Numerical Analysis of Stented Aorta FEM
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1) The document presents a numerical analysis of a stented aorta using finite element modeling. It summarizes the anatomy of the aorta, mechanical testing of the endothelium layer using atomic force microscopy, and the materials and methods used in the finite element model. 2) The results show that with a stent, the aorta diameter increases by 25% at systole compared to 10% without a stent. The top endothelium layer experiences the greatest deformation and stress. The peak wall stress with a stent is around 40% of the failure strength, while without a stent it is around 12% of the failure strength. 3) The analysis provides insights into the stress and deformation characteristics of the aorta layers with
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Numerical Analysis of Stented Aorta FEM
- 1. 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. 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. 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. 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. 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. 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. 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. 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. 9 ASME 2012,HOUSTON,TEXAS T B L R Friction(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. 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:- ResultsPurpose/Intro Anatomy of Aorta Mechanical Properties AFM Materials and method Boundary condition Results Conclusions Limitations
- 11. 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
- 12. • 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
- 13. 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
- 14. ASME 2012,HOUSTON,TEXAS Boundary conditions 10 Cell model 14 30X10=300 µmLength 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. 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. 16 ASME 2012,HOUSTON,TEXAS LS No. Time[s] Blood Pressure considering residual [mmHg] Net Blood Pressure[P a] 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 1BloodPressure[N/m2] Time[Sec] Calculation of Blood Pressure Purpose/Intro Anatomy of Aorta Mechanical Properties AFM Materials and method Boundary condition Results Conclusions Limitations
- 17. 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. 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. 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
- 20. 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 Diameter[cm] Load Step Purpose/Intro Anatomy of Aorta Mechanical Properties AFM Materials and method Boundary condition Results Conclusions Limitations
- 21. 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 Von-MisesStress[N/m2] Load Step Number Purpose/Intro Anatomy of Aorta Mechanical Properties AFM Materials and method Boundary condition Results Conclusions Limitations
- 22. 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 Diameter[m] Distance[m] Purpose/Intro Anatomy of Aorta Mechanical Properties AFM Materials and method Boundary condition Results Conclusions Limitations
- 23. 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 VonMisesStress[Pa] Load Step number Purpose/Intro Anatomy of Aorta Mechanical Properties AFM Materials and method Boundary condition Results Conclusions Limitations
- 24. 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
- 25. 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/Mech anical 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.
- 26. 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
- 27. ASME 2012,HOUSTON,TEXAS Thank You for your attention
- 28. 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%