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Mechanical Response of a Metallic Stent

This study evaluates the mechanical response of a metallic stent used in vascular applications, including failure modes and deformation analysis. It also explores the coupled response of the stent and the blood vessel. Experimental apparatus and analytical models are utilized to develop a structural mechanics description.

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Mechanical Response of a Metallic Stent

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  1. Mechanical Response of a Metallic Stent K. Ravi-Chandar andRenjun Wang Department of Aerospace Engineering and Engineering Mechanics Center for Mechanics of Solids, Structures and Materials Collaborators: Prof. Suncica Canic, UH, Dr. Zvonko Krajcer, St. Luke’s

  2. Outline • Stents in vascular applications • Failure modes • Mechanics problem • Experimental characterization • Analysis of the deformation • Coupled stent-artery deformation • Outlook

  3. Arteries J Humphrey, Cardiovascular Solid Mechanics, Springer, 2002

  4. Abdominal Aortic Aneurysm C.E. Ruiz, et al, Circulation, 1997;96:2438-2448

  5. Structural changes in the artery • Dramatic decrease in elastin and smooth muscle cell content • Increase in collagen • Degradation of arterial resistance to the blood pressure

  6. Treatment • Surgical placement of stent-grafts • Extensive surgery – not all patients are suitable for this procedure • Endovascular placement of stents and stent-grafts • Quick, simple procedure – currently still experimental • Long-term consequences are not well characterized

  7. AnueRx Bifurcated Stent

  8. WallStent Villareal, Howell, and Krajcer Tex Heart Inst J 2000;27:146-9

  9. Abdominal Aortic Aneurysm Stent-graft Stent C.E. Ruiz, et al, Circulation, 1995;91:2470-2477

  10. Abdominal Aortic Aneurysm • Short term • Reduction in the size of aneurysm • Long term • Dilation of proximal side of artery • Wever et al., (2000), European Journal of Vascular and Endovascular Surgery, 19: 197–201. • Endoleaks • Chuter et al. (2001), Journal of Vascular Surgery, 34, 98–105. • Migration and other forms of failure • Shames, Sanchez, Rubin and Sicard, (2002) Vascular and Endovascular Surgery, 36, 77-83 • Bell (2002), Editorial, Vascular Medicine 7, 253–255

  11. Our Objectives • Evaluate the mechanical response of the stent in appropriate configurations – Experimental • Develop the appropriate structural mechanics description - Analytical • Evaluate the coupled response of the stent and the blood vessel - Analytical

  12. Experimental apparatus External Pressure Internal Pressure

  13. Pressure-diameter relationship Normal range of the aorta

  14. Pressure-length relationship

  15. Helical spring model – Kirchhoff-Love theory r0, a0 – initial radius and pitch angle r, a – radius and pitch angle Pa – axial force; Ps – transverse shear force MB – bending moment; Mt – twisting moment q – effect of pressure loading on the wire Fz – external axial force

  16. Equilibrium equations (1) (2) (3)

  17. Pressure loading The internal pressure loading is distributed uniformly over the n wires, resulting in the load distribution q:

  18. Curvature and twist evolution Curvature: Twist: Bernoulli-Euler Beam Theory: (4) Coulomb Torsion Theory: (5)

  19. Geometrical constraint The braiding of the n wires results in contact at the cross-over points; these are constrained frictionally and therefore the wire is not allowed to unwind helically as the stent expands. This can be expressed as a constraint between the radius and the pitch angle of the helix: (6)

  20. Pressure-diameter relationship This is an exact relationship within the restrictions of the Kirchhoff-Love slender rod theory, without any adjustable parameters.

  21. Parameters of the stent n Number of wires 36 E Modulus of elasticity 200 GPa G Shear modulus 77 GPa a Radius of the stent wire 0.170 mm a0Pitch angle of the helix at zero pressure 34 r0Radius of the stent at zero pressure 0.01 m L Length of the stent 0.08 m

  22. Effect of friction Friction acts on the cylindrical surface of the stent in the axial direction, and is given by:

  23. Pressure-diameter relationship

  24. Pressure-length relationship

  25. Axial force measurements

  26. Axial force measurement

  27. v(x) r(x) x 2r0 (a) Spatially varying pressure – A beam-on-elastic-foundation model ~f(r)

  28. Governing differential equation Fixed boundary: Free boundary: Compliant boundary:

  29. Example 1 –Fixed ends

  30. Comparison to experiments

  31. Example 2 – stent exiting a catheter

  32. Coupled response of the aorta and stent

  33. Response of the aorta Curve fit to data from: Länne T et al 1992,Noninvasive measurement of diameter changes in the distal abdominal aorta in man, Ultrasound in Med & Biol,18:451-457.

  34. Coupled response - results

  35. Summary • Experimental methods developed to evaluate the mechanical response of stents • Analytical models were developed to characterize the response of the stent by itself and coupled with the aorta • The procedures established should enable design of AAA stents • Prof Canic is working on embedding these models with fluid flow simulations

  36. Dilation of the aorta Source: Wever et al., (2000), European Journal of Vascular and Endovascular Surgery, 19: 197–201.

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