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Proceedings of the ASME 2013 Summer Bioengineering Conference
June 26-29, 2013, Sunriver, Oregon, USA
Hai-Chao Han, Avione Y. Lee, Ramsey H. Shadfan, Yangming Xiao
Department of Mechanical Engineering,
University of Texas at San Antonio
Biomedical Engineering Program,
University of Texas at San Antonio- University of
Texas Health Science Center at San Antonio
arteries were then cut into sections and fixed in 10% formaldehyde for
Rupture of aneurysms is a leading cause of death in the United
States. Extensive biomechanical studies have shown that mechanical
stress in aneurysm walls plays a critical role in the rupture of
aneurysms. Highly elevated local stress and degraded aneurismal walls
are believed to make aneurysms vulnerable to rupture [1-3].
Asymmetric aneurysms with irregular shape and wall thickness are
vulnerable to rupture. Aneurismal arteries are often tortuous such as in
the Loeys-Dietz syndrome [4], but the mechanism is unclear.
Our recent studies have demonstrated that arteries could become
mechanically unstable under hypertensive pressure or reduced axial
tension[5, 6]; Elastin degradation, which is associated with aneurysm
formation in arteries, significantly reduces arterial critical buckling
pressure[7]. The rupture of aneurysms has been related to the high
wall stress due to large size, thinner walls, and asymmetric wall
curvature of aneurysms.
The objectives of this study were to determine whether
aneurismal arteries are vulnerable to mechanical buckling and how
buckling affects wall stress distribution in aneurysms.
Finite element simulations
Aneurismal arteries models were created using Solidworks. The
arteries were created of a outside diameter of 6mm, wall thickness of
1mm, and a length of 100 mm based on our previous measured
dimensions of porcine carotid arteries [7]. Idealized spherical
aneurysms were drawn with various aneurysm diameter (DA),
aneurysm length (LA), and aneurysm wall thickness tA to investigate
the effect of aneurysm dimensions. We varied the size of the
aneurysms by 2 to 4 times the outer diameter of the control artery.
Aneurysms wall thickness was assumed to be half of the arterial wall
thickness. The normal arterial wall and aneurysm were modeled as
homogenous, incompressible, anisotropic, nonlinear materials with a
Fung strain energy function. Convex material constants were
determined from normal and elastase treated porcine carotid arteries
from our previous studies[7].
The finite element analyses were implemented using Abaqus. A
static internal pressure was applied to the lumen of the arterial models
and the external pressure was set at zero. Both ends of the arteries
were assumed as fix-supported with no lateral displacement or rotation
but were allowed to expand radially. These end conditions simulated
the expansion of arteries under pressure in vivo and minimized the
possible edge effects at the ends. Since arteries are under significant
longitudinal strain in vivo. Axial stretch ratios of 1.1, 1.3, and 1.5 were
applied to the artery models by applying designated axial
displacements to all nodes comprising the distal end of the arteries to
achieve the given stretch ratios[7]. A Static General Analysis under
stretch was performed.
Experimental tests:
Porcine common carotid arteries harvested from farm pigs
(bodyweight ~100 kg) postmortem at local slaughterhouses were
carefully inverted and treated at the midsection with a cotton pad
containing 500 μL of elastase at a concentration of 280 U/mL
(Worthington, NJ) for two hours to create an aneurysm at the
midsection. The critical buckling pressures were determined before
and after elastase treatment using pressurized buckling tests. All tests
were performed at a physiological axial stretch ratio of 1.5. The
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Both experiments and FEA simulations demonstrated that
aneurismal arteries buckled at a lower critical pressure than the
cylindrical controls without an aneurysm (Fig. 1). Aneurysm
formation significantly decreased the critical buckling pressure of
porcine carotid arteries. (p < 0.05). FEA simulations showed that the
dimensions and shape of the aneurysms affected the critical buckling
pressure. At a fixed diameter, increasing aneurysm length increased
the critical buckling pressure. At a fixed length, increasing the
diameter increased the critical buckling pressure. Asymmetric
aneurysms had a lower critical buckling pressure than symmetric
aneurysms. Elastin degradation in the aneurismal wall further
decreased the critical pressure.
By changing neck length of arteries, we were able to facilitate or
avoid buckling of a pair of identical aneurysms with different neck
lengths under the same lumen pressure. When comparing the stress
profiles of buckled versus unbuckled aneurysms at a given pressure, it
was found that the area with increased stress is larger and the stress
concentration is higher in the buckled aneurysm (Fig. 2).
Critical Pressure (kPa)
Our experimental data indicated that the weakening of the wall by
elastase overset the effect of local diameter increase, resulting in a
decrease in critical buckling pressure. Our lab’s previous research
indicated that artery buckling leads to tortuous blood vessels with
changes in blood flow and wall stress, which can cause numerous
complications such as thrombosis or embolism. The current results
demonstrated that aneurismal arteries are more prone to buckling than
normal arteries, indicating that mechanical buckling could be an
explanation for the tortuous aneurismal arteries observed clinically,
such as the Loeys-Dietz syndrome. Fillinger et al showed that peak
wall stress in aneurysms with tortuosity were twice as high as the
stress in an aneurysm of the same diameter with no tortuosity and were
more likely to rupture [8]. The stress concentration caused by
aneurismal artery buckling could be a possible mechanism for the
Braverman, A. C., Byers, P. H., De Paepe, A. M., and Dietz, H. C.,
2006, "Aneurysm syndromes caused by mutations in the TGF-beta
receptor," N Engl J Med, 355(8), pp. 788-798.
Han, H. C., 2009, "Blood vessel buckling within soft surrounding
tissue generates tortuosity," J Biomech, 42(16), pp. 2797-2801.
Han, H. C., 2012, "Twisted Blood Vessels: Symptoms, Etiology,
and Biomechanical Mechanisms," J Vasc Res, 49(3), pp. 185-197.
Lee, A. Y., Han, B., Lamm, S. D., Fierro, C. A., and Han, H. C.,
2012, "Effects of elastin degradation and surrounding matrix
support on artery stability," Am J Physiol Heart Circ Physiol,
302(4), pp. H873-884.
Fillinger, M. F., Marra, S. P., Raghavan, M. L., and Kennedy, F.
E., 2003, "Prediction of rupture risk in abdominal aortic aneurysm
during observation: Wall stress versus diameter," J Vasc Surg,
37(4), pp. 724-732.
Figure 1. Comparison of the critical buckling pressure of arteries
(mean ± SD, n=4) before (control) and after local elastase treatment
(aneurysm). * p < 0.05.
Aneurismal arteries demonstrated a lower critical buckling
pressure than the normal arteries indicating that aneurismal arteries are
more prone to mechanical buckling than normal arteries. Mechanical
buckling could increase the stress concentration in aneurismal walls.
These results shed light on the mechanism of tortuous aneurismal
arteries and its vulnerability to rupture.
This work was supported by NIH grant HL095852 and NSF
CAREER award 0644646.
[1] Vorp, D. A., 2007, "Biomechanics of abdominal aortic aneurysm,"
Journal of Biomechanics, 40(9), pp. 1887-1902.
[2] Geest, J. P. V., Schmidt, D. E., Sacks, M. S., and Vorp, D. A.,
2008, "The effects of anisotropy on the stress analyses of patientspecific abdominal aortic aneurysms," Annals of Biomedical
Engineering, 36(6), pp. 921-932.
[3] Humphrey, J. D., and Taylor, C. A., 2008, "Intracranial and
abdominal aortic aneurysms: Similarities, differences, and need for
a new class of computational models," Annual Review of
Biomedical Engineering, 10, pp. 221-246.
[4] Loeys, B. L., Schwarze, U., Holm, T., Callewaert, B. L., Thomas,
G. H., Pannu, H., De Backer, J. F., Oswald, G. L., Symoens, S.,
Manouvrier, S., Roberts, A. E., Faravelli, F., Greco, M. A.,
Pyeritz, R. E., Milewicz, D. M., Coucke, P. J., Cameron, D. E.,
Figure 2.Von Mises stress profile (kPa) in un-buckled and buckled
aneurysms under internal pressure. The cylindrical portion was shorted
in the controls to avoid buckling. Both aneurysms are of the same
dimensions (D = 18mm, L= 18mm t= 1mm) and under the same lumen
pressure (225 mmHg).
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