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.     

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.     

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.     

An in vivo parameter identification method for arteries: numerical validation for the human abdominal aorta

A method for identifying mechanical properties of arterial tissue in vivo is proposed in this paper and it is numerically validated for the human abdominal aorta. Supplied with pressure-radius data, the method determines six parameters representing relevant mechanical properties of an artery. In order to validate the method, 22 finite element arteries are created using published data for the human abdominal aorta. With these in silico abdominal aortas, which serve as mock experiments with exactly known material properties and boundary conditions, pressure-radius data sets are generated and the mechanical properties are identified using the proposed parameter identification method. By comparing the identified and pre-defined parameters, the method is quantitatively validated. For healthy abdominal aortas, the parameters show good agreement for the material constant associated with elastin and the radius of the stress-free state over a large range of values. Slightly larger discrepancies occur for the material constants associated with collagen, and the largest relative difference is obtained for the in situ axial prestretch. For pathological abdominal aortas incorrect parameters are identified, but the identification method reveals the presence of diseased aortas. The numerical validation indicates that the proposed parameter identification method is able to identify adequate parameters for healthy abdominal aortas and reveals pathological aortas from in vivo-like data.     

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.     

Passive elastic properties of the rat aorta

The passive anisotropic elastic properties of rat's aorta were studied in vitro by subjecting cylindrical segments of thoracic and abdominal aorta to a wide range of deformations. Using data on pressure, axial stretch, outer diameter, axial force and wall thickness, incremental moduli of elasticity in the circumferential, axial and radial directions were computed. Results indicate that while the elastic behavior of the aortic wall is globally anisotropic, there exists a state of deformation at which the vessel displays incremental isotropy. This state of deformation corresponds approximately to the loading conditions to which the aorta is exposed in situ. Values of the moduli, analyzed as a function of transmural pressure, show that the stiffness of the aortic wall is fairly constant at low pressures but raises steeply for pressures higher than physiological. For axial stretches as occurring in situ, the magnitudes of the circumferential and radial moduli do not differ significantly for the thoracic aorta; hence this vessel can be regarded as transversely isotropic over a wide range of pressures. The same observation is valid also for the abdominal aorta when pressures equal or smaller than physiological are considered. For both the thoracic and abdominal segments of the aorta, the circumferential and radial moduli are smaller than the axial modulus at low pressures, while the reverse is true for large pressures.     

Axial nonuniformity of geometric and mechanical properties of mouse aorta is increased during postnatal growth

The hemodynamic conditions of aorta are relatively uniform prenatally and become more heterogeneous postnatally. Our objective was to quantify the heterogeneity of geometry and mechanical properties during growth and development. To accomplish this objective, we obtained a systematic set of data on the geometry and mechanical properties along the length of mouse aorta during postnatal development. C57BL/6 mice of ages 1-33 days were studied. The ascending aorta was cannulated in situ and preconditioned with several cyclic changes in pressure. We investigated the axial variations of geometry (diameter and length) and mechanical properties (stress-stain relation, elastic modulus and compliance) of the mouse aorta from the aortic valve to the common iliac. Our results show that the arterial blood pressure of mice increased from approximately 30 to 80 mmHg during the first 2 wk of life. The stretch ratio, diameter, wall (intima-media) thickness, and total lumen volume of mouse aorta increased with age. The aorta was transformed from a cylindrical tube at birth to a tapered structure during growth. Furthermore, we found the mechanical properties were fairly uniform along the length of the aorta at birth and become more nonuniform with age. We conclude that the rapid change of blood pressure and blood flow after birth alter the geometric and mechanical properties differentially along the length of the aorta. Hence, the axial nonuniformity of the aorta increases as the organ becomes more specialized during growth and development.     

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.     

Asynchrony of ventricular activation affects magnitude and timing of fiber stretch in late-activated regions of the canine heart

Abnormal electrical activation of the left ventricle results in mechanical dyssynchrony, which is in part characterized by early stretch of late-activated myofibers. To describe the pattern of deformation during "prestretch" and gain insight into its causes and sequelae, we implanted midwall and transmural arrays of radiopaque markers into the left ventricular anterolateral wall of open-chest, isoflurane-anesthetized, adult mongrel dogs. Biplane cineradiography (125 Hz) was used to determine the time course of two- and three-dimensional strains while pacing from a remote, posterior wall site. Strain maps were generated as a function of time. Electrical activation was assessed with bipolar electrodes. Posterior wall pacing generated prestretch at the measurement site, which peaked 44 ms after local electrical activation. Overall magnitudes and transmural gradients of strain were reduced when compared with passive inflation. Fiber stretch was larger at aortic valve opening compared with end diastole (P < 0.05). Fiber stretch at aortic valve opening was weakly but significantly correlated with local activation time (r(2) = 0.319, P < 0.001). With a short atrioventricular delay, fiber lengths were not significantly different at the time of aortic valve opening during ventricular pacing compared with atrial pacing. However, ejection strain did significantly increase (P < 0.05). We conclude that the majority of fiber stretch occurs after local electrical activation and mitral valve closure and is different from passive inflation. The increased shortening of these regions appears to be because of a reduced afterload rather than an effect of length-dependent activation in this preparation.     

Effects of instantaneous prestretching on force degradation characteristics of orthodontic plastic modules

The object of this study was to investigate the effect of instantaneous prestretching on the force degradation behavior of three kinds of four-link plastic modules. A simple sliding apparatus was used to prestretch instantaneously the plastic modules to 100, 200 and 300% of their original length. After prestretching, specimens were tested at 20, 25 and 30 mm stretch distances. Force measurements were performed at the following occasions: before prestretching; at the end of prestretching; after 1, 4 and 24 hours; and after 1, 2 and 3 weeks. The following conclusions can be drawn from this investigation: The control specimens which had not been instantaneously prestretched exhibited considerable force loss over the three-week test period. Most of the force loss occurred rapidly during the first few hours, with a much lower subsequent force degradation rate. Instantaneous prestretching to a greater length resulted in a lower force value remaining at the end of prestretching. Instantaneous prestretching of the plastic modules is an efficient method to dissipate the high initial force level which is clinically undesirable. Prestretching of the modules around or slightly longer than the stretch distance could reduce the high initial force level and still maintain the same force level as the control groups. However, if the length of instantaneous prestretching of the four-link plastic module was much longer than the testing stretch distance which corresponds to the average distance from the first molar to the canine in the same quadrant, the prestretching would reduce both the high initial force value and the force value during the three-week test period, as compared with the control group.     

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.     

Theoretical study of intracellular stress fiber orientation under cyclic deformation

We studied stress fiber orientation under a wide range of uniaxial cyclic deformations. We devised and validated a hypothesis consisting of two parts, as follows: (1) a stress fiber aligns to avoid a mechanical stimulus in the fiber direction under cyclic deformation. This means that, among all allowable directions, a stress fiber aligns in the direction which minimizes the stimulus, i. e., the summation of the changes in length of the stress fiber over one stretch cycle; and (2) there is a limit in the sensitivity of the cellular response to the mechanical stimulus. Due to this sensing limit, the orientation angle in stress fibers is distributed around the angle corresponding to the minimum stimulus. To validate this hypothesis, we approximated an anisotropic deformation of the membrane on which cells were to be cultured. We then obtained the relationships between the stretch range and the fiber angle in the undeformed state which minimize the mechanical stimuli, assuming that the membrane on which stress fibers and cells adhered was homogeneous and incompressible. Numerical simulation results showed that the proposed hypothesis described our previous experimental results well and was consistent with the experimental results in the literature. The simulation results, taking account of the second part of the hypothesis with a small value for the limit in sensitivity to the mechanical stimulus, could explain why cell orientation is distributed so widely with cyclic stretch ranges of <10%. The proposed hypothesis can be applied to various types of deformation because the mechanical stimulus is always sensed and accumulates under cyclic deformation without the necessity of a reference state to measure the stimulus.     

Twist buckling of veins under torsional loading

Veins are often subjected to torsion and twisted veins can hinder and disrupt normal blood flow but their mechanical behavior under torsion is poorly understood. The objective of this study was to investigate the twist deformation and buckling behavior of veins under torsion. Twist buckling tests were performed on porcine internal jugular veins (IJVs) and human great saphenous veins (GSVs) at various axial stretch ratio and lumen pressure conditions to determine their critical buckling torques and critical buckling twist angles. The mechanical behavior under torsion was characterized using a two-fiber strain energy density function and the buckling behavior was then simulated using finite element analysis. Our results demonstrated that twist buckling occurred in all veins under excessive torque characterized by a sudden kink formation. The critical buckling torque increased significantly with increasing lumen pressure for both porcine IJV and human GSV. But lumen pressure and axial stretch had little effect on the critical twist angle. The human GSVs are stiffer than the porcine IJVs. Finite element simulations captured the buckling behavior for individual veins under simultaneous extension, inflation, and torsion with strong correlation between predicted critical buckling torques and experimental data (R² = 0.96). We conclude that veins can buckle under torsion loading and the lumen pressure significantly affects the critical buckling torque. These results improve our understanding of vein twist behavior and help identify key factors associated in the formation of twisted veins.     

Fluid-structure interaction modeling of aneurysmal arteries under steady-state and pulsatile blood flow: a stability analysis

Tortuous aneurysmal arteries are often associated with a higher risk of rupture but the mechanism remains unclear. The goal of this study was to analyze the buckling and post-buckling behaviors of aneurysmal arteries under pulsatile flow. To accomplish this goal, we analyzed the buckling behavior of model carotid and abdominal aorta with aneurysms by utilizing fluid-structure interaction (FSI) method with realistic waveforms boundary conditions. FSI simulations were done under steady-state and pulsatile flow for normal (1.5) and reduced (1.3) axial stretch ratios to investigate the influence of aneurysm, pulsatile lumen pressure and axial tension on stability. Our results indicated that aneurysmal artery buckled at the critical buckling pressure and its deflection nonlinearly increased with increasing lumen pressure. Buckling elevates the peak stress (up to 118%). The maximum aneurysm wall stress at pulsatile FSI flow was (29%) higher than under static pressure at the peak lumen pressure of 130 mmHg. Buckling results show an increase in lumen shear stress at the inner side of the maximum deflection. Vortex flow was dramatically enlarged with increasing lumen pressure and artery diameter. Aneurysmal arteries are more susceptible than normal arteries to mechanical instability which causes high stresses in the aneurysm wall that could lead to aneurysm rupture.     

Towards in vivo aorta material identification and stress estimation

This paper addresses the problem of constructing a mechanical model for the abdominal aorta and calibrating its parameters to in vivo measurable data. The aorta is modeled as a pseudoelastic, thick-walled, orthotropic, residually stressed cylindrical tube, subjected to an internal pressure. The model parameters are determined by stating a minimization problem for the model pressure and computing the optimal solution by a minimization algorithm. The data used in this study is in vivo pressure–diameter data for the abdominal aorta of a 24-year-old man. The results show that the axial, circumferential and radial stresses have magnitudes in the span 0 to 180 kPa. Furthermore, the results show that it is possible to determine model parameters directly from in vivo measurable data. In particular, the parameters describing the residual stress distribution can be obtained without interventional procedures.     

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.     

Biaxial vasoactivity of porcine coronary artery

The passive mechanical properties of blood vessel mainly stem from the interaction of collagen and elastin fibers, but vessel constriction is attributed to smooth muscle cell (SMC) contraction. Although the passive properties of coronary arteries have been well characterized, the active biaxial stress-strain relationship is not known. Here, we carry out biaxial (inflation and axial extension) mechanical tests in right coronary arteries that provide the active coronary stress-strain relationship in circumferential and axial directions. Based on the measurements, a biaxial active strain energy function is proposed to quantify the constitutive stress-strain relationship in the physiological range of loading. The strain energy is expressed as a Gauss error function in the physiological pressure range. In K(+)-induced vasoconstriction, the mean ± SE values of outer diameters at transmural pressure of 80 mmHg were 3.41 ± 0.17 and 3.28 ± 0.24 mm at axial stretch ratios of 1.3 and 1.5, respectively, which were significantly smaller than those in Ca(2+)-free-induced vasodilated state (i.e., 4.01 ± 0.16 and 3.75 ± 0.20 mm, respectively). The mean ± SE values of the inner and outer diameters in no-load state and the opening angles in zero-stress state were 1.69 ± 0.04 mm and 2.25 ± 0.08 mm and 126 ± 22°, respectively. The active stresses have a maximal value at the passive pressure of 80-100 mmHg and at the active pressure of 140-160 mmHg. Moreover, a mechanical analysis shows a significant reduction of mean stress and strain (averaged through the vessel wall). These findings have important implications for understanding SMC mechanics.     

Stretch-induced hypertrophy activates NFkB-mediated VEGF secretion in adult cardiomyocytes

Hypertension and myocardial infarction are associated with the onset of hypertrophy. Hypertrophy is a compensatory response mechanism to increases in mechanical load due to pressure or volume overload. It is characterized by extracellular matrix remodeling and hypertrophic growth of adult cardiomyocytes. Production of Vascular Endothelial Growth Factor (VEGF), which acts as an angiogenic factor and a modulator of cardiomyocyte function, is regulated by mechanical stretch. Mechanical stretch promotes VEGF secretion in neonatal cardiomyocytes. Whether this effect is retained in adult cells and the molecular mechanism mediating stretch-induced VEGF secretion has not been elucidated. Our objective was to investigate whether cyclic mechanical stretch induces VEGF secretion in adult cardiomyocytes and to identify the molecular mechanism mediating VEGF secretion in these cells. Isolated primary adult rat cardiomyocytes (ARCMs) were subjected to cyclic mechanical stretch at an extension level of 10% at 30 cycles/min that induces hypertrophic responses. Cyclic mechanical stretch induced a 3-fold increase in VEGF secretion in ARCMs compared to non-stretch controls. This increase in stretch-induced VEGF secretion correlated with NFkB activation. Cyclic mechanical stretch-mediated VEGF secretion was blocked by an NFkB peptide inhibitor and expression of a dominant negative mutant IkBα, but not by inhibitors of the MAPK/ERK1/2 or PI3K pathways. Chromatin immunoprecipitation assays demonstrated an interaction of NFkB with the VEGF promoter in stretched primary cardiomyocytes. Moreover, VEGF secretion is increased in the stretched myocardium during pressure overload-induced hypertrophy. These findings are the first to demonstrate that NFkB activation plays a role in mediating VEGF secretion upon cyclic mechanical stretch in adult cardiomyocytes. Signaling by NFkB initiated in response to cyclic mechanical stretch may therefore coordinate the hypertrophic response in adult cardiomyocytes. Elucidation of this novel mechanism may provide a target for developing future pharmacotherapy to treat hypertension and heart disease.     

Factors influencing the angular velocity of a human limb segment

The angular velocity of a knee extension performed after flexion with different range and velocity, i.e. the kicking movement with stabilized thigh, was investigated and described. In addition, the maximum velocity of extension reached after prestretch was compared to that obtained in trials without prestretch. The maximum velocity of extension varied from 213 to 1087 degrees s-1 depending on the range and velocity of prestretch. In trials without prestretch the velocity of extension was worse up to 43% when small range of movement was involved. In trials with full range of movement the velocity of extension was similar in the tasks with and without prestretch. In this context the possible role of elastic energy is discussed. The method used was electrogoniometry.