Mechanical Response of a Metallic Stent

1
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. Lukes
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Outline

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

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Arteries
J Humphrey, Cardiovascular Solid Mechanics,
Springer, 2002
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Abdominal Aortic Aneurysm
C.E. Ruiz, et al, Circulation, 1997962438-2448
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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

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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

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AnueRx Bifurcated Stent
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WallStent
Villareal, Howell, and Krajcer Tex Heart Inst J
200027146-9
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Abdominal Aortic Aneurysm
Stent-graft Stent
C.E. Ruiz, et al, Circulation, 1995912470-2477
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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 197201.
• Endoleaks
• Chuter et al. (2001), Journal of Vascular
  Surgery, 34, 98105.
• 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,
  253255

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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

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Experimental apparatus
External Pressure
Internal Pressure
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Pressure-diameter relationship
Normal range of the aorta
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Pressure-length relationship
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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
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Equilibrium equations
(1)
(2)
(3)
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Pressure loading
The internal pressure loading is distributed
uniformly over the n wires, resulting in the load
distribution q
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Curvature and twist evolution
Curvature
Twist
Bernoulli-Euler Beam Theory
(4)
Coulomb Torsion Theory
(5)
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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)
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Pressure-diameter relationship
This is an exact relationship within the
restrictions of the Kirchhoff-Love slender rod
theory, without any adjustable parameters.
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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 a0 Pitch angle of the helix at zero
pressure 34? r0 Radius of the stent at zero
pressure 0.01 m L Length of the stent 0.08 m
 
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Effect of friction
Friction acts on the cylindrical surface of the
stent in the axial direction, and is given by
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Pressure-diameter relationship
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Pressure-length relationship
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Axial force measurements
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Axial force measurement
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Spatially varying pressure A
beam-on-elastic-foundation model
f(r)
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Governing differential equation
Fixed boundary
Free boundary
Compliant boundary
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Example 1 Fixed ends
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Comparison to experiments
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Example 2 stent exiting a catheter
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Coupled response of the aorta and stent
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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,18451-457.
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Coupled response - results
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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

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Dilation of the aorta
Source Wever et al., (2000), European Journal of
Vascular and Endovascular Surgery, 19 197201.