A biomechanical model of artery buckling

The stability of arteries under blood pressure load is essential to the maintenance of normal arterial function and the loss of stability can lead to tortuosity and kinking that are associated with significant clinical complications. However, mechanical analysis of arterial bent buckling is lacking. To address this issue, this paper presents a biomechanical model of arterial buckling. Using an elastic cylindrical arterial model, the mechanical equations for arterial buckling were developed and the critical buckling pressure was found to be a function of the wall stiffness (Young's modulus), arterial radius, length, wall thickness, and the axial strain. Both the model equations and experimental results demonstrated that the critical pressure is related to the axial strain. Arteries may buckle and become tortuous due to reduced (subphysiological) axial strain, hypertensive pressure, and a weakened wall. These results are in accordance with, and provide a possible explanation to the clinical observations that hypertension and aging are the risk factors for arterial tortuosity and kinking. The current model is also applicable to veins and ureters.     

Effects of elastin degradation and surrounding matrix support on artery stability

Tortuous arteries are often associated with aging, hypertension, atherosclerosis, and degenerative vascular diseases, but the mechanisms are poorly understood. Our recent theoretical analysis suggested that mechanical instability (buckling) may lead to tortuous blood vessels. The objectives of this study were to determine the critical pressure of artery buckling and the effects of elastin degradation and surrounding matrix support on the mechanical stability of arteries. The mechanical properties and critical buckling pressures, at which arteries become unstable and deform into tortuous shapes, were determined for a group of five normal arteries using pressurized inflation and buckling tests. Another group of nine porcine arteries were treated with elastase (8 U/ml), and the mechanical stiffness and critical pressure were obtained before and after treatment. The effect of surrounding tissue support was simulated using a gelatin gel. The critical pressures of the five normal arteries were 9.52 kPa (SD 1.53) and 17.10 kPa (SD 5.11) at axial stretch ratios of 1.3 and 1.5, respectively, while model predicted critical pressures were 10.11 kPa (SD 3.12) and 17.86 kPa (SD 5.21), respectively. Elastase treatment significantly reduced the critical buckling pressure (P < 0.01). Arteries with surrounding matrix support buckled into multiple waves at a higher critical pressure. We concluded that artery buckling under luminal pressure can be predicted by a buckling equation. Elastin degradation weakens the arterial wall and reduces the critical pressure, which thus leads to tortuous vessels. These results shed light on the mechanisms of the development of tortuous vessels due to elastin deficiency.     

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.     

Mechanical instability of normal and aneurysmal arteries

Tortuous arteries associated with aneurysms have been observed in aged patients with atherosclerosis and hypertension. However, the underlying mechanism is poorly understood. The objective of this study was to determine the effect of aneurysms on arterial buckling instability and the effect of buckling on aneurysm wall stress. We investigated the mechanical buckling and post-buckling behavior of normal and aneurysmal carotid arteries and aorta’s using computational simulations and experimental measurements to elucidate the interrelationship between artery buckling and aneurysms. Buckling tests were done in porcine carotid arteries with small aneurysms created using elastase treatment. Parametric studies were done for model aneurysms with orthotropic nonlinear elastic walls using finite element simulations. Our results demonstrated that arteries buckled at a critical buckling pressure and the post-buckling deflection increased nonlinearly with increasing pressure. The presence of an aneurysm can reduce the critical buckling pressure of arteries, although the effect depends on the aneurysm’s dimensions. Buckled aneurysms demonstrated a higher peak wall stress compared to unbuckled aneurysms under the same lumen pressure. We conclude that aneurysmal arteries are vulnerable to mechanical buckling and mechanical buckling could lead to high stresses in the aneurysm wall. Buckling could be a possible mechanism for the development of tortuous aneurysmal arteries such as in the Loeys–Dietz syndrome.     

Mechanical buckling of artery under pulsatile pressure

Tortuosity that often occurs in carotid and other arteries has been shown to be associated with high blood pressure, atherosclerosis, and other diseases. However the mechanisms of tortuosity development are not clear. Our previous studies have suggested that arteries buckling could be a possible mechanism for the initiation of tortuous shape but artery buckling under pulsatile flow condition has not been fully studied. The objectives of this study were to determine the artery critical buckling pressure under pulsatile pressure both experimentally and theoretically, and to elucidate the relationship of critical pressures under pulsatile flow, steady flow, and static pressure. We first tested the buckling pressures of porcine carotid arteries under these loading conditions, and then proposed a nonlinear elastic artery model to examine the buckling pressures under pulsatile pressure conditions. Experimental results showed that under pulsatile pressure arteries buckled when the peak pressures were approximately equal to the critical buckling pressures under static pressure. This was also confirmed by model simulations at low pulse frequencies. Our results provide an effective tool to predict artery buckling pressure under pulsatile pressure.     

Twist buckling behavior of arteries

Arteries are often subjected to torsion due to body movement and surgical procedures. While it is essential that arteries remain stable and patent under twisting loads, the stability of arteries under torsion is poorly understood. The goal of this work was to experimentally investigate the buckling behavior of arteries under torsion and to determine the critical buckling torque, the critical buckling twist angle, and the buckling shape. Porcine common carotid arteries were slowly twisted in vitro until buckling occurred while subjected to a constant axial stretch ratio (1.1, 1.3, 1.5 (in vivo level) and 1.7) and lumen pressure (20, 40, 70 and 100 mmHg). Upon buckling, the arteries snapped to form a kink. For a group of six arteries, the axial stretch ratio significantly affected the critical buckling torque (\(p<0.002\)) and the critical buckling twist angle (\(p<0.001\)). Lumen pressure also significantly affected the critical buckling torque (\(p<0.001\)) but had no significant effect on the critical twist angle (\(p=0.067\)). Convex material constants for a Fung strain energy function were determined and fit well with the axial force, lumen pressure, and torque data measured pre-buckling. The material constants are valid for axial stretch ratios, lumen pressures, and rotation angles of 1.3–1.5, 20–100 mmHg, and 0–270\(^\circ \), respectively. The current study elucidates the buckling behavior of arteries under torsion and provides new insight into mechanical instability of blood vessels.     

Nonlinear buckling of blood vessels: a theoretical study

Tortuosity and kinking often occur in arteries and veins but the underlying mechanisms are poorly understood. It has been suggested recently that long arteries may buckle and become tortuosity due to reduced axial tension or hypertensive pressure, but very few studies have been done to establish the biomechanical basis for artery buckling. Here we developed the arterial buckling equation using a nonlinear elastic thick-walled cylindrical model with residual stress. Our results demonstrated that arteries may buckle due to high blood pressure or low axial tension and that residual stress in the arteries increases the buckling pressure. These results are in general agreement with the previous linear elastic model. The buckling equation provides a useful tool for studying artery tortuosity and kinking.     

Magnesium supplementation and deoxycorticosterone acetate--salt hypertension: effect on arterial mechanical properties and on activity of endothelin-1

The aim of this study was to show whether the decrease in blood pressure induced by Mg supplementation in deoxycorticosterone acetate - salt (DOCA-salt) hypertensive rats is associated with mechanical modifications of blood vessels and (or) changes in tissular production and (or) vasoconstrictor activity to endothelin-1. DOCA-salt treatment increased blood pressure, media thickness, cross-sectional area, and lumen diameter of carotid arteries. Distensibility and incremental elastic modulus versus stress were not altered in carotid arteries, suggesting that the DOCA-salt vessel wall adapts structurally to preserve its blood pressure buffering capacity. Magnesium supplementation attenuated DOCA-salt hypertension. In comparison with normotensive rats, systolic, mean, and pulse pressures were higher whereas diastolic pressure was not different in Mg-supplemented DOCA-salt rats. Magnesium supplementation did not significantly modify the elastic parameters of carotid arteries. In resistance mesenteric arteries, DOCA-salt hypertension induces an inward hypertrophic remodeling. Magnesium supplementation attenuates wall hypertrophy and increases lumen diameter to the normotensive diameter, suggesting a decrease in peripheral resistance. Magnesium supplementation normalizes the altered vasoconstrictor activity of endothelin-1 in mesenteric arteries and attenuates endothelin-1 overproduction in kidney, left ventricle, and aorta of DOCA-salt rats. These findings suggest that Mg supplementation prevents blood pressure elevation by attenuating peripheral resistance and by decreasing hypertrophic effect of endothelin-1 via inhibition of endothelin-1 production.     

The effect of collagenase on the critical buckling pressure of arteries

The stability of arteries is essential to normal arterial functions and loss of stability can lead to arterial tortuosity and kinking. Collagen is a main extracellular matrix component that modulates the mechanical properties of arteries and collagen degradation at pathological conditions weakens the mechanical strength of arteries. However, the effects of collagen degradation on the mechanical stability of arteries are unclear. The objective of this study was to investigate the effects of collagen degradation on the critical buckling pressure of arteries. Arterial specimens were subjected to pressurized inflation testing and fitted with nonlinear thick-walled cylindrical model equations to determine their stress strain relationships. The arteries were then tested for the critical buckling pressure at a set of axial stretch ratios. Then, arteries were divided into three groups and treated with Type III collagenase at three different concentrations (64, 128, and 400 U/ml). Mechanical properties and buckling pressures of the arteries were determined after collagenase treatment. Additionally, the theoretical buckling pressures were also determined using a buckling equation. Our results demonstrated that the buckling pressure of arteries was lower after collagenase treatment. The difference between pre- and post- treatment was statistically significant for the highest concentration of 400U/ml but not at the lower concentrations. The buckling equation was found to yield a fair estimation to the experimental critical pressure measurements. These results shed light on the role of matrix remodeling on the mechanical stability of arteries and developments of tortuous arteries.     

The Effect of Collagenase on the Critical Buckling Pressure of Arteries^*

The stability of arteries is essential to normal arterial functions and loss of stability can lead to arterial tortuosity and kinking. Collagen is a main extracellular matrix component that modulates the mechanical properties of arteries and collagen degradation at pathological conditions weakens the mechanical strength of arteries. However, the effects of collagen degradation on the mechanical stability of arteries are unclear. The objective of this study was to investigate the effects of collagen degradation on the critical buckling pressure of arteries. Arterial specimens were subjected to pressurized inflation testing and fitted with nonlinear thick-walled cylindrical model equations to determine their stress strain relationships. The arteries were then tested for the critical buckling pressure at a set of axial stretch ratios. Then, arteries were divided into three groups and treated with Type III collagenase at three different concentrations (64, 128, and 400U/ml). Mechanical properties and buckling pressures of the arteries were determined after collagenase treatment. Additionally, the theoretical buckling pressures were also determined using a buckling equation. Our results demonstrated that the buckling pressure of arteries was lower after collagenase treatment. The difference between pre- and post- treatment was statistically significant for the highest concentration of 400U/ml but not at the lower concentrations. The buckling equation was found to yield a fair estimation to the experimental critical pressure measurements. These results shed light on the role of matrix remodeling on the mechanical stability of arteries and developments of tortuous arteries.     

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

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

Numerical simulation of blood flow and pressure drop in the pulmonary arterial and venous circulation

A novel multiscale mathematical and computational model of the pulmonary circulation is presented and used to analyse both arterial and venous pressure and flow. This work is a major advance over previous studies by Olufsen et al. (Ann Biomed Eng 28:1281–1299, 2012) which only considered the arterial circulation. For the first three generations of vessels within the pulmonary circulation, geometry is specified from patient-specific measurements obtained using magnetic resonance imaging (MRI). Blood flow and pressure in the larger arteries and veins are predicted using a nonlinear, cross-sectional-area-averaged system of equations for a Newtonian fluid in an elastic tube. Inflow into the main pulmonary artery is obtained from MRI measurements, while pressure entering the left atrium from the main pulmonary vein is kept constant at the normal mean value of 2 mmHg. Each terminal vessel in the network of ‘large’ arteries is connected to its corresponding terminal vein via a network of vessels representing the vascular bed of smaller arteries and veins. We develop and implement an algorithm to calculate the admittance of each vascular bed, using bifurcating structured trees and recursion. The structured-tree models take into account the geometry and material properties of the ‘smaller’ arteries and veins of radii \(\ge \) 50  \(\upmu \) m. We study the effects on flow and pressure associated with three classes of pulmonary hypertension expressed via stiffening of larger and smaller vessels, and vascular rarefaction. The results of simulating these pathological conditions are in agreement with clinical observations, showing that the model has potential for assisting with diagnosis and treatment for circulatory diseases within the lung.     

Observations on the vasculature of the reproductive tract in some Australian marsupials

The origin, distribution and structure of the blood vessels of the female reproductive tract and the testis of the brush possum (Trichosurus vulpecula) were studied using latex and silicone rubber casting and histological techniques. Latex casts of the vessels of the female tract were also studied in five macropod species – Macropus giganteus, M. eugenii, M. agilis, Megaleia rufa and Thylogale billardierii, and in the common wombat (Vombatus ursinus). The female reproductive tract in the brush possum was supplied and drained by four major sets of paired vessels – ovarian, cranial urogenital, caudal urogenital, and internal pudendal arteries and veins. These vessels formed substantial anastomoses with one another on each side of the midline, and also across-the-midline anastomoses. The proximal part of the ovarian artery ran in close apposition to the ovarian vein, which received one or more large uterine branches. In its distal protion the ovarian artery gave rise to a leash of small, tortuous ovarian branches, which wound around and between the plexiform ovarian veins. The testicular arteries and veins in this species also ran in close apposition to one another. Both arteries and veins branched into many smaller, mildly tortuous, parallel vessels in the spermatic cord, which reunited before entering the testis. The blood vessels of the reproductive tract in all of the macropod species studied, and in the common wombat, were basically similar to those of the brush possum. The intimate structural relationships between ovarian arteries and veins, and their ovarian branches, in these marsupials are suggestive of specializations for counter-current exchange between venous and arterial blood. However, in contrast to those of the testicular vessels where heat exchange is a demonstrated function, their physiological significance remains unknown.     

Structural and functional characteristics of the special regulatory devices in the peripheral pulmonary circulation in rabbits

The present study intended to describe in detail the several blood vessels harboring special regulatory devices in rabbit’s pulmonary tissue using light and electron microscopy and immuno-histochemistry. Numerous throttle arteries were recorded within the adventitia of the segmental and sub-segmental bronchi and within pulmonary pleura. These arteries showed characteristic narrow or obliterated lumens and some of them bear longitudinal muscular intimal bolsters. For the first time, TEM revealed some structural modifications of the vascular endothelial cells of these arteries indicating that they become more activated to perform some additional functions. Arteriovenous anastomoses (AVAs) including direct shunt vessels and glomus organs were also recognized. Direct arteriovenous shunts appeared as small connecting devices communicating between small arteries and small veins while glomus organs consisted of the tortuous glomus vessels and the related afferent and efferent vessels. Several arteries and veins showing unique unusual structural characteristics were also described. For the first time, serotonin (5-HT) was strongly expressed in the vascular endothelium and muscle fibers of throttle arteries, in glomus cells of the glomus vessels, and in vascular endothelium of some veins and venules of special structure. The exact role of 5-HT is still unknown and further investigations are required to determine the types and distribution of 5-HT receptors present in these vascular devices. We concluded that these special vascular devices can play a critical role in controlling blood flow and pressure in the peripheral pulmonary circulation; however, the exact physiological mechanisms by which they work or are controlled remain unknown providing a ripe area for further investigation.     

Differential effects of prostaglandins A1 and A2 on pulmonary vascular resistance in the dog.

The effects of PGA1 and PGA2 were studied in the canine pulmonary vascular bed. Infusion of PGA1 into the lobar artery decreased lobar arterial and venous pressure but did not change left atrial pressure. In contrast, PGA2 infusion increased lobar arterial and venous pressure and the effects of this substance were similar in experiments in which the lung was perfused with dextran or with blood. These data indicate that under conditions of controlled blood flow PGA1 decreases pulmonary vascular resistance by dilating intrapulmonary veins and to a lesser extent vessels upstream to the small veins, presumably small arteries. The present data show that PGA2 increases pulmonary vascular resistance by constricting intrapulmonary veins and upstream vessels. The predominant effect of PGA2 was on upstream vessels and the pressor effect was not due to interaction with formed elements in the blood or platelet aggregation.     

Cross-sectional shape of flexible tubes

Differential equations are derived whose solution gives the cross-sectional shape of a flexible tube as a function of the transmural pressure. These equations are solved digitally to produce a series of closed curves, each curve representing the shape of a cross section for a particular set of conditions. These are then applied to the case of systemic arteries, pulmonary arteries, and large veins. The results predict that systemic arteries must always be circular, even when the internal and external pressures are equal. In veins, a small positive internal pressure causes them to become circular, regardless of their initial state, with negligible stretching. Further increases in internal pressure cause the area of the cross section to increase due only to stretching, the shape remaining essentially circular. With pulmonary arteries, known to be noncircular, changes in the cross-sectional area result from a combination of stretching and changes of shape. Presented at the Society for Mathematical Biology Meeting, University of Pennsylvania, Philadelphia, August 19–21, 1976.     

Pressure and flow in the systemic arterial system

The dynamic characteristics of the proximal arterial system are studied by solving the nonlinear momentum and mass conservation equations for pressure and flow. The equations are solved for a model systemic arterial system that includes the aorta, common iliacs, and the internal and external iliac arteries. The model includes geometric and elastic taper of the aorta, nonlinearly elastic arteries, side flows, and a complex distal impedance. The model pressure wave shape, inlet and outlet impedance, wave travel, and apparent wave velocity compare favorably with the values measured on humans. Calculations indicate that: (i) reflections are the major factor determining the shape and distal amplification of the pressure wave in the arterial tree; (ii) although important in attenuating the proximal transmission of reflecting waves, geometric taper is not the major cause of the distal pressure wave amplification; (iii) the dicrotic wave is a result of peripheral reflection and is not due to the sudden change in flow at the end of systole; (iv) the elastic taper and nonlinearity of the wall elasticity are of minor significance in determining the flow and pressure profiles; and (v) in spite of numerous nonlinearities, the system behaves in a somewhat linear fashion for the lower frequency components.     

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 4 weeks. 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 4 weeks 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.     

Structure and Stress-Strain Relationship of Soft Tissues

The mechanical properties of a soft tissue are related to itsstructure. Weshall illustrate this by the properties of thearteries and the lung. Viscoelasticity, strain rate effects,pseudo-elasticity, and constitutive equations ar discussed.The mecahnical properties of an organ is, however, not onlybased onthe tissues of the organ, but also on its geometry andrelationship to the neighboring organs. A typical example isthe blood vessel. The capillary blood vessels of the mesenteryare "rigid"; those in the bat's wing are "distensible"; whereasthe capillaries of the lung are "sheet" like: rigid in one plane,and compliant in another. The stress-strain relationship ofthe systemic arteries is highly nonlinear, stiffening exponentiallywith increasing strains; yet that of the pulmonary arteriesin the lung is linear. The systemic veins are easily collapsible;yet the pulmonary veins in the lung are not: they remain patentwhen the blood pressure falls below the alveolargas pressure.The explanation of these differences lies in the varied interactionsbetween the blood vessels and the surrounding tissues in differentorgans. The implications of these differences on blood circulationare pointed out. Therole of ultrastructure is discussed.     

A Distinct Mechanism of Vascular Lumen Formation in Xenopus Requires EGFL7

During vertebrate blood vessel development, lumen formation is the critical process by which cords of endothelial cells transition into functional tubular vessels. Here, we use Xenopus embryos to explore the cellular and molecular mechanisms underlying lumen formation of the dorsal aorta and the posterior cardinal veins, the primary major vessels that arise via vasculogenesis within the first 48 hours of life. We demonstrate that endothelial cells are initially found in close association with one another through the formation of tight junctions expressing ZO-1. The emergence of vascular lumens is characterized by elongation of endothelial cell shape, reorganization of junctions away from the cord center to the periphery of the vessel, and onset of Claudin-5 expression within tight junctions. Furthermore, unlike most vertebrate vessels that exhibit specialized apical and basal domains, we show that early Xenopus vessels are not polarized. Moreover, we demonstrate that in embryos depleted of the extracellular matrix factor Epidermal Growth Factor-Like Domain 7 (EGFL7), an evolutionarily conserved factor associated with vertebrate vessel development, vascular lumens fail to form. While Claudin-5 localizes to endothelial tight junctions of EGFL7-depleted embryos in a timely manner, endothelial cells of the aorta and veins fail to undergo appropriate cell shape changes or clear junctions from the cell-cell contact. Taken together, we demonstrate for the first time the mechanisms by which lumens are generated within the major vessels in Xenopus and implicate EGFL7 in modulating cell shape and cell-cell junctions to drive proper lumen morphogenesis.