Biaxial elastic material properties of porcine coronary media and adventitia

The importance of mechanical stresses and strains has become well recognized in vascular physiology and pathology. To compute the stress and strain on the various components of the vessel wall, we must know the constitutive equations for the different layers of the vessel wall. The objective of the present study is to determine the constitutive equation of the coronary artery treated as a two-layer composite: intima-media and adventitial layers. Twelve hearts were obtained from a local slaughterhouse, and the right coronary artery and left anterior descending artery were dissected free from the myocardium. The vessel wall was initially mechanically tested biaxially (inflation and axial extension) as a whole (intact wall) and subsequently as intima-media or adventitial layer. A Fung-type exponential strain energy function was used to curve fit the experimental data for the intact wall and individual layers for the right coronary artery and left anterior descending artery. Two methods were used for the determination of material constants, including the Marquardt-Levenberg nonlinear least squares method and the genetic algorithm method. Our results show that there were no statistically significant differences in the material constants obtained from the two methods and that either set of elastic constants results in good fit of the data. Furthermore, at an in vivo value of axial stretch ratio, we find that the stiffness is as follows: intima-media > intact > adventitia. These results underscore the composite nature of coronary arteries with different material properties in each layer. The present results are necessary for analysis of coronary artery mechanics and to provide a fundamental understanding of vessel physiology.     

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.     

Biaxial incremental homeostatic elastic moduli of coronary artery: two-layer model

The detailed mechanical properties of various layers of the coronary artery are important for understanding the function of the vessel. The present article is focused on the determination of the incremental modulus in different layers and directions in the neighborhood of the in vivo state. The incremental modulus can be defined for any material subjected to a large deformation if small perturbations in strain lead to small perturbations of stresses in a linear fashion. This analysis was applied to the porcine coronary artery, which was treated as a two-layered structure consisting of an inner intima-media layer and an outer adventitia layer. We adopted a theory based on small-perturbation experiments at homeostatic conditions for determination of incremental moduli in circumferential, axial, and cross directions in the two layers. The experiments were based on inflation and axial stretch. We demonstrate that under homeostatic conditions the incremental moduli are layer- and direction dependent. The incremental modulus is highest in the circumferential direction. Furthermore, in the circumferential direction, the media is stiffer than the whole wall, which is stiffer than the adventitia. In the axial direction, the adventitia is stiffer than the intact wall, which is stiffer than the media. Hence, the coronary artery must be treated as a composite, nonisotropic body. The data acquire physiological relevance in relation to coronary artery health and disease.     

Regional distribution of layer-specific circumferential residual deformations and opening angles in the porcine aorta

Information on the layer-specific residual deformations of aortic tissue and how these vary throughout the vessel is important for understanding the regionally-varying aortic functions and pathophysiology, but not so much can be found in the literature. Toward this end, porcine aortas were sectioned into eighteen rings, with one ring from each anatomical position radially cut to obtain the zero-stress state for the intact wall and the other ring dissected into intimal-medial and adventitial layers; these rings were then radially cut to reach the zero-stress state for the intima-media and adventitia. Peripheral variations in internal/external circumferences, thickness, and opening angle of the intact wall and its layers were measured through image analysis at the no-load and zero-stress states. Intact wall and layer circumferences at both states significantly declined along the aorta, as did intact wall and intimal-medial but not adventitial thickness. Adventitia exhibited the greatest opening angles, approaching 180 deg all over the aorta. The opening angles of the intima-media and intact wall were quite similar, with the highest values in the ascending aorta, the lowest at the diaphragm, and increasing subsequently. Bending-related residual stretches were released by radial cutting that were compressive internally and tensile externally, displaying distinct axial variation for the intima-media and intact wall, and non-significant variation for the adventitia. Evidence is provided for the release upon layer separation of compressive stretches in the intima-media and of tensile stretches in the adventitia, whose values were smallest in the descending thoracic aorta and highest near the iliac artery bifurcation.     

The validation of a generalized Hooke's law for coronary arteries

The exponential form of constitutive model is widely used in biomechanical studies of blood vessels. There are two main issues, however, with this model: 1) the curve fits of experimental data are not always satisfactory, and 2) the material parameters may be oversensitive. A new type of strain measure in a generalized Hooke's law for blood vessels was recently proposed by our group to address these issues. The new model has one nonlinear parameter and six linear parameters. In this study, the stress-strain equation is validated by fitting the model to experimental data of porcine coronary arteries. Material constants of left anterior descending artery and right coronary artery for the Hooke's law were computed with a separable nonlinear least-squares method with an excellent goodness of fit. A parameter sensitivity analysis shows that the stability of material constants is improved compared with the exponential model and a biphasic model. A boundary value problem was solved to demonstrate that the model prediction can match the measured arterial deformation under experimental loading conditions. The validated constitutive relation will serve as a basis for the solution of various boundary value problems of cardiovascular biomechanics.     

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.     

Impact of coronary vasa vasorum functional structure on coronary vessel wall perfusion distribution

Noncoronary vasa vasorum have been described as networks of microvessels in the wall of arteries and veins. However, we have shown, using microcomputerized tomography (micro-CT) imaging methods, that porcine coronary vasa vasorum have a tree-like branching structure similar to the vasculature in general. In this study, we elucidate functional aspects of coronary vasa vasorum perfusion territories. Three pig hearts were injected with radiopaque Microfil via the coronary sinus to fill the left anterior descending coronary arteries (LADs) retrogradely at atmospheric pressure. In three other hearts, LADs were injected antegradely at 100-mmHg pressure via the left main carotid artery. Additionally, six LADs were injected in vivo with a suspension of 100- or 300-microm-diameter microspheres before harvesting of the hearts and injection of the LADs with Microfil. All harvested LADs were scanned intact with micro-CT (20 microm cubic voxels). The spatial density of vasa vasorum (no. of vasa/mm2) was measured in 20-microm-thick cross sections (at 0.4-mm intervals). Retrogradely injected LADs showed high and uniformly distributed vasa vasorum densities in the adventitia (means +/- SE; 5.38 +/- 0.09 vs. 3.58 +/- 0.1 vasa/mm2 in antegradely prepared LADs; P < 0.001). Antegradely prepared LADs showed patchy distributed, low-vasa-vasorum-density territories especially on the myocardial side of the coronary artery wall (epicardial density: 4.29 +/- 0.13 vasa/mm2 vs. myocardial density: 2.80 +/- 0.1 vasa/mm2, P < 0.001). Microembolization reduced vasa vasorum densities significantly (100-mum-diameter microspheres: 3.26 +/- 0.07 vasa/mm2, P < 0.05; 300-microm-diameter microspheres: 2.66 +/- 0.07 vasa/mm2, P < 0.001 vs. antegrade controls) and increased the size of low-vasa-vasorum-density territories. We conclude that coronary vasa vasorum are functional endarteries not connected via a plexus. This characteristic may have a significant impact on the spatial distribution of perfusion and drainage of the coronary vessel wall.     

Biomechanical properties of the layered oesophagus and its remodelling in experimental type-1 diabetes

Passive biomechanical properties in term of the stress-strain relationship and the shear modulus were studied in separated muscle layer and mucosa-submucosa layer in the oesophagus of normal and STZ (streptozotocin)-induced diabetic rats. The mucosa-submucosa and muscle layers were separated using microsurgery and studied in vitro using a self-developed test machine. Stepwise elongation and inflation plus continuous twist were applied to the samples. A constitutive equation based on a strain energy function was used for the stress-strain analysis. Five material constants were obtained for both layers. The mucosa-submucosa layer was significantly stiffer than the muscle layer in longitudinal, circumferential and circumferential-longitudinal shear direction. The mechanical constants of the oesophagus show that the oesophageal wall was anisotropic, the stiffness in the longitudinal direction was higher than in the circumferential direction in the intact oesophagus (P < 0.001) and in the muscle layer (P < 0.05). Diabetes-induced pronounced increase in the outer perimeter, inner perimeter and lumen area in both the muscle and mucosa-submucosa layer. The growth of the mucosa-submucosa layer (P < 0.001) was more pronounced than the muscle layer (P < 0.05). Furthermore, the circumferential stiffness of the mucosa-submucosa layer increased 28 days after STZ treatment. In conclusion, the oesophagus is a non-homogeneous anisotropic tube. Thus, the mechanical properties differed between layers as well as in different directions. Morphological and biomechanical remodelling is prominent in the diabetic oesophagus.     

Material parameter identification of arterial wall layers from homogenised stress-strain data

Multilayer structure of the artery can have significant effects on the resulting mechanical behaviour of the artery wall. Separation of the artery into individual layers is sometimes performed to identify the layer-specific parameters of constitutive model proposed by Holzapfel, Gasser and Ogden (HGO model). Inspired by this single-layer model, a double-layer model was formulated and used for identification of material parameters from homogenised stress-strain data (of non-separated artery wall). The paper demonstrates that the layer-specific parameters of the double-layer constitutive model can be identified without the need of artery separation. The resulting double-layer model can credibly describe the homogenised stress-strain behaviour of the real artery wall including large-strain stiffening effects attributed to multilayer nature of the artery.     

Determination of material models for arterial walls from uniaxial extension tests and histological structure

An approach is proposed that allows the determination of material models from uniaxial tests and histostructural data including fiber orientation of the tissue. A combination of neo-Hookean and Fung-type strain-energy functions is utilized, and inequality constraints imposed on the constitutive parameters are derived providing strict local convexity and preferred fiber orientations. It is shown how the Fung-type model gets a pseudo-structural aspect inherent in the phenomenological model; a correlation between the fiber structure and the parameters of the Fung-type model is explicitly provided. In order to apply the proposed approach, quasi-static uniaxial extension tests of preconditioned prepared strips from the intima, media and adventitia of a human aorta with non-atherosclerotic intimal thickening are acquired in axial and circumferential directions; structural information from histological analyses for each aortic tissue are documented. Data reveal a remarkable thickness, load-bearing capacity and stiffness of the intimal samples in comparison with the media and adventitia. Constitutive parameters for each aortic tissue layer are determined by solving the constrained problem using a penalty function method; a new approach for the estimation of appropriate start values is proposed. Finally, the predictivity and efficacy of the material models is shown by comparing model data with data from the uniaxial extension tests and histological image analyses.     

Some fibrinolytic properties of the human arteries and veins walls

The plasminogen activator of normal and atherosclerotic different arteries was studied with the histochemical method of Todd. An increase of plasminogen activator in atherosclerotic arteries of adventitia was found. The inhibition of plasmin fibrinolysis of intima-media and adventitia of normal and atherosclerotic different arteries was studied by means of the slide sandwich technique according to Noordhoek Hegt. In atherosclerotic arteries there was an increase of plasmin inhibitory activity of the intima-media layer in comparison with normal arteries. The mean plasmin inhibitory activity was higher in the vein wall of lower part of the body than in the higher one.     

Layer-specific arterial micromechanics and microstructure: Influences of age,anatomical location,and processing technique

The importance of matrix micromechanics is increasingly recognized in cardiovascular research due to the intimate role they play in local vascular cell physiology. However, variations in micromechanics among arterial layers (i.e. intima, media, adventitia), as well as dependency on local matrix composition and/or structure, anatomical location or developmental stage remain largely unknown. This study determined layer-specific stiffness in elastic arteries, including the main pulmonary artery, ascending aorta, and carotid artery using atomic force indentation. To compare stiffness with age and frozen processing techniques, neonatal and adult pulmonary arteries were tested, while fresh (vibratomed) and frozen (cryotomed) tissues were tested from the adult aorta. Results revealed that the mean compressive modulus varied among the intima, sub-luminal media, inner-middle media, and adventitia layers in the range of 1–10 kPa for adult arteries. Adult samples, when compared to neonatal pulmonary arteries, exhibited increased stiffness in all layers except adventitia. Compared to freshly isolated samples, frozen preparation yielded small stiffness increases in each layer to varied degrees, thus inaccurately representing physiological stiffness. To interpret micromechanics measurements, composition and structure analyses of structural matrix proteins were conducted with histology and multiphoton imaging modalities including second harmonic generation and two-photon fluorescence. Composition analysis of matrix protein area density demonstrated that decrease in the elastin-to-collagen and/or glycosaminoglycan-to-collagen ratios corresponded to stiffness increases in identical layers among different types of arteries. However, composition analysis was insufficient to interpret stiffness variations between layers which had dissimilar microstructure. Detailed microstructure analyses may contribute to more complete understanding of arterial micromechanics.     

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.     

Role of vasa vasorum in transendothelial solute transport in the coronary vessel wall: a study with cryostatic micro-CT

Using cryostatic microscopic computed tomography (micro-CT), we sought to determine the role of coronary vasa vasorum (VV) in transendothelial solute transport in arteries with normal and increased permeability due to high plasma cholesterol levels. In 6-mo-old pigs on a normal (n=23) and 2% high cholesterol (HC) diet (n=8), 2-cm segments of the proximal left anterior descending coronary arteries were removed in vivo after a selective injection of X-ray contrast solution. Harvesting of the specimens occurred at 0, 15, 25, 35, or 45 s after completion of the contrast injection. Specimens were snap frozen and scanned in our cryostatic micro-CT. The spatial distribution of contrast in the coronary artery wall was quantified using the CT images. Right coronary arteries were infused with Microfil to determine VV density (VV/mm2) and the cumulative lumen surface area (mm2/mm3). Transendothelial diffusion of contrast into the coronary vessel wall is a dynamic process starting at both the subintima and the adventitia. The subintimal opacification moves as a wave toward the adventitia, whereas the adventitial wave resolves. The coronary vessel wall in animals on a HC diet shows higher opacification than in normal coronary arteries without an increase of VV total luminal surface area. The loss of endothelial integrity in hypercholesterolemia significantly alters VV solute washin to, and washout from, the coronary artery wall.     

Effect of residual stress and heterogeneity on circumferential stress in the arterial wall

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

A new constitutive model for multi-layered collagenous tissues

Collagenous tissues such as the aneurysmal wall or the aorta are multi-layered structures with the mean fibre alignments distinguishing one layer from another. A constitutive representation of the multiple collagen layers is not yet developed, and hence the aim of the present study. The proposed model is based on the constitutive theory of finite elasticity and is characterized by an anisotropic strain-energy function which takes the material structure into account. The passive tissue behaviour is modelled and the related mechanical response is assumed to be dominated by elastin and collagen. While elastin is modelled by the neo-Hookean material the constitutive response of collagen is assumed to be transversely isotropic for each individual layer and based on an exponential function. The proposed constitutive function is polyconvex which ensures material stability. The model has five independent material parameters, each of which has a clear physical interpretation: the initial stiffnesses of the collagen fabric in the two principal directions, the shear modulus pertaining to the non-collagenous matrix material, a parameter describing the level of nonlinearity of the collagen fabric, and the angle between the principal directions of the collagen fabric and the reference coordinate system. An extension-inflation test of the adventitia of a human femoral artery is simulated by means of the finite element method and an error function is minimized by adjusting the material parameters yielding a good agreement between the model and the experimental data.     

Activation of G protein-coupled estrogen receptor induces endothelium-independent relaxation of coronary artery smooth muscle

Estrogens can either relax or contract arteries via rapid, nongenomic mechanisms involving classic estrogen receptors (ER). In addition to ERα and ERβ, estrogen may also stimulate G protein-coupled estrogen receptor 1 (GPER) in nonvascular tissue; however, a potential role for GPER in coronary arteries is unclear. The purpose of this study was to determine how GPER activity influenced coronary artery reactivity. In vitro isometric force recordings were performed on endothelium-denuded porcine arteries. These studies were augmented by RT-PCR and single-cell patch-clamp experiments. RT-PCR and immunoblot studies confirmed expression of GPER mRNA and protein, respectively, in smooth muscle from either porcine or human coronary arteries. G-1, a selective GPER agonist, produced a concentration-dependent relaxation of endothelium-denuded porcine coronary arteries in vitro. This response was attenuated by G15, a GPER-selective antagonist, or by inhibiting large-conductance calcium-activated potassium (BK(Ca)) channels with iberiotoxin, but not by inhibiting NO signaling. Last, single-channel patch-clamp studies demonstrated that G-1 stimulates BK(Ca) channel activity in intact smooth muscle cells from either porcine or human coronary arteries but had no effect on channels isolated in excised membrane patches. In summary, GPER activation relaxes coronary artery smooth muscle by increasing potassium efflux via BK(Ca) channels and requires an intact cellular signaling mechanism. This novel action of estrogen-like compounds may help clarify some of the controversy surrounding the vascular effects of estrogens.     

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.