ASTM F2514-08
(Guide)Standard Guide for Finite Element Analysis (FEA) of Metallic Vascular Stents Subjected to Uniform Radial Loading
Standard Guide for Finite Element Analysis (FEA) of Metallic Vascular Stents Subjected to Uniform Radial Loading
SIGNIFICANCE AND USE
Finite element analysis is a valuable method for evaluating the performance of metallic stents and in quantifying quantities such as internal stresses, internal strains, and deformation patterns due to applied external loads and boundary conditions. Many times an analysis is performed to correlate to and plan experimental tests. A finite element analysis is especially valuable in determining quantities that cannot be readily measured.
SCOPE
1.1 Purpose—This guide establishes general requirements and considerations for the development of finite element models used in the evaluation of the performance of a metallic vascular stent design under 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 and analysis results. Finally, the recommended content of an engineering report covering the mechanical simulations is presented.
1.2 Limits:
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.
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.
1.2.6 This guide is not intended to include complete descriptions of the finite element method, nor its theoretical basis and formulation.
1.3 The values stated in SI units are to be regarded as the standard. The values given in parentheses are for information only.
General Information
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Standards Content (Sample)
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Designation: F2514 − 08
StandardGuide 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 requirements 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 1.2.5 This guide does not provide guidance in the applica-
tion or interpretation of FEA in determining fatigue life.
1.1 Purpose—This guide establishes general requirements
1.2.6 This guide is not intended to include complete de-
and considerations for the development of finite element
scriptions of the finite element method, nor its theoretical basis
models used in the evaluation of the performance of a metallic
and formulation.
vascular stent design under uniform radial loading. Suggested
criteria are provided for evaluating the typical cases of metallic
1.3 The values stated in SI units are to be regarded as the
stents under uniform radially oriented and pulsatile loading.
standard. The values given in parentheses are for information
Recommended procedures for checking and validating the
only.
finite element model(s) are provided as a means to assess the
model and analysis results. Finally, the recommended content
2. Terminology
ofanengineeringreportcoveringthemechanicalsimulationsis
2.1 Definitions:
presented.
2.1.1 balloon expandable stent, n—a stent that is expanded
1.2 Limits:
at the treatment site by a balloon catheter. The purpose of the
1.2.1 Thisguideislimitedindiscussiontothefiniteelement
balloon is to plastically deform the stent material such that the
structural analysis of metallic stents of the following types:
stent remains expanded after the deflation of the balloon.
1.2.1.1 Plastically deformable metal stents.
2.1.2 conceptual model, n—model produced by analyzing
1.2.1.2 Self-expanding metal stents.
and observing the physical system of interest composed of
1.2.1.3 Plastically deformable metal portions of covered
mathematical models and equations representing that system.
stents.
2.1.3 computational model, n—implementationofaconcep-
1.2.1.4 Metal portions of self-expanding covered metal
tual model in software.
stents.
1.2.2 Theemphasisofthetechniquesdescribedinthisguide
2.1.4 crimp, v—to secure the stent on a delivery system by
is intended for both elasto-plastic materials such as stainless radially compressing the stent into a delivery device such as a
steel, and superelastic materials such as nitinol. Unique con-
catheter or onto an expanding delivery device such as a
cerns associated with stents designed for shape memory
balloon.
behavior are not addressed within this guide.
2.1.5 delivery system, n—a mechanical system that is used
1.2.3 This guide does not consider changes to possible time
to deliver and deploy a stent at a target site.
varying conditions or different loadings related to vascular
2.1.6 elasto-plastic material, n—a material behavioral
remodeling.
model that exhibits elastic behavior (recoverable) up to its
1.2.4 This guide is restricted to cases that involve the
yield point and plastic behavior (irrecoverable) above its yield
application of uniform radially oriented loading.
point.
1 2.1.7 endurance limit, n—stress or strain level at which the
This guide is under the jurisdiction of ASTM Committee F04 on Medical and
Surgical Materials and Devices and is the direct responsibility of Subcommittee
material is considered to have “infinite” life.
F04.30 on Cardiovascular Standards.
2.1.8 finite element analysis (FEA), n—a general purpose
Current edition approved July 15, 2008. Published August 2008. DOI: 10.1520/
F2514-08. numerical technique.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
F2514 − 08
2.1.8.1 Discussion—In this guide, the structural continuum vessel patency. For the purposes of this guide, a stent is
is discretized into regions known as elements, in which the metallic and may be covered by a coating, synthetic textile, or
mechanical behavior is defined. Continuity is enforced at the tissue graft material.
vertices of the elements where node points are defined. The
3. Summary of Practice
mechanical behavior of the continuum is then defined accord-
ing to mathematical expressions of physical laws at the node
3.1 This guide addresses the use of the finite element
points. This results in the definition of a set of simultaneous
method for structural analysis of metallic vascular stents under
equations that are solved for state variables from which such
various types of simulated uniform radial loading.The purpose
important quantities as displacements, stresses, and strains can
of a structural analysis of the stent is to determine such
be derived.
quantities as the displacements, stresses, and strains within a
device resulting from external loading. This includes stresses
2.1.9 geometrical nonlinearity, n—a type of nonlinearity
and strains potentially due, but not limited, to manufacturing
related to structural deformation where the relation between
processes, to delivery in the body, and to pulsatile loading in
strain and displacement are not linearly proportional.
vivo.
2.1.10 linear elastic material, n—a material in which the
3.2 Current United States government guidelines (1) rec-
stress resulting from an applied force is directly proportional to
ommend structural analysis of a proposed device under physi-
the corresponding strain it produces. Thus, linear elastic
ologically appropriate loading. The analysis technique dis-
materials do not retain any stress or strain when all external
cussed in this guide is restricted to the finite element analysis
loads and boundary conditions are removed and all deforma-
technique (2-5), although other techniques may be equally
tions are recoverable.
suitable for the required analysis.
2.1.11 model calibration, n—the process through which the
3.3 Prior to the finalization of a device design, rigorous
parameters of a computational model are checked or adjusted
experimentaltestingisrecommendedtocomplementtheanaly-
to create a model with the proper measure of accuracy.
ses performed. During these tests, care should be taken to
2.1.12 model validation, n—the process of determining the
represent the loading and boundary support conditions consis-
degree to which a computational model accurately represents
tent with those used not only in the finite element analysis and
the real world behavior it was intended to represent. It is an
experimental tests but also those expected in clinical use.
evaluation of the fidelity of the computational model and the
Experimental tests should be carefully monitored. Any behav-
real world.
iorthatwasnotcapturedbythenumericalsimulationshouldbe
2.1.13 model verification, n—the process of assessing that
identified and evaluated for its effect on safety and reliability.
the implementation of the computational model accurately
represents the engineer’s conceptual model and of the solution
4. Significance and Use
tothemodel.Itisanevaluationofthefidelityoftheconceptual
4.1 Finite element analysis is a valuable method for evalu-
model and the computational model.
ating the performance of metallic stents and in quantifying
2.1.14 nonlinear material, n—a material behavior in which
quantities such as internal stresses, internal strains, and defor-
the stress resulting from an applied external load is not directly
mation patterns due to applied external loads and boundary
proportional to the induced strain.
conditions. Many times an analysis is performed to correlate to
and plan experimental tests. A finite element analysis is
2.1.15 permanent deformation, n—residual or irrecoverable
especially valuable in determining quantities that cannot be
strain and deformation in a structure after all loads and
readily measured.
boundary conditions are removed.
2.1.16 plasticity, n—material behavior characteristic where
5. Overall Technical Approach
permanent or irrecoverable deformation remains when the
5.1 The application of finite element analysis is intended for
external loading is removed.
the development of a quantifiable level of confidence in the
2.1.17 pulsatile, adj—recurring alternate increase and de-
stent design. The overall approach described in this guide
crease of a quantity such as the pressure that would occur in an
focuses on the development of a systematic technical approach
artery.
to using the finite element analysis technique to evaluate stent
2.1.18 self-expanding stent, n—a stent that expands at the
performance. The basic process includes:
treatment site without mechanical assistance. The material
5.1.1 Detailed definition of the geometry of the stent being
typically used for the stent has the ability to return either
evaluated.
partially or fully to a previous size and shape and remain
5.1.2 Thedetermination,quantificationandvalidationofthe
expanded after the delivery system is removed.
important mechanical material properties.
5.1.3 Selection of the appropriate finite element tools and
2.1.19 solution sensitivity, n—a measure of the relative
programs to ensure effective and reliable representations of the
change in solution results caused by changing one or more
stent being evaluated.
parameters in a computational model.
2.1.20 stent, n—a tubular structure that is permanently
implanted in the native or grafted vasculature and that is
The boldface numbers in parentheses refer to a list of references at the end of
intended to provide mechanical radial support to enhance this standard.
F2514 − 08
5.1.4 Selection and validation of the appropriate finite standard engineering references. The results of such simula-
element model and type of element(s) used. tions will be considered preliminary results.
5.1.5 Calibration, validation, and verification of model 6.1.3 Material Property Tests:
input, parameters for the numerical simulation, solution results
6.1.3.1 Mechanical properties of the material should be
and comparison to experimental tests.
determined from rigorous experimental testing of the material
5.1.6 Definition of all important loading steps.
that has undergone all pertinent manufacturing processes
5.1.7 Selection and application of appropriate boundary
including finishing, cleaning, and sterilization, if appropriate.
conditions, such as symmetry.
Themechanicalmaterialpropertiesforafiniteelementanalysis
5.1.8 Effective and proper application of the finite element are most often determined through tensile testing of the
analysis program for the intended evaluation.
material. During the test, load and displacement data is to be
5.1.9 The generation and interpretation of results to perform collected to define the entire material curve. All relevant
an effective evaluation. hysteresis and/or temperature effects on the material response
5.1.10 Documentation of the analysis, including all support- must be included.
ing citations and references, analysis methodology, and
6.1.3.2 When testing for material properties, extreme care
assumptions, results interpretation, and overall stent design
should be taken to ensure accurate measurements using suit-
evaluation.
able fixturing and appropriately calibrated devices for measur-
ing both load and displacement.
6. Input Data
6.1.3.3 If warranted by the material, the material curve(s)
should be measured at the appropriate temperature(s) of the
6.1 Finite element analysis is a numerical technique use for
intended use. The effects of temperature on the material
simulating the mechanical response of structures. A finite
response are extremely critical for superelastic alloys. Differ-
element structural analysis requires input to numerically rep-
ences in the material behavior in tension and compression
resent geometric and material information, as well as mechani-
should also be considered along with any load history depen-
cal support and loading conditions. Two important parts of any
dent tension/compression asymmetry phenomena or work
finite element analysis is the proper representation of material
hardening of the material.
properties and the definition of load cases and boundary
6.1.4 Material Property Validation:
conditions. These must reflect the entire process and perfor-
6.1.4.1 The material mechanical property values must be
mance history and environment of the device. The load history
should include all relevant manufacturing loads and all steps of converted into a format and form consistent with the finite
element representation.
the intended clinical end use of the device. If all steps are not
included, the reason for the omission should be described.
6.1.4.2 Validation tests should be performed to validate the
6.1.1 Geometric Data: material model used in the analysis. The effects of the test
6.1.1.1 Finite element models are based on a geometric specimen size or shape (tube, wire, sheet) must be considered
in applying the material model to the validation model.
representation of the device being studied. The source of the
details of the geometry can be drawings, computer aided
6.1.4.3 Amaterial validation test could include the determi-
design (CAD) and solid models, preliminary sketches, or any nation of the load-displacement behavior of a finite element
other source consistent with defining the device model geom-
model of a simple tensile test. For example, a model is first
etry. created of a simple geometric specimen of material using the
6.1.1.2 Finite element modeling is used extensively in the element type for which the validation is being performed. The
design phase of product development, many times before any geometry and number of elements in the validation model
should be sufficient to enable the definition of proper loading
prototyping has occurred. As such, models are often based on
preliminary designs from CAD drawings. Changes associated and constraints, yet simple enough to isolate the key load-
displacement behavior for correlation. A validation simulation
with the progress of the development of the design and
manufacturing processes should be addressed in the finite is performed using the appropriate tensile loading and con-
element model to accurately represent actual stent geometry. straint conditions. The deformations at various loading steps
6.1.1.3 Stent
...
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