Open Stent Design

Open Stent DesignComputer Methods for

Cardiovascular Devices 2010

Craig [email protected]

Thursday, June 10, 2010

mailto:[email protected]

mailto:[email protected]

© 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

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© 2010 NDC. Reuse and adaptation permitted with attribution per the Creative Commons Attribution-Share Alike 3.0 United States License 23


























































A simple stent pattern

37





Array of “Z” shaped elements

38





Array of “V” shaped elements

39





Array of Simple BEAMS

40





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





Strain and Force for a Simple Beam Stent

42

!

F =Etw3

L3!" !

! = 3wL2

"# !

t

wL





x

strain

stre

ss

≈0.1-0.2% ≈1.0-2.0%

Nitinol

Steel










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





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





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-#%,$3%&#4#.5*$%+,-.)!"!# =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





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]





Trend Analysis: Diameter





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





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





Trend Analysis: Wall Thickness





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





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





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)






Trend Analysis: Strut Length





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





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





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





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





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)






Beyond Spreadsheets





Stent Calculator Python Script





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


minimum

0.129420.123570.120640.117270.114360.111030.107640.104510.10118

0.09790.09246

Quantiles


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


minimum

28.981228.303927.980827.637227.348227.007726.678426.373126.033625.742325.2261

Quantiles


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


minimum

7.470987.122316.987446.814386.672216.506466.334046.184136.021625.855845.58439

Quantiles


6.50358340.24627380.00348286.51041136.4967555

5000

Moments

D_ves

Distributions





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


minimum

43.71140.672838.959437.077935.428533.577131.8344

30.24528.5801

27.18923.0055

Quantiles


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


minimum

0.866310.693050.625510.560280.499340.440510.386890.342040.295760.268790.19739

Quantiles


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


minimum

239.065210.871185.473163.718146.462127.811110.67996.092381.183767.417444.0718

Quantiles


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


minimum

0.019290.017160.015820.014470.013270.011880.010580.009420.008040.006930.00429

Quantiles


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


minimum

0.001810.001710.001670.001620.001580.001540.001490.00145

0.00140.001370.00131

Quantiles


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


minimum

3.047662.924132.849172.753682.678072.599382.525022.462352.397312.339632.20963

Quantiles


2.60400630.11379180.00160932.60716112.6008514

5000

Moments

N_sf

Distributions





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





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










Open Stent Design: The Book

69





Open Stent Design: SolidWorks

70





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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Open Stent Design