Analysis of the passive mechanical properties of rat carotid arteries

The passive mechanical properties of rat carotid arteries were studied in vitro. Using a tensile testing machine and a piston pump, intact segments of carotid arteries were subjected to large deformations both in the longitudinal and circumferential directions. Internal pressure, external diameter, length and longitudinal force were measured during the experiment and compared with the in vivo dimensions of the segments prior to excision. The anisotropic mechanical properties of the vessel wall material were analyzed using incremental elastic moduli and incremental Poisson's ratios. The results suggest that there is a characteristic deformation pattern common to all vessels investigated which is highly correlated with the conditions of loading that occur in vivo. That is, under average physiological deformation of the vessel, the longitudinal force is nearly independent of internal pressure. In this range of loading the circumferential incremental elastic modulus is nearly independent of longitudinal strain. However, the longitudinal and radial incremental elastic moduli vary significantly with deformation in this direction. The values of the moduli in all three directions increase with raising internal pressure. The weak coupling between circumferential and longitudinal direction in the wall material of carotid arteries is shown by the small value of the corresponding incremental Poisson's ratios.     

On parameter estimation for biaxial mechanical behavior of arteries

This article considers the parameter estimation of multi-fiber family models for biaxial mechanical behavior of passive arteries in the presence of the measurement errors. First, the uncertainty propagation due to the errors in variables has been carefully characterized using the constitutive model. Then, the parameter estimation of the artery model has been formulated into nonlinear least squares optimization with an appropriately chosen weight from the uncertainty model. The proposed technique is evaluated using multiple sets of synthesized data with fictitious measurement noises. The results of the estimation are compared with those of the conventional nonlinear least squares optimization without a proper weight factor. The proposed method significantly improves the quality of parameter estimation as the amplitude of the errors in variables becomes larger. We also investigate model selection criteria to decide the optimal number of fiber families in the multi-fiber family model with respect to the experimental data balancing between variance and bias errors.     

Differential passive and active biaxial mechanical behaviors of muscular and elastic arteries: basilar versus common carotid

Cerebrovascular disease continues to be responsible for significant morbidity and mortality. There is, therefore, a pressing need to understand better the biomechanics of both intracranial arteries and the extracranial arteries that feed these vessels. We used a validated four-fiber family constitutive relation to model passive biaxial stress-stretch behaviors of basilar and common carotid arteries and we developed a new relation to model their active biaxial responses. These data and constitutive relations allow the first full comparison of circumferential and axial biomechanical behaviors between a muscular (basilar) and an elastic (carotid) artery from the same species. Our active model describes the responses by both types of vessels to four doses of the vasoconstrictor endothelin-1 (10(-10)M, 10(-9)M, 10(-8)M, and 10(-7)M) and predicts levels of smooth muscle cell activation associated with basal tone under specific in vitro testing conditions. These results advance our understanding of the biomechanics of intracranial and extracranial arteries, which is needed to understand better their differential responses to similar perturbations in hemodynamic loading.     

Linked mechanical and biological aspects of remodeling in mouse pulmonary arteries with hypoxia-induced hypertension

Supravalvular aortic stenosis (SVAS) is associated with decreased elastin and altered arterial mechanics. Mice with a single deletion in the elastin gene (ELN(+/-)) are models for SVAS. Previous studies have shown that elastin haploinsufficiency in these mice causes hypertension, decreased arterial compliance, and changes in arterial wall structure. Despite these differences, ELN(+/-) mice have a normal life span, suggesting that the arteries remodel and adapt to the decreased amount of elastin. To test this hypothesis, we performed in vitro mechanical tests on abdominal aorta, ascending aorta, and left common carotid artery from ELN(+/-) and wild-type (C57BL/6J) mice. We compared the circumferential and longitudinal stress-stretch relationships and residual strains. The circumferential stress-stretch relationship is similar between genotypes and changes <3% with longitudinal stretch at lengths within 10% of the in vivo value. At mean arterial pressure, the circumferential stress in the ascending aorta is higher in ELN(+/-) than in wild type. Although arterial pressures are higher, the increased number of elastic lamellae in ELN(+/-) arteries results in similar tension/lamellae compared with wild type. The longitudinal stress-stretch relationship is similar between genotypes for most arteries. Compared with wild type, the in vivo longitudinal stretch is lower in ELN(+/-) abdominal and carotid arteries and the circumferential residual strain is higher in ELN(+/-) ascending aorta. The increased circumferential residual strain brings the transmural strain distribution in ELN(+/-) ascending aorta close to wild-type values. The mechanical behavior of ELN(+/-) arteries is likely due to the reduced elastin content combined with adaptive remodeling during vascular development.     

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 and passive properties of carotid arteries]

A mathematical model of carotid arteries is constructed from the known experimental data. Passive properties of the vascular wall are characterized by an alternating module of elasticity, the active ones by the specific power of muscle contraction. Its maximum value (0,023 n/m-3) is shown to be reached with intravascular pressure 190 mm Hg. The dependence of inner radius on the power of muscle contraction is studied at different values of intravascular pressure. It is shown that theactive properties of carotid arteries are essentially determined by their passive properties and depend on the stretching of the vessel wall.     

Biomechanical properties of canine vertebral and internal carotid arteries

In order to understand the participation of the geometrical and elastic properties of the large cerebral arteries in the maintenance of brain circulatory homeostasis, biomechanical properties of isolated internal carotid artery (extracranial part) and vertebral artery (intrathoracic part) were investigated both in a relaxed and in an activated (3x 10(-6) mol.l-1 norepinephrine) state of the smooth muscle. Quasi-static large deformation mechanical test was carried out by means of changing the intraluminal pressure slowly (2.5 mmHg.sec-1) and cyclicly in a range of 0-250 mmHg at in vivo length while external diameter was recorded continuously as a function of the intraluminal pressure. Maximum active tangential strain was found to be -2.7 +/- 1.6% at 70 mmHg for the internal carotid artery, and -5.9 +/- 1.1% at 100 mmHg for the vertebral artery. Incremental elastic modulus decreased and distensibility increased in both arteries following smooth muscle activation, these alterations, however, were larger in the case of the vertebral artery. A U-shaped characteristic impedance of vertebral artery was found both in relaxed and in constricted states of this vessel. Minimum values for the relaxed and the activated segments were found at 90 mmHg and 120 mmHg, respectively. These results support the hypothesis that certain biomechanical properties of the large arteries, like impedance, can be regarded as controlled variables that may contribute to the optimization of circulatory functions.     

Effects of collagen deposition on passive and active mechanical properties of large pulmonary arteries in hypoxic pulmonary hypertension

Proximal pulmonary artery (PA) stiffening is a strong predictor of mortality in pulmonary hypertension. Collagen accumulation is mainly responsible for PA stiffening in hypoxia-induced pulmonary hypertension (HPH) in mouse models. We hypothesized that collagen cross-linking and the type I isoform are the main determinants of large PA mechanical changes during HPH, which we tested by exposing mice that resist type I collagen degradation (Col1a1 $^\mathrm{R/R})$ and littermate controls (Col1a1 $^{+/+})$ to hypoxia for 10 days with or without $\beta $ -aminopropionitrile (BAPN) treatment to prevent cross-link formation. Static and dynamic mechanical tests were performed on isolated PAs with smooth muscle cells (SMC) in passive and active states. Percentages of type I and III collagen were quantified by histology; total collagen content and cross-linking were measured biochemically. In the SMC passive state, for both genotypes, hypoxia tended to increase PA stiffness and damping capacity, and BAPN treatment limited these increases. These changes were correlated with collagen cross-linking ( $p<0.05$ ). In the SMC active state, hypoxia increased PA dynamic stiffness and BAPN had no effect in Col1a1 $^{+/+}$ mice ( $p<0.05$ ). PA stiffness did not change in Col1a1 $^\mathrm{R/R}$ mice. Similarly, damping capacity did not change for either genotype. Type I collagen accumulated more in Col1a1 $^{+/+}$ mice, whereas type III collagen increased more in Col1a1 $^\mathrm{R/R}$ mice during HPH. In summary, PA passive mechanical properties (both static and dynamic) are related to collagen cross-linking. Type I collagen turnover is critical to large PA remodeling during HPH when collagen metabolism is not mutated and type III collagen may serve as a reserve.     

Effect of cigarette smoking on nitric oxide, structural, and mechanical properties of mouse arteries

Cigarette smoking (CS) is a major risk factor for vascular disease. The aim of this study was to quantitatively assess the influence of CS on mouse arteries. We studied the effect of short-term (6 wk) and long-term (16 wk) CS exposure on structural and mechanical properties of coronary arteries compared with that of control mice. We also examined the reversibility of the deleterious effects of CS on structural [e.g., wall thickness (WT)], mechanical (e.g., stiffness), and biochemical [e.g., nitric oxide (NO) by-products] properties with the cessation of CS. The left and right coronary arteries were cannulated in situ and mechanically distended. The stress, strain, elastic modulus, and WT of coronary arteries were determined. Western blot analysis was used to analyze endothelial NO synthase (eNOS) in the femoral and carotid arteries of the same mice, and NO by-products were determined by measuring the levels of nitrite. Our results show that the mean arterial pressure was increased by CS. Furthermore, CS significantly increased the elastic modulus, decreased stress and strain, and increased the WT and WT-to-radius ratio compared with those of control mice. The reduction of eNOS protein expression was found only after long-term CS exposure. Moreover, the NO metabolite was markedly decreased in CS mice after short- and long-term exposure of CS. These findings suggest that 16 wk of CS exposure can cause an irreversible deterioration of structural and elastic properties of mouse coronary arteries. The decrease in endothelium-derived NO in CS mice was seen to significantly correlate with the remodeling of arterial wall.     

Studies of biaxial mechanical properties and nonlinear finite element modeling of skin

The objective of this research is to conduct mechanical property studies of skin from two individual but potentially connected aspects. One is to determine the mechanical properties of the skin experimentally by biaxial tests, and the other is to use the finite element method to model the skin properties. Dynamic biaxial tests were performed on 16 pieces of abdominal skin specimen from rats. Typical biaxial stress-strain responses show that skin possesses anisotropy, nonlinearity and hysteresis. To describe the stress-strain relationship in forms of strain energy function, the material constants of each specimen were obtained and the results show a high correlation between theory and experiments. Based on the experimental results, a finite element model of skin was built to model the skin's special properties including anisotropy and nonlinearity. This model was based on Arruda and Boyce's eight-chain model and Bischoff et al.'s finite element model of skin. The simulation results show that the isotropic, nonlinear eight-chain model could predict the skin's anisotropic and nonlinear responses to biaxial loading by the presence of an anisotropic prestress state.     

Constitutive modeling of mouse carotid arteries using experimentally measured microstructural parameters

Changes in the local mechanical environment and tissue mechanical properties affect the biological activity of cells and play a key role in a variety of diseases, such as cancer, arthritis, nephropathy, and cardiovascular disease. Constitutive relations have long been used to predict the local mechanical environment within biological tissues and to investigate the relationship between biological responses and mechanical stimuli. Recent constitutive relations for soft tissues consider both material and structural properties by incorporating parameters that describe microstructural organization, such as fiber distributions, fiber angles, fiber crimping, and constituent volume fractions. The recently developed technique of imaging the microstructure of a single artery as it undergoes multiple deformations provides quantitative structural data that can reduce the number of estimated parameters by using parameters that are truly experimentally intractable. Here, we employed nonlinear multiphoton microscopy to quantify collagen fiber organization in mouse carotid arteries and incorporated measured fiber distribution data into structurally motivated constitutive relations. Microscopy results demonstrate that collagen fibers deform in an affine manner over physiologically relevant deformations. The incorporation of measured fiber angle distributions into constitutive relations improves the model's predictive accuracy and does not significantly reduce the goodness of fit. The use of measured structural parameters rather than estimated structural parameters promises to improve the predictive capabilities of the local mechanical environment, and to extend the utility of intravital imaging methods for estimating the mechanical behavior of tissues using in situ structural information.     

Comparative analysis of the biaxial mechanical behavior of carotid wall tissue and biological and synthetic materials used for carotid patch angioplasty

Patch angioplasty is the most common technique used for the performance of carotid endarterectomy. A large number of patching materials are available for use while new materials are being continuously developed. Surprisingly little is known about the mechanical properties of these materials and how these properties compare with those of the carotid artery wall. Mismatch of the mechanical properties can produce mechanical and hemodynamic effects that may compromise the long-term patency of the endarterectomized arterial segment. The aim of this paper was to systematically evaluate and compare the biaxial mechanical behavior of the most commonly used patching materials. We compared PTFE (n = 1), Dacron (n = 2), bovine pericardium (n = 10), autogenous greater saphenous vein (n = 10), and autogenous external jugular vein (n = 9) with the wall of the common carotid artery (n = 18). All patching materials were found to be significantly stiffer than the carotid wall in both the longitudinal and circumferential directions. Synthetic patches demonstrated the most mismatch in stiffness values and vein patches the least mismatch in stiffness values compared to those of the native carotid artery. All biological materials, including the carotid artery, demonstrated substantial nonlinearity, anisotropy, and variability; however, the behavior of biological and biologically-derived patches was both qualitatively and quantitatively different from the behavior of the carotid wall. The majority of carotid arteries tested were stiffer in the circumferential direction, while the opposite anisotropy was observed for all types of vein patches and bovine pericardium. The rates of increase in the nonlinear stiffness over the physiological stress range were also different for the carotid and patching materials. Several carotid wall samples exhibited reverse anisotropy compared to the average behavior of the carotid tissue. A similar characteristic was observed for two of 19 vein patches. The obtained results quantify, for the first time, significant mechanical dissimilarity of the currently available patching materials and the carotid artery. The results can be used as guidance for designing more efficient patches with mechanical properties resembling those of the carotid wall. The presented systematic comparative mechanical analysis of the existing patching materials provides valuable information for patch selection in the daily practice of carotid surgery and can be used in future clinical studies comparing the efficacy of different patches in the performance of carotid endarterectomy.     

Quantification of the mechanical properties of noncontracting canine myocardium under simultaneous biaxial loading

Detailed understanding of cardiac mechanics depends upon accurate and complete characterization of the three-dimensional properties of both normal and diseased myocardial tissue. This, however, can only be obtained by performing multiaxial tests on cardiac tissue. In this study we subjected thin sheets of passive canine left ventricular myocardium to various combinations of simultaneous biaxial stretching. During each stretch the ratio of the orthogonal strains was kept constant and the corresponding stresses remained proportional. We fitted the biaxial stress-strain data both with exponential strain-energy functions with quadratic powers of strains as well as with an alternative function with nonintegral powers of strains. We used our recently developed nonparametric method to assess the reliability of the coefficients for each of these functions. The quadratic strain-energy functions resulted in wide intra- and interspecimen variability in the coefficients. Moreover, both their absolute and relative values demonstrated marked load history dependence such that interpretation of the direction of anisotropy was difficult. Fitting the data with the alternative nonintegral strain-energy function seemed to alleviate these problems. This alternative strain-energy function may provide more self-consistent results than the more commonly used quadratic strain-energy functions.     

On the biaxial mechanical properties of the layers of the aortic valve leaflet

All existing constitutive models for heart valve leaflet tissues either assume a uniform transmural stress distribution or utilize a membrane tension formulation. Both approaches ignore layer specific mechanical contributions and the implicit nonuniformity of the transmural stress distribution. To begin to address these limitations, we conducted novel studies to quantify the biaxial mechanical behavior of the two structurally distinct, load bearing aortic valve (AV) leaflet layers: the fibrosa and ventricularis. Strip biaxial tests, with extremely sensitive force sensing capabilities, were further utilized to determine the mechanical behavior of the separated ventricularis layer at very low stress levels. Results indicated that both layers exhibited very different nonlinear, highly anisotropic mechanical behaviors. While the leaflet tissue mechanical response was dominated by the fibrosa layer, the ventricularis contributed double the amount of the fibrosa to the total radial tension and experienced four times the stress level. The strip biaxial test results further indicated that the ventricularis exhibited substantial anisotropic mechanical properties at very low stress levels. This result suggested that for all strain levels, the ventricularis layer is dominated by circumferentially oriented collagen fibers, and the initial loading phase of this layer cannot be modeled as an isotropic material. Histological-based thickness measurements indicated that the fibrosa and ventricularis constitute 41% and 29% of the total layer thickness, respectively. Moreover, the extensive network of interlayer connections and identical strains under biaxial loading in the intact state suggests that these layers are tightly bonded. In addition to advancing our knowledge of the subtle but important mechanical properties of the AV leaflet, this study provided a comprehensive database required for the development of a true 3D stress constitutive model for the native AV leaflet.     

Biaxial biomechanical adaptations of mouse carotid arteries cultured at altered axial extension

Many have studied the roles of altered blood flow and pressure on adaptive responses of blood vessels, but few have studied the role of altered axial loads. We exposed common carotid arteries from wild-type mice to low, medium, or high axial extensions while maintaining the same pressure and luminal flow rate for two days in culture, and studied adaptations in vessel geometry, in vitro loads, and stresses while collecting biaxial biomechanical (pressure-diameter and axial force-length) data on Day 0 (initial control conditions), Day 1, and Day 2. In addition, we compared vasoreactive responses to phenylephrine, carbamylcholine chloride, and sodium nitroprusside at the end of the 2-day culture period. We found significant differences in the structural (e.g., pressure-axial force and axial force-length) responses between groups as well as within each group over time. These adaptations seem to be aimed at restoring the mechanical state from a perturbed condition (e.g., low or high axial extension) toward a normal 'homeostatic' condition. Although structural responses (e.g., pressure-axial force and axial force-length) differed between groups on Day 2, the material behavior (e.g., circumferential and axial stress-stretch responses) did not differ significantly between groups.     

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.     

Differential mechanical response and microstructural organization between non-human primate femoral and carotid arteries

Unique anatomic locations and physiologic functions predispose different arteries to varying mechanical responses and pathologies. However, the underlying causes of these mechanical differences are not well understood. The objective of this study was to first identify structural differences in the arterial matrix that would account for the mechanical differences between healthy femoral and carotid arteries and second to utilize these structural observations to perform a microstructurally motivated constitutive analysis. Femoral and carotid arteries were subjected to cylindrical biaxial loading and their microstructure was quantified using two-photon microscopy. The femoral arteries were found to be less compliant than the carotid arteries at physiologic loads, consistent with previous studies, despite similar extracellular compositions of collagen and elastin ( \(P> 0.05\) ). The femoral arteries exhibited significantly less circumferential dispersion of collagen fibers ( \(P< 0.05\) ), despite a similar mean fiber alignment direction as the carotid arteries. Elastin transmural distribution, in vivo axial stretch, and opening angles were also found to be distinctly different between the arteries. Lastly, we modeled the arteries’ mechanical behaviors using a microstructural-based, distributed collagen fiber constitutive model. With this approach, the material parameters of the model were solved using the experimental microstructural observations. The findings of this study support an important role for microstructural organization in arterial stiffness.