Three-Dimensional Finite Element Analysis of Residual Stress in Arteries

Abstract

Calculation of residual stress in arteries, using the analytical approach has been quite valuable in our understanding of its critical role in vascular mechanics. Stresses are calculated at the central section of an infinitely long tube by imposing a constant axial stretch while deforming the artery from the stress-free state to its unloaded state. However, segments used to perform opening-angle measurements have finite lengths. Further, the stress-free artery configuration is assumed to be circular. Experiments show that they are slightly noncircular. The numerical approach to residual stress calculation can allow us to study both these issues. Using 3D cylindrical geometries and an isotropic material model, we investigated how segment length can affect residual stress calculations and identified the appropriate segment length for experiments. Further, we recorded and used the true noncircular stress-free state of an artery segment, computed the residual stress distribution, and compared it to that from a similar, but circular segment. Our findings suggest that segment length must be ten times the wall thickness for it to be "long" enough. We also found that the circularity assumption may be a reasonable approximation for typical arteries.

Modelling the layer-specific three-dimensional residual stresses in arteries, with an application to the human aorta

“…Rachev 1997;Rachev & Hayashi 1999;Holzapfel et al 2000;Humphrey 2002, ch. 7;Raghavan et al 2004;Ohayon et al 2007). Similar comments apply to the work of Olsson et al (2006), who *Author for correspondence (rwo@maths.gla.ac.uk).…”

Biomechanical properties of the Marfan's aortic root and ascending aorta before and after personalised external aortic root support surgery

“…In reality, a zero-stress state does not exist in vivo, however, it was found that the magnitude of residual stresses were negligible (up to 3 kPa [34]) in comparison with the aortic root stresses observed at the peak pressure. However, it must be acknowledged that residual stresses and strains act in homogenising the stress field in the arterial wall and allows greater compliance [35].…”

Evolution and rupture of vulnerable plaques: a review of mechanical effects

“…In Fung, 90 the stretch ratio in rabbit arteries varies from 1.6 in the carotid to 1.4 for the upper abdominal aorta, whereas Fung and Liu 91 showed that the opening angle in normal rats varies from 160° in the ascending aorta and 90° in the arch to 60° in the thoracic region. Details of the use of these parameters for the modeling of the vessel properties are not discussed here, but the reader can refer to Lee et al, 92 Holzapfel et al, 93 or Raghavan et al 94 for additional information on this issue. Concerning the variation of the elastic properties as a function of the load applied (pressure, tension, and flow, for instance), one can refer to Martinez et al 95 and Lee et al 92 In these papers, the authors measure the evolution of the longitudinal and circumferential stretch ratio as a function of internal pressure during an inflation test.…”