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.     

Correlation between mechanical properties and wall composition of the canine superior vena cava

The mechanical properties (modulus of elasticity and stress-relaxation) of different venous segments of the canine superior vena cava were determined as well as the composition of the vessel wall by means of physical, biochemical and histological methods. It was found that the wall of the vena cava was structurally and mechanically a function of the metric position with respect to the right heart: the modulus of elasticity increased, the stress-relaxation decreased, the concentration of hydroxyproline, collagen and elastin increased and the amount of muscle fibres decreased with increasing distal distance from the right heart. A significant linear correlation coefficient was observed between the modulus of elasticity and the structural wall components. The data presented show the axial heterogeneity and the dependency of the mechanical properties upon the venous vessel wall composition.     

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.     

TGF-beta- and CTGF-mediated fibroblast recruitment influences early outward vein graft remodeling

Luminal shearing forces have been shown to impact both geometric remodeling and the development of intimal hyperplasia. Less well studied is the influence of intramural wall stresses on vessel growth and adaptation. Using a vein graft-fistula configuration to isolate the impact of circumferential wall stress, we identify the reorganization of adventitial myofibroblasts as the dominant histological event that limits early outward remodeling of vein grafts in response to elevated wall stress. We hypothesize that increased production of transforming growth factor-beta (TGF-beta) and connective tissue growth factor (CTGF) induces recruitment of myofibroblasts, promotes adventitial reorganization, and limits early outward remodeling in response to increased intramural wall stress. Vein grafts with a distal arteriovenous fistula in the neck of rabbits were constructed, resulting in a fourfold differential in circumferential wall stress. Using this model, we demonstrate 1) elevated wall stress augments the production of TGF-beta and CTGF, 2) increased TGF-beta expression and CTGF expression are correlated with the enhanced differentiation from fibroblasts to myofibroblasts, as evidenced by the significant increase in the alpha-actin-positive cells in adventitia, and 3) the levels of TGF-beta, CTGF, and alpha-actin are inversely correlated with the magnitude of outward remodeling of the graft wall. Increased wall stress after vein graft implantation appears to induce a TGF-beta- and CTGF-mediated recruitment of adventitial fibroblasts and a conversion to a myofibroblast phenotype. Although important in the maintenance of wall stability in the face of an increased mechanical load, this adventitial adaptation limits early outward remodeling of the vein conduit and may prove deleterious in maintaining long-term vein graft patency.     

Flow around cells adhered to a microvessel wall. I. Fluid stresses and forces acting on the cells

To evaluate the fluid forces acting on cells adhered to a microvessel wall, we numerically studied the flow field around adherent cells and the distribution of the stresses on their surfaces. For simplicity, the cells were modeled as rigid particles attached to a wall of a circular cylindrical tube regularly in the flow direction, in a row or two rows. It was found that not the detailed shape of the model cells but their height from the vessel wall is a key determinant of the fluid forces and torque acting on them. In both arrangements of one row and two rows, the axial spacing between neighboring adherent cells significantly affects the distributions of the stresses on them, which results in drastic variations of the fluid forces with the axial spacing and the relative positions with respect to their neighboring cells. The drag force acting on an adherent cell in the vessel was evaluated to be larger than the value in the 2D chamber flow at the same wall shear stress, mainly due to much larger variations of the pressure distribution on the cell surface in the vessel flow.     

Effect of variations in pressure and flow on the geometry of isolated canine carotid arteries

A study is described in which the effects of hemodynamics on arterial geometry are investigated in vitro. A novel perfusion apparatus is employed to deliver pulsatile flow through excised canine carotid arteries under carefully controlled conditions. Data of perfused vessel diameter and arterial wall thickness are derived from the radial displacement of the pulsating vessel as measured using a scanning laser micrometer whose accuracy is determined to be 0.0125 mm (0.0005 in). The results of 30 perfusion experiments suggest that the hemodynamic variables of transmural pressure, pulse pressure and flow rate influence vessel size and radial strain. The physiologic implications of these findings are discussed.     

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.     

Procedure for Human Saphenous Veins Ex Vivo Perfusion and External Reinforcement

The mainstay of contemporary therapies for extensive occlusive arterial disease is venous bypass graft. However, its durability is threatened by intimal hyperplasia (IH) that eventually leads to vessel occlusion and graft failure. Mechanical forces, particularly low shear stress and high wall tension, are thought to initiate and to sustain these cellular and molecular changes, but their exact contribution remains to be unraveled. To selectively evaluate the role of pressure and shear stress on the biology of IH, an ex vivo perfusion system (EVPS) was created to perfuse segments of human saphenous veins under arterial regimen (high shear stress and high pressure). Further technical innovations allowed the simultaneous perfusion of two segments from the same vein, one reinforced with an external mesh. Veins were harvested using a no-touch technique and immediately transferred to the laboratory for assembly in the EVPS. One segment of the freshly isolated vein was not perfused (control, day 0). The two others segments were perfused for up to 7 days, one being completely sheltered with a 4 mm (diameter) external mesh. The pressure, flow velocity, and pulse rate were continuously monitored and adjusted to mimic the hemodynamic conditions prevailing in the femoral artery. Upon completion of the perfusion, veins were dismounted and used for histological and molecular analysis. Under ex vivo conditions, high pressure perfusion (arterial, mean = 100 mm Hg) is sufficient to generate IH and remodeling of human veins. These alterations are reduced in the presence of an external polyester mesh.     

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.     

Experimental determination of mechanical shear stress about an anastomotic junction

The present study is undertaken to determine whether the elastic tube model originally developed by Kuchar and Ostrach (Biomedical Fluid Mechanics Symposium, pp. 45-69, 1966) accurately provides a first approximation of the biomechanics of the anastomotic junction. The experimental protocol involves the use of canine carotid arteries as the host vessel and several graft materials including autogenous and prosthetic substitutes. The host artery-graft combinations are perfused in vitro in a pulsatile perfusion apparatus which simulates the natural hemodynamic environment. This apparatus provides accurate dynamic measurements of radial wall motion (measured at various longitudinal increments), associated pressures and rates of fluid flow. These data are then applied to the theoretical model for calculation of anastomotic induced bending stresses. The results indicate that the predictions derived from the elastic model consistently overestimate the measured radial change adjacent to the anastomotic junction. As a result shear stresses based on elastic theory deviate from values derived from a numerical curve fit to the experimental data.     

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.     

A multiscale approach for modelling wave propagation in an arterial segment

A mathematical model of blood flow through an arterial vessel is presented and the wave propagation in it is studied numerically. Based on the assumption of long wavelength and small amplitude of the pressure waves, a quasi-one-dimensional (1D) differential model is adopted. It describes the non-linear fluid-wall interaction and includes wall deformation in both radial and axial directions. The 1D model is coupled with a six compartment lumped parameter model, which accounts for the global circulatory features and provides boundary conditions. The differential equations are first linearized to investigate the nature of the propagation phenomena. The full non-linear equations are then approximated with a numerical finite difference method on a staggered grid. Some numerical simulations show the characteristics of the wave propagation. The dependence of the flow, of the wall deformation and of the wave velocity on the elasticity parameter has been highlighted. The importance of the axial deformation is evidenced by its variation in correspondence of the pressure peaks. The wave disturbances consequent to a local stiffening of the vessel and to a compliance jump due to prosthetic implantations are finally studied.     

Wave Propagation in a Viscous Fluid Contained in an Orthotropic Elastic Tube

The problem of pressure wave propagation through a viscous fluid contained in an orthotropic elastic tube is considered in connection with arterial blood flow. Solutions to the fluid flow and elasticity equations are obtained for the presence of a reflected wave. Numerical results are presented for both isotropic and orthotropic elastic tubes. In particular, the pressure pulse, flow rate, axial fluid velocity, and wall displacements are plotted vs. time at various stations along the ascending aorta of man. The results indicate an increase in the peak value of the pressure pulse and a decrease in the flow rate as the pulse propagates away from the heart. Finally, the velocity of wave propagation depends mainly on the tangential modulus of elasticity of the arterial wall, and anisotropy of the wall accounts in part for the reduction of longitudinal movements and an increase in the hydraulic resistance.     

Stress analysis of vasoconstriction at arterial branch sites

The object of the research was to estimate wall stresses caused by vasoconstriction at arterial branches. The basic procedure was a combination of experimental strain measurement and analytical stress analysis. Segments of canine renal arteries were perfused and stimulated to constrict with dopamine hydrochloride and norepinephrine. Surface wall deformation was measured with a stereo-photographic technique. A plane stress finite element analysis was used to calculate wall stresses based on the experimentally derived deformations. The major result of the study was to demonstrate tensile stresses, and in some cases biaxial tension, in contracting vessels. Peak stresses in the apex of the acute angle of the branches were approximately three times unpenetrated hoop stress in the parent vessels. The results imply that constriction at a branch site may be capable of generating sufficient wall tension to tear arterial tissue, and that smooth muscle reactivity is important with respect to the etiology of cerebral aneurysms and the clinical management of acute branch site pathology.     

Experimental determination of wall shear rate in canine carotid arteries perfused in vitro

The mathematical model of Hung (Tsai and Hung, 1984) is employed to determine the wall shear rate acting on canine carotid arteries perfused in vitro. Model equations for pulsatile flow in a deformable vessel are coupled with experimental data of dynamic pressure drop, flow rate, vessel radius and radial wall motion. Derived quantities, e.g. velocity profiles and wall shear, are obtained for vessels exposed to 'normotensive' hemodynamics, 'hypertension' simulations and perfusions in which the compliance of the vessel wall is deliberately altered. Our results indicate that wall shear varies markedly as a function of the hemodynamic environment. The effects of vessel radius vs flow rate on the development of wall shear are also demonstrated. It is found that convective processes correlate with the magnitude of wall shear in the 'hypertension' simulations. The present findings and complementary published data may explain, at least in part, the variations in vessel wall transport and endothelial cell biology we observe as a function of the hemodynamic environment. For example we have documented that the exposure of canine carotids to 'hypertensive' (vs 'normotensive') hemodynamics is associated with an increased flux of lipoproteins (LDL) into the intima and luminal media. Alternations in wall compliance, on the other hand, profoundly influence endothelial shape, orientation and cytoskeletal array.     

Mechanical properties of native and ex vivo remodeled porcine saphenous veins

When grafted into an arterial environment in vivo, veins remodel in response to the new mechanical environment, thereby changing their mechanical properties and potentially impacting their patency as bypass grafts. Porcine saphenous veins were subjected for one week to four different ex vivo hemodynamic environments in which pressure and shear stress were varied independently, as well as an environment that mimicked that of an arterial bypass graft. After one week of ex vivo culture, the mechanical properties of intact saphenous veins were evaluated to relate specific aspects of the mechanical environment to vein remodeling and corresponding changes in mechanics. The compliance of all cultured veins tended to be less than that of fresh veins; however, this trend was more due to changes in medial and luminal areas than changes in the intrinsic properties of the vein wall. A combination of medial hypertrophy and eutrophic remodeling leads to significantly smaller (p<0.05) wall stresses measured in all cultured veins except those subjected to bypass graft conditions relative to stresses measured in fresh veins at corresponding pressures. Our results suggest that the mechanical environment effects changes in vessel size, as well as the nature of the remodeling, which contribute to altering vein mechanical properties.     

A framework for incorporating 3D hyperelastic vascular wall models in 1D blood flow simulations

We present a novel framework for investigating the role of vascular structure on arterial haemodynamics in large vessels, with a special focus on the human common carotid artery (CCA). The analysis is carried out by adopting a three-dimensional (3D) derived, fibre-reinforced, hyperelastic structural model, which is coupled with an axisymmetric, reduced order model describing blood flow. The vessel transmural pressure and lumen area are related via a Holzapfel–Ogden type of law, and the residual stresses along the thickness and length of the vessel are also accounted for. After a structural characterization of the adopted hyperelastic model, we investigate the link underlying the vascular wall response and blood-flow dynamics by comparing the proposed framework results against a popular tube law. The comparison shows that the behaviour of the model can be captured by the simpler linear surrogate only if a representative value of compliance is applied. Sobol’s multi-variable sensitivity analysis is then carried out in order to identify the extent to which the structural parameters have an impact on the CCA haemodynamics. In this case, the local pulse wave velocity (PWV) is used as index for representing the arterial transmission capacity of blood pressure waveforms. The sensitivity analysis suggests that some geometrical factors, such as the stress-free inner radius and opening angle, play a major role on the system’s haemodynamics. Subsequently, we quantified the differences in haemodynamic variables obtained from different virtual CCAs, tube laws and flow conditions. Although each artery presents a distinct vascular response, the differences obtained across different flow regimes are not significant. As expected, the linear tube law is unable to accurately capture all the haemodynamic features characterizing the current model. The findings from the sensitivity analysis are further confirmed by investigating the axial stretching effect on the CCA fluid dynamics. This factor does not seem to alter the pressure and flow waveforms. On the contrary, it is shown that, for an axially stretched vessel, the vascular wall exhibits an attenuation in absolute distension and an increase in circumferential stress, corroborating the findings of previous studies. This analysis shows that the new model offers a good balance between computational complexity and physics captured, making it an ideal framework for studies aiming to investigate the profound link between vascular mechanobiology and blood flow.

     

Effects of stent design parameters on normal artery wall mechanics

A stent is a device designed to restore flow through constricted arteries. These tubular scaffold devices are delivered to the afflicted region and deployed using minimally invasive techniques. Stents must have sufficient radial strength to prop the diseased artery open. The presence of a stent can subject the artery to abnormally high stresses that can trigger adverse biologic responses culminating in restenosis. The primary aim of this investigation was to investigate the effects of varying stent "design parameters" on the stress field induced in the normal artery wall and the radial displacement achieved by the stent. The generic stent models were designed to represent a sample of the attributes incorporated in present commercially available stents. Each stent was deployed in a homogeneous, nonlinear hyperelastic artery model and evaluated using commercially available finite element analysis software. Of the designs investigated herein, those employing large axial strut spacing, blunted corners, and higher amplitudes in the ring segments induced high circumferential stresses over smaller areas of the artery's inner surface than all other configurations. Axial strut spacing was the dominant parameter in this study, i.e., all designs employing a small stent strut spacing induced higher stresses over larger areas than designs employing the large strut spacing. Increasing either radius of curvature or strut amplitude generally resulted in smaller areas exposed to high stresses. At larger strut spacing, sensitivity to radius of curvature was increased in comparison to the small strut spacing. With the larger strut spacing designs, the effects of varying amplitude could be offset by varying the radius of curvature and vice versa. The range of minimum radial displacements from the unstented diastolic radius observed among all designs was less than 90 microm. Evidence presented herein suggests that stent designs incorporating large axial strut spacing, blunted corners at bends, and higher amplitudes exposed smaller regions of the artery to high stresses, while maintaining a radial displacement that should be sufficient to restore adequate flow.     

Radial artery wall shear stress evaluation in patients with arteriovenous fistula for hemodialysis access

It has been extensively documented that changes in blood flow induce vascular remodeling and this phenomenon seems to be correlated to the shear forces imposed on the vessel wall by motion of blood. Wall shear stress, the tractive force that acts on the endothelium, has been shown to influence endothelial cell function. To study changes in wall shear stress that develop on the vessel wall upon changes of blood flow, we set up a technique that allows estimation of shear stress in the radial artery of patients on chronic hemodialysis therapy. The technique is based on color-flow Doppler examination of the radial artery before and after surgical creation of radiocephalic fistula for hemodialysis. Calculation of time function wall shear stress and blood flow rate in the radial artery is performed on the basis of arterial diameter, center-line velocity waveform and blood viscosity, using a numerical method developed according to Womersley's theory for pulsatile flow in tubes. The results presented confirm that the model developed is suitable for calculation of the wall shear stress that develops in the radial artery of patients before and after surgical creation of an arteriovenous fistula for hemodialysis. This methodology was developed for characterization of wall shear stress in the radial artery but may be well applied to other vessels that can be examined by echo-Doppler technique.