Page 21 - Read Online

Schiavone et al. Modelling of metallic and polymeric stents

node incompatible brick elements, with full integration weaker than Co-Cr L605. Table 1 gives the essential
(C3D8I). The incompatible mode is chosen for the properties for both materials as obtained from the
purpose of modelling large bending deformation during tensile curves. Strain hardening was realised in
stent crimping and subsequent expansion. There are ABAQUS by stating the yield stress as a function of the
4-layer elements through the width and the thickness plastic strain, as also obtained from the tensile curves.
of all struts. The geometrical designs and FE meshes The plaque was assumed to be hypocellular, and its
for both stents are given in Figure 1. behaviour was described by the Ogden hyperelastic
model. The hyperelastic model parameters were
The balloon used to inflate the stents had a tri-folded provided in Zahedmanesh and Lally. The tri-folded
[22]
geometry which was produced using the NX software. balloon was treated as a linear elastic material. The
The diameter of the fully folded part is 1.25 mm and material density, Young’s modulus and Poisson’s ratio
the total length of the balloon is 14 mm. To create the were taken as 1.1 × 10 kg/mm , 900 MPa and 0.3,
6
3
pattern, the tri-folded cross section was sketched first, respectively. [23]
and subsequently extruded for a length of 12 mm.
Towards the ends, the balloon smoothly transits into It is well recognised that the arterial layers possess
a circle, 0.75 mm in diameter, over a length of 1 mm. distinct anisotropic behaviour as they are reinforced by
This was done by using the sweeping tools in NX. The two families of collagen fibres. Here, the established
balloon was totally constrained at both ends as they Holzapfel-Gasser-Ogden (HGO) anisotropic hyperelastic
are fixed to a catheter. The diameter of the expanded model was employed to describe the anisotropic
[24]
balloon was set to be 3 mm, matching the targeted behaviour of individual coronary arterial layer. In this
stent or vessel diameter after deployment. Four-node model, the hyperelastic strain energy potential W is
shell elements, with reduced integration (S4R), were given by: [24]
adopted to mesh the tri-folded balloon.
W = C (I - 3) + (k /2k )[exp(k <E> ) - 1] + (1/D)[(J -1)/2 - lnJ]
2
2
2
10 1
1
f
2
The diseased artery has a total length of 40 mm and a
lumen diameter of 3 mm for the heathy part. The middle E = k(I - 3) + (1 - 3k)(I - 1)
4
1
f
portion of the artery is covered by 10 mm plaque. The
stenosis, defined as the ratio of plaque thickness to where C , D, k , k and k are model parameters, I
1
2
1
10
healthy lumen radius, was chosen to be 50%. The and J are the first and third stretch invariants, and I is
4
artery comprises three individual tissue layers, and the the invariant of Cauchy-Green deformation tensor. The
wall thickness is 0.27 mm, 0.35 mm and 0.38 mm for Macauley bracket is indicated by the operator <>, whilst
the intima, media and adventitia layers, respectively. γ represents the angle between the mean directions of
Eight-node brick elements with reduced integration the two families of fibres whose deformation is defined
(C3D8R) were used to mesh the artery and the plaque. by E . The model parameters [Table 2] were calibrated
f
Four layers of elements were assigned through the against the experimental data. Both longitudinal and
[25]
wall of each tissue layer and eight layers of elements circumferential stress-stretch responses, computed by
were assigned through the plaque thickness. using the HGO model, agreed with the experimental
data very well for all three vessel layers [Figure 4].
[25]
Geometry and mesh of the balloon-artery assembly are
shown in Figure 2. Mesh-sensitivity studies confirmed The HGO model used in this work is for incompressible
the convergence of numerical results, with regards to hyperelastic materials. To consider compressible
stent expansion, stent recoiling and stresses in the deformation, the HGO-C model was suggested, with
stent-artery system, for the mesh adopted in this work. the anisotropic part expressed by isochoric invariants
Material model Table 1: Properties for the Co-Cr L605 and Poly-L lactide
stent materials
[20,21]
Both stents were modelled as elastic-plastic, with non-
3
linear strain hardening [Figure 3]. The tensile stress- Material ρ (kg/mm ) E (GPa) ν σy (MPa)
strain curves for Co-Cr L605 and PLLA were taken Co-Cr L605 9.1E-6 243 0.30 476
from literature. [20,21] It can be noted that PLLA is much Poly-L lactide 1.4E-6 2.2 0.30 60
Table 2: Parameter values of the anisotropic Holzapfel-Gasser-Ogden model for the arterial layers
Layer ρ (kg/mm ) C D k k k γ
3
10 1 2
Intima 1.066E-6 0.03 8.95E-7 4.0 1200.0 0.303 60°
Media 1.066E-6 0.005 5.31E-6 0.57 80.0 0.313 20°
Adventitia 1.066E-6 8.32E-3 4.67E-6 1.0 1000.0 0.303 67°
14 Vessel Plus ¦ Volume 1 ¦ March 31, 2017