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.     

Pipette aspiration technique for the measurement of nonlinear and anisotropic mechanical properties of blood vessel walls under biaxial stretch

A pipette aspiration technique was proposed for the measurement of nonlinear mechanical properties of arteries under biaxial stretching. A cross-shaped specimen of porcine thoracic aorta whose principal axes corresponded with the axial and circumferential directions of the aortic walls was excised. The intraluminal surface of the specimen was aspirated with a circular cross-sectioned glass pipette while the specimen was stretching in the axial and circumferential directions in 10% increments. The elastic modulus agreed with the incremental elastic modulus obtained through a conventional pressure-diameter test of the same specimen to within an error of 30% at a circumferential stretch ratio below 1.3 and an axial stretch ratio of 1.0, 1.1 or 1.2, which represent lower range of physiological stretch ratios for the porcine aorta. A rectangular cross-sectioned pipette was utilized to measure anisotropic properties of the specimen under biaxial stretching. When aspirated with such a pipette, the specimens' elastic properties along the length of the rectangular pipette cross section can be neglected. The elastic modulus was found to increase rapidly when the specimen was stretched in the direction of the pipette's width. Thus, pipette aspiration should have many advantages such as well measurement of the local nonlinear and anisotropic mechanical properties of blood vessel walls.     

Multiphoton microscopy observations of 3D elastin and collagen fiber microstructure changes during pressurization in aortic media

Elastin and collagen fibers play important roles in the mechanical properties of aortic media. Because knowledge of local fiber structures is required for detailed analysis of blood vessel wall mechanics, we investigated 3D microstructures of elastin and collagen fibers in thoracic aortas and monitored changes during pressurization. Using multiphoton microscopy, autofluorescence images from elastin and second harmonic generation signals from collagen were acquired in media from rabbit thoracic aortas that were stretched biaxially to restore physiological dimensions. Both elastin and collagen fibers were observed in all longitudinal–circumferential plane images, whereas alternate bright and dark layers were observed along the radial direction and were recognized as elastic laminas (ELs) and smooth muscle-rich layers (SMLs), respectively. Elastin and collagen fibers are mainly oriented in the circumferential direction, and waviness of collagen fibers was significantly higher than that of elastin fibers. Collagen fibers were more undulated in longitudinal than in radial direction, whereas undulation of elastin fibers was equibiaxial. Changes in waviness of collagen fibers during pressurization were then evaluated using 2-dimensional fast Fourier transform in mouse aortas, and indices of waviness of collagen fibers decreased with increases in intraluminal pressure. These indices also showed that collagen fibers in SMLs became straight at lower intraluminal pressures than those in EL, indicating that SMLs stretched more than ELs. These results indicate that deformation of the aorta due to pressurization is complicated because of the heterogeneity of tissue layers and differences in elastic properties of ELs, SMLs, and surrounding collagen and elastin.     

Rheological properties of the thoracic aorta in normal and WHHL rabbits

The tension-strain, stress-strain and stress relaxation curves of longitudinal and circumferential strips of proximal thoracic aortas in normal and WHHL rabbits of different ages were determined using a tensile testing instrument. Wall distensibility of longitudinal and circumferential strips was the greatest in the normal aorta and decreased with advancing age in the atherosclerotic aorta. The wall thickness of the atherosclerotic aorta was positively related to age with a correlation coefficient of 0.66(p less than 0.01). The incremental elastic moduli calculated from the stress-strain curves increased with advancing age in the atherosclerotic aorta. Accordingly, the decreased distensibility of the atherosclerotic wall may be due to the increased wall thickness caused by the intimal thickening as well as to the increase in wall stiffness caused by the increased elastic modulus. The viscoelasticity of the atherosclerotic aorta was larger than that of the normal aorta. This reflects the mechanical effect of atherosclerotic changes that occurred in the thickened intima.     

Contribution of elastin and collagen to the inflation response of the pig thoracic aorta: assessing elastin's role in mechanical homeostasis

This study was undertaken to understand elastin's role in the mechanical homeostasis of the arterial wall. The mechanical properties of elastin vary along the aorta, and we hypothesized this maintained a uniform mechanical environment for the elastin, despite regional variation in loading. Elastin's physiological loading was determined by comparing the inflation response of intact and autoclave purified elastin aortas from the proximal and distal thoracic aorta. Elastin's stretch and stress depend on collagen recruitment. Collagen recruitment started in the proximal aorta at systolic pressures (13.3 to 14.6 kPa) and in the distal at sub-diastolic pressures (9.3 to 10.6 kPa). In the proximal aorta collagen did not contribute significantly to the stress or stiffness, indicating that elastin determined the vessel properties. In the distal aorta, the circumferential incremental modulus was 70% higher than in the proximal aorta, half of which (37%) was due to a stiffening of the elastin. Compared to the elastin tissue in the proximal aorta, the distal elastin suffered higher physiological circumferential stretch (29%, P=0.03), circumferential stress (39%, P=0.02), and circumferential stiffness (37%, P=0.006). Elastin's physiological axial stresses were also higher (67%, P=0.003). These findings do not support the hypothesis that the loading on elastin is constant along the aorta as we expected from homeostasis.     

Determination of homeostatic elastic moduli in two layers of the esophagus

The function of the esophagus is mechanical. To understand the function, it is necessary to know how the stress and strain in the esophagus can be computed, and how to determine the stress-strain relationship of the wall materials. The present article is devoted to the issue of determining the incremental elastic moduli in the layers of the esophagus under homeostatic conditions. The esophagus is treated as a two-layered structure consisting of an inner collagen-rich submucosa layer and an outer muscle layer. We adopt 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 are inflation, axial stretching, circumferential bending, and axial bending. The analysis takes advantage of knowing the esophageal zero-stress state (an open sector with an opening angle of 59.4 +/- 13.2 deg). The neutral axis was located 27% +/- 1.9%away from the mucosal surface. It is demonstrated that under homeostatic conditions, the incremental moduli are layer and direction dependent. The incremental modulus is the highest in the axial direction. Furthermore, the axial moduli for the two layers are similar, whereas in the circumferential direction, the incremental modulus is a factor of 6 higher in the mucosa-submucosa layer compared to the muscle layer. Hence, the esophagus has to be treated as a composite, anisotropic body. With this additional information, we can then look forward to a vision of truly understanding the mechanical events of the esophagus.     

A biphasic, anisotropic model of the aortic wall

A biphasic, anisotropic elastic model of the aortict wall is developed and compared to literature values of experimental measurements of vessel wall radii, thickness, and hvdraulic conductivity as a function of intraluminal pressure. The model gives good predictions using a constant wall modulus for pressures less than 60 mmHg, but requires a strain-dependent modulus for pressures greater than this. In both bovine and rabbit aorta, the tangential modulus is found to be approximately 20 times greater than the radial modulus. These moduli lead to predictions that, when perfused in a cylindrical geometry, the aortic volume and its specific hydraulic coonductivity are relatively independent of perfusion pressure, in agreement with experimental measurements. M, the parameter that relates specific hydraulic conductivy, to tissue dilation, is found to be a positive quantity correcting a previous error in the literature.     

Mechanical characteristics of the canine thoracic duct: what are the driving forces of the lymph flow?

This study is designed to better understand the mode of lymph transport, particularly through the extrinsic pumping by external compression of the lymph vessel. The pressure-diameter relationship of lymphatic segments isolated from the canine thoracic duct was examined using a laser optical micrometer measurement system. Results revealed that the thoracic duct displayed a high extensibility or compliance in the physiological pressure range, yet became progressively less so with increasing internal pressure. The calculated incremental circumferential modulus of the thoracic duct under physiological pressure (range of 2 to 6 cm H2O) showed values ranging from 1.2 x 10(4) to 3.61 x 10(5) dyn/cm2. At a pressure of 35 cm H2O, the modulus reached a limiting value of approximately 6.0 x 10(6) dyn/cm2. In the physiological pressure range, the relative wall thickness (h/R0) of the canine thoracic duct was approximately 3.5%, which was much lower than that reported for canine arterial segments and similar in value to that of the canine jugular vein. In conclusion, the pressure-diameter curve of the canine thoracic duct was shown to resemble that of venous vessels. However, the circumferential elastic modulus of the thoracic duct wall was lower than the moduli of veins, proving that lymphatics are more compliant than veins. This suggests lymph flow in the thoracic duct may be better promoted by external compression of the lymphatic vessel.     

A stress-strain relation for a rat abdominal aorta

Assuming the arterial wall is homogeneous, incompressible, isotropic and elastic, a stress-strain relation has been presented for a rat's abdominal aorta. As an illustrating example, the problem of simultaneous inflation and the axial stretch of a cylindrical artery under physiological loading has been solved and then the material coefficients are determined by comparing theoretical results with the existing experiments. The result indicates that the maximum deviation between the theory and experiment for various pressure levels is 3.7% which seems to be a good approximation of theory to the experiments. The variation of circumferential stress and the incremental pressure modulus with inner pressure are also depicted in the work.     

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.     

Effect of osmolarity on the zero-stress state and mechanical properties of aorta

Some pathological conditions may affect osmolarity, which can impact cell, tissue, and organ volume. The hypothesis of this study is that changes in osmolarity affect the zero-stress state and mechanical properties of the aorta. To test this hypothesis, a segment of mouse abdominal aorta was cannulated in vivo and mechanically distended by perfusion of physiological salt (NaCl) solutions with graded osmolarities from 145 to 562 mosM. The mechanical (circumferential stress, strain, and elastic modulus) and morphological (wall thickness and wall area) parameters in the loaded state were determined. To determine the osmolarity-induced changes of zero-stress state, the opening angle was observed by immersion of the sectors of mouse, rat, and pig thoracic aorta in NaCl solution with different osmolarities. Wall volume and tissue water content of the rings were also recorded at different osmolarities. Our results show that acute aortic swelling due to low osmolarity leads to an increase in wall thickness and area, a change in the stress-strain relationship, and an increase in the elastic modulus (stiffness) in mouse aorta. The opening angle, wall volume, and water content decreased significantly with increase in osmolarity. These findings suggest that acute aortic swelling and shrinking result in immediate mechanical changes in the aorta. Osmotic pressure-induced changes in the zero-stress state may serve to regulate mechanical homeostasis.     

Isotropy and anisotropy of the arterial wall

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

Nonlinear model of human descending thoracic aortic segments with residual stresses

The nonlinear static deformation of human descending thoracic aortic segments is investigated. The aorta segments are modeled as straight axisymmetric circular cylindrical shells with three hyperelastic anisotropic layers and residual stresses by using an advanced nonlinear shell theory with higher-order thickness deformation not available in commercial finite element codes. The residual stresses are evaluated in the closed configuration in an original way making use of the multiplicative decomposition. The model was initially validated through comparison with published numerical and experimental data for artery and aorta segments. Then, two different cases of healthy thoracic descending aorta segments were numerically simulated. Material data and residual stresses used in the models came from published layer-specific experiments for human aortas. The material model adopted in the study is the mechanically based Gasser–Ogden–Holzapfel, which takes into account collagen fiber dispersion. Numerical results present a difference between systolic and diastolic inner radii close to the data available in literature from in vivo measurements for the corresponding age groups. Constant length of the aortic segment between systolic and diastolic pressures was obtained for the material model that takes the dispersion of the fiber orientations into account.     

Biomechanical and morphometric properties of the arterial wall referenced to the zero-stress state in experimental diabetes

Morphometric and passive biomechanical properties were studied in isolated segments of the thoracic and abdominal aorta, left common carotid artery, left femoral artery and the left pulmonary artery in 20 non-diabetic and 28 streptozotocin (STZ)-induced diabetic rats. The diabetic and non-diabetic rats were divided into groups living 1, 4, 8, and 12 weeks after the induction of diabetes (n = 7 for each diabetic group) or sham injection (n = 5 for each group). The mechanical test was performed as a distension experiment where the proximal end of the arterial segment was connected via a tube to the container used for applying pressures to the segment and the distal end was left free. The vessel diameter and length were obtained from digitized images of the arterial segments at pre-selected pressures and at no-load and zero-stress states. Circumferential and longitudinal stresses (force per area) and strains (deformation) were computed from the length, diameter and pressure data and from the zero-stress state data. The zero-stress state was obtained by cutting vessel rings radially causing the rings to open up into a sector. Diabetes was associated with pronounced morphometric changes, e.g., wall thickness. With respect to the biomechanical data, the opening angle increased and reached a plateau in 4 weeks after which it decreased again (p < 0.05). The opening angle was smallest in the thoracic aorta and largest in the pulmonary artery. Furthermore, it was found that the circumferential stiffness of the arteries studied increased with the duration of diabetes. In the longitudinal direction significant differences were found 8 weeks after injection of STZ in all arteries except the pulmonary artery. In the 12 weeks group, the femoral artery was stiffest in the circumferential direction whereas the thoracic aorta was stiffest in the longitudinal direction. The accumulated serum glucose level correlated with the arterial wall thickness and elastic modulus (correlation coefficient between 0.56 and 0.81).     

Dissection properties of the human aortic media: an experimental study

Aortic dissection occurs frequently and is clinically challenging; the underlying mechanics remain unclear. The present study investigates the dissection properties of the media of 15 human abdominal aortas (AAs) by means of direct tension tests (n=8) and peeling tests (n=12). The direct tension test demonstrates the strength of the media in the radial direction, while the peeling test allows a steady-state investigation of the dissection propagation. To explore the development of irreversible microscopic changes during medial dissection, histological images (n=8) from four AAs at different peeling stages are prepared and analyzed. Direct tension tests of coin-shaped medial specimens result in a radial failure stress of 140.1+/-15.9 kPa (mean+/-SD, n=8). Peeling tests of rectangular-shaped medial strips along the circumferential and axial directions provide peeling force/width ratios of 22.9+/-2.9 mN/mm (n=5) and 34.8+/-15.5 mN/mm (n=7); the related dissection energies per reference area are 5.1+/-0.6 mJ/cm(2) and 7.6+/-2.7 mJ/cm(2), respectively. Although student's t-tests indicate that force/width values of both experimental tests are not significantly different (alpha=0.05, p=0.125), the strikingly higher resisting force/width obtained for the axial peeling tests is perhaps indicative of anisotropic dissection properties of the human aortic media. Peeling in the axial direction of the aorta generates a remarkably "rougher" dissection surface with respect to the surface generated by peeling in the circumferential direction. Histological analysis of the stressed specimens reveals that tissue damage spreads over approximately six to seven elastic laminae, which is about 15-18% of the thickness of the abdominal aortic media, which forms a pronounced cohesive zone at the dissection front.     

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.     

Biaxial anisotropy of dog carotid artery: estimation of circumferential elastic modulus

Experiments were performed to study biaxial anisotropy in relaxed canine carotid arteries subjected to a wide range of longitudinal lengths and transmural pressures. In order to encompass the range of vessel lengths which occurs in situ, 120 carotid arteries were studied at 20%, 40%, 60% and 80% extension relative to retracted vessel length. These studies were performed in systematically randomized order. At each length, the vessels were pressurized in steps up to 200 mmHg transmural pressure, or until the traction force fell to zero. Results showed that longitudinal extension markedly increased the longitudinal elastic modulus, but had only a slight effect on the circumferential modulus. At physiological pressures, the vessels were nearly isotropic at about 70% longitudinal extension, but were anisotropic at shorter lengths. Estimates of the anisotropic circumferential modulus by a number of simplified methods revealed that use of a 'pressure-elastic modulus' (Ep) underestimated the anisotropic modulus by 80%, but was extremely consistent. Therefore when suitably corrected, Ep could be used to reliably estimate the anisotropic modulus of carotid arteries over a wide range of pressures and vessel lengths.     

Effects of physical exercise on the elasticity and elastic components of the rat aorta

To evaluate the effects of exercise on aortic wall elasticity and elastic components, young male rats underwent various exercise regimes for 16 weeks. In the exercised rats, the aortic incremental elastic modulus decreased significantly when under physiological strain. The aortic content of elastin increased significantly and the calcium content of elastin decreased significantly in the exercised group. The accumulated data from the exercised and sedentary groups revealed that the elastin calcium content was related positively to the incremental elastic modulus. We concluded that physical exercise from an early age decreases the calcium deposit in aortic wall elastin and that this effect probably produced in the exercised rats a distensible aorta.     

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.     

A biophysical and histological analysis of factors that lead to aortic rupture in normal and lathyritic turkeys

These experiments were designed to determine if local differences in elastic properties or wall structure contributed to the development of aortic rupture in turkeys. Static elastic properties were measured from pressure-volume curves of cylindrical segments of upper and lower thoracic aorta and innominate artery in two groups of lathyritic birds and two age-matched control groups. The biggest changes were in the young lathyritic group that was on 0.04% beta-aminoproprionitrile at 3 weeks of age and continued for 2, 3, or 4 weeks. Much smaller changes were seen in the older group that started on 0.05% beta-aminoproprionitrile at 6 weeks of age for 10 days and then 0.02% beta-aminoproprionitrile for the next 9-12 weeks. The biggest changes were seen in the abdominal aorta, which ruptured spontaneously in 50% of the young lathyritic group. The birds had a marked decrease in the number of elastin layers per unit wall thickness. Analysis of the elastic diagrams showed that the elastance of both elastin and collagen were altered in the young lathyritic group. Rupture appeared to follow partial dissection of plaques, but true longitudinal dissection did not occur.