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1
ASME 2012,HOUSTON,TEXAS
Numerical Analysis of Stented Aorta
Aman Agarwal(a),Bou-Said Benyebka(b), G. C. Mohan Kumar(a)
Mélusine Bouchet(b)
(a)National Institute of Technology Karnataka Surathkal, INDIA,
(b)INSA-Lyon, LaMCoS, CNRS UMR 5259, FRANCE
2
ASME 2012,HOUSTON,TEXAS
Outline
1. Introduction
2. Anatomy of Aorta
3. Atomic Force Microscope Experiment
4. Methods and Material
5. Boundary Conditions
6. Results and discussion
7. Conclusion
3
ASME 2012,HOUSTON,TEXAS
Purpose/Introduction
Aortic Aneurysms Atherosclerosis
More than 50% of patients who experience a rupture of artery die before reaching hospital Rest experience excessive expansion of stent during deployment may cause extensive wall damage
Purpose/Intro
Anatomy of Aorta
Mechanical
Properties
AFM
Materials and
method
Boundary
condition
Results
Conclusions
Limitations
4
ASME 2012,HOUSTON,TEXAS
Purpose/Introduction
Image:-NHLBI MD USA, Huntervascular Sydney
Coronary heart disease(CHD) caused by alteration in arterial wall properties cause destruction of human body.
Purpose/Intro
Anatomy of Aorta
Mechanical
Properties
AFM
Materials and
method
Boundary
condition
Results
Conclusions
Limitations
5
ASME 2012,HOUSTON,TEXAS
Anatomy of Aorta
Muscular tissues
Elastin fibers
Collagen fibers
Purpose/Intro
Anatomy of
Aorta
Mechanical
Properties
AFM
Materials and
method
Boundary
condition
Results
Conclusions
Limitations
6
ASME 2012,HOUSTON,TEXAS
Innermost layer, endothelium layer is under direct influence with all external forces i.e blood pressure, shear force and force due to stent.
Atomic Force Microscopic(AFM) experiment was carried out to find the mechanical properties of endothelium layer
3Ei=Em=3Ea (Fisher et al,2002)
Ei ti+Emtm+Eata=Et
ti:tm:ta=13:56:31 (Schuleze et al)
Mechanical Properties Purpose/Intro
Anatomy of Aorta
Mechanical
Properties
AFM
Materials and
method
Boundary
condition
Results
Conclusions
Limitations
7
ASME 2012,HOUSTON,TEXAS
Used to study micro to nano scale living structure.
Atomic Force Microscope Experiment
AFM
Elastic properties of cells
Tissue topography
Interaction between surface and tip gives topography
Force acting on tip cause indentation gives elastic properties
Purpose/Intro
Anatomy of Aorta
Mechanical
Properties
AFM
Materials and
method
Boundary
condition
Results
Conclusions
Limitations
8
ASME 2012,HOUSTON,TEXAS
20µm
k = 0.15 N/m ; 0.2 N/m R ~ 20 µm
k = 0.1 N/m h ~ 15 µm ; R ~ 6
nm
AFM : 2 types of geometry Topography 100 µm x 100 µm
Indentation Distance 1-2 µm
Variable speed ~ 1 ; 5 ; 12 µm/s
Hydration Medium
Lever AFM
Specimen
AFM:-To find elastic property of endothelium Purpose/Intro
Anatomy of Aorta
Mechanical
Properties
AFM
Materials and
method
Boundary
condition
Results
Conclusions
Limitations
9
ASME 2012,HOUSTON,TEXAS
T
B
L R
Fric
tio
n (
nN
)
Distance X (µm) Scanning along X-axis
Friction Distance X ~ 20µm Constant normal force : ~ 0,4 µN Velocity ~ 4 µm/s
AFM lever k tors ~ 150 N/m
20µm
AFM:-To find topography of endothelium Purpose/Intro
Anatomy of Aorta
Mechanical
Properties
AFM
Materials and
method
Boundary
condition
Results
Conclusions
Limitations
10
ASME 2012,HOUSTON,TEXAS
• E=0.668KPa • Force Limit 3.32-9.23nN • σt max : 1.39 – 3.02 Pa
(a) Elastic Property
(b) Topography
• Thickness 3.33 ± 0.5 µm • Length 32.1 ±6.6 µm
AFM:- Results Purpose/Intro
Anatomy of Aorta
Mechanical
Properties
AFM
Materials and
method
Boundary
condition
Results
Conclusions
Limitations
FEM analysis is performed on ANSYS 11 APDL, on 4 layers artery wall.
Tetrahedral mesh with 67000 elements.
2-D 4 node structural plane element (PLANE 182) is used in complete model.
11
ASME 2012,HOUSTON,TEXAS
Materials and Method Purpose/Intro
Anatomy of Aorta
Mechanical
Properties
AFM
Materials and
method
Boundary
condition
Results
Conclusions
Limitations
• 121212
12
ASME 2012,HOUSTON,TEXAS
Endothelium
Connective tissue
Elastic membrane
Media
100 µm
60 µm
1200 µm
Elastic Linear E = 0.668 KPa ν = 0.49
Viscoelastic non-linear E = 3 MPa ν = 0.40 Prony shear response table
Elastic Linear E = 5 MPa ν = 0.40
Viscoelastic non-linear E = 8.95 MPa ν = 0.40 Prony shear response table
α1 τ1
0.2 0.166
0.2 0.02
0.6 0.06
α1 τ1
0.2 0.166
0.2 0.02
0.3 0.03
30 µm 1 µm Length of model 300 µm
Intima-Media model
E of Media is 8.95Mpa and Intima ~3Mpa,Mosora’s experiment , Shear and volumetric response.
Purpose/Intro
Anatomy of Aorta
Mechanical
Properties
AFM
Materials and
method
Boundary
condition
Results
Conclusions
Limitations
Blood Viscosity= 0.0035Pas Density 1050Kgm-3.
13
ASME 2012,HOUSTON,TEXAS
Non-Newtonian Flows by R.Shankar Subramanian from Clarkson University
Blood :-What type of fluid? Purpose/Intro
Anatomy of Aorta
Mechanical
Properties
AFM
Materials and
method
Boundary
condition
Results
Conclusions
Limitations
ASME 2012,HOUSTON,TEXAS
Boundary conditions 10 Cell model
14
30X10=300 µm Length of model
Blood Shear force d i
Endothelium
Connective tissue
Elastic membrane
Media
X
Y
Purpose/Intro
Anatomy of Aorta
Mechanical
Properties
AFM
Materials and
method
Boundary
condition
Results
Conclusions
Limitations
Force due to stent
Blood Pressure
15
ASME 2012,HOUSTON,TEXAS
Rigid Vessels No Slip btw layers
Systolic=120mm Hg Residual=9mm Hg
72 Beats Per Min Inner dia ~0.8cm
Purpose/Intro
Anatomy of Aorta
Mechanical
Properties
AFM
Materials and
method
Boundary
condition
Results
Conclusions
Limitations
16
ASME 2012,HOUSTON,TEXAS
LS No. Time[s] Blood Pressure considering residual [mmHg]
Net Blood Pressure[Pa]
1 0.1 011 - 9 =002
266.64
2 0.2 092 - 9 =083
11065.75
3 0.3 120 - 9 =111
14798.78
4 0.4 020 - 9 =011
1466.54
5 0.5 018 - 9 =009
1200
6 0.6 024 - 9 =015
200
7 0.7 018 - 9 =009
1200
8 0.8 010 - 9 =001
133.32
0
2000
4000
6000
8000
10000
12000
14000
16000
0 0.2 0.4 0.6 0.8 1 B
loo
d P
ress
ure
[N/m
2]
Time[Sec]
Calculation of Blood Pressure
Purpose/Intro
Anatomy of Aorta
Mechanical
Properties
AFM
Materials and
method
Boundary
condition
Results
Conclusions
Limitations
17
ASME 2012,HOUSTON,TEXAS
Time[s] Flow rate[ml/s]
0.0 1
0.1 360
0.2 440
0.3 200
0.4 5
0.5 40
0.6 7
0.7 4
0.8 1
Study by Umberto Morbiducci “Blood flow in human Aorta”
Steady state Hagen-Poiseuille equation
τ(mean):- is temporal and spatial shear stress µ :- dynamic viscosity of blood Q:-total volume flow R:-lumen radius
LS No Time[s] Wall Shear Stress[N/m2]]
1 0.1 0.93852
2 0.2 1.14708
3 0.3 0.5214
4 0.4 0.013035
5 0.5 0.10428
6 0.6 0.018249
7 0.7 0.010428
8 0.8 0.002607
Calculation of shear stress
Purpose/Intro
Anatomy of Aorta
Mechanical
Properties
AFM
Materials and
method
Boundary
condition
Results
Conclusions
Limitations
18
ASME 2012,HOUSTON,TEXAS
Port angle 45o
Stent DIA 16mm
Wire DIA 0.5mm
9mm
Design of stent depends on stent length ,stent dia., number of struts, struts dia, port angle
Material Name Stainless Steel
Young’s Modulus 201GPa
Poisson's ratio 0.3
Yield Stress 170MPa
Diameter of Aorta become 1.2 times the original
Stent Structural analysis
Purpose/Intro
Anatomy of Aorta
Mechanical
Properties
AFM
Materials and
method
Boundary
condition
Results
Conclusions
Limitations
19
ASME 2012,HOUSTON,TEXAS
Structural analysis of stent model was performed with twice the maximum pressure i.e 32KPa The model was constraint cylindrically so that stent can expand radially. A contact patch of 100 micrometer was applied to FEM model of 2-D aorta.
The stress generated were much below the safe point of the material
Purpose/Intro
Anatomy of Aorta
Mechanical
Properties
AFM
Materials and
method
Boundary
condition
Results
Conclusions
Limitations
Final Diameter=2(deformation)+d initial
20
ASME 2012,HOUSTON,TEXAS
Results :-Without stent
0.86
0.88
0.9
0.92
0.94
0.96
0.98
1
0 2 4 6 8 10
Dia
me
ter[
cm]
Load Step
Purpose/Intro
Anatomy of Aorta
Mechanical
Properties
AFM
Materials and
method
Boundary
condition
Results Conclusions
Limitations
21
ASME 2012,HOUSTON,TEXAS
Results :-Without stent
-2.00E+04
0.00E+00
2.00E+04
4.00E+04
6.00E+04
8.00E+04
1.00E+05
1.20E+05
1.40E+05
1.60E+05
0 5 10
Vo
n-M
ise
s St
ress
[N
/m2]
Load Step Number
Purpose/Intro
Anatomy of Aorta
Mechanical
Properties
AFM
Materials and
method
Boundary
condition
Results Conclusions
Limitations
22
ASME 2012,HOUSTON,TEXAS
Results:- With Stent
1.05
1.06
1.07
1.08
1.09
1.1
1.11
1.12
0 2 4 6 8 10
Dia
me
ter[
m]
Distance[m]
Purpose/Intro
Anatomy of Aorta
Mechanical
Properties
AFM
Materials and
method
Boundary
condition
Results Conclusions
Limitations
23
ASME 2012,HOUSTON,TEXAS
Results :-With Stent
-1.00E+05
0.00E+00
1.00E+05
2.00E+05
3.00E+05
4.00E+05
5.00E+05
6.00E+05
7.00E+05
8.00E+05
9.00E+05
0 2 4 6 8 10
Vo
n M
ise
s S
tre
ss [
Pa]
Load Step number
Purpose/Intro
Anatomy of Aorta
Mechanical
Properties
AFM
Materials and
method
Boundary
condition
Results
Conclusions
Limitations
24
ASME 2012,HOUSTON,TEXAS
Intima Media
Purpose/Intro
Anatomy of Aorta
Mechanical
Properties
AFM
Materials and
method
Boundary
condition
Results Conclusions
Limitations
Stress Distribution
ASME 2012,HOUSTON,TEXAS
Purpose/Intro
Anatomy of Aorta
Mechanical
Properties
AFM
Materials and
method
Boundary
condition
Results
Conclusions Limitations
Discussion
• At systolic diameter increases by 10%(without Stent) 25%( with Stent).
• Topmost layer get maximum deformation and has highest possibilities of getting ruptured.
• The peak wall stress with stent is around 40% of failure strength ,whereas the peak wall stress without is around 12% of failure strength.
Conclusion
• Characteristics/Mechanical Behavior of Aorta
• Quantify time varying stress
• Provides deformation on layers of Aorta –with and without stent
• The topmost layer-endothelium suffer maximum deformation highest possibilities of getting ruptured
Impact
• Help Clinicians to specific balloon size and inflation pressure
• Substantial pulsating stress on endothelium layer cause damage ,result in atheroma.
• Mechanical fatigue depends on max and min stress ratio, which explain restenosis occurring in 20% of stent deploitation.
ASME 2012,HOUSTON,TEXAS
Limitations
• Blood is assumed to be incompressible , Newtonian fluid.
• Simulation require further refinement with exact mechanical properties of aortic layers
• Additional shock waves generated from heart is not accounted
Future work
• Stress comparison , deformation comparison between healthy and non healthy stented aorta.(properties)
• Similar simulations can be performed on iliac arteries and carotid arteries
• Study of waves generated by heart which affect shear stress
Purpose/Intro
Anatomy of Aorta
Mechanical
Properties
AFM
Materials and
method
Boundary
condition
Results
Conclusions
Limitations
ASME 2012,HOUSTON,TEXAS
Thank You for your attention
28
ASME 2012,HOUSTON,TEXAS
Results and discussion H NH
Pulse Pressure
Thickness
Stiffness
H [mmHg]
NH [mmHg]
Ps 120 140
Pd 70 70
PP 50 70
H NH
Connective tissue
100 200
Elastic membrane
60 120
media 1200 2300
Stiffer artery in pathologic patients and old people Elastic modulus increase by 60%