Finite Element simulation of buckling-induced vein tortuosity and influence of the wall constitutive properties

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.

ARVCF catenin controls force production during vertebrate convergent extension

The design of an animal's body plan is encoded in the genome, and the execution of this program is a mechanical progression involving coordinated movement of proteins, cells, and whole tissues. Thus, a challenge to understanding morphogenesis is connecting events that occur across various length scales. Here, we describe how a poorly characterized adhesion effector, Arvcf catenin, controls Xenopus head-to-tail axis extension. We find that Arvcf is required for axis extension within the intact organism but not within isolated tissues. We show that the organism-scale phenotype results from a defect in tissue-scale force production. Finally, we determine that the force defect results from the dampening of the pulsatile recruitment of cell adhesion and cytoskeletal proteins to membranes. These results provide a comprehensive understanding of Arvcf function during axis extension and produce an insight into how a cellular-scale defect in adhesion results in an organism-scale failure of development.

Mechanics-driven mechanobiological mechanisms of arterial tortuosity

Arterial tortuosity manifests in many conditions, including hypertension, genetic mutations predisposing to thoracic aortopathy, and vascular aging. Despite evidence that tortuosity disrupts efficient blood flow and that it may be an important clinical biomarker, underlying mechanisms remain poorly understood but are widely appreciated to be largely biomechanical. Many previous studies suggested that tortuosity may arise via an elastic structural buckling instability, but the novel experimental-computational approach used here suggests that tortuosity arises from mechanosensitive, cell-mediated responses to local aberrations in the microstructural integrity of the arterial wall. In particular, computations informed by multimodality imaging show that aberrations in elastic fiber integrity, collagen alignment, and collagen turnover can lead to a progressive loss of structural stability that entrenches during the development of tortuosity. Interpreted in this way, microstructural defects or irregularities of the arterial wall initiate the condition and hypertension is a confounding factor.

Tortuosity of superior cerebral veins: Comparative magnetic resonance imaging morphometrics in normal subjects and arteriovenous malformation patients

Blood vessel tortuosity results from increased diameter and length in response to higher hemodynamic loads. Tortuosity metrics have not been determined for abnormal superior cerebral veins (SCVs) draining cerebral arteriovenous malformations (AVMs). Draining vein (DV) tortuosity may influence safety and efficacy of retrograde microcatheter navigation during transvenous treatment of pial AVMs. Here, we quantify SCV tortuosity in normal subjects and AVM patients using two image segmentation methods. We used contrast-enhanced brain magnetic resonance (MR) images to define the axis of each SCV through a regularly spaced set of three-dimensional (3D) points defining its skeleton curve. We then calculated two metrics: the "sum of angles metric" (SOAM), which adds all angles of curvature along a vessel and normalizes by vessel length, and the "distance metric" (DM), a tortuosity measure providing a ratio of vessel length to linear distance between vessel endpoints. We analyzed 168 metrics in 43 veins of eight normal subjects and 41 veins of seven AVM patients. In normal subjects, the mean SOAM and DM for SCVs were 21.34 ± 7.49 °/mm and 1.42 ± 0.25, respectively. In AVM patients, DVs had a significantly higher mean SOAM of 30.43 ± 11.38 °/mm (p = .02) and DM of 2.79 ± 1.77 (p = .01) than normal subjects. In AVM patients, DVs were significantly more tortuous than matched contralateral uninvolved SCVs, which were similar in tortuosity to normal subject SCVs. We thus report normative tortuosity metrics of brain SCVs and show that AVM cortical DVs are significantly more tortuous than normal SCVs. Knowledge of these comparative tortuosities is valuable in planning endovenous AVM embolotherapies.

Computational evaluation of an extra-aortic elastic-wrap applied to simulated aging anisotropic human aorta models

Structural changes occurring to the aortic wall can result in vascular stiffening. This is represented by a loss of vascular compliance during pulsatile flow, resulting in increased systolic and pulse blood pressure, particularly in populations aged 50 and over. Aortic stiffness is thought to be permanent and an active de-stiffening strategy is yet to be developed. Extra aortic elastic wrapping has been proposed as a surgical technique to boost aortic distensibility and treat hypertension in the elderly. Previously, in-vivo and in-vitro testing have suggested a pulse-pressure reduction potential of elastic wrapping in the stiffened aortas. Herein, we explore the feasibility of elastic aortic wrapping to improve simulated aortic compliance across the age span. Detailed computational studies of the anisotropic aortic wall mechanics, using data from human subjects, were performed, evaluating key performance properties for the interaction between the aortic wall and elastic aortic wrap procedure. Main determinants of the procedure’s efficiency are identified using a pre-defined aortic stiffness and wrap elasticity. Finite element analysis predicts that segmental aortic distensibility can be increased if elastic wrapping is applied to a simulated stiff aorta. Elastic aortic wrapping is calculated to have little impact on the compliance of an initially distensible aorta.

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.

Over-Wrapping of the Aortic Wall with an Elastic Extra-Aortic Wrap Results in Luminal Creasing

Elastic extra-aortic wrapping is a potential non-pharmacological way to improve aortic compliance and treat isolated systolic hypertension associated with a stiffened aorta. We aimed to use computer simulations to re-evaluate whether there is aortic shape distortion in aortic wrapping to achieve greater elasticity of the wrapped aortic segment. Non-linear transient numerical analysis based on an idealized hyper-elastic single-layered aorta model was performed to simulate the force/displacement regimes of external aortic wrapping. Pressure-displacement relationships were used to establish model aortic wall distensibilities of 4.3 and 5.5 (10⁻³ mmHg⁻¹). A physiological pulsatile lumen pressure was employed to estimate the potential improvements in aortic distensibility by compression forces representing elastic aortic wrapping. In the less distensible model of the aortic wall there was increased systolic expansion in the wrapped segment. We found a risk of creasing of the aortic luminal wall with wrapping. Sufficient unloading of a thick and elastic aortic wall to induce increased compliance, as observed in elastic wrapping, is associated with the potential risk of over compression and folding (creasing) inside the lumen.

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.

Artery buckling analysis using a two-layered wall model with collagen dispersion

Artery buckling has been proposed as a possible cause for artery tortuosity associated with various vascular diseases. Since microstructure of arterial wall changes with aging and diseases, it is essential to establish the relationship between microscopic wall structure and artery buckling behavior. The objective of this study was to developed arterial buckling equations to incorporate the two-layered wall structure with dispersed collagen fiber distribution. Seven porcine carotid arteries were tested for buckling to determine their critical buckling pressures at different axial stretch ratios. The mechanical properties of these intact arteries and their intima-media layer were determined via pressurized inflation test. Collagen alignment was measured from histological sections and modeled by a modified von-Mises distribution. Buckling equations were developed accordingly using microstructure-motivated strain energy function. Our results demonstrated that collagen fibers disperse around two mean orientations symmetrically to the circumferential direction (39.02°±3.04°) in the adventitia layer; while aligning closely in the circumferential direction (2.06°±3.88°) in the media layer. The microstructure based two-layered model with collagen fiber dispersion described the buckling behavior of arteries well with the model predicted critical pressures match well with the experimental measurement. Parametric studies showed that with increasing fiber dispersion parameter, the predicted critical buckling pressure increases. These results validate the microstructure-based model equations for artery buckling and set a base for further studies to predict the stability of arteries due to microstructural changes associated with vascular diseases and aging.

Critical buckling pressure in mouse carotid arteries with altered elastic fibers

Arteries can buckle axially under applied critical buckling pressure due to a mechanical instability. Buckling can cause arterial tortuosity leading to flow irregularities and stroke. Genetic mutations in elastic fiber proteins are associated with arterial tortuosity in humans and mice, and may be the result of alterations in critical buckling pressure. Hence, the objective of this study is to investigate how genetic defects in elastic fibers affect buckling pressure. We use mouse models of human disease with reduced amounts of elastin (Eln+/-) and with defects in elastic fiber assembly due to the absence of fibulin-5 (Fbln5-/-). We find that Eln+/- arteries have reduced buckling pressure compared to their wild-type controls. Fbln5-/- arteries have similar buckling pressure to wild-type at low axial stretch, but increased buckling pressure at high stretch. We fit material parameters to mechanical test data for Eln+/-, Fbln5-/- and wild-type arteries using Fung and four-fiber strain energy functions. Fitted parameters are used to predict theoretical buckling pressure based on equilibrium of an inflated, buckled, thick-walled cylinder. In general, the theoretical predictions underestimate the buckling pressure at low axial stretch and overestimate the buckling pressure at high stretch. The theoretical predictions with both models replicate the increased buckling pressure at high stretch for Fbln5-/- arteries, but the four-fiber model predictions best match the experimental trends in buckling pressure changes with axial stretch. This study provides experimental and theoretical methods for further investigating the influence of genetic mutations in elastic fibers on buckling behavior and the development of arterial tortuosity.