Open Stent Design Poster by NDC

Open Stent Design

Craig Bonsignore NDC. 47533 Westinghouse Drive. Fremont, CA 95466.

For all the differences between the myriad stents that have been designed and produced over the years, the fundamental architecture of most expandable stent designs is actually quite universal. Stents can be considered to be an array of structural beams, connected in a series to form a circumferentially 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 being 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 Commons Attribution-Share Alike 3.0 United States license. Resources provided include a detailed parametrically driven CAD solid

Stent Calculator Python Script

Open Stent Design: The Book

Predicting Relationships: Radial Force vs. Mass Bivariate Fit of RF_hoop By mass

0.8

0.7

0.6 RF_hoop

model to create flat and wrapped stent geometry, available for download in its native SolidWorks format. Also available are a spreadsheet based Stent Calculator application, 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 development include a Python script to automate the stent calculator application, enabling statistical interrogation of thousands of possible conditions within expected design limits. Finite Element Analysis templates are also being developed to complement the analytical models.

0.5

0.4

0.3

0.2 23

Polynomial Fit Degree=2 RF_hoop = -0.55894 + 0.0297866*mass + 0.0005111*(mass-33.642)^2

Summary of Fit

RSquare RSquare Adj Root Mean Square Error Mean of Response Observations (or Sum Wgts)

0.88079 0.880742 0.029217 0.446724 5000

Open Stent Design: SolidWorks

Input Parameter Variation

Fatigue Performance: Constant Life Diagram Bivariate Fit of strain_amplitude By strain_mean

Distributions w_strut

Af 0.13

0.1

D_ves 29

7.4 7.2

0.12

0.09

0.0018

6.8 0.11

0.08

6.6

6.4

0.0017

6.2 0.1

Quantiles

100.0% maximum 99.5% 97.5% 90.0% 75.0% quartile 50.0% median 25.0% quartile 10.0% 2.5% 0.5% 0.0% minimum

0.10188 0.09478 0.09224 0.08877 0.08571 0.0822 0.07887 0.07568 0.07245 0.06979 0.0654

Moments

Mean Std Dev Std Err Mean Upper 95% Mean Lower 95% Mean N

5.8

0.0016

0.0822706 0.0050412 0.0000713 0.0824104 0.0821309 5000

Quantiles

100.0% maximum 99.5% 97.5% 90.0% 75.0% quartile 50.0% median 25.0% quartile 10.0% 2.5% 0.5% 0.0% minimum

0.12942 0.12357 0.12064 0.11727 0.11436 0.11103 0.10764 0.10451 0.10118 0.0979 0.09246

Moments

Mean Std Dev Std Err Mean Upper 95% Mean Lower 95% Mean N

Quantiles

100.0% maximum 99.5% 97.5% 90.0% 75.0% quartile 50.0% median 25.0% quartile 10.0% 2.5% 0.5% 0.0% minimum

Moments

0.1109817 0.0049797 7.0423e-5 0.1111197 0.1108436 5000

Mean Std Dev Std Err Mean Upper 95% Mean Lower 95% Mean N

28.9812 28.3039 27.9808 27.6372 27.3482 27.0077 26.6784 26.3731 26.0336 25.7423 25.2261

100.0% maximum 99.5% 97.5% 90.0% 75.0% quartile 50.0% median 25.0% quartile 10.0% 2.5% 0.5% 0.0% minimum

Moments

27.010197 0.497228 0.0070319 27.023983 26.996412 5000

Mean Std Dev Std Err Mean Upper 95% Mean Lower 95% Mean N

7.47098 7.12231 6.98744 6.81438 6.67221 6.50646 6.33404 6.18413 6.02162 5.85584 5.58439

0.0015

0.0014

6.5035834 0.2462738 0.0034828 6.5104113 6.4967555 5000

0.0013 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

Performance Output Variation

Open Stent Design: Calculator

NitinolUniversity.com

Distributions CHAPTER 4. STENT CALCULATOR FORMULAS

4.10

Force and Strain Calculations

The relationships between stress, load, deflection, and strain have been thoroughly documented for a variety of beam loading conditions. Force and strain related to a specified strut deflection are based on the formulation for a beam fixed at one end, and free but guided at the other as documented in Machinery’s Handbook [1]. Strain = ! =

Force = F =

3w "# L2

FL 2

CHAPTER 4. STENT CALCULATOR FORMULAS

3wstrut · δd �d = (Lstrut )2 �d = 1.64 %

12EI !" L3

�1mm

L = strut length

Figure 4.5: Beam fixed at one end, and free but guided at the other.

4.11

Fhoop is the hoop component of the force exerted by a single strut when the stent is constrained from the fully expanded state to the analysis diameter. This is equal to F in Figure 4.5 by the definition of the ”free but guided” beam as described in Machinery’s Handbook [1].

Fhoop

3wstrut · δ1mm (Lstrut )2 = 1.10 %

�1mm =

12 · E · I · δd (Lstrut )3 −1 = 1.03 · 10 N

(4.78)

Fhoop 1mm is the hoop component of the force exerted by a single strut when the stent is constrained from the fully expanded state to a diameter one millimeter less than the analysis diameter. This allows for later calculation of stent forces normalized per millimeter diameter constraint.

12 · E · I · δ1mm (Lstrut )3 = 6.92 · 10−2 N

Fhoop 1mm = Fhoop 1mm

35 33

(4.79)

Quantiles

RFhoop RFhoop

Moments

Mean Std Dev Std Err Mean Upper 95% Mean Lower 95% Mean N

(4.82)

RFtrf is the true radial component of the force exerted when the stent is constrained from the fully expanded state to 1mm less than the expanded diameter, normalized by length in centimeters. 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 of newtons per centimeter length, and is thus also normalized by length, and evaluated for a 1mm diameter constraint.

0.2

Quantiles 43.711 40.6728 38.9594 37.0779 35.4285 33.5771 31.8344 30.245 28.5801 27.189 23.0055 33.641953 2.6485309 0.0374559 33.715383 33.568523 5000

100.0% maximum 99.5% 97.5% 90.0% 75.0% quartile 50.0% median 25.0% quartile 10.0% 2.5% 0.5% 0.0% minimum

Moments

Mean Std Dev Std Err Mean Upper 95% Mean Lower 95% Mean N

Quantiles 0.86631 0.69305 0.62551 0.56028 0.49934 0.44051 0.38689 0.34204 0.29576 0.26879 0.19739 0.446724 0.0846035 0.0011965 0.4490696 0.4443784 5000

100.0% maximum 99.5% 97.5% 90.0% 75.0% quartile 50.0% median 25.0% quartile 10.0% 2.5% 0.5% 0.0% minimum

Moments

Mean Std Dev Std Err Mean Upper 95% Mean Lower 95% Mean N

129.27845 26.814249 0.3792107 130.02187 128.53503 5000

100.0% maximum 99.5% 97.5% 90.0% 75.0% quartile 50.0% median 25.0% quartile 10.0% 2.5% 0.5% 0.0% minimum

Moments

Mean Std Dev Std Err Mean Upper 95% Mean Lower 95% Mean N

2.6 2.5 2.4 2.3

0.0013

Quantiles 239.065 210.871 185.473 163.718 146.462 127.811 110.679 96.0923 81.1837 67.4174 44.0718

2.7

0.0014

0.005 0.004

2.8

0.0015

0.008 0.007 0.006

0.3

RFhoop is the hoop component of the force exerted when the stent is constrained from the fully expanded state to 1mm less than the expansion diameter, normalized by length in centimeters. 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 Newtons per centimeter length, and is thus normalized by length.

100

2.9

0.0016

0.011 0.01 0.009

120

0.0017

0.013 0.012

140

0.4

In this section, the forces and other calculations derived above are used to estimate radial resistive force in terms that are common for bench testing.

160

N_sf

0.0018

0.016 0.015 0.014

180

0.5

100.0% maximum 99.5% 97.5% 90.0% 75.0% quartile 50.0% median 25.0% quartile 10.0% 2.5% 0.5% 0.0% minimum

200

0.6

strain_amplitude

0.019 0.018 0.017

220

0.7

(4.81)

strain_mean

240

(4.80)

P_contact

0.8

Pressure and Stiﬀness Calculations

Fhoop 1mm � mm � = · 10 · Xcell cm = 0.44 N/cm

RF_hoop

�1mm is the maximum strain experienced within the strut when the stent is constrained from the fully expanded state to one millimeter less than the analysis diameter.

FL 2

I = moment of inertia, beam cross section w = strut width

Fhoop =

mass

�d is the maximum strain experienced within the strut when the stent is constrained from the fully expanded state to the analysis diameter. This is equal to epsilon in Figure 4.5 by the definition of the ”free but guided” beam as described in Machinery’s Handbook [1].

E = modulus of elasticity

http://NitinolUniversity.com

Polynomial Fit Degree=2

5.6

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

mass

0.07

These resources are provided freely to the community to make stent development easier and more approachable for new entrants in the field, and thus encourage continuing innovation, improvements, and progress. We hope that these tools are especially helpful for researchers in academia seeking to study stents and related structures, and related biomechanics, fluid flow, or other phenomena.

strain_amplitude

Cardiovascular stents are widely used to treat a variety of vascular diseases. Hundreds of designs have been proposed, developed, 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.

2.2

Quantiles 0.01929 0.01716 0.01582 0.01447 0.01327 0.01188 0.01058 0.00942 0.00804 0.00693 0.00429 0.0119248 0.0019716 2.7882e-5 0.0119794 0.0118701 5000

100.0% maximum 99.5% 97.5% 90.0% 75.0% quartile 50.0% median 25.0% quartile 10.0% 2.5% 0.5% 0.0% minimum

Moments

Mean Std Dev Std Err Mean Upper 95% Mean Lower 95% Mean N

Quantiles 0.00181 0.00171 0.00167 0.00162 0.00158 0.00154 0.00149 0.00145 0.0014 0.00137 0.00131 0.001539 0.0000669 9.4597e-7 0.0015409 0.0015372 5000

100.0% maximum 99.5% 97.5% 90.0% 75.0% quartile 50.0% median 25.0% quartile 10.0% 2.5% 0.5% 0.0% minimum

Moments

Mean Std Dev Std Err Mean Upper 95% Mean Lower 95% Mean N

3.04766 2.92413 2.84917 2.75368 2.67807 2.59938 2.52502 2.46235 2.39731 2.33963 2.20963 2.6040063 0.1137918 0.0016093 2.6071611 2.6008514 5000