ASTM F2514-21

Standard Guide for Finite Element Analysis (FEA) of Metallic Vascular Stents Subjected to Uniform Radial Loading

SIGNIFICANCE AND USE
4.1 Finite element analysis is a valuable tool for evaluating the performance of metallic stents and in estimating quantities such as stress, strain, and displacement due to applied external loads and boundary conditions. FEA of stents is frequently performed to determine the worst-case size for experimental fatigue (or durability) testing and differentiation of performance between designs. A finite element analysis is especially valuable in determining quantities that cannot be readily measured.
SCOPE
1.1 Purpose—This guide establishes recommendations and considerations for the development, verification, validation, and reporting of structural finite element models used in the evaluation of the performance of a metallic vascular stent design undergoing uniform radial loading. This standard guide does not directly apply to non-metallic or absorbable stents, though many aspects of it may be applicable. The purpose of a structural analysis of a stent is to determine quantities such as the displacements, stresses, and strains within a device resulting from external loading, such as crimping or during the catheter loading process, and in-vivo processes, such as expansion and pulsatile loading.  
1.2 Limitations—The analysis technique discussed in this guide is restricted to structural analysis using the finite element method. This document provides specific guidance for verification and validation (V&V) of finite element (FE) models of vascular stents subjected to uniform radial loading using ASME V&V40 as the basis for developing and executing risk-informed V&V plans.  
1.2.1 Users of this document are encouraged to read ASME V&V40 for an introduction to risk-informed V&V, and to read ASME V&V10 for further guidance on performing V&V of computational solid mechanics models. This document is not intended to cover all aspects of developing a finite element model of radial deformation of a stent. It is intended for a FE analyst with structural modeling experience.  
1.2.2 While risk-informed V&V is encouraged, it is not required. Analysts may utilize alternate V&V methods. The methodology employed should be developed by knowledgeable stakeholders with consideration as to the expectations and requirements of internal teams and external bodies that will assess the performance of the stent and the credibility of the model used to make performance predictions.  
1.2.3 If an alternative V&V method is employed, then Sections 5, 6, 7, and 10 that follow ASME V&V40 guidelines may be viewed as suggestions only. Other portions of the document that refer to question of interest, risk, and context of use may be viewed in the same manner.  
1.3 The values stated in SI units are to be regarded as the standard. The values given in parentheses are for informational purposes only.  
1.4 This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the Development of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.

General Information

• Status: Published
• Publication Date: 31-Jul-2021
• ICS: 11.040.40 - Implants for surgery, prosthetics and orthotics
• Technical Committee: F04 - Medical and Surgical Materials and Devices
• Drafting Committee: F04.30 - Cardiovascular Standards

Relations

• Refers: ASTM E8/E8M-24 - Standard Test Methods for Tension Testing of Metallic Materials
• Effective Date: 01-Jan-2024
• Refers: ASTM E2655-14(2020) - Standard Guide for Reporting Uncertainty of Test Results and Use of the Term Measurement Uncertainty in ASTM Test Methods
• Effective Date: 01-Jan-2020
• Refers: ASTM E8/E8M-16 - Standard Test Methods for Tension Testing of Metallic Materials
• Effective Date: 15-Jul-2016
• Refers: ASTM E8/E8M-15 - Standard Test Methods for Tension Testing of Metallic Materials
• Effective Date: 01-Feb-2015
• Refers: ASTM F2516-14 - Standard Test Method for Tension Testing of Nickel-Titanium Superelastic Materials
• Effective Date: 01-Oct-2014
• Refers: ASTM E8/E8M-13 - Standard Test Methods for Tension Testing of Metallic Materials
• Effective Date: 01-Jun-2013
• Refers: ASTM F2477-07(2013) - Standard Test Methods for <emph type="bdit">in vitro</emph> Pulsatile Durability Testing of Vascular Stents
• Effective Date: 01-Mar-2013
• Refers: ASTM E8/E8M-11 - Standard Test Methods for Tension Testing of Metallic Materials
• Effective Date: 01-Dec-2011
• Refers: ASTM E2655-08 - Standard Guide for Reporting Uncertainty of Test Results and Use of the Term Measurement Uncertainty in ASTM Test Methods
• Effective Date: 01-Oct-2008
• Refers: ASTM F2516-07 - Standard Test Method for Tension Testing of Nickel-Titanium Superelastic Materials
• Effective Date: 01-Dec-2007
• Refers: ASTM F2516-07e2 - Standard Test Method for Tension Testing of Nickel-Titanium Superelastic Materials
• Effective Date: 01-Dec-2007
• Refers: ASTM F2516-07e1 - Standard Test Method for Tension Testing of Nickel-Titanium Superelastic Materials
• Effective Date: 01-Dec-2007
• Refers: ASTM F2477-07 - Standard Test Methods for <i>in vitro</i> Pulsatile Durability Testing of Vascular Stents
• Effective Date: 01-Apr-2007
• Refers: ASTM F2477-06 - Standard Test Methods for <bdit>in vitro</bdit> Pulsatile Durability Testing of Vascular Stents
• Effective Date: 01-Nov-2006
• Refers: ASTM F2516-06 - Standard Test Method for Tension Testing of Nickel-Titanium Superelastic Materials
• Effective Date: 01-Jun-2006

Overview

ASTM F2514-21 is the internationally recognized standard guide issued by ASTM International for the finite element analysis (FEA) of metallic vascular stents subjected to uniform radial loading. This guide offers recommendations and critical considerations for the development, verification, validation, and reporting of structural finite element models in evaluating the mechanical performance of metallic stents. It applies to both balloon-expandable and self-expanding metallic stents, typically used to maintain patency in the human vascular system.

Finite element analysis as outlined in this standard serves as a vital tool for understanding and predicting mechanical response, such as displacements, stresses, and strains in stents under loading conditions that mimic both procedural (crimping, catheter loading) and physiological (expansion, pulsatile loading) environments. The guidance provided is tailored to experienced FE analysts and is relevant for both product development and regulatory submission processes.

Key Topics

• Finite Element Modeling of Metallic Stents

  • Guidance is specific to structural analysis using the finite element method (FEM).
  • Focus on uniform radial loading scenarios encountered in clinical use and benchtop testing.

• Verification and Validation (V&V)

  • Emphasizes risk-informed V&V activities, referencing ASME V&V40 for credibility assessment.
  • Encourages rigorous model verification to ensure that computational models accurately represent the conceptual model.
  • Model validation is addressed by comparing simulation results to experimental or clinical data.

• Model Development

  • Instructions on defining the question of interest, the context of use, and decision-making supported by FEA outcomes.
  • Consideration of assumptions on geometry, boundary conditions, symmetry, and contact interactions.
  • Description of model input parameters and their influence on simulation results.

• Assessment of Model Risk

  • Systematic approach to determining model risk and its impact on the required depth of V&V.
  • Factors such as model influence (the weight of the model in decision-making) and decision consequence (potential impact of incorrect decisions) are discussed in detail.

Applications

ASTM F2514-21 is widely utilized in the following areas:

• Design and Development of Vascular Stents

  • Supports stent designers and engineers in evaluating prototype and final designs by simulating expected loading conditions.
  • Aids identification of worst-case scenarios for experimental fatigue and durability testing.

• Regulatory Submissions

  • Provides a standardized basis for demonstrating device safety and performance to regulatory bodies.
  • Helps in compiling engineering reports required during medical device approval processes.

• Comparative Performance Analysis

  • Enables differentiation between stent designs, material selections, and manufacturing processes.
  • Assists in optimizing stent geometry and material properties for improved mechanical performance.

• Quality Assurance and Risk Management

  • Integrates with broader risk management frameworks such as ISO 14971 to assess and mitigate potential device failures.
  • Enhances product credibility through transparent and traceable computational modeling practices.

Related Standards

Several other standards complement ASTM F2514-21 by addressing material testing, durability, and verification practices:

• ASTM F2477 - In vitro pulsatile durability testing of vascular stents
• ASTM F2516 - Tension testing of nickel-titanium superelastic materials
• ASTM F3067 - Radial loading of balloon-expandable and self-expanding vascular stents
• ASME V&V10 / V&V40 - Guidelines for verification and validation in computational solid mechanics and medical device modeling
• ISO 14971 - Application of risk management for medical devices

Conclusion

Adhering to ASTM F2514-21 facilitates a systematic, repeatable approach to finite element analysis of metallic vascular stents, supporting improved design integrity, robust risk assessment, and regulatory compliance. By following the recommendations for model development, verification, validation, and reporting, stakeholders can enhance device safety, efficacy, and product lifecycle management within the cardiovascular device industry.

Standards Content (Sample)

This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the
Development of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.
Designation: F2514 − 21
Standard Guide for
Finite Element Analysis (FEA) of Metallic Vascular Stents
Subjected to Uniform Radial Loading
This standard is issued under the fixed designation F2514; the number immediately following the designation indicates the year of
original adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. A
superscript epsilon (´) indicates an editorial change since the last revision or reapproval.
INTRODUCTION
Thisguideestablishesgeneralrecommendationsandconsiderationsforusingfiniteelementanalysis
techniques for the numerical simulation of metallic stents subjected to uniform radial loading. These
stents are intended for use within the human vascular system.
1. Scope able stakeholders with consideration as to the expectations and
requirements of internal teams and external bodies that will
1.1 Purpose—This guide establishes recommendations and
assess the performance of the stent and the credibility of the
considerations for the development, verification, validation,
model used to make performance predictions.
and reporting of structural finite element models used in the
1.2.3 If an alternative V&V method is employed, then
evaluation of the performance of a metallic vascular stent
Sections 5, 6, 7, and 10 that followASME V&V40 guidelines
design undergoing uniform radial loading. This standard guide
may be viewed as suggestions only. Other portions of the
does not directly apply to non-metallic or absorbable stents,
document that refer to question of interest, risk, and context of
though many aspects of it may be applicable. The purpose of a
use may be viewed in the same manner.
structural analysis of a stent is to determine quantities such as
the displacements, stresses, and strains within a device result- 1.3 The values stated in SI units are to be regarded as the
ing from external loading, such as crimping or during the standard.The values given in parentheses are for informational
catheter loading process, and in-vivo processes, such as expan- purposes only.
sion and pulsatile loading.
1.4 This international standard was developed in accor-
dance with internationally recognized principles on standard-
1.2 Limitations—The analysis technique discussed in this
ization established in the Decision on Principles for the
guide is restricted to structural analysis using the finite element
Development of International Standards, Guides and Recom-
method. This document provides specific guidance for verifi-
mendations issued by the World Trade Organization Technical
cation and validation (V&V) of finite element (FE) models of
Barriers to Trade (TBT) Committee.
vascular stents subjected to uniform radial loading using
ASME V&V40 as the basis for developing and executing
2. Referenced Documents
risk-informed V&V plans.
1.2.1 Users of this document are encouraged to readASME
2.1 ASTM Standards:
V&V40 for an introduction to risk-informed V&V, and to read
E8/E8M Test Methods for Tension Testing of Metallic Ma-
ASME V&V10 for further guidance on performing V&V of
terials
computational solid mechanics models. This document is not
E2655 Guide for Reporting Uncertainty of Test Results and
intended to cover all aspects of developing a finite element
Use of the Term Measurement Uncertainty inASTM Test
model of radial deformation of a stent. It is intended for a FE
Methods
analyst with structural modeling experience.
F2477 Test Methods for in vitro Pulsatile Durability Testing
1.2.2 While risk-informed V&V is encouraged, it is not
of Vascular Stents
required. Analysts may utilize alternate V&V methods. The
F2516 Test Method for Tension Testing of Nickel-Titanium
methodology employed should be developed by knowledge-
Superelastic Materials
F3067 GuideforRadialLoadingofBalloon-Expandableand
This guide is under the jurisdiction of ASTM Committee F04 on Medical and
Surgical Materials and Devices and is the direct responsibility of Subcommittee
F04.30 on Cardiovascular Standards. For referenced ASTM standards, visit the ASTM website, www.astm.org, or
Current edition approved Aug. 1, 2021. Published August 2021. Originally contact ASTM Customer Service at [e-mail]. For Annual Book of ASTM
approved in 2008. Last previous edition approved in 2014 as F2514 – 08 (2014). Standards volume information, refer to the standard’s Document Summary page on
DOI: 10.1520/F2514-21. the ASTM website.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
F2514 − 21
Self-Expanding Vascular Stents 3.1.9 pulsatile, adj—recurring alternate increase and de-
crease of a quantity, such as the pressure oscillations that occur
2.2 Other Standards:
in an artery.
ASME V&V10–2019 Standard for Verification and Valida-
tion in Computational Solid Mechanics 3.1.10 radial loading, n—a mechanical loading mode in
ASME V&V10.1–2012 An Illustration of the Concepts of whichtheloadisdirectedperpendiculartothelongitudinalaxis
Verification and Validation in Computational Solid Me- of a cylinder and applied to the outer and/or inner cylindrical
chanics surface of the stent. The load is applied to the entire outer
ASME V&V20–2016 Standard for Verification and Valida- and/or inner surface or to at least three areas that are equally
tion in Computational Fluid Dynamics and HeatTransfer distributed around the outer and/or inner circumference and
extend over the entire cylinder length. Load might be ex-
ASME V&V40–2018 Assessing Credibility of Computa-
tional Modeling Through Verification and Validation: pressed as radial force or radial pressure.
Application to Medical Devices
3.1.11 safety factor, n—ratio of the device performance to
ASME PTC-19.1 Test Uncertainty
the specification requirement (for example, how much stronger
ISO 14971 Medical Devices—Application of Risk Manage-
the device is than it needs to be to meet its specification
ment to Medical Devices
requirement).
JCGM 100 Evaluation of Measurement Data—Guide to the
5 3.1.12 self-expanding stent, n—a stent that expands at the
Expression of Uncertainty in Measurement
treatment site without mechanical assistance. The material
typically used for the stent has the ability to return either
3. Terminology
partially or fully to a previous size and shape and remain
3.1 Definitions:
expanded after the delivery system is removed.
3.1.1 balloon-expandable stent, n—a stent that is expanded
3.1.13 stent, n—a tubular structure that is permanently
at the treatment site by a balloon catheter. The stent material is
implanted in the native or grafted vasculature and that is
plastically deformed by the balloon expansion such that the
intended to provide mechanical support to enhance vessel
stent remains expanded after deflation of the balloon.
patency. For the purposes of this guide, a stent is metallic and
3.1.2 delivery system, n—a mechanical system that is used
can be covered by a coating, synthetic textile, or tissue graft
to deliver and deploy a stent at a target site.
material.
3.1.3 fatigue life, N,n—the number of cycles of a specified
f
3.2 Definitions of Terms Specific to This Standard:
character that a given specimen sustains before failure of a
3.2.1 catheter load, v—to secure the stent into a delivery
specifiednatureoccurs.Fatiguelife,orthelogarithmoffatigue
system by radially compressing and inserting the stent into a
life, is a dependent variable.
delivery device, such as a sheath.
3.1.4 fatigue limit, S ,n—the limiting value of the median
F
3.2.2 computational model, n—a mathematical model of a
fatigue strength as the fatigue life, N, becomes very large.
f
system or a physical process implemented on a numerical
3.1.5 fatigue strength at a specified life, n—the maximum
analysis software platform.
load the test specimen can be expected to survive for a
3.2.3 conceptual model, n—the collection of assumptions
specified number of cycles with a stated confidence and
and descriptions of physical processes representing the solid
reliability.
mechanics behavior from which the mathematical model and
3.1.6 load, n—used to denote continuous and time-varying
validation experiments can be constructed (ASME V&V10).
forces, pressures, stresses, strains, torques, deflections, twists,
3.2.4 constant life diagram, n—in fatigue, a plot of one or
or other parameters that describe the applied fatigue stimuli.
more curves, each of which is for a single fatigue life, N. The
Typically, these fatigue stimuli are described by a mean value
curve(s) relates fatigue strength (example loads include alter-
and an alternating value.
nating stress or strain) to the mean load. The constant life
3.1.7 median fatigue life, n—the middle value of the ob-
fatigue diagram is usually derived from one or more stress or
served fatigue lives, arranged in order of magnitude, of the
strain versus number of cycles (S-N) curves.
individual specimens in a group tested under essentially
3.2.5 constant life line, n—a linear or piecewise linear
identical conditions.
function connecting fatigue strengths plotted on a constant life
3.1.8 plasticity, n—material behavior characteristic where
diagram. It is used to interpolate a fatigue strength for a mean
permanent or irrecoverable deformation remains when the
strain/stress that is between two mean strain/stress values that
external loading is removed.
have a fatigue strength determined through experimental test
data.
3.2.6 context of use (COU), n—a statement that defines the
Available from American Society of Mechanical Engineers (ASME), ASME
specific role and scope of the computational model used to
International Headquarters, Two Park Ave., New York, NY 10016-5990, http://
address the question of interest (ASME V&V40).
www.asme.org.
Available fromAmerican National Standards Institute (ANSI), 25 W. 43rd St.,
3.2.7 credibility factor, n—elements of the V&V process
4th Floor, New York, NY 10036, http://www.ansi.org.
that are used to establish the credibility of the computational
Available from Bureau International des Poids et Mesures (BIPM), Pavillon de
Breteuil, F-92312 Sèvres Cedex France, http://www.bipm.org. model for the COU (ASME V&V40). Examples include, but
F2514 − 21
are not limited to, software quality assurance, model form, and 3.2.23 question of interest, n—the specific question that is
test conditions. See ASME V&V40 for more details on V&V being addressed by the computational model.
activities and credibility factors.
3.2.24 reality of interest, n—the physical system and its
3.2.8 crimp, v—to secure the stent on an expanding delivery
associated environment to which the computational model will
device, such as a balloon, by radially compressing the stent.
be applied (ASME V&V10).
3.2.9 decision, n—a postulated action, or lack of action, that
3.2.25 strain/stress state, n—the combination of the mean
may commence; or a claim that may be made, upon consider-
and alternating stress or strain.
ing all evidence used to answer the question of interest.
3.2.26 test conditions, n—the inputs that are used to define
3.2.10 fatigue safety factor, n—the ratio of the specification
a test. Examples include temperature, diameter change rate,
limit (fatigue limit or fatigue strength at a specified life) to the
device position, etc.
predicted stress/strain state.
3.2.27 uncertainty quantification, n—quantification of the
3.2.11 finite element analysis (FEA), n—application of the
effect of uncertainty in the value of one or more model inputs
finite element method to analyze a physical phenomenon.
on the simulation output(s), or quantification of the uncertainty
3.2.12 finite element material calibration model, n—a finite
in the measured or calculated output(s) of an experimental test.
element model that is used to hone the parameters that define
3.2.28 validation point, n—a model is validated against
a material model through comparison of the stress and strain
experimental results at a specific set of test conditions, which
output to experimental test data.
can be referred to as a validation point (ASME V&V10).
3.2.13 finite element method (FEM), n—a general-purpose
3.2.29 x, n—a variable used to stand in for an unspecified
numerical technique used to provide approximate solutions to
value.
one or more differential equations.
3.2.14 key characteristic/parameter/assumption, n—anedu-
4. Significance and Use
cated assumption on what characteristics/parameters/
assumptions of a test or computational model meaningfully 4.1 Finite element analysis is a valuable tool for evaluating
impacts the output(s) of the test/model.
the performance of metallic stents and in estimating quantities
such as stress, strain, and displacement due to applied external
3.2.15 linear elastic material, n—a material in which the
loads and boundary conditions. FEA of stents is frequently
stressresultingfromanappliedforceisdirectlyproportionalto
performed to determine the worst-case size for experimental
the corresponding strain it produces. Thus, linear elastic
fatigue (or durability) testing and differentiation of perfor-
materials do not retain any stress or strain when all external
mance between designs.Afinite element analysis is especially
loads and boundary conditions are removed, and all deforma-
valuable in determining quantities that cannot be readily
tions are recoverable.
measured.
3.2.16 margin of safety, n—smallestdistancebetweenstrain/
stress state and a constant life line on a constant life diagram.
5. Summary of Practice
3.2.17 mathematical model, n—the mathematical equations,
5.1 This guide provides a systematic approach to develop,
boundary values, initial conditions, and modeling data needed
verify, validate, and report the use of a computational model to
to describe the conceptual model (ASME V&V10).
evaluate stent performance under a uniform radial loading
3.2.18 model form, n—the conceptual and mathematical
condition. The process includes the following steps:
formulation of the computational model. It includes not only
5.1.1 State the question of interest and the posited decision,
the form of the governing equations but also the form of the
and define the context of use of the model (Section 6).
systemconfiguration,systemproperties,andsystemconditions
5.1.2 Determine model risk (Section 7).
(ASME V&V40).
5.1.3 Define the computational model (Section 8).
3.2.19 model inputs, n—geometry, material properties,
5.1.3.1 Determine model form (8.2).
boundary conditions, and other information required to com-
5.1.3.2 Define computational model inputs (8.3).
pletely describe the finite element model.
5.1.4 Select the appropriate finite element analysis software
3.2.20 model risk, n—the possibility that the computational
(Section 9).
model and the simulation results may lead to an incorrect
5.1.5 Establish the verification and validation plan (Section
decision that would lead to an adverse outcome (ASME
10).
V&V40).
5.1.6 Carry out the verification and validation plan (Section
3.2.21 model validation, n—the process of determining the
11).
degree to which a model is an accurate representation of the
reality of interest. 5.1.7 Determine if the computational model is credible for
the context of use (Section 11).
3.2.22 model verification, n—the process of determining
5.1.8 Simulatestentradialloading/deformationaccordingto
that a computational model accurately represents the underly-
the context of use (Section 12).
ing mathematical model and its solution from the perspective
of the intended uses of modeling and simulation (ASME 5.1.9 Describe the model, method, results, and conclusions
V&V40). in the final engineering report (Section 13).
F2514 − 21
6. State Question of Interest and the Posited Decision, pulsatile fatigue testing, an animal study, or comparison to
and Define the Context of Use of the Model modeling results for a predicate device that has met perfor-
mance requirements.
6.1 The question of interest is the specific question the
organization is trying to answer utilizing an FEAmodel as part
7. Determine Model Risk
of the decision-making process. Examples of a question of
interest include but are not limited to:
7.1 Model risk is the driving factor for determining the
6.1.1 Is the family of stents resistant to fractures that amount of verification and validation activities necessary to
compromise device function when exposed to physiologically establish computational model credibility. The model risk is a
relevant radial pulsatile loading boundary conditions over the combinationoftheinfluenceofthecomputationalmodelonthe
decision being made (model influence) and the consequence of
expected lifetime of the device?
an adverse outcome resulting from an incorrect decision
6.1.2 Does the stent experience strains outside the tolerated
(decision consequence). Considerations regarding each of
compressive and tensile range of values for the material during
these factors relating to this document are provided in this
catheter loading?
section. The reader is referred to ASME V&V40 for general
6.1.3 For all possible geometry and material property com-
guidance on determining model risk through consideration of
binationswithintheproposedspecificationtolerances,doesthe
the influence of the model in making a product-related
stent generate adequate radial pressure to seal off blood flow
decision, and the consequence of an incorrect decision.
into the aneurysmal sac for all indicated vessel diameter and
compliance combinations?
7.2 It is a good practice to incorporate clinical and risk
assessment expertise beyond that of the analyst to determine
6.2 The decision is the postulated action, or lack of action,
the influence of the model and the consequence of an incorrect
that may commence; or a claim that may be made, upon
decision.
considering all evidence used to answer the question of
interest. Examples of decisions for the questions of interest
7.3 Model Influence:
listed in 6.1 are detailed below:
7.3.1 Model influence refers to the relative weight that the
6.2.1 Claim that the family of stents meet the design input
model has in answering the question of interest.
requirements for frame durability under pulsatile loading
7.3.2 Evidence other than computational modeling of a
conditions.
stent’s performance relative to the COU can be used to address
6.2.2 The peak minimum and maximum principal strains
the question of interest. Using other data sources decreases the
induced during catheter loading meet the design input require-
influence of computational model results on the decision,
ments and an order for a lot of stents can be placed to be used
which may reduce the risk associated with the computational
for delivery system development and radial force testing.
model.
6.2.3 Claim that the stent design meets the minimum radial
7.3.3 An example is using computational modeling as part
compression resistance pressure design requirement.
of an assessment of a stent’s fatigue resistance to in-vivo
pulsatile loading. This example is developed further in Ex-
6.3 The context of use (COU) defines how the FEA model
ample 1: Evaluating Model Risk.
and other supporting evidence are used to answer the question
of interest. The context of use may include, but is not limited
7.4 Decision Consequence:
to, the following elements:
7.4.1 The decision consequence refers to the potential
6.3.1 Adescription of how the computational model will be
consequenceofaharmtothepatientand/ornon-patient-related
used to address the question of interest.An example statement
impactsasaresultofanincorrectdecision.Theconsequenceof
is, “An FE model of each stent size will simulate catheter
the incorrect decision can be categorized on a scale of the
loading and in-vivo cycling at various physiological conditions
analyst’s or organization’s choosing. Examples of an incorrect
to determine the size and condition combination that is most
decision include but are not limited to:
likely to result in a fracture over the course of the intended
7.4.1.1 Determining that the family of stents met pulsatile
implantation lifespan.”
durability requirements when one or more sizes would not if
6.3.2 Identification of the output(s) used to address the
properly assessed.The root cause may be that the models were
question of interest and define how it will be used.
inadequate to differentiate between some of the sizes, the
6.3.2.1 An example for a balloon-expandable stent is, “The testing did not sufficiently replicate the physiological
mean and alternating maximum principal stresses are com-
conditions, errors were made in calculating the boundary/
pared to the Goodman line to calculate a safety factor. This
loading conditions, or another issue tied to any of the sources
safety factor is used to identify the device size with lowest
of data. The consequence of an incorrect decision is not
fatigue resistance.”
answering the question of “What if the model is wrong?” but
6.3.2.2 The model outputs used for validation are not “What if the decision that was made based on the entirety of
requiredtomatchthoseusedtoaddressthequestionofinterest. evidence is in error?”
For example, stress or strain may be of interest in addressing 7.4.1.2 The FE model underestimates the peak maximum
fatigue resistance, while radial force might be used for valida-
principal strain, which is actually above the maximum allowed
tion as it is more easily measured (10.6.5).
valueperthedesigninputrequirement,seenbythestentduring
6.3.3 Details regarding other forms of evidence used to catheter loading when it was claimed that it was below the
address the question of interest. Examples include benchtop maximum allowed value.
F2514 − 21
7.4.1.3 Thecombinationofnearleastmaterialgeometryand
Note: The scale for model risk is determined by the analyst or the analyst’s or-
ganization. This example used a five-point scale of low, low-medium, medium,
near minimum strength material properties results in a stent
medium-high, and high, but this should not be considered as guidance or a rec-
that does not meet the minimum radial compression resistance
ommendation. The degree of assessed model risk influences the extent of veri-
pressure design requirement when the decision was to claim fication and validation activities that are performed. A model with a low model
risk would require successful completion of limited activities and meet loose ac-
that the design did meet the design requirement.
ceptance criteria to be deemed credible for its intended use. Users of this stan-
7.4.2 Whencategorizingtheimpactofanincorrectdecision,
dard are encouraged to determine goals, delineated by risk level, for each V&V
the determination may consider both the severity and the rate activity (see Example 2) apriori to evaluating the risk associated with the com-
putational model. A goal that is associated with a lower model risk can be per-
of occurrence of clinical sequelae. Since these factors are
formed instead if deemed more appropriate for the application, and a more rig-
integral to risk assessment methodologies such as ISO 14971,
orous goal can be pursued without justification.
existing risk assessments for the stent can be used to evaluate
decision consequence. The chosen gradation should reflect
8. Define the Computational Model
what is a reasonable consequence for the targeted patient
8.1 The model is a representation of the stent exposed to
population.
relevant uniform radial loading conditions. The model can
7.4.3 With respect to modeling radial loading of stents, an
include simplifying assumptions on the underlying physics,
incorrect decision could lead to insufficient radial force and/or
geometry, material properties, boundary conditions, symmetry,
stent fracture. For example, fractures of stents resulting from
and applied loads.
radial pulsatile loading have been reported to lead to various
clinical sequelae. Sequelae leading to morbidity and mortality
8.2 Model Form:
include thrombus formation, neo-intimal tissue growth, artery
8.2.1 The assumptions made and governing equations used
perforation, migration, and restenosis (1, 2). An example
are important factors when formulating a model. Examples of
regarding stent fracture is developed further in Example 1:
model form decisions include, but are not limited to: using
Evaluating Model Risk.
simplified geometry, using symmetry, 2D versus 3D, linear
versusnonlinearmaterialproperties,anddynamicversusstatic.
7.5 An example that incorporates model risk in determining
8.2.2 The influence of various assumptions can be explored
the extent of validation activities to perform is detailed in
by comparing the output of the model to a different or more
Example 2: Model Form Exploration.
complex model, or to empirical test data.
Example 1: Evaluating Model Risk
8.2.3 Consider the required accuracy, the expected cost
Medical Device: Peripheral vascular stent
(time and resources) of the simulation, and how the output will
be used in decisions that can impact the device development
Question of Interest: Is the family of stents resistant to fractures that
compromise device function when exposed to physiologically relevant radial
and/or patient safety when selecting an appropriate model
pulsatile loading boundary conditions?
form.
Posited Decision: The family of stents have met the design input requirements 8.2.4 Many stent designs are composed of repeating pat-
for frame durability under pulsatile loading conditions.
terns that exhibit symmetry. Under circumferentially symmet-
ric uniform radial load, this repetition may allow for the
Context of Use: The computational models are used to predict the combination
of stent size and physiological boundary conditions (that is, vessel diameter, analysis of a stent subsection while enforcing appropriate
compliance, pulse pressure) most likely to lead to an in-vivo fracture during the
conditions of symmetry on truncated boundaries. Results may
expected lifetime of the implant. Mean and alternating maximum principal
be reviewed to ensure that all boundary conditions have been
stresses are compared to the Goodman line to calculate the fatigue safety
factor, which is used to identify the device size with the lowest fatigue applied correctly and that deformations are consistent with
resistance. The combination will be fatigue tested to a ten-year life expectancy.
experimental observations.
The decision is based primarily upon the results of the fatigue test, with the
lowest fatigue safety factors for each stent size determined by the 8.2.5 Stent edge radii are typically excluded from the finite
computational model also weighing on the decision.
element model to simplify meshing, improve mesh quality,
and/or reduce element count. If the edge radius is expected to
Model Influence: The fatigue safety factors for each stent size are determined
by the computational model, but the stent durability assessment is based upon significantly change the cross-sectional area of a strut, then a
the benchtop fatigue test performed according to Test Method F2477. The fa-
justification should be provided as to why the results are still
tigue test is used to confirm the prediction of fatigue resistance for the worst-
valid.JustificationcouldincludeanFEAstudyoftheimpactof
case condition determined by the computational model. Because of the similari-
ties between the stents within the family, the benchtop test can be considered
including/excluding the edge radius on the quantities of
representative of other sizes. Therefore, the computational model has a low-
interest, either on a complete stent model or a sub-model.
medium influence on the decision.
8.2.6 Theinfluenceofthecontactformulationusedbetween
Decision Consequence: An incorrect decision on the durability of the device
the stent and radial compression and/or expansion surface, and
family under pulsatile loading conditions can result in a clinically significant frac-
contact of the device with itself (selfcontact), on the model
ture that requires physician intervention but is not life-threatening. This decision
output and stent deformations should be considered.
consequence is categorized as medium.
8.2.6.1 Some contact methods or parameter values can
Model Risk: The combination of a low-medium model influence and medium for
result in the device diameter not matching that of the constrict-
decision consequence yields a model risk of low-medium.
ing surface. For example, nodal penetration due to softened
contact or when there is a mismatch between the mesh density
of the stent and constricting surface. Direct diameter measure-
ment or verification of apposition of the stent to the constrict-
The boldface numbers in parentheses refer to a list of references at the end of
this standard. ing surface can be used to assess the intended deformation.
F2514 − 21
8.2.6.2 For computational models of balloon expansion, the
Model Assumptions and Simplifications:
•The geometry does not include the edge rounding created during
value of the friction coefficient used in the contact definition
electropolishing.
can be chosen to match the quantities observed on the bench
•A 1/8th circumferential symmetry model with theta and axial constraints is
such as the fore-shortening/elongation characteristics of the representative of the full stent.
•Geometric and radial force differences between a model that uses a rigid
stent.
cylinder for expansion versus a simulated balloon are insignificant.
8.2.6.3 Contact definitions for braided stents can require
•Geometric and radial force differences between a model that uses a rigid
cylinder for compression versus a multi-plane iris are insignificant.
special attention due to the wire-to-wire overlap at crossover
points.
Note: The model form activities to be pursued are what the developers of the
8.2.7 Interactions between a balloon-expandable stent and model and users of the model’s data think are appropriate based on the risk
assigned to the computational model. In this fictitious scenario, the expected
the balloon can impact the uniformity of stent deformation.
activity for a model with a low-medium risk grade are for one or more key
Approximating the expansion of the stent with a rigid cylinder
model assumptions and/or simplifications to be explored for their influence on
is a common practice, but consideration should be given as to the output of the computational model. The symmetry model form assumption is
chosen based on its simplicity. If a tested device deviates from the predicted
whether it is appropriate for the context of use of the model.
output of the model, the unexplored assumptions and simplifications are an
8.2.8 The extent of the exploration of the assumptions option for investigating the deviation. The low-medium and medium model risk
have the same model form goal in this scenario as the number of gradations of
and/or simplifications to the model’s form is dependent on the
goals for each credibility factor do not have to match the number of model risk
model risk.
levels.
8.2.9 Example 2: Model Form Exploration illustrates the
8.3 Computational Model Inputs:
steps in this standard guide up through defining the model
8.3.1 Geometric Data:
form.
8.3.1.1 Finite element models are a geometric representa-
Example 2: Model Form Exploration
tionofthedevicebeingstudied.Thesourceofthedetailsofthe
Medical Device: Balloon-expandable peripheral vascular stent geometry may include drawings, computer-aided design
(CAD), preliminary sketches, imaging (for example, visual
Question of Interest: Does the proposed stent design meet or exceed the radial
microscopy, CT, SEM), or any other source consistent with
stiffness target when expanded to the minimum indicated diameter?
defining the device model geometry.
Posited Decision: The proposed stent design meets the radial stiffness target
8.3.1.2 In the design phase of product development, finite
for the minimum indicated diameter and therefore a small lot of the new design
element modeling may be used even before any physical
will be manufactured.
prototyping has occurred. As such, models are often based on
Context of Use: The computational model is used to predict the radial stiffness
idealized geometry. As prototypes are built, the measured
of an expanded and recoiled peripheral stent concept at nominal geometry. If
dimensions can be substituted to reflect the dimensions of the
the concept meets the minimum expectations, then the design may be
manufactured, and the stiffness predictions confirmed via benchtop radial force
prototype devices. Differences between the geometry of the
testing. The computational model simulates the test method that includes crimp
tested prototypes and idealized geometry can lead to perfor-
to the minimum process diameter, expansion to the deployed diameter, and
mance predictions that differ from the results of the benchtop
then radial compression to measure the stiffness.
tests.
Model Influence: The model is the only source of data used to make the
8.3.1.3 The as-manufactured stent geometry can be deter-
decision. Therefore, the computational model has a high influence on the
decision.
mined by measuring and inspecting representative stent
samples that have undergone all processing steps prior to
Decision Consequence: The consequence of an incorrect decision is an
loading onto the catheter. This processing can include, but is
expenditure of resources and project time to manufacture a test concept that
does not meet the radial stiffness requirements. This decision consequence is
not limited to, cleaning and polishing.
categorized as low.
8.3.2 Material Property Tests:
Model Risk: The combination of a high model influence and low decision 8.3.2.1 Thetwomaintypesofstentsareballoon-expandable
consequence yield a low-medium risk level.
and self-expanding. Each type is produced from different types
of materials that have specific needs for material property
Goals of Model Form Validation Activities by Model Risk:
•Low: No model assumptions and/or simplifications are explored to determine
testing and calibration.
their influence on the output of the computational model.
8.3.2.2 The mechanical material properties for a finite
•Low-Medium & Medium: One or more key model assumptions and/or
simplifications are explored to determine their influence on the output of the element analysis are commonly determined through tensile
computational model.
testing of the material, but compressive properties can also be
•Medium-High: All key model assumptions and/or simplifications are explored
relevant to predicting the radial force, stress, strain, and
to determine their influence on the output of the computational model.
•High: All model assumptions and/or simplifications are explored to determine deformation of a stent.
their influence on the output of the computational model.
8.3.2.3 Mechanical properties of the material should be
determined from material samples (coupons) that have under-
Define the Model:
•Material Model: Elastic-plastic
gone all pertinent manufacturing processes, including relevant
•Solver: Quasi-static
thermal processes, finishing, cleaning, and sterilization. If
•Geometry: 3D 1/8th circumferential symmetry, full length
material samples are not subjected to all relevant processing
•Constraints: Theta and axial on the cut surfaces
•Radial Expansion: Rigid cylindrical tool
steps, then the omissions should be described and rationalized.
•Radial Compression: Rigid cylindrical tool
8.3.2.4 For materials with a known tension-compression
•Contact: No overclosure (hard contact), friction applied
asymmetry (such as nitinol), differences in the material behav-
ior in tension and compression may also be considered along
F2514 − 21
with any load history dependent tension/compression asymme- 8.3.4.7 Common methods for determining the deformations
try phenomena, or work hardening of the material. ofanimplanteddevicesubjecttoradialloadinginclude,butare
not limited to:
8.3.2.5 Test Method E8/E8M provides a standard test
(1) The load applied by the vessel as a function of the
method for tension testing of metallic materials. Test Method
vessel diameter and the blood pressure;
F2516 provides guidance for tensile test methods appropriate
(2) Empirical measurements of a device implanted in vivo
for nitinol.
or in a mock vessel; and
8.3.3 Material Property Calibration:
(3) Calculations that incorporate the stiffness or compli-
8.3.3.1 The correlation between the material test data and
anceofthevessel,theforce-versus-diameterrelationshipofthe
the finite element material calibration model results should be
stent, and blood pressure.
sufficient to provide confidence that the finite element repre-
8.3.5 Material, dimensional, and loading conditions vari-
sentation of the material is an accurate representation of the
abilitiescancreatearangeforastent’sperformanceandsafety.
actual material over its range of use.
Methods for assessing variabilities include:
8.3.3.2 For self-expanding superelastic materials with pro-
8.3.5.1 Modeling the maximum and minimum geometry
nounced hysteresis, the material model calibration should
and/or material properties based on either specification toler-
includetherelevantloadingdirection(s).Forexample,ifastent ances or the mean plus and minus x standard deviations, which
is simulated to be radially compressed and then released, the
is unlikely to be representative of a device that is
material model calibration should include both loading (ten- manufactured, but may represent the extremes of possible
sion) and unloading. geometry and/or material properties.
8.3.5.2 Creating a mathematical model of the stent’s perfor-
8.3.3.3 Comparisons between material stress-strain data and
mance and/or safety margin with dimensions, material
finite element material calibration model results may include
properties, and loading conditions as variables, with limits
individual sample stress-strain results to illustrate sample-to-
spanning the possible variability from manufacturing and
sample variability in addition to the averaged curve of material
expecteduse.AMonteCarlo-likeapproachcanthenbeapplied
test data. Incorporation of multiple lots in the test samples may
to analyze a large number of design possibilities within
induce greater, and more representative, variability in the
manufacturing limits to identify conditions that may be outside
output. If material property uncertainty is considered, then
the acceptable performance metric.
representative nominal and stochastic FEA material curves
8.3.5.3 WhenperformingaMonteCarloanalysis,onemight
may also be reported.
consider a broad design space beyond the assumed manufac-
8.3.4 Loading Conditions and History:
turing and use limits. Having data beyond the manufacturing
8.3.4.1 Torepresentthebehaviorofthestentasitundergoes
limitsenablestheunderstandingofhowadesigncouldperform
the various stages of its design life, sets of loading steps and
if the tolerances are expanded, as well as alerting the analyst if
conditions are defined. These conditions are in the form of
a possible design is near a region of unsatisfactory safety
imposed deformations and/or forces and pressures that are
margin or performance.
applied to the device or portions of the device.
9. Finite Element Software Capabilities
8.3.4.2 For analyses including the implantation of a stent,
9.1 The requirements of finite element software used in the
the applied loading steps should include the delivery system
analysisofradialloadingofmetallicstentswillvarydepending
loading, implant deployment, and recoil (if applicable). The
on the specific analysis being performed. One may end up with
steps should also include representative uniform radial loading
large model form error if the finite element software does not
conditions that the implant is expected to experience in vivo.
meet the model form requirements for a given question of
8.3.4.3 This guide is restricted to cases involving uniform
interest. For this reason, the following capabilities in combi-
radial loading. Such loading can occur during stent
nation are important for the user to consider when selecting
manufacturing, stent crimping, stent delivery, or cyclic loading
FEA software for modeling of radial deformation of stents.
from placement within a pulsating vessel. It is important to
9.1.1 Computer-Aided Design (CAD) Integration—The
note that the sequence of loading events for a balloon-
ability of the software to import or have integrated CAD may
expandable stent will differ from a self-expanding stent.
be important for the user to access the stent geometry.
8.3.4.4 The loading history of the device, from manufactur-
9.1.2 Meshing—The software used to mesh the stent should
ing through deployment and in-vivo use as applicable to the
be capable of providing all element types under consideration
question of interest, may be analyzed.
for the analysis. The meshing capabilities of the FEAsoftware
8.3.4.5 It may be necessary to include the effects of residual
can be considered when selecting software, although the
stresses, such as from attaching a graft (covering) to the stent
meshing software may be different from the software used to
and/or loading the stent on the delivery system.
create the model, run the simulation, or view the results.
8.3.4.6 It may be necessary to include the effects of residual
9.1.3 Large Deformations—Simulation of manufacturing
stresses resulting from the use of crimping to mount the stent processes, deployments, and physiological loading may gener-
onto the delivery system. The fatigue strength of nitinol has
ate large displacements, rotations, and strains of the structures.
been found to be sensitive to residual stresses from crimping Large deformation formulations should therefore be activated
with increases or decreases in fatigue life possible depending in the simulation software to capture these geometric nonlin-
on the magnitude and sense of the crimp loading (3). earities.
F2514 − 21
9.1.4 Nonlinear Material Constitutive Models—The combi- series of models with the same element type and decreasing
nation of typical stent materials and deformations during element length that are used to estimate the discretization error
deployment and physiological loading will likely induce non- for outputs such as strain, stress, and radial force.
linearstress-strainresponses.TheFEAsoftwarewillneedtobe
10.4.2.1 The mesh used for the refinement study can be a
able to adequately model those effects, either using built-in
representative sample based on cyclic (or other) symmetries,
constitutive models or through the incorporation of user
such as a strut, apex, or cell, that sees deformation that is
subroutines.
representative of the radial loading experienced by the stent.
9.1.5 Contact—FEAmodels of radial loading of stents may
10.4.2.2 Themeshrefinementstudycanfocusonalocalized
require multiple bodies within the model and, therefore,
area that is expected to encounter the highest stress/strain or
contact between those bodies. The capability of the FEA code
radial force.
to adequately manage complicated contact (edge on edge, edge
10.4.2.3 The quantities of interest, for example strain or
on surface, and point to surface) may be important in these
stress, used in the mesh refinement study should match those
situations.
from the COU.The output is dependent on what is relevant for
9.1.6 Large Model Capability—Some stent models can
theCOUandmorethanoneoutputcanbeusedsimultaneously.
includelargenumbersofnodesandelements.Theabilityofthe
10.4.2.4 Additional resources to those listed in 10.4.1 for
software to manage a large model, including solver
conducting a mesh refinement study and estimating discretiza-
parallelization, may be important.
tion error include articles by Roache (6) and Sinclair (7).
10.4.3 Skinning the stent model, which is the practice of
10. Establish the Verification and Validation Plan
adding very thin membrane or shell elements to the stent
surface, is one way to reduce the number of three-dimensional
10.1 Thorough descriptions for developing an appropriate
verification and validation plan are covered inASME V&V40, continuum elements needed for the analysis. Adding these
elements provides integration points at the surface of the
ASME V&V10, and ASME V&V10.1.
device, where the strain and stress are expected to be greates
...

This document is not an ASTM standard and is intended only to provide the user of an ASTM standard an indication of what changes have been made to the previous version. Because
it may not be technically possible to adequately depict all changes accurately, ASTM recommends that users consult prior editions as appropriate. In all cases only the current version
of the standard as published by ASTM is to be considered the official document.
Designation: F2514 − 08 (Reapproved 2014) F2514 − 21
Standard Guide for
Finite Element Analysis (FEA) of Metallic Vascular Stents
Subjected to Uniform Radial Loading
This standard is issued under the fixed designation F2514; the number immediately following the designation indicates the year of
original adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. A
superscript epsilon (´) indicates an editorial change since the last revision or reapproval.
INTRODUCTION
This guide establishes general requirementsrecommendations and considerations for using finite
element analysis techniques for the numerical simulation of metallic stents subjected to uniform radial
loading. These stents are intended for use within the human vascular system.
1. Scope
1.1 Purpose—This guide establishes general requirements recommendations and considerations for the development of
development, verification, validation, and reporting of structural finite element models used in the evaluation of the performance
of a metallic vascular stent design underundergoing uniform radial loading. Suggested criteria are provided for evaluating the
typical cases of metallic stents under uniform radially oriented and pulsatile loading. Recommended procedures for checking and
validating the finite element model(s) are provided as a means to assess the model This standard guide does not directly apply to
non-metallic or absorbable stents, though many aspects of it may be applicable. The purpose of a structural analysis of a stent is
to determine quantities such as the displacements, stresses, and strains within a device resulting from external loading, such as
crimping or during the catheter loading process, and analysisin-vivo results. Finally, the recommended content of an engineering
report covering the mechanical simulations is presented.processes, such as expansion and pulsatile loading.
1.2 Limits: Limitations—
1.2.1 This guide is limited in discussion to the finite element structural analysis of metallic stents of the following types:
1.2.1.1 Plastically deformable metal stents.
1.2.1.2 Self-expanding metal stents.
1.2.1.3 Plastically deformable metal portions of covered stents.
1.2.1.4 Metal portions of self-expanding covered metal stents. The analysis technique discussed in this guide is restricted to
structural analysis using the finite element method. This document provides specific guidance for verification and validation
(V&V) of finite element (FE) models of vascular stents subjected to uniform radial loading using ASME V&V40 as the basis for
developing and executing risk-informed V&V plans.
This guide is under the jurisdiction of ASTM Committee F04 on Medical and Surgical Materials and Devices and is the direct responsibility of Subcommittee F04.30
on Cardiovascular Standards.
Current edition approved March 1, 2014Aug. 1, 2021. Published April 2014August 2021. Originally approved in 2008. Last previous edition approved in 20082014 as
F2514 – 08. 08 (2014). DOI: 10.1520/F2514-08R14.10.1520/F2514-21.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
F2514 − 21
1.2.2 The emphasis of the techniques described in this guide is intended for both elasto-plastic materials such as stainless steel,
and superelastic materials such as nitinol. Unique concerns associated with stents designed for shape memory behavior are not
addressed within this guide.
1.2.3 This guide does not consider changes to possible time varying conditions or different loadings related to vascular
remodeling.
1.2.4 This guide is restricted to cases that involve the application of uniform radially oriented loading.
1.2.5 This guide does not provide guidance in the application or interpretation of FEA in determining fatigue life.
1.2.1 This guideUsers of this document are encouraged to read ASME V&V40 for an introduction to risk-informed V&V, and to
read ASME V&V10 for further guidance on performing V&V of computational solid mechanics models. This document is not
intended to include complete descriptions of the finite element method, nor its theoretical basis and formulation. cover all aspects
of developing a finite element model of radial deformation of a stent. It is intended for a FE analyst with structural modeling
experience.
1.2.2 While risk-informed V&V is encouraged, it is not required. Analysts may utilize alternate V&V methods. The methodology
employed should be developed by knowledgeable stakeholders with consideration as to the expectations and requirements of
internal teams and external bodies that will assess the performance of the stent and the credibility of the model used to make
performance predictions.
1.2.3 If an alternative V&V method is employed, then Sections 5, 6, 7, and 10 that follow ASME V&V40 guidelines may be
viewed as suggestions only. Other portions of the document that refer to question of interest, risk, and context of use may be viewed
in the same manner.
1.3 The values stated in SI units are to be regarded as the standard. The values given in parentheses are for information only.
informational purposes only.
1.4 This international standard was developed in accordance with internationally recognized principles on standardization
established in the Decision on Principles for the Development of International Standards, Guides and Recommendations issued
by the World Trade Organization Technical Barriers to Trade (TBT) Committee.
2. Referenced Documents
2.1 ASTM Standards:
E8/E8M Test Methods for Tension Testing of Metallic Materials
E2655 Guide for Reporting Uncertainty of Test Results and Use of the Term Measurement Uncertainty in ASTM Test Methods
F2477 Test Methods for in vitro Pulsatile Durability Testing of Vascular Stents
F2516 Test Method for Tension Testing of Nickel-Titanium Superelastic Materials
F3067 Guide for Radial Loading of Balloon-Expandable and Self-Expanding Vascular Stents
2.2 Other Standards:
ASME V&V10–2019 Standard for Verification and Validation in Computational Solid Mechanics
ASME V&V10.1–2012 An Illustration of the Concepts of Verification and Validation in Computational Solid Mechanics
ASME V&V20–2016 Standard for Verification and Validation in Computational Fluid Dynamics and Heat Transfer
ASME V&V40–2018 Assessing Credibility of Computational Modeling Through Verification and Validation: Application to
Medical Devices
ASME PTC-19.1 Test Uncertainty
ISO 14971 Medical Devices—Application of Risk Management to Medical Devices
JCGM 100 Evaluation of Measurement Data—Guide to the Expression of Uncertainty in Measurement
For referenced ASTM standards, visit the ASTM website, www.astm.org, or contact ASTM Customer Service at [e-mail]. For Annual Book of ASTM Standards
volume information, refer to the standard’s Document Summary page on the ASTM website.
Available from American Society of Mechanical Engineers (ASME), ASME International Headquarters, Two Park Ave., New York, NY 10016-5990, http://
www.asme.org.
Available from American National Standards Institute (ANSI), 25 W. 43rd St., 4th Floor, New York, NY 10036, http://www.ansi.org.
Available from Bureau International des Poids et Mesures (BIPM), Pavillon de Breteuil, F-92312 Sèvres Cedex France, http://www.bipm.org.
F2514 − 21
3. Terminology
3.1 Definitions:
3.1.1 balloon-expandable stent, n—a stent that is expanded at the treatment site by a balloon catheter. The stent material is
plastically deformed by the balloon expansion such that the stent remains expanded after deflation of the balloon.
3.1.2 delivery system, n—a mechanical system that is used to deliver and deploy a stent at a target site.
3.1.3 fatigue life, N , n—the number of cycles of a specified character that a given specimen sustains before failure of a specified
f
nature occurs. Fatigue life, or the logarithm of fatigue life, is a dependent variable.
3.1.4 fatigue limit, S , n—the limiting value of the median fatigue strength as the fatigue life, N , becomes very large.
F f
3.1.5 fatigue strength at a specified life, n—the maximum load the test specimen can be expected to survive for a specified number
of cycles with a stated confidence and reliability.
3.1.6 load, n—used to denote continuous and time-varying forces, pressures, stresses, strains, torques, deflections, twists, or other
parameters that describe the applied fatigue stimuli. Typically, these fatigue stimuli are described by a mean value and an
alternating value.
3.1.7 median fatigue life, n—the middle value of the observed fatigue lives, arranged in order of magnitude, of the individual
specimens in a group tested under essentially identical conditions.
3.1.8 plasticity, n—material behavior characteristic where permanent or irrecoverable deformation remains when the external
loading is removed.
3.1.9 pulsatile, adj—recurring alternate increase and decrease of a quantity, such as the pressure oscillations that occur in an artery.
3.1.10 radial loading, n—a mechanical loading mode in which the load is directed perpendicular to the longitudinal axis of a
cylinder and applied to the outer and/or inner cylindrical surface of the stent. The load is applied to the entire outer and/or inner
surface or to at least three areas that are equally distributed around the outer and/or inner circumference and extend over the entire
cylinder length. Load might be expressed as radial force or radial pressure.
3.1.11 safety factor, n—ratio of the device performance to the specification requirement (for example, how much stronger the
device is than it needs to be to meet its specification requirement).
3.1.12 self-expanding stent, n—a stent that expands at the treatment site without mechanical assistance. The material typically used
for the stent has the ability to return either partially or fully to a previous size and shape and remain expanded after the delivery
system is removed.
3.1.13 stent, n—a tubular structure that is permanently implanted in the native or grafted vasculature and that is intended to provide
mechanical support to enhance vessel patency. For the purposes of this guide, a stent is metallic and can be covered by a coating,
synthetic textile, or tissue graft material.
3.2 Symbols:Definitions of Terms Specific to This Standard:
3.2.1 catheter load, v—to secure the stent into a delivery system by radially compressing and inserting the stent into a delivery
device, such as a sheath.
3.2.2 balloon expandable stent, computational model, n—a stent that is expanded at the treatment site by a balloon catheter. The
purpose of the balloon is to plastically deform the stent material such that the stent remains expanded after the deflation of the
balloon.mathematical model of a system or a physical process implemented on a numerical analysis software platform.
3.2.3 conceptual model, n—model produced by analyzing and observing the physical system of interest composed of mathematical
F2514 − 21
models and equations representing that system.the collection of assumptions and descriptions of physical processes representing
the solid mechanics behavior from which the mathematical model and validation experiments can be constructed (ASME V&V10).
3.2.4 constant life diagram, n—in fatigue, a plot of one or more curves, each of which is for a single fatigue life, N. The curve(s)
relates fatigue strength (example loads include alternating stress or strain) to the mean load. The constant life fatigue diagram is
usually derived from one or more stress or strain versus number of cycles (S-N) curves.
3.2.5 constant life line, n—a linear or piecewise linear function connecting fatigue strengths plotted on a constant life diagram.
It is used to interpolate a fatigue strength for a mean strain/stress that is between two mean strain/stress values that have a fatigue
strength determined through experimental test data.
3.2.6 context of use (COU), n—a statement that defines the specific role and scope of the computational model used to address
the question of interest (ASME V&V40).
3.2.7 computational model,credibility factor, n—implementation of a conceptual model in software.elements of the V&V process
that are used to establish the credibility of the computational model for the COU (ASME V&V40). Examples include, but are not
limited to, software quality assurance, model form, and test conditions. See ASME V&V40 for more details on V&V activities and
credibility factors.
3.2.8 crimp, v—to secure the stent on a delivery system an expanding delivery device, such as a balloon, by radially compressing
the stent into a delivery device such as a catheter or onto an expanding delivery device such as a balloon.stent.
3.2.9 delivery system, decision, n—a mechanical system that is used to deliver and deploy a stent at a target site.postulated action,
or lack of action, that may commence; or a claim that may be made, upon considering all evidence used to answer the question
of interest.
3.2.10 elasto-plastic material, fatigue safety factor, n—a material behavioral model that exhibits elastic behavior (recoverable) up
to its yield point and plastic behavior (irrecoverable) above its yield point.the ratio of the specification limit (fatigue limit or fatigue
strength at a specified life) to the predicted stress/strain state.
2.1.7 endurance limit, n—stress or strain level at which the material is considered to have “infinite” life.
3.2.11 finite element analysis (FEA), n— a general purpose numerical technique.application of the finite element method to
analyze a physical phenomenon.
2.1.8.1 Discussion—
In this guide, the structural continuum is discretized into regions known as elements, in which the mechanical behavior is defined.
Continuity is enforced at the vertices of the elements where node points are defined. The mechanical behavior of the continuum
is then defined according to mathematical expressions of physical laws at the node points. This results in the definition of a set
of simultaneous equations that are solved for state variables from which such important quantities as displacements, stresses, and
strains can be derived.
3.2.12 finite element material calibration model, n—a finite element model that is used to hone the parameters that define a
material model through comparison of the stress and strain output to experimental test data.
3.2.13 geometrical nonlinearity, finite element method (FEM), n—a type of nonlinearity related to structural deformation where
the relation between strain and displacement are not linearly proportional.general-purpose numerical technique used to provide
approximate solutions to one or more differential equations.
3.2.14 key characteristic/parameter/assumption, n—an educated assumption on what characteristics/parameters/assumptions of a
test or computational model meaningfully impacts the output(s) of the test/model.
3.2.15 linear elastic material, n—a material in which the stress resulting from an applied force is directly proportional to the
corresponding strain it produces. Thus, linear elastic materials do not retain any stress or strain when all external loads and
boundary conditions are removed, and all deformations are recoverable.
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3.2.16 margin of safety, n—smallest distance between strain/stress state and a constant life line on a constant life diagram.
3.2.17 mathematical model, n—the mathematical equations, boundary values, initial conditions, and modeling data needed to
describe the conceptual model (ASME V&V10).
3.2.18 model calibration,form, n—the process through which the parameters of a computational model are checked or adjusted
to create a model with the proper measure of accuracy.conceptual and mathematical formulation of the computational model. It
includes not only the form of the governing equations but also the form of the system configuration, system properties, and system
conditions (ASME V&V40).
3.2.19 model inputs, n—geometry, material properties, boundary conditions, and other information required to completely describe
the finite element model.
3.2.20 model risk, n—the possibility that the computational model and the simulation results may lead to an incorrect decision that
would lead to an adverse outcome (ASME V&V40).
3.2.21 model validation, n—the process of determining the degree to which a computational model accurately represents the real
world behavior it was intended to represent. It is an evaluation of the fidelity of the computational model and the real world.model
is an accurate representation of the reality of interest.
3.2.22 model verification, n—the process of assessing that the implementation of the determining that a computational model
accurately represents the engineer’s conceptualunderlying mathematical model and of the its solution to the model. It is an
evaluation of the fidelity of the conceptual model and the computational model.from the perspective of the intended uses of
modeling and simulation (ASME V&V40).
3.2.23 question of interest, n—the specific question that is being addressed by the computational model.
3.2.24 nonlinear material, reality of interest, n—a material behavior in which the stress resulting from an applied external load
is not directly proportional to the induced strain.the physical system and its associated environment to which the computational
model will be applied (ASME V&V10).
3.2.25 permanent deformation,strain/stress state, n—residual or irrecoverable strain and deformation in a structure after all loads
and boundary conditions are removed. the combination of the mean and alternating stress or strain.
2.1.16 plasticity, n—material behavior characteristic where permanent or irrecoverable deformation remains when the external
loading is removed.
2.1.17 pulsatile, adj—recurring alternate increase and decrease of a quantity such as the pressure that would occur in an artery.
3.2.26 self-expanding stent,test conditions, n—a stent that expands at the treatment site without mechanical assistance. The
material typically used for the stent has the ability to return either partially or fully to a previous size and shape and remain
expanded after the delivery system is removed.the inputs that are used to define a test. Examples include temperature, diameter
change rate, device position, etc.
3.2.27 solution sensitivity,uncertainty quantification, n—a measure quantification of the relative change in solution results caused
by changing effect of uncertainty in the value of one or more parameters in a computational model.model inputs on the simulation
output(s), or quantification of the uncertainty in the measured or calculated output(s) of an experimental test.
3.2.28 stent, validation point, n—a tubular structure that is permanently implanted in the native or grafted vasculature and that is
intended to provide mechanical radial support to enhance vessel patency. For the purposes of this guide, a stent is metallic and may
be covered by a coating, synthetic textile, or tissue graft material.model is validated against experimental results at a specific set
of test conditions, which can be referred to as a validation point (ASME V&V10).
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3.2.29 x, n—a variable used to stand in for an unspecified value.
3. Summary of Practice
3.1 This guide addresses the use of the finite element method for structural analysis of metallic vascular stents under various types
of simulated uniform radial loading. The purpose of a structural analysis of the stent is to determine such quantities as the
displacements, stresses, and strains within a device resulting from external loading. This includes stresses and strains potentially
due, but not limited, to manufacturing processes, to delivery in the body, and to pulsatile loading in vivo.
3.2 Current United States government guidelines (1) recommend structural analysis of a proposed device under physiologically
appropriate loading. The analysis technique discussed in this guide is restricted to the finite element analysis technique (2-5),
although other techniques may be equally suitable for the required analysis.
3.3 Prior to the finalization of a device design, rigorous experimental testing is recommended to complement the analyses
performed. During these tests, care should be taken to represent the loading and boundary support conditions consistent with those
used not only in the finite element analysis and experimental tests but also those expected in clinical use. Experimental tests should
be carefully monitored. Any behavior that was not captured by the numerical simulation should be identified and evaluated for its
effect on safety and reliability.
4. Significance and Use
4.1 Finite element analysis is a valuable methodtool for evaluating the performance of metallic stents and in quantifyingestimating
quantities such as internal stresses, internal strains, and deformation patterns stress, strain, and displacement due to applied external
loads and boundary conditions. Many times an analysis is performed to correlate to and plan experimental tests. FEA of stents is
frequently performed to determine the worst-case size for experimental fatigue (or durability) testing and differentiation of
performance between designs. A finite element analysis is especially valuable in determining quantities that cannot be readily
measured.
5. Summary of Practice
5.1 This guide provides a systematic approach to develop, verify, validate, and report the use of a computational model to evaluate
stent performance under a uniform radial loading condition. The process includes the following steps:
5.1.1 State the question of interest and the posited decision, and define the context of use of the model (Section 6).
5.1.2 Determine model risk (Section 7).
5.1.3 Define the computational model (Section 8).
5.1.3.1 Determine model form (8.2).
5.1.3.2 Define computational model inputs (8.3).
5.1.4 Select the appropriate finite element analysis software (Section 9).
5.1.5 Establish the verification and validation plan (Section 10).
5.1.6 Carry out the verification and validation plan (Section 11).
5.1.7 Determine if the computational model is credible for the context of use (Section 11).
5.1.8 Simulate stent radial loading/deformation according to the context of use (Section 12).
5.1.9 Describe the model, method, results, and conclusions in the final engineering report (Section 13).
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6. Overall Technical ApproachState Question of Interest and the Posited Decision, and Define the Context of Use of the
Model
6.1 The question of interest is the specific question the organization is trying to answer utilizing an FEA model as part of the
decision-making process. Examples of a question of interest include but are not limited to:
6.1.1 Is the family of stents resistant to fractures that compromise device function when exposed to physiologically relevant radial
pulsatile loading boundary conditions over the expected lifetime of the device?
6.1.2 Does the stent experience strains outside the tolerated compressive and tensile range of values for the material during
catheter loading?
6.1.3 For all possible geometry and material property combinations within the proposed specification tolerances, does the stent
generate adequate radial pressure to seal off blood flow into the aneurysmal sac for all indicated vessel diameter and compliance
combinations?
6.2 The decision is the postulated action, or lack of action, that may commence; or a claim that may be made, upon considering
all evidence used to answer the question of interest. Examples of decisions for the questions of interest listed in 6.1 are detailed
below:
6.2.1 Claim that the family of stents meet the design input requirements for frame durability under pulsatile loading conditions.
6.2.2 The peak minimum and maximum principal strains induced during catheter loading meet the design input requirements and
an order for a lot of stents can be placed to be used for delivery system development and radial force testing.
6.2.3 Claim that the stent design meets the minimum radial compression resistance pressure design requirement.
6.3 The application of finite element analysis is intended for the development of a quantifiable level of confidence in the stent
design. The overall approach described in this guide focuses on the development of a systematic technical approach to using the
finite element analysis technique to evaluate stent performance. The basic process includes: context of use (COU) defines how the
FEA model and other supporting evidence are used to answer the question of interest. The context of use may include, but is not
limited to, the following elements:
6.3.1 Detailed definitionA description of the geometry of how the computational model will be used to address the question of
interest. An example statement is, “An FE model of each stent size will simulate catheter loading and in-vivothe stent being
evaluated. cycling at various physiological conditions to determine the size and condition combination that is most likely to result
in a fracture over the course of the intended implantation lifespan.”
5.1.2 The determination, quantification and validation of the important mechanical material properties.
6.3.2 SelectionIdentification of the appropriate finite element tools and programs to ensure effective and reliable representations
of the stent being evaluated.output(s) used to address the question of interest and define how it will be used.
6.3.2.1 An example for a balloon-expandable stent is, “The mean and alternating maximum principal stresses are compared to the
Goodman line to calculate a safety factor. This safety factor is used to identify the device size with lowest fatigue resistance.”
6.3.2.2 The model outputs used for validation are not required to match those used to address the question of interest. For example,
stress or strain may be of interest in addressing fatigue resistance, while radial force might be used for validation as it is more easily
measured (10.6.5).
5.1.4 Selection and validation of the appropriate finite element model and type of element(s) used.
5.1.5 Calibration, validation, and verification of model input, parameters for the numerical simulation, solution results and
comparison to experimental tests.
5.1.6 Definition of all important loading steps.
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5.1.7 Selection and application of appropriate boundary conditions, such as symmetry.
5.1.8 Effective and proper application of the finite element analysis program for the intended evaluation.
5.1.9 The generation and interpretation of results to perform an effective evaluation.
6.3.3 Documentation of the analysis, including all supporting citations and references, analysis methodology, and assumptions,
results interpretation, and overall stent design evaluation.Details regarding other forms of evidence used to address the question
of interest. Examples include benchtop pulsatile fatigue testing, an animal study, or comparison to modeling results for a predicate
device that has met performance requirements.
7. Determine Model Risk
7.1 Model risk is the driving factor for determining the amount of verification and validation activities necessary to establish
computational model credibility. The model risk is a combination of the influence of the computational model on the decision being
made (model influence) and the consequence of an adverse outcome resulting from an incorrect decision (decision consequence).
Considerations regarding each of these factors relating to this document are provided in this section. The reader is referred to
ASME V&V40 for general guidance on determining model risk through consideration of the influence of the model in making a
product-related decision, and the consequence of an incorrect decision.
7.2 It is a good practice to incorporate clinical and risk assessment expertise beyond that of the analyst to determine the influence
of the model and the consequence of an incorrect decision.
7.3 Model Influence:
7.3.1 Model influence refers to the relative weight that the model has in answering the question of interest.
7.3.2 Evidence other than computational modeling of a stent’s performance relative to the COU can be used to address the
question of interest. Using other data sources decreases the influence of computational model results on the decision, which may
reduce the risk associated with the computational model.
7.3.3 An example is using computational modeling as part of an assessment of a stent’s fatigue resistance to in-vivo pulsatile
loading. This example is developed further in Example 1: Evaluating Model Risk.
7.4 Decision Consequence:
7.4.1 The decision consequence refers to the potential consequence of a harm to the patient and/or non-patient-related impacts as
a result of an incorrect decision. The consequence of the incorrect decision can be categorized on a scale of the analyst’s or
organization’s choosing. Examples of an incorrect decision include but are not limited to:
7.4.1.1 Determining that the family of stents met pulsatile durability requirements when one or more sizes would not if properly
assessed. The root cause may be that the models were inadequate to differentiate between some of the sizes, the testing did not
sufficiently replicate the physiological conditions, errors were made in calculating the boundary/loading conditions, or another
issue tied to any of the sources of data. The consequence of an incorrect decision is not answering the question of “What if the
model is wrong?” but “What if the decision that was made based on the entirety of evidence is in error?”
7.4.1.2 The FE model underestimates the peak maximum principal strain, which is actually above the maximum allowed value
per the design input requirement, seen by the stent during catheter loading when it was claimed that it was below the maximum
allowed value.
7.4.1.3 The combination of near least material geometry and near minimum strength material properties results in a stent that does
not meet the minimum radial compression resistance pressure design requirement when the decision was to claim that the design
did meet the design requirement.
7.4.2 When categorizing the impact of an incorrect decision, the determination may consider both the severity and the rate of
occurrence of clinical sequelae. Since these factors are integral to risk assessment methodologies such as ISO 14971, existing risk
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assessments for the stent can be used to evaluate decision consequence. The chosen gradation should reflect what is a reasonable
consequence for the targeted patient population.
7.4.3 With respect to modeling radial loading of stents, an incorrect decision could lead to insufficient radial force and/or stent
fracture. For example, fractures of stents resulting from radial pulsatile loading have been reported to lead to various clinical
sequelae. Sequelae leading to morbidity and mortality include thrombus formation, neo-intimal tissue growth, artery perforation,
migration, and restenosis (1, 2). An example regarding stent fracture is developed further in Example 1: Evaluating Model Risk.
7.5 An example that incorporates model risk in determining the extent of validation activities to perform is detailed in Example
2: Model Form Exploration.
Example 1: Evaluating Model Risk
Medical Device: Peripheral vascular stent
Question of Interest: Is the family of stents resistant to fractures that compromise device function when exposed to physiologically relevant radial pulsatile loading
boundary conditions?
Posited Decision: The family of stents have met the design input requirements for frame durability under pulsatile loading conditions.
Context of Use: The computational models are used to predict the combination of stent size and physiological boundary conditions (that is, vessel diameter,
compliance, pulse pressure) most likely to lead to an in-vivo fracture during the expected lifetime of the implant. Mean and alternating maximum principal stresses are
compared to the Goodman line to calculate the fatigue safety factor, which is used to identify the device size with the lowest fatigue resistance. The combination will
be fatigue tested to a ten-year life expectancy. The decision is based primarily upon the results of the fatigue test, with the lowest fatigue safety factors for each stent
size determined by the computational model also weighing on the decision.
Model Influence: The fatigue safety factors for each stent size are determined by the computational model, but the stent durability assessment is based upon the
benchtop fatigue test performed according to Test Method F2477. The fatigue test is used to confirm the prediction of fatigue resistance for the worst-case condition
determined by the computational model. Because of the similarities between the stents within the family, the benchtop test can be considered representative of other
sizes. Therefore, the computational model has a low-medium influence on the decision.
Decision Consequence: An incorrect decision on the durability of the device family under pulsatile loading conditions can result in a clinically significant fracture that
requires physician intervention but is not life-threatening. This decision consequence is categorized as medium.
Model Risk: The combination of a low-medium model influence and medium for decision consequence yields a model risk of low-medium.
Note: The scale for model risk is determined by the analyst or the analyst’s organization. This example used a five-point scale of low, low-medium, medium, medium-
high, and high, but this should not be considered as guidance or a recommendation. The degree of assessed model risk influences the extent of verification and vali-
dation activities that are performed. A model with a low model risk would require successful completion of limited activities and meet loose acceptance criteria to be
deemed credible for its intended use. Users of this standard are encouraged to determine goals, delineated by risk level, for each V&V activity (see Example 2)
apriori to evaluating the risk associated with the computational model. A goal that is associated with a lower model risk can be performed instead if deemed more ap-
propriate for the application, and a more rigorous goal can be pursued without justification.
8. Input DataDefine the Computational Model
8.1 The model is a representation of the stent exposed to relevant uniform radial loading conditions. The model can include
simplifying assumptions on the underlying physics, geometry, material properties, boundary conditions, symmetry, and applied
loads.
8.2 Model Form:
8.2.1 The assumptions made and governing equations used are important factors when formulating a model. Examples of model
form decisions include, but are not limited to: using simplified geometry, using symmetry, 2D versus 3D, linear versus nonlinear
material properties, and dynamic versus static.
8.2.2 The influence of various assumptions can be explored by comparing the output of the model to a different or more complex
model, or to empirical test data.
8.2.3 Consider the required accuracy, the expected cost (time and resources) of the simulation, and how the output will be used
in decisions that can impact the device development and/or patient safety when selecting an appropriate model form.
8.2.4 Many stent designs are composed of repeating patterns that exhibit symmetry. Under circumferentially symmetric uniform
radial load, this repetition may allow for the analysis of a stent subsection while enforcing appropriate conditions of symmetry on
The boldface numbers in parentheses refer to a list of references at the end of this standard.
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truncated boundaries. Results may be reviewed to ensure that all boundary conditions have been applied correctly and that
deformations are consistent with experimental observations.
8.2.5 Stent edge radii are typically excluded from the finite element model to simplify meshing, improve mesh quality, and/or
reduce element count. If the edge radius is expected to significantly change the cross-sectional area of a strut, then a justification
should be provided as to why the results are still valid. Justification could include an FEA study of the impact of
including/excluding the edge radius on the quantities of interest, either on a complete stent model or a sub-model.
8.2.6 The influence of the contact formulation used between the stent and radial compression and/or expansion surface, and
contact of the device with itself (selfcontact), on the model output and stent deformations should be considered.
8.2.6.1 Some contact methods or parameter values can result in the device diameter not matching that of the constricting surface.
For example, nodal penetration due to softened contact or when there is a mismatch between the mesh density of the stent and
constricting surface. Direct diameter measurement or verification of apposition of the stent to the constricting surface can be used
to assess the intended deformation.
8.2.6.2 For computational models of balloon expansion, the value of the friction coefficient used in the contact definition can be
chosen to match the quantities observed on the bench such as the fore-shortening/elongation characteristics of the stent.
8.2.6.3 Contact definitions for braided stents can require special attention due to the wire-to-wire overlap at crossover points.
8.2.7 Interactions between a balloon-expandable stent and the balloon can impact the uniformity of stent deformation.
Approximating the expansion of the stent with a rigid cylinder is a common practice, but consideration should be given as to
whether it is appropriate for the context of use of the model.
8.2.8 The extent of the exploration of the assumptions and/or simplifications to the model’s form is dependent on the model risk.
8.2.9 Example 2: Model Form Exploration illustrates the steps in this standard guide up through defining the model form.
Example 2: Model Form Exploration
Medical Device: Balloon-expandable peripheral vascular stent
Question of Interest: Does the proposed stent design meet or exceed the radial stiffness target when expanded to the minimum indicated diameter?
Posited Decision: The proposed stent design meets the radial stiffness target for the minimum indicated diameter and therefore a small lot of the new design will be
manufactured.
Context of Use: The computational model is used to predict the radial stiffness of an expanded and recoiled peripheral stent concept at nominal geometry. If the
concept meets the minimum expectations, then the design may be manufactured, and the stiffness predictions confirmed via benchtop radial force testing. The
computational model simulates the test method that includes crimp to the minimum process diameter, expansion to the deployed diameter, and then radial
compression to measure the stiffness.
Model Influence: The model is the only source of data used to make the decision. Therefore, the computational model has a high influence on the decision.
Decision Consequence: The consequence of an incorrect decision is an expenditure of resources and project time to manufacture a test concept that does not meet
the radial stiffness requirements. This decision consequence is categorized as low.
Model Risk: The combination of a high model influence and low decision consequence yield a low-medium risk level.
Goals of Model Form Validation Activities by Model Risk:
•Low: No model assumptions and/or simplifications are explored to determine their influence on the output of the computational model.
•Low-Medium & Medium: One or more key model assumptions and/or simplifications are explored to determine their influence on the output of the computational
model.
•Medium-High: All key model assumptions and/or simplifications are explored to determine their influence on the output of the computational model.
•High: All model assumptions and/or simplifications are explored to determine their influence on the output of the computational model.
Define the Model:
•Material Model: Elastic-plastic
•Solver: Quasi-static
•Geometry: 3D 1/8th circumferential symmetry, full length
•Constraints: Theta and axial on the cut surfaces
•Radial Expansion: Rigid cylindrical tool
•Radial Compression: Rigid cylindrical tool
•Contact: No overclosure (hard contact), friction applied
Model Assumptions and Simplifications:
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•The geometry does not include the edge rounding created during electropolishing.
•A 1/8th circumferential symmetry model with theta and axial constraints is representative of the full stent.
•Geometric and radial force differences between a model that uses a rigid cylinder for expansion versus a simulated balloon are insignificant.
•Geometric and radial force differences between a model that uses a rigid cylinder for compression versus a multi-plane iris are insignificant.
Note: The model form activities to be pursued are what the developers of the model and users of the model’s data think are appropriate based on the risk assigned to
the computational model. In this fictitious scenario, the expected activity for a model with a low-medium risk grade are for one or more key model assumptions and/or
simplifications to be explored for their influence on the output of the computational model. The symmetry model form assumption is chosen based on its simplicity. If a
tested device deviates from the predicted output of the model, the unexplored assumptions and simplifications are an option for investigating the deviation. The low-
medium and medium model risk have the same model form goal in this scenario as the number of gradations of goals for each credibility factor do not have to match
the number of model risk levels.
8.3 Finite element analysis is a numerical technique use for simulating the mechanical response of structures. A finite element
structural analysis requires input to numerically represent geometric and material information, as well as mechanical support and
loading conditions. Two important parts of any finite element analysis is the proper representation of material properties and the
definition of load cases and boundary conditions. These must reflect the entire process and performance history and environment
of the device. The load history should include all relevant manufacturing loads and all steps of the intended clinical end use of
the device. If all steps are not included, the reason for the omission should be described.Computational Model Inputs:
8.3.1 Geometric Data:
8.3.1.1 Finite element models are based on a geometric representation of the device being studied. The source of the details of
the geometry can be drawings, computer aided design (CAD) and solid models, preliminary sketches, may include drawings,
computer-aided design (CAD), preliminary sketches, imaging (for example, visual microscopy, CT, SEM), or any other source
consistent with defining the device model geometry.
8.3.1.2 Finite element modeling is used extensively in In the design phase of product development, many times before any finite
element modeling may be used even before any physical prototyping has occurred. As such, models are often based on preliminary
designs from CAD drawings. Changes associated with the progress of the development of the design and manufacturing processes
should be addressed in the finite element model to accurately represent actual stent geometry. idealized geometry. As prototypes
are built, the measured dimensions can be substituted to reflect the dimensions of the prototype devices. Differences between the
geometry of the tested prototypes and idealized geometry can lead to performance predictions that differ from the results of the
benchtop tests.
8.3.1.3 Stent geometry is oftenThe as-manufactured stent geometry can be determined by measuring and inspecting representative
stent samples of stents that have undergone all processing steps prior to insertion inloading onto the body.catheter. This proces
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