Shear modulus of porcine coronary artery: contributions of media and adventitia

The epicardial coronary arteries experience significant torsion in the axial direction due to changes in the shape of the heart during the cardiac cycle. The objective of this study was to determine the torsional mechanical properties of the coronary arteries under various circumferential and longitudinal loadings. The coronary artery was treated as a two-layer composite vessel consisting of intima-medial and adventitial layers, and the shear modulus of each layer was determined. Eight porcine hearts were obtained at a local abattoir, and their right coronary and left anterior descending arteries were isolated and tested in vitro with a triaxial torsion machine (inflation, longitudinal stretch, and circumferential twist). After the intact vessel was tested, the adventitia was dissected away, leaving an intact media that was then tested under identical triaxial loading conditions. We proposed a biomechanical analysis to compute the shear modulus of the adventitia from the measured shear moduli of the intact vessel and the media. To validate our predictions, we used four additional hearts in which the shear modulus of the adventitia was measured after dissection of media. Our results show that the shear modulus does not depend on the shear stress or strain but varies linearly with circumferential and longitudinal stresses and in a nonlinear way with the corresponding strains. Furthermore, we found that the shear modulus of the adventitia is larger than that of the intact vessel, which is larger than the vessel media. These results may have important implications for baroreceptor sensitivity, circulation of the vasa vasorum, and coronary dissection.     

Determination of layer-specific mechanical properties of human coronary arteries with nonatherosclerotic intimal thickening and related constitutive modeling

At autopsy, 13 nonstenotic human left anterior descending coronary arteries [71.5 +/- 7.3 (mean +/- SD) yr old] were harvested, and related anamnesis was documented. Preconditioned prepared strips (n = 78) of segments from the midregion of the left anterior descending coronary artery from the individual layers in axial and circumferential directions were subjected to cyclic quasi-static uniaxial tension tests, and ultimate tensile stresses and stretches were documented. The ratio of outer diameter to total wall thickness was 0.189 +/- 0.014; ratios of adventitia, media, and intima thickness to total wall thickness were 0.4 +/- 0.03, 0.36 +/- 0.03, and 0.27 +/- 0.02, respectively; axial in situ stretch of 1.044 +/- 0.06 decreased with age. Stress-stretch responses for the individual tissues showed pronounced mechanical heterogeneity. The intima is the stiffest layer over the whole deformation domain, whereas the media in the longitudinal direction is the softest. All specimens exhibited small hysteresis and anisotropic and strong nonlinear behavior in both loading directions. The media and intima showed similar ultimate tensile stresses, which are on average three times smaller than ultimate tensile stresses in the adventitia (1,430 +/- 604 kPa circumferential and 1,300 +/- 692 kPa longitudinal). The ultimate tensile stretches are similar for all tissue layers. A recently proposed constitutive model was extended and used to represent the deformation behavior for each tissue type over the entire loading range. The study showed the need to model nonstenotic human coronary arteries with nonatherosclerotic intimal thickening as a composite structure composed of three solid mechanically relevant layers with different mechanical properties. The intima showed significant thickness, load-bearing capacity, and mechanical strength compared with the media and adventitia.     

Effects of biaxial stretch on arteriolar function in vitro

Mounting evidence suggests that the normal biomechanical state of arteries may include a nearly equibiaxial intramural stress and that arteries tend to undergo rapid and dramatic remodeling when perturbed from this normal state. Technical developments since the early 1980s have enabled in vitro (acute) and ex vivo (chronic culture) study of isolated, perfused microvessels, and it is clear that these vessels share many functional similarities with arteries. To date, however, there has been no systematic study of the effects of in-plane biaxial loading on the biomechanical behavior of arterioles. Here we describe a modification to a prior in vitro arterial test system that allowed us to investigate the role of altered axial stretch on the passive, myogenic, and norepinephrine-stimulated biaxial behavior of isolated rat cremaster arterioles. We show that axial stretches from 85% to 110% of values often used in the laboratory and consistent with those normally experienced in situ induce modest changes in the measured mean circumferential and axial stress-stretch behavior and in measures of distensibility and myogenic index. Nevertheless, altered axial stretch has a dramatic effect on the biaxial state of stress, and nearly equibiaxial stresses occur at axial stretches larger than those typically used in isolated arteriole studies. This finding is consistent with estimates of material and functional behavior in arterioles and suggests that long-term ex vivo studies, wherein vessel growth and remodeling are critical, should be performed at higher axial lengths than have been used during most prior in vitro tests.     

Mechanics of the human femoral adventitia including the high-pressure response

Adventitial mechanics were studied on the basis of adventitial tube tests and associated stress analyses utilizing a thin-walled model. Inflation tests of 11 nonstenotic human femoral arteries (79.3 +/- 8.2 yr, means +/- SD) were performed during autopsy. Adventitial tubes were separated anatomically and underwent cyclic, quasistatic extension-inflation tests using physiological pressures and high pressures up to 100 kPa. Associated circumferential and axial stretches were typically <20%, indicating "adventitiosclerosis." Adventitias behaved nearly elastically for both loading domains, demonstrating high tensile strengths (>1 MPa). The anisotropic and strongly nonlinear mechanical responses were represented appropriately by two-dimensional Fung-type stored-energy functions. At physiological pressure (13.3 kPa), adventitias carry ~25% of the pressure load in situ, whereas their circumferential and axial stresses were similar to the total wall stresses (~50 kPa in both directions), supporting a "uniform stress hypothesis." At higher pressures, they became the mechanically predominant layer, carrying >50% of the pressure load. These significant load-carrying capabilities depended strongly on circumferential and axial in-vessel prestretches (mean values: 0.95 and 1.08). On the basis of these results, the mechanical role of the adventitia at physiological and hypertensive states and during balloon angioplasty was characterized.     

Duration of no-load state affects opening angle of porcine coronary arteries

The zero-stress state of a blood vessel has been extensively studied because it is the reference state for which all calculations of intramural stress and strain must be based. It has also been found to reflect nonuniformity in growth and remodeling in response to chemical or physical changes. The zero-stress state can be characterized by an opening angle, defined as the angle subtended by two radii connecting the midpoint of the inner wall. All prior studies documented the zero-stress state or opening angle with no regard to duration of the no-load state. Our hypotheses were that, given the viscoelastic properties of blood vessels, the zero-stress state may have "memory" of prior circumferential and axial loading, i.e., duration of the no-load state influences opening angle. To test these hypotheses, we considered ring pairs of porcine coronary arteries to examine the effect of duration in the no-load state after circumferential distension. Our results show a significant reduction in opening angle as duration of the no-load state increases, i.e., vessels that are reduced to the zero-stress state directly from the loaded state attain much larger opening angles at 30 min after the radial cut than rings that are in the no-load state for various durations. To examine the effect of axial loading, we found similar reductions in opening angle with duration in the no-load from the in situ state, albeit the effect was significantly smaller than that of circumferential loading. Hence, we found that the zero-stress state has memory of both circumferential and axial loading. These results are important for understanding viscoelastic properties of coronary arteries, interpretation of the enormous data on the opening angle and strain in the literature, and standardization of future measurements on the zero-stress state.     

Effect of cyclic axial stretch of rat arteries on endothelial cytoskeletal morphology and vascular reactivity

Pulsatile fluid shear stress and circumferential stretch are responsible for the axial alignment of vascular endothelial cells and their actin stress fibers in vivo. We studied the effect of cyclic alterations in axial stretch independent of flow on endothelial cytoskeletal organization in intact arteries and determined if functional alterations accompanied morphologic alterations. Rat renal arteries were axially stretched (20%, 0.5 Hz) around their in vivo lengths, for up to 4h. Actin stress fibers were examined by immunofluorescent staining. We found that cyclic axial stretching of intact vessels under normal transmural pressure in the absence of shear stress induces within a few hours realignment of endothelial actin stress fibers toward the circumferential direction. Concomitant with this morphologic alteration, the sensitivity (log(EC(50))) to the endothelium-dependent vasodilator (acetylcholine) was significantly decreased in the stretched vessels (after stretching -5.15+/-0.79 and before stretching -6.71+/-0.78, resp.), while there was no difference in sodium nitroprusside (SNP) sensitivity. There was no difference in sensitivity to both acetylcholine and SNP in time control vessels. Similar to cultured cells, endothelial cells in intact vessels subjected to cyclic stretching reorganize their actin filaments almost perpendicular to the stretching direction. Accompanying this morphological alteration is a loss of endothelium-dependent vasodilation but not of smooth muscle responsiveness.     

Three-dimensional stress and strain distribution in a two-layer model of a coronary artery

For a right coronary artery, three-dimensional stress and strain distributions at a physiological intraluminal pressure and an axial extension ratio were computed on the basis of a two-layer elastic model. To validate the model, curves of external radius versus pressure and of axial force versus pressure were computed for three axial extension ratios. To analyze mechanical properties, stress-free configurations of media and adventitia, and the constitutive law of each layer in literature, were used. The present study showed that the peak circumferential stress and the peak axial stress appear in the media at the boundary between the media and adventitia. This result is due to the opening angle of the media being larger than π (rad) and the larger value of a material constant of the strain energy function for the media than for the adventitia. The circumferential stress and strain were discontinuous at the boundary. On the other hand, the radial stress was continuous at the boundary because of the boundary condition for stress. The circumferential stress and axial stress in the adventitia were almost uniformly distributed, and smaller than in the media. The residual stress and strain were also computed. The circumferential residual stress and strain were almost linearly distributed in each layer, although discontinuity appeared at the boundary between the two layers.     

A piece-wise non-linear elastic stress expression of human and pig coronary arteries tested in vitro.

Eight human and nineteen pig unembalmed proximal left anterior descending and circumflex coronary arteries were subjected to linear volume changes (2 s ramp time) at three fixed axial extensions while immersed in a physiological saline bath at body temperature. Measured parameters included: lumen pressure, outside diameter, axial force, and axial extension. The deformations were measured using a video dimensional analyzer. The arteries were inflated to pressures well above the physiological range at each axial extension. A latex inner tube was placed inside of each specimen to prevent leakage, and its effects upon the measured stresses were corrected analytically. With this method, the average circumferential and axial stresses could be computed directly from the experimental data. In both directions the average stresses measured displayed two distinct regions: stresses occurring for small diameter changes (physiological pressures) and stresses occurring for large diameter changes (high pressures). The resulting average small strain and large strain stress components were curve-fit separately and, when reassembled, provided a piece-wise model of the stress response of coronary arteries over a wide range of inflation pressures and axial extensions.     

Isotropy and anisotropy of the arterial wall

The passive biomechanical response of intact cylindrical rat carotid arteries is studied in vitro and compared with the mechanical response of rubber tubes. Using true stress and natural strain in the definition of the incremental modulus of elasticity, the tissue wall properties are analyzed over wide ranges of simultaneous circumferential and longitudinal deformations. The type of loading chosen is 'physiological' i.e. symmetric: the cylindrical segments are subjected to internal pressure and axial prestretch without torsion or shear. Several aspects pertaining to the choice of parameters characterizing the material are discussed and the analysis pertaining to the deformational behavior of a hypothetical compliant tube with Hookean wall material is presented. The experimental results show that while rubber response can be adequately represented as linearly elastic and isotropic, the overall response of vascular tissue is highly non-linear and anisotropic. However, for states of deformation that occur in vivo, the elasticity of arteries is quite similar to that of rubber tubes and as such the arterial wall may be viewed as incrementally isotropic for the range of deformations that occur in vivo.     

Stress gradients in the walls of large arteries

Elastic behavior of vascular wall, assuming the vessels to be ‘thick-walled’ and utilizing finite deformation theory, was investigated. It was found that canine carotid arterial wall is neither isotropic nor transversely isotropic. Previously, stress-strain relations were obtained for carotid arteries on the basis of membrane theory (Doyle and Dobrin, 1971). Since strain gradients across the wall are fairly steep, the applicability of such expressions, for pointwise evaluation of stress, required examination. The study indicated that these relationships between mean circumferential stress and mean extension ratio in the circumferential direction could be used to relate the specific circumferential stress value to the specific extension ratio at any designated point within the wall. From this analysis it was possible to evaluate circumferential and radial wall stresses. Both of these stresses are maximal at the inner surface of the intima. At this point the radial stress is equal to the transmural pressure and is compressive, while the circumferential stress is tensile and is 1·5 to 2 times the value of the mean stress, i.e. the product of transmural pressure and the ratio of internal radius-to-wall thickness. Both stresses are lowest at the outer edge of the adventitia. These stress distributions were considered with respect to the spacing of the elastic lamellae and the absence of discernible vasa vasora in the inner third of the wall.     

Effect of surrounding tissue on vessel fluid and solid mechanics

There is no doubt that atherosclerosis is one of the most important health problems in the Western Societies. It is well accepted that atherosclerosis is associated with abnormal stress and strain conditions. A compelling observation is that the epicardial arteries develop atherosclerosis while the intramural arteries do not. Atherosclerotic changes involving the epicardial portion of the coronary artery stop where the artery penetrates the myocardium. The objective of the present study is to understand the fluid and solid mechanical differences between the two types of vessels. A finite element analysis was employed to investigate the effect of external tissue contraction on the characteristics of pulsatile blood flow and the vessel wall stress distribution. The sequential coupling of fluid-solid interaction (FSI) revealed that the changes of flow velocity and wall shear stress, in response to cyclical external loading, appear less important than the circumferential stress and strain reduction in the vessel wall under the proposed boundary conditions. These results have important implications since high stresses and strains can induce growth, remodeling, and atherosclerosis; and hence we speculate that a reduction of stress and strain may be atheroprotective. The importance of FSI in deformable vessels with pulsatile flow is discussed and the fluid and solid mechanics differences between epicardial and intramural vessels are highlighted.     

Active axial stress in mouse aorta

The study verifies the development of active axial stress in the wall of mouse aorta over a range of physiological loads when the smooth muscle cells are stimulated to contract. The results obtained show that the active axial stress is virtually independent of the magnitude of pressure, but depends predominately on the longitudinal stretch ratio. The dependence is non-monotonic and is similar to the active stress-stretch dependence in the circumferential direction reported in the literature. The expression for the active axial stress fitted to the experimental data shows that the maximum active stress is developed at longitudinal stretch ratio 1.81, and 1.56 is the longitudinal stretch ratio below which the stimulation does not generate active stress. The study shows that the magnitude of active axial stress is smaller than the active circumferential stress. There is need for more experimental investigations on the active response of different types of arteries from different species and pathological conditions. The results of these studies can promote building of refined constrictive models in vascular rheology.     

Cooperative Effects of Matrix Stiffness and Fluid Shear Stress on Endothelial Cell Behavior

Arterial hemodynamic shear stress and blood vessel stiffening both significantly influence the arterial endothelial cell (EC) phenotype and atherosclerosis progression, and both have been shown to signal through cell-matrix adhesions. However, the cooperative effects of fluid shear stress and matrix stiffness on ECs remain unknown. To investigate these cooperative effects, we cultured bovine aortic ECs on hydrogels matching the elasticity of the intima of compliant, young, or stiff, aging arteries. The cells were then exposed to laminar fluid shear stress of 12 dyn/cm². Cells grown on more compliant matrices displayed increased elongation and tighter EC-cell junctions. Notably, cells cultured on more compliant substrates also showed decreased RhoA activation under laminar shear stress. Additionally, endothelial nitric oxide synthase and extracellular signal-regulated kinase phosphorylation in response to fluid shear stress occurred more rapidly in ECs cultured on more compliant substrates, and nitric oxide production was enhanced. Together, our results demonstrate that a signaling cross talk between stiffness and fluid shear stress exists within the vascular microenvironment, and, importantly, matrices mimicking young and healthy blood vessels can promote and augment the atheroprotective signals induced by fluid shear stress. These data suggest that targeting intimal stiffening and/or the EC response to intima stiffening clinically may improve vascular health.     

The effect of blood viscoelasticity on pulsatile flow in stationary and axially moving tubes

An analytical solution for pulsatile flow of a generalized Maxwell fluid in straight rigid tubes, with and without axial vessel motion, has been used to calculate the effect of blood viscoelasticity on velocity profiles and shear stress in flows representative of those in the large arteries. Measured bulk flow rate Q waveforms were used as starting points in the calculations for the aorta and femoral arteries, from which axial pressure gradient ▿P waves were derived that would reproduce the starting Q waves for viscoelastic flow. The ▿P waves were then used to calculate velocity profiles for both viscoelastic and purely viscous flow. For the coronary artery, published ▿P and axial vessel acceleration waveforms were used in a similar procedure to determine the separate and combined influences of viscoelasticity and vessel motion.Differences in local velocities, comparing viscous flow to viscoelastic flow, were in all cases less than about 2% of the peak local velocity. Differences in peak wall shear stress were less than about 3%.In the coronary artery, wall shear stress differences between viscous and viscoelastic flow were small, regardless of whether axial vessel motion was included. The shape of the wall shear stress waveform and its difference, however, changed dramatically between the stationary and moving vessel cases. The peaks in wall shear stress difference corresponded with large temporal gradients in the combined driving force for the flow.     

A linearized and incompressible constitutive model for arteries

In many biomechanical studies, blood vessels can be modeled as pseudoelastic orthotropic materials that are incompressible (volume-preserving) under physiological loading. To use a minimum number of elastic constants to describe the constitutive behavior of arteries, we adopt a generalized Hooke's law for the co-rotational Cauchy stress and a recently proposed logarithmic-exponential strain. This strain tensor absorbs the material nonlinearity and its trace is zero for volume-preserving deformations. Thus, the relationships between model parameters due to the incompressibility constraint are easy to analyze and interpret. In particular, the number of independent elastic constants reduces from ten to seven in the orthotropic model. As an illustratory study, we fit this model to measured data of porcine coronary arteries in inflation-stretch tests. Four parameters, n (material nonlinearity), Young's moduli E? (circumferential), E? (axial), and E? (radial) are necessary to fit the data. The advantages and limitations of this model are discussed.     

Diameter-dependent axial prestretch of porcine coronary arteries and veins

The pressure-diameter relation (PDR) and the wall strain of coronary blood vessels have important implications for coronary blood flow and arthrosclerosis, respectively. Previous studies have shown that these mechanical quantities are significantly affected by the axial stretch of the vessels. The objective of this study was to measure the physiological axial stretch in the coronary vasculature; i.e., from left anterior descending (LAD) artery tree to coronary sinus vein and to determine its effect on the PDR and hence wall stiffness. Silicone elastomer was perfused through the LAD artery and coronary sinus trees to cast the vessels at the physiologic pressure. The results show that the physiological axial stretch exists for orders 4 to 11 (> 24 μm in diameter) arteries and orders -4 to -12 (>38 μm in diameter) veins but vanishes for the smaller vessels. Statistically, the axial stretch is higher for larger vessels and is higher for arteries than veins. The axial stretch λ(z) shows a linear variation with the order number (n) as: λ(z) = 0.062n + 0.75 (R(2) = 0.99) for artery and λ(z) = -0.029n + 0.89 (R(2) = 0.99) for vein. The mechanical analysis shows that the axial stretch significantly affects the PDR of the larger vessels. The circumferential stretch/strain was found to be significantly higher for the epicardial arteries (orders 9-11), which are free of myocardium constraint, than the intramyocardial arteries (orders 4-8). These findings have fundamental implications for coronary blood vessel mechanics.     

Cartilage responses to a novel triaxial mechanostimulatory culture system

We have developed a novel mechanically active cartilage culture device capable of modulating the interplay between compression and shear, at physiologic stress levels (2-5 MPa). This triaxial compression culture system subjects cylindrical cartilage explants to pulsatile axial compression from platen contact, plus pulsatile radially transverse compression from external fluid compression. These compressive loads can be independently modulated to impose stress states that resemble normal physiologic loading, and to investigate perturbations of individual components of the multi-axial stress state, such as increased shear stress. Based on the observation that joint incongruity predisposes cartilage to premature degeneration, we hypothesized that cartilage extracellular matrix (ECM) synthesis would be inhibited under conditions of low transverse buttressing (high shear stress). To test this hypothesis, we compared ECM synthesis in human cartilage explants exposed to axial compression without transverse compression (high shear stress), versus explants exposed to axial compression plus an equal level of transverse compression (low shear stress). Both total (35)SO(4) incorporation and aggrecan-specific (35)SO(4) incorporation were significantly inhibited by axial compression, relative to axial plus transverse compression.     

Some unusual considerations about vessel walls and wall stresses

The "zero-stress state" of blood vessels is usually defined with respect to the atmospheric pressure p(a) ( approximately 750 mmHg). As a consequence, circumferential and axial wall stresses due to a positive transmural pressure can only be positive and thus, by definition, only tensile. If the zero-stress state were defined with respect to vacuum pressure (0 mmHg), the compressive stress -p(a) generated by p(a) everywhere in the wall would, however, be included so that negative (=compressive) wall stresses would formally become possible. In order to examine the consequences this alternative definition would have for arteries, we have compared radial, circumferential, and axial stresses calculated "conventionally" to the values they take when the zero-stress state is defined "correctly" by reference to the vacuum pressure. It turns out that, under normal physiologic conditions, axial stress and perhaps also circumferential stress might well be compressive in many elastic and conductance arteries, contrary to the intuitive conviction of many people. Since the type of stresses a vessel wall is submitted to may be highly relevant for its structure and mechanical properties, this unconventional way of considering wall stresses may reveal unsuspected relationships between wall stresses on one side, and wall structure, vessel growth, adaptation and repair processes, atherosclerosis, angioplasty or stenting on the other side. Similar considerations might also prove useful with regard to cardiac hypertrophy.     

Shear strain in the adventitial layer of the arterial wall facilitates development of vulnerable plaques

Myocardial infarction and stroke are two of the leading causes of death and primarily triggered by destabilization of atherosclerotic plaques. Fatty streaks are known to develop at sites in the arterial wall where shear stress is low. These fatty streaks can develop into more advanced plaques that are prone to rupture. Rupture leads to thrombus formation, which may subsequently result in a myocardial infarction or stroke. The relation between shear stress on the inner (endothelial) layer of the arterial wall in relation to plaque development has been studied extensively. However, a causal relation between adventitial shear forces and atherosclerosis development has never been considered.Arterial stiffening increases with age and may facilitate an increase in shear strain in the adventitial layer, an axial shear between artery and surrounding tissue. In the adventitial layer, a large number of inflammatory cells and perivascular structures are present that are subjected to shear strain. Cyclic strain applied to endothelial cells stimulates neovascularisation via different pathways. The conduit arteries in the human body (e.g. coronary and carotid artery) have their own nutrition supply: the vasa vasorum, which is located in the adventitial layer and sprouts into the intimal layer when atherosclerotic plaque develops. Increased plaque neovascularisation makes the plaques more prone to rupture. Therefore we hypothesize that increased shear strain facilitates the development of vulnerable plaques by stimulation of atherosclerotic plaque neovascularisation that sprouts from the adventitial vasa vasorum. Validation of this hypothesis paves the road to the use of adventitial shear strain (measured using a noninvasive ultrasound technique) as risk assessment in plaque.     

Fundamental role of axial stress in compensatory adaptations by arteries

Arteries exhibit a remarkable ability to adapt to diverse genetic defects and sustained alterations in mechanical loading. For example, changes in blood flow induced wall shear stress tend to control arterial caliber and changes in blood pressure induced circumferential wall stress tend to control wall thickness. We submit, however, that the axial component of wall stress plays a similarly fundamental role in controlling arterial geometry, structure, and function, that is, compensatory adaptations. This observation comes from a review of findings reported in the literature and a comparison of four recent studies from our laboratory that quantified changes in the biaxial mechanical properties of mouse carotid arteries in cases of altered cell-matrix interactions, extracellular matrix composition, blood pressure, or axial extension. There is, therefore, a pressing need to include the fundamental role of axial wall stress in conceptual and theoretical models of arterial growth and remodeling and, consequently, there is a need for increased attention to evolving biaxial mechanical properties in cases of altered genetics and mechanical stimuli.