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Open Stent Design, presented at the 2010 FDA / NHLBI / NSF Workshop for Computer Methods in Cardiovascular Devices
Citation preview
Open Stent DesignComputer Methods for
Cardiovascular Devices 2010
Craig [email protected]
Thursday, June 10, 2010
© 2010 NDC. Reuse and adaptation permitted with attribution per the Creative Commons Attribution-Share Alike 3.0 United States License
• Introduction to Open Source•Open Stent Design•Stent Mechanics•Stent Calculator•Community and Resources
2Thursday, June 10, 2010
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Linux
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Mozilla Firefox ™
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Sun Microsystems Java ™
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Google Android ™
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openmoko.org: open design mobile phone / pda
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wired.com: VIA OpenBook
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compuIng hardware plaJorm: arduino.cc
Example Applica,onsThermostat
Line tracking robotLED controllerMo,on trackerIntrusion alarm
Home HVAC control
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“world’s Iniest open source violin” hNp://www.thingiverse.com/thing:3193
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reprap.org: “ReplicaIng Rapid-‐Prototyper”
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sciencecommons.org, healthcommons.net
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Human genome – DNA sequencing interferogram: wikimedia.org
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plos.org
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simtk.org
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commons.wikimedia.org
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ASPECT
creaIvecommons.org
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!Thursday, June 10, 2010
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• Introduction to Open Source•Open Stent Design•Stent Mechanics•Stent Calculator•Community and Resources
22Thursday, June 10, 2010
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Thursday, June 10, 2010
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Thursday, June 10, 2010
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Thursday, June 10, 2010
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Thursday, June 10, 2010
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Thursday, June 10, 2010
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Thursday, June 10, 2010
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• Introduction to Open Source•Open Stent Design•Stent Mechanics•Stent Calculator•Community and Resources
36Thursday, June 10, 2010
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A simple stent pattern
37
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Array of “Z” shaped elements
38
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Array of “V” shaped elements
39
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Array of Simple BEAMS
40
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Solve for STRAIN and FORCE
41
E = modulus of elasticity
I = moment of inertia, beam cross sectionw = Strut WidthL = strut length
Strain = ε = 3wL2 ⋅δ
Force = F =12EIL3 ⋅δ
FL2
FL2
F
F L
Thursday, June 10, 2010
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Strain and Force for a Simple Beam Stent
42
!
F =Etw3
L3!" !
! = 3wL2
"# !
t
wL
Thursday, June 10, 2010
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x
strain
stre
ss
≈0.1-0.2% ≈1.0-2.0%
Nitinol
Steel
Thursday, June 10, 2010
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• Introduction to Open Source•Open Stent Design•Stent Mechanics•Stent Calculator•Community and Resources
44Thursday, June 10, 2010
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Stent CalculatorRelating design INPUTS and OUTPUTS
45
strength / stiffnessscaffolding
constrained profile
expansion anglesforeshortening
surface areacontact area
percent open areacontact pressure
mean strainstrain amplitude
safety factor
radiopacity
tube diametermodulus of elasticity
densitymass absorption coefficient
number of strutsstrut widthstrut length
strut thickness
material removaltransition temperature
vessel diametervessel compliancesystolic pressurediastolic pressure
mean strainstrain amplitude
safety factor
Thursday, June 10, 2010
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Stent Calculator Worksheet: 34 Design Inputs
46
!"#$"%&#'()$%*$+,"' -$("' ./0,#!"# $%&'( )*+,-./'0/&'(*+)1 2 #3!"4 $%15.*51 15.*51/6.'*)7/&8.&*+0-.-)&- 2 !4!"9 :%5*,- '*5-./786+5-./'0/5*,8); ++ #"<#=!"! 5%.6> >6((/5?8&@)-11/'0/.6>/5*,8); ++ 3"#A3!"= B%15.*5%8))-. 15.*5/(-);5?/5'/8))-./56);-)51 ++ #"433!"C >%6D-E%.6> 6D-E/>875?F/61G&*5 ++ 3"#93!"A H%,.87;- 6E86(/;6D/,-5>--)/'*5-./56);-)51 ++ 3"#=3!"I J%,.87;- &8.&*+0-.-)K6(/1D6)/'0/,.87;- ++ 3"333!"< >%,.87;-%.6> >875?/'0/,.87;- ++ 3"#4=
!"#3 $%,.87;-1 )*+,-./'0/,.87;-1/6.'*)7/&8.&" 2 A
1234#''%1/2/5#"#2'!"## >%@-.0 +8)8+*+/-L-&85M-/@-.0/>875? ++ 3"34=!"#4 +%>875? >875?/.-+'M6(/8)/N)81?8); ++ 3"39C!"#9 +%5?8&@)-11 >6((/5?8&@)-11/.-+'M6( ++ 3"3=<!"#! O0 O0/'0/N)81?-7/&'+D')-)5 7-;P 4A
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
!#28(4#%1/2/5#"#2'!"4A :%1-5 -ED6)7-7/8))-./786+-5-./'0/15-)5 ++ I"33!"4I :%M-1 786+-5-./'0/M-11-( ++ C"=3!"4< : 6)6(R181/786+-5-. ++ C"=3!"93 P%D-.&-)5 &'+D(86)&-^/]/&?6);-/8)/786+-5-. ] C]!"9# P%D.-11*.- &'+D(86)&-^/D.-11*.-/0'./]/&?6);- ++T; #33!"94 X%1R15'(8& 1R15'(8&/D.-11*.-/65/8+D(6)5/185- ++T; #=3!"99 X%78615'(8& 78615'(8&/D.-11*.-/65/8+D(6)5/185- ++T; =3!"9! X%+-6) +-6)/D.-11*.-/65/8+D(6)5/185- ++T; #33
Thursday, June 10, 2010
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Stent Calculator Worksheet: 78 Design Outputs
47
!"#$"%&'(#$)'*$%+,-.)!"#$ %&'())* +,-.(/0120'())*03/1,+40'5/' 6 78
!"#9 :&'/5-; 2,))<0'1+*=/35+(401,=(/0453-(=(/ -- 8">8$
!"#? @&*=/,= (A('BC(0)(+D=E0120*=/,= -- 8"##F
!"#G H&*=/,=&/3H H54=E0120*=/,=I03*J',= -- F"88G
!"#> H&*=/,= H54=E0120*=/,=I0K+5*E(4 -- F"FG7
!"!F H&./54D( H54=E0120./54D(I0K+5*E(4 -- F"FG>
!"!8 H&3;(L H54=E01203;(LI0K+5*E(4 -- F"F>!
!"!7 = H3))0=E5'M+(**I0K+5*E(4 -- F"888
!"/0"%1$2-#%,$3%#.5*$%+,-.)!"!# =E(=3&*(= *=/,=03+D)(03=02,))0(L;3+*51+ 4(D 7F"F
!"!! =E(=3&4 *=/,=03+D)(03=03+3)<*5*0453-(=(/ 4(D 8!">
!"!$ 4()=3&=E(=3&4 'E3+D(05+03+D)( 4(D $"8
!"!9 =H1&=E(=3 -3L5-,-05+'),4(403+D)( 4(D !F"F
!"!? 4()=3&4 *=/,=04(N('B1+ -- F"88G
!"!G =E(=3&8-- *=/,=03+D)(08--0O0(L;0453-(=(/ 4(D 89"9
!"!> 4()=3&=E(=3&8-- 'E3+D(05+03+D)(08--0O0(L;0453-(=(/ 4(D #"!
!"$F 4()=3&8-- *=/,=04(N('B1+08--0O0(L;0453-(=(/ -- F"F?>
6#$2"7%+,-.)!"$8 P&'())&'/5-; )(+D=E0120'())05+0'/5-;(40*=3=( -- 8"98F
!"$7 P&=1=3)&'/5-; )(+D=E0120*=(+=05+0'/5-;(40*=3=( -- 8$">$F
!"$# P&'()) )(+D=E0120'())03=03+3)<*5*0453-(=(/ -- 8"$9>
!"$! P&=1=3) )(+D=E0120*=(+=03=03+3)<*5*0453-(=(/ -- 8$"$!!
!"$$ QR 21/(*E1/=(+5+D03=03+3)<*5*0453-(=(/ S 7"$!S
!0/8,.#%1/#,9%:*-0(#9%;,))%<)5(,"#)!"$9 T&*=/,= 1,=(/0*,/23'(03/(3012030*=/,= --U7 F"F>?
!"$? V&3;(L 1,=(/0/345,*01203+03;(L -- F"88#
!"$G T&3;(L 1,=(/0*,/23'(03/(301203+03;(L --U7 F"F78
!"$> T&./54D( 1,=(/0*,/23'(03/(3012030./54D( --U7 F"F8#
!"9F T&'1+=3'= =1=3)0*=(+=01,=(/0'1+=3'=03/(3 --U7 $F"#
!"98 T&'<)5+4(/ 3/(30120'<)5+4(/01'',;5(40.<0*=(+= --U7 #8?"!
!"97 WXT ;(/'(+=3D(0'1C(/3D(03/(3 S 8$">S
!"9# WYT ;(/'(+=3D(01;(+03/(3 S G!"8S
!"9! H&*=/,=&54 *=/,=0H54=E03=05++(/0453-(=(/ -- F"F99
!"9$ T&*=/,=&54 5++(/0*,/23'(03/(3012030*=/,= --U7 F"F??
!"99 T&3;(L&54 5++(/0*,/23'(03/(301203+03;(L --U7 F"F8?
!"9? T&./54D(&54 5++(/0*,/23'(03/(3012030./54D( --U7 F"F88
!"9G Z&*=/,= *=/,=0C1),-( --U# F"F8F
!"9> Z&3;(L 3;(L0C1),-( --U# F"FF7
!"?F Z&./54D( ./54D(0C1),-( --U# F"FF8
!"?8 Z&=1=3) =1=3)0C1),-( --U# $"F78
!"?7 -3** (*B-3=(40-3** -D ##"9!F
;*(#$"%*8%=$#/5,!"?# V 1,=(/0/345,*0120=,.( -- F">$?$F
!"?! = H3))0=E5'M+(** -- F"888FF
!"?$ H *=/,=0H54=E -- F"FG77!
!"?9 3);E3 3);E30;3/3-(=(/ /34 F"F!7>$
!"?? [ -1-(+=01205+(/B3 --U! !"#7\JF9
>*/.#9%!"/#))9%!"/,'$!"?G Q&E11; E11;0'1-;1+(+=0120*=/,=021/'( % G"G7\JF7
!"?> Q&E11;&8-- E11;0'1-;1+(+=0120*=/,=021/'( % $">8\JF7
!"GF *=/35+&4 -3L0*=/35+03=03+3)<*5*0453-(=(/ S 8"9!S
!"G8 *=/35+&8-- -3L0*=/35+03=03+3)<*5*0453-(=(/ S 8"8FS
!"#$$%"#&'()"*+,'-.+$/0+/!"#$ %&'())* +),-./01234,250567248),92:4())* ;<9- =">#!"#> %&'?,8 +),-./01234,250567248),92:4?,@24,.30./ ;<9- $">A!"#! B'2C 2C@07./2+?4)@?D.,34*,255@,2 --EF G$H"A!"#I B'9)+?.9? 9)+?.9?4*,255@,2 JB. GG="G!"#K J'5?2+? 5?2+?456L+255 ;<-- ="=IH
1#$$#2'3."4#&'(56+#$$!"#A MN'*,255@,2 72552/49)-*/0.+924*,255@,2 OB. ="=G>!"## PN'/)D 30.-2?2,4)8472552/:412,)4*,255@,2 -- K"I==!"#H PN'(0F( 30.-2?2,4)8472552/:4*,255@,24Q4B -- K"#H=!"H= &N'())* ())*48),9240+472552/:4*,255@,24Q4B ;<-- ="=A$!"HG J'72552/ 72552/456L+255 ;<-- ="G#I
7020+4#8'9*0:#/#"!"H$ P'7- P0.-2?2,4)84?(2472552/4.?4B'-2.+ -- K"I=!"H> P'73 P0.-2?2,4)84?(2472552/4.?4B'30.5?)/09 -- K">G!"H! P'75 P0.-2?2,4)84?(2472552/4.?4B'5R5?)/09 -- K"A=!"HI P'S- T./.+9234P0.-4)845?2+?23472552/4.?4B'-2.+ -- K"#K!"HK P'S3 T./.+9234P0.-4)845?2+?23472552/4.?4B'30.5?)/09 -- K"AG!"HA P'S5 T./.+9234P0.-4)845?2+?23472552/4.?4B'5R5?)/09 -- A"=G
(/"%/'9#;#45.+$'0/'7020+4#8'9*0:#/#"$!"H# ?(2?.'-2.+ 5?,@?4.+F/24.?4S./.+923430.-2?2, 32F GK"GI!!"HH 32/?.'?(2?.'-2.+ 9(.+F240+45?,@?4.+F/24.?4S./.+923430.- 32F >"#I#
!"G== 32/?.'-2.+ 5?,@?432U296)+4.?4S./.+923430.-2?2, -- ="=H=
!"G=G ?(2?.'30.5?)/09 5?,@?4.+F/24.?430.5?)/094*,255@,2 32F GI"KIH!"G=$ 32/?.'?(2?.'30.5?)/099(.+F240+45?,@?4.+F24.?430.5?)/094 32F !">I!!"G=> 32/?.'30.5?)/09 5?,@?432U296)+4.?430.5?)/09 -- ="G=G
!"G=! ?(2?.'5R5?)/09 5?,@?4.+F/24.?45R5?)/094*,255@,2 32F GK"KIG!"G=I 32/?.'?(2?.'5R5?)/099(.+F240+45?,@?4.+F24.?45R5?)/09 32F >">KG!"G=K 32/?.'5R5?)/09 5?,@?432U296)+4.?45R5?)/09 -- ="=A#
(/"0*+'102%#$!"G=A 5?,.0+'72552/ 5?,.0+4.?472552/430.-2?2, V G"K!V!"G=# 5?,.0+'S./.+923 5?,.0+4.?4-2.+4S./.+923430.-2?2, V G"$IV!"G=H 5?,.0+'30.5?)/09 5?,.0+4.?430.5?)/094*,255@,2 V G"!GV!"GG= 5?,.0+'5R5?)/09 5?,.0+4.?45R5?)/094*,255@,2 V G"=HV
305,%#'(0<#/='304/."!"GGG 5?,.0+'-2.+ -2.+45?,.0+ V G"$IV!"GG$ 5?,.0+'.-*/0?@32 5?,.0+4.-*/0?@32 V ="GKV!"GG> ;'58 [email protected]?R48.9?), W $"!H
Thursday, June 10, 2010
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Stent Calculator Worksheet: What-If Analysis
48
!"#$"%&#'()$%*$+,"' -$("' ./0,# ./0,# ./0,# ./0,# ./0,# ./0,# ./0,# ./0,# ./0,# ./0,# ./0,#!"# $%&'( )*+,-./'0/&'(*+)1 2 #3 #3 #3 #3 #3 #3 #3 #3 #3 #3 #3!"4 $%15.*51 15.*51/6.'*)7/&8.&*+0-.-)&- 2 !4 !4 !4 !4 !4 !4 !4 !4 !4 !4 !4!"9 :%5*,- '*5-./786+5-./'0/5*,8); ++ #"<#= #"<#= #"<#= #"<#= #"<#= #"<#= #"<#= #"<#= #"<#= #"<#= #"<#=!"! 5%.6> >6((/5?8&@)-11/'0/.6>/5*,8); ++ 3"#A3 3"#A3 3"#A3 3"#A3 3"#A3 3"#A3 3"#A3 3"#A3 3"#A3 3"#A3 3"#A3!"= B%15.*5%8))-. 15.*5/(-);5?/5'/8))-./56);-)51 ++ 12311 12411 12511 62111 62611 62711 62811 62911 62:11 62;11 62311!"C >%6D-E%.6> 6D-E/>875?F/61G&*5 ++ 3"#93 3"#93 3"#93 3"#93 3"#93 3"#93 3"#93 3"#93 3"#93 3"#93 3"#93!"A H%,.87;- 6E86(/;6D/,-5>--)/'*5-./56);-)51 ++ 3"#=3 3"#=3 3"#=3 3"#=3 3"#=3 3"#=3 3"#=3 3"#=3 3"#=3 3"#=3 3"#=3!"I J%,.87;- &8.&*+0-.-)K6(/1D6)/'0/,.87;- ++ 3"333 3"333 3"333 3"333 3"333 3"333 3"333 3"333 3"333 3"333 3"333!"< >%,.87;-%.6> >875?/'0/,.87;- ++ 3"#4= 3"#4= 3"#4= 3"#4= 3"#4= 3"#4= 3"#4= 3"#4= 3"#4= 3"#4= 3"#4=
!"#3 $%,.87;-1 )*+,-./'0/,.87;-1/6.'*)7/&8.&" 2 A A A A A A A A A A A
<=>?#''%</=/@#"#='!"## >%@-.0 +8)8+*+/-L-&85M-/@-.0/>875? ++ 3"34= 3"34= 3"34= 3"34= 3"34= 3"34= 3"34= 3"34= 3"34= 3"34= 3"34=!"#4 +%>875? >875?/.-+'M6(/8)/N)81?8); ++ 3"39C 3"39C 3"39C 3"39C 3"39C 3"39C 3"39C 3"39C 3"39C 3"39C 3"39C!"#9 +%5?8&@)-11 >6((/5?8&@)-11/.-+'M6( ++ 3"3=< 3"3=< 3"3=< 3"3=< 3"3=< 3"3=< 3"3=< 3"3=< 3"3=< 3"3=< 3"3=<!"#! O0 O0/'0/N)81?-7/&'+D')-)5 7-;P 4A 4A 4A 4A 4A 4A 4A 4A 4A 4A 4A
A/"#=(/0%<=>+#=B#'!"#= Q%O0%('> +'7*(*1/'0/-(61K&85R/65/B'>/O0 SD6 <!333 <!333 <!333 <!333 <!333 <!333 <!333 <!333 <!333 <!333 <!333!"#C O0%('> B'>/O0/0'./7-N)8);/Q 7-;P G= G= G= G= G= G= G= G= G= G= G=!"#A Q%O0%?8;? +'7*(*1/'0/-(61K&85R/65/O0/T8;? SD6 9!333 9!333 9!333 9!333 9!333 9!333 9!333 9!333 9!333 9!333 9!333!"#I O0%?8;? T8;?/O0/0'./7-N)8);/Q 7-;P 9A 9A 9A 9A 9A 9A 9A 9A 9A 9A 9A!"#< O0%8)U-&K') V)U-&K')/D'8)5/8)/Q/M1/O0 7-;P #< #< #< #< #< #< #< #< #< #< #<!"43 Q%&61-# Q/0'./O0/W/O0%('> SX6 <!333 <!333 <!333 <!333 <!333 <!333 <!333 <!333 <!333 <!333 <!333!"4# Q%&61-4 Q/0'./O0%('>/W/O0/W/O0%8)U-&K') SX6 9#A!# 9#A!# 9#A!# 9#A!# 9#A!# 9#A!# 9#A!# 9#A!# 9#A!# 9#A!# 9#A!#!"44 Q%&61-9 Q/0'./O0%8)U-&K')/W/O0/W/O0%?8;? SX6 9!3=< 9!3=< 9!3=< 9!3=< 9!3=< 9!3=< 9!3=< 9!3=< 9!3=< 9!3=< 9!3=<!"49 Q%&61-# Q/0'./O0/Y/O0%?8;? SX6 9!333 9!333 9!333 9!333 9!333 9!333 9!333 9!333 9!333 9!333 9!333!"4! Q +'7*(*1/'0/-(61K&85R/65/1D-&Z-7/O0 SX6 9!3=< 9!3=< 9!3=< 9!3=< 9!3=< 9!3=< 9!3=< 9!3=< 9!3=< 9!3=< 9!3=<!"4= 7-)185R%)8K 7-)185R/'0/$8K)'( +;[++\9 C"A C"A C"A C"A C"A C"A C"A C"A C"A C"A C"A!"4C 15.68)%-)7*.6)&- -)7*.6)&-/(8+85 ] 3"!3] 3"!3] 3"!3] 3"!3] 3"!3] 3"!3] 3"!3] 3"!3] 3"!3] 3"!3] 3"!3]
Thursday, June 10, 2010
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Trend Analysis: Diameter
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Trend Analysis: Strain v. Diameter
50
0.0%
0.2%
0.4%
0.6%
0.8%
1.0%
1.2%
1.4%
1.6%
1.8%
5.9 6.1 6.3 6.5 6.7 6.9 7.1
Stra
in
Vessel Diameter (mm) mean strain strain amplitude
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Trend Analysis: Fatigue Safety Factor v. Diameter
51
0.0
0.5
1.0
1.5
2.0
2.5
3.0
5.9 6.1 6.3 6.5 6.7 6.9 7.1
Nsf
Vessel Diameter (mm)
Fatigue Safety Factor
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Trend Analysis: Wall Thickness
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Trend Analysis: Radial Force v. Wall Thickness
53
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.10 0.12 0.14 0.16 0.18 0.20 0.22 0.24
RR
F (N
/cm
)
Starting Wall Thickness (mm)
Radial Resistive Force
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Trend Analysis: Strain v. Wall Thickness
54
0.0%
0.2%
0.4%
0.6%
0.8%
1.0%
1.2%
1.4%
1.6%
0.10 0.12 0.14 0.16 0.18 0.20 0.22 0.24
Stra
in
Starting Wall Thickness (mm) mean strain strain amplitude
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Trend Analysis: Fatigue Safety Factor v. Wall Thickness
55
0.0
0.5
1.0
1.5
2.0
2.5
3.0
0.10 0.12 0.14 0.16 0.18 0.20 0.22 0.24
Nsf
Starting Wall Thickness (mm)
Fatigue Safety Factor
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Trend Analysis: Strut Length
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Trend Analysis: Balanced Diameter v. Strut Length
57
6.2
6.4
6.6
6.8
7.0
7.2
7.4
7.6
7.8
0.5 0.7 0.9 1.1 1.3 1.5 1.7 1.9
Dia
met
er (m
m)
Strut Length (mm) Balanced Diameter, Diastolic Pressure Balanced Diameter, Systolic Pressure
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Trend Analysis: Strain v. Strut Length
58
0.0%
0.2%
0.4%
0.6%
0.8%
1.0%
1.2%
1.4%
1.6%
1.8%
0.5 0.7 0.9 1.1 1.3 1.5 1.7 1.9
Stra
in
Strut Length (mm) Mean Strain Strain Amplitude
Thursday, June 10, 2010
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Trend Analysis: Stiffness v. Strut Length
59
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.5 0.7 0.9 1.1 1.3 1.5 1.7 1.9
k (N
/mm
)
Strut Length (mm) stent stiffness vessel stiffness
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Trend Analysis: Radial Force v. Strut Length
60
0.0
0.5
1.0
1.5
2.0
2.5
3.0
0.5 0.7 0.9 1.1 1.3 1.5 1.7 1.9
RR
F (N
/cm
)
Strut Length (mm)
Radial Resistive Force
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Trend Analysis: Fatigue Safety Factor v. Strut Length
61
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
0.5 0.7 0.9 1.1 1.3 1.5 1.7 1.9
Nsf
Strut Length (mm)
Fatigue Safety Factor
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Beyond Spreadsheets
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Stent Calculator Python Script
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Input Parameter Variation
0.07
0.08
0.09
0.1
100.0%99.5%97.5%90.0%75.0%50.0%25.0%10.0%2.5%0.5%0.0%
maximum
quartilemedianquartile
minimum
0.101880.094780.092240.088770.08571
0.08220.078870.075680.072450.06979
0.0654
Quantiles
MeanStd DevStd Err MeanUpper 95% MeanLower 95% MeanN
0.08227060.00504120.00007130.08241040.0821309
5000
Moments
w_strut
0.1
0.11
0.12
0.13
100.0%99.5%97.5%90.0%75.0%50.0%25.0%10.0%2.5%0.5%0.0%
maximum
quartilemedianquartile
minimum
0.129420.123570.120640.117270.114360.111030.107640.104510.10118
0.09790.09246
Quantiles
MeanStd DevStd Err MeanUpper 95% MeanLower 95% MeanN
0.11098170.00497977.0423e-50.11111970.1108436
5000
Moments
t
26
27
28
29
100.0%99.5%97.5%90.0%75.0%50.0%25.0%10.0%2.5%0.5%0.0%
maximum
quartilemedianquartile
minimum
28.981228.303927.980827.637227.348227.007726.678426.373126.033625.742325.2261
Quantiles
MeanStd DevStd Err MeanUpper 95% MeanLower 95% MeanN
27.0101970.497228
0.007031927.02398326.996412
5000
Moments
Af
5.6
5.8
6
6.2
6.4
6.6
6.8
7
7.2
7.4
100.0%99.5%97.5%90.0%75.0%50.0%25.0%10.0%2.5%0.5%0.0%
maximum
quartilemedianquartile
minimum
7.470987.122316.987446.814386.672216.506466.334046.184136.021625.855845.58439
Quantiles
MeanStd DevStd Err MeanUpper 95% MeanLower 95% MeanN
6.50358340.24627380.00348286.51041136.4967555
5000
Moments
D_ves
Distributions
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Performance Output Variation
23
25
27
29
31
33
35
37
39
41
43
100.0%99.5%97.5%90.0%75.0%50.0%25.0%10.0%2.5%0.5%0.0%
maximum
quartilemedianquartile
minimum
43.71140.672838.959437.077935.428533.577131.8344
30.24528.5801
27.18923.0055
Quantiles
MeanStd DevStd Err MeanUpper 95% MeanLower 95% MeanN
33.6419532.64853090.037455933.71538333.568523
5000
Moments
mass
0.2
0.3
0.4
0.5
0.6
0.7
0.8
100.0%99.5%97.5%90.0%75.0%50.0%25.0%10.0%2.5%0.5%0.0%
maximum
quartilemedianquartile
minimum
0.866310.693050.625510.560280.499340.440510.386890.342040.295760.268790.19739
Quantiles
MeanStd DevStd Err MeanUpper 95% MeanLower 95% MeanN
0.4467240.08460350.00119650.44906960.4443784
5000
Moments
RF_hoop
40
60
80
100
120
140
160
180
200
220
240
100.0%99.5%97.5%90.0%75.0%50.0%25.0%10.0%2.5%0.5%0.0%
maximum
quartilemedianquartile
minimum
239.065210.871185.473163.718146.462127.811110.67996.092381.183767.417444.0718
Quantiles
MeanStd DevStd Err MeanUpper 95% MeanLower 95% MeanN
129.2784526.8142490.3792107130.02187128.53503
5000
Moments
P_contact
0.0040.0050.0060.0070.0080.009
0.010.0110.0120.0130.0140.0150.0160.0170.0180.019
100.0%99.5%97.5%90.0%75.0%50.0%25.0%10.0%2.5%0.5%0.0%
maximum
quartilemedianquartile
minimum
0.019290.017160.015820.014470.013270.011880.010580.009420.008040.006930.00429
Quantiles
MeanStd DevStd Err MeanUpper 95% MeanLower 95% MeanN
0.01192480.00197162.7882e-50.01197940.0118701
5000
Moments
strain_mean
0.0013
0.0014
0.0015
0.0016
0.0017
0.0018
100.0%99.5%97.5%90.0%75.0%50.0%25.0%10.0%2.5%0.5%0.0%
maximum
quartilemedianquartile
minimum
0.001810.001710.001670.001620.001580.001540.001490.00145
0.00140.001370.00131
Quantiles
MeanStd DevStd Err MeanUpper 95% MeanLower 95% MeanN
0.0015390.00006699.4597e-70.00154090.0015372
5000
Moments
strain_amplitude
2.2
2.3
2.4
2.5
2.6
2.7
2.8
2.9
3
100.0%99.5%97.5%90.0%75.0%50.0%25.0%10.0%2.5%0.5%0.0%
maximum
quartilemedianquartile
minimum
3.047662.924132.849172.753682.678072.599382.525022.462352.397312.339632.20963
Quantiles
MeanStd DevStd Err MeanUpper 95% MeanLower 95% MeanN
2.60400630.11379180.00160932.60716112.6008514
5000
Moments
N_sf
Distributions
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Predicting Relationships: Radial Force vs. Mass
0.2
0.3
0.4
0.5
0.6
0.7
0.8
RF_h
oop
23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44
mass
Polynomial Fit Degree=2
RF_hoop = -0.55894 + 0.0297866*mass + 0.0005111*(mass-33.642)^2
RSquareRSquare AdjRoot Mean Square ErrorMean of ResponseObservations (or Sum Wgts)
0.880790.8807420.0292170.446724
5000
Summary of Fit
Polynomial Fit Degree=2
Bivariate Fit of RF_hoop By mass
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Fatigue Performance: Mean Strain and Strain Amplitude
0.0013
0.0014
0.0015
0.0016
0.0017
0.0018
strain_amplitude
0.004 0.006 0.007 0.008 0.009 0.01 0.011 0.012 0.013 0.014 0.015 0.016 0.017 0.018 0.019
strain_mean
Bivariate Fit of strain_amplitude By strain_mean
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• Introduction to Open Source•Open Stent Design•Stent Mechanics•Stent Calculator•Community and Resources
68Thursday, June 10, 2010
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Open Stent Design: The Book
69
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Open Stent Design: SolidWorks
70
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Open Stent Design: Stent Calculator Formulas
71
CHAPTER 4. STENT CALCULATOR FORMULAS 53
4.10 Force and Strain Calculations
The relationships between stress, load, deflection, and strain have been thoroughly docu-mented for a variety of beam loading conditions. Force and strain related to a specifiedstrut deflection are based on the formulation for a beam fixed at one end, and free butguided at the other as documented in Machinery’s Handbook [1].
E = modulus of elasticity
I = moment of inertia, beam cross sectionw = strut widthL = strut length
Strain = ! = 3wL2 "#
Force = F =12EIL3 !"
FL2
FL2
F
F L
Figure 4.5: Beam fixed at one end, and free but guided at the other.
Fhoop is the hoop component of the force exerted by a single strut when the stent isconstrained from the fully expanded state to the analysis diameter. This is equal to Fin Figure 4.5 by the definition of the ”free but guided” beam as described in Machinery’s
Handbook [1].
Fhoop =12 · E · I(Lstrut)
3 · δd
Fhoop = 1.03 · 10−1 N
(4.78)
Fhoop 1mm is the hoop component of the force exerted by a single strut when the stentis constrained from the fully expanded state to a diameter one millimeter less than theanalysis diameter. This allows for later calculation of stent forces normalized per millimeterdiameter constraint.
Fhoop 1mm =12 · E · I(Lstrut)
3 · δ1mm
Fhoop 1mm = 6.92 · 10−2 N
(4.79)
CHAPTER 4. STENT CALCULATOR FORMULAS 54
�d is the maximum strain experienced within the strut when the stent is constrained fromthe fully expanded state to the analysis diameter. This is equal to epsilon in Figure 4.5by the definition of the ”free but guided” beam as described in Machinery’s Handbook
[1].
�d =3wstrut
(Lstrut)2 · δd
�d = 1.64 %
(4.80)
�1mm is the maximum strain experienced within the strut when the stent is constrainedfrom the fully expanded state to one millimeter less than the analysis diameter.
�1mm =3wstrut
(Lstrut)2 · δ1mm
�1mm = 1.10 %
(4.81)
4.11 Pressure and Stiffness Calculations
In this section, the forces and other calculations derived above are used to estimate radialresistive force in terms that are common for bench testing.
RFhoop is the hoop component of the force exerted when the stent is constrained from thefully expanded state to 1mm less than the expansion diameter, normalized by length incentimeters. This value is consistent with radial resistive force type measurement (RRF)generated from a collar type fixture. By convention, it is expressed in terms of Newtonsper centimeter length, and is thus normalized by length.
RFhoop =Fhoop 1mm
Xcell·�10 · mm
cm
�
RFhoop = 0.44 N/cm(4.82)
RFtrf is the true radial component of the force exerted when the stent is constrained fromthe fully expanded state to 1mm less than the expanded diameter, normalized by length incentimeters. This value is consistent with radial resistive force type measurement (RRF)generated from a Blockwise or MSI type testing fixture. This is also expressed in terms ofnewtons per centimeter length, and is thus also normalized by length, and evaluated for a1mm diameter constraint.
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NitinolUniversity.com
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