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Pejcic et al. Vessel Plus 2019;3:32 I http://dx.doi.org/10.20517/2574-1209.2019.18 Page 5 of 12

by some means to replicate axial loading, and fluid is run through the conduit to enact circumferential
loading [Figure 1D]. Optical methods may be used to track displacement and force of pre-set markers on
[27]
the blood vessel [25,26] . Courtial et al. present, in detail, an inflation device that was coupled with non-
invasive imaging techniques such as ultrasound, in order to identify the parameters of a silicone tube
based hyperviscoelastic model that represented the native aorta. They found that the inflation-extension
test was adequate in validating this model. The inflation-extension property of the aorta was further
[28]
tested by Horny et al. in an analytical simulation, using parameters from autopsy measurements. They
established that while axial pre-stretch, which allows the aorta to minimize deformation during systole and
diastole, decreases with age, the prespecified value of axial pre-stretch can still have a significant effect on
the mechanical properties of the vessel wall. Inflation-extensions tests are valuable for understanding the
operating mode of arteries. However, inverse analysis and simplification is typically required to find the
[13]
stress-strain relationship from the pressure-diameter measurements .

Opening angle test
Residual stresses are present in the circumferential direction of the arterial wall, and this can be visually
shown by cutting open a ring segment of an artery along the axial direction [25,26] . Subsequently the opening
angle formed by the specimen may be optically measured until the cut section stabilizes [Figure 1E].
Accounting for these residual stresses, which have been shown to be present in the axial direction as
[30]
[29]
well , leads to a significantly lower circumferential stress gradient along the thickness of the vessel . This
observation is better explained when considering the circumferential residual strains, wherein accounting
for these strains works to decrease the stretch ratio at the inner surface, while increasing that of the outer
surface [31,32] . In essence, to account for residual stresses, “state 0” (stress-free state) is taken as the reference
[30]
configuration, rather than “state 1” (unloaded state - outlined in Ref. ). Moreover, the presence of residual
stresses in arteries results in a more uniform stress distribution throughout the vessel wall [33,34] . Zheng and
[35]
Ren further explored the effects of three-dimensional residual stresses in each of the three arterial layers.
They showed that the residual circumferential stress is compressive within the intima, while tensile in the
remaining two layers, and that the bending of the media in the longitudinal direction noticeably affects the
mechanical behavior of the arterial wall. Cardamone et al. attribute the origin of this residual stress to
[36]
non-uniform growth and remodelling as well as temporo-spatial variances in wall components.

[37]
Sokolis et al. examined the regional distribution of circumferential residual strains in the human aorta
according to age and gender to gain a more detailed understanding of the zero-stress and no-load states
of the human aorta. The opening angle measurement, which characterizes the circumferential residual
strain, was highest in the aortic arch and declined in the descending aorta. Opening angle measurements
for aneurysmal tissue are difficult to obtain due to the irregular shape of the diseased vessel wall. Sokolis [38]
discussed the residual stresses within the ATAA in great depth, presenting several important conclusions
regarding the vessel wall behaviour: (1) change in the wall composition, mainly the decreased presence
of elastin within the aneurysmal vessel wall, results in greater viscoelastic behaviour; (2) residual strains
vary along the circumferential direction within each of the three layers of the wall; and (3) analysing the
residual stresses of the layers individually reveals that the intima is held in compression, while the media
is in tension. Contrary to previous studies performed on the abdominal aorta, the adventitia was shown
to be under compression in the circumferential direction, though still under tension longitudinally.
Higher opening angles were measured in the aneurysmal tissue and it was postulated that this might be
[39]
a compensatory mechanism to increase the vessel’s resistance to dissection . This is perhaps similar to
a compensatory increase in opening angle measurements with increased stiffness of the aorta with age.
[40]
Most recently, Sokolis et al. employed opening angle testing to study the axial residual strain variations
in the human aorta according to age and gender. Interestingly, they found that the axial opening angle and
residual stress decreased with age as compared to the circumferential residual strain which had increased
with age.