Twist buckling behavior of arteries

Suppressing torsional buckling in auxetic meta-shells

Take a thin cylindrical shell and twist it; it will buckle immediately. Such unavoidable torsional buckling can lead to systemic failure, for example by disrupting the blood flow through arteries. In this study, we prevent this torsional buckling instability using a combination of auxeticity and orthotropy in cylindrical metamaterial shells with a holey pattern. When the principal axes of the orthotropic meta-shell are relatively aligned with that of the compressive component of the applied stress during twisting, the meta-shell uniformly shrinks in the radial direction as a result of a local buckling instability. This shrinkage coincides with a softening-stiffening transition that leads to ordered stacking of unit cells along the compressive component of the applied stress. These transitions due to local instabilities circumvent the usual torsional instability even under a large twist angle. This study highlights the potential of tailoring anisotropy and programming instabilities in metamaterials, with potential applications in designing mechanical elements for soft robotics, biomechanics or fluidics. As an example of such applications, we demonstrate soft torsional compressor for generating pulsatile flows through a torsion release mechanism.

Mechanical characterization and torsional buckling of pediatric cardiovascular materials

In complex cardiovascular surgical reconstructions, conduit materials that avoid possible large-scale structural deformations should be considered. A fundamental mode of mechanical complication is torsional buckling which occurs at the anastomosis site due to the mechanical instability, leading surgical conduit/patch surface deformation. The objective of this study is to investigate the torsional buckling behavior of commonly used materials and to develop a practical method for estimating the critical buckling rotation angle under physiological intramural vessel pressures. For this task, mechanical tests of four clinically approved materials, expanded polytetrafluoroethylene (ePTFE), Dacron, porcine and bovine pericardia, commonly used in pediatric cardiovascular surgeries, are conducted (n = 6). Torsional buckling initiation tests with n = 4 for the baseline case (L = 7.5 cm) and n = 3 for the validation of ePTFE (L = 15 cm) and Dacron (L = 15 cm and L = 25 cm) for each are also conducted at low venous pressures. A practical predictive formulation for the buckling potential is proposed using experimental observations and available theory. The relationship between the critical buckling rotation angle and the lumen pressure is determined by balancing the circumferential component of the compressive principal stress with the shear stress generated by the modified critical buckling torque, where the modified critical buckling torque depends linearly on the lumen pressure. While the proposed technique successfully predicted the critical rotation angle values lying within two standard deviations of the mean in the baseline case for all four materials at all lumen pressures, it could reliably predict the critical buckling rotation angles for ePTFE and Dacron samples of length 15 cm with maximum relative errors of 31% and 38%, respectively, in the validation phase. However, the validation of the performance of the technique demonstrated lower accuracy for Dacron samples of length 25 cm at higher pressure levels of 12 mmHg and 15 mmHg. Applicable to all surgical materials, this formulation enables surgeons to assess the torsional buckling potential of vascular conduits noninvasively. Bovine pericardium has been found to exhibit the highest stability, while Dacron (the lowest) and porcine pericardium have been identified as the least stable with the (unitless) torsional buckling resistance constants, 43,800, 12,300 and 14,000, respectively. There was no significant difference between ePTFE and Dacron, and between porcine and bovine pericardia. However, both porcine and bovine pericardia were found to be statistically different from ePTFE and Dacron individually (p < 0.0001). ePTFE exhibited highly nonlinear behavior across the entire strain range [0, 0.1] (or 10% elongation). The significant differences among the surgical materials reported here require special care in conduit construction and anastomosis design.

The effects of axial twisting and material non-symmetry on arterial bent buckling

Artery buckling occurs due to hypertensive lumen pressure or reduced axial tension and other pathological conditions. Since arteries in vivo often experience axial twisting and the collagen fiber alignment in the arterial wall may become nonsymmetric, it is imperative to know how axial twisting and nonsymmetric collagen alignment would affect the buckling behavior of arteries. To this end, the objective of this study was to determine the effect of axial twisting and nonsymmetric collagen fiber distribution on the critical pressure of arterial bent buckling. The buckling model analysis was generalized to incorporate an axial twist angle and nonsymmetric fiber alignment. The effect of axial twisting on the critical pressure was simulated and experimentally tested in a group of porcine carotid arteries. Our results showed that axial twisting tends to reduce the critical pressure depending on the axial stretch ratio and twist angle. In addition, nonsymmetric fiber alignment reduces the critical pressure. Experimental results confirmed that a twist angle of 90° reduces the critical pressure significantly (p < 0.05). It was concluded that axial twisting and non-axisymmetric collagen fibers distribution could make arteries prone to bent buckling. These results enrich our understanding of artery buckling and vessel tortuosity. The model analysis and results could also be applicable to other fiber reinforced tubes under lumen pressure and axial twisting.

Numerical simulations of the nonsymmetric growth and remodeling of arteries under axial twisting

Blood vessels are often subjected to axial twisting during body movement or surgery. Sustained twisting may lead to blood vessel growth and remodeling, however, it remains unclear how the extracellular matrix in the blood vessels remodel under sustained axial twisting. This study aimed to develop a computational model to simulate stress-induced growth and remodeling (G&R) of thin-walled blood vessels under axial twisting. Cylindrical vessels were subjected to a step increase in axial torque while the axial stretch and lumen pressure remained constant. The vessel walls were modeled based on the constrained mixture theory given as microstructure-based discrete fiber families with isotropic matrix structure models. Simulation results demonstrated that in response to a constant twist angle loading, arterial wall thickness, mass, and twisting torque gradually increase towards a new steady state. However, the stress and mass decrease in one diagonal fiber family while increasing in the other diagonal fiber family before reaching plateaus. A novel finding was that the two helical collagen fiber families showed different growth rates and patterns during remodeling, driven by the different fiber stresses generated by the twisting, and led to non-symmetric material properties. This study sheds new light on arterial wall remodeling under axial twisting.

Buckling of Arteries With Noncircular Cross Sections: Theory and Finite Element Simulations

The stability of blood vessels is essential for maintaining the normal arterial function, and loss of stability may result in blood vessel tortuosity. The previous theoretical models of artery buckling were developed for circular vessel models, but arteries often demonstrate geometric variations such as elliptic and eccentric cross-sections. The objective of this study was to establish the theoretical foundation for noncircular blood vessel bent (i.e., lateral) buckling and simulate the buckling behavior of arteries with elliptic and eccentric cross-sections using finite element analysis. A generalized buckling equation for noncircular vessels was derived and finite element analysis was conducted to simulate the artery buckling behavior under lumen pressure and axial tension. The arterial wall was modeled as a thick-walled cylinder with hyper-elastic anisotropic and homogeneous material. The results demonstrated that oval or eccentric cross-section increases the critical buckling pressure of arteries and having both ovalness and eccentricity would further enhance the effect. We conclude that variations of the cross-sectional shape affect the critical pressure of arteries. These results improve the understanding of the mechanical stability of arteries.

Analysis of sequential ultrasound frames for the measurement of hemodynamic stresses, critical bent buckling pressure, and critical buckling torque of human common carotid atherosclerosis

BACKGROUND

Structural properties of the arterial wall are important diagnostic parameters. The current study aimed at investigating the hemodynamic properties and intima-media thickness changes of the common carotid artery in human subjects with atherosclerosis in order to determine the relationships between these indices.

METHODS

This study presented methods to detect instantaneous changes in the lumen diameter, intima media thickness, longitudinal movement and acceleration, and velocity of the left side of common carotid artery. These parameters were measured in 155 male patients, categorized into control (n = 42), mild (n = 39), moderate (n = 37), and severe (n = 37) carotid stenosis groups by B-mode and Doppler ultrasonography. Extracted parameters were used to estimate the biomechanical properties of arteries, including radial strain, arterial stiffness index, Young's elastic modulus, circumferential stress, shear stress, axial stress, critical bent buckling pressure, and critical buckling torque.

FINDINGS

All biomechanical parameters of common carotid artery were significantly different in patients with mild, moderate, and severe stenosis, compared to the control group (P < 0.05). Moreover, the current results showed a significant correlation between intima media thickness and non-intima media thickness-based biomechanical indices including circumferential strain, stiffness index, and shear stress in different stenosis groups (P < 0.05).

INTERPRETATION

We concluded that the conventional and new indicators such as axial stress, critical bent buckling pressure, critical buckling torque could be useful for evaluating atherosclerosis development and also, may provide more information for physicians and interventional radiologists in designing strategies for decreasing risk in interventional treatment such as stent replacement and differentiation of vulnerable plaques.

Arterial Wall Stiffening in Caveolin-1 Deficiency-Induced Pulmonary Artery Hypertension in Mice

BACKGROUND

Pulmonary artery hypertension (PAH) is a complex disorder that can lead to right heart failure. The generation of caveolin-1 deficient mice (CAV-1-/-) has provided an alternative genetic model to study the mechanisms of pulmonary hypertension. However, the vascular adaptations in these mice have not been characterized.

OBJECTIVE

To determine the histological and functional changes in the pulmonary and carotid arteries in CAV-1-/- induced PAH.

METHODS

Pulmonary and carotid arteries of young (4-6 months old) and mature (9-12 months old) CAV-1-/- mice were tested and compared to normal wild type mice.

RESULTS

Artery stiffness increases in CAV-1-/- mice, especially the circumferential stiffness of the pulmonary arteries. Increases in stiffness were quantified by a decrease in circumferential stretch and transition strain, increases in elastic moduli, and an increase in total strain energy at physiologic strains. Changes in mechanical properties for the pulmonary artery correlated with increased collagen content while carotid artery mechanical properties correlated with decreased elastin content.

CONCLUSIONS

We demonstrated that an increase in artery stiffness is associated with CAV-1 deficiency-induced pulmonary hypertension. These results improve our understanding of artery remodeling in PAH.

Stability Analysis of Arteries Under Torsion

Vascular tortuosity may impede blood flow, occlude the lumen, and ultimately lead to ischemia or even infarction. Mechanical loads like blood pressure, axial force, and also torsion are key factors participating in this complex mechanobiological process. The available studies on arterial torsion instability followed computational or experimental approaches, yet single available theoretical study had modeled the artery as isotropic linear elastic. This paper aim is to validate a theoretical model of arterial torsion instability against experimental data. The artery is modeled as a single-layered, nonlinear, hyperelastic, anisotropic solid, with parameters calibrated from experiment. Linear bifurcation analysis is then performed to predict experimentally measured stability margins. Uncertainties in geometrical parameters and in measured mechanical response were considered. Also, the type of rate (incremental) boundary conditions (RBCs) impact on the results was examined (e.g., dead load, fluid pressure). The predicted critical torque and twist angle followed the experimentally measured trends. The closest prediction errors in the critical torque and twist rate were 22% and 67%, respectively. Using the different RBCs incurred differences of up to 50% difference within the model predictions. The present results suggest that the model may require further improvements. However, it offers an approach that can be used to predict allowable twist levels in surgical procedures (like anastomosis and grafting) and in the design of stents for arteries subjected to high torsion levels (like the femoropopliteal arteries). It may also be instructive in understanding biomechanical processes like arterial tortuosity, kinking, and coiling.

Computational simulations of the helical buckling behavior of blood vessels

Tortuous vessels are often observed in vivo and could hinder or even disrupt blood flow to distal organs. Besides genetic and biological factors, the in vivo mechanical loading seems to play a role in the formation of tortuous vessels, but the mechanism for formation of helical vessel shape remains unclear. Accordingly, the aim of this study was to investigate the biomechanical loads that trigger the occurrence of helical buckling in blood vessels using finite element analysis. Porcine carotid arteries were modeled as thick-walled cylindrical tubes using generalized Fung and Holzapfel-Gasser-Ogden constitutive models. Physiological loadings, including axial tension, lumen pressure, and axial torque, were applied. Simulations of various geometric dimensions, different constitutive models and at various levels of axial stretch ratios, lumen pressures, and twist angles were performed to identify the mechanical factors that determine the helical stability. Our results demonstrated that axial torsion can cause wringing (twist buckling) that leads to kinking or helical coiling and even looping and winding. The specific buckling patterns depend on the combination of lumen pressure, axial torque, axial tension, and the dimensions of the vessels. This study elucidates the mechanism of how blood vessels buckle under various mechanical loads and how complex mechanical loads yield helical buckling.

Sensitivity of Arterial Hyperelastic Models to Uncertainties in Stress-Free Measurements

Despite major advances made in modeling vascular tissue biomechanics, the predictive power of constitutive models is still limited by uncertainty of the input data. Specifically, key measurements, like the geometry of the stress-free (SF) state, involve a definite, sometimes non-negligible, degree of uncertainty. Here, we introduce a new approach for sensitivity analysis of vascular hyperelastic constitutive models to uncertainty in SF measurements. We have considered two vascular hyperelastic models: the phenomenological Fung model and the structure-motivated Holzapfel-Gasser-Ogden (HGO) model. Our results indicate up to 160% errors in the identified constitutive parameters for a 5% measurement uncertainty in the SF data. Relative margins of errors of up to 30% in the luminal pressure, 36% in the axial force, and over 200% in the stress predictions were recorded for 10% uncertainties. These findings are relevant to the large body of studies involving experimentally based modeling and analysis of vascular tissues. The impact of uncertainties on calibrated constitutive parameters is significant in context of studies that use constitutive parameters to draw conclusions about the underlying microstructure of vascular tissues, their growth and remodeling processes, and aging and disease states. The propagation of uncertainties into the predictions of biophysical parameters, e.g., force, luminal pressure, and wall stresses, is of practical importance in the design and execution of clinical devices and interventions. Furthermore, insights provided by the present findings may lead to more robust parameters identification techniques, and serve as selection criteria in the trade-off between model complexity and sensitivity.

Three-dimensional analysis of the thoracic aorta microscopic deformation during intraluminal pressurization

The aorta is composed of various constituents with different mechanical properties. This heterogeneous structure implies non-uniform deformation in the aorta, which could affect local cell functions. The present study investigates 3D strains of the aorta at a cell scale induced by intraluminal pressurization. After resected mouse, thoracic aortas were stretched to their in vivo length, and the aortas were pressurized at 15, 40, 80, 120, and 160 mmHg. Images of autofluorescent light of elastin were captured under a two-photon microscope. From the movement of markers in elastic laminas (ELs) created by photo-bleaching, 3D strains (ε_θθ, ε_zz, ε_rr, ε_rθ, ε_rz, ε_θz) between two neighboring ELs in the circumferential (θ), longitudinal (z), and radial (r) directions with reference to the dimensions at 15 mmHg were calculated. The results demonstrated that the average of shear strain ε_rθ was almost 0 in a physiological pressure range (from 80 to 120 mmHg) with an absolute value |ε_rθ| changing approximately by 5%. This indicates that ELs experience radial–circumferential shear at the cell scale, but not at the whole tissue scale. The normal strains in the circumferential ε_θθ and longitudinal direction ε_zz were positive but that in the radial direction ε_rr was almost 0, which demonstrates that aortic tissue is not an incompressible material. The first principal direction in the radial–circumferential plane was 29° ± 13° from the circumferential direction. We show that the aorta is not simply stretched in the circumferential direction during pressurization and that cells in the aorta undergo complex deformations by nature.

Effect of Axial Stretch on Lumen Collapse of Arteries

The stability of the arteries under in vivo pressure and axial tension loads is essential to normal arterial function, and lumen collapse due to buckling can hinder the blood flow. The objective of this study was to develop the lumen buckling equation for nonlinear anisotropic thick-walled arteries to determine the effect of axial tension. The theoretical equation was developed using exponential Fung strain function, and the effects of axial tension and residual stress on the critical buckling pressure were illustrated for porcine coronary arteries. The buckling behavior was also simulated using finite-element analysis. Our results demonstrated that lumen collapse of arteries could occur when the transmural pressure is negative and exceeded a critical value. This value depends upon the axial stretch ratio and material properties of the arterial wall. Axial tensions show a biphasic effect on the critical buckling pressure. The lumen aspect ratio of arteries increases nonlinearly with increasing external pressure beyond the critical value as the lumen collapses. These results enhance our understanding of artery lumen collapse behavior.

Haemodynamic Recovery Properties of the Torsioned Testicular Artery Lumen

Testicular artery torsion (twisting) is one such severe vascular condition that leads spermatic cord injury. In this study, we investigate the recovery response of a torsioned ram testicular artery in an isolated organ-culture flow loop with clinically relevant twisting modes (90°, 180°, 270° and 360° angles). Quantitative optical coherence tomography technique was employed to track changes in the lumen diameter, wall thickness and the three-dimensional shape of the vessel in the physiological pressure range (10-50 mmHg). As a control, pressure-flow characteristics of the untwisted arteries were studied when subjected to augmented blood flow conditions with physiological flow rates up to 36 ml/min. Both twist and C-shaped buckling modes were observed. Acute increase in pressure levels opened the narrowed lumen of the twisted arteries noninvasively at all twist angles (at ∼22 mmHg and ∼35 mmHg for 360°-twisted vessels during static and dynamic flow experiments, respectively). The association between the twist-opening flow rate and the vessel diameter was greatly influenced by the initial twist angle. The biomechanical characteristics of the normal (untwisted) and torsioned testicular arteries supported the utilization of blood flow augmentation as an effective therapeutic approach to modulate the vessel lumen and recover organ reperfusion.

Arterial wall remodeling under sustained axial twisting in rats

Blood vessels often experience torsion along their axes and it is essential to understand their biological responses and wall remodeling under torsion. To this end, a rat model was developed to investigate the arterial wall remodeling under sustained axial twisting in vivo. Rat carotid arteries were twisted at 180° along the longitudinal axis through a surgical procedure and maintained for different durations up to 4weeks. The wall remodeling in these twisted arteries was examined using histology, immunohistochemistry and fluorescent microscopy. Our data showed that arteries remodeled under twisting in a time-dependent manner during the 4weeks post-surgery. Cell proliferation, MMP-2 and MMP-9 expressions, medial wall thickness and lumen diameter increased while collagen to elastin ratio decreased. The size and number of internal elastic lamina fenestrae increased with elongated shapes, while the endothelial cells elongated and aligned towards the blood flow direction gradually. These results demonstrated that sustained axial twisting results in artery remodeling in vivo. The rat carotid artery twisting model is an effective in vivo model for studying arterial wall remodeling under long-term torsion. These results enrich our understanding of vascular biology and arterial wall remodeling under mechanical stresses.

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.

Increased Energy Loss Due to Twist and Offset Buckling of the Total Cavopulmonary Connection

The hemodynamic energy loss through the surgically implanted conduits determines the postoperative cardiac output and exercise capacity following the palliative repair of single-ventricle congenital heart defects. In this study, the hemodynamics of severely deformed surgical pathways due to torsional deformation and anastomosis offset are investigated. We designed a mock-up total cavopulmonary connection (TCPC) circuit to replicate the mechanically failed inferior vena cava (IVC) anastomosis morphologies under physiological venous pressure (9, 12, 15 mmHg), in vitro, employing the commonly used conduit materials: Polytetrafluoroethylene (PTFE), Dacron, and porcine pericardium. The sensitivity of hemodynamic performance to torsional deformation for three different twist angles (0 deg, 30 deg, and 60 deg) and three different caval offsets (0 diameter (D), 0.5D, and 1D) are digitized in three dimensions and employed in computational fluid dynamic (CFD) simulations to determine the corresponding hydrodynamic efficiency levels. A total of 81 deformed conduit configurations are analyzed; the pressure drop values increased from 80 to 1070% with respect to the ideal uniform diameter IVC conduit flow. The investigated surgical materials resulted in significant variations in terms of flow separation and energy loss. For example, the porcine pericardium resulted in a pressure drop that was eight times greater than the Dacron conduit. Likewise, PTFE conduit resulted in a pressure drop that was three times greater than the Dacron conduit under the same venous pressure loading. If anastomosis twist and/or caval offset cannot be avoided intraoperatively due to the anatomy of the patient, alternative conduit materials with high structural stiffness and less influence on hemodynamics can be considered.

An in Vitro Twist Fatigue Test of Fabric Stent-Grafts Supported by Z-Stents vs. Ringed Stents

Whereas buckling can cause type III endoleaks, long-term twisting of a stent-graft was investigated here as a mechanism leading to type V endoleak or endotension. Two experimental device designs supported with Z-stents having strut angles of 35° or 45° were compared to a ringed control under accelerated twisting. Damage to each device was assessed and compared after different durations of twisting, with focus on damage that may allow leakage. Stent-grafts with 35° Z-stents had the most severe distortion and damage to the graft fabric. The 45° Z-stents caused less fabric damage. However, consistent stretching was still seen around the holes for sutures, which attach the stents to the graft fabric. Larger holes may become channels for fluid percolation through the wall. The ringed stent-graft had the least damage observed. Stent apexes with sharp angles appear to be responsible for major damage to the fabrics. Device manufacturers should consider stent apex angle when designing stent-grafts, and ensure their devices are resistant to twisting.

The phase diagram and radial collapse of an inflated soft tube under twist

When an inflated soft tube such as a cylindrical balloon is twisted, mechanical instability can arise and produces a kink-like radius collapsing in the middle of the tube. Here this phenomenon inspires us to theoretically analyze a standard non-linear model of rubber elasticity for soft tubes. We show that there exists a critical pressure beyond which such instability arises. The critical pressure depends on the elastic properties of the tube material and the geometric dimensions of the thin-walled tube. This general theory covers a large class of soft materials and explains why twist-induced collapsing is observable in soft and thin elastic tubes such as balloons, but not in hard and thick tubes such as water hoses.

Artery Remodeling Under Axial Twist in Three Days Organ Culture

Arteries often endure axial twist due to body movement and surgical procedures, but how arteries remodel under axial twist remains unclear. The objective of this study was to investigate early stage arterial wall remodeling under axial twist. Porcine carotid arteries were twisted axially and maintained for three days in ex vivo organ culture systems while the pressure and flow remained the same as untwisted controls. Cell proliferation, internal elastic lamina (IEL) fenestrae shape and size, endothelial cell (EC) morphology and orientation, as well as the expression of matrix metalloproteinases (MMPs), MMP-2 and MMP-9, and tissue inhibitor of metalloproteinase-2 (TIMP-2) were quantified using immunohistochemistry staining and immunoblotting. Our results demonstrated that cell proliferation in both the intima and media were significantly higher in the twisted arteries compared to the controls. The cell proliferation in the intima increased from 1.33 ± 0.21% to 7.63 ± 1.89%, and in the media from 1.93 ± 0.84% to 8.27 ± 2.92% (p < 0.05). IEL fenestrae total area decreased from 26.07 ± 2.13% to 14.74 ± 0.61% and average size decreased from 169.03 ± 18.85 μm(2) to 80.14 ± 1.96 μm(2) (p < 0.01), but aspect ratio increased in the twist group from 2.39 ± 0.15 to 2.83 ± 0.29 (p < 0.05). MMP-2 expression significantly increased (p < 0.05) while MMP-9 and TIMP-2 showed no significant difference in the twist group. The ECs in the twisted arteries were significantly elongated compared to the controls after three days. The angle between the major axis of the ECs and blood flow direction under twist was 7.46 ± 2.44 degrees after 3 days organ culture, a decrease from the initial 15.58 ± 1.29 degrees. These results demonstrate that axial twist can stimulate artery remodeling. These findings complement our understanding of arterial wall remodeling under mechanical stress resulting from pressure and flow variations.

Artery buckling: new phenotypes, models, and applications

Arteries are under significant mechanical loads from blood pressure, flow, tissue tethering, and body movement. It is critical that arteries remain patent and stable under these loads. This review summarizes the common forms of buckling that occur in blood vessels including cross-sectional collapse, longitudinal twist buckling, and bent buckling. The phenomena, model analyses, experimental measurements, effects on blood flow, and clinical relevance are discussed. It is concluded that mechanical buckling is an important issue for vasculature, in addition to wall stiffness and strength, and requires further studies to address the challenges. Studies of vessel buckling not only enrich vascular biomechanics but also have important clinical applications.