Transmural strain distribution in the blood vessel wall

The transmural distributions of stress and strain at the in vivo state have important implications for the physiology and pathology of the vessel wall. The uniform transmural strain hypothesis was proposed by Takamyzawa and Hayashi (Takamizawa K and Hayashi K. J Biomech 20: 7-17, 1987; Biorheology 25: 555-565, 1988) as describing the state of arteries in vivo. From this hypothesis, they derived the residual stress and strain at the no-load condition and the opening angle at the zero-stress state. However, the experimental evidence cited by Takamyzawa and Hayashi (J Biomech 20: 7-17, 1987; and Biorheology 25: 555-565, 1988) to support this hypothesis was limited to arteries whose opening angles (theta) are <180 degrees. It is well known, however, that theta > 180 degrees do exist in the cardiovascular system. Our hypothesis is that the transmural strain distribution cannot be uniform when theta; is >180 degrees. We present both theoretical and experimental evidence for this hypothesis. Theoretically, we show that the circumferential stretch ratio cannot physically be uniform across the vessel wall when theta; exceeds 180 degrees and the deviation from uniformity will increase with an increase in theta; beyond 180 degrees. Experimentally, we present data on the transmural strain distribution in segments of the porcine aorta and coronary arterial tree. Our data validate the theoretical prediction that the outer strain will exceed the inner strain when theta > 180 degrees. This is the converse of the gradient observed when the residual strain is not taken into account. Although the strain distribution may not be uniform when theta exceeds 180 degrees, the uniformity of stress distribution is still possible because of the composite nature of the blood vessel wall, i.e., the intima-medial layer is stiffer than the adventitial layer. Hence, the larger strain at the adventitia can result in a smaller stress because the adventitia is softer at physiological 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.     

Mechanical properties of elastin along the thoracic aorta in the pig

Understanding the mechanical environment of each component within the arterial wall is fundamental for understanding vascular growth and remodelling and for engineering artificial vascular conduits. We have investigated the mechanical status of arterial elastin by measuring the circumferential mechanical properties of purified elastin as function of position along the descending thoracic aorta of the pig. The tensile circumferential secant modulus, E(sec), measured in uniaxial mechanical tests, increased 30% (P<0.001), from a value of 0.88 MPa in the proximal tissue near the aortic arch to 1.14 MPa in the distal tissue near the diaphragm, indicating the stiffness of the elastin sample increased with position. Breaking stress was 54% higher in the distal tissue compared to the proximal (P<0.001), but the breaking stretch ratio did not change. E(sec) correlated with the ratio of radius to wall thickness measured in the no load state, r(nl)/h(nl), suggesting that the rise in stiffness was linked to ring morphology. The higher stiffness and strength of the distal tissue might be explained by a higher proportion of circumferentially oriented fibres in the distal tissue, which would indicate that the elastin meshwork in the thoracic aorta may become progressively anisotropic with distance from the heart. The ratio r(nl)/(h(nl)E (sec))rose only 7%, which suggests that the in vivo circumferential strain on the elastin may be constant along the pig thoracic aorta. The positional variation in elastin's properties should be taken into account in mechanical studies on purified elastin and in mathematical models of aorta mechanics.     

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.     

Diameter-dependent axial prestretch of porcine coronary arteries and veins

The pressure-diameter relation (PDR) and the wall strain of coronary blood vessels have important implications for coronary blood flow and arthrosclerosis, respectively. Previous studies have shown that these mechanical quantities are significantly affected by the axial stretch of the vessels. The objective of this study was to measure the physiological axial stretch in the coronary vasculature; i.e., from left anterior descending (LAD) artery tree to coronary sinus vein and to determine its effect on the PDR and hence wall stiffness. Silicone elastomer was perfused through the LAD artery and coronary sinus trees to cast the vessels at the physiologic pressure. The results show that the physiological axial stretch exists for orders 4 to 11 (> 24 μm in diameter) arteries and orders -4 to -12 (>38 μm in diameter) veins but vanishes for the smaller vessels. Statistically, the axial stretch is higher for larger vessels and is higher for arteries than veins. The axial stretch λ(z) shows a linear variation with the order number (n) as: λ(z) = 0.062n + 0.75 (R(2) = 0.99) for artery and λ(z) = -0.029n + 0.89 (R(2) = 0.99) for vein. The mechanical analysis shows that the axial stretch significantly affects the PDR of the larger vessels. The circumferential stretch/strain was found to be significantly higher for the epicardial arteries (orders 9-11), which are free of myocardium constraint, than the intramyocardial arteries (orders 4-8). These findings have fundamental implications for coronary blood vessel mechanics.     

Circumferential variations of mechanical behavior of the porcine thoracic aorta during the inflation test

We developed an extension-inflation experimental apparatus with a stereo vision system and a stress-strain analysis method to determine the regional mechanical properties of a blood vessel. Seven proximal descending thoracic aortas were investigated during the inflation test at a fixed longitudinal stretch ratio of 1.35 over a transmural pressure range from 1.33 to 21.33 kPa. Four circumferential regions of each aorta were designated as the anterior (A), left lateral (L), posterior (P), and right lateral (R) regions, and the inflation test was repeated for each region of the aortas. We used continuous functions to approximate the surfaces of the regional aortic wall in the reference configuration and the deformed configuration. Circumferential stretch and stress at the four circumferential regions of the aorta were computed. Circumferential stiffness, defined as the tangent of the stress-stretch curve, and physiological aortic stiffness, named pressure-strain elastic modulus, were also computed for each region. In the low pressure range, the stress increased linearly with increased stretch, but the mechanical response became progressively stiffer in the high-pressure range above a transition point. At a transmural pressure of 12.00 kPa, mean values of stiffness were 416±104 kPa (A), 523±99 kPa (L), 634±91 kPa (P), and 489±82 kPa (R). The stiffness of the posterior region was significantly higher than that of the anterior region, but no significant difference was found in pressure-strain elastic modulus.     

Mechanical properties in the human gastric antrum using B-mode ultrasonography and antral distension

The aims of this study were to investigate gastric antral geometry and stress-strain properties by using transabdominal ultrasound scanning during volume-controlled distensions in the human gastric antrum. Seven healthy volunteers underwent stepwise inflation of a bag located in the antrum with volumes up to 60 ml. The stretch ratio and Cauchy stress and strain were calculated from measurements of pressure, diameter, and wall thickness. A second distension series was conducted in three volunteers during administration of the anticholinergic drug butylscopolamine. Analysis of stretch ratios demonstrated positive strain in the circumferential direction, negative strain in the radial direction, and no strain in the longitudinal direction. The stress-strain relation was exponential and did not differ without or with the administration of butylscopolamine. The wall stress was decomposed into its active and passive components. The well-known length-tension diagram from in vitro studies of smooth muscle strips was reproduced. The maximum active tension appeared at a volume of 50 ml, corresponding to a stretch ratio of 1.5. We conclude that the method provides measures of antral biomechanical wall properties and can be used to reproduce the muscle length-tension diagram in humans.     

Mechanotransduction and endothelial cell homeostasis: the wisdom of the cell

Vascular endothelial cells (ECs) play significant roles in regulating circulatory functions. Mechanical stimuli, including the stretch and shear stress resulting from circulatory pressure and flow, modulate EC functions by activating mechanosensors, signaling pathways, and gene and protein expressions. Mechanical forces with a clear direction (e.g., the pulsatile shear stress and the uniaxial circumferential stretch existing in the straight part of the arterial tree) cause only transient molecular signaling of pro-inflammatory and proliferative pathways, which become downregulated when such directed mechanical forces are sustained. In contrast, mechanical forces without a definitive direction (e.g., disturbed flow and relatively undirected stretch seen at branch points and other regions of complex geometry) cause sustained molecular signaling of pro-inflammatory and proliferative pathways. The EC responses to directed mechanical stimuli involve the remodeling of EC structure to minimize alterations in intracellular stress/strain and elicit adaptive changes in EC signaling in the face of sustained stimuli; these cellular events constitute a feedback control mechanism to maintain vascular homeostasis and are atheroprotective. Such a feedback mechanism does not operate effectively in regions of complex geometry, where the mechanical stimuli do not have clear directions, thus placing these areas at risk for atherogenesis. The mechanotransduction-induced EC adaptive processes in the straight part of the aorta represent a case of the "Wisdom of the Cell," as a part of the more general concept of the "Wisdom of the Body" promulgated by Cannon, to maintain cellular homeostasis in the face of external perturbations.     

Age dependency of the biaxial biomechanical behavior of human abdominal aorta

BACKGROUND: The biomechanical behavior of the human abdominal aorta has been studied with great interest primarily due to its propensity to develop such maladies as atherosclerotic occlusive disease, dissections, and aneurysms. The purpose of this study was to investigate the age-related biaxial biomechanical behavior of human infrarenal aortic tissue. METHODS OF APPROACH: A total of 18 samples (13 autopsy, 5 organ donor) were harvested from patients in each of three age groups: Group 1 (<30 years old, n=5), Group 2 (between 30 and 60 years old, n=7), and Group 3 (>60 years old, n=6). Each specimen was tested biaxially using a tension-controlled protocol which spanned a large portion of the strain plane. Response functions fit to experimental data were used as a tool to guide the appropriate choice of the strain energy function W. RESULTS: Under an equibiaxial tension of 120 N/m, the average peak stretch values in the circumferential direction for Groups 1, 2, and 3 were (mean +/-SD) 1.46 +/- 0.07, 1.15 +/- 0.07, and 1.11 +/- 0.06, respectively, while the peak stretch values in the longitudinal direction were 1.41 +/- 0.03, 1.19 +/- 0.11, and 1.10 +/- 0.04, respectively. There were no significant differences between the average longitudinal and circumferential peak stretch within each group (p > 0.1), but both of these values were significantly less (p < 0.001) for Groups 2 and 3 when compared to Group 1. Patients in Group 1 were modeled using a polynomial strain energy function W, while patients in Groups 2 and 3 were modeled using an exponential form of W, suggesting an age-dependent shift in the mechanical response of this tissue. CONCLUSION: The biaxial tensile testing results reported here are, to our knowledge, the first given for the human infrarenal aorta and reinforce the importance of determining the functional form of W from experimental data. Such information may be useful for the clinician or researcher in identifying key changes in the biomechanical response of abdominal aorta in the presence of an aneurysm.     

Molecular basis of rheological modulation of endothelial functions: importance of stress direction

Vascular endothelial cells (EC) play significant roles in regulating circulatory functions. Shear stress and stretch can modulate EC functions by activating mechano-sensors, signaling pathways, and gene and protein expressions. Laminar shear stress with a significant forward direction causes transient activations of monocyte chemotactic protein-1 (MCP-1), sterol response element binding protein (SREBP), and proliferative genes. Sustained laminar shear stress down-regulates these genes and up-regulates genes that inhibit EC growth. In EC subjected to complex flow patterns with little forward direction, activations of MCP-1, SREBP, and proliferation genes become sustained, and mitosis and apoptosis are enhanced. Cyclic uniaxial stretch causes actin stress fibers to orient perpendicular to stretch direction, with a consequent reduction of intracellular stress, transient JNK activation, and protection of EC against apoptosis. Cyclic biaxial stretch without a preferred direction has opposite effects. In the straight part of arterial tree, laminar shear stress with a net forward direction and uniaxial strain in the circumferential direction have anti-atherogenic effects. At vascular branch points, the complex shear flow and mechanical strain with little net direction are atherogenic. Therefore, the direction of stress has important influences on the biorheological effects of flow and deformation on vascular endothelium in health and disease.     

A comparison of biomechanical properties between human and porcine cornea

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

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.     

Active axial stress in mouse aorta

The study verifies the development of active axial stress in the wall of mouse aorta over a range of physiological loads when the smooth muscle cells are stimulated to contract. The results obtained show that the active axial stress is virtually independent of the magnitude of pressure, but depends predominately on the longitudinal stretch ratio. The dependence is non-monotonic and is similar to the active stress-stretch dependence in the circumferential direction reported in the literature. The expression for the active axial stress fitted to the experimental data shows that the maximum active stress is developed at longitudinal stretch ratio 1.81, and 1.56 is the longitudinal stretch ratio below which the stimulation does not generate active stress. The study shows that the magnitude of active axial stress is smaller than the active circumferential stress. There is need for more experimental investigations on the active response of different types of arteries from different species and pathological conditions. The results of these studies can promote building of refined constrictive models in vascular rheology.     

Mechanical behavior of human aortas: Experiments,material constants and 3-D finite element modeling including residual stress

Segments of fresh human ascending, thoracic descending and abdominal aortas from eight male sexagenarians were pressurized under closed-end and free extension conditions. The median unpressurized inner radii for the ascending, thoracic and abdominal locations were 14.21, 9.67 and 7.16 mm, respectively. The median thickness was similar in the ascending and thoracic regions, at about 1.6 mm, while it was 1.2 mm in the abdominal region. The opening angle was not statistically different between regions, with a median of ?38°. Under 13.3 kPa pressure, the median circumferential stretch ratio was about 1.26 in all three aortic locations; the median longitudinal stretch ratio was similar in the ascending and thoracic regions, at about 1.13, while it was 1.05 in the abdominal region. Material constants for a three-dimensional hyperelastic anisotropic constitutive model were determined. Experimental, analytical and finite element results showed excellent agreement, validating the novel experimental approach and the numerical methods used. When residual stress was not taken into account, stresses were highest on the inside of the aorta, with a gradient across the wall of about 200 and 50 kPa in the circumferential and longitudinal directions, respectively. When residual stress was included as described by negative opening angles, stresses were highest on the outside of the aorta, with a gradient across the wall in excess of 400 kPa for the circumferential direction, and on the order of 150 kPa for the longitudinal direction. The mechanical consequences of negative opening angles had not been appreciated so far, and deserve further investigation.     

Measurement of strain in the left ventricle during diastole with cine-MRI and deformable image registration

The assessment of regional heart wall motion (local strain) can localize ischemic myocardial disease, evaluate myocardial viability, and identify impaired cardiac function due to hypertrophic or dilated cardiomyopathies. The objectives of this research were to develop and validate a technique known as hyperelastic warping for the measurement of local strains in the left ventricle from clinical cine-magnetic resonance imaging (MRI) image datasets. The technique uses differences in image intensities between template (reference) and target (loaded) image datasets to generate a body force that deforms a finite element (FE) representation of the template so that it registers with the target image. To validate the technique, MRI image datasets representing two deformation states of a left ventricle were created such that the deformation map between the states represented in the images was known. A beginning diastolic cine-MRI image dataset from a normal human subject was defined as the template. A second image dataset (target) was created by mapping the template image using the deformation results obtained from a forward FE model of diastolic filling. Fiber stretch and strain predictions from hyperelastic warping showed good agreement with those of the forward solution (R2=0.67 stretch, R2=0.76 circumferential strain, R2=0.75 radial strain, and R2=0.70 in-plane shear). The technique had low sensitivity to changes in material parameters (deltaR2= -0.023 fiber stretch, deltaR2=-0.020 circumferential strain, deltaR2=-0.005 radial strain, and deltaR2=0.0125 shear strain with little or no change in rms error), with the exception of changes in bulk modulus of the material. The use of an isotropic hyperelastic constitutive model in the warping analyses degraded the predictions of fiber stretch. Results were unaffected by simulated noise down to a signal-to-noise ratio (SNR) of 4.0 (deltaR2= -0.032 fiber stretch, deltaR2=-0.023 circumferential strain, deltaR2=-0.04 radial strain, and deltaAR2=0.0211 shear strain with little or no increase in rms error). This study demonstrates that warping in conjunction with cine-MRI imaging can be used to determine local ventricular strains during diastole.     

Shear Stress and Cyclic Circumferential Stretch, But Not Pressure, Alter Connexin43 Expression in Endothelial Cells

Hemodynamic forces play a critical role in atherogenesis, as evidenced by the focal pattern of development of atherosclerotic lesions. Whereas disturbed flow in the branches and curved regions of large arteries is proatherogenic, laminar flow in the straight parts of vessels is atheroprotective. In addition, hypertension and age-related changes in arterial stiffness are important risk factors of the disease. Hemodynamic forces induce various changes in the structure and function of vascular endothelium, many of which reflect alterations in gene expression. Endothelial cells are linked by gap junctions, which facilitate the propagation of electrical and chemical signals along the vascular wall. Using an in vitro perfusion system, we investigated the effects of pulsed unidirectional and oscillatory flows in combination with different levels of hydrostatic pressure and circumferential stretch on the expression of Cx43 in endothelial cells. Our results show that shear stress and circumferential stretch, but not pressure, modulate the expression of Cx43. In view of the distribution of this protein along the vascular tree, our findings provide new insights into the role of mechanical forces on gap junctional communication in regions prone to the development of atherosclerosis.     

Shear stress and cyclic circumferential stretch, but not pressure, alter connexin43 expression in endothelial cells

Hemodynamic forces play a critical role in atherogenesis, as evidenced by the focal pattern of development of atherosclerotic lesions. Whereas disturbed flow in the branches and curved regions of large arteries is proatherogenic, laminar flow in the straight parts of vessels is atheroprotective. In addition, hypertension and age-related changes in arterial stiffness are important risk factors of the disease. Hemodynamic forces induce various changes in the structure and function of vascular endothelium, many of which reflect alterations in gene expression. Endothelial cells are linked by gap junctions, which facilitate the propagation of electrical and chemical signals along the vascular wall. Using an in vitro perfusion system, we investigated the effects of pulsed unidirectional and oscillatory flows in combination with different levels of hydrostatic pressure and circumferential stretch on the expression of Cx43 in endothelial cells. Our results show that shear stress and circumferential stretch, but not pressure, modulate the expression of Cx43. In view of the distribution of this protein along the vascular tree, our findings provide new insights into the role of mechanical forces on gap junctional communication in regions prone to the development of atherosclerosis.     

Site specific inelasticity of arterial tissue

Understanding the mechanical behaviour of arterial tissue is vital to the development and analysis of medical devices targeting diseased vessels. During angioplasty and stenting, stress softening and permanent deformation of the vessel wall occur during implantation of the device, however little data exists on the inelastic behaviour of cardiovascular tissue and how this varies through the arterial tree. The aim of this study was to characterise the magnitude of stress softening and inelastic deformations due to loading throughout the arterial tree and to investigate the anisotropic inelastic behaviour of the tissue. Cyclic compression tests were used to investigate the differences in inelastic behaviour for carotid, aorta, femoral and coronary arteries harvested from 3-4 month old female pigs, while the anisotropic behaviour of aortic and carotid tissue was determined using cyclic tensile tests in the longitudinal and circumferential directions. The differences in inelastic behaviour were correlated to the ratio of collagen to elastin content of the arteries. It was found that larger inelastic deformations occurred in muscular arteries (coronary), which had a higher collagen to elastin ratio than elastic arteries (aorta), where the smallest inelastic deformations were observed. Lower magnitude inelastic deformations were observed in the circumferential tensile direction than in the longitudinal tensile direction or due to radial compression. This may be as a result of non-collagenous components in the artery becoming more easily damaged than the collagen fibres during loading. Stress softening was also found to be dependent on artery type. In the future, computational models should consider such site dependant, anisotropic inelastic behaviour in order to better predict the outcomes of interventional procedures such as angioplasty and stenting.     

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 study on large radial motion of arteries in vivo

This study analyses the radial periodic motion of an artery which is modelled as a thin cylinder of uniform cross-section subjected to dynamic inner pressure using the theory of finite deformation of elastic materials. The arterial tissue properties (anisotropy, homogeneity and incompressibility) are taken into account in an analysis based on the use of the strain energy function. The validity of the mathematical analysis is illustrated through numerical computation applying the available in vivo data for elastic constants of the canine middle descending thoracic aorta to the expressions for the intramural pressure and circumferential stresses obtained by solving the necessary equation of motion together with the boundary conditions. Results obtained in this study indicate very low stresses which suggest that the arteriosclerosis resulting from high stress gradients is effectively ruled out in this model.