ARUP; ISBN: 978-0-9562121-5-3 - CMBBE 2012 - Cardiff University

Half symmetry along the axial direction has been assumed. The extremes of the vessel
are constrained in the axial (z) direction, both with and without application of a 40%
longitudinal pre-tension, whilst the vessel is free to expand in the x and y directions.
The stent is simplified in order to focus on changes in stress arising from the boundary
conditions and material properties. The stent strut is represented by a cylinder with
rounded end, which expands to a final radius which is 40% larger than the internal
radius of the vessel. This large overexpansion of the stent has been used in porcine
models of restenosis to induce arterial injury [6] in the absence of initial vessel disease.
The arterial wall behaviour is described by a SEDF third-order hyperelastic model,
which is suitable for an incompressible isotropic material (Equation 1) and describes the
typical behaviour of arteries during tensile tests [7].
U = 0.04 · (I1 - 3) + 0.003 · (I2 - 3) 2 + 0.085 · (I2 - 3) 3 (1)
3.1 Influence of initial conditions: pre-stretch and systolic pressure
In order to obtain an accurate representation of the stress distribution and magnitude
within the vessel wall due to stent expansion it should be noted that the arteries are not
at a stress-free state in vivo. Zhang et al. [8] proposes that an axial pre-stretch of the
coronary artery is present in order to homogenize the distribution of stress and strain in
the wall. These studies focus on arterial behavior under normal physiological
conditions, whilst stent deployment will impose an additional loading to the vessel wall.
This study compares two models; stent expansion in a vessel which is initially stressfree
and expansion in a vessel where a pressure representative of systolic conditions (16
kPa = 120 mmHg) and a longitudinal prestretch of 40% are imposed.
3.2 Influence of viscoelasticity: stress relaxation
When considering arterial tissue growth, the time-dependent evolution of vessel stress
becomes important. There are a number of time scales which are relevant to the
development of arterial restenosis. Both stent expansion and variation of blood pressure
during the cardiac cycle occur over a period of seconds. Arterial tissue relaxation has
been reported over a period of hours [9], whilst restenosis in patients typically develops
over months [1].
As the stress in the arterial wall may contribute to the development of in-stent
restenosis, changes in stress over time may change the stimulus for tissue growth. This
time variation of stress is considered in this study using the Prony series given by
Equation 2.
G(t) = G∞ + G1 exp (-t/τ1) (2)
Where G∞ is the long term elastic modulus and τi are the relaxation times for each Prony
component. Previous studies [9] of porcine coronary arteries have shown viscoelastic
behaviour during ex vivo tests corresponding to a time constant of the order of 500
seconds. The magnitude of stress relaxation over these timescales does not appear to be
well characterised, previous studies of short term stress relaxation in arteries indicate
changes in magnitude of the order 30% after sudden initial loading of the vessel [10].
In this model we have used a single time constant of 500 seconds and a value of
G1 = 0.43G∞ which reproduces similar behaviour.
Following the application of a longitudinal prestretch of 40% stresses are evaluated both