open stent design poster

Open Stent DesignCraig Bonsignore

NDC. 47533 Westinghouse Drive. Fremont, CA 95466.

© 2010 NDC. Reuse and adaptation permitted with attribution per the Creative Commons Attribution-Share Alike 3.0 United States License 64

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

0.0040.0050.0060.0070.0080.0090.01

0.0110.0120.0130.0140.0150.0160.0170.0180.019

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: Constant Life Diagram

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


NitinolUniversity.com

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

Open Stent Design: The Book

70


Open Stent Design: SolidWorks

71


Open Stent Design: Calculator

72

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.

Cardiovascular stents are widely used to treat a variety of vascular diseases. Hun-dreds of designs have been proposed, devel-oped, and commercialized since the 1990’s when these devices became commonplace in clinical practice. Competitive pressures in the commercial marketplace have been intense, and many battles have been waged relating to stent design intellectual property. Naturally, tools, techniques, and resources for stent design have been closely guarded and proprietary.

For all the differences between the myri-ad stents that have been designed and pro-duced over the years, the fundamental archi-tecture of most expandable stent designs is actually quite universal. Stents can be con-sidered to be an array of structural beams, connected in a series to form a circumfer-entially expandable spring. As such, these structures can be modeled using analytical tools to predict many relevant performance characteristics with reasonable accuracy.

Open Stent Design is a manuscript draft be-ing developed by NDC to provide general guidance for design and development of a simple, generic Nitinol stent. The manuscript and related resources are freely available to the community under a Creative Com-mons Attribution-Share Alike 3.0 United States license. Resources provided include a detailed parametrically driven CAD solid

model to create flat and wrapped stent ge-ometry, available for download in its na-tive SolidWorks format. Also available are a spreadsheet based Stent Calculator appli-cation, which can be used to relate input parameters such as tubing diameter, strut length, strut width, and wall thickness to performance predictions including service strains, radial strength, and pulsatile fatigue performance. Additional resources in de-velopment include a Python script to au-tomate the stent calculator application, en-abling statistical interrogation of thousands of possible conditions within expected de-sign limits. Finite Element Analysis tem-plates are also being developed to comple-ment the analytical models.

These resources are provided freely to the community to make stent development eas-ier and more approachable for new entrants in the field, and thus encourage continuing innovation, improvements, and progress. We hope that these tools are especially help-ful for researchers in academia seeking to study stents and related structures, and re-lated biomechanics, fluid flow, or other phe-nomena.

These resources are available for download at NDC’s educational website:

http://NitinolUniversity.com

open stent design poster

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