Blood vessel buckling within soft surrounding tissue generates tortuosity

Vicious Circle With Venous Hypertension, Irregular Flow, Pathological Venous Wall Remodeling, and Valve Destruction in Chronic Venous Disease: A Review

Substantial advances occurred in phlebological practice in the last two decades. With the use of modern diagnostic equipment, the patients' venous hemodynamics can be examined in detail in everyday practice. Application of venous segments for arterial bypasses motivated studies on the effect of hemodynamic load on the venous wall. New animal models have been developed to study hemodynamic effects on the venous system. In vivo and in vitro studies revealed cellular phase transitions of venous endothelial, smooth muscle, and fibroblastic cells and changes in connective tissue composition, under hemodynamic load and at different locations of the chronically diseased venous system. This review is an attempt to integrate our knowledge from epidemiology, paleoanthropology and anthropology, clinical and experimental hemodynamic studies, histology, cell physiology, cell pathology, and molecular biology on the complex pathomechanism of this frequent disease. Our conclusion is that the disease is initiated by limited genetic adaptation of mankind not to bipedalism but to bipedalism in the unmoving standing or sitting position. In the course of the disease several pathologic vicious circles emerge, sustained venous hypertension inducing cellular phase transitions, chronic wall inflammation, apoptosis of cells, pathologic dilation, and valvular damage which, in turn, further aggravate the venous hypertension.

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.

Nailfold capillary patterns correlate with age, gender, lifestyle habits, and fingertip temperature

Nailfold capillaroscopy is a simple and noninvasive imaging tool to visualize the pattern of capillaries. Microvascular abnormalities have been previously observed in autoimmune disease such as systemic sclerosis and diabetes. Thus, early detection of microvascular dysfunction or changes has promising way for the one of the disease preventions. In this study, for routine health checkups, we evaluated the relationship between the structure of nailfold capillaries and lifestyle habits in healthy participants. First, we analyzed the correlation of structural parameters of nailfold capillaries with values of responses to questions on their lifestyle habits in 224 participants. The results suggested that an unhealthy lifestyle, including poor sleeping habits, smoking, intense exercise, and drinking alcohol, causes a change in the pattern of nailfold capillaries. We then investigated whether the pattern of nailfold capillaries changed after a conscious improvement in lifestyle habits. One to two weeks after the self-improvement of lifestyle habits, the hairpin loops sharpened or straightened. In conclusion, this study is the first report indicating a correlation between the structure of nailfold capillaries and lifestyle habits in a non-clinical population. The simple, inexpensive, and noninvasive method using nailfold microscopy can be employed for routine health checkups everywhere even at a bedside.

Directing Multicellular Organization by Varying the Aspect Ratio of Soft Hydrogel Microwells

Multicellular organization with precise spatial definition is essential to various biological processes, including morphogenesis, development, and healing in vascular and other tissues. Gradients and patterns of chemoattractants are well-described guides of multicellular organization, but the influences of 3D geometry of soft hydrogels are less well defined. Here, the discovery of a new mode of endothelial cell self-organization guided by combinatorial effects of stiffness and geometry, independent of protein or chemical patterning, is described. Endothelial cells in 2 kPa microwells are found to be ≈30 times more likely to migrate to the edge to organize in ring-like patterns than in stiff 35 kPa microwells. This organization is independent of curvature and significantly more pronounced in 2 kPa microwells with aspect ratio (perimeter/depth) < 25. Physical factors of cells and substrates that drive this behavior are systematically investigated and a mathematical model that explains the organization by balancing the dynamic interaction between tangential cytoskeletal tension, cell-cell, and cell-substrate adhesion is presented. These findings demonstrate the importance of combinatorial effects of geometry and stiffness in complex cellular organization that can be leveraged to facilitate the engineering of bionics and integrated model organoid systems with customized nutrient vascular networks.

The effect of pharmaceutical nanoparticles and atherosclerosis in aorta artery on the instable blood velocity based on numerical method

In medicine field, dynamic investigation of aorta artery has received attention due to its notable functions and significance upon performance of heart and individual health. Because, aortic injuries cause lethal occurrences having numerous mortality rates. Therefore, more probes, in particular, dynamic response of aorta arteries conveying blood flow containing pharmaceutical nanoparticles is essential. In present research, we attempt to model biomechanically the dynamic instability assessment of aorta arteries with atherosclerosis in tissue matrix conveying blood including pharmaceutical magnetic nanoparticles. Thus, according to classical cylindrical shell theory, the aorta arteries will be considered as elastic cylindrical vessels and symmetric lipid tissue is utilized in order to model atherosclerosis in the artery. Applying magnetic field to nanoparticles results in attraction of lipid tissue in artery. Moreover, the nature of blood flow is regarded non-Newtonian based on Casson, Carreau, and power law models. Using Hamilton's principle, the motion equations are derived and based on differential quadrature method, the dynamic instability region of aorta artery is obtained. The influences of different variables such as magnetic field, magnetic nanoparticle's volume percent, combined effects of the tissue, lipid's height and length, and non-Newtonian models upon dynamic behavior of aorta artery are investigated. According to the results, increase in lipid's height leads to increase in resonance frequency of aorta arteries.

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.

Associations of urinary dichloroacetic acid and trichloroacetic acid exposure with platelet indices: Exploring the mediating role of blood pressure in the general population

Human exposure to drinking water disinfection by-products (DBPs) is potentially linked to high blood pressure (BP), which may be associated with abnormal platelet activation. This study investigated whether the relationship between DBP exposure with platelet change was mediated by BP. DBP biomarkers, such as urinary dichloroacetic acid (DCAA) and trichloroacetic acid (TCAA), BP and platelet indices from 505 adults from a hospital in Shijiazhuang, China were measured. The cross-sectional associations among DCAA and TCAA exposure, BP and platelet indices were explored through multivariable linear regressions, and the mediation effect of BP was evaluated using the Sobel-Goodman test. We observed that DCAA and TCAA were positively associated with systolic BP (all p for trends < 0.01), which was positively associated with platelet count (PLC) (p for trend < 0.05). Mediation analysis indicated that systolic BP fully mediated the associations of DCAA and TCAA with PLC. When BP was controlled, a previously inverse significant relation between DCAA and platelet distribution width (PDW) remained significant (p < 0.05). Obtained results suggested that exposure to DCAA may contribute to decreased PDW in humans. Systolic BP is a possible mediator of the association between DCAA exposure and PLC. TCAA may indirectly positively affect PLC by increasing systolic BP.

Improving Blood Vessel Tortuosity Measurements via Highly Sampled Numerical Integration of the Frenet-Serret Equations

Measures of vascular tortuosity-how curved and twisted a vessel is-are associated with a variety of vascular diseases. Consequently, measurements of vessel tortuosity that are accurate and comparable across modality, resolution, and size are greatly needed. Yet in practice, precise and consistent measurements are problematic-mismeasurements, inability to calculate, or contradictory and inconsistent measurements occur within and across studies. Here, we present a new method of measuring vessel tortuosity that ensures improved accuracy. Our method relies on numerical integration of the Frenet-Serret equations. By reconstructing the three-dimensional vessel coordinates from tortuosity measurements, we explain how to identify and use a minimally-sufficient sampling rate based on vessel radius while avoiding errors associated with oversampling and overfitting. Our work identifies a key failing in current practices of filtering asymptotic measurements and highlights inconsistencies and redundancies between existing tortuosity metrics. We demonstrate our method by applying it to manually constructed vessel phantoms with known measures of tortuousity, and 9,000 vessels from medical image data spanning human cerebral, coronary, and pulmonary vascular trees, and the carotid, abdominal, renal, and iliac arteries.

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.

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.

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.

Buckling Reduces eNOS Production and Stimulates Extracellular Matrix Remodeling in Arteries in Organ Culture

Artery buckling alters the fluid shear stress and wall stress in the artery but its temporal effect on vascular wall remodeling is poorly understood. The purpose of this study was to investigate the early effect of artery buckling on endothelial nitric oxide synthase (eNOS) expression and extracellular matrix remodeling. Bilateral porcine carotid arteries were maintained in an ex vivo organ culture system with and without buckling while under the same physiological pressure and flow rate for 3-7 days. Matrix metalloproteinase-2 (MMP-2), MMP-9, fibronectin, elastin, collagen I, III and IV, tissue inhibitor of metalloproteinase-2 (TIMP-2), and eNOS were determined using Western blotting and immunohistochemistry. Our results showed that MMP-2 expression level was significantly higher in buckled arteries than in the controls and higher at the inner curve than at the outer curve of buckled arteries, while collagen IV content showed an opposite trend, suggesting that artery buckling increased MMP-2 expression and collagen IV degradation in a site-specific fashion. However, no differences for MMP-9, fibronectin, elastin, collagen I, III, and TIMP-2 were observed among the outer and inner curve sides of buckled arteries and straight controls. Additionally, eNOS expression was significantly decreased in buckled arteries. These results suggest that artery buckling triggers uneven wall remodeling that could lead to development of tortuous arteries.

Murine Kidney Transplant Technique

The first mouse kidney transplant technique was published in 1973(1) by the Russell laboratory. Although it took some years for other labs to become proficient in and utilize this technique, it is now widely used by many laboratories around the world. A significant refinement to the original technique using the donor aorta to form the arterial anastomosis instead of the renal artery was developed and reported in 1993 by Kalina and Mottram (2) with a further advancement coming from the same laboratory in 1999 (3). While one can become proficient in this model, a search of the literature reveals that many labs still experience a high proportion of graft loss due to arterial thrombosis. We describe here a technique that was devised in our laboratory that vastly reduces the arterial thrombus reported by others (4,5). This is achieved by forming a heel-and-toe cuff of the donor infra-renal aorta that facilitates a larger anastomosis and straighter blood flow into the kidney.

Artery buckling stimulates cell proliferation and NF-κB signaling

Tortuous carotid arteries are often seen in aged populations and are associated with atherosclerosis, but the underlying mechanisms to explain this preference are unclear. Artery buckling has been suggested as one potential mechanism for the development of tortuous arteries. The objective of this study, accordingly, was to determine the effect of buckling on cell proliferation and associated NF-κB activation in arteries. We developed a technique to generate buckling in porcine carotid arteries using long artery segments in organ culture without changing the pressure, flow rate, and axial stretch ratio. Using this technique, we examined the effect of buckling on arterial wall remodeling in 4-day organ culture under normal and hypertensive pressures. Cell proliferation, NF-κB p65, IκB-α, ERK1/2, and caspase-3 were detected using immunohistochemistry staining and immunoblot analysis. Our results showed that cell proliferation was elevated 5.8-fold in the buckling group under hypertensive pressure (n = 7, P < 0.01) with higher levels of NF-κB nuclear translocation and IκB-α degradation (P < 0.05 for both). Greater numbers of proliferating cells were observed on the inner curve side of the buckled arteries compared with the outer curve side (P < 0.01). NF-κB colocalized with proliferative nuclei. Computational simulations using a fluid-structure interaction model showed reduced wall stress on the inner side of buckled arteries and elevated wall stress on the outer side. We conclude that arterial buckling promotes site-specific wall remodeling with increased cell proliferation and NF-κB activation. These findings shed light on the biomechanical and molecular mechanisms of the pathogenesis of atherosclerosis in tortuous arteries.

Dual stent migration to the heart and pulmonary artery

The practice of intravascular stenting largely grew out of the concept of stenting the coronaries in acute myocardial infarction. According to the recent United States Renal Data System data registry, there has been a significant increase in endovascular intervention (1.8-fold increase-from 52,380 to 98,148) with a 2.2-fold increase in stent deployment in hemodialysis access (3792-8514). With the increasing use of endovascular stents in the management of dialysis access stenosis, the incidence of stent-related complications has increased significantly. Stent-related complications include stent restenosis, thrombosis (narrowing of the vessel lumen and being a nidus for thombus formation), stent shortening, stent fracture, stent infection, and stent migration. Physiologic variation in the diameter of veins due to respiration, which along with the geometry of the stent, can lead to a shortening lengthening of the stent-resulting in poor wall contact or high-speed impact of shock; in the case of trauma, mechanical bucking can result in tortuous blood vessels thereby resulting in stent migration (however proving this association was not the aim of this article). We report a case of a 44-year-old female with end-stage renal disease on hemodialysis, with stent placement to treat a compromised arteriovenous graft. There have been many cases of stent migration in the past; however, this is the first case of dual stent migration to the heart and pulmonary artery from an unusual (lower extremity) arteriovenous graft location.

Revised Arterial Anastomosis for Improving Murine Kidney Transplant Outcomes

AIM

One of the most challenging research microsurgical techniques is the mouse kidney transplant however, very few laboratories have made use of this important model due to its difficulty. One of the main obstacles to utilizing this procedure is the high incidence of post-operative arterial thrombosis. We believe this is caused by the path in which blood is required to flow from the recipient abdominal aorta, via the donor recipient aorta and on into the renal artery creating a tortuous route and areas of turbulence, which are prone to thrombus formation and failure of the graft.

METHODS

We describe revised methods of donor artery recovery, whereby the traditional transection of the donor aorta is replaced with a heel and toe cuff, which is created by dividing the donor abdominal aorta obliquely across the face of the renal arterial ostium, which then provides for an arterial end-to-side anastomosis of a scale similar to that used for the heterotopic heart model. This technique produces an anastomosis that facilitates free blood flow from the recipient abdominal aorta at less than 90° thereby reducing the likelihood of thrombus formation.

RESULTS

Utilizing this new technique the incidence of arterial thrombosis has decreased from 35% to 0% (n = 20 and 24, respectively) with no change in ischemia times.

CONCLUSION

We describe a revised method of performing the arterial anastomosis during mouse kidney transplantation, which facilitates improved fluid dynamics by straightening the flow path for blood to the graft resulting in significantly reduced thrombus formation, excellent graft function, histology, and post-transplant survival.

Stability of carotid artery under steady-state and pulsatile blood flow: a fluid-structure interaction study

It has been shown that arteries may buckle into tortuous shapes under lumen pressure, which in turn could alter blood flow. However, the mechanisms of artery instability under pulsatile flow have not been fully understood. The objective of this study was to simulate the buckling and post-buckling behaviors of the carotid artery under pulsatile flow using a fully coupled fluid-structure interaction (FSI) method. The artery wall was modeled as a nonlinear material with a two-fiber strain-energy function. FSI simulations were performed under steady-state flow and pulsatile flow conditions with a prescribed flow velocity profile at the inlet and different pressures at the outlet to determine the critical buckling pressure. Simulations were performed for normal (160 ml/min) and high (350 ml/min) flow rates and normal (1.5) and reduced (1.3) axial stretch ratios to determine the effects of flow rate and axial tension on stability. The results showed that an artery buckled when the lumen pressure exceeded a critical value. The critical mean buckling pressure at pulsatile flow was 17-23% smaller than at steady-state flow. For both steady-state and pulsatile flow, the high flow rate had very little effect (&lt;5%) on the critical buckling pressure. The fluid and wall stresses were drastically altered at the location with maximum deflection. The maximum lumen shear stress occurred at the inner side of the bend and maximum tensile wall stresses occurred at the outer side. These findings improve our understanding of artery instability in vivo.

Artery buckling affects the mechanical stress in atherosclerotic plaques

Background

Tortuous arteries are often seen in patients with hypertension and atherosclerosis. While the mechanical stress in atherosclerotic plaque under lumen pressure has been studied extensively, the mechanical stability of atherosclerotic arteries and subsequent effect on the plaque stress remain unknown. To this end, we investigated the buckling and post-buckling behavior of model stenotic coronary arteries with symmetric and asymmetric plaque.

Methods

Buckling analysis for a model coronary artery with symmetric and asymmetric plaque was conducted using finite element analysis based on the dimensions and nonlinear anisotropic materials properties reported in the literature.

Results

Artery with asymmetric plaque had lower critical buckling pressure compared to the artery with symmetric plaque and control artery. Buckling increased the peak stress in the plaque and led to the development of a high stress concentration in artery with asymmetric plaque. Stiffer calcified tissue and severe stenosis increased the critical buckling pressure of the artery with asymmetric plaque.

Conclusions

Arteries with atherosclerotic plaques are prone to mechanical buckling which leads to a high stress concentration in the plaques that can possibly make the plaques prone to rupture.

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.

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.

An in vivo rat model of artery buckling for studying wall remodeling

Theoretical modeling and in vitro experiments have demonstrated that arterial buckling is a possible mechanism for the development of artery tortuosity. However, there has been no report of whether artery buckling develops into tortuosity, partially due to the lack of in vivo models for long-term studies. The objective of this study was to establish an in vivo buckling model in rat carotid arteries for studying arterial wall remodeling after buckling. Rat left carotid arteries were transplanted to the right carotid arteries to generate buckling under in vivo pressure and were maintained for 1 week to examine wall remodeling and adaptation. Our results showed that a significant buckling was achieved in the carotid arterial grafts with altered wall stress. Cell proliferation and matrix metalloprotinease-2 (MMP-2) expression in the buckled arteries increased significantly compared with the controls. The tortuosity level of the grafts also slightly increased 1 week post-surgery, while there was no change in vessel dimensions, blood pressure, and blood flow velocity. The artery buckling model provides a useful tool for further study of the adaptation of arteries into tortuous shapes.

Cap buckling as a potential mechanism of atherosclerotic plaque vulnerability

Plaque rupture in atherosclerosis is the primary cause of potentially deadly coronary events, yet about 40% of ruptures occur away from the plaque cap shoulders and cannot be fully explained with the current biomechanical theories. Here, cap buckling is considered as a potential destabilizing factor which increases the propensity of the atherosclerotic plaque to rupture and which may also explain plaque failure away from the cap shoulders. To investigate this phenomenon, quasistatic 2D finite element simulations are performed, considering the salient geometrical and nonlinear material properties of diverse atherosclerotic plaques over the range of physiological loads. The numerical results indicate that buckling may displace the location of the peak von Mises stresses in the deflected caps. Plaque buckling, together with its deleterious effects is further observed experimentally in plaque caps using a physical model of deformable mock coronary arteries with fibroatheroma. Moreover, an analytical approach combining quasistatic equilibrium equations with the Navier-Bresse formulas is used to demonstrate the buckling potential of a simplified arched slender cap under intraluminal pressure and supported by foundations. This analysis shows that plaque caps - calcified, fibrotic or cellular - may buckle in specific undulated shapes once submitted to critical loads. Finally, a preliminary analysis of intravascular ultrasonography recordings of patients with atherosclerotic coronary arteries corroborates the numerical, experimental and theoretical findings and shows that various plaque caps buckle in vivo. By displacing the sites of high stresses in the plaque cap, buckling may explain the atherosclerotic plaque cap rupture at various locations, including cap shoulders.

Modulated pressure waves in large elastic tubes

Modulational instability is the direct way for the emergence of wave patterns and localized structures in nonlinear systems. We show in this work that it can be explored in the framework of blood flow models. The whole modified Navier-Stokes equations are reduced to a difference-differential amplitude equation. The modulational instability criterion is therefore derived from the latter, and unstable patterns occurrence is discussed on the basis of the nonlinear parameter model of the vessel. It is found that the critical amplitude is an increasing function of α, whereas the region of instability expands. The subsequent modulated pressure waves are obtained through numerical simulations, in agreement with our analytical expectations. Different classes of modulated pressure waves are obtained, and their close relationship with Mayer waves is discussed.

Mechanical buckling of arterioles in collateral development

Collateral arterioles enlarge in both diameter and length, and develop corkscrew-like tortuous patterns during remodeling. Recent studies showed that artery buckling could lead to tortuosity. The objective of this study was to determine arteriole critical buckling pressure and buckling pattern during arteriole remodeling. Arterioles were modeled as elastic cylindrical vessels with an elastic matrix support and underwent axial and radial growth. Our results demonstrated that arteriole critical buckling pressure decreased with increasing axial growth ratio and radius growth ratio, but increased with increasing wall thickness. Arteriole buckling mode number increased (wavelength decreased) with increasing axial growth ratio, but decreased with increasing radius growth ratio and wall thickness. Our study suggests that axial growth in arterioles makes them prone to buckling and that buckling leads to tortuous collaterals. These results shed light on the mechanism of collateral arteriole tortuosity.

Smooth muscle cell contraction increases the critical buckling pressure of arteries

Recent in vitro experiments demonstrated that arteries under increased internal pressure or decreased axial stretch may buckle into the tortuous pattern that is commonly observed in aging or diseased arteries in vivo. It suggests that buckling is a possible mechanism for the development of artery tortuosity. Vascular tone has significant effects on arterial mechanical properties but its effect on artery buckling is unknown. The objective of this study was to determine the effects of smooth muscle cell contraction on the critical buckling pressure of arteries. Porcine common carotid arteries were perfused in an ex vivo organ culture system overnight under physiological flow and pressure. The perfusion pressure was adjusted to determine the critical buckling pressure of these arteries at in vivo and reduced axial stretch ratios (1.5 and 1.3) at baseline and after smooth muscle contraction and relaxation stimulated by norepinephrine and sodium nitroprusside, respectively. Our results demonstrated that the critical buckling pressure was significantly higher when the smooth muscle was contracted compared with relaxed condition (97.3mmHg vs 72.9mmHg at axial stretch ratio of 1.3 and 93.7mmHg vs 58.6mmHg at 1.5, p<0.05). These results indicate that arterial smooth muscle cell contraction increased artery stability.

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.

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 ([Formula: see text]) and the critical buckling twist angle ([Formula: see text]). Lumen pressure also significantly affected the critical buckling torque ([Formula: see text]) but had no significant effect on the critical twist angle ([Formula: see text]). 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[Formula: see text], respectively. The current study elucidates the buckling behavior of arteries under torsion and provides new insight into mechanical instability of blood vessels.

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.

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.

Effects of Geometric Variations on the Buckling of Arteries

Arteries often demonstrate geometric variations such as elliptic and eccentric cross sections, stenosis, and tapering along the longitudinal axis. Effects of these variations on the mechanical stability of the arterial wall have not been investigated. The objective of this study was to determine the buckling behavior of arteries with elliptic, eccentric, stenotic, and tapered cross sections. The arterial wall was modeled as a homogenous anisotropic nonlinear material. Finite element analysis was used to simulate the buckling process of these arteries under lumen pressure and axial stretch. Our results demonstrated that arteries with an oval cross section buckled in the short axis direction at lower critical pressures compared to circular arteries. Eccentric cross-sections, stenosis, and tapering also decreased the critical pressure. Stenosis led to dramatic pressure variations along the vessel and reduced the buckling pressure. In addition, tapering shifted the buckling deformation profile of the artery towards the distal end. We conclude that geometric variations reduce the critical pressure of arteries and thus make the arteries more prone to mechanical instability than circular cylindrical arteries. These results improve our understanding of the mechanical behavior of arteries.

Pulmonary arterial hypertension: what the large pulmonary arteries tell us

The morphology of the large intrapulmonary arteries (PAs) in pulmonary hypertension (PH) has received limited attention. Dilation, pruning, abrupt tapering, and tortuosity of PAs occur, but whether different patients have distinct PA phenotypes is unknown. Pulmonary arteriograms from 41 pediatric patients with PH were blindly reviewed by four experts who assigned each angiogram one of three designations: straight (S), tortuous (T), or ambiguous (A). Hemodynamic variables and outcomes were compared to the phenotypes. Thirty patients were either T (19) or S (11); 11 were A. The phenotypes were not associated with age. Tortuous patients had higher PA pressure and resistance than the S group and less likely to react to inhaled nitric oxide than S patients (p < 0.05). Clinical outcomes were similar for the three groups. Thus, in PH patients two subtypes of PA morphology can often be discerned, a reflection of variability in PA tortuosity. These morphological subtypes have differing hemodynamic characteristics. The mechanism(s) underlying these differences is unknown, but neither hydrodynamic factors nor duration of PH are fully explanatory. Because PA morphology might reveal information regarding the biology of pathological remodeling, it might prove enlightening to assess the large PA phenotype in future studies of PH.

Determination of the critical buckling pressure of blood vessels using the energy approach

The stability of blood vessels under lumen blood pressure is essential to the maintenance of normal vascular function. Differential buckling equations have been established recently for linear and nonlinear elastic artery models. However, the strain energy in bent buckling and the corresponding energy method have not been investigated for blood vessels under lumen pressure. The purpose of this study was to establish the energy equation for blood vessel buckling under internal pressure. A buckling equation was established to determine the critical pressure based on the potential energy. The critical pressures of blood vessels with small tapering along their axis were estimated using the energy approach. It was demonstrated that the energy approach yields both the same differential equation and critical pressure for cylindrical blood vessel buckling as obtained previously using the adjacent equilibrium approach. Tapering reduced the critical pressure of blood vessels compared to the cylindrical ones. This energy approach provides a useful tool for studying blood vessel buckling and will be useful in dealing with various imperfections of the vessel wall.

A Nonlinear Thin-Wall Model for Vein Buckling

Tortuous or twisted veins are often seen in the retina, cerebrum, and legs (varicose veins) of one-third of the aged population, but the underlying mechanisms are poorly understood. While the collapse of veins under external pressure has been well documented, the bent buckling of long vein segments has not been studied. The objectives of this study were to develop a biomechanical model of vein buckling under internal pressure and to predict the critical pressure. Veins were modeled as thin-walled nonlinear elastic tubes with the Fung exponential strain energy function. Our results demonstrated that veins buckle due to high blood pressure or low axial tension. High axial tension stabilized veins under internal pressure. Our buckling model estimated the critical pressure accurately compared to the experimental measurements. The buckling equation provides a useful tool for studying the development of tortuous veins.

Effects of Axial Stretch on Cell Proliferation and Intimal Thickness in Arteries in Organ Culture

Intimal hyperplasia (IH) remains the major cause of intermediate and long-term failure of vascular grafts and endovascular interventions. Arteries are subjected to a significant longitudinal stress in addition to the shear stress and tensile stress from the blood flow. The aim of this study was to determine the effect of axial stretch on cell proliferation and IH in arteries. Porcine carotid arteries, intact or endothelial cell (EC) denudated, were maintained ex vivo at different stretch ratios (1.3, 1.5, and 1.8) and flow rates (16 or 160 mL/min) while remaining at physiologic pressure for 7 days. The viability of the arteries was verified with norepinephrine, carbachol, and sodium nitroprusside stimulations, and the cell proliferation was detected using bromodeoxyuridine labeling and immunostaining. Our results showed that the axial stretch ratio did not significantly affect intimal thickness and cell proliferation in normal arteries. However, axial stretch increased the neointimal thickness in EC denudated arteries cultured under low flow conditions. The cell proliferation increased significantly in the intima and inner half of the media of the EC denudated arteries under normal or elevated axial stretch in comparison to intact arteries at the same stretch ratio. These results demonstrated that axial stretch with EC denudation and low flow increases neointimal formation and cell proliferation in the arteries.

Mechanical buckling of veins under internal pressure

Venous tortuosity is associated with multiple disease states and is often thought to be a consequence of venous hypertension and chronic venous disease. However, the underlying mechanisms of vein tortuosity are unclear. We hypothesized that increased pressure causes vein buckling that leads to a tortuous appearance. The specific aim of this study was to determine the critical buckling pressure of veins. We determined the buckling pressure of porcine jugular veins and measured the mechanical properties of these veins. Our results showed that the veins buckle when the transmural pressure exceeds a critical pressure that is strongly related to the axial stretch ratio in the veins. The critical pressures of the eight veins tested were 14.2 +/- 5.4 and 26.4 +/- 9.0 mmHg at axial stretch ratio 1.5 and 1.7, respectively. In conclusion, veins buckle into a tortuous shape at high lumen pressures or reduced axial stretch ratios. Our results are useful in understanding the development of venous tortuosity associated with varicose veins, venous valvular insufficiency, diabetic retinopathy, and vein grafts.

[Patient education in chronic polyarthritis. 3. Intermediate results of a prospective, controlled study of the effectiveness and side effects of patient seminars for polyarthritis patients]

Efficacy and possible negative side effects of a patient education program for rheumatoid arthritis were evaluated in a controlled, prospective study over 3 months. 34 outpatients were educated over a total of 8 h in three groups within a patient-centred design. Before the program the knowledge of the disease depended only on the formal grade of education but not on disease-related variables such as disease duration or disability. Probably due to its individualizing method, the program improved the knowledge of all patients to the same extent, regardless of their intellectual and social prerequisites. The increased cognitive knowledge did not result in negative side effects like increased pain or depression. The pain score remained unchanged. Depression decreased after the education. The group sessions made us suppose that the participants may have represented a selected group of active, psychologically stable patients, who cope well with rheumatoid arthritis. In contrast, we felt that non-participation was the response of the inactive, fatalistic patients with rheumatoid arthritis, who live in social isolation and especially need our care. Therefore, future efforts must particularly focus on the problem of motivation and on an increase in the rate of participation.

Physical and occupational therapy for children with rheumatic diseases

Total management of rheumatic disorders of children includes antiinflammatory drugs, active therapy, maintenance of ADLs, and attention to the psychosocial development of the child. This article focuses on the role that physical and occupational therapists play in the management of children with arthritis. The complexity of the problems of these children necessitates a multidisciplinary team approach, with professionals who are committed to helping the child lead as normal a life as possible. This objective can be accomplished only by teaching families and school personnel how to manage the child's daily therapeutic needs.