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

Arteries J Humphrey, Cardiovascular Solid Mechanics, Springer, 2002

Abdominal Aortic Aneurysm C.E. Ruiz, et al, Circulation, 1997;96:

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

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

AnueRx Bifurcated Stent

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

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

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, Bell (2002), Editorial, Vascular Medicine 7, 253–255

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

Experimental apparatus Internal Pressure External Pressure

Pressure-diameter relationship Normal range of the aorta

Pressure-length relationship

Helical spring model – Kirchhoff-Love theory r 0,  0 – initial radius and pitch angle r,  – radius and pitch angle P a – axial force; P s – transverse shear force M B – bending moment; M t – twisting moment q – effect of pressure loading on the wire F z – external axial force

Equilibrium equations (1) (2) (3)

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

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

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)

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

Parameters of the stent nNumber of wires36 EModulus of elasticity200 GPa GShear modulus77 GPa aRadius of the stent wire0.170  m   Pitch angle of the helix at zero pressure34  r  Radius of the stent at zero pressure 0.01 m LLength of the stent0.08 m

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

Pressure-diameter relationship

Pressure-length relationship

Axial force measurements

Axial force measurement

Spatially varying pressure – A beam-on-elastic-foundation model x 2r02r0 v (x) r(x) (a) ~ f(r)

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

Example 1 –Fixed ends

Comparison to experiments

Example 2 – stent exiting a catheter

Coupled response of the aorta and stent

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:

Coupled response - results

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

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