Study of stress concentration in the walls of the bovine coronary arterial branch

The intramural stress concentration in the arterial wall is studied at the bovine circumflex coronary arterial branch. The material properties, geometry, and strains in the arterial branch are determined from experiments. The stresses are determined using a finite element analysis. The arterial branch is modeled as two interesecting thin cylindrical shells incorporating local variations in the branch geometry, thickness, and material properties. The artery is considered orthotropic and loaded with an incremental pressure of 40 mmHg. The highest intramural stresses are found to be localized at the proximal and distal regions of the ostium and are not significantly affected by the elastic properties. The stresses are 3 to 4 times greater in the branch at the inner surface than in the straight segment. The strains are twice as large at the branch than in the straight segment. We speculate that this stress concentration could injure the artery and make the branch region susceptible to atherosclerosis.     

Gene expression in Eucalyptus branch wood with marked variation in cellulose microfibril orientation and lacking G-layers

In response to gravitational stresses, angiosperm trees form tension wood in the upper sides of branches and leaning stems in which cellulose content is higher, microfibrils are typically aligned closely with the fibre axis and the fibres often have a thick inner gelatinous cell wall layer (G-layer). Gene expression was studied in Eucalyptus nitens branches oriented at 45 degrees using microarrays containing 4900 xylem cDNAs, and wood fibre characteristics revealed by X-ray diffraction, chemical and histochemical methods. Xylem fibres in tension wood (upper branch) had a low microfibril angle, contained few fibres with G-layers and had higher cellulose and decreased Klason lignin compared with lower branch wood. Expression of two closely related fasciclin-like arabinogalactan proteins and a beta-tubulin was inversely correlated with microfibril angle in upper and lower xylem from branches. Structural and chemical modifications throughout the secondary cell walls of fibres sufficient to resist tension forces in branches can occur in the absence of G-layer enriched fibres and some important genes involved in responses to gravitational stress in eucalypt xylem are identified.     

Altered artery mechanics and structure in monocrotaline pulmonary hypertension

Pulmonary hypertension in rats, induced by an injection of monocrotaline, is associated with changes in the wall structure of the pulmonary arterial bed. We have studied the effects of this remodeling on mechanical properties of cylindrical pulmonary artery segments from rats 21 days after monocrotaline (MCT) injection. Resting and active (KCl induced) circumference-tension relationships were established for segments of extrapulmonary and intrapulmonary arteries isolated from the hilum and the fifth lateral branch from the axial pathway (all preacinar). The thicknesses of the vessel wall, the media, and adventitia were measured at several positions around the circumference of the artery by computerized analysis of histological cross sections of the segments fixed at a standard circumference. Resting and active stress were also calculated. The study shows that active circumferential tension and active stress are reduced in vessels from MCT-treated rats. Based on our findings, it is unlikely that altered contractile function of preacinar arteries contributes significantly to the increased vascular resistance seen in this model.     

Computation in the rabbit aorta of a new metric – the transverse wall shear stress – to quantify the multidirectional character of disturbed blood flow

Spatial variation of the haemodynamic stresses acting on the arterial wall is commonly assumed to explain the focal development of atherosclerosis. Disturbed flow in particular is thought to play a key role. However, widely-used metrics developed to quantify its extent are unable to distinguish between uniaxial and multidirectional flows. We analysed pulsatile flow fields obtained in idealised and anatomically-realistic arterial geometries using computational fluid dynamics techniques, and in particular investigated the multidirectionality of the flow fields, capturing this aspect of near-wall blood flow with a new metric – the transverse wall shear stress (transWSS) – calculated as the time-average of wall shear stress components perpendicular to the mean flow direction. In the idealised branching geometry, multidirectional flow was observed downstream of the branch ostium, a region of flow stagnation, and to the sides of the ostium. The distribution of the transWSS was different from the pattern of traditional haemodynamic metrics and more dependent on the velocity waveform imposed at the branch outlet. In rabbit aortas, transWSS patterns were again different from patterns of traditional metrics. The near-branch pattern varied between intercostal ostia, as is the case for lesion distribution; for some branches there were striking resemblances to the age-dependent patterns of disease seen in rabbit and human aortas. The new metric may lead to improved understanding of atherogenesis.     

Sequential structural and fluid dynamic numerical simulations of a stented bifurcated coronary artery

Despite their success, stenting procedures are still associated to some clinical problems like sub-acute thrombosis and in-stent restenosis. Several clinical studies associate these phenomena to a combination of both structural and hemodynamic alterations caused by stent implantation. Recently, numerical models have been widely used in the literature to investigate stenting procedures but always from either a purely structural or fluid dynamic point of view. The aim of this work is the implementation of sequential structural and fluid dynamic numerical models to provide a better understanding of stenting procedures in coronary bifurcations. In particular, the realistic geometrical configurations obtained with structural simulations were used to create the fluid domains employed within transient fluid dynamic analyses. This sequential approach was applied to investigate the final kissing balloon (FKB) inflation during the provisional side branch technique. Mechanical stresses in the arterial wall and the stent as well as wall shear stresses along the arterial wall were examined before and after the FKB deployment. FKB provoked average mechanical stresses in the arterial wall almost 2.5 times higher with respect to those induced by inflation of the stent in the main branch only. Results also enlightened FKB benefits in terms of improved local blood flow pattern for the side branch access. As a drawback, the FKB generates a larger region of low wall shear stress. In particular, after FKB the percentage of area characterized by wall shear stresses lower than 0.5?Pa was 79.0%, while before the FKB it was 62.3%. For these reasons, a new tapered balloon dedicated to bifurcations was proposed. The inclusion of the modified balloon has reduced the mechanical stresses in the proximal arterial vessel to 40% and the low wall shear stress coverage area to 71.3%. In conclusion, these results show the relevance of the adopted sequential approach to study the wall mechanics and the hemodynamics created by stent deployment.     

Stress gradients in the walls of large arteries

Elastic behavior of vascular wall, assuming the vessels to be ‘thick-walled’ and utilizing finite deformation theory, was investigated. It was found that canine carotid arterial wall is neither isotropic nor transversely isotropic. Previously, stress-strain relations were obtained for carotid arteries on the basis of membrane theory (Doyle and Dobrin, 1971). Since strain gradients across the wall are fairly steep, the applicability of such expressions, for pointwise evaluation of stress, required examination. The study indicated that these relationships between mean circumferential stress and mean extension ratio in the circumferential direction could be used to relate the specific circumferential stress value to the specific extension ratio at any designated point within the wall. From this analysis it was possible to evaluate circumferential and radial wall stresses. Both of these stresses are maximal at the inner surface of the intima. At this point the radial stress is equal to the transmural pressure and is compressive, while the circumferential stress is tensile and is 1·5 to 2 times the value of the mean stress, i.e. the product of transmural pressure and the ratio of internal radius-to-wall thickness. Both stresses are lowest at the outer edge of the adventitia. These stress distributions were considered with respect to the spacing of the elastic lamellae and the absence of discernible vasa vasora in the inner third of the wall.     

A Novel Tram Stent Method in the Treatment of Coronary Bifurcation Lesions – Finite Element Study

A novel stent was designed for the treatment of coronary bifurcation lesion, and it was investigated for its performance by finite element analysis. This study was performed in search of a novel method of treatment of bifurcation lesion with provisional stenting. A bifurcation model was created with the proximal vessel of 3.2 mm diameter, and the distal vessel after the side branch (2.3 mm) was 2.7 mm. A novel stent was designed with connection links that had a profile of a tram. Laser cutting and shape setting of the stent was performed, and thereafter it was crimped and deployed over a balloon. The contact pressure, stresses on the arterial wall, stresses on the stent, the maximal principal log strain of the main artery and the side-branch were studied. The study was performed in Abaqus, Simulia. The stresses on the main branch and the distal branch were minimally increased after deployment of this novel stent. The side branch was preserved, and the stresses on the side branch were lesser; and at the confluence of bifurcation on either side of the side branch origin the von-Mises stress was marginally increased. The stresses and strain at the bifurcation were significantly lesser than the stresses and strain of the currently existing techniques used in the treatment of bifurcation lesions though the study was primarily focused only on the utility of the new technology. There is a potential for a novel Tram-stent method in the treatment of coronary bifurcation lesions.     

Development of a general method for designing microvascular networks using distribution of wall shear stress

In the present study, theoretical formulations for calculation of optimal bifurcation angle and relationship between the diameters of mother and daughter vessels using the power law model for non-Newtonian fluids are developed. The method is based on the distribution of wall shear stress in the mother and daughter vessels. Also, the effect of distribution of wall shear stress on the minimization of energy loss and flow resistance is considered. It is shown that constant wall shear stress in the mother and daughter vessels provides the minimum flow resistance and energy loss of biological flows. Moreover, the effects of different wall shear stresses in the mother and daughter branches, different lengths of daughter branches in the asymmetric bifurcations and non-Newtonian effect of biological fluid flows on the bifurcation angle and the relationship between the diameters of mother and daughter branches are considered. Using numerical simulations for non-Newtonian models such as power law and Carreau models, the effects of optimal bifurcation angle on the pressure drop and flow resistance of blood flow in the symmetric bifurcation are investigated. Numerical simulations show that optimal bifurcation angle decreases the pressure drop and flow resistance especially for bifurcations at large Reynolds number.     

The subscapular arterial tree as a source of microvascular arterial grafts

The subscapular arterial tree may be used as a source of microvascular grafts to replace damaged or diseased portions of arteries, particularly in the hand and forearm. By studying cadaver dissections, it is possible to estimate the number of branches that may be found at different arterial segment lengths from the origin of the subscapular artery. Fifty-five preserved cadaver subscapular arterial trees were dissected, and the branching patterns were documented. Three major arterial branching patterns of the subscapular artery were observed with one, two, and three major branches to the serratus anterior in 60 percent, 29 percent, and 9 percent of the cases, respectively. The authors determined the number of 1-mm-diameter, 1-cm-long branches arising from each of six 3-cm regions of the arterial tree measured from the origin of the subscapular artery to the end of the longest terminal branch. The probability of finding at least one usable terminal branch that is at least 12.0 cm in length was found to be 98 percent. Typically, there are two to five useful branches at this distance. Such information may help surgeons fine tune their process of selecting an appropriate arterial donor site for a particular arterial defect and supports the use of the subscapular arterial tree as a donor site for microvascular arterial grafts.     

The Effect of Longitudinal Pre-Stretch and Radial Constraint on the Stress Distribution in the Vessel Wall: A New Hypothesis

It is well known that blood vessels shorten axially when excised. This is due to the perivascular tethering constraint by side branches and the existence of pre-stretch of blood vessels at the \textit {in situ} state. Furthermore, vessels are radially constrained to various extents by the surrounding tissues at physiological loading. Our hypothesis is that the axial pre-stretch and radial constraint by the surrounding tissue homogenizes the stress and strain distributions in the vessel wall. A finite element analysis of porcine coronary artery and rabbit thoracic aorta based on measured material properties, geometry, residual strain and physiological loading is used to compute the intramural stresses and strains. We systematically examined the effect of pre-stretch and external radial constraint in both vessels. Our results show that both stretching in the axial direction and compression in the radial direction lead to a more homogeneous strain and stress state in the blood vessel wall. A ``uniform biaxial strain' hypothesis is proposed for the blood vessel wall and the ramifications are discussed.     

Vascular smooth muscle cell stress as a determinant of cerebral artery myogenic tone

Although the level of myogenic tone (MT) varies considerably from vessel to vessel, the regulatory mechanisms through which the actual diameter set point is determined are not known. We hypothesized that a unifying principle may be the equalization of active force at the contractile filament level, which would be reflected in a normalization of wall stress or, more specifically, media stress. Branched segments of rat cerebral arteries ranging from <50 microm to >200 microm in diameter were cannulated and held at 60 mmHg with the objectives of: 1) evaluating the relationship between arterial diameter and the extent of myogenic tone, 2) determining whether differences in MT correlate with changes in cytosolic calcium ([Ca(2+)](i)), and 3) testing the hypothesis that a normalization of wall or media stress occurs during the process of tone development. The level of MT increased significantly as vessel size decreased. At 60 mmHg, vascular smooth muscle [Ca(2+)](i) concentrations were similar in all vessels studied (averaging 230 +/- 9.2 nM) and not correlated with vessel size or the extent of tone. Wall tension increased with increasing arterial size, but wall stress and media stress were similar in large versus small arteries. Media stress, in particular, was quite uniform in all vessels studied. Both morphological and calcium data support the concept of equalization of media stress (and, hence, vascular smooth muscle cell stress and force) as an underlying mechanism in determining the level of tone present in any particular vessel. The equalization of active (vascular smooth muscle cell) stress may thus explain differences in MT observed in the different-sized vessels constituting the arterial network and provide a link between arterial structure and function, in both short- and long-term (hypertension) pressure adaptation.     

Effect of aging on mechanical stresses,deformations, and hemodynamics in human femoropopliteal artery due to limb flexion

Femoropopliteal artery (FPA) reconstructions are notorious for poor clinical outcomes. Mechanical and flow conditions that occur in the FPA with limb flexion are thought to play a significant role, but are poorly characterized. FPA deformations due to acute limb flexion were quantified using a human cadaver model and used to build a finite element model that simulated surrounding tissue forces associated with limb flexion-induced deformations. Strains and intramural principal mechanical stresses were determined for seven age groups. Computational fluid dynamics analysis was performed to assess hemodynamic variables. FPA shape, stresses, and hemodynamics significantly changed with age. Younger arteries assumed straighter positions in the flexed limb with less pronounced bends and more uniform stress distribution along the length of the artery. Even in the flexed limb posture, FPAs younger than 50 years of age experienced tension, while older FPAs experienced compression. Aging resulted in localization of principal mechanical stresses to the adductor hiatus and popliteal artery below the knee that are typically prone to developing vascular pathology. Maximum principal stresses in these areas increased threefold to fivefold with age with largest increase observed at the adductor hiatus. Atheroprotective wall shear stress reduced after 35 years of age, and atheroprone and oscillatory shear stresses increased after the age of 50. These data can help better understand FPA pathophysiology and can inform the design of targeted materials and devices for peripheral arterial disease treatments.     

Breaking symmetry in non-planar bifurcations: distribution of flow and wall shear stress

Non-planarity in blood vessels is known to influence arterial flows and wall shear stress. To gain insight, computational fluid dynamics (CFD) has been used to investigate effects of curvature and out-of-plane geometry on the distribution of fluid flows and wall shear stresses in a hypothetical non-planar bifurcation. Three-dimensional Navier-Stokes equations for a steady state Newtonian fluid were solved numerically using a finite element method. Non-planarity in one of the two daughter vessels is found to deflect flow from the inner wall of the vessel to the outer wall and to cause changes in the distribution of wall shear stresses. Results from this study agree to experimental observations and CFD simulations in the literature, and support the view that non-planarity in blood vessels is a factor with important haemodynamic significance and may play a key role in vascular biology and pathophysiology.     

On the sensitivity of wall stresses in diseased arteries to variable material properties

Accurate estimates of stress in an atherosclerotic lesion require knowledge of the material properties of its components (e.g., normal wall, fibrous plaque, calcified regions, lipid pools) that can only be approximated. This leads to considerable uncertainty in these computational predictions. A study was conducted to test the sensitivity of predicted levels of stress and strain to the parameter values of plaque used in finite element analysis. Results show that the stresses within the arterial wall, fibrous plaque, calcified plaque, and lipid pool have low sensitivities for variation in the elastic modulus. Even a +/- 50% variation in elastic modulus leads to less than a 10% change in stress at the site of rupture. Sensitivity to variations in elastic modulus is comparable between isotropic nonlinear, isotropic nonlinear with residual strains, and transversely isotropic linear models. Therefore, stress analysis may be used with confidence that uncertainty in the material properties generates relatively small errors in the prediction of wall stresses. Either isotropic nonlinear or anisotropic linear models provide useful estimates, however the predictions in regions of stress concentration (e.g., the site of rupture) are somewhat more sensitive to the specific model used, increasing by up to 30% from the isotropic nonlinear to orthotropic model in the present example. Changes resulting from the introduction of residual stresses are much smaller.     

Distribution of stress and strain along the porcine aorta and coronary arterial tree

The existence of a homeostatic state of stresses and strains has been axiomatic in the cardiovascular system. The objective of this study was to determine the distribution of circumferential stress and strain along the aorta and throughout the coronary arterial tree to test this hypothesis. Silicone elastomer was perfused through the porcine aorta and coronary arterial tree to cast the arteries at physiological pressure. The loaded and zero-stress dimensions of the vessels were measured. The aorta (1.8 cm) and its secondary branches were considered down to 1.5 mm diameter. The left anterior descending artery (4.5 mm) and its branches down to 10 microm were also measured. The Cauchy mean circumferential stress and midwall stretch ratio were calculated. Our results show that the stretch ratio and Cauchy stress were lower in the thoracic than in the abdominal aorta and its secondary branches. The opening angle (theta) and midwall stretch ratio (lambda) showed a linear variation with order number (n) as follows: theta = 10.2n + 63.4 (R(2) = 0.989) and lambda = 4.47 x 10(-2)n + 1.1 (R(2) = 0.995). Finally, the stretch ratio and stress varied between 1.2 and 1.6 and between 10 and 150 kPa, respectively, along the aorta and left anterior descending arterial tree. The relative uniformity of strain (50% variation) from the proximal aorta to a 10-microm arteriole implies that the vascular system closely regulates the degree of deformation. This suggests a homeostasis of strain in the cardiovascular system, which has important implications for mechanotransduction and for vascular growth and remodeling.     

Pulmonary artery calcification in racehorses may be related to transient and repeated increases in arterial pressure during exercise

Calcification of the pulmonary artery has been found in a large number of racing horses. The majority of calcified lesions are found immediately distal to the primary arterial bifurcation. Increased arterial wall stress levels have been previously demonstrated at these locations, with the wall stress levels increasing under intra-luminal pressures associated with exercise. We hypothesize therefore that the formation of calcified lesions is mediated by transient and repeated increases in pulmonary artery intra-luminal pressure. The presence of calcified lesions would likely further exacerbate the levels of wall stress, leading to growth of the lesions. A level of wall stress may exist above which calcified lesions form, and a second level may exist above which the calcified lesions grow at an increased rate. A computer model of pulmonary artery wall stress with calcified lesions was created, and wall stress levels were found to be greatest at the periphery of the calcified lesions. Osteo/chondrocyte-like cells have also been found at the periphery of the calcified lesions and could be responsible for collagen deposition and lesion growth, mediated by local wall stress levels. These increased levels of wall stress could place racehorses at a greater risk of acute pulmonary arterial rupture at the site of the calcified lesions, due to the high levels of intra-luminal pressure within the pulmonary artery during exercise. The hypothesis may also have implications in the etiology of human vascular diseases.     

Wall shear stress at the initiation site of cerebral aneurysms

Hemodynamics are believed to play an important role in the initiation of cerebral aneurysms. In particular, studies have focused on wall shear stress (WSS), which is a key regulator of vascular biology and pathology. In line with the observation that aneurysms predominantly occur at regions of high WSS, such as bifurcation apices or outer walls of vascular bends, correlations have been found between the aneurysm initiation site and high WSS. The aim of our study was to analyze the WSS field at an aneurysm initiation site that was neither a bifurcation apex nor the outer wall of a vascular bend. Ten cases with aneurysms on the A1 segment of the anterior cerebral artery were analyzed and compared with ten controls. Aneurysms were virtually removed from the vascular models of the cases to mimic the pre-aneurysm geometry. Computational fluid dynamics (CFD) simulations were created to assess the magnitude, gradient, multidirectionality, and pulsatility of the WSS. To aid the inter-subject comparison of hemodynamic variables, we mapped the branch surfaces onto a two-dimensional parametric space. This approach made it possible to view the whole branch at once for qualitative evaluation. It also allowed us to empirically define a patch for quantitative analysis, which was consistent among subjects and encapsulated the aneurysm initiation sites in our dataset. To test the sensitivity of our results, CFD simulations were repeated with a second independent observer virtually removing the aneurysms and with a 20 % higher flow rate at the inlet. We found that branches harboring aneurysms were characterized by high WSS and high WSS gradients. Among all assessed variables, the aneurysm initiation site most consistently coincided with peaks of temporal variation in the WSS magnitude.     

Stress and hormone interrelationship in branch growth

Calculated stress patterns in lateral branches place the locations of maximum flexural stresses at the same places as the maximum concentrations of growth hormones. The gradients of stress and hormone concentration also have similarity.

In branch epinasty and negative geotropism of branches, the directions of the stress vectors correlate with the imbalance of auxin in the upper and lower portions of the branches.

     

Numerical simulation of flow fields in a tube with two branches

In the present study, a numerical calculation procedure based on the finite volume method was employed to simulate flow fields in double-branched tubes. The configuration was a tube with two vertical branches; the two branches were either on the same side or on the opposite side. The study focused on the baseline flow fields and the possible flow interaction between the two branches. The branching ratio and the branch /main tube diameter ratio were fixed in this study. The results showed that when the two branches were on the same side, the low/oscillating shear regions were found on the ventral walls of the branches and on the dorsal wall of the main tube distal to the branches. The flow field proximal to each branch was similar to that in a single-branched tube when the two branches were distant. When the branches were on the opposite side with the staggering distance S=0 (symmetric case), the low/oscillating shear regions were found on the lateral walls of the main tube. As S increased, the interaction between the two branches weakened, the low/oscillating shear regions were found on the lateral walls of the main tube to the side of the second branch. The flow field near the branch was significantly different from that of a single-branched tube. Care should be taken on localization of plaques in multi-branched vessels due to the flow pattern change. The numerical results were qualitatively consistent with what observed experimentally, by other investigators.     

Mass Transport Properties of the Rabbit Aortic Wall

Uptake of circulating macromolecules by the arterial wall may be a critical step in atherogenesis. Here we investigate the age-related changes in patterns of uptake that occur in the rabbit. In immature aortas, uptake was elevated in a triangle downstream of branch ostia, a region prone to disease in immature rabbits and children. By 16-22 months, uptake was high lateral to ostia, as is lesion prevalence in mature rabbits and young adults. In older rabbits there was a more upstream pattern, similar to the disease distribution in older people. These variations were predominantly caused by the branches themselves, rather than reflecting larger patterns within which the branches happened to be situated (as may occur with patterns of haemodynamic wall shear stress). The narrow streaks of high uptake reported in some previous studies were shown to be post mortem artefacts. Finally, heparin (which interferes with the NO pathway) had no effect on the difference in uptake between regions upstream and downstream of branches in immature rabbits but reversed the difference in older rabbits, as does inhibiting NO synthesis directly. Nevertheless, examination of uptake all around the branch showed that changes occurred at both ages and that they were quite subtle, potentially explaining why inhibiting NO has only minor effects on lesion patterns in mature rabbits and contradicting the earlier conclusion that mechanotransduction pathways change with age. We suggest that recently-established changes in the patterns of haemodynamic forces themselves are more likely to account for the age-dependence of uptake patterns.