Effect of Residual Stress and Heterogeneity on Circumferential Stress in the Arterial Wall

2000 ◽  
Vol 122 (4) ◽  
pp. 454-456 ◽  
Author(s):  
S. J. Peterson ◽  
R. J. Okamoto
Keyword(s):  
Residual Stress ◽  
Stress Distribution ◽  
Material Properties ◽  
Arterial Wall ◽  
Circumferential Stress ◽  
Single Species ◽  
Opening Angle ◽  
Layer Model ◽  
Multiple Sources ◽  
The Media

Quantifying the stress distribution through the arterial wall is essential to studies of arterial growth and disease. Previous studies have shown that both residual stress, as measured by opening angle, and differing material properties for the media-intima and the adventitial layers affect the transmural circumferential stress σθ distribution. Because a lack of comprehensive data on a single species and artery has led to combinations from multiple sources, this study determined the sensitivity of σθ to published variations in both opening angle and layer thickness data. We fit material properties to previously published experimental data for pressure–diameter relations and opening angles of rabbit carotid artery, and predicted σθ through the arterial wall at physiologic conditions. Using a one-layer model, the ratio of σθ at the internal wall to the mean σθ decreased from 2.34 to 0.98 as the opening angle increased from 60 to 130 deg. In a two-layer model using a 95 deg opening angle, mean σθ in the adventitia increased (112 percent for 25 percent adventitia) and mean σθ in the media decreased (47 percent for 25 percent adventitia). These results suggest that both residual stress and wall layers have important effects on transmural stress distribution. Thus, experimental measurements of loading curves, opening angles, and wall composition from the same species and artery are needed to accurately predict the transmural stress distribution in the arterial wall. [S0148-0731(00)02204-4]

Residual Stress and Circumferential Stress Distribution in a Finite Element Model of the Arterial Wall

Volume 2 ◽  
2004 ◽  
Author(s):  
Nooshin Haghighipour ◽  
Mohammad Tafazzoli Shadpour ◽  
Albert Avolio
Keyword(s):  
Residual Stress ◽  
Finite Element ◽  
Stress Distribution ◽  
Tensile Stress ◽  
Arterial Wall ◽  
Stress Component ◽  
Circumferential Stress ◽  
Opening Angle ◽  
Human Aorta ◽  
Endothelial Lining

Stress distribution of the arterial wall is an important factor in biomechanics of arteries. It has been suggested that excessive stress leads to arterial degeneration and lesion formation. In addition to circumferential tensile stress caused by luminal pressure, arterial wall contains circumferential residual stress with compressive and tensile components with maximum values on intima and adventitia respectively. The compressive residual stress component compensates part of maximum tensile stress, and therefore decreases severity of tension on endothelial lining. If an arterial ring is cut in radial direction it opens. The degree of opening angle is a determinant of circumferential residual stress. In this investigation, Finite element modeling was used to evaluate circumferential residual stress in a typical model of cross section of human aorta with differing opening angle and Young’s modulus of elasticity. Results show that residual stress values are influenced by structural and mechanical parameters. Elevation of the opening angle and stiffening of the arterial wall resulted in increase of residual stress level.

Stress Distribution in a Bilayer Elastic Model of a Coronary Artery

2013 ◽  
Vol 80 (4) ◽  
Author(s):  
Keiichi Takamizawa ◽  
Yasuhide Nakayama
Keyword(s):  
Blood Pressure ◽  
Residual Stress ◽  
Stress Distribution ◽  
Residual Strain ◽  
Arterial Wall ◽  
Circumferential Stress ◽  
Outer Region ◽  
Constitutive Law ◽  
Elastic Model ◽  
The Media

In earlier studies on stress distribution in arteries, a monolayer wall model was often used. An arterial wall consists of three layers, the intima, the media, and the adventitia. The intima is mechanically negligible as a stress supporting layer against the blood pressure in young healthy vessels, although it is important as an interface between blood and arterial wall. The media and adventitia layers are considered to support blood pressure. Recently, residual strain and a constitutive law for porcine coronary arteries have been investigated in separated media and adventitia. Using the data obtained through these investigations, a stress analysis considering residual stress (strain) in each layer was performed in this study, and residual strain and stress were computed for a bilayer model. The circumferential residual stress was compressive in the inner region, tensile in the outer region, and had discontinuity at the boundary between the media and adventitia. A peak circumferential stress occurred in the media at the boundary between the media and adventitia under a physiological condition, and an almost flat distribution was obtained in the adventitia. This pattern does not change under a hypertensive condition. These results suggest that a remodeling with hypertension occurs in the media.

Circumferential Residual Stress Distribution and Its Influence in a Diseased Carotid Artery

2009 ◽  
Author(s):  
Massimo Pocaterra ◽  
Hao Gao ◽  
Saroj Das ◽  
Michele Pinelli ◽  
Quan Long
Keyword(s):  
Residual Stress ◽  
Carotid Artery ◽  
Stress Distribution ◽  
Material Properties ◽  
Arterial Wall ◽  
Biological Tissues ◽  
Residual Stress Distribution ◽  
Normal Blood Pressure ◽  
Pressure Loading ◽  
Linear Material

Residual stresses are present in a variety of biological tissues, such as the arteries [1]. It is believed that residual stress tends to make stress distribution more uniform throughout normal arterial wall [2]. However, the influence of residual stress in a diseased artery remains unclear. The aim of this study is to investigate the circumferential residual stress in a diseased carotid artery (atherosclerotic plaque) and its influence on the stress distribution under normal blood pressure loading. To achieve a more realistic stress analysis, an anisotropic non-linear material properties based on ANSYS™ framework with parameter constants, obtained according to Gasser et al [3], was used for all simulations in the study.

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.

Non-Euclidean Stress-Free Configuration of Arteries Accounting for Curl of Axial Strips Sectioned From Vessels

2013 ◽  
Vol 135 (11) ◽  
Author(s):  
Keiichi Takamizawa ◽  
Yasuhide Nakayama
Keyword(s):  
Residual Stress ◽  
Stress Distribution ◽  
Residual Stresses ◽  
Stress Analysis ◽  
Riemannian Geometry ◽  
Axial Stress ◽  
Circumferential Stress ◽  
Arterial Walls ◽  
Physiological Loading ◽  
Residual Strains

It is well known that arteries are subject to residual stress. In earlier studies, the residual stress in the arterial ring relieved by a radial cut was considered in stress analysis. However, it has been found that axial strips sectioned from arteries also curled into arcs, showing that the axial residual stresses were relieved from the arterial walls. The combined relief of circumferential and axial residual stresses must be considered to accurately analyze stress and strain distributions under physiological loading conditions. In the present study, a mathematical model of a stress-free configuration of artery was proposed using Riemannian geometry. Stress analysis for arterial walls under unloaded and physiologically loaded conditions was performed using exponential strain energy functions for porcine and human common carotid arteries. In the porcine artery, the circumferential stress distribution under physiological loading became uniform compared with that without axial residual strain, whereas a gradient of axial stress distribution increased through the wall thickness. This behavior showed almost the same pattern that was observed in a recent study in which approximate analysis accounting for circumferential and axial residual strains was performed, whereas the circumferential and axial stresses increased from the inner surface to the outer surface under a physiological condition in the human common carotid artery of a two-layer model based on data of other recent studies. In both analyses, Riemannian geometry was appropriate to define the stress-free configurations of the arterial walls with both circumferential and axial residual strains.

Residual stress distribution in a lamellar model of the arterial wall

2010 ◽  
Vol 34 (7-8) ◽  
pp. 422-428 ◽  
Author(s):  
Nooshin Haghighipour ◽  
Mohammad Tafazzoli-Shadpour ◽  
Albert Avolio
Keyword(s):  
Residual Stress ◽  
Stress Distribution ◽  
Arterial Wall ◽  
Residual Stress Distribution

Passive Material Properties of Intact Ventricular Myocardium Determined From a Cylindrical Model

1991 ◽  
Vol 113 (1) ◽  
pp. 42-55 ◽  
Author(s):  
J. M. Guccione ◽  
A. D. McCulloch ◽  
L. K. Waldman
Keyword(s):  
Residual Stress ◽  
Left Ventricle ◽  
Material Properties ◽  
Circumferential Stress ◽  
Transversely Isotropic ◽  
Ventricular Myocardium ◽  
Equatorial Region ◽  
Fiber Axis ◽  
Fiber Direction ◽  
Incompressible Hyperelastic Material

The equatorial region of the canine left ventricle was modeled as a thick-walled cylinder consisting of an incompressible hyperelastic material with homogeneous exponential properties. The anisotropic properties of the passive myocardium were assumed to be locally transversely isotropic with respect to a fiber axis whose orientation varied linearly across the wall. Simultaneous inflation, extension, and torsion were applied to the cylinder to produce epicardial strains that were measured previously in the potassium-arrested dog heart. Residual stress in the unloaded state was included by considering the stress-free configuration to be a warped cylindrical arc. In the special case of isotropic material properties, torsion and residual stress both significantly reduced the high circumferential stress peaks predicted at the endocardium by previous models. However, a resultant axial force and moment were necessary to cause the observed epicardial deformations. Therefore, the anisotropic material parameters were found that minimized these resultants and allowed the prescribed displacements to occur subject to the known ventricular pressure loads. The global minimum solution of this parameter optimization problem indicated that the stiffness of passive myocardium (defined for a 20 percent equibiaxial extension) would be 2.4 to 6.6 times greater in the fiber direction than in the transverse plane for a broad range of assumed fiber angle distributions and residual stresses. This agrees with the results of biaxial tissue testing. The predicted transmural distributions of fiber stress were relatively flat with slight peaks in the subepicardium, and the fiber strain profiles agreed closely with experimentally observed sarcomere length distributions. The results indicate that torsion, residual stress and material anisotropy associated with the fiber architecture all can act to reduce endocardial stress gradients in the passive left ventricle.

Influence of residual stress/strain on the biomechanical stability of vulnerable coronary plaques: potential impact for evaluating the risk of plaque rupture

2007 ◽  
Vol 293 (3) ◽  
pp. H1987-H1996 ◽  
Author(s):  
Jacques Ohayon ◽  
Olivier Dubreuil ◽  
Philippe Tracqui ◽  
Simon Le Floc'h ◽  
Gilles Rioufol ◽  
...  
Keyword(s):  
Residual Stress ◽  
Stress Distribution ◽  
Developmental Process ◽  
Plaque Rupture ◽  
Ex Vivo ◽  
High Stress ◽  
External Loading ◽  
Opening Angle ◽  
Biomechanical Stability ◽  
Stress Strain

In a vulnerable plaque (VP), rupture often occurs at a site of high stress within the cap. It is also known that vessels do not become free of stress when all external loads are removed. Previous studies have shown that such residual stress/strain (RS/S) tends to make the stress distribution more uniform throughout the media of a normal artery. However, the influence of RS/S on the wall stress distribution in pathological coronaries remains unclear. The aim of this study was to investigate the effects of RS/S on the biomechanical stability of VPs. RS/S patterns were studied ex vivo in six human vulnerable coronary plaque samples. Because the existence of RS/S can only be assessed by releasing it, the opening angle technique was the experimental approach used to study the geometrical opening configurations of the diseased arteries, producing an arterial wall in a near-zero stress state. Reciprocally, these opening geometries were used in finite element simulations to reconstruct the RS/S distributions in closed arteries. It was found that the RS/S 1) is not negligible, 2) dramatically affects the physiological peak stress amplitude in the thin fibrous cap, 3) spotlights some new high stress areas, and 4) could be a landmark of the lipid core's developmental process within a VP. This study demonstrates that plaque rupture is not to be viewed as a consequence of intravascular pressure alone, but rather of a subtle combination of external loading and intraplaque RS/S.

scholarly journals A New Observation on the Stress Distribution in the Coronary Artery Wall

2009 ◽  
Vol 131 (11) ◽  
Author(s):  
Chong Wang ◽  
Xiaomei Guo ◽  
Ghassan S. Kassab
Keyword(s):  
Coronary Artery ◽  
Stress Distribution ◽  
Vascular Function ◽  
Stress Gradient ◽  
Circumferential Stress ◽  
Wall Stress ◽  
Opening Angle ◽  
Porcine Coronary Artery ◽  
Physiological Loading ◽  
Health And Disease

The stress distribution in the vessel wall has an important bearing on vascular function in health and disease. We studied the relationship between the transmural stress distribution and the opening angle (OA) to determine the stress gradient. The simulation of wall stress was based on transmural measurements of strain and material properties of coronary arteries in reference to the zero-stress state. A one-layer model with material constants of the intact vessel was used to calculate the circumferential stress distribution. A sensitivity analysis using both one- and two-layer models (intima-media and adventitia layers) was carried out to study the effect of the OA on the circumferential stress distribution and average circumferential stress. A larger OA always shifts the circumferential stress from the intima-media to the adventitia layer. We report a new observation that the circumferential stress at the adventitia may exceed that at the intima at physiological loading due to the larger OA in the porcine coronary artery. This has important implications for growth and remodeling, where an increase in opening angle may shift excessive stress from the inner layer to the outer layer.

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