Effect of Strut Thickness, Crimping and Expansion Diameters
on Radial Strength, Recoil and Foreshortening of a Coronary
Stent.
AMIT DATYE, K. H.WU
Department of Mechanical and Materials Engineering
Florida International University
10555 West Flagler Street, Miami, Florida 33174
USA
Abstract
A nonlinear finite element simulation was performed to analyze the elasto-plastic behavior
a coronary stent undergoing crimping and deploying processes and to understand the effects of
crimping diameter, expansion diameter and strut thickness on radial strength, recoil and
foreshortening of the coronary stent. The commercial package ABAQUS was used for the analysis
and PATRAN was used as the pre-processor. Only half the stent was considered due to symmetry.
Both the crimping and the expansion of the stent involve large deformations, therefore the
non-linearities of the material are also considered. The stent is meshed using solid brick (C3D8 in
ABAQUS) and tetrahedral (C3D4) elements for the analysis. It was found that the magnitude of the
accumulated plastic strain induced by crimping and deployment has a significant effect on the radial
strength, recoil and foreshortening of the stent.
1. Introduction
Coronary heart disease is the most
common cause of death in major Western
countries. The narrowing of the arteries that
feed the heart causes Coronary Heart Disease
(CHD). The excess cholesterol attaches to the
inner smooth artery wall and attracts cellular
waste products, calcium and fibrin, which
result in plaque. This leads to a thickening of
the vessel wall, which can narrow or even
block an artery.
Stents
are
small
spring-like,
cylindrical mesh tubes placed in arteries to
restore the blood flow through the arteries
and to keep them from collapsing after
angioplasty. An ideal stent should be easy to
implant, have excellent recrossability, have
markers at different locations for accurate
positioning, good radial strength to keep the
arteries open, be available in different
lengths, have good resistance to thrombosis
and must have excellent bio and blood
compatibility. Stents can be classified into
two basic types: Self-expanding and Balloonexpanding. They can be further classified
according to their design, the basic material
they are made and the method of deployment.
It has been known that stent design is
an important factor in the restenosis rate of
the artery and also the radial strength of the
stent; the stent strut thickness has also been
linked to the endothelialization of the stent
surface after implant. To optimize the
performance of the new stent design and to
further understand the important stent
parameters
such
as
radial
recoil,
foreshortening, stress concentrations and
deploying pressure, a cardiovascular stent
was systematically analyzed using non-linear
Finite Element Analysis with varying strut
thickness and deployment diameters.
2. Finite element model
In this analysis, a 3D geometrical
model of the new heart-shaped-joint stent is
shown in the Figure 1.1. The stent is
fabricated from a 316L stainless-steel
cylindrical tube by laser cutting and then
polished using suitable methods. The sharp
edges at the joints are rounded to reduce the
stress concentrations at the joints and also
reduce the chances of the stent cutting into
the artery walls. The stent was modeled with
a strut thickness of 0.127, 0.15, 0.20, and
0.25mm to determine the optimum thickness.
models were made using ProEngineer
Modeling Software. The nodes and the
elements are generated in ABAQUS using
size controls. Results were compared to find
the effects of mesh refinement and also the
effect of using different type of elements.
The effect of the mesh size i.e. the mesh
sensitivity on the solution of the model of the
stent is also
analyzed using
various mesh refinements. The stent mesh is
as shown in Figure 3.1.
Figure 1-1: Geometric Models of the new
Stent
The dimensions of the stent used in this
analysis are as listed below:
As fabricated outer diameter:
Crimped diameter:
Length:
Number of coils:
The metal artery contact ratio:
Width of the strut:
Thickness of the strut:
3.048 mm
variable
12.445mm
8
0.17
0.127mm
variable
Solid elements are used in this
analysis of the stent, including brick elements
(C3D8, C3D8R), wedge elements (C3D6)
and tetrahedral elements (C3D4). Since there
is significant plastic strain involved in the
crimping and deploying stages, an elastoplastic large deformation analysis was carried
out on the stent. An isotropic hardening rule
is assumed in this study.
3. Loading and Solution
The stent is assumed to have a
uniform internal pressure due to the balloon
inflation. Furthermore, since the stent is
symmetric about the XY plane the nodes on
the plane are constrained by using symmetric
boundary conditions.
The meshing of the stent was done
using the FEA commercial code ABAQUS
Version 6.2.7 (Hibbitt, Karlsson & Sorenson,
Inc., Pawtucket, RI, USA). The 3D stent
Figure 3-1: Mesh of the stent
The stent was crimped to an external
diameter of about 2.4 mm, which is the
average diameter of the stent when it is
mounted on the delivery system, i.e., the
balloon catheter for deployment.
Figure 3-2: Loads during crimping and
expansion of the stent.
Elastic Recoil after Crimping:
All boundary conditions are released
to allow the elastic recoil after crimping.
Expansion of the stent:
The stent is expanded to a maximum
outer diameter of 4, 4.25, 4.50 and 5 mm.
Elastic Recoil after Expansion
Again, all boundary conditions are
released during this step. Only the nodes in
the symmetric plane were constrained and
one other node was constrained to remove the
fixed body rotations.
4. Results and Discussion
Mesh Sensitivity
Simulations were carried out with
varying degrees of mesh refinement to
characterize the mesh sensitivity of the
analysis. The stent was compressed radially
to the crimped outer diameter of 2.4mm and
the results obtained are shown in Table 4-1.It
can be seen from Table 4-1 that this analysis
is not particularly sensitive to mesh
refinement after the third mesh refinement i.e.
after the mesh has been increased to about
15,000 nodes.
expected, the radial force increases linearly
with an increasing strut thickness.
The stent radial force data obtained
from this analysis were verified with the
actual inflated force in practice. For instance,
in this analysis a stent with 0.2 and 0.15mm
strut thickness require a radial force of 13.18
N (2.9617 lbs) and 9.54 N (2.14 lbs),
respectively. Theses forces are compatible
with real force in the implantation stage of a
stent. The Figures 4-2 and 4-3 show the
Mises stress distribution in the stent with a
0.1mm radial compression it can be seen that
the Mises stress levels are not above the yield
stress of stainless steel.
RADIAL STRENGTH (N)
20
Table 4-1: Mesh sensitivity
ELEMENT
TYPE
# NODES
# ELEMENTS
TOTAL RADIAL FORCE
(N)
C3D8
5134
10214
15394
31359
43568
52246
60124
1764
3854
6144
16082
24320
34468
41124
12.87
13.03
13.10
13.24
13.31
13.43
13.76
26196
20888
13.17
C3D6
The maximum change between the
total radial force for 15,000 nodes and for
60,124 nodes is about 5%. Therefore all the
other analysis for effect of thickness and
effect of deployment diameter are run with a
mesh of approximately 15,000 nodes to
decrease the analysis time.
18
RADIAL FORCE (N)
CRIMP TO OUTER DIAMTER =2.4 mm
16
14
COMPRESSION - 2.2 mm
DIA
EXPANSION - DIA:
3.25mm
12
10
8
6
4
0.12
0.14
0.16
0.18
0.2
0.22
0.24
0.26
STRUT THICKNESS (mm)
Figure 4-1: Radial force with varying
thickness during crimp and expansion.
Effect of Thickness
Various stent models were prepared
with different strut thickness. The thickness
of the strut of the stent was varied from
0.125mm to 0.25mm with an increment of
0.025mm. To illustrate the effect of the strut
thickness on the radial strength of a stent, the
stress/strain and the reaction force data were
collected from the crimping and the
expansion steps to optimize the stent
thickness to provide the best balance between
the radial force and the flexibility of the stent.
The results are tabulated in Table 4-2 for a
crimped diameter of 2.4mm and an expansion
diameter of 3.25mm. Figure 4-1 shows the
relationship between the radial force during
the crimping and deployment stages. As
Figure 4-2: Mises stress distribution over the
stent at 0.1 mm radial compression.
Figure 4-3: Mises stress distribution front
view at 0.1mm radial compression.
Table 4-2: Radial strength and max. Mises
stress with varying thickness.
TOTAL RADIAL FORCE vs DEPLOYMENT DIAMETER
TOTAL RADIAL FORCE (N)
20
19
18
17
16
15
14
13
12
11
10
3
4
5
DEPLOYMENT DIAMETER (mm)
Figure 4-5: Total radial force with varying
deployment diameters using FEA.
FORSHORTENING vs DEPLOYMENT DIAMETER
9
% FORESHORTENING
8
7
6
5
4
3
2
1
0
3
3.5
4
4.5
5
5.5
DEPLOYMENT DIAMETER (mm)
To understand the effect of
deployment diameter on the overall
mechanical behavior of a stent, an FE
analysis was performed on a stent with
varying deployed diameters of 3.25, 4 and 5
mm. The crimped diameter of the stent was
fixed at 2.4 mm. It can be seen from Figures
4-5 to 4-7 that the radial force required to
expand the stent increases as the deployment
diameter
increases.
The
percentage
foreshortening increases while the percentage
radial recoil decreases as expected with an
increase in deployment diameter.
RADIAL RECOIL vs DEPLOYMENT DIAMETER
0.45
0.4
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0
3
4
5
DEPLOYMENT DIAMETER (mm)
Figure 4-7: Percentage Radial Recoil with
varying deployment diameters using FEA.
MAX. MISES STRESS DURING EXPANSION AND RECOIL vs
EXPANSION DIAMETER
500
MISES STRESS (N/mm^2)
Figure 4-6: Percentage foreshortening with
varying deployment diameters using FEA.
% RADIAL RECOIL
Effect of Deployed Diameter
Effects of Accumulated Plastic Strain on
Radial
Strength,
Recoil
and
Foreshortening
480
460
440
AFTER FINAL RECOIL
AFTER EXPANSION
420
400
3
3.5
4
4.5
5
5.5
EXPANSION DIAMETER (mm)
Figure 4-4: Mises stresses during/after recoil
In order to clearly understand the
effect of accumulated plastic strain on the
radial strength, recoil and foreshortening, the
following analysis was conducted by varying
the crimped diameter while maintaining the
initial outside diameter constant.
Table 4-3 shows the accumulated
plastic strain after the crimping process.
Table 4-3: Analysis of plastic strains with
varying crimp diameters
1
2
3
4
5
CRIMP
RADIUS
mm
PEEQ
S-MISES
1.100
1.125
1.150
1.175
1.189
9.59E-02
8.97E-02
8.35E-02
7.73E-02
7.39E-02
N/mm^2
422.89
422.74
422.59
422.44
422.35
Figure 4-8: Mises stress and plastic strain
with varying crimping diameter
Analysis of the plastic strain during crimping
shows that the equivalent plastic strain
increases with a decrease in the crimp radius,
radial force required for crimping also
increases though not by a significant amount
with a decrease in the crimping radius. The
elastic recoil after crimping stays nearly the
same with the maximum recoil being at the
largest crimping diameter.
The Mises stress and the equivalent
plastic strain during crimping to various radii
is shown in Figure 4-8.
After crimping, the stent was deployed to
various diameters.
Once this step was
completed, the radial strength, recoil, and
foreshortening of the stent were determined.
Table 4-4 demonstrates the effect of totally
accumulated plastic strain on these important
indicators of a coronary stent
Figures 4-9 through to 4-12 show
the analysis of the stent during expansion
to varying diameters the effects of the
accumulated plastic strain can be seen
from these figures.
Table 4-4: Analysis of stent with varying crimp and expansion diameters
CRIMP
RADIUS
mm
EXPANSION
DIAMETER
mm
S-MISES
RADIAL
% CHANGE % CHANGE
STRENGTH IN RADIAL
IN MISES
N/mm^2
(N)
STRENGTH
STRESS
1
1.100
2
1.125
3
1.150
3.25
4.00
5.00
3.25
4.00
5.00
3.25
4.00
5.00
428.4
462.1
495.6
426.5
458.4
490.4
422.1
449.3
487.2
11.83
15.94
19.14
11.54
15.33
18.7
11.23
14.91
18.62
5.34%
6.91%
2.79%
2.76%
2.82%
0.43%
0
0
0
CRIMP EXPANSION % RADIAL
% FORE RADIUS DIAMETER
RECOIL SHORTENING
mm
mm
1
1.100
2
1.125
3
1.150
3.25
4.00
5.00
3.25
4.00
5.00
3.25
4.00
5.00
0.388
0.164
0.138
0.42
0.173
0.142
0.498
0.285
0.193
0.27
5.58
8.42
0.25
5.62
8.46
0.22
5.78
8.51
1.49%
2.85%
1.72%
1.04%
2.03%
0.66%
0
0
0
RADIAL RECOIL VS EXPANSION DIAMETER
0.55
1.100
0.5
1.125
% RADIAL RECOIL
It can be seen that the maximum
Mises stress in the stent after expansion
increase with an increase in the
accumulated plastic strain. This is not a
concern because the maximum stress
levels are below the yield stress for 316L
stainless steel.
Figure 4-10 shows that the radial
strength of the stent increases with an
increase in the accumulated plastic strain.
This means that the stent can hold more
pressure from the arterial walls i.e the
stent is stronger.
It can also be seen from Figures 411 and 4-12 that the radial recoil and the
foreshortening is reduced due to
accumulated plastic strains.
0.45
1.150
0.4
0.35
0.3
0.25
0.2
0.15
0.1
3.00
3.50
4.00
4.50
5.00
EXPANSION DIAMETER (mm)
Figure 4-11: Radial recoil with changes in
expansion diameter for different crimp
diameters
FORESHORTENING
9
8
1.100
% FORESHORTENING
1.125
7
1.150
6
5
4
3
2
1
0
3.00
3.50
4.00
4.50
5.00
EXPANSION DIAMETER (mm)
Figure 4-12: Foreshortening with changes in
expansion diameter for different crimp
diameters
Figure 4-9: Mises stress with changes in
expansion diameter for different crimp
diameters
RADIAL STRENGTH
RADIAL STRENGTH ( N)
20
19
1.100E+00
18
1.125E+00
17
1.150E+00
16
15
14
13
12
11
10
2.5
3.0
3.5
4.0
4.5
5.0
5.5
EXPANSION DIAMETER (mm)
Figure 4-10: Radial force with changes in
expansion diameter for different crimp
diameters
5. CONCLUSION
In this paper the effect of the strut
thickness, the deploying diameter and the
effect of residual plastic strain is presented.
Also other important parameters like radial
recoil and foreshortening after deployment
are studied in this paper.
A finite element model of a coronary
stent is created and analyzed to characterize
the effects of the various parameters
mentioned above on the mechanical
properties of the stent. It is found that the
thickness of the strut has a major effect on the
radial strength of the stent. The radial
strength increases with an increase in the strut
thickness of the stent, this corresponds to a
decrease in the flexibility of the stent. Since
the stent is used in very complex areas it is
important to have a balance between the
radial strength and flexibility of the stent.
The stent strut thickness has an important
effect on the radial strength of the stent. The
radial strength increases with an increase in
the strut thickness while the max stress in the
stent also increases.
The deploying diameter also has an
effect on the radial strength, the
foreshortening and the radial recoil. The
radial strength increases, as there is an
increase in the deployment diameter, which
means that there is an increase in the stress
levels with an increase in the deployment
diameter. The foreshortening increases with
an increase in the deploying diameter while
the percentage radial recoil reduces with an
increase in the deployment diameter.
The analysis of the effects of
accumulated plastic strain shows that the
radial strength of the stent increases when
there is an increase in the accumulated plastic
strain also there is less radial recoil and
foreshortening of the stent. This demonstrates
that if the stent can be fabricated at a greater
diameter and then crimped to its minimum
diameter then the radial strength of the stent
can be further increased.
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