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.     

Passive elastic properties of the rat aorta

The passive anisotropic elastic properties of rat's aorta were studied in vitro by subjecting cylindrical segments of thoracic and abdominal aorta to a wide range of deformations. Using data on pressure, axial stretch, outer diameter, axial force and wall thickness, incremental moduli of elasticity in the circumferential, axial and radial directions were computed. Results indicate that while the elastic behavior of the aortic wall is globally anisotropic, there exists a state of deformation at which the vessel displays incremental isotropy. This state of deformation corresponds approximately to the loading conditions to which the aorta is exposed in situ. Values of the moduli, analyzed as a function of transmural pressure, show that the stiffness of the aortic wall is fairly constant at low pressures but raises steeply for pressures higher than physiological. For axial stretches as occurring in situ, the magnitudes of the circumferential and radial moduli do not differ significantly for the thoracic aorta; hence this vessel can be regarded as transversely isotropic over a wide range of pressures. The same observation is valid also for the abdominal aorta when pressures equal or smaller than physiological are considered. For both the thoracic and abdominal segments of the aorta, the circumferential and radial moduli are smaller than the axial modulus at low pressures, while the reverse is true for large pressures.     

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.     

A multiaxial computer-controlled organ culture and biomechanical device for mouse carotid arteries

Much of our understanding of vascular mechanotransduction has come from studies using either cell culture or in vivo animal models, but the recent success of organ culture systems offers an exciting alternative. In studying cell-mediated vascular adaptations to altered loading, organ culture allows one to impose well-controlled mechanical loads and to perform multiaxial mechanical tests on the same vessel throughout the culture period, and thereby to observe cell-mediated vascular adaptations independent of neural and hormonal effects. Here, we present a computer-controlled perfused organ culture and biomechanical testing device designed for small caliber (50-5000 micron) blood vessels. This device can control precisely the pulsatile pressure, luminal flow, and axial load (or stretch) and perform intermittent biaxial (pressure-diameter and axial load-length) and functional tests to quantify adaptations in mechanical behavior and cellular function, respectively. Device capabilities are demonstrated by culturing mouse carotid arteries for 4 days.     

Mechanical anisotropy of inflated elastic tissue from the pig aorta

Uniaxial and biaxial mechanical properties of purified elastic tissue from the proximal thoracic aorta were studied to understand physiological load distributions within the arterial wall. Stress–strain behaviour was non-linear in uniaxial and inflation tests. Elastic tissue was 40% stiffer in the circumferential direction compared to axial in uniaxial tests and～100% stiffer in vessels at an axial stretch ratio of 1.2 or 1.3 and inflated to physiological pressure. Poisson’s ratio v_θz averaged 0.2 and v_zθ increased with circumferential stretch from ～0.2 to ～0.4. Axial stretch had little impact on circumferential behaviour. In intact (unpurified) vessels at constant length, axial forces decreased with pressure at low axial stretches but remained constant at higher stretches. Such a constant axial force is characteristic of incrementally isotropic arteries at their in vivo dimensions. In purified elastic tissue, force decreased with pressure at all axial strains, showing no trend towards isotropy. Analysis of the force–length–pressure data indicated a vessel with v_θz≈0.2 would stretch axially 2–4% with the cardiac pulse yet maintain constant axial force. We compared the ability of 4 mathematical models to predict the pressure-circumferential stretch behaviour of tethered, purified elastic tissue. Models that assumed isotropy could not predict the stretch at zero pressure. The neo-Hookean model overestimated the non-linearity of the response and two non-linear models underestimated it. A model incorporating contributions from orthogonal fibres captured the non-linearity but not the zero-pressure response. Models incorporating anisotropy and non-linearity should better predict the mechanical behaviour of elastic tissue of the proximal thoracic aorta.     

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.     

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.     

Altered biomechanical properties of carotid arteries in two mouse models of muscular dystrophy.

Muscular dystrophy is characterized by skeletal muscle weakness and wasting, but little is known about possible alterations to the vasculature. Many muscular dystrophies are caused by a defective dystrophin-glycoprotein complex (DGC), which plays an important role in mechanotransduction and maintenance of structural integrity in muscle cells. The DGC is a group of membrane-associated proteins, including dystrophin and sarcoglycan-delta, that helps connect the cytoskeleton of muscle cells to the extracellular matrix. In this paper, mice lacking genes encoding dystrophin (mdx) or sarcoglycan-delta (sgcd-/-) were studied to detect possible alterations to vascular wall mechanics. Pressure-diameter and axial force-length tests were performed on common carotid arteries from mdx, sgcd-/-, and wild-type mice in active (basal) and passive smooth muscle states, and functional responses to three vasoactive compounds were determined at constant pressure and length. Apparent biomechanical differences included the following: mdx and sgcd-/- arteries had decreased distensibilities in pressure-diameter tests, with mdx arteries exhibiting elevated circumferential stresses, and mdx and sgcd-/- arteries generated elevated axial loads and stresses in axial force-length tests. Interestingly, however, mdx and sgcd-/- arteries also had significantly lower in vivo axial stretches than did the wild type. Accounting for this possible adaptation largely eliminated the apparent differences in circumferential and axial stiffness, thus suggesting that loss of DGC proteins may induce adaptive biomechanical changes that can maintain overall wall mechanics in response to normal loads. Nevertheless, there remains a need to understand better possible vascular adaptations in response to sustained altered loads in patients with muscular dystrophy.     

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.     

Anisotropic mechanical properties of tissue components in human atherosclerotic plaques

Knowledge of the biomechanical properties of human atherosclerotic plaques is of essential importance for developing more insights in the pathophysiology of the cardiovascular system and for better predicting the outcome of interventional treatments such as balloon angioplasty. Available data are mainly based on uniaxial tests, and most of the studies investigate the mechanical response of fibrous plaque caps only. However, stress distributions during, for example, balloon angioplasty are strongly influenced by all components of atherosclerotic lesions. A total number of 107 samples from nine human high-grade stenotic iliac arteries were tested; associated anamnesis of donors reported. Magnetic resonance imaging was employed to test the usability of the harvested arteries. Histological analyses has served to characterize the different tissue types. Prepared strips of 7 different tissue types underwent cyclic quasistatic uniaxial tension tests in axial and circumferential directions; ultimate tensile stresses and stretches were documented. Experimental data of individual samples indicated anisotropic and highly nonlinear tissue properties as well as considerable interspecimen differences. The calcification showed, however a linear property, with about the same stiffness as observed for the adventitia in high stress regions. The stress and stretch values at calcification fracture are smaller (179 +/- 56 kPa and 1.02 +/- 0.005) than for each of the other tissue components. Of all intimal tissues investigated, the lowest fracture stress occurred in the circumferential direction of the fibrous cap (254.8 +/- 79.8 kPa at stretch 1.182 +/- 0.1). The adventitia demonstrated the highest and the nondiseased media the lowest mechanical strength on average.     

Biaxial vasoactivity of porcine coronary artery

The passive mechanical properties of blood vessel mainly stem from the interaction of collagen and elastin fibers, but vessel constriction is attributed to smooth muscle cell (SMC) contraction. Although the passive properties of coronary arteries have been well characterized, the active biaxial stress-strain relationship is not known. Here, we carry out biaxial (inflation and axial extension) mechanical tests in right coronary arteries that provide the active coronary stress-strain relationship in circumferential and axial directions. Based on the measurements, a biaxial active strain energy function is proposed to quantify the constitutive stress-strain relationship in the physiological range of loading. The strain energy is expressed as a Gauss error function in the physiological pressure range. In K(+)-induced vasoconstriction, the mean ± SE values of outer diameters at transmural pressure of 80 mmHg were 3.41 ± 0.17 and 3.28 ± 0.24 mm at axial stretch ratios of 1.3 and 1.5, respectively, which were significantly smaller than those in Ca(2+)-free-induced vasodilated state (i.e., 4.01 ± 0.16 and 3.75 ± 0.20 mm, respectively). The mean ± SE values of the inner and outer diameters in no-load state and the opening angles in zero-stress state were 1.69 ± 0.04 mm and 2.25 ± 0.08 mm and 126 ± 22°, respectively. The active stresses have a maximal value at the passive pressure of 80-100 mmHg and at the active pressure of 140-160 mmHg. Moreover, a mechanical analysis shows a significant reduction of mean stress and strain (averaged through the vessel wall). These findings have important implications for understanding SMC mechanics.     

A comparison of biomechanical properties between human and porcine cornea

Due to the difficulty in obtaining human corneas, pig corneas are often substituted as models for cornea research. The purpose of this study is to find the similarities and differences in the biomechanical properties between human and porcine corneas. Uniaxial tests were conducted using an Instron apparatus to determine their tensile strength, stress-strain relationship, and stress-relaxation properties. The tensile strength and stress-strain relation were very similar but significant differences between the two tissues were observed in the stress-relaxation relationship. Under the same stretch ratio lambda=1.5, porcine cornea relaxed much more than human cornea. If tensile strength and the stress-strain relation are the only mechanical factors to be investigated, porcine cornea can be used as a substitute model for human cornea research. However, when stress relaxation is a factor, porcine corneas cannot be used as an appropriate model for human corneas in mechanical property studies. It is very difficult to get enough specimens of human cornea, so we did the experiments for stress-strain relationship at a specific value of strain rate (corresponding to the velocity of loading 10mm/min), and for stress relaxation at a specific stretch ratio lambda=1.5.     

Effects of longitudinal stretch on VSM tone and distensibility of muscular conduit arteries

With progressing age, large arteries diminish their longitudinal stretch, which in extreme cases results in tortuosity. Increased age is also associated with loss of vessel distensibility. We measured pressure-diameter curves from muscular porcine carotid arteries ex vivo at different longitudinal stretch ratios (lambda(z) = 1.4 and 1.8) and under different vascular smooth muscle (VSM) conditions (fully relaxed, normal VSM tone, and maximally contracted). Distensibility was found to be halved by decreasing longitudinal stretch from lambda(z) = 1.8 to 1.4 at physiological pressures. This counterintuitive observation is possible because highly nonlinear elastic modulus of the artery and anisotropic properties. Furthermore, a significantly larger basal VSM contraction was observed at lambda(z) = 1.8 than 1.4, although this was clearly not related to a myogenic response during inflation. This dependence of VSM tone to longitudinal stretch may have possible implications on the functional characteristics of the arterial wall.     

Fluid-structure interaction modeling of aneurysmal arteries under steady-state and pulsatile blood flow: a stability analysis

Tortuous aneurysmal arteries are often associated with a higher risk of rupture but the mechanism remains unclear. The goal of this study was to analyze the buckling and post-buckling behaviors of aneurysmal arteries under pulsatile flow. To accomplish this goal, we analyzed the buckling behavior of model carotid and abdominal aorta with aneurysms by utilizing fluid-structure interaction (FSI) method with realistic waveforms boundary conditions. FSI simulations were done under steady-state and pulsatile flow for normal (1.5) and reduced (1.3) axial stretch ratios to investigate the influence of aneurysm, pulsatile lumen pressure and axial tension on stability. Our results indicated that aneurysmal artery buckled at the critical buckling pressure and its deflection nonlinearly increased with increasing lumen pressure. Buckling elevates the peak stress (up to 118%). The maximum aneurysm wall stress at pulsatile FSI flow was (29%) higher than under static pressure at the peak lumen pressure of 130 mmHg. Buckling results show an increase in lumen shear stress at the inner side of the maximum deflection. Vortex flow was dramatically enlarged with increasing lumen pressure and artery diameter. Aneurysmal arteries are more susceptible than normal arteries to mechanical instability which causes high stresses in the aneurysm wall that could lead to aneurysm rupture.     

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.     

Morphologic adaptation of arterial endothelial cells to longitudinal stretch in organ culture

Arteries in vivo are subjected to large longitudinal stretch, which changes significantly due to vascular disease and surgery. However, little is known about the effect of longitudinal stretch on arterial endothelium. The aim of this study was to determine the morphologic adaptation of arterial endothelial cells (ECs) to elevated axial stretch. Porcine carotid arteries were stretched 20% more than their in vivo length while being maintained at physiological pressure and flow rate in an organ culture system. The ECs were elongated with the application of the axial stretch (aspect ratio 2.81+/-0.25 versus 3.65+/-0.38, n=8, p<0.001). The elongation was slightly decreased after three days and the ECs recovered their normal shape after seven days, as measured by the shape index and aspect ratio (0.55+/-0.03 versus 0.56+/-0.04, and 2.93+/-0.28 versus 2.88+/-0.20, respectively, n=5). Cell proliferation was increased in the intima of stretched arteries in three days as compared to control arteries but showed no difference after seven days in organ culture. These results demonstrate that the ECs adapt to axial stretch and maintain their normal shape.     

Influence of phase angle between axial and torsional loadings on fatigue fractures of bone

Fatigue fractures of cortical bone involve combined axial-torsional loading yet it is unknown how the relationship between axial and torsional loadings affects the fatigue behavior of bone. In this study the effect of superimposing in-phase and out-of-phase torsional on axial loading on the fatigue behavior of bone was investigated by conducting in vitro tests involving 0 degrees and 90 degrees phase shift between cyclic torsional and axial loadings. Results obtained indicate that fatigue life, patterns of moduli loss, microcracking and modes of fractures are dependent on the phase angle between axial and torsional loadings. Specimens subjected to in-phase torsional on axial loading demonstrated greater mixed mode interaction, underwent proportionate stiffness losses in tension, compression, and torsion, and consequently had a shorter fatigue life. In contrast, specimens subjected to out-of-phase loading regime displayed a smaller contribution of mixed mode failure, underwent a disproportionately large stiffness loss in torsion, and had a longer fatigue life. Furthermore, increase in phase angle provided additional planes on which damage was diffused delaying the final failure. Change in phase angle, seen in vivo during a number of physiological activities including walking, running and sprinting, will therefore affect fatigue behavior and contribute to pathogenesis of fatigue fractures.     

The Mechanical Buckling of Curved Arteries^*

Though tortuosity and kinking are often observed in various arteries and arterioles, little is known about the underlying mechanisms. This paper presents a biomechanical analysis of bent buckling in long arterial segments with a small initial curvature using a thick-walled elastic cylindrical arterial model. The critical buckling pressure was established as a function of wall stiffness, wall dimensions, and the axial tension (or axial stretch ratio). The effects of both wall dimensions and axial stretch ratio on the critical pressure, as well as the thin-walled approximation were discussed. The buckling equation sheds light on the biomechanical mechanism of artery tortuosity and provides guidance for the development of new techniques to treat and prevent artery tortuosity and kinking.     

Experimentally validated microstructural 3D constitutive model of coronary arterial media

Accurate modeling of arterial response to physiological or pathological loads may shed light on the processes leading to initiation and progression of a number of vascular diseases and may serve as a tool for prediction and diagnosis. In this study, a microstructure based hyperelastic constitutive model is developed for passive media of porcine coronary arteries. The most general model contains 12 independent parameters representing the three-dimensional inner fibrous structure of the media and includes the effects of residual stresses and osmotic swelling. Parameter estimation and model validation were based on mechanical data of porcine left anterior descending (LAD) media under radial inflation, axial extension, and twist tests. The results show that a reduced four parameter model is sufficient to reliably predict the passive mechanical properties. These parameters represent the stiffness and the helical orientation of each lamellae fiber and the stiffness of the interlamellar struts interconnecting these lamellae. Other structural features, such as orientational distribution of helical fibers and anisotropy of the interlamellar network, as well as possible transmural distribution of structural features, were found to have little effect on the global media mechanical response. It is shown that the model provides good predictions of the LAD media twist response based on parameters estimated from only biaxial tests of inflation and extension. In addition, good predictive capabilities are demonstrated for the model behavior at high axial stretch ratio based on data of law stretches.