Luận văn a computational framework for simulating cardiovascular flows in patient specific anatomies

A COMPUTATIONAL FRAMEWORK FOR SIMULATING CARDIOVASCULAR FLOWS IN PATIENT-SPECIFIC ANATOMIES A DISSERTATION SUBMITTED TO THE FACULTY OF THE GRADUATE SCHOOL OF THE UNIVERSITY OF MINNESOTA da da i ho da i ho c da i ho c th da i ho c th uy da i ho c th uy loi da i ho c th uy loi da da i ho c th uy loi da i ho da i ho c th uy loi da i ho c da i ho c th uy loi da i ho c thuy da i ho c th uy loi da i ho c thuy lo da i ho c th uy loi da i ho c thuy i da i ho c th uy loi da i ho c thuy lo loi da dai ho da i ho c th uy loi da i ho c thuy i da i ho c th uy loi da i ho c thuy lo loi da dai i ho c th ho c da i ho c th uy loi da i ho c thuy i uy da i ho c th uy loi da i ho c thuy lo loi da dai i ho c th thuy lo ho c da i ho c th uy loi da i ho c thuy i uy lo i da i ho c th uy loi da i ho c thuy lo loi da dai i ho c th thuy lo i ho c da i ho c th uy loi da i ho c thuy i uy lo i da i ho c th uy loi da i ho c thuy lo loi da dai i ho c th thuy lo i uy i c thuy lo loi da dai i ho c th thuy lo i da i hoc c th uy lo i th ho i uy lo i da i ho hoc c th uy loi i da i ho c thuy uy loi lo i da i ho c th uy loi da i ho c thuy lo loi i da i uy lo da i ho c th i c th i ho hoc th uy loi i da i ho c thuy uy lo loi uy c thuy lo loi da dai i ho c th thuy lo i th c uy lo i da i ho hoc th uy loi i lo i da i ho c th uy loi i da i uy lo c th i ho hoc th uy loi i uy lo th c th uy loi i uy lo lo i i BY Trung Bao Le IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF Doctor of Philosophy Professor Fotis Sotiropoulos December, 2011 Mangh■■ng Luôn 123doc Th■a thu■n l■icam s■ tr■ h■u k■t s■ nghi■m t■im■t d■ng s■website mang kho m■i th■ m■ l■i d■n CH■P vi■n nh■ng cho ■■u kh■ng ng■■i NH■N quy■n chia dùng, l■ CÁC s■l■i v■i và■I■U t■t công h■n mua nh■t 2.000.000 ngh■ bán KHO■N cho tàihi■n ng■■i li■u TH■A tài th■ hàng li■u dùng hi■n THU■N ■■u ■ t■t Khi ■■i, Vi■t c■ khách b■n l■nh Nam Chào online hàng v■c: Tác m■ng tr■ khơng tài phong thành b■n khác chun ■■n thành tíngì d■ng, v■i so nghi■p, viên 123doc v■i cơng c■a b■n hồn ngh■ 123doc g■c h■o, thơng B■n và■■ n■p có tin, cao th■ ti■n ngo■i tính phóng vào ng■, Khách trách tài to,kho■n nhi■m thu nh■ c■a ■■i hàng tùy123doc, v■i ý cót■ng th■b■n d■ ng■■i dàng s■ dùng ■■■c tra c■u M■c h■■ng tàitiêu li■u nh■ng hàng m■t■■u quy■n cáchc■a l■i123doc.net sau xác,n■p nhanh ti■n tr■ chóng thành website th■ vi■n tài li■u online l■n nh■t Vi■t Nam, cung c■p nh■ng tài li■u ■■c không th■ tìm th■y th■ tr■■ng ngo■i tr■ 123doc.net Nhi■u event thú v■, event ki■m ti■n thi■t th■c 123doc luôn t■o c■ h■i gia t■ng thu nh■p online cho t■t c■ thành viên c■a website Mangh■n Luôn Th■a Xu■t Sau Nhi■u 123doc h■■ng phát thu■n l■i event cam s■ nh■n m■t tr■ t■ h■u k■t s■ thú nghi■m t■i ýxác n■m t■■ng m■t d■ng v■, s■ nh■n website mang event kho m■i ■■i, t■o t■ th■ m■ l■i c■ng ki■m ■■ng d■n 123doc CH■P vi■n nh■ng cho ■■u ■■ng ti■n h■ kh■ng ng■■i NH■N ■ã quy■n th■ng thi■t chia t■ng ki■m dùng, l■ CÁC s■ th■c s■ l■i b■■c v■i ti■n vàchuy■n ■I■U t■t công h■n mua 123doc online kh■ng nh■t 2.000.000 ngh■ bán KHO■N sang b■ng cho tài ■■nh hi■n ng■■i li■u ph■n tài TH■A tài v■ th■ li■u hàng t■o li■u thơng dùng tríhi■n THU■N hi■u c■ c■a ■■u ■ tin t■t h■i Khi ■■i, qu■ Vi■t xác c■ khách gia b■n nh■t, minh l■nh Nam t■ng Chào online hàng uy tài v■c: l■nh thu Tác m■ng tín kho■n tr■ nh■p không tài phong v■c cao thành b■n email nh■t tài online khác chuyên ■■n li■u thành tínb■n Mong cho d■ng, v■i so nghi■p, viên kinh ■ã t■t 123doc 123doc.net! v■i mu■n công ■■ng c■a c■ doanh b■n hoàn mang ngh■ 123doc ký g■c online thành v■i h■o, Chúng l■i thông B■n 123doc.netLink cho viên Tính ■■ n■p có tơi tin, c■ng c■a cao th■ ■■n cung ti■n ngo■i tính website phóng ■■ng th■i vào c■p ng■, Khách trách xác tài ■i■m D■ch xã to,kho■n th■c nhi■m h■i thutháng V■ nh■ m■t s■ c■a (nh■ ■■i hàng ■■■c tùy ngu■n 5/2014; 123doc, v■i ■■■c ý cóg■i t■ng th■ tài 123doc v■ mơ ngun b■n d■ ng■■i ■■a t■ dàng s■ v■■t d■■i tri dùng ■■■c ch■ tra th■c m■c ■ây) email c■u M■c h■■ng quý 100.000 cho tài b■n tiêu báu, li■u b■n, nh■ng ■ã hàng phong m■t l■■t tùy ■■ng ■■u quy■n cách truy thu■c phú, ky, c■a c■p ■a l■i b■n vào 123doc.net m■i d■ng, sau xác, vuingày, n■p lòng “■i■u nhanh giàu ti■n s■ ■■ng tr■ giá Kho■n chóng h■u thành tr■ nh■p 2.000.000 website ■■ng Th■a th■ email vi■n th■i Thu■n c■a thành mong tài v■ li■u viên mu■n S■ online ■■ng D■ng click t■o l■n ký, D■ch ■i■u vào nh■t l■t link ki■n V■” vào Vi■t 123doc top sau cho Nam, 200 ■ây cho ■ã cung các (sau g■iwebsite c■p users ■âynh■ng ■■■c cóph■ thêm tài bi■n g■i thu li■u t■t nh■t nh■p ■■c T■it■i khơng t■ng Chính Vi■tth■i th■ Nam, v■y ■i■m, tìm t■123doc.net th■y l■chúng tìm ki■m tơi th■ racóthu■c ■■i tr■■ng th■nh■m c■p top ngo■i 3nh■t ■áp Google tr■ ■KTTSDDV ■ng 123doc.net Nh■n nhu c■u ■■■c theo chiaquy■t danh s■ tài hi■u li■udo ch■t c■ng l■■ng ■■ng vàbình ki■mch■n ti■n online website ki■m ti■n online hi■u qu■ uy tín nh■t Lnh■n 123doc Sau Th■a Xu■t h■■ng phát thu■n cam nh■n m■t t■k■t s■ t■i ýxác n■m t■■ng d■ng s■ nh■n website mang ■■i, t■o t■l■i c■ng ■■ng d■n 123doc CH■P nh■ng ■■u ■■ng h■ NH■N ■ã quy■n th■ng chia t■ng ki■m CÁC s■s■ l■i b■■c ti■n vàchuy■n ■I■U t■t mua online kh■ng nh■t bán KHO■N sang b■ng cho tài ■■nh ng■■i li■u ph■n tài TH■A v■ li■u hàng thơng dùng tríTHU■N hi■u c■a ■■u tin Khi qu■ Vi■t xác khách nh■t, minh Nam Chào hàng uy tài l■nh Tác m■ng tín kho■n tr■ phong v■c cao thành b■n email nh■t tàichuyên ■■n li■u thành b■n Mong v■i nghi■p, viên kinh ■ã 123doc 123doc.net! mu■n ■■ng c■a doanh hoàn mang 123doc kýonline v■i h■o, Chúng l■ivà 123doc.netLink cho Tính ■■ n■p tơi c■ng cao ■■n cung ti■n tính ■■ng th■i vào c■p trách xác tài ■i■m D■ch xãkho■n th■c nhi■m h■itháng V■ m■t s■ c■a (nh■ ■■i ■■■c ngu■n 5/2014; 123doc, v■i ■■■c g■i t■ng tài 123doc v■ mô nguyên b■n ng■■i ■■a t■s■ v■■t d■■i tri dùng ■■■c ch■ th■c m■c ■ây) email M■c h■■ng quý 100.000 cho b■n tiêu báu, b■n, nh■ng ■ã hàng phong l■■t tùy ■■ng ■■u quy■n truy thu■c phú, ky, c■a c■p ■a l■i b■n vào 123doc.net m■i d■ng, sau vuingày, n■p lòng “■i■u giàu ti■n s■ ■■ng tr■ giá Kho■n h■u thành tr■ nh■p 2.000.000 website ■■ng Th■a th■ email vi■n th■i Thu■n c■a thành mong tài v■ li■u viên mu■n S■ online ■■ng D■ng click t■o l■n ký, D■ch ■i■u vào nh■t l■t link ki■n V■” vào Vi■t 123doc top sau cho Nam, 200 ■ây cho ■ã cung các (sau g■iwebsite c■p users ■âynh■ng ■■■c cóph■ thêm tài bi■n g■i thu li■u t■t nh■t nh■p ■■c T■it■i khơng t■ng Chính Vi■tth■i th■ Nam, v■y ■i■m, tìm t■123doc.net th■y l■chúng tìm ki■m tơi th■ racóthu■c ■■i tr■■ng th■nh■m c■p top ngo■i 3nh■t ■áp Google tr■ ■KTTSDDV ■ng 123doc.net Nh■n nhu c■u ■■■c theo chiaquy■t danh s■ tài hi■u li■udo ch■t c■ng l■■ng ■■ng vàbình ki■mch■n ti■n online website ki■m ti■n online hi■u qu■ uy tín nh■t Lnh■n Th■a Xu■t Sau Nhi■u 123doc Mang h■■ng phát thu■n l■i event cam s■ nh■n m■t tr■ t■ h■u k■t s■ thú nghi■m t■i ýxác n■m t■■ng m■t d■ng v■, s■ nh■n website mang event kho m■i ■■i, t■o t■ th■ m■ l■i c■ng ki■m ■■ng d■n 123doc CH■P vi■n nh■ng cho ■■u ■■ng ti■n h■ kh■ng ng■■i NH■N ■ã quy■n th■ng thi■t chia t■ng ki■m dùng, l■ CÁC s■ th■c s■ l■i b■■c v■i ti■n vàchuy■n ■I■U t■t công h■n mua 123doc online kh■ng nh■t 2.000.000 ngh■ bán KHO■N sang b■ng cho tài ■■nh hi■n ng■■i li■u ph■n tài TH■A tài v■ th■ li■u hàng t■o li■u thơng dùng tríhi■n THU■N hi■u c■ c■a ■■u ■ tin t■t h■i Khi ■■i, qu■ Vi■t xác c■ khách gia b■n nh■t, minh l■nh Nam t■ng Chào online hàng uy tài v■c: l■nh thu Tác m■ng tín kho■n tr■ nh■p khơng tài phong v■c cao thành b■n email nh■t tài online khác chun ■■n li■u thành tínb■n Mong cho d■ng, v■i so nghi■p, viên kinh ■ã t■t 123doc 123doc.net! v■i mu■n công ■■ng c■a c■ doanh b■n hoàn mang ngh■ 123doc ký g■c online thành v■i h■o, Chúng l■i thơng B■n 123doc.netLink cho viên Tính ■■ n■p có tơi tin, c■ng c■a cao th■ ■■n cung ti■n ngo■i tính website phóng ■■ng th■i vào c■p ng■, Khách trách xác tài ■i■m D■ch xã to,kho■n th■c nhi■m h■i thutháng V■ nh■ m■t s■ c■a (nh■ ■■i hàng ■■■c tùy ngu■n 5/2014; 123doc, v■i ■■■c ý cóg■i t■ng th■ tài 123doc v■ mô nguyên b■n d■ ng■■i ■■a t■ dàng s■ v■■t d■■i tri dùng ■■■c ch■ tra th■c m■c ■ây) email c■u M■c h■■ng quý 100.000 cho tài b■n tiêu báu, li■u b■n, nh■ng ■ã hàng phong m■t l■■t tùy ■■ng ■■u quy■n cách truy thu■c phú, ky, c■a c■p ■a l■i b■n vào 123doc.net m■i d■ng, sau xác, vuingày, n■p lòng “■i■u nhanh giàu ti■n s■ ■■ng tr■ giá Kho■n chóng h■u thành tr■ nh■p 2.000.000 website ■■ng Th■a th■ email vi■n th■i Thu■n c■a thành mong tài v■ li■u viên mu■n S■ online ■■ng D■ng click t■o l■n ký, D■ch ■i■u vào nh■t l■t link ki■n V■” vào Vi■t 123doc top sau cho Nam, 200 ■ây cho ■ã cung các (sau g■iwebsite c■p users ■âynh■ng ■■■c cóph■ thêm tài bi■n g■i thu li■u t■t nh■t nh■p ■■c T■it■i không t■ng Chính Vi■tth■i th■ Nam, v■y ■i■m, tìm t■123doc.net th■y l■chúng tìm ki■m tơi th■ racóthu■c ■■i tr■■ng th■nh■m c■p top ngo■i 3nh■t ■áp Google tr■ ■KTTSDDV ■ng 123doc.net Nh■n nhu c■u ■■■c theo chiaquy■t danh s■ tài hi■u li■udo ch■t c■ng l■■ng ■■ng vàbình ki■mch■n ti■n online website ki■m ti■n online hi■u qu■ uy tín nh■t u■t phát Nhi■u Mang Luôn 123doc Th■a Xu■t Sau h■n h■■ng phát thu■n l■i event s■ cam nh■n t■ m■t tr■ t■ h■u ýk■t s■ thú nghi■m t■i ýt■■ng xác n■m t■■ng m■t d■ng v■, s■ nh■n website mang event t■o kho m■i ■■i, t■o t■ c■ng th■ m■ l■i c■ng ki■m ■■ng d■n 123doc CH■P vi■n nh■ng cho ■■ng ■■u ■■ng ti■n h■ kh■ng ng■■i NH■N ■ã quy■n th■ng thi■t chia ki■m t■ng ki■m dùng, l■ CÁC s■ th■c ti■n s■ l■i b■■c v■i ti■n vàchuy■n ■I■U t■t công online h■n mua 123doc online kh■ng nh■t 2.000.000 ngh■ bán KHO■N b■ng sang b■ng cho tài ■■nh hi■n tài ng■■i li■u ph■n tài TH■A li■u tài v■ th■ li■u hàng t■o li■u thông dùng trí hi■u hi■n THU■N hi■u c■ c■a ■■u ■ tin qu■ t■t h■i Khi ■■i, qu■ Vi■t xác c■ khách gia nh■t, b■n nh■t, minh l■nh Nam t■ng Chào online uy hàng uy tài v■c: l■nh thu Tác tín m■ng tín kho■n tr■ cao nh■p khơng tài phong v■c cao thành b■n nh■t email nh■t tài online khác chuyên ■■n li■u thành tín Mong b■n Mong cho d■ng, v■i so nghi■p, viên kinh ■ã mu■n t■t 123doc 123doc.net! v■i mu■n công ■■ng c■a c■ doanh b■n mang hoàn mang ngh■ 123doc ký g■c online thành v■i l■i h■o, Chúng l■i thông B■n cho 123doc.netLink cho viên Tính ■■ n■p có c■ng tơi tin, c■ng c■a cao th■ ■■n cung ti■n ngo■i ■■ng tính website phóng ■■ng th■i vào c■p ng■, Khách trách xác xã tài ■i■m D■ch xã to,h■i kho■n th■c nhi■m h■i thum■t tháng V■ nh■ m■t s■ c■a (nh■ ■■i hàng ngu■n ■■■c tùy ngu■n 5/2014; 123doc, v■i ■■■c ý cótài g■i t■ng th■ tài 123doc ngun v■ mơ ngun b■n d■ ng■■i ■■a t■ dàng s■ v■■t tri d■■i tri dùng ■■■c ch■ th■c tra th■c m■c ■ây) email c■u quý M■c h■■ng quý 100.000 cho tài báu, b■n tiêu báu, li■u b■n, nh■ng phong ■ã hàng phong m■t l■■t tùy ■■ng ■■u phú, quy■n cách truy thu■c phú, ky, c■a c■p ■a ■a l■i b■n vào d■ng, 123doc.net m■i d■ng, sau xác, vuingày, n■p giàu lòng “■i■u nhanh giàu ti■n giá s■ ■■ng tr■ giá Kho■n chóng h■u tr■ thành tr■ nh■p ■■ng 2.000.000 website ■■ng Th■a th■ email th■i vi■n th■i Thu■n mong c■a thành mong tài v■ li■u mu■n viên mu■n S■ online ■■ng D■ng t■o click t■o l■n ■i■u ký, D■ch ■i■u vào nh■t l■t link ki■n ki■n V■” vào Vi■t 123doc cho top sau cho Nam, cho 200 ■ây cho ■ã cung các (sau g■i users website c■p users ■âynh■ng có ■■■c cóph■ thêm thêm tài bi■n g■i thu thu li■u t■t nh■p nh■t nh■p ■■c T■it■i Chính khơng t■ng Chính Vi■tth■i vìth■ Nam, vìv■y v■y ■i■m, tìm 123doc.net t■123doc.net th■y l■chúng tìm ki■m tơi th■ racó ■■i thu■c ■■i tr■■ng th■ nh■m nh■m c■p top ngo■i ■áp 3nh■t ■áp Google ■ng tr■ ■KTTSDDV ■ng 123doc.net nhu Nh■n nhuc■u c■u ■■■c chia theo chias■ quy■t danh s■tàitài hi■u li■u li■uch■t ch■t c■ng l■■ng l■■ng ■■ng vàvàki■m bình ki■mch■n ti■n ti■nonline online website ki■m ti■n online hi■u qu■ uy tín nh■t Nhi■u Mang Luôn 123doc Th■a Xu■t Sau h■n h■■ng phát thu■n l■i event s■ cam nh■n m■t tr■ t■ h■u k■t s■ thú nghi■m t■i ýxác n■m t■■ng m■t d■ng v■, s■ nh■n website mang event kho m■i ■■i, t■o t■ th■ m■ l■i c■ng ki■m ■■ng d■n 123doc CH■P vi■n nh■ng cho ■■u ■■ng ti■n h■ kh■ng ng■■i NH■N ■ã quy■n th■ng thi■t chia t■ng ki■m dùng, l■ CÁC s■ th■c s■ l■i b■■c v■i ti■n vàchuy■n ■I■U t■t công h■n mua 123doc online kh■ng nh■t 2.000.000 ngh■ bán KHO■N sang b■ng cho tài ■■nh hi■n ng■■i li■u ph■n tài TH■A tài v■ th■ li■u hàng t■o li■u thơng dùng tríhi■n THU■N hi■u c■ c■a ■■u ■ tin t■t h■i Khi ■■i, qu■ Vi■t xác c■ khách gia b■n nh■t, minh l■nh Nam t■ng Chào online hàng uy tài v■c: l■nh thu Tác m■ng tín kho■n tr■ nh■p khơng tài phong v■c cao thành b■n email nh■t tài online khác chuyên ■■n li■u thành tínb■n Mong cho d■ng, v■i so nghi■p, viên kinh ■ã t■t 123doc 123doc.net! v■i mu■n công ■■ng c■a c■ doanh b■n hoàn mang ngh■ 123doc ký g■c online thành v■i h■o, Chúng l■i thông B■n 123doc.netLink cho viên Tính ■■ n■p có tơi tin, c■ng c■a cao th■ ■■n cung ti■n ngo■i tính website phóng ■■ng th■i vào c■p ng■, Khách trách xác tài ■i■m D■ch xã to,kho■n th■c nhi■m h■i thutháng V■ nh■ m■t s■ c■a (nh■ ■■i hàng ■■■c tùy ngu■n 5/2014; 123doc, v■i ■■■c ý cóg■i t■ng th■ tài 123doc v■ mô nguyên b■n d■ ng■■i ■■a t■ dàng s■ v■■t d■■i tri dùng ■■■c ch■ tra th■c m■c ■ây) email c■u M■c h■■ng quý 100.000 cho tài b■n tiêu báu, li■u b■n, nh■ng ■ã hàng phong m■t l■■t tùy ■■ng ■■u quy■n cách truy thu■c phú, ky, c■a c■p ■a l■i b■n vào 123doc.net m■i d■ng, sau xác, vuingày, n■p lòng “■i■u nhanh giàu ti■n s■ ■■ng tr■ giá Kho■n chóng h■u thành tr■ nh■p 2.000.000 website ■■ng Th■a th■ email vi■n th■i Thu■n c■a thành mong tài v■ li■u viên mu■n S■ online ■■ng D■ng click t■o l■n ký, D■ch ■i■u vào nh■t l■t link ki■n V■” vào Vi■t 123doc top sau cho Nam, 200 ■ây cho ■ã cung các (sau g■iwebsite c■p users ■âynh■ng ■■■c cóph■ thêm tài bi■n g■i thu li■u t■t nh■t nh■p ■■c T■it■i khơng t■ng Chính Vi■tth■i th■ Nam, v■y ■i■m, tìm t■123doc.net th■y l■chúng tìm ki■m tơi th■ racóthu■c ■■i tr■■ng th■nh■m c■p top ngo■i 3nh■t ■áp Google tr■ ■KTTSDDV ■ng 123doc.net Nh■n nhu c■u ■■■c theo chiaquy■t danh s■ tài hi■u li■udo ch■t c■ng l■■ng ■■ng vàbình ki■mch■n ti■n online website ki■m ti■n online hi■u qu■ uy tín nh■t da da i ho da i ho c da i ho c th da i ho c th uy da i ho c th uy loi da i ho c th uy loi da da i ho c th uy loi da i ho da i ho c th uy loi da i ho c da i ho c th uy loi da i ho c thuy da i ho c th uy loi da i ho c thuy lo da i ho c th uy loi da i ho c thuy i da i ho c th uy loi da i ho c thuy lo loi da dai ho da i ho c th uy loi da i ho c thuy i da i ho c th uy loi da i ho c thuy lo loi da dai i ho c th ho c da i ho c th uy loi da i ho c thuy i uy da i ho c th uy loi da i ho c thuy lo loi da dai i ho c th thuy lo ho c da i ho c th uy loi da i ho c thuy i uy lo i da i ho c th uy loi da i ho c thuy lo loi da dai i ho c th thuy lo i ho c da i ho c th uy loi da i ho c thuy i uy lo i da i ho c th uy loi da i ho c thuy lo loi da dai i ho c th thuy lo i uy i c thuy lo loi da dai i ho c th thuy lo i da i hoc c th uy lo i th ho i uy lo i da i ho hoc c th uy loi i da i ho c thuy uy loi lo i da i ho c th uy loi da i ho c thuy lo loi i da i uy lo da i ho c th i c th i ho hoc th uy loi i da i ho c thuy uy lo loi uy c thuy lo loi da dai i ho c th thuy lo i th c uy lo i da i ho hoc th uy loi i lo i da i ho c th uy loi i da i uy lo c th i ho hoc th uy loi i uy lo th c th uy loi i uy lo lo i i c Trung Bao Le 2011 ALL RIGHTS RESERVED Acknowledgements I gratefully acknowledge the instruction of my advisor, Professor Sotiropoulos, who guided me all the ways through a series of challenges during my time at Saint Anthony Falls Lab I am in debt of his encouragement and belief in my capability of putting out my curiosity into actual research projects I believe that his advices will go a long way with me throughout the rest of my scientific adventure Cockburn, whom I greatly admire their knowledge and instruction during my course work, for giving me kind advices on my research Thanks extended to Dr Kallmes at Mayo Clinic who provided me all the medical scanned images in the aneurysm project I would also like to thank Professor Yoganathan at Georgia Tech, who provided me the experimental data for the left ventricle Sincere thanks to Professor Webster at Georgia Tech, Professor Longmire at U of Minnesota and Dr Troolin at TSI for their dataset of the inclined nozzle case, which intrigued me so much for its beauty and simplicity Thanks to my friend, Iman Borazjani, who constantly gives me kind advices and supports at the initial stages of my research Thanks to my friends at the room 370: Fan Yi, Paola Passalacqua, Arvind Singh, Bereket Yohannes Tewoldebrhan, Ted Fuller, Man Liang, Vamsi Ganti and Mohammad Hajit The members of my research group: Seokkoo Kang, Liang Ge, Cristian Escauriaza provided me lots of feedback from my research questions I would like to thank all people at SAFL for being kind, supportive and empathetic Finally, I would also like to acknowledge Vietnam Education Foundation and United States National Academies for the fellowship, which provide me the opportunity to expand my horizon on science This work is also supported by grant NIH RO1-HL07262, the Minnesota SuperComputing Institute and Mayo Clinic i da da i ho da i ho c da i ho c th da i ho c th uy da i ho c th uy loi da i ho c th uy loi da da i ho c th uy loi da i ho da i ho c th uy loi da i ho c da i ho c th uy loi da i ho c thuy da i ho c th uy loi da i ho c thuy lo da i ho c th uy loi da i ho c thuy i da i ho c th uy loi da i ho c thuy lo loi da dai ho da i ho c th uy loi da i ho c thuy i da i ho c th uy loi da i ho c thuy lo loi da dai i ho c th ho c da i ho c th uy loi da i ho c thuy i uy da i ho c th uy loi da i ho c thuy lo loi da dai i ho c th thuy lo ho c da i ho c th uy loi da i ho c thuy i uy lo i da i ho c th uy loi da i ho c thuy lo loi da dai i ho c th thuy lo i ho c da i ho c th uy loi da i ho c thuy i uy lo i da i ho c th uy loi da i ho c thuy lo loi da dai i ho c th thuy lo i uy i c thuy lo loi da dai i ho c th thuy lo i da i hoc c th uy lo i th ho i uy lo i da i ho hoc c th uy loi i da i ho c thuy uy loi lo i da i ho c th uy loi da i ho c thuy lo loi i da i uy lo da i ho c th i c th i ho hoc th uy loi i da i ho c thuy uy lo loi uy c thuy lo loi da dai i ho c th thuy lo i th c uy lo i da i ho hoc th uy loi i lo i da i ho c th uy loi i da i uy lo c th i ho hoc th uy loi i uy lo th c th uy loi i uy lo lo i i Thanks to my committee members Professor Voller, Hondzo, Candler, Mahesh and da da i ho da i ho c da i ho c th da i ho c th uy da i ho c th uy loi da i ho c th uy loi da da i ho c th uy loi da i ho da i ho c th uy loi da i ho c da i ho c th uy loi da i ho c thuy da i ho c th uy loi da i ho c thuy lo da i ho c th uy loi da i ho c thuy i da i ho c th uy loi da i ho c thuy lo loi da dai ho da i ho c th uy loi da i ho c thuy i da i ho c th uy loi da i ho c thuy lo loi da dai i ho c th ho c da i ho c th uy loi da i ho c thuy i uy da i ho c th uy loi da i ho c thuy lo loi da dai i ho c th thuy lo ho c da i ho c th uy loi da i ho c thuy i uy lo i da i ho c th uy loi da i ho c thuy lo loi da dai i ho c th thuy lo i ho c da i ho c th uy loi da i ho c thuy i uy lo i da i ho c th uy loi da i ho c thuy lo loi da dai i ho c th thuy lo i uy i c thuy lo loi da dai i ho c th thuy lo i da i hoc c th uy lo i th ho i uy lo i da i ho hoc c th uy loi i da i ho c thuy uy loi lo i da i ho c th uy loi da i ho c thuy lo loi i da i uy lo da i ho c th i c th i ho hoc th uy loi i da i ho c thuy uy lo loi uy c thuy lo loi da dai i ho c th thuy lo i th c uy lo i da i ho hoc th uy loi i lo i da i ho c th uy loi i da i uy lo c th i ho hoc th uy loi i uy lo th c th uy loi i uy lo lo i i Dedication To my wife and my son, who have constantly supported me throughout challenging years ii Abstract The goal of the thesis is to develop a computational framework for simulating cardiovascular flows in patient-specific anatomies The numerical method is based on the curvilinear immersed method approach and is able to simulate pulsatile flow in complex anatomical geometries, incorporates a novel, lumped-parameter kinematic model of the left ventricle wall driven by electrical excitation, and can carry out fluid-structure interaction simulations between the blood flow and implanted bi-leaflet mechanical heart valves (BMHV) The ability of the method to resolve and illuminate the physics of dynamically rich vortex phenomena is demonstrated by carrying out simulations of impulsively driven flow through inclined nozzles and comparing the computed results with tex formation and wall shear-stress dynamics inside an intracranial aneurysm; 2) the hemodynamics of early diastolic filling in a patient-specific left ventricle (LV); and 3) and fluid-structure interaction of a BMHV implanted in the aortic position of a patientspecific LV/aorta configuration driven by electrical excitation of the LV wall motion For all cases the computed results yield new, clinically-relevant insights into the underlying flow phenomena and underscore the potential of the numerical method as a powerful tool for carrying out high-resolution simulations in patient-specific anatomic geometries Future work will focus on extending the fluid-structure interaction scheme to simulate soft tissues and other medical devices, such as stents, bio-prosthetic tri-leaflet and percutaneous heart valves iii da da i ho da i ho c da i ho c th da i ho c th uy da i ho c th uy loi da i ho c th uy loi da da i ho c th uy loi da i ho da i ho c th uy loi da i ho c da i ho c th uy loi da i ho c thuy da i ho c th uy loi da i ho c thuy lo da i ho c th uy loi da i ho c thuy i da i ho c th uy loi da i ho c thuy lo loi da dai ho da i ho c th uy loi da i ho c thuy i da i ho c th uy loi da i ho c thuy lo loi da dai i ho c th ho c da i ho c th uy loi da i ho c thuy i uy da i ho c th uy loi da i ho c thuy lo loi da dai i ho c th thuy lo ho c da i ho c th uy loi da i ho c thuy i uy lo i da i ho c th uy loi da i ho c thuy lo loi da dai i ho c th thuy lo i ho c da i ho c th uy loi da i ho c thuy i uy lo i da i ho c th uy loi da i ho c thuy lo loi da dai i ho c th thuy lo i uy i c thuy lo loi da dai i ho c th thuy lo i da i hoc c th uy lo i th ho i uy lo i da i ho hoc c th uy loi i da i ho c thuy uy loi lo i da i ho c th uy loi da i ho c thuy lo loi i da i uy lo da i ho c th i c th i ho hoc th uy loi i da i ho c thuy uy lo loi uy c thuy lo loi da dai i ho c th thuy lo i th c uy lo i da i ho hoc th uy loi i lo i da i ho c th uy loi i da i uy lo c th i ho hoc th uy loi i uy lo th c th uy loi i uy lo lo i i experimental measurements The method is subsequently applied to simulate: 1) vor- Acknowledgements Dedication Abstract iii List of Tables vii List of Figures ix Introduction 1.3 1.1 Motivation 1.2 Literature review 1.2.1 In − vivo and In − vitro studies 1.2.2 Computational studies Thesis objectives and outlines Methodology 10 2.1 Problem statements 10 2.2 Governing equations and boundary conditions for fluid domain Ωf 12 2.3 Governing equations for solid domain Ωs 14 2.4 The Fluid-Structure Interaction algorithm to calculate ΓF SI 16 2.5 Numerical discretization and integration 18 2.5.1 Governing equations in generalized coordinate system 19 2.5.2 Hybrid staggered/non-staggered grid approach 20 iv da da i ho da i ho c da i ho c th da i ho c th uy da i ho c th uy loi da i ho c th uy loi da da i ho c th uy loi da i ho da i ho c th uy loi da i ho c da i ho c th uy loi da i ho c thuy da i ho c th uy loi da i ho c thuy lo da i ho c th uy loi da i ho c thuy i da i ho c th uy loi da i ho c thuy lo loi da dai ho da i ho c th uy loi da i ho c thuy i da i ho c th uy loi da i ho c thuy lo loi da dai i ho c th ho c da i ho c th uy loi da i ho c thuy i uy da i ho c th uy loi da i ho c thuy lo loi da dai i ho c th thuy lo ho c da i ho c th uy loi da i ho c thuy i uy lo i da i ho c th uy loi da i ho c thuy lo loi da dai i ho c th thuy lo i ho c da i ho c th uy loi da i ho c thuy i uy lo i da i ho c th uy loi da i ho c thuy lo loi da dai i ho c th thuy lo i uy i c thuy lo loi da dai i ho c th thuy lo i da i hoc c th uy lo i th ho i uy lo i da i ho hoc c th uy loi i da i ho c thuy uy loi lo i da i ho c th uy loi da i ho c thuy lo loi i da i uy lo da i ho c th i c th i ho hoc th uy loi i da i ho c thuy uy lo loi uy c thuy lo loi da dai i ho c th thuy lo i th c uy lo i da i ho hoc th uy loi i lo i da i ho c th uy loi i da i uy lo c th i ho hoc th uy loi i uy lo th c th uy loi i uy lo lo i i Contents i ii 2.5.3 Velocity reconstruction at the immersed boundary nodes 22 2.5.4 Time integration and fractional step method 23 2.5.5 Iterative methods for the non-linear momentum equation 24 2.6 Poisson solver 26 2.7 Domain decomposition 27 2.8 Load calculation 29 clined nozzles 31 3.1 Introduction 32 3.2 Governing equations and numerical method 37 3.3 Description of simulated test cases 37 3.4 Computational details 41 3.5 Validation of the numerical method 43 3.5.1 Case 1: The axisymmetric nozzle 43 3.5.2 Case 2: The D/2 inclined nozzle 45 3.5.3 Case 3: The D inclined nozzle 49 3.6 3D vortex dynamics at the exit of inclined nozzles 50 3.7 The kinematics of the circumferential flow 64 3.8 Conclusions 65 The hemodynamics of intracranial aneurysms 4.1 Introduction 4.2 Vortex formation and wall shear stress dynamics in side-wall aneurysms: 4.3 69 The effect of flow wave form 73 4.2.1 Introduction 73 4.2.2 Materials and methods 74 4.2.3 Results 83 4.2.4 Discussion 94 Conclusions 100 The kinematic model of the left ventricle 5.1 69 101 The left ventricular anatomy 101 v da da i ho da i ho c da i ho c th da i ho c th uy da i ho c th uy loi da i ho c th uy loi da da i ho c th uy loi da i ho da i ho c th uy loi da i ho c da i ho c th uy loi da i ho c thuy da i ho c th uy loi da i ho c thuy lo da i ho c th uy loi da i ho c thuy i da i ho c th uy loi da i ho c thuy lo loi da dai ho da i ho c th uy loi da i ho c thuy i da i ho c th uy loi da i ho c thuy lo loi da dai i ho c th ho c da i ho c th uy loi da i ho c thuy i uy da i ho c th uy loi da i ho c thuy lo loi da dai i ho c th thuy lo ho c da i ho c th uy loi da i ho c thuy i uy lo i da i ho c th uy loi da i ho c thuy lo loi da dai i ho c th thuy lo i ho c da i ho c th uy loi da i ho c thuy i uy lo i da i ho c th uy loi da i ho c thuy lo loi da dai i ho c th thuy lo i uy i c thuy lo loi da dai i ho c th thuy lo i da i hoc c th uy lo i th ho i uy lo i da i ho hoc c th uy loi i da i ho c thuy uy loi lo i da i ho c th uy loi da i ho c thuy lo loi i da i uy lo da i ho c th i c th i ho hoc th uy loi i da i ho c thuy uy lo loi uy c thuy lo loi da dai i ho c th thuy lo i th c uy lo i da i ho hoc th uy loi i lo i da i ho c th uy loi i da i uy lo c th i ho hoc th uy loi i uy lo th c th uy loi i uy lo lo i i The dynamics of vortex rings in impulsively driven flow through in- 5.2 Left ventricular modeling 103 5.3 A cell-based electrical activation model for the left ventricle 106 5.4 5.3.1 The anatomic model 106 5.3.2 Derivation of the kinematics model 107 5.3.3 Results 115 Conclusions 121 Hemodynamics of the left ventricle 122 6.1 Introduction 122 6.2 Computational setup 124 6.3 Results and discussions 6.4 Conclusions 135 126 Fluid-Structure Interaction of an aortic mechanical heart valve pros140 7.1 Introduction 140 7.2 Computational setup 143 7.3 Results and discussions 7.4 Conclusions 158 146 Summary and conclusions 159 8.0.1 Summary and conclusions 159 8.0.2 Future work 162 Bibliography 164 vi da da i ho da i ho c da i ho c th da i ho c th uy da i ho c th uy loi da i ho c th uy loi da da i ho c th uy loi da i ho da i ho c th uy loi da i ho c da i ho c th uy loi da i ho c thuy da i ho c th uy loi da i ho c thuy lo da i ho c th uy loi da i ho c thuy i da i ho c th uy loi da i ho c thuy lo loi da dai ho da i ho c th uy loi da i ho c thuy i da i ho c th uy loi da i ho c thuy lo loi da dai i ho c th ho c da i ho c th uy loi da i ho c thuy i uy da i ho c th uy loi da i ho c thuy lo loi da dai i ho c th thuy lo ho c da i ho c th uy loi da i ho c thuy i uy lo i da i ho c th uy loi da i ho c thuy lo loi da dai i ho c th thuy lo i ho c da i ho c th uy loi da i ho c thuy i uy lo i da i ho c th uy loi da i ho c thuy lo loi da dai i ho c th thuy lo i uy i c thuy lo loi da dai i ho c th thuy lo i da i hoc c th uy lo i th ho i uy lo i da i ho hoc c th uy loi i da i ho c thuy uy loi lo i da i ho c th uy loi da i ho c thuy lo loi i da i uy lo da i ho c th i c th i ho hoc th uy loi i da i ho c thuy uy lo loi uy c thuy lo loi da dai i ho c th thuy lo i th c uy lo i da i ho hoc th uy loi i lo i da i ho c th uy loi i da i uy lo c th i ho hoc th uy loi i uy lo th c th uy loi i uy lo lo i i thesis in the left heart List of Tables 3.1 Summary of geometrical parameters for the three simulated test cases With reference to Fig 3.2, I is the initial position of the piston S is the axial distance from the stopping location of the piston to the shortest lip of the nozzle, T is the location of the average nozzle exit lip along the cylinder centerline (it is also the distance from origin O to the tank top along Z direction) C is the angle of the cutting plane to the nozzle axis The computational grids used for the grid sensitivity study ∆x, ∆y and da da i ho da i ho c da i ho c th da i ho c th uy da i ho c th uy loi da i ho c th uy loi da da i ho c th uy loi da i ho da i ho c th uy loi da i ho c da i ho c th uy loi da i ho c thuy da i ho c th uy loi da i ho c thuy lo da i ho c th uy loi da i ho c thuy i da i ho c th uy loi da i ho c thuy lo loi da dai ho da i ho c th uy loi da i ho c thuy i da i ho c th uy loi da i ho c thuy lo loi da dai i ho c th ho c da i ho c th uy loi da i ho c thuy i uy da i ho c th uy loi da i ho c thuy lo loi da dai i ho c th thuy lo ho c da i ho c th uy loi da i ho c thuy i uy lo i da i ho c th uy loi da i ho c thuy lo loi da dai i ho c th thuy lo i ho c da i ho c th uy loi da i ho c thuy i uy lo i da i ho c th uy loi da i ho c thuy lo loi da dai i ho c th thuy lo i uy i c thuy lo loi da dai i ho c th thuy lo i da i hoc c th uy lo i th ho i uy lo i da i ho hoc c th uy loi i da i ho c thuy uy loi lo i da i ho c th uy loi da i ho c thuy lo loi i da i uy lo da i ho c th i c th i ho hoc th uy loi i da i ho c thuy uy lo loi uy c thuy lo loi da dai i ho c th thuy lo i th c uy lo i da i ho hoc th uy loi i lo i da i ho c th uy loi i da i uy lo c th i ho hoc th uy loi i uy lo th c th uy loi i uy lo lo i i 3.2 41 ∆z are the grid spacing in X, Y and Z directions in the region of interest, respectively The grid is refined only within the region of interest marked with the thick black line in Fig 3.2 4.1 42 Parameters characterizing various waveforms and flow patterns that emerge C and V denote the cavity and vortex ring modes, respectively Italics identify the original waveforms used to construct additional wave forms through scaling for each case Abbreviation: a)Remax : peak systolic Reynolds number, b)Re: Time-averaged over one cardiac cycle Reynolds number, c)α: Womersley number, d)P I: Pulsatility Index and e)An: Aneurysm Number vii 82 (see Eq 5.11 for definition) 5.2 da da i ho da i ho c da i ho c th da i ho c th uy da i ho c th uy loi da i ho c th uy loi da da i ho c th uy loi da i ho da i ho c th uy loi da i ho c da i ho c th uy loi da i ho c thuy da i ho c th uy loi da i ho c thuy lo da i ho c th uy loi da i ho c thuy i da i ho c th uy loi da i ho c thuy lo loi da dai ho da i ho c th uy loi da i ho c thuy i da i ho c th uy loi da i ho c thuy lo loi da dai i ho c th ho c da i ho c th uy loi da i ho c thuy i uy da i ho c th uy loi da i ho c thuy lo loi da dai i ho c th thuy lo ho c da i ho c th uy loi da i ho c thuy i uy lo i da i ho c th uy loi da i ho c thuy lo loi da dai i ho c th thuy lo i ho c da i ho c th uy loi da i ho c thuy i uy lo i da i ho c th uy loi da i ho c thuy lo loi da dai i ho c th thuy lo i uy i c thuy lo loi da dai i ho c th thuy lo i da i hoc c th uy lo i th ho i uy lo i da i ho hoc c th uy loi i da i ho c thuy uy loi lo i da i ho c th uy loi da i ho c thuy lo loi i da i uy lo da i ho c th i c th i ho hoc th uy loi i da i ho c thuy uy lo loi uy c thuy lo loi da dai i ho c th thuy lo i th c uy lo i da i ho hoc th uy loi i lo i da i ho c th uy loi i da i 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