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.     

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.     

An experimental study on the ultimate strength of the adventitia and media of human atherosclerotic carotid arteries in circumferential and axial directions

Atherosclerotic plaque may rupture without warning causing heart attack or stroke. Knowledge of the ultimate strength of human atherosclerotic tissues is essential for understanding the rupture mechanism and predicting cardiovascular events. Despite its great importance, experimental data on ultimate strength of human atherosclerotic carotid artery remains very sparse. This study determined the uniaxial tensile strength of human carotid artery sections containing type II and III lesions (AHA classifications). Axial and circumferential oriented adventitia, media and intact specimens (total=73) were prepared from 6 arteries. The ultimate strength in uniaxial tension was taken as the peak stress recorded when the specimen showed the first evidence of failure and the extensibility was taken as the stretch ratio at failure. The mean adventitia strength values calculated using the first Piola–Kirchoff stress were 1996±867 and 1802±703 kPa in the axial and circumferential directions respectively, while the corresponding values for the media sections were 519±270 and 1230±533 kPa. The intact specimens showed ultimate strengths similar to media in circumferential direction but were twice as strong as the media in the axial direction. Results also indicated that adventitia, media and intact specimens exhibited similar extensibility at failure, in both the axial and circumferential directions (stretch ratio 1.50±0.22). These measurements of the material strength limits for human atherosclerotic carotid arteries could be useful in improving computational models that assess plaque vulnerability.     

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.     

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.     

Determination of strain energy function for arterial elastin: Experiments using histology and mechanical tests

The long-range reversible deformation of vertebrate arteries is primarily mediated by elastin networks that endure several million deformation cycles without appreciable fatigue. To determine how elastin contributes to the composite arterial properties, we studied the three-dimensional microstructure and biomechanics of isolated elastin. We initially estimated the sensitivity of these studies by comparing two elastin isolation protocols, autoclaving and alkali-extraction, and measured their effect on isolated elastin using uniaxial tests and histology. These studies show that autoclaved tissues have a trend for higher modulus (900.79+/-678.02 kPa) than alkali-extracted samples (417.74+/-162.23 kPa)albeit with higher collagen-proteoglycan impurities, and (2) greater optical density (78.6+/-9.1%) than alkali-extracted groups (46.2+/-5.9%), suggesting that autoclaving is superior to alkali-extraction for biomechanical tests on elastin. Using these data we show that an isotopic Mooney-Rivlin model cannot adequately represent arterial elastin. The neo-Hookean model, with coefficient 162.57 (+/-115.44) kPa for autoclaved and 76.94 (+/-27.76) kPa for alkali-extracted samples, fits the uniaxial data better. Autoclaved elastins also show linear stress-strain response and equal stiffness in circumferential and axial directions suggesting equal number of layers in these directions and that elastin may help distribute tensile stresses during vessel inflation. Histology of autoclaved and control porcine arteries reveals axial elastin fibers in intimal and adventitial layers but circumferential medial fibers. We propose an orthotropic material symmetry for arterial elastin with two orthogonally oriented and symmetrically placed mechanically equivalent fibers. An exact form of the constitutive equation will be obtained in a future study.     

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.     

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.     

Flow-induced shear strain in intima of porcine coronary arteries.

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

Gender differences in biomechanical properties of intramural coronary resistance arteries of rats, an in vitro microarteriographic study

The prevalence of ischemic heart disease is lower in premenopausal females than in males of corresponding age. This should be related to gender differences in coronary functions. We tested whether biomechanical differences exist between intramural coronary resistance arteries of male and female rats. Intramural branches of the left anterior descending coronary artery (uniformly approximately 200microm in diameter) were isolated, cannulated and studied by microarteriography. Intraluminal pressure was increased from 2 to 90mmHg in steps and steady-state diameters were measured. Measurements were repeated in the presence of vasoconstrictor U46619 (10(-6)M) and the endothelial coronary vasodilator bradykinin (BK) (10(-6)M). Finally, passive diameters were recorded in calcium-free saline. A similar inner radius and a higher wall thickness (41.5+/-2.9microm vs. 31.4+/-2.7microm at 50mmHg in the passive condition, p<0.05) resulted in lower tangential wall stresses in male rats (18.9+/-1.9kPa vs. 24.9+/-2.5kPa at 50mmHg, p<0.05). Isobaric elastic modulus of vessels from male animals was significantly smaller at higher pressures. Vasoconstrictor response was significantly stronger in male than in female animals. Endothelial relaxations induced by BK were not different. This is the first demonstration that biomechanical characteristics of intramural coronary resistance arteries of a mammalian species are different in the male and female sexes. Higher wall thickness and higher vascular contractility in males are associated with similar endothelial function and larger high-pressure elasticity compared to females. These gender differences in biomechanics of coronary resistance arteries of rats may contribute to our better understanding the characteristic physiological and pathological differences in humans.     

Immunolocalization of collagen types I and III in the arterial wall of the rat

Summary Collagen types I and III were located by immunofluorescence procedures in the aorta and coronary arteries of the rat. Type I collagen was most prevalent in the adventitia of the aorta with only small amounts present in the intima and media. Type III collagen appeared to be a significant component in the media of the aorta and also in the adventitia of both blood vessels. The intima and media of the coronary arteries did not stain strongly for either type I or III collagen. Neither staining procedure was altered with preincubation of the sections with hyaluronidase or chondroitinase ABC. These studies indicate that type III collagen is a major component of the adventitia which has previously not been recognized by immunohistochemical techniques, possibly due to masking of collagen staining with glycosaminoglycans.     

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.     

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.     

3D computational parametric analysis of eccentric atheroma plaque: influence of axial and circumferential residual stresses

Plaque rupture plays a role in the majority of acute coronary syndromes. Rupture has usually been associated with stress concentrations, which are mainly affected by the plaque geometry and the tissue properties. The aim of this study is to evaluate the influence of morphology on the risk of plaque rupture, including the main geometrical factors, and to assess the role of circumferential and axial residual stresses by means of a parametric 3D finite element model. For this purpose, a 3D parametric finite element model of the coronary artery with eccentric atheroma plaque was developed. Healthy (adventitia and media in areas without atheroma plaque) and diseased (fibrotic and lipidic) tissues were considered in the model. The geometrical parameters used to define and design the idealized coronary plaque anatomy were the lipid core length, the stenosis ratio, the fibrous cap thickness, and the lipid core ratio. Finally, residual stresses in longitudinal and circumferential directions were incorporated into the model to analyse the influence of the important mechanical factors in the vulnerability of the plaque. Viewing the results, we conclude that residual stresses should be considered in the modelling of this kind of problems since they cause a significant alteration of the vulnerable plaque region limits. The obtained results show that the fibrous cap thickness and the lipid core length, in combination with the lipid core width, appear to be the key morphological parameters that play a determinant role in the maximal principal stress (MPS). However, the stenosis ratio is found to not play a significant role in vulnerability related to the MPS. Plaque rupture should therefore be observed as a consequence, not only of the cap thickness, but as a combination of the stenosis ratio, the fibrous cap thickness and the lipid core dimensions.     

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.     

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.     

Dynamic capacitance of epicardial coronary arteries in vivo

The dynamic capacitance of epicardial coronary arteries (i.d. greater than or equal to 0.4 mm) in vivo was assessed from the volume stiffness and volume of these arteries. The volume stiffness was derived from the pressure wave front velocity as determined in dogs by measuring the delay time between the pressure pulses recorded proximal and distal to a segment of the anterior descending branch of the left coronary artery. The pressure pulse was generated elsewhere in the arterial system during diastole. The volume of the epicardial coronary arteries was calculated from the lengths and diameters as measured in araldite casts, making corrections for in-vitro/in-vivo differences in dimensions. The dynamic capacitance of the right coronary artery, and the anterior descending and circumflex branches of the left coronary artery at an arterial pressure of 13.3 kPa and a frequency between 7 and 30 Hz was found to be 0.0024 +/- 0.0013, 0.0062 +/- 0.0028 and 0.0079 +/- 0.0035 mL/kPa (mean +/- SD), respectively. The total capacitance of the epicardial coronary arteries was calculated to be (0.007 mL/kPa)/100 g, which is small as compared to the total capacitance of the coronary vasculature, including the intramyocardial compartment, which is in the order of (0.5 mL/kPa)/100 g [1].     

Constitutive modeling of porcine coronary arteries using designed experiments

The development of new coronary artery constitutive models is of critical importance in the design and analysis of coronary replacement grafts. In this study, a two-parameter logarithmic complementary energy function, with normalized measured force and internal pressure as the independent variables and strains as the dependent variables, was developed for healthy porcine coronary arteries. Data was collected according to an experimental design with measured force ranging from 9.8 to 201 mN and internal pressure ranging from 0.1 to 16.1 kPa (1 to 121 mmHg). Comparisons of the estimated constitutive parameters showed statistically significant differences between the left anterior descending [LAD] and right coronary artery [RCA], but no differences between the LAD and left circumflex [LCX] or between the LCX and RCA. Point-by-point strain comparisons confirm the findings of the model parameter study and isolate the difference to the axial strain response. Average axial strains for the LAD, LCX, and RCA are 0.026 +/- 0.009, 0.015 +/- 0.005, and 0.011 +/- 0.009, respectively, at all physiologic loads, suggesting that the axial strains in the LAD are significantly higher than in the other regions.