Layer-Specific Residual Deformations and Their Variation Along the Human Aorta

2021 ◽  
Author(s):  
Dimitrios P. Sokolis ◽  
Nausicaa Gouskou ◽  
Stavroula Papadodima ◽  
Stavros K. Kourkoulis
Keyword(s):  
Image Analysis ◽  
Stress State ◽  
Regional Distribution ◽  
Opening Angle ◽  
Human Aorta ◽  
Descending Thoracic Aorta ◽  
The Media ◽  
State Changes ◽  
Residual Deformations ◽  
Axial Opening

Abstract This study described the regional distribution of layer-specific residual deformations in fifteen human aortas collected during autopsy. Circumferentially- and axially-cut strips of standardized dimensions from the anterior quadrant of nine consecutive aortic levels were photographed to obtain the zero-stress state for the intact wall. The strips were then dissected into layers that were also photographed to obtain their zero-stress state. Changes in layer-specific opening angle, residual stretches, and thickness at each aortic level and direction were determined via image analysis. The circumferential and axial opening angles of the intima were ~240° and ~30°, respectively, throughout the aorta; those of the adventitia were ~150° and -20° to 70°. The opening angles of the intact wall and media were similar in either direction. The circumferential residual stretches of the intima and the axial residual stretches of the media showed high values in the aortic arch, decreasing in the descending thoracic aorta and increasing toward the iliac artery bifurcation, while the axial residual stretches of the adventitia increased distally. The remaining residual stretches did not vary significantly with aortic level, suggesting an intimal role in determining circumferential, as well as medial and adventitial roles in determining axial residual stretches. We conclude that the tensile residual stretches released in the intima and media upon separation, and the compressive residual stretches released in the adventitia may moderate the inverse transmural stress gradients under physiologic loads, resulting from the >180° circumferential opening angle of the intact wall.

Variation of Axial Residual Strains Along the Course and Circumference of Human Aorta Considering Age and Gender

2019 ◽  
Vol 142 (2) ◽  
Author(s):  
Dimitrios P. Sokolis ◽  
Andreas Bompas ◽  
Stavroula A. Papadodima ◽  
Stavros K. Kourkoulis
Keyword(s):  
Opening Angle ◽  
Human Aorta ◽  
Age And Gender ◽  
Outer Quadrant ◽  
Lack Of Information ◽  
Residual Strains ◽  
And Gender ◽  
Rectangular Strips ◽  
Axial Opening ◽  
Residual Stretch

Abstract Our understanding of aortic biomechanics is customarily limited by lack of information on the axial residual stretches of the vessel in both humans and experimental animals that would facilitate the identification of its actual zero-stress state. The aim of this study was thus to acquire hitherto unreported quantitative knowledge of axial opening angle and residual stretches in different segments and quadrants of the human aorta according to age and gender. Twenty-three aortas were harvested during autopsy from the aortic root to the iliac bifurcation and were divided into ≥12 segments and 4 quadrants. Morphometric measurements were taken in the excised/curled configuration of rectangular strips considered to be under zero-stress using image-analysis software to study the axial/circumferential variation of axial opening angle, internal/external residual stretch, and thickness of the aortic wall. The measured data demonstrated: (1) an axial opening angle peak at the arch branches, decreasing toward the ascending and to a near-constant value in the descending thoracic aorta, and increasing in the abdominal aorta; (2) the variation of residual stretches resembled that of opening angle, but axial differences in external residual stretch were more prominent; (3) wall thickness showed a progressive diminution along the vessel; (4) the highest opening angle/residual stretches were found in the inner quadrant and the lowest in the outer quadrant; (5) the anterior was the thinnest quadrant throughout the aorta; (6) age caused thickening but greatly reduced axial opening angle/residual stretches, without differences between males and females.

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

2009 ◽  
Vol 7 (46) ◽  
pp. 787-799 ◽  
Author(s):  
Gerhard A. Holzapfel ◽  
Ray W. Ogden
Keyword(s):  
Residual Stress ◽  
Circumferential Stress ◽  
Three Dimensional ◽  
Residual Deformation ◽  
Cylindrical Tube ◽  
Opening Angle ◽  
Human Aorta ◽  
Geometrical Parameters ◽  
Artery Wall ◽  
The Media

This paper provides the first analysis of the three-dimensional state of residual stress and stretch in an artery wall consisting of three layers (intima, media and adventitia), modelled as a circular cylindrical tube. The analysis is based on experimental results on human aortas with non-atherosclerotic intimal thickening documented in a recent paper by Holzapfel et al. ( Holzapfel et al. 2007 Ann. Biomed. Eng. 35 , 530–545 ( doi:10.1007/s10439-006-9252-z )). The intima is included in the analysis because it has significant thickness and load-bearing capacity, unlike in a young, healthy human aorta. The mathematical model takes account of bending and stretching in both the circumferential and axial directions in each layer of the wall. Previous analysis of residual stress was essentially based on a simple application of the opening-angle method, which cannot accommodate the three-dimensional residual stretch and stress states observed in experiments. The geometry and nonlinear kinematics of the intima, media and adventitia are derived and the associated stress components determined explicitly using the nonlinear theory of elasticity. The theoretical results are then combined with the mean numerical values of the geometrical parameters and material constants from the experiments to illustrate the three-dimensional distributions of the stretches and stresses throughout the wall. The results highlight the compressive nature of the circumferential stress in the intima, which may be associated with buckling of the intima and its delamination from the media, and show that the qualitative features of the stretch and stress distributions in the media and adventitia are unaffected by the presence or absence of the intima. The circumferential residual stress in the intima increases significantly as the associated residual deformation in the intima increases while the corresponding stress in the media (which is compressive at its inner boundary and tensile at its outer boundary) is only slightly affected. The theoretical framework developed herein enables the state of residual stress to be calculated directly, serves to improve insight into the mechanical response of an unloaded artery wall and can be extended to accommodate more general geometries, kinematics and states of residual stress as well as more general constitutive models.

scholarly journals Time influence of tunnel support on the factor of safety

2020 ◽  
Vol 157 ◽  
pp. 06002
Author(s):  
Ivana Nedevska ◽  
Zlatko Zafirovski ◽  
Slobodan Ognjenovic ◽  
Ivona Nedevska ◽  
Vasko Gacevski
Keyword(s):  
Rock Mass ◽  
Stress State ◽  
Factor Of Safety ◽  
Tunnel Excavation ◽  
Tunnel Support ◽  
Plastic Deformations ◽  
Primary Stress ◽  
Reaction Curve ◽  
State Changes ◽  
The Moment

Before taking any measures to build a tunnel, the rock (soil) is in a primary stress state, which means that the stress state is a function of the thickness of the overburden. At the moment when the measures necessary to excavate a tunnel are taken, the rock state changes from primary to secondary, leading to stress concentration, especially in the tunnel abutments. If the rock is capable of accepting these stresses, a state of equilibrium is reached after certain deformations. Plastic deformations can occur if the stresses are larger than the strength of the rock mass. To avoid excessive deformations or collapse of the rock and the tunnel excavation, it is necessary to place a support. The achieved factor of safety is a function of both the support type and the time when the support is installed. This paper shall present a numerical example of different pressures considered in order to obtain the rock’s reaction curve.

scholarly journals Anisotropic residual stresses in arteries

2019 ◽  
Vol 16 (151) ◽  
pp. 20190029 ◽  
Author(s):  
Taisiya Sigaeva ◽  
Gerhard Sommer ◽  
Gerhard A. Holzapfel ◽  
Elena S. Di Martino
Keyword(s):  
Experimental Data ◽  
Residual Stresses ◽  
Abdominal Aorta ◽  
Strain Energy Function ◽  
Opening Angle ◽  
Link Type ◽  
Residual Deformations ◽  
Angle Method ◽  
The Individual

The paper provides a deepened insight into the role of anisotropy in the analysis of residual stresses in arteries. Residual deformations are modelled following Holzapfel and Ogden (Holzapfel and Ogden 2010, J. R. Soc. Interface 7 , 787–799. ( doi:10.1098/rsif.2009.0357 )), which is based on extensive experimental data on human abdominal aortas (Holzapfel et al. 2007, Ann. Biomed. Eng. 35 , 530–545. ( doi:10.1007/s10439-006-9252-z )) and accounts for both circumferential and axial residual deformations of the individual layers of arteries—intima, media and adventitia. Each layer exhibits distinctive nonlinear and anisotropic mechanical behaviour originating from its unique microstructure; therefore, we use the most general form of strain-energy function (Holzapfel et al. 2015, J. R. Soc. Interface 12 , 20150188. ( doi:10.1098/rsif.2015.0188 )) to derive residual stresses for each layer individually. Finally, the systematic experimental data (Niestrawska et al. 2016, J. R. Soc. Interface 13 , 20160620. ( doi:10.1098/rsif.2016.0620 )) on both mechanical and structural properties of the different layers of the human abdominal aorta facilitate our discussion on (i) the importance of anisotropy in modelling residual stresses; (ii) the variability of residual stresses within the same class of tissue, the abdominal aorta; (iii) the limitations of conventional opening angle method to account for complex residual deformations; and (iv) the effect of residual stresses on the loaded configuration of the aorta mimicking in vivo conditions.

Regional distribution of circumferential residual strains in the human aorta according to age and gender

2017 ◽  
Vol 67 ◽  
pp. 87-100 ◽  
Author(s):  
Dimitrios P. Sokolis ◽  
Giannis D. Savva ◽  
Stavroula A. Papadodima ◽  
Stavros K. Kourkoulis
Keyword(s):  
Regional Distribution ◽  
Human Aorta ◽  
Age And Gender ◽  
Residual Strains ◽  
And Gender

scholarly journals Stress state of metal dome meridional ribs at different stages of overhang erection process

2020 ◽  
Vol 16 (2) ◽  
pp. 111-121
Author(s):  
Evgeny V. Lebed ◽  
Vladimir P. Vershinin
Keyword(s):  
Mathematical Model ◽  
Stress State ◽  
Structural Reliability ◽  
Dead Weight ◽  
Bottom Up ◽  
Steel Strength ◽  
State Changes ◽  
The Relationship ◽  
Skeleton Stress

Research aim. The aim of the present research was an analysis of a metal ribbed ring-shaped dome metallic ribs stress state at different stages of a skeleton overhang erection process. The considered dome is hemispherical and is assembled bottom-up of individual elements. Due to a varying slope of meridional ribs elements at different relative elevations their stress state changes during mounting. The effect of the overhang erection process onto the stress state of the metal dome meridional ribs has been investigated. The relationship between the stress state of a meridional rib and mounting of each next dome skeleton tier has been established. Methods. A mathematical model of the metal ribbed ring-shaped dome assembled of steel H-shaped elements with rigid connections has been developed. Several extra models corresponding to different skeleton erection stages have been also generated to determine stresses in the meridional ribs at these stages. Response of each dome mathematical model under dead-weight load has been simulated. The obtained values of stresses in the meridional ribs within different models have been compared with corresponding design stresses values. Results. The dependence of the metal dome meridional rib stress state onto the stages of overhang erection process has been plotted. A degree of utilization of ribs steel strength at different erection stages has been represented by diagrams. An estimation of the dome skeleton stress state during overhang erection has been given. Imminence of assembly stresses during overhang erection and their influence onto dome structural reliability has been pointed out.

Strain distribution in small blood vessels with zero-stress state taken into consideration

1992 ◽  
Vol 262 (2) ◽  
pp. H544-H552 ◽  
Author(s):  
Y. C. Fung ◽  
S. Q. Liu
Keyword(s):  
Stress State ◽  
Blood Vessels ◽  
Pulmonary Arteries ◽  
Vena Cava ◽  
Large Error ◽  
Opening Angle ◽  
Stress And Strain ◽  
Passive Deformation ◽  
Angle Alpha ◽  
Residual Strains

The active and passive deformation of a blood vessel is related to the stress in it. Any analysis of stress and strain must begin with the zero-stress state. Recent reports on large blood vessels such as the aorta, pulmonary arteries, and vena cava have shown that, at zero-stress state, blood vessels are not tubes, but opens sectors. This report presents data on the zero-stress state of small blood vessels with lumen diameters down to approximately 50 microns. Zero-stress state of a vessel was obtained by cutting the vessel into rings and then the rings into sectors; each sector is characterized by an opening angle, alpha. In rat ileal and plantar arterioles, the opening angles are in the order of 100-250 degrees; those in the venules are in the order of 50-100 degrees. The effect of norepinephrine on the opening angle alpha is minor; it decreases alpha of the superior mesenteric artery, and increases alpha of the ileocecocolic and ileal arteries. EDTA has little effect on alpha of arteries greater than 100 microns in diameter, but decreases alpha of arteries less than 100 microns. The physiological meaning of the opening angle is demonstrated in terms of the residual strains in a vessel at the no-load state and homeostatic strains at normal blood pressure. The strains in real vessels are compared with those in hypothetical vessels having an opening angle of zero. It is shown that ignoring the opening angle will cause a large error in strain evaluation.(ABSTRACT TRUNCATED AT 250 WORDS)

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