1. Simulation of Endovascular Repair of
Abdominal Aortic Aneurysms
David Roy, PhD student
“Les entretiens vasculaires XXXI” (ACVQ)
(May 3rd 2013)
1
Directed by: Dr Gilles Soulez,
Interventional Radiologist (Notre-Dame Hospital),
Full Professor of Radiology (University of Montréal)
Co-directed by: Dr Claude Kauffmann,
Physicist in Medical Imaging (Notre-Dame Hospital)

2. 1/15
1 Finite element analysis: applications
Lumen
Thrombus
(blood clot)
Calcifications

3. 2/15
2 Stent-Graft
2.1 Mechanical properties and modeling strategy
Graft:
polyethylene
terephthalate.
Stent:
316L steel.
Graft tensile tests:
• Young Moduli
E1 = 2E2 = 400MPa
• Poisson’s ratios
12 = 2 21 = 0.42
• Shear modulus
G12 = 12MPa
1 (Axial Dir.)
2 (Circ. Dir.)
Graft: bending stiffness
How to “relax” graft bending stiffness to allow a realistic folding behavior ???
Kirchhoff-Love thin plate theory provides the bending stiffness:
It’s enough to reduce the thickness, while increasing the moduli (E1, E2 and G12)
by the same factor (~ 10), to maintain the same tensile membrane stiffness.
)1(12 2
3
Et
D
E: Young’s modulus
t: thickness (influent parameter)
: Poisson’s ratio

4. 3/15
2 Stent-Graft
Stent: beam elements
Graft: shell elements.
Displacement = 80mm
Clamped
proximal
section
Graft elements size = 0.25mm
max displacement = 78mm.
Graft Element size = 0.12mm
max displacement = 79mm.
2.2 Simple bending of an iliac extension
=> “Mesh size” independent solution !
Force = 0.3N
Displacements (mm) Displacements (mm)

5. 4/15
2 Stent-Graft
2.3 Three-points bending of a main body
Force = 1.1N
Displacement = 27mm
Force = 1.1N
Displacement = 28.6mmSupports made of a "slightly rough"
polymeric material.
Estimated coefficient of friction = 0.6
(Vad, Eskinazi & Corbett, 2010).

6. 5/15
2.4 Transversal compression of a (main body) “sealing” stent
0.00
0.10
0.20
0.30
0.40
0.50
0.60
0.70
0.0 5.0 10.0 15.0
Reactionforce(N)
Displacement (mm)
Imposed displacement = 12mm
Reaction force = 0.62N
Reaction force = 0.60N
Linear behavior !
Undeformed stent. Imposed displacement = 12mm
2 Stent-Graft

7. 6/15
2.5 Radial compression of a (main body) “sealing” stent
1) Radial load (arbitrary
value) distributed on the
undeformed stent.
Initial diameter = 28mm.
3) Final diameter of the
compressed stent including the
graft: 19.07mm.
Negligible compressive
stiffness from the Graft, as it
should be !
2) Final diameter of the
compressed stent: 18.55mm.
2 Stent-Graft

8. 7/15
2 Stent-Graft
Independent
variable
Tests dependent
variable
FEM dependent
variable
Variation (%)
Leg: simple bending force = 0.30 disp. = 79 disp. = 78 1.27
Boby: simple bending force = 0.65 disp. = 96 disp. = 101.40 5.62
Boby: three points bending force = 1.10 disp. = 27 disp. = 28.60 5.93
Boby: axial compression disp. = 12 force = 0.74 force = 0.75 1.35
Boby: transversal compression disp. = 12 force = 0.62 force = 0.60 3.23
Forces and displacements are in N and mm respectively.
2.6 Level of accuracy between mechanical tests and simulation

9. 8/15
3 AAA
3.1 Algorithms for 3D geometry and centerlines reconstruction
Centerlines allow: collagen fibers orientation (material definition), and definition of a path for stent-graft deployment.

10. 9/15
3 AAA
3.2 Element-wise local coordinate system for collagen fibers orientation
Element x axis
(obtained by
centerline projection)
Element y axis
Collagen fibers
Looking normally to
a single element.
Centerline (iliac) branch.
Z axis
“Selection cone”:
to pick the right
centerline point.

11. 10/15
3 AAA
3.3 Anisotropic hyperelastic material
2
2
00
eqxx kx
kxdxFdxU
eqeq
eq
x
kx
x
U
F
eq
Strain energy =
area under the
curve
F
xeqx
dx
F
x
eqF
k
Biaxial stretch tests of
AAA specimen samples:
circ.-load:axial-load = 0.5:1
Axial
dir.
Circum.
dir.
Missing parameters to be fitted with test data: C10, k1, k2, and collagen fiber angle .
Isotropic isochoric
(<=> elastin contribution).
Undeformed
(Reference)
Uniaxial stretch
(@ equilibrium)
eqx
t
rP
ntialcircumfere
Could be the axial force
exerted by catheters.
222
1 tacI
1222
tac
el
J
0/ LLf
cc
c
U
S
1
aa
a
U
S
1
22
1
22
1)11(4 1 ac ccI
)11(4)22(4 II
)cos(1c
2/EEE
Working in tension only.
Isotropic volumetric
(<=> compressibility).
Anisotropy
(<=> collagen fibers).
2nd Piola-Kirchhoff stress components:

12. 11/15
3 AAA
3.4 Parameters based on 2nd Piola-Kirchhoff stresses vs. Green strains best fit
circ.-load:axial-load ratio
Experiments
(26 cadaveric
samples)
.
2
.. 1
2
1
circcirccircE
C10 = 1.10x10e-6 kPa (low value  elastin loss)
k1 = 2853.63 kPa
k2 = 9321.99 dimensionless
= 0.32 dimensionless
= 5o degrees
n
SSSSerror
1ppoint
2model
axial,p
erienceexp
axial,p
2model
circ.,p
experience
circ.,p
Error function to be minimized:
axialaxialaxialE 1
2
1 2
Model
Average Coefficient of determination (R2) = 0.86

13. 12/15
3 AAA
3.5 Pressure case & comparison with literature (in terms of Max. Princ. stresses)
Our model:
• Shell elements
• Thickness: 1.5mm
• Pressure: 120mmHg
• Anisotropic hyperelastic material
• Patient-specific geometry
• Only free radial expansion allowed at extremities.
Rodriguez, Ruiz & Doblaré, 2008:
• Solid elements
• Thickness: 1.5mm
• Pressure: 120mmHg
• Anisotropic hyperelastic material
• Virtual geometry
• Fully fixed extremities (not influencing stresses far from
the prescribed boundary conditions).
Princ. stresses (kPa) Princ. stresses (kPa)
Force “F” (mN)
Fixed face Section area “A” (mm2)
Stress = F/A (kPa)

14. 13/15
3 AAA
3.6 Loads and Boundary conditions (BCs)
Equivalent
pressure for
surrounding
tissues.
Mean blood
pressure on
the lumen.
Tied contact
between
AAA and
thrombus.
Thrombus: hyperelastic isotropic material.
(Wang, Makaroun & Webster, 2001)
2
2221 33 IcIcW
Free renal
artery.
Only radial
expansion
allowed at
extremities.
Only radial
expansion
allowed at
extremities.
Contact
with spine. Nonlinear
equivalent
springs.
F
D
No calcifications yet,
but a promising strategy
under development.

15. 14/15
3 AAA
1) Geometry from imaging 2) Loaded geometry from imaging (120mmHg) 2-bis) Loaded geometry from imaging - cut
Displacements
(mm)
3) Zero-pressure geometry 4) Loaded zero-pressure geometry 4-bis) Stresses in loaded zero-pressure geometry
Zero-pressure geometry =
Geometry from imaging –
displacements due to
Blood pressure.
Displacements
(mm)
Stresses
(kPa)
Should be the similar
geometries
3.7 Identification of the “true zero-pressure” geometry

16. 15/15
4 Contact between the AAA lumen and Guidewire/catheters
1) Guidewire forced to fit the centerline
(contact with the vessel deactivated).
2) Guidewire in contact with the vessel
(forcing load released & contact activated).
The Guidewire actuates as a released spring
and enters in contact with the rigid boundary.
Objective in 2013: put everything together (stent-graft implanted in AAA)
Objective in 2014: workflow automatization

17. Merci !
Vos questions sont bienvenues
Thank you !
Your questions are welcome

18. REFERENCES
Vad, S., Eskinazi, A., Corbett, T., McGloughlin, T., & Vande Geest, J.-P. (2010). Determination of coefficient of friction for
self-expanding stent-grafts. Journal of Biomechanical Engineering, 132 (12), 121007-1 to 121007-10.
Rodriguez, J.-F., Ruiz, C., Doblaré, M., & Holzapfel, G.-A. (2008). Mechanical stresses in abdominal aortic aneurysms:
influence of diameter, asymmetry, and material anisotropy. Journal of Biomechanical Engineering, 130, 021023-1 to
021023-10.
Wang, D.-H., Makaroun, M.-S., Webster, M.-W., & Vorp, D.-A. (2001). Mechanical properties and microstructure of
intraluminal thrombus from abdominal aortic aneurysm. Journal of Biomechanical Engineering, 123, 536-539.