Analysis of circular bordered pit function I. Angiosperm vessels with homogenous pit membranes

A model predicted pit and vessel conductivity, the air-seed pressure for cavitation, and the implosion pressure causing vessel collapse. Predictions were based on measurements from 27 angiosperm species with circular bordered pits and air-seed pressures of 0.2-11.3 MPa. Vessel implosion pressure exceeded air-seed pressure by a safety factor of 1.8 achieved by the increase in vessel wall thickness per vessel diameter with air-seed pressure. Intervessel pitting reduced the implosion pressure by 20 to 40%. Pit hydraulic conductivity decreased by 30-fold from low (<1 MPa) to high (>10 MPa) air-seed pressure primarily because of decreasing pit membrane conductivity. Vessel conductivity (per length and wall area) increased with vessel length as higher lumen conductivity overcame low pit conductivity. At the "saturating vessel length," vessel conductivity maximized at the Hagen-Poiseuille value for the lumen per wall area. Saturated vessel conductivity declined by sixfold with increasing air-seed pressure because of increased wall thickness associated with increased implosion resistance. The saturated vessel length is likely the optimal length because: (a) shorter vessels have lower conductivities, (b) longer vessels do not increase conductivity when functional yet decrease it more when cavitated, (c) observed pit structure most closely optimized vessel conductivity at the saturated length, and (d) saturated lengths were similar to measured lengths.     

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.     

Biomechanics of the venous wall under simulated arterial conditions

The failure of vein graft conduits implanted in the arterial circulation has been hypothesized to occur in part due to the exposure of the graft to altered biomechanical and fluid shearing forces. In the present study, these forces are characterized for canine internal jugular veins (IJV) exposed to realistic arterial flow dynamics. Freshly excised vein segments were mounted into a pulsatile perfusion apparatus and exposed to arterial flow conditions (P = 115/75 mmHg and Q = 110 ml min-1) for 2 h. Dynamic measurements of intraluminal pressure and flow rate and vessel wall radial distension were acquired to accurately quantitate the incremental modulus of elasticity; hoop, axial and radial wall stresses; and fluid shearing forces within the vessel. Identical measurements were performed on canine carotid arteries (CCA) to serve as a comparison. Under arterial conditions, IJV segments demonstrated a significant elevation (p less than 0.05) over the CCA in the incremental elasticity modulus, along with a corresponding elevation in hoop and axial wall stresses. Additionally the average wall shearing rate to which the IJV endothelial surface was exposed was a factor of six less than that observed in the CCA. These results are discussed in relationship to the clinical situation of vein graft adaptation to arterial hemodynamics.     

Flow resistance and drag forces due to multiple adherent leukocytes in postcapillary vessels.

Computational fluid dynamics was used to model flow past multiple adherent leukocytes in postcapillary size vessels. A finite-element package was used to solve the Navier-Stokes equations for low Reynolds number flow of a Newtonian fluid past spheres adhering to the wall of a cylindrical vessel. We determined the effects of sphere number, relative geometry, and spacing on the flow resistance in the vessel and the fluid flow drag force acting to sweep the sphere off the vessel wall. The computations show that when adherent leukocytes are aligned on the same side of the vessel, the drag force on each of the interacting leukocytes is less than the drag force on an isolated adherent leukocyte and can decrease by up to 50%. The magnitude of the reduction depends on the ratio of leukocyte to blood vessel diameter and distance between adherent leukocytes. However, there is an increase in the drag force when leukocytes adhere to opposite sides of the vessel wall. The increase in resistance generated by adherent leukocytes in vessels of various sizes is calculated from the computational results. The resistance increases with decreasing vessel size and is most pronounced when leukocytes adhere to opposite sides of the vessel.     

Effect of high altitude exposure on the hemodynamics of the bidirectional Glenn physiology: Modeling incremented pulmonary vascular resistance and heart rate

The considerable blood mixing in the bidirectional Glenn (BDG) physiology further limits the capacity of the single working ventricle to pump enough oxygenated blood to the circulatory system. This condition is exacerbated under severe conditions such as physical activity or high altitude. In this study, the effect of high altitude exposure on hemodynamics and ventricular function of the BDG physiology is investigated. For this purpose, a mathematical approach based on a lumped parameter model was developed to model the BDG circulation. Catheterization data from 39 BDG patients at stabilized oxygen conditions was used to determine baseline flows and pressures for the model. The effect of high altitude exposure was modeled by increasing the pulmonary vascular resistance (PVR) and heart rate (HR) in increments up to 80% and 40%, respectively. The resulting differences in vascular flows, pressures and ventricular function parameters were analyzed. By simultaneously increasing PVR and HR, significant changes (p <0.05) were observed in cardiac index (11% increase at an 80% PVR and 40% HR increase) and pulmonary flow (26% decrease at an 80% PVR and 40% HR increase). Significant increase in mean systemic pressure (9%) was observed at 80% PVR (40% HR) increase. The results show that the poor ventricular function fails to overcome the increased preload and implied low oxygenation in BDG patients at higher altitudes, especially for those with high baseline PVRs. The presented mathematical model provides a framework to estimate the hemodynamic performance of BDG patients at different PVR increments.     

Heterogeneous mechanics of the mouse pulmonary arterial network

Individualized modeling and simulation of blood flow mechanics find applications in both animal research and patient care. Individual animal or patient models for blood vessel mechanics are based on combining measured vascular geometry with a fluid structure model coupling formulations describing dynamics of the fluid and mechanics of the wall. For example, one-dimensional fluid flow modeling requires a constitutive law relating vessel cross-sectional deformation to pressure in the lumen. To investigate means of identifying appropriate constitutive relationships, an automated segmentation algorithm was applied to micro-computerized tomography images from a mouse lung obtained at four different static pressures to identify the static pressure–radius relationship for four generations of vessels in the pulmonary arterial network. A shape-fitting function was parameterized for each vessel in the network to characterize the nonlinear and heterogeneous nature of vessel distensibility in the pulmonary arteries. These data on morphometric and mechanical properties were used to simulate pressure and flow velocity propagation in the network using one-dimensional representations of fluid and vessel wall mechanics. Moreover, wave intensity analysis was used to study effects of wall mechanics on generation and propagation of pressure wave reflections. Simulations were conducted to investigate the role of linear versus nonlinear formulations of wall elasticity and homogeneous versus heterogeneous treatments of vessel wall properties. Accounting for heterogeneity, by parameterizing the pressure/distention equation of state individually for each vessel segment, was found to have little effect on the predicted pressure profiles and wave propagation compared to a homogeneous parameterization based on average behavior. However, substantially different results were obtained using a linear elastic thin-shell model than were obtained using a nonlinear model that has a more physiologically realistic pressure versus radius relationship.     

Transient increases in diameter and [Ca(2+)](i) are not obligatory for myogenic constriction

Studies were performed to determine the significance of temporal variation in vascular smooth muscle Ca(2+) signaling during acute arteriolar myogenic constriction and, in particular, the importance of the stretch-induced intracellular Ca(2+) concentration ([Ca(2+)](i)) transient in attaining a steady-state mechanical response. Rat cremaster arterioles (diameter approximately 100 microm) were dissected from surrounding tissues, and vessel segments were pressurized in the absence of intraluminal flow. For [Ca(2+)](i) measurements, vessels were loaded with fura 2 and fluorescence emitted by excitation at 340 and 380 nm was measured using video-based image analysis. Ca(2+) and diameter responses were examined after increases in intravascular pressure were applied as an acute step increase or a ramp function. Additional studies examined the effect of longitudinal vessel stretch on [Ca(2+)](i) and arteriolar diameter. Step increase in intraluminal pressure (from 50 to 120 mmHg) caused biphasic change in [Ca(2+)](i) and diameter. [Ca(2+)](i) transiently increased to 114.0 +/- 2.0% of basal levels and subsequently declined to 106.7 +/- 4.4% at steady state. Diameter initially distended to 125.4 +/- 2.1% of basal levels before constricting to 71.1 +/- 1.2%. In contrast, when the same pressure increase was applied as a ramp function (over 5 min) transient vessel distension and transient increase in [Ca(2+)](i) were prevented, yet at steady state vessels constricted to 71.3 +/- 2.5%. Longitudinal stretch resulted in a large [Ca(2+)](i) transient (158 +/- 19% of basal) that returned to baseline despite maintenance of the stretch stimulus. The data demonstrate that the initial vessel distension (reflecting myocyte stretch) and associated global [Ca(2+)](i) transient are not obligatory for myogenic contraction. Thus, although arteriolar smooth muscle cells are responsive to acute stretch, the resulting changes in myogenic tone may be more closely related to other mechanical variables such as wall tension.     

Mechanical control of cation channels in the myogenic response

Microcirculatory vessel response to changes in pressure, known as the myogenic response, is a key component of a tissue's ability to regulate blood flow. Experimental studies have not clearly elucidated the mechanical signal in the vessel wall governing steady-state reduction in vessel diameter upon an increase in intraluminal pressure. In this study, a multiscale computational model is constructed from established models of vessel wall mechanics, vascular smooth muscle (VSM) force generation, and VSM Ca(2+) handling and electrophysiology to compare the plausibility of vessel wall stress or strain as an effective mechanical signal controlling steady-state vascular contraction in the myogenic response. It is shown that, at the scale of a resistance vessel, wall stress, and not stretch (strain), is the likely physiological signal controlling the steady-state myogenic response. The model is then used to test nine candidate VSM stress-controlled channel variants by fitting two separate sets of steady-state myogenic response data. The channel variants include nonselective cation (NSC), supplementary Ca(2+) and Na(+), L-type Ca(2+), and large conductance Ca(2+)-activated K(+) channels. The nine variants are tested in turn, and model fits suggest that stress control of Ca(2+) or Na(+) influx through NSC, supplementary Ca(2+) or Na(+), or L-type Ca(2+) channels is sufficient to produce observed steady-state diameter changes with pressure. However, simulations of steady-state VSM membrane potential, cytosolic Ca(2+), and Na(+) with pressure show only that Na(+) influx through NSC channel also generates known trends with increasing pressure, indicating that stress-controlled Na(+) influx through NSC is sufficient to generate the myogenic response.     

Pulsatile flow inside moderately elastic arteries,its modelling and effects of elasticity

Pulsatile flow inside a moderately elastic circular conduit with a smooth expansion is studied as a model to understand the influence of wall elasticity in artery flow. The solution of the simultaneous fluid-wall evolution is evaluated by a perturbative method, where the zeroth order solution is represented by the flow in a rigid vessel; the first order correction gives the wall motion and induced flow modification without the need to solve the difficult coupled problem. Such an approach essentially assumes a locally infinite celerity, therefore it represent a good approximation for the fluid-wall interaction in sites of limited extent (branches, stenosis, aneurism, etc.), which include typical situations associated with vascular diseases. The problem is solved numerically in the axisymmetric approximation; the influence of wall elasticity on the flow and on the unsteady wall shear stress is studied in correspondence of parameters taken from realistic artery flow. Attention is posed to the role of phase difference between the incoming pressure and flow pulses.     

Partial hepatectomy hemodynamics changes: Experimental data explained by closed-loop lumped modeling

The liver function may be degraded after partial liver ablation surgery. Adverse liver hemodynamics have been shown to be associated to liver failure. The link between these hemodynamics changes and ablation size is however poorly understood. This article proposes to explain with a closed-loop lumped model the hemodynamics changes observed during twelve surgeries in pigs. The portal venous tree is modeled with a pressure-dependent variable resistor. The variables measured, before liver ablation, are used to tune the model parameters. Then, the liver partial ablation is simulated with the model and the simulated pressures and flows are compared with post-operative measurements. Fluid infusion and blood losses occur during the surgery. The closed-loop model presented accounts for these blood volume changes. Moreover, the impact of blood volume changes and the liver lobe mass estimations on the simulated variables is studied. The typical increase of portal pressure, increase of liver pressure loss, slight decrease of portal flow and major decrease in arterial flow are quantitatively captured by the model for a 75% hepatectomy. It appears that the 75% decrease in hepatic arterial flow can be explained by the resistance increase induced by the surgery, and that no hepatic arterial buffer response (HABR) mechanism is needed to account for this change. The different post-operative states, observed in experiments, are reproduced with the proposed model. Thus, an explanation for inter-subjects post-operative variability is proposed. The presented framework can easily be adapted to other species circulations and to different pathologies for clinical hepatic applications.     

Finite element analysis of the biomechanical interaction between coronary sinus and proximal anchoring stent in coronary sinus annuloplasty

Recent clinical studies of the percutaneous transvenous mitral annuloplasty (PTMA) devices have shown a short-term reduction of mitral regurgitation after implantation. However, adverse events associated with the devices such as compression and perforation of vessel branches, device migration and fracture were reported. In this study, a finite element analysis was carried out to investigate the biomechanical interaction between the proximal anchor stent of a PTMA device and the coronary sinus (CS) vessel in three steps including: (i) the stent release and contact with the CS wall, (ii) the axial pull t the stent connector and (iii) the pressure inflation of the vessel wall. To investigate the impact of the material properties of tissues and stents on the interactive responses, the CS vessel was modelled with human and porcine material properties, and the proximal stent was modelled with two different Nitinol materials with one being stiffer than the other. The results indicated that the vessel wall stresses and contact forces imposed by the stents were much higher in the human model than the porcine model. However, the mechanical differences induced by the two stent types were relatively small. The softer stent exhibited a better fatigue safety factor when deployed in the human model than in the porcine model. These results underscored the importance of the CS tissue mechanical properties. Vessel wall stress and stent radial force obtained in the human model were higher than those obtained in the porcine model, which also brought up questions as to the validity of using the porcine model to assess device mechanical function. The quantification of these biomechanical interactions can offer scientific insight into the development and optimisation of the PTMA device design.     

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.     

Effective permeability of hydrophilic substances through walls of lymph vessels: roles of endothelial barrier

The wall effective permeability of hydrophilic substances labeled with fluorescent dyes was evaluated in an isolated cannulated rat single lymph vessel through a videomicroscope system. Sodium fluorescein (NaFl; 332 mol wt) and FITC-dextrans (4,400, 12,000, and 71,200 mol wt) were administered into the intraluminal space of the lymph vessels and then excited by a Xenon lamp. Changes in the fluorescence intensity of the dyes were continuously measured by a silicon-intensified target camera through appropriate filters. The net flux of each dye in the wall of the lymph vessels was calculated by the relationship between the fluorescence intensity and the concentration of the dyes. NaFl and FITC-dextran 4,400 in the intraluminal space of isolated rat lymph vessels significantly penetrated the wall of the lymph vessels. FITC-dextran 12,000 in the intraluminal space of isolated rat lymph vessels slightly passed through the lymphatic wall, whereas FITC-dextran 71,200 did not penetrate the wall. Intraluminal pressures ranging from 4 to 8 cm H(2)O did not significantly affect the net flux of dyes used in the present study. After administration of 3-[(3-cholamidopropyl)dimethylammonio]-1-propanesulfonate into the lymph vessels, the net flux of FITC-dextran 4,400 and 12,000 but not 71,200 was augmented significantly. These results suggest that small molecular hydrophilic substances (< or =4,400) are permeable from the intraluminal to extraluminal space of isolated lymph vessels and that the endothelial cell surface structure may play a barrier role in the effective permeability of large molecular hydrophilic substances (4,400 to 12,000) through the wall of the lymph vessels.     

Pulsatile Flow Inside Moderately Elastic Arteries,Its Modelling and Effects of Elasticity

Pulsatile flow inside a moderately elastic circular conduit with a smooth expansion is studied as a model to understand the influence of wall elasticity in artery flow. The solution of the simultaneous fluid-wall evolution is evaluated by a perturbative method, where the zeroth order solution is represented by the flow in a rigid vessel; the first order correction gives the wall motion and induced flow modification without the need to solve the difficult coupled problem. Such an approach essentially assumes a locally infinite celerity, therefore it represent a good approximation for the fluid-wall interaction in sites of limited extent (branches, stenosis, aneurism, etc.), which include typical situations associated with vascular diseases. The problem is solved numerically in the axisymmetric approximation; the influence of wall elasticity on the flow and on the unsteady wall shear stress is studied in correspondence of parameters taken from realistic artery flow. Attention is posed to the role of phase difference between the incoming pressure and flow pulses.     

Impact of calcifications on patient-specific wall stress analysis of abdominal aortic aneurysms

As a degenerative and inflammatory desease of elderly patients, about 80% of abdominal aortic aneurysms (AAA) show considerable wall calcification. Effect of calcifications on computational wall stress analyses of AAAs has been rarely treated in literature so far. Calcifications are heterogeneously distributed, non-fibrous, stiff plaques which are most commonly found near the luminal surface in between the intima and the media layer of the vessel wall. In this study, we therefore investigate the influence of calcifications as separate AAA constituents on finite element simulation results. Thus, three AAAs are reconstructed with regard to intraluminal thrombus (ILT), calcifications and vessel wall. Each patient-specific AAA is simulated twice, once including all three AAA constituents and once neglecting calcifications as it is still common in literature. Parameters for constitutive modeling of calcifications are thereby taken from experiments performed by the authors, showing that calcifications exhibit an almost linear stress–strain behavior with a Young’s modulus E ≥ 40 MPa. Simulation results show that calcifications exhibit significant load-bearing effects and reduce stress in adjacent vessel wall. Average stress within the vessel wall is reduced by 9.7 to 59.2%. For two out of three AAAs, peak wall stress decreases when taking calcifications into consideration (8.9 and 28.9%). For one AAA, simulated peak wall stress increases by 5.5% due to stress peaks near calcification borders. However, such stress singularities due to sudden stiffness jumps are physiologically doubtful. It can further be observed that large calcifications are mostly situated in concavely shaped regions of the AAA wall. We deduce that AAA shape is influenced by existent calcifications, thus crucial errors occur if they are neglected in computational wall stress analyses. A general increase in rupture risk for calcified AAAs is doubted.     

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.     

Soybean Bowman–Birk Inhibitor Conjugates with Clinical Dextran. Synthesis and Antiproteolytic Activity

Conjugates of the classical soybean Bowman-Birk inhibitor (BBI) with clinical dextran were synthesized. Clinical dextran was preliminarily oxidized with periodate to dialdehydedextran (DAD). The effect of the degree of oxidation of DAD on coupling of the inhibitor was evaluated. The binding of the protein was shown to increase with increasing degree of DAD oxidation (5, 10, 20%). Total coupling of the inhibitor occurred when the degree of oxidation of the dextran was 20%. The BBI-DAD (20%) conjugate contained 13% protein with BBI/DAD molar ratio 1 : 1. The conjugates retained the ability to inhibit trypsin (Ki = 0.2-0.3 nM) and alpha-chymotrypsin (Ki = 15-30 nM). Thus, the coupling of BBI with the polymeric carrier caused practically no decrease in the antiproteolytic activity of the inhibitor.     

Influence of arterial wall-stenosis compliance on the coronary diagnostic parameters

Functional diagnostic parameters such as Fractional Flow Reserve (FFR), which is calculated from pressure measurements across stenosed arteries, are often used to determine the functional severity of coronary artery stenosis. This study evaluated the effect of arterial wall-stenosis compliance, with limiting scenarios of stenosis severity, on the diagnostic parameters. The diagnostic parameters considered in this study include an established index, FFR and two recently developed parameters: Pressure Drop Coefficient (CDP) and Lesion Flow Coefficient (LFC). The parameters were assessed for rigid artery (RR; signifying high plaque elasticity), compliant artery with calcified plaque (CC; intermediate plaque elasticity) and compliant artery with smooth muscle cell proliferation (CS; low plaque elasticity), with varying degrees of epicardial stenosis. A hyperelastic Mooney-Rivlin model was used to model the arterial wall and plaque materials. Blood was modeled as a shear thinning, non-Newtonian fluid using the Carreau model. The arterial wall compliance was evaluated using the finite element method. The present study found that, with an increase in stenosis severity, FFR decreased whereas CDP and LFC increased. The cutoff value of 0.75 for FFR was observed at 78.7% area stenosis for RR, whereas for CC and CS the cutoff values were obtained at higher stenosis severities of 81.3% and 82.7%, respectively. For a fixed stenosis, CDP value decreased and LFC value increased with a decrease in plaque elasticity (RR to CS). We conclude that the differences in diagnostic parameters with compliance at intermediate stenosis (78.7-82.7% area blockage) could lead to misinterpretation of the stenosis severity.     

Plasma and vessel wall lipoprotein lipase have different roles in atherosclerosis

Lipoprotein lipase (LPL) is a key enzyme in lipoprotein metabolism, and has been hypothesized to exert either pro- or anti-atherogenic effects, depending on its localization. Decreased plasma LPL activity is associated with the high triglyceride (TG);-low HDL phenotype that is often observed in patients with premature vascular disease. In contrast, in the vessel wall, decreased LPL may be associated with less lipoprotein retention due to many potential mechanisms and, therefore, decreased foam cell formation. To directly assess this hypothesis, we have distinguished between the effects of variations in plasma and/or vessel wall LPL on atherosclerosis susceptibility in apoE-deficient mice. Reduced LPL in both plasma and vessel wall (LPL(+/-)E(-/-)) was associated with increased TG and increased total cholesterol (TC) compared with LPL(+/+)E(-/-) sibs. However despite their dyslipidemia, LPL(+/-)E(-/-) mice had significantly reduced lesion areas compared to the LPL(+/+)E(-/-) mice. Thus, decreased vessel wall LPL was associated with decreased lesion formation even in the presence of reduced plasma LPL activity. In contrast, transgenic mice with increased plasma LPL but with no increase in LPL expression in macrophages, and thus the vessel wall, had decreased TG and TC and significantly decreased lesion areas compared with LPL(+/+)E(-/-) mice. This demonstrates that increased plasma LPL activity alone, in the absence of an increase in vessel wall LPL, is associated with reduced susceptibility to atherosclerosis.Taken together, these results provide in vivo evidence that the contribution of LPL to atherogenesis is significantly influenced by the balance between vessel wall protein (pro-atherogenic) and plasma activity (anti-atherogenic).     

Artery buckling analysis using a four-fiber wall model

Artery bent buckling has been suggested as a possible mechanism that leads to artery tortuosity, which is associated with aging, hypertension, atherosclerosis, and other pathological conditions. It is necessary to understand the relationship between microscopic wall structural changes and macroscopic artery buckling behavior. To this end, the objectives of this study were to develop arterial buckling equations using a microstructure-based 4-fiber reinforced wall model, and to simulate the effects of vessel wall microstructural changes on artery buckling. Our results showed that the critical pressure increased nonlinearly with the axial stretch ratio, and the 4-fiber model predicted higher critical buckling pressures than what the Fung model predicted. The buckling equation using the 4-fiber model captured the experimentally observed reduction of critical pressure induced by elastin degradation and collagen fiber orientation changes in the arterial wall. These results improve our understanding of arterial stability and its relationship to microscopic wall remodeling, and the model provides a useful tool for further studies.