW@AP <|ä � H Pfß;L5BS@ < B�X : J I JW@tXW@ <=x J H X : u[LáQV=@t?5V�XMV=P�áQXÄLWV�BKL-LOB I6H JW@ <=x PSR�LOV H Z H XWX H u I PSXML I P < H X-XWV=P³?5î�RvPfJMNéBKLW@AP <�ä � HI JWP�Z³@ Þ H B <BSJ xf: N H < L£RvPfJcáQV�\'LOV=@tX£@AX£LOV H ?�BSX H äa V H <m: N H JM@A?�BSumXWPfu : LO@tP < X�á H J H PSß�L5BS@ < H Þ%: XM@ <=x LOV H � @t?5VmLWN�\ H J7L]á¡P!XrL H�I w B�â � H <�Þ JWP �N H LOV�P Þ {=BSX Þ H XM?�JW@tß H Þ @ < ê ��k�í�ä � H : X H 9 LOJWB <=x X I uA@tLMLO@ <=x LOP Þ H BSu|áQ@tLWV2LWV H XWP : JW? H L H JWN ä� H Þ H XM?�JM@Aß H LWV H <m: N H JM@A?�BSu�N H LOV=P Þ @ <¸9³: ß=X H ? LW@AP < ì³ät� {Çá HéI J H X H < L LOV H J H X : u[LOX%J H j

uÈB�L H Þ LOPLOV H XMV=P;?5î'RvPfJMNéB�LO@AP < @ < ?�PfN I uA@AB < L£Z H XWX H uAXsáQ@tLOV"?�P < XML5B < L :=< XrLOJ H XWX H Þ JWB Þ @ : X`@ <9;: ß�X H ?ELO@tP <Ñì;ä�g B <=Þ B < BSut\ � H XWV=P³?5î"RvPfJMNéB�LO@AP < @ < L5B I¶H J H Þ ? PfN I uA@ÈB < LQZ H XWX H utX%@ <)9;: ß�X H ? jLO@tP <"ì;ä­k�ä

� � Ô ,.-'/¸ÖÇÛ'� /ÌØ�Ý�Ü � 57� /�× -ÇÙ_Ú� H áQJM@tL H�H ïm: BKLO@tP < X"ã g³ät��i�å @ < ?�P < X H JrZKBKLO@tP < RvPfJWNëB <=Þ XMPfutZ H : XW@ <=x LOV H L]á¡P j XrL H�I w B�â j� H <=Þ JMP � N H LOV=P Þ|ä � H L5BSî H @ < LWP BK?�?�P :=< L�LWV�BKL � 6 ?�B < Þ H�I¶H <=Þ P < ÊB <=Þ áQJM@tL H LOV H

gSh

Page 21: 6 - UHcanic/papers/hemodynamics/hemopaper.pdfÖÇÝ Ü ÖÇÚ Ý ê ì í ò bkxwx: n @

� /6�!Ù±Ú � Ö � �!Ý�Ü 9

H ïm: B�LO@AP < XQ@ < ?�P < X H JrZKBKLO@tP < RvPfJWN BSX£RvPfuAutP�áQX���! 4 " �� 0 ��� � ã ì;ät��å

áQV H J H

4 � ( �� ) � 0 ã 4 å � �� � �� " � F �� M ��� � R � �� F � � � � � � � 6 � � ã ì;ä¨gSå

B <=Þ

�sã 4 å � h

, g �� N�� � � " � F �� M ��� � R � �� F � � � � � � �>O 6 � 1 ã ì;ä�kfå

a V H%H @ x H < ZKBSu : H X£PSR7LOV H � BS? Pfß=@AB < PSR 0 BSJ H

8 � � � � �� � ã , ��å � � � � � " � 6 �g $ � �� 6 � � � 1 ã ì;ä­i�å

� V H < � 6 � � 6 ã� å @tXZKBSJM@ÈBSß�u H {�LWV H à=: â R :=< ?ELO@AP < B <�Þ LOV H XMP : JW? H L H JMN BSuAXMP Þ H I6H <=ÞP < B <=Þ LWV H XM\³XrL H NëPKRQ?�P < X H JrZSB�LO@AP < uÈB�áQX$@AX < P�uAP <�x H J V�PfN�P x H < H P : X ä � H XMPfutZ H B <@ < @tLO@ABSu£ß¶P :=<=Þ BKJM\ ZKBSu : H�I JWPfß=u H N Þ H ( < H Þ P < LWV H ?�PfN I : LOBKLO@tP < BSu Þ PSNéBS@ < � ã h ��� åáQ@tLWVzLWV H @ < @[LO@ÈBKu�?�P <=Þ @tLW@AP < X � � �$ã � h�å � � 6 B <=Þ ��� �Ñã� � h�å � h {³B <�Þ LOV H ߶P :=<=Þ BSJM\Þ BKLOB ?�PSJWJ H X I P <=Þ @ <=x LWP LOV H�I : uAXWBKLO@tu H Z H uAP³?�@tL]\ I JMP (�u H P < LWV H u H R�L/߶P :=<�Þ BSJM\S{sB <=Þ LOV HórLWJOB < X I BSJ H < Lsß6P :�<=Þ BSJr\'?�P <�Þ @tLW@AP < ô P < LWV H JW@ x VmL H <=Þ|ä� H B I=I ut\�LOV H L]á¡P j XrL H I²w B�â j � H <=Þ JMP �èN H LOV=P Þ|ä�} XWX : N H LWV�BKL%LOV H x JW@ Þ @tX :=< @tRvPSJWN

áQ@tLWV� Þ H < PSLW@ <=x LOV H N H XWV áQ@ Þ LOV B <=Þ � ! LOV H LO@AN H XML H�I ä G!H ( < H 4�� LOP"ß H LOV H B I jI JMP�â;@tNéBKLW@AP < PSR±LWV H XWPfu : LO@tP < BKL�ã ��� �� �� ! åEä�a V H N H LOV=P Þ L5BSî H XQLOV H RvPfJMN

4 � �� � 4 � , � !� ã 0 ã 4 � ��� �� � ��� � å , 0 ã 4 � ��� �� N���� � åMå " � !

g ã��Qã 4 � ��� �� � ��� � å " �Qã 4 � ��� �� N���� � åWåáQV H J H

4 � ��� �� � 4�� � ��� � " 4�� N���� �g

" � !g � , 0 ã 4 � � ��� � å , 0 ã 4 � N���� � å� " �Qã 4 � � ��� � å " �Qã 4 � N���� � åg �

RvPfJ�� � � " � � g B <=Þ � � � , � � g;äa V H N H LOV=P Þ @AX£XMLOBSß=u H @tR7LOV H C � w ?�P <=Þ @tLO@tP <

N�B�â 8 � � � � !� � N�B�âEEEEEE �� � ã , ��å � � � � � " � 6 �

g $ � �� 6 � � � EEEEEE � !� �� �g;�

Page 22: 6 - UHcanic/papers/hemodynamics/hemopaper.pdfÖÇÝ Ü ÖÇÚ Ý ê ì í ò bkxwx: n @

�������� ÖÇÝ�Ü � ÖÇÚ� ��� ��� Ý��

@AX£XWBKLO@tX ( H Þ|äa V H Þ BKL5B : X H Þ @ < LOV H XW@tN : uÈB�LO@AP < BSJ H <�ß=uAP³P ÞèÞ H < XM@tL]\ $ � ��h�ìSh � J � � � {~Z³@AXM?�PfXM@tL]\' � k21¨g%,Æ��h N�� � � � � B <=Þ²:=< XMLOJ H XMX H Þ JWB Þ @ : X�PSR£LWV H BSß Þ PfNz@ < BKu¡BKPfJMLOB : 6 � h21�hShf��g � äa V H$H uÈBSXrLO@A? @tL]\�?�P H � ? @ H < L � 6 � i , ��h � � � � � @AX!Pfß;L5BS@ < H Þ RvJMPfN ê ��iSí áQ@tLWV�� � g;äÄa V HLO@tN H XML H I : X H Þ @ < BSutu�LOV H XM@AN : uABKLO@tP < X¡@AX � ! � k 1t���-,¸��h N � ä

0.5 1 1.5 2 2.5 3 3.5 4 4.5 58

8.2

8.4

8.6

8.8

x 10−3

vessel length in meters

ve

sse

l ra

diu

s in

me

ters

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1−0.2

0

0.2

0.4

0.6

0.8

1

1.2

cardiac cycle

Inflo

w v

elo

city (

m/s

)

0.5 1 1.5 2 2.5 3 3.5 4 4.5 58

8.2

8.4

8.6

8.8

x 10−3

vessel length in meters

ve

sse

l ra

diu

s in

me

ters

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1−0.2

0

0.2

0.4

0.6

0.8

1

1.2

cardiac cycle

Inflo

w v

elo

city (

m/s

)

� Ý � ÛÇØ / � � + � ¿���©�¤ÂÀsªÉ©E��¢£�5� ��©E�!���!� ���¡�§¦��§� �r¢ç���µ���!� ��� � �r��©Q� ©E¬��¤l�_� �M� ¢Í[� ©E¥��¨´`¥������WÎ��E��´!���­� �!� ���� ©E¬��¤l�~� �M� ¢ ¯E��¹E�M� °�¦����¼���2ÍtÏ�º�����Î~Í[´�� �§���W´ ¥­�����OÎ]º!»|���£�v��©-����¤l� ¬����M��©E��� ���s¥­�rª �~� ��©5�)�����5�������£Ã��Â�§�� ��©�¤ÂÀ ªÉ©E��¢c�1� ��©E���­�é� ���!� ¦��v���r¢ ���­� ��� ��� � �r��©�� ©E¬���¤r�s���r��¢ ©�¤r¤l¬����c�5�sÏ�º Ð�¢+´�©5�����§� ���M�E¢ªÉ� © ¢ � �������¥­�r��°S©E¬���´��1��¦Eº��±�¶�����_¥­�­�§��¥­�U¤l����¤r¥­�_�5��� ���_°S©1�§��©E¢²���¨¤]��¬����±����´��¨¤r�1� �M�MÁ�� ���¨�|¤l© � ���M� �K© ��´��=��©¡��©E¬�¯E��¥�¦��º ��� �M¤l© ��´��|���¼� ����¤M�1�´��¨�E¤_¤l¦�¤l¥��Eº¶»|���UÃ�¯E¬����M�|© �¼� �������­¯ ����� ��©5���§��©�¤ÂÀQªÉ©E��¢c�1� ��©E�¼�­�¼�������§¦��§� �M¢è���­� �!� �����© � � �M� ©U�§© ¬��¤l�6� �r��¢èÍt´��E� ���M´¡¥��­���OÎ������¨¤Â�¡©�¤r¤r¬��Â�=� © ¬�¯E��¥�¦��5� �_¢Ñ´�©5���K�v��� �W�1¢�ªÉ��©E¢��������­��¥­�r�Ì°K© ¬���´��E� ¦ Á�5�Ç�E°K© ¬�� ��º�� �U�§�W¤l© ��´��|���`������¤r�E��´���� ¤±¤r¦�¤r¥­� º

� � + � -ÇÙ±Ü � 2³Ù±Ø � � ×�Ý�Ù±ÖÊÝ�Ö � 9�×�Ø � Ý � -�×èÜ|Ù�� � 5mÝ � Ö�× 13/69 9 /65� H BSJ H BSXMX : Nz@ <�x V H J H LOV�BKL�LOV H :=< XMLOJ H XMX H Þ ? JWPfXMX j X H ?ELO@AP < BSu¶BSJ H B � 6 @AX�?�P < XMLOB < L ä � H BSJ Hx Pf@ <=x LWP I J H X H < L L]á~P�XrL :=Þ @ H X ä �!< H ? P < ? H J < X�XWV=P³?5î�RvPfJMNéB�LO@AP < @ < XM\³XrL H N ã g;ä[��imå áQ@tLWVLOV H � H JWP%XWP : JW? H L H JWN�{³B <=Þ LOV H PSLOV H J�@ < ? u :=Þ H X�LOV H XWP : JW? H L H JWN �`x @tZ H < ß�\�ã g;ä[��k�å áQV�@A?5VBS? ?�P :=< LWXsRvPfJcLWV H Z³@AXW? P : X H � H ?ELOX ä �!: J <m: N H JW@t?�BSu�XW@AN : uÈBKLW@AP < X¡áQ@Autu�XMV=P�áLOV�B�L��� @ < LOV H Xr\³XML H N áQ@tLOV$LWV H � H JMP�XMP : JM? H L H JMNeLOV H (�JMXML�XWV�P;?5î Þ H Z H uAP I X¡BSJMP :=<=Þ�g;ä­� N H L H JMXÞ P�á < XrLOJ H BSN RvJWPfNLWV H @ < u H L7ß6P :=<=Þ BSJr\éãváQV=@t?5V�@AX±BSJMP :=<=Þ�h�ä­if� X H ?�P <�Þ @ < LOV H ?�BSJ Þ @ÈBS?

?E\;? u H åEò LOV�@AX£@AX£@ < B$Z H Jr\ x P;P Þ B x J H�H N H < LQáQ@tLWV'LOV HÄI J H Þ @t? LO@tP < X£@ <�9 H ? LW@AP <2i=ò#$� @ < LWV H XM\³XML H N áQ@tLWV$LOV H XMP : JW? H L H JMN x @[Z H < ß�\ � @ < ã g;ä[��k�å {fLOV H LW@AN H B <=Þ LWV H uAP³?�BKLW@AP <

PSRÇLWV H (�JWXrLQXWV=P³?5îéRvPfJMNéBKLW@AP < @AX£XMuA@ x VmLWut\ Þ H uÈB�\ H Þ ã�L�� h�ä�ì;� X H ?%@ < LOV H ?�BSJ Þ @ÈBS?!?E\³?�u H åB <�Þ LOV H XWV=P³?5îz@AX�uAP³?�BKL H Þ BKJWP :=<�Þ'k N H L H JWX Þ P�á < XMLWJ H BKN RvJMPfN LOV H @ < u H L�ß6P :=<=Þ BSJr\ òLWV=@AXÄ@AXÄ@ < BK?�?�PSJ Þ B < ? H áQ@[LOV)LOV H < P <=Þ @AN H < XW@AP < BSu�B < BSut\³XW@tX I J H X H < L H Þ @ <¸9 H ? LW@AP < g

gfg

Page 23: 6 - UHcanic/papers/hemodynamics/hemopaper.pdfÖÇÝ Ü ÖÇÚ Ý ê ì í ò bkxwx: n @

� /6�!Ù±Ú � Ö � �!Ý�Ü 9

0.5 1 1.5 2 2.5 3 3.5 4 4.5 58

8.1

8.2

8.3

8.4

8.5

8.6

8.7x 10

−3

vessel length in meters

ve

sse

l ra

diu

s in

me

ters

Tapering=0Tapering=1%

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1−0.2

0

0.2

0.4

0.6

0.8

1

1.2

cardiac cycle

Inflo

w v

elo

city (

m/s

)

0.5 1 1.5 2 2.5 3 3.5 4 4.5 58

8.1

8.2

8.3

8.4

8.5

8.6

8.7x 10

−3

vessel length in meters

ve

sse

l ra

diu

s in

me

ters

Tapering=0Tapering=1%

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1−0.2

0

0.2

0.4

0.6

0.8

1

1.2

cardiac cycle

Inflo

w v

elo

city (

m/s

)� Ý � ÛÇØ / � ��� � ¿���©�¤ÂÀéªÉ©E��¢£�5���­© �2�­�2� ��� �§¦��§� �M¢e���­� � � �M� ©$�Â�1�S�r���­��¯"Í[´��E� ���M´'¥������WÎ`�1��´2���µ���2� ������E�K�M� ����¯~©1ª ��� Í[� ©E¥���´s¥­�����OÎ]ºÌ»|���±�v�6©~���¨¤]��¬�� �W��©E�Q�����U¥­�rª �Ç�§��©5�/������¤l© � ���M� �K© ��´�����¯��Â�E´�����Í ��©E�KÎ��1�K´£� ���¢c©E¢c�r������� � ���Q¤M�1�´��¨�E¤c¤l¦�¤l¥��ÄÍÉ°S©1� � © ¢£Î������r��� ���£Ã��Â�v��� ��©�¤ÂÀzÍ[´��E� ���M´�¥��­���OÎU�¨�UªÉ©E��¢c�M´�º �±�������£¥­�­�§��¥­�¤l���¤l¥����­��´���¤M�5� �W�rÁ�� ���¨�_¤l©E�����M� �K© ��´���� ©s� © ¬�¯E��¥�¦ ��º � ���§�W¤l©E�K´������!� ����¤M�1�´��¨�E¤�¤l¦�¤r¥­� º|»|�����v�6©£����¤l� ¬����M��© �� ���¡���­¯ ���_� ��©5��� ���c���1¢c������ªÉ©E��¢£�5���­© �-���EÀE�r���5� ��º����c� �M¤��­�%� ���c¤r�E��´��¨�E¤¡¤l¦�¤l¥��������r�Ä�����c�§�W¤l©E�K´Ä�§��©�¤ÂÀÍ[� ©E¥��¨´s¥��­���WÎ�´��M¹E�M¥­© ���rº

áQV=@t?5V XWV=P�áQX$LOV�B�L$LOV H XMP : JW? H L H JMN @tX PSRsP < H PfJ Þ H J$PKR`N�B xf< @tL :�Þ H XMNéBSutu H J�LOV=B <LWV H J H XML PSRcLOV H XM\³XML H N ä�a V : X�{ULWV H B < BSut\³XW@tX�PKRcLOV H (�JWXrL XWV�P;?5î)RvPfJWN�BKLW@AP < ß�BSX H ÞP < LOV H � H JWP�XWP : JM? H L H JMN I JWP�Z³@ Þ H X¼B x P³P Þ H XrLO@AN�BKL H RvPSJQLWV H (=JWXML`XWV�P;?5î'RvPfJMNéBKLW@AP <@ < ã g;ä[��imå5ä

� @ xf: J H ì;ä�g XWV=P�áQXcLOV H JOB Þ @t@ I JWP (�u H X£BKuAP <=x B ì�j N H L H J~utP <=x Z H XMX H u {ÌBKL~L]á¡P@ < XrL5B < ? H X�< h�ä­if�X H ?�P <�Þ X�B <=ÞÑh�ä¨ì³� X H ? P <=Þ X%@ < LWV H ?�BSJ Þ @ÈBK?$? \³?�u H ä a V H XMPfuA@ Þ ? : JrZ H Þ H XM?�JW@tß H X-LOV H JWB Þ @ : XI JMP (�u H Pfß;L5BS@ < H Þ @ < LOV H XW@tN : uÈB�LO@AP < PSRcXr\;XrL H N ã g;ät��imå áQ@tLOVÑLOV H � H JWP"XWP : JM? H L H JMN äéa V HÞ BSXMV H Þ ? : JrZ H Þ H XW? JW@tß H X¡LOV H XMPfu : LW@AP < PSR6LOV H XM\³XrL H N áQ@tLWVzLWV H XMP : JM? H L H JMN x @tZ H < ßm\ � @ <ã g³ät��kfå1ä ! PSLO@t? H LOV=BKL£LOV H JWB Þ @ : X Þ H I @A?EL H Þ áQ@tLWV/LOV H XMPfuA@ Þ ? : JrZ H Þ H Z H utP I XsB$XWV=P³?5î/XMP;P < H J�{@ <�Þ @A?�BKLO@ <=x LOV�BKLzLOV H XWN�BSutu%ã < H x BKLO@[Z H å XWP : JW? H � XWut@ x V�LOu[\ I PfXML I P < H XéXMV=P³?5î RvPSJWN�BKLO@tP <|äa V H JOB Þ @ : X I JWP (�u H XML H�H I6H < X$BSX-LOV H�I : uAX H LOJWB�Z H utX%LWV=JWP :=x V�LWV H Z H XMX H u ä � P :=x V=u[\)BKL g;ä­�N H L H JWX£LOV H JWB Þ @ : X I JWP (�u H Þ H Z H uAP I X`B$XWV=P³?5î ä

� ��� � -ÇÙ±Ü � 2³Ù±Ø � � ×�Ý�Ù±ÖÊÝ�Ö � × � � /ÌØ /ÌÚÆÜ|Ù3���65mÝ � Ö�× 13/ 9 9 /65� H BSJ H BSXWX : N�@ <=x V H J H LWV�BKL�� 6 ã� å @tXzB Þ H ?�J H BSXM@ <=x R :=< ?ELO@AP < PSR ä � < LOV H <m: N H JW@t?�BSuXW@tN : uABKLO@tP < X I J H X H < L H Þ V H J H á H V=B�Z H BSXMX : N H Þ LOV�B�L � 6 ã å @AX%B2uA@ < H BSJ!R :�< ? LW@AP < PSR. PSRLOV H RvPSJWN � 6 ã å � � 6 , T � � 6 � �

gSk

Page 24: 6 - UHcanic/papers/hemodynamics/hemopaper.pdfÖÇÝ Ü ÖÇÚ Ý ê ì í ò bkxwx: n @

�������� ÖÇÝ�Ü � ÖÇÚ� ��� ��� Ý��

áQV H J H h G T �&� @AX�LOV H ólL5B I¶H JM@ <=x R§BK? LOPSJ ô B <=Þ � 6 � ã h21­hfhf��g � å �$@AX�LWV H :=< XMLOJ H XMX H Þ?�JMPfXWX j X H ? LW@AP < BSucBSJ H B : X H Þ @ < LWV HéI J H Z³@AP : X�X : ß=X H ? LW@AP <|ä�} uAu�LWV H <m: N H JW@t?�BSu�XM@AN : uABKLO@tP < XRvJWPSN LOV�@AX I PS@ < L£P < áQ@Autu�ß H%I¶H JrRvPfJWN H Þ áQ@[LOV'LOV H < P < � H JWPzXWP : JM? H L H JWN ä

0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

8

8.5

9

9.5

x 10−3

vessel length in meters

vessel ra

diu

s in m

ete

rs

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.2

0.4

0.6

0.8

1

cardiac cycle

Inflow

velo

city (

m/s

)

0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

8

8.5

9

9.5

x 10−3

vessel length in meters

vessel ra

diu

s in m

ete

rs

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.2

0.4

0.6

0.8

1

cardiac cycle

Inflow

velo

city (

m/s

)

� Ý � ÛÇØ / � ��� � ¿���©�¤ÂÀ%ªÉ© � ¢£�1� ��©E� �­�� ���¼�§¦��§� �r¢ ���­� � � �M� ©Ä���1�S�r������¯Ä�1��´���µ��� � ���s���1�S�r������¯Ä©1ª � �Qº»|���`�v�6©����¨¤]� ¬�� �W�¡© ������`¥��lª �£� ��©5�²� ���¼¤r©E��� �W�§�S©E��´��­��¯%��� ´��­�UÍ ��©E�KÎ~�E��´ � ���¼¢c© ¢~�M���~���z© ���`¤M�1�´���� ¤¤l¦�¤r¥­�sÍ[°K©E�§��©E¢QÎ������M�-� ����Ã��Â�v�_�§��©�¤ÂÀ Í � �r��©c���1�S�r������¯�ÎÇ���±�1°S©E¬��Ç��©QªÉ© � ¢!º �7�Ç� ���¡¥­�­�§��¥­�~¤l����¤r¥­���­��´���¤M�5� �W�rÁ� �����U¤l© � ���M� �S©E��´��Ç� ©¼� © ¬�¯E��¥­¦ ��º�� �¡�§�W¤l©E�K´��7����� ���c¤r�E��´��¨�E¤�¤l¦�¤l¥��Eº�»|���¡�v��©s���¨¤]��¬�� �W�_©E�-�����c� ��¯E���_� ��©5�� ���¼���1¢c�s����ªÉ© � ¢£�5���­© �$���EÀE�M�z�5� ��º �1Ï-� �M¤s�­�z� ���!¤r�E��´���� ¤Q¤l¦�¤l¥��¼�����r�z� �M¤r©E��´z�§��©�¤ÂÀ'Í � � ���E�K�M� ����¯�Î����°S�r¯E����������¯c��©c´��r¹E�M¥­© �¼�1� �º ��¢c�r� �r�Â��´�©5�����§� ���M�E¢¸ªÉ� © ¢ �������­��¥­�r�Ç°K© ¬���´��E� ¦ º}¼< B I=I JWP�BS?5Væß=BSX H Þ P < LOV H < P <=Þ @tN H < XW@tP < BSu`B < BSu[\³XW@AX I J H X H < L H Þ @ <Ê9 H ? LW@AP < g {sPSJ

XW@tN I ut\2Bé? PfN I BSJW@tXWP < ß H L]á H H < LWV H N�B xf< @[L :=Þ H X`PKRULOV H XWP : JW? H L H JMN�X � B <=Þ LWV H XMP : JW? HL H JWN BKJW@AXM@ <=x$Þ�: H LOP$LOV H ZKBSJM@ÈBSß=u H ?�JMPfXWX j X H ? LW@AP < ã§X H�H ã ì;ä­k�åMå~x @tZ H < ßm\

� � F � � 6 �$ ã � " gfå � �� 6 � � � � � � O 6 �@AN I ut@ H X�LWV�BKLcLOB I6H JW@ <=x PSR7u H XWX¡LOV�B <�� � I¶H J~N H L H J!ã�T �#L2ã ��h N � åMå¡x @[Z H X¡LOV H XMP : JM? H L H JWNáQV=@t?5V²@AX PSR£LWV H XOBKN H N�B xf< @tL :�Þ H PSJ XWN�BSuAu H JÄLOV�B < � Sä)a V H J H RvPfJ H {�LWV H J H áQ@Autu�ß H ut@tLWLWu H?5V�B <�x H @ < LWV H utP;?�BKLO@tP < PSR~LWV H XWV=P³?5îÑRvPSJWN�BKLO@tP <�Þ=: H LOP2LOV H L5B I¶H JM@ <=x PSR£u H XMX%LWV�B < � � ä� < � @ xf: J H ì³ä�k á H ?�PfN I BSJ H LWV H XMPfu : LO@AP < XÄPfß�L5BK@ < H Þ : XM@ <=x"<³: N H JW@A?�BSu�XW@tN : uABKLO@tP < PSRcLOV HH ïm: B�LO@AP < X"ã g;ä[��imå áQ@tLWVèLWV H ZKBSJW@ABSß=u H :�< XMLWJ H XMX H Þ ?�JMPfXWX j X H ? LW@AP < BKu`BKJ H B � 6 ã� å áQV H J H LOV HL5B I6H JW@ <�x R§BS? LWPfJ£@AX I J H ?�@AX H u[\ � � I6H J£N H L H J�{XT5� h21­h�� ã§XMPfuA@ Þ uA@ < H å B <=Þ LOV H XWPfu : LO@tP < áQ@tLWV� H JWPsL5B I¶H JM@ <=x ã Þ BSXWV H Þ uA@ < H å1ä � < BSutuSLOV H XW@tN : uABKLO@tP < X|V H J H LOV H XWP : JW? H L H JWNáQV=@t?5V BS? ?�P :�< LWXRvPfJÄLOV H Z³@AXM?�PfXM@tL]\f{ � {_V�BSX�ß H H < LOBSî H < @ < LWP�BS? ?�P :�< L ä2a V H XMV=P;?5î)@ < LWV H LOB I6H J H Þ Z H XWX H uXMLOBSJMLWX_LOP Þ H Z H utP I BSJWP :=<=Þ$h�ä�ìfd X H ?c@ < B¼?�BSJ Þ @ÈBS?�? \³?�u H BKL k21�k N H L H JMX Þ P�á < XrLOJ H BSN+RvJWPfN LOV H@ < u H LÇ߶P :=<�Þ BSJM\ ä � H Þ JOB�á²LOV H RvPfutuAP�áQ@ <=x L]á¡P!? P < ?�u : XW@tP < X�<'(=JWXML�{KLWV H (=JWXML±XWV�P;?5î-RvPfJMNéBKLW@AP <@ < B$L5B I¶H J H Þ Z H XWX H u±áQ@[LOV'LOV H L5B I6H JW@ <�x R§BS? LWPfJQPSR_u H XMXsLWV�B <Ñ� � I¶H JQN H L H J£@AXQ?�utPfX H LOPLOV H

gKi

Page 25: 6 - UHcanic/papers/hemodynamics/hemopaper.pdfÖÇÝ Ü ÖÇÚ Ý ê ì í ò bkxwx: n @

� /6�!Ù±Ú � Ö � �!Ý�Ü 9

(�JMXML�XWV=P³?5î�RvPfJWN�BKLW@AP < @ < B < P <;j LOB I6H J H Þ Z H XWX H u {UBSX H â I¶H ? L H Þ|ò X H ? P <=Þ {±XWV=P³?5î�RvPfJMNéBKLW@AP <@ < L5B I6H J H Þ Z H XWX H uAX�@tX Þ H uAB�\ H Þ|ä a V�@AX�@AX�X : J I JW@tXW@ <�x ß H ?�B : X H LOV H ß H V�B�Z³@APfJ :=< ? P�Z H J H ÞV H J H @tX�P I=I PSXW@tL H LOP"LWV HéH â I6H ? L H Þ ß H V�B�Z³@APfJ%PSR~LWV HéI @AXMLWP < Þ JW@tZ H < ?�PfN I J H XWXM@Aß=u H à P�á @ <JW@ x @ Þ L : ß H X ä �QH ?�BKuAucLOV=BKLé@ <Æ9 H ? LW@AP < k á H ? PfN I BSJ H Þ LOV H XrLOJ : ? L : J H PSR`LOV H"H ïm: BKLW@AP < XXML :=Þ @ H Þ V H J H LOP¸LWV H�H ïm: BKLW@AP < X/PSR%?�PfN I J H XWXM@Aß=u H x BSX Þ \ < BSNz@A?�X Þ H XW? JW@tß=@ <=x LWV H�I @tXMLWP <Þ JM@tZ H <�à P�áe@ < B2JM@ x @ Þ L : ß H ä � L%@AX-á H uAu�î < P�á < LWV�BKL Þ H ?�J H BSXW@ <=x ? JWPfXMX j X H ?ELO@tP < BSu�BSJ H B'PSRLOV H JW@ x @ Þ L : ß H @ < LWV H$I @tXMLOP <�Þ JW@[Z H <�à P�á+áQ@Autu x @tZ H JW@AX H LOP'? PfN I J H XWXW@tP < @ < LOV H XMPfu : LO@AP <B <=Þ XMV=P³?5î³XáQ@Autu�RvPSJWN XWP³P < H J ä�a P�?�P < (�JWN LOV H Þ H uÈB�\³@ <�x H � H ?EL�PKR£LOV H Z H XWX H u£L5B I6H JW@ <�x@ < LWV H ß=utP;P Þ à P�á N�P Þ H u {_á H JWB <²<m: N H JW@t?�BSu¡XW@tN : uÈB�LO@AP < X%áQ@[LOV ì � L5B I¶H JM@ <=x�ä � <�Þ H�H Þ {� @ xf: J H ì³ä­i XWV=P�áQX%LOV�BKL%@ < B'L5B I6H J H Þ Z H XWX H u!ãvXWPfut@ Þ uA@ < H å áQ@[LOV T � h21�hfì LWV H (�JWXrL�XMV=P;?5îÞ H Z H utP I XsBKLQBKJWP :=<�Þ�i�ä¨d N H L H JWX Þ P�á < XMLOJ H BSN RvJWPfN LOV H @ < u H L£ß¶P :=<=Þ BKJM\f{;áQV=@A?5V2@AXcBSJWP :�<=Þh�ä�dfg X H ?�P <=Þ X-@ < LOV H ?�BSJ Þ @ÈBS?%? \³? u H ä T"P�Z;@ H X!XMV=P�áQ@ <=x XMV=P³?5î�RvPfJMNéB�LO@AP < ?�B < ß H RvP :=<=Þ P <á£á£á 1 N�BKLWV 1­: V 1 H Þ=: � > ?�B < @A? � V H NzP � XMV=P³?5î³X 1� PfXrL I P < H Þ XMV=P;?5î�RvPfJWN�BKLO@tP < ?�B < ß H£H â I uÈBS@ < H Þ ß�\ BÄ? PfN ß=@ < BKLW@AP < PSRÌL]á~P I V H < PfN H < B2<ã ��å LWJOB < XWN : JWBSu I J H XWX : J H JM@AX H X¡BSX�LWV H ?�JWPSXWX j X H ? LO@tP < BSu¶BSJ H B Þ H ? J H BKX H X-ã§X H H ã g;ät��ìfåMå B <�Þ ã gSåXW@ xf< BSutX�LOJWB�Z H u�R§BSXrL H J7@ < L5B I¶H J H Þ Z H XMX H uAX~ã§X H H ã ì;äµimåMåUä ^`@ x V-LOJOB < XWN : JOBSu I J H XMX : J H @ < LOB I¶H J H ÞZ H XWX H uAX�@ < L : J <�x @tZ H X�JW@AX H LWP"LWV H uABSJ x H JÄ?�JWPSXWX j X H ? LO@tP < BSu�BSJ H B"B <=Þ LWV=@AX < H á @ < ?�J H BSX H @ <?�JMPfXWX j X H ? LW@AP < BSu!BSJ H B�LWJOB�Z H uAXzR§BSXML/LWV=JWP :=x V LWV H�H < LW@AJ H Z H XWX H u�{Qß : L/XMLO@tuAuQ@ < B órLOB I6H J H Þ ôR§BSXMV=@AP <�ä�9 H H � @ xf: J H ì;äµi=äUa V=@tX�BSuAutP�áQXUV=@ x V H JUZSPfu : N H à P�á LWV=JWP :=x V$LOV H ?5V�B <=< H u¶B <�Þ LWV : XuÈB�L H J�XWV=P³?5î�RvPfJMNéB�LO@AP <|ä�a V=@AX$@tX$B�?�J : ?�@ABSu I uÈBS? H áQV H J H LOV H L]á¡P I JWPfß=u H NzX'ã�LOV H'I @tXMLWP <Þ JM@tZ H < ?�PfN I J H XWXM@Aß=u H à P�áÊLWV=JWP :�x VéLOV H ?5V�B <�< H u�áQ@[LOV (�â H Þ ácBKuAuAX¡B <=Þ LOV H ó I : utXOBKLW@Au H à P�áÞ JM@tZ H < ô @ < ? PfN I J H XMXW@tß=u H à P�á LOV=JMP :=x V�?�PSN I ut@ÈB < LcZ H XMX H utX å£Þ @ � H J£X : ß=XrL5B < LO@ABSuAu[\ ä! PSLW@A? H LOV�B�L-@tR�á H : X H$H ï³: BKLO@tP < ã i=ä[����å LOP H XrLO@tNéBKL H LWV H LO@tN H PSR�LOV H (�JMXML-XMV=P³?5î�RvPfJ j

N�BKLO@tP < H Z H < @ < LOV H ?�BKX H áQV H < LWV H :�< XMLWJ H XMX H Þ ?�JWPSXWX j X H ? LO@tP < BSu7BSJ H Bz@AX£ZKBSJW@ABSß=u H {�XWN�BSuAu H J� 6 u H B Þ XcLWP LOV H uÈB�L H J~XWV=P³?5îéRvPfJMNéBKLW@AP < {³áQV=@t?5V"@tX£?�P < XW@AXrL H < LQáQ@[LOV'P : J ( <=Þ @ <�x X ä p H�H I @ <Nz@ <=Þ {¶V=P�á H Z H J�{ÇLOV�B�L H ïm: B�LO@AP < ã i=ä[����å ácBSX-PSß�L5BS@ < H Þ ßm\�BSXWX : Nz@ <=x LWV�BKL � 6 @AX`?�P < XrL5B < L ä� PfJ�XWN�BSuAu Þ H Z;@ABKLO@tP < X�@ < � 6 H ï³: BKLO@tP < ã i�ät���få XMV=P : u Þ XMLW@AuAu I JWP�Z³@ Þ H B x P³P Þ H XMLW@AN�BKL H RvPfJ !�� ä� H ? P < ? u :=Þ H LWV=@AX¼X H ?ELO@tP < ß�\�B/?�PSN�N H < L-J H uÈB�L H Þ LWP/LOV H @ <�à�: H < ? H PKR I BSJOBSN H L H J ��{Þ H XW?�JM@Aß=@ <=x LOV H uA@ < H BSJ�� < P < uA@ < H BSJ`J H X I P < X H PSR~LWV H Z H XMX H u�ácBKuAu�{ÇP < XWV=P³?5î�RvPfJMNéBKLW@AP <�äz} X

N H < LO@tP < H Þ @ <æ9 H ? LW@AP <Æg {cLOV H uA@tN�@[L � � � ? PfJWJ H X I P <�Þ XéLOP XMLO@��ÊácBSutuAX {QB <=Þ uABSJ x H �áQ@Autu�u H B Þ LOP H BKJWut\ ô XOB�L : JWBKLO@tP < ô @ < JWB Þ @ÈBKu Þ @tX I uABS? H N H < L ä � < PSLOV H J�á~PSJ Þ X {;V=@ x V H J I J H XWX : J HÞ @�� H J H < ? H � % @AX < H�H Þ H Þ RvPfJ_B x @tZ H < JWB Þ @ÈBKu Þ @tX I uABS? H N H < L Þ @�� H J H < ? H � : { : � : 6 {f@ < ?�BSX HPSRÇB%uÈBSJ x H J � ä ��: JrLOV H JWNzPfJ H {³LWV H¼H â I J H XMXW@tP < RvPfJ�LOV H`H @ x H < ZKBSu : H X-ã ì;äµimå @ <=Þ @t?�BKL H X�LOV�B�L~LOV HN�B xf< @[L : L H PKR~LOV HéH @ x H < ZKBSu : H X%@ < ? J H BSX H X�áQ@tLWV�@ < ?�J H BSXM@ <=x ��{±áQV=@t?5V N H B < X%LWV�BKL�XW@ xS< BSuAXLOJWB�Z H u±R§BSXML H J¼LWV=JWP :�x V�XMLW@ � H J`á~BSutuAX$ã§BSutLWV=P :=x V�áQ@tLWV�XWN�BSuAu H JsBSN I uA@[L :=Þ H X å1äH� @ < BSuAu[\f{Ì@tR�á H: X H�H ïm: BKLO@tP < X¡ã i�ät���få B <=Þ ã i=ä[����å LOP H XrLO@AN�BKL H LOV H utP;?�BKLO@tP < PSR³LOV H (�JMXMLÇXMV=P;?5î!RvPSJWN�BKLO@tP < {�á HX H H LOV�B�L�@ < XrLO@ ��Z H XWX H uAX�XWV�P;?5îmX�RvPfJWN R : JrLOV H J Þ P�á < XMLWJ H BKNeRvJWPfN LOV H @ < u H LU߶P :=<�Þ BSJM\ äUa V=@tX@AXQX : I=I PfJML H Þ ß�\2LOV H <m: N H JW@t?�BSu�XM@AN : uABKLO@tP < X I J H X H < L H Þ @ < � @ xf: J H ì;ä�ì;ä ! PKLO@A? H LWV�BKL H Z H <RvPfJ±B`XMNéBSutu Þ @ � H J H < ? H @ < LWV H~I BKJOBSN H L H J ��{ < BSN H u[\�� � g Z³X ä � � k {�LOV H Þ @ � H J H < ? H @ < LOV HuAP³?�B�LO@AP < PSR7LOV H (�JMXMLsXWV�P;?5îéRvPSJWN�BKLO@tP < @AX£JWBKLOV H J I JMP < P :=< ? H Þ ã g 1­� � Z³X ä�i � Þ P�á < XMLWJ H BKNRvJWPSN LOV H @ < u H L!߶P :=<=Þ BSJM\ åEä$a V�@AX-@AX-ß H ?�B : X H XM@ xf< BKuAX¼LWJOB�Z H uUR§BSXML H J-@ < XrLO@ � H J!Z H XMX H utX�B <=Þß H ?�B : X H (�JWXrL!XWV�P;?5î'RvPfJMN�XQuÈB�L H JQ@ < XMLW@ � H J£Z H XWX H uAX ä � @ xf: J H ì;ä¨ì BSuAXMP�@ <=Þ @t?�BKL H XQJOB Þ @ÈBSu|á~BSuAuÞ H RvPfJWN�BKLO@tP < X£BKJ H XWN�BSuAu H J¡@ < XMLW@ � H JcZ H XWX H uAX ä

gfì

Page 26: 6 - UHcanic/papers/hemodynamics/hemopaper.pdfÖÇÝ Ü ÖÇÚ Ý ê ì í ò bkxwx: n @

�������� ÖÇÝ�Ü � ÖÇÚ� ��� ��� Ý��

0.5 1 1.5 2 2.5 3 3.5 4 4.5 58

8.1

8.2

8.3

8.4

8.5

8.6

8.7x 10

−3

vessel length in meters

ve

sse

l ra

diu

s in

me

ters

beta=2beta=3

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1−0.2

0

0.2

0.4

0.6

0.8

1

1.2

cardiac cycle

Inflo

w v

elo

city (

m/s

)

0.5 1 1.5 2 2.5 3 3.5 4 4.5 58

8.1

8.2

8.3

8.4

8.5

8.6

8.7x 10

−3

vessel length in meters

ve

sse

l ra

diu

s in

me

ters

beta=2beta=3

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1−0.2

0

0.2

0.4

0.6

0.8

1

1.2

cardiac cycle

Inflo

w v

elo

city (

m/s

)� Ý � ÛÇØ / � � � � ¿���©�¤ÂÀ ªÉ©E��¢c�1� ��©E�é¤l©E¢c���E� �¨� ©E�°S�l�v���r�M�z�����!¢~©�´��M¥��~���­� � �2� Ï��1�K´��2� ��º�»|����v��©-����¤l� ¬����M��©E��� ���Q¥­�rª �~� ��©5��� ���s¤r©E��� �W�§�S©E�K´��­��¯¼�Â�E´��­�7ÍÉ� © �KÎ��1�K´�� ���Q¢c© ¢~�M�����­�$© ���Q¤r�E��´���� ¤~¤r¦�¤l¥��ÍÉ°S©1� � © ¢£Î������r�¡� ���|Ã��Â�§��� ��©�¤ÂÀQÍ�� ��ÏEÎ;��� ���v¬��v��ªÉ© � ¢c�W´�º �±�=� ���|¥��µ� � ¥��Ǥl����¤r¥­������´��¨¤r�5���M�MÁ1��������¤r©E��� �W�§�S©E�K´��� ©c��©E¬�¯ ��¥�¦ ��º���� �M¤r©E��´������-�¡¤M�1�´���� ¤±¤r¦�¤l¥��Eº�»|���U�v��©¡���¨¤]��¬����M�|©E�`� ���_����¯E���|� ��©5��� �������1¢c�U�­��ªÉ© � ¢£�1� ��©E����EÀE�M�¼�1� ��º � �c�§�W¤±���-�c¤r�1�´��¨�E¤_¤l¦�¤l¥��U�����r�¼�������§�W¤l© ��´`� ��©�¤ÂÀ%Í�� � � Î��K�E���v¬��§��ªÉ©E��¢c�M´�º

� � Ù±ÖÇÜ$5mÛ09�Ý�Ù±Ö� < LWV=@AX I B I¶H J"á H Þ @tXW? : XWX H Þ XWPfN H ß�BKXW@A?�NéB�LOV H NéBKLW@A?�BSu!@AXMX : H X�J H uÈBKL H Þ LWP LOV H @ < @[LO@ABSu߶P :=<=Þ BKJM\ j ZKBSu : HQI JWPfß�u H N RvPfJ�B ïm: BSXM@Aut@ < H BSJ�XM\³XML H N PSR�Vm\ I¶H JMß6Pfut@A? H ïm: B�LO@AP < X!ã g;ä[��imå N�P Þ;jH ut@ <=x I : utXOBKLW@Au H ß�uAP³P Þ�à P�á @ < uABSJ x H Z H XWX H utX ä � H RvP³? : X H Þ P < LWV H ïm: BKXWuA@ < H BKJ H � H ? LOX¼X : ?5VBSXÄXWV�P;?5î�RvPSJWN�BKLO@tP < @ < XrLOJOBK@ x V�LÄB <�Þ LOB I6H J H Þ ? PfN I uA@ÈB < L`Z H XWX H uAX {UB <=Þ B I JW@APSJW@ H XMLW@AN�BKL H XáQV=@t?5V xS: BSJOB < L H�H XrLOJM@A? LcVm\ I¶H JMß6Pfut@A? @tL]\zPSRÇLOV H-H ïm: BKLO@tP < X ä�a V H J H X : u[LOX I J H X H < L H Þ V H J H BSJ H: X H R : u < PSL`P < ut\2@ < LWV H N�BKLOV H N�BKLO@t?�BSu :�<=Þ H JMXMLOB <=Þ @ <=x PSRULWV H NzP Þ H u H ïm: B�LO@AP < X�{¶ß : L!BSuAXMP@ < LWV H <m: N H JM@A?�BSu=XW@tN : uABKLO@tP <|ä p < P�áQ@ <=x LOV HQH XMLO@tNéB�L H X�P < LOV H @ < @tLW@ÈBSu;B <=Þ ß6P :=<=Þ BSJr\ Þ BKLOBáQV=@t?5V xf: BSJOB < L H�H XMLWJW@t? LV�\ I6H JW߶PfuA@t?�@tL]\�@AX�@AN I PfJrL5B < L�{URvPfJ H â�BSN I u H {�RvPfJ LOV H XML5BKß=@Aut@tL]\ÑPSR( < @[L H Þ @�� H J H < ? H N H LOV�P Þ X ä �!< LWV H PSLOV H J�V�B <�Þ { :=<=Þ H JWXMLOB <=Þ @ <=x LOV H @ <;à�: H < ? H PSR¶LOV H Þ BKLOBP < XMV=P;?5î2RvPfJMNéBKLW@AP < @AX¼?�J : ?�@ÈBKu7RvPfJsLOV H XW@AN : uÈBKLW@AP < PSR�LWV H :=<=Þ H JWu[\³@ <=x H ïm: BKLO@tP < X : XW@ <�x B( < @[L H-H u H N H < LsN H LOV�P Þ|ä�!: J�NzPSLW@tZKBKLO@tP < RvPfJ-LOV�@AX%XML :�Þ \Ñ?�BSN H RvJMPfN�B�J H uABKL H Þ I JWPfß=u H N < :�<=Þ H JMXMLOB <=Þ @ <=x LOV Hà P�áÆPKR6ß�uAP³P Þ B <=Þ P I LO@tNéBKu Þ H XW@ xf< PSR�X H u[R j H â I B <=Þ @ <�x I JWPfXrLOV H X H X!ãvXML H < LOX å @ < H <=Þ P�ZKBSXW? : uÈBKJLOJ H BKLWN H < L'PSR�BSß Þ PfNz@ < BSusB < H : Jr\;XMN ä � < PfJ Þ H JéLWP²XML :=Þ \æBKX I¶H ? LWX'PSR%ß=uAP³P Þçà P�á&BKR�L H JLOV H @ < X H JMLO@tP < PSR-B < H <=Þ P�ZKBSXM? : uABSJ I JWPfXrLOV H XW@tX�{£@tL@tX < H ? H XWXWBSJM\èLOP (�JWXrL :�<=Þ H JMXMLOB <=Þ LOV HI JMP I6H JMLW@ H X¼PSR�ß=uAP³P Þ"à P�á I JW@APSJ¼LOP/LWV H I JMP;? H Þ=: J H ä�a V=@AX!@tX¼áQV H J H LOV H J H X : utLWX I J H X H < L H Þ@ < LWV HÄI J H X H < L I B I¶H JQß H ?�BKN H @ <=Þ @AX I6H < XOBKß=u H ä� H V=P I¶H LWV�BKLzLOV=@tXNéB <m: XM?�JM@ I LzáQ@AutucX H JMZ H BSXéBÑß�BSXM@A?�J H R H J H < ? H @ <è:=<=Þ H JWXMLOB <=Þ @ <=x

LOV H ïm: BSXM@Aut@ < H BSJ H � H ?ELOX�PKR H ïm: B�LO@AP < X/ã g;ä[��imå @ < LOV H XrL :=Þ \ÑPSR~ß=uAP³P Þ)à P�áeLOV=JMP :=x V�uÈBSJ x H {B�â;@AXr\³N�N H LWJW@A?¼?�PfN I uA@AB < LcZ H XWX H uAX ä

gSn

Page 27: 6 - UHcanic/papers/hemodynamics/hemopaper.pdfÖÇÝ Ü ÖÇÚ Ý ê ì í ò bkxwx: n @

� /6�!Ù±Ú � Ö � �!Ý�Ü 9

� � Ü �_ÖÇÙ���5 /ÌÚ � /6� /ÌÖ�× 9a V H B : LWV=PfJMXÄá¡P : u Þ ut@Aî H LOP2LOV�B < î }¼<�Þ JWP"T"@tî H ut@ED?K{ w : ?�B � PSJWN�B xfx @AB�{ G JWB x B < T"@tJWîKP�Z³@ED?B <=Þ�} u�(�P�� : BSJrL H JMP < @|RvPfJcLWV H @tJ£@ < I : LsB <=Þ H < ? P : JWB x H N H < L ä

� � /62 /ÌØ /ÌÖÇÜ$/69

ê ��í T äÌ}¼< ut@Aî H JsB <=Þ � ä � P;?5î�á H utu ä ! P < ut@ < H BSJQB < BSu[\³XW@AXQPSR à P�á I : utX H X`B <=Þ XWV=P³?5î'ácB�Z H X@ < BSJrL H JW@ H X ä�� ����� { gfg < g;��d�gKi�n { ����d³�fä

ê g�í%}�äÌC¼ä w ä=y BSJ < BSJ Þ { � ä=}�ä ^ :=< L�{ � ä �7ä=a @ANzuÈBKî H {�B <=Þ o ä�� BSJMu H \ äU} LWV H PfJr\'PSR à�: @ Þà P�á@ < ? PfN I uA@AB < L~L : ß H X ä� ,��������9&���& { n < d³��d��dfg�i { ���Snfn�äê kKí�96ä >C B < @ED? äÇa V H @ <�à�: H < ? H PSR�X H utR j H â I B <�Þ @ <=x XML H < LOX£P < LOV H ß=uAP³P Þzà P�á BKR�L H J H <=Þ P�ZKBSX j

? : uABSJcJ H�I BS@tJ ä � < I J H I BSJWBKLO@tP <|ä

ê iSí�96ä >C B < @ED? ä�y utP;P Þ�à P�á LWV=JWP :=x V)?�PfN I ut@ÈB < LsZ H XMX H uAX�BKR�L H J H <=Þ P�ZKBSXM? : uABSJ-J H I BS@AJ�<`á~BSuAuÞ H RvPSJWN�BKLO@tP < X£@ <�Þ=: ? H Þ ß�\2LOV H Þ @AXM?�P < LO@ <m: P : XQácBKuAu I JWP I6H JMLO@ H X ä � �; �4�C�0,�.�G?��.4$�� ,���3� ��#7,������0,��.�,�. � 3,� 3. � { i ã k�å < ��imd�j5��ìfì { gShfh�g;ä

ê ì�í�96ä >C B < @ED?¼B <=Þ G ä T�@AJWîKP�Z;@ED? ä|} V�\ I6H JW߶PfuA@t?sXr\³XML H N PKR|?�P < X H JMZKBKLO@tP < uÈB�áQX¡@ < NzP Þ H ut@ <=xH <=Þ P�ZKBSXM? : uABSJ'LOJ H BKLWN H < L2PKR BSß Þ PfNz@ < BSu!BSPSJMLO@t?�B < H : JM\³XMN ä � ��� 35 13�#7, ���58�19#: 3;-�"� � ��5�� <�� ��; 353, �� < � ���4#7, =���0,��.�� { ��i=� ã ��å < gfgSd�jrgSkSn { gKhfhfh�ä

ê nKí w ä � PfJMNéB xfx @ÈB;{ �~ä ! PSß=@Au H {³B <=Þ�}�ä � : BSJML H JWP < @ ä|} P < H Þ @AN H < XW@AP < BSu=NzP Þ H u�RvPfJ�ß=uAP³P Þà P�á=<�B I=I ut@A?�B�LO@AP < LOP$ZKBSXW? : uÈBKJ I JWPfXrLOV H XW@tX ä¡9;: ß=Nz@tLML H Þ|ä

ê d�í � ä�C¼ä ��:=<=x�ä)y @APfN H ?5V=B < @A? X <�T H ?5V�B < @t?�BSu � JMP I6H JMLW@ H X�PSR w @tZ³@ <=x�a @AXWX : H X ä�9 I JW@ <=x H J!`H á � PfJMî ���f�fk;ä

ê �Kí G ä ^s@Autß H JML ä7}¼< H�� ? @ H < L ! B�Z;@ H J jr9 LWPfî H X£XWPfu[Z H JQB <=Þ @tLOX~B I=I ut@A?�BKLO@tP < X¡LWP à�: @ Þ/à P�á @ <H uABSXMLW@A?¼L : ß H X ä � �#�#:9D9��,0�"�Q 3,� 3�B���0,:������. �� �#7����, ìKh < i�gSk�j]ifk�� { ���f��d;äê �Kí w ä�� PfJWN�B xfx @AB�{ �~ä ! PSß=@Au H { }�ä � : BSJML H JWP < @�{�B <=Þ"}�ä�� H < H ��@AB < @ ä T : utLW@AXW?�BSu H NzP Þ H ut@ <=x

PSR_LWV H ?�@AJM? : uABKLOPSJM\'Xr\;XrL H N <£B I J H uA@tN�@ < BSJM\/B < BSu[\³XW@AX ä � �; �4���/,�.�G?��.4$�� ,:�3� ��#7,������0,��.,�. � 3,� 3. � { g < dfì�³�fk { ���f�f��ä

ê ��hKí � ä p H H < H J'B <=Þ � ä~9;< H \ Þ|ä � ���*� 3;"���0, =��#�� �����3,��#:=G�� ä � < L H J Þ @tXW?�@ I uA@ < BSJr\ } I=I ut@ H ÞT�BKLWV H N�BKLO@t?�X ä�� Pfu : N H � { 9 I JM@ <=x H J !`H á � PfJWîÌ{ ���S�f��ä

ê �f��í �±ä G ä w B�â ä ^s\ I¶H JW߶Pfut@A?QXM\³XML H NzXcPSR�? P < X H JMZKBKLW@AP < uÈB�áQX¡@A@ ä � �;>;>��., =���/,��.��(�.����C58 ��.4$ � ���4#7,� =$�� ����� 3;"���0, �� { ��h < ìSk�d�;ìfìSn { ����ìfd;ä

ê ��g�í �±ä G ä w B�â ä G!H Z H uAP I N H < L±PSR�XW@ <�xf: uÈBKJW@tLW@ H X|PSR=XMPfu : LO@AP < PSR < P < ut@ < H BSJ�V�\ I6H JW߶PfuA@t? I BSJMLW@ÈBSuÞ @ � H J H < LO@ABSu H ïm: BKLO@tP < X ä ����5�.4��# )�� ����� 3;"���0, =��#�� �����3, �� { ì < n��f��;n���k { ���fnSi�ä

gfd

Page 28: 6 - UHcanic/papers/hemodynamics/hemopaper.pdfÖÇÝ Ü ÖÇÚ Ý ê ì í ò bkxwx: n @

�������� ÖÇÝ�Ü � ÖÇÚ� ��� ��� Ý��

ê ��kKí � ä � ä w�H � H ï³: H ä�� ��; 35�, =��# � 3�*�9$�� ) �5 � �.��� 35 6 ���0,��. � � � � ä�y @tJWîmV��B : X H J { y PfXrLOP < {���f��g³äê ��iSí�96äSa-ä � ä T�BS? 9 á H H < H \f{�� ä � P :=<=x { � ä T ä �-J H H < V=BSu x V�{�B <=Þ � äKa-ä � P�á H u ä T H ?5V�B < @A?�BKuI JWP I6H JMLO@ H X£PSR7LOV H B < H : Jr\³XWN�BSuÇBSPfJrL5B ä 5 &���&2����5/G�& { dS� < ��gS��� Ì��gS�Si { ���f�fg;äê ��ì�í T ä�� u : RvX H < { C¼ä � H XMîm@ < { � ä p-@AN�{ o ä� H Þ H JWX H < { }�ä ! B Þ @tN"{�B <�Þ � ä w BKJWX H <|ä ! : N H JW@t?�BSu

XW@tN : uÈB�LO@AP < B <=Þ H â I6H JW@tN H < LOBSu=ZKBSuA@ Þ BKLW@AP < PSR�ß=uAP³P Þà P�áÆ@ < BSJML H JW@ H X�áQ@tLWV�XrLOJ : ? L : J H Þ;jLOJ H�H P : L à P�á?�P <=Þ @tLW@AP < X ä � ..4��# � ) ,��; =$�, =��#���.�G�,�. � 35�,�.�G { gS� < ��gS�;� ¶��gS�S� { gKhfhfh�ä

ê ��nKí p ä � H JWî�LOPSu Þ {mB <�Þ � ä � B I=I @tLOXM?5V ä T�BKLOV H N�BKLO@t?�BSu³N�P Þ H uA@ <�x PSR6uAP³?�BSu;BSJrL H JM@ÈBSu à P�áæB <=ÞZ H XWX H u�N H ?5V�B < @A? X ä � < � ä³C JWPfu H L¡B <=Þ � ä?� V�B�\fP < ã H Þ X ä�å¡C PSN I : L5BKLW@AP < BKuÌT H LWV=P Þ X�RvPSJ� u : @ Þ%9 LWJ : ?EL : J H � < L H JOBS?ELO@tP <|ä � @tLON�B < �QH X H BSJW?5V ! PSL H X7@ < T�BKLWV H N�BKLO@t?�X ! P äKkShfn < gSkfh�jgKimì ^`BSJWutP�á=< w P <�x NéB <Ñ���f�Si=ä

ê ��d�í�C¼ä � H XMî³@ <|ä � ��53�0,0��#��, 358 3.�/,0��#�� D9� ���0,��.�� ,�. ,��#:=G�� äÇC P : JOB < L � < XMLO@[L : L H PSRÇT�BKLOV jH N�BKLO@t?�BSu 9 ?�@ H < ? H X { w�H ? L : J H ! PSL H X { !sH á � PfJWîÌ{ ����dSì;ä

ê ���Kí%}�ä � : BSJML H JWP < @�{ÇT ä|a±: Z H JM@�{ÇB <�ÞÑ}�ä�� H < H ��@AB < @ ä�C PSN I : L5BKLW@AP < BKu7ZKBSXM? : uABSJ à�: @ Þ�Þ \ j< BSNz@A? X < I JMPfß=u H N�X {SNzP Þ H uAX7B <�Þ N H LOV�P Þ X ä � �; �4���/,�.�G���.4$ � ,:�3����#7,������0,��. ,�. � 3,� 3. � g < ��nfk�jO����d { gShfhfh;ä

ê ���Kí ! ä �7ä79 N�@[LOV|{ }�ä � ä ��: uAuÈB < {7B <=Þ �±ä � ä ^ :=< L H J ä�}¼< B < BKLWPfNz@A?�BKuAut\�ß�BKX H Þ N�P Þ H uUPSRLOJWB < XW@ H < LQ?�PSJWP < BKJM\'ß=utP;P Þ/à P�á@ < LOV H V H BSJML ä�} ?�? H�I L H Þ @ <"9 � } T � ä�} I=I u ä T�B�LOV ä

ê gShKí ! ä �±ä~9 Nz@tLWV|{ }�ä � ä ��: utuÈB < {~B <=Þ �7ä � ä ^ :=< L H J äÊa V H x H < H JWBKLO@tP < PKRÄB < B < BKLOPSN j@A?�BSuAu[\ BK?�? : JOBKL H x H PfN H LOJM@A?'? PfJWP < BSJM\²NzP Þ H u ä � ..4��# � ) ,��; =$�, =��#�� .�G�,�. � 35�,�.�G {9;: ß=Nz@tLML H Þ { ���f�S��ä

ê g;��í w ä¶a B j LOXW@ H <|ä� #:�1���# � #%�����3, =��#Q�Q�#7�C�0,��.�� ) �5�� � ���3,�#7,�. =��5(� ��� 35 13�#7, !�����3�F 3;-� ä �sH jX H BSJW?5Vç@ < } I=I uA@ H Þ T"BKLOV H NéB�LO@A? X òs9 H JW@ H X o Þ @tLWPfJWX�< �7ä � ä�C @ÈBSJMu H LB <=Þ w ä j w ä w @tP < X�{� PfV < � @Au H \�� 9 P < X�{ !`H á � PfJMî¶{ ���f�Si=ä

ê gfg�í � ä � B <=x B <=Þ p ä � B�Z³@ jrC V�B <�Þ BSJ ä T H ?5V�B < @A?�BKu±J H X I P < X H PSRUB�N H L5BKuAuA@t?ÄBSPfJrLO@A?ÄXrL H < L äC H < L H J_RvPfJUT H ?5V�B < @A? X�PSR 9 Pfut@ Þ X { 9 LWJ : ?EL : J H X�B <=Þ T�BKL H JW@ABSuAX a V HQY < @tZ H JWXM@tL]\�PSR a H â�BSXBKL }¼: XMLO@ < { o T �sw �QH�I PfJML ! : N ß H J < h��Ejlh��fä

ê gSkKí �~ä � V=@[L H ä�� @AXM?�P : X � u : @ ÞA� uAP�á ä !sH á � PfJMî ä T"?��-JOB�á j ^s@Autu ���f�Sn�ä

gS�