Numerical Simulation of Stented Aorta

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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

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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

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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


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


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


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

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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

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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

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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

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• 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.

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Materials and Method Purpose/Intro

Anatomy of Aorta

Mechanical

Properties

AFM

Materials and

method

Boundary

condition

Results

Conclusions

Limitations

• 121212

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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.

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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


Boundary conditions 10 Cell model

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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Intima Media

Purpose/Intro

Anatomy of Aorta

Mechanical

Properties

AFM

Materials and

method

Boundary

condition

Results Conclusions

Limitations

Stress Distribution


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.


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


Thank You for your attention

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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%

Numerical Simulation of Stented Aorta

Health & Medicine

Transcript of Numerical Simulation of Stented Aorta