Transmural strain distribution in the blood vessel wall

Analysis of the geometrical influence of ring-opening samples on arterial circumferential residual stress reconstruction

This work consists of analyzing the impact of geometrical features (thickness and curvature) on the estimation of circumferential residual stresses in arteries. For this purpose, a specific sample of lamb abdominal artery is chosen for analysis and, through computational tools based on Python libraries, the stress-free geometry is captured after the ring opening test. Numerical simulations are then used to reconstruct the sample in order to estimate the circumferential residual stresses. Then, four stress-free geometry models are analyzed: an ideal geometry, i.e., constant curvature and thickness; a constant curvature and variable thickness geometry; a variable curvature and constant thickness geometry; and a variable curvature and thickness geometry. The numerical results show that models perform well from a geometric point of view, where the most different feature was the closed outer perimeter that differs about 14% from the closed real sample. As far as residual stress is concerned, differences up to 198% were found in more realistic models taking a constant curvature and thickness model as reference. Thus, the analysis of a realistic geometry with highly variable curvature and thickness can introduce, compared to an idealized geometry, significant differences in the estimation of residual stresses. This could indicate that the characterization of arterial residual stresses is not sufficient when considering only the opening angle and, therefore, it is also necessary to incorporate more geometrical variables.

Considerations for analysis of endothelial shear stress and strain in FSI models of atherosclerosis

Atherosclerosis is a lipid driven chronic inflammatory disease that is characterized by the formation of plaques at predilection sites. These predilection sites (side branches, curved segments, and bifurcations) have often been associated with disturbed shear stress profiles. However, in addition to shear stress, endothelial cells also experience artery wall strain that could contribute to atherosclerosis progression. Herein, we describe a method to accurately obtain these shear stress and strain profiles. We developed a fluid-structure interaction (FSI) framework for modelling arteries within a commercially available package (Abaqus, version 6.14) that included known prestresses (circumferential, axial and pressure associated). In addition, we co-registered 3D histology to a micro-CT-derived 3D reconstruction of an atherosclerotic carotid artery from a cholesterol-fed ApoE^-/- mouse to include the spatial distribution of lipids within a subject-specific model. The FSI model also incorporated a nonlinear hyperelastic material model with regionally-varying properties that distinguished between healthy vessel wall and plaque. FSI predicted a lower shear stress than CFD (~-12%), but further decreases in plaque regions with softer properties (~-24%) were dependent on the approach used to implement the prestresses in the artery wall. When implemented with our new hybrid approach (zero prestresses in regions of lipid deposition), there was significant heterogeneity in endothelial shear stress in the atherosclerotic artery due to variations in stiffness and, in turn, wall strain. In conclusion, when obtaining endothelial shear stress and strain in diseased arteries, a careful consideration of prestresses is necessary. This paper offers a way to implement them.

Modeling Active Mechanosensing in Cell-Matrix Interactions

Cells actively sense the mechanical properties of the extracellular matrix, such as its rigidity, morphology, and deformation. The cell-matrix interaction influences a range of cellular processes, including cell adhesion, migration, and differentiation, among others. This article aims to review some of the recent progress that has been made in modeling mechanosensing in cell-matrix interactions at different length scales. The issues discussed include specific interactions between proteins, the structure and mechanosensitivity of focal adhesions, the cluster effects of the specific binding, the structure and behavior of stress fibers, cells' sensing of substrate stiffness, and cell reorientation on cyclically stretched substrates. The review concludes by looking toward future opportunities in the field and at the challenges to understanding active cell-matrix interactions.

Impact of residual stretch and remodeling on collagen engagement in healthy and pulmonary hypertensive calf pulmonary arteries at physiological pressures

Understanding the mechanical behavior of proximal pulmonary arteries (PAs) is crucial to evaluating pulmonary vascular function and right ventricular afterload. Early and current efforts focus on these arteries' histological changes, in vivo pressure-diameter behavior and mechanical properties under in vitro mechanical testing. However, the in vivo stretch and stress states remain poorly characterized. To further understand the mechanical behavior of the proximal PAs under physiological conditions, this study computed the residual stretch and the in vivo circumferential stretch state in the main pulmonary arteries in both control and hypertensive calves by using in vitro and in vivo artery geometry data, and modeled the impact of residual stretch and arterial remodeling on the in vivo circumferential stretch distribution and collagen engagement in the main pulmonary artery. We found that the in vivo circumferential stretch distribution in both groups was nonuniform across the vessel wall with the largest stretch at the outer wall, suggesting that collagen at the outer wall would engage first. It was also found that the circumferential stretch was more uniform in the hypertensive group, partially due to arterial remodeling that occurred during their hypoxic treatment, and that their onset of collagen engagement occurred at a higher pressure. It is concluded that the residual stretch and arterial remodeling have strong impact on the in vivo stretch state and the collagen engagement and thus the mechanical behavior of the main pulmonary artery in calves.

Catalase overexpression in aortic smooth muscle prevents pathological mechanical changes underlying abdominal aortic aneurysm formation

The causality of the associations between cellular and mechanical mechanisms of abdominal aortic aneurysm (AAA) formation has not been completely defined. Because reactive oxygen species are established mediators of AAA growth and remodeling, our objective was to investigate oxidative stress-induced alterations in aortic biomechanics and microstructure during subclinical AAA development. We investigated the mechanisms of AAA in an angiotensin II (ANG II) infusion model of AAA in apolipoprotein E-deficient (apoE(-/-)) mice that overexpress catalase in vascular smooth muscle cells (apoE(-/-)xTg(SMC-Cat)). At baseline, aortas from apoE(-/-)xTg(SMC-Cat) exhibited increased stiffness and the microstructure was characterized by 50% more collagen content and less elastin fragmentation. ANG II treatment for 7 days in apoE(-/-) mice altered the transmural distribution of suprarenal aortic circumferential strain (quantified by opening angle, which increased from 130 ± 1° at baseline to 198 ± 8° after 7 days of ANG II treatment) without obvious changes in the aortic microstructure. No differences in aortic mechanical behavior or suprarenal opening angle were observed in apoE(-/-)xTg(SMC-Cat) after 7 days of ANG II treatment. These data suggest that at the earliest stages of AAA development H(2)O(2) is functionally important and is involved in the control of local variations in remodeling across the vessel wall. They further suggest that reduced elastin integrity at baseline may predispose the abdominal aorta to aneurysmal mechanical remodeling.

Residual stress distribution in a lamellar model of the arterial wall

Excessive wall circumferential stress in arteries caused by luminal pressure leads to endothelial damage and clinical consequences. In addition to circumferential stress, arterial wall contains residual stress with compressive and tensile components on intima and adventitia sides. The intimal compressive component compensates part of tensile stress induced by blood pressure, hence reduces severity of endothelial tension. The opening angle caused by radial cut of arterial ring defines residual stress. In this study, finite element modelling is used to evaluate residual stress in a lamellar model of human aorta with differing opening angle and elastic modulus. Results show non-linear residual stress profiles across wall thickness, influenced by structural and mechanical parameters. Elevation of opening angle from 50° to 90° leads to increase of intimal compressive component compensating up to 32.6% of the pressure-induced tensile stress. Results may be applied in study of endothelial injury caused by excessive stress in situations such as aging, hypertension and atherosclerosis.

Strain-energy function and three-dimensional stress distribution in esophageal biomechanics

Knowledge of the transmural stress and stretch fields in esophageal wall is necessary to quantify growth and remodeling, and the response to mechanically based clinical interventions or traumatic injury, but there are currently conflicting reports on this issue and the mechanical properties of intact esophagus have not been rigorously addressed. This paper offers multiaxial data on rabbit esophagus, warranted for proper identification of the 3D mechanical properties. The Fung-type strain-energy function was adopted to model our data for esophagus, taken as a thick-walled (1 or 2-layer) tubular structure subjected to inflation and longitudinal extension. Accurate predictions of the pressure-radius-force data were obtained using the 1-layer model, covering a broad range of extensions; the calculated material parameters indicated that intact wall was equally stiff as mucosa-submucosa, but stiffer than muscle in both principal axes, and tissue was stiffer longitudinally, concurring our histological findings (Stavropoulou et al., Journal of Biomechanics. 42 (2009) 2654-2663). Employing the material parameters of individual layers, with reference to their zero-stress state, a reasonable fit was obtained to the data for intact wall, modeled as a 2-layer tissue. Different from the stress distributions presented hitherto in the esophagus literature, consideration of residual stresses led to less dramatic homogenization of stresses under loading. Comparison of the 1- and 2-layer models of esophagus demonstrated that heterogeneity induced a more uniform distribution of residual stresses in each layer, a discontinuity in circumferential and longitudinal stresses at the interface among layers, and a considerable rise of stresses in mucosa, with a reduction in muscle.

A new observation on the stress distribution in the coronary artery wall

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.

A generalized Maxwell model for creep behavior of artery opening angle

An artery ring springs open into a sector after a radial cut. The opening angle characterizes the residual strain in the unloaded state, which is fundamental in understanding stress and strain in the vessel wall. A recent study revealed that the opening angle decreases with time if the artery is cut from the loaded state, while it increases if the cut is made from the no-load state due to viscoelasticity. In both cases, the opening angle approaches the same value in 3 h. This implies that the characteristic relaxation time is about 10,000 s. Here, the creep function of a generalized Maxwell model (a spring in series with six Voigt bodies) is used to predict the temporal change of opening angle in multiple time scales. It is demonstrated that the theoretical model captures the salient features of the experimental results. The proposed creep function may be extended to study the viscoelastic response of blood vessels under various loading conditions.

Flow-induced shear strain in intima of porcine coronary arteries

The in vivo circumferential strain has a small variation throughout the vascular system (aorta to arterioles). The axial strain has also been shown to be nearly the same as the circumferential strain under physiological loading. Since the endothelium is mechanically much softer than the media-adventitia in healthy arteries, the porcine intima was considered as a mechanically distinct layer from the media-adventitia in a two-layer computational model. Based on the simulation result, we hypothesize that the flow-induced shear strain in intima can be of similar value as the pressure-induced circumferential strain in healthy coronary arteries, even though the shear stress is orders of magnitude smaller than the circumferential stress. The nearly isotropic deformation (circumferential, axial, and shear strains) may have important implications for mechanical homeostasis of endothelial cells, mechanotransduction, growth, and remodeling of blood vessels.

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

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.

Limits to the durability of arterial elastic tissue

To engineer a better blood vessel, we must identify which structural, mechanical, and biological features of the native vessel must be replicated to ensure long-term survival of the implant. In this study, we tested autoclave-purified elastic tissue from along the pig thoracic aorta under long-term static and cyclic loading to identify factors that affected its durability. Samples were tested in water or in sucrose, which enhances viscoelasticity. Samples failed between 50% and 80% extension, which is lower than the failure extension in shorter, quasi-static tensile tests. Cyclic loading had a small effect on the durability of samples tested in water. Samples from the distal thoracic aorta and samples pre-treated in 70% ethanol showed enhanced durability. Failure between 50% and 80% extension appears associated with structural features of the individual fibre, and indirect evidence suggests it may be due to failure of the microfibrils, not the elastin. Cross-linked elastin may be necessary but insufficient to prevent failure. Durability appears also affected by regional differences in tissue structure, possibly the three-dimensional fibre organization. These results suggest ensuring normal fibre synthesis and organization may be crucial to the design of a successful vascular implant.

Biomechanics of the cardiovascular system: the aorta as an illustratory example

Biomechanics relates the function of a physiological system to its structure. The objective of biomechanics is to deduce the function of a system from its geometry, material properties and boundary conditions based on the balance laws of mechanics (e.g. conservation of mass, momentum and energy). In the present review, we shall outline the general approach of biomechanics. As this is an enormously broad field, we shall consider a detailed biomechanical analysis of the aorta as an illustration. Specifically, we will consider the geometry and material properties of the aorta in conjunction with appropriate boundary conditions to formulate and solve several well-posed boundary value problems. Among other issues, we shall consider the effect of longitudinal pre-stretch and surrounding tissue on the mechanical status of the vessel wall. The solutions of the boundary value problems predict the presence of mechanical homeostasis in the vessel wall. The implications of mechanical homeostasis on growth, remodelling and postnatal development of the aorta are considered.

Tensile Residual Strains on the Elastic Lamellae along the Porcine Thoracic Aorta

AIMS

This study determines the residual strains on the elastic lamellae in the porcine thoracic aorta to understand the distribution of strains amongst the components of the vascular wall.

METHODS

Residual strains in aortic rings were released by cutting and purifying the elastin. Strains were calculated from lamellar contour lengths based on lamellar waviness and from mechanical tests.

RESULTS

On the release of residual strains, waviness decreased 2-7%, the inner lamellae shortened 2.1 +/- 0.6% and the outer lamellae shortened 7.1 +/- 0.4% (p < 0.001), indicating that all lamellar elastin was under tension in fresh aortic tissue. Lamellar shortening was 3% greater in the distal than in the proximal tissue. Mechanical tests confirmed the morphological results and showed that the residual strains in fresh tissue required both the elastic tissue and the vascular smooth muscle. Tensile residual strains averaging 1.0% remained in the uncut elastin rings.

CONCLUSION

When waviness is considered, the residual strains on the individual wall components can differ from the surface residual strains based only on the ring perimeter. The residual strains on the inner elastic lamellae are tensile, not compressive. The strain distribution amongst the individual components is non-uniform and not adequately understood to determine the physiological strains in the aortic wall.