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Mechanical Response of a Metallic Stent

Mechanical Response of a Metallic Stent. K. Ravi-Chandar and Renjun 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. Outline.

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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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