Fundamental role of axial stress in compensatory adaptations by arteries

Arteries exhibit a remarkable ability to adapt to diverse genetic defects and sustained alterations in mechanical loading. For example, changes in blood flow induced wall shear stress tend to control arterial caliber and changes in blood pressure induced circumferential wall stress tend to control wall thickness. We submit, however, that the axial component of wall stress plays a similarly fundamental role in controlling arterial geometry, structure, and function, that is, compensatory adaptations. This observation comes from a review of findings reported in the literature and a comparison of four recent studies from our laboratory that quantified changes in the biaxial mechanical properties of mouse carotid arteries in cases of altered cell-matrix interactions, extracellular matrix composition, blood pressure, or axial extension. There is, therefore, a pressing need to include the fundamental role of axial wall stress in conceptual and theoretical models of arterial growth and remodeling and, consequently, there is a need for increased attention to evolving biaxial mechanical properties in cases of altered genetics and mechanical stimuli.     

Impact of transmural heterogeneities on arterial adaptation

Recent experimental and computational studies have shown that transmurally heterogeneous material properties through the arterial wall are critical to understanding the heterogeneous expressions of constituent degrading molecules. Given that expression of such molecules is thought to be intimately linked to local magnitudes of stress, modelling the transmural stress distribution is critical to understanding arterial adaption during disease. The aim of this study was to develop an arterial growth and remodelling framework that can incorporate both transmurally heterogeneous constituent distributions and residual stresses, into a 3-D finite element model. As an illustrative example, we model the development of a fusiform aneurysm and investigate the effects of elastinous and collagenous heterogeneities on the stress distribution during evolution. It is observed that the adaptive processes of growth and remodelling exhibit transmural variations. For physiological heterogeneous constituent distributions, a stress peak appears in the media towards the intima, and a stress plateau occurs towards the adventitia. These features can be primarily attributed to the underlying heterogeneity of elastinous constituents. During arterial adaption, the collagen strain is regulated to remain in its homoeostatic level; consequently, the partial stress of collagen has less influence on the total stress than the elastin. However, following significant elastin degradation, collagen plays the dominant role for the transmural stress profile and a marked stress peak occurs towards the adventitia. We conclude that to improve our understanding of the arterial adaption and the aetiology of arterial disease, there is a need to: quantify transmural constituent distributions during histopathological examinations, understand and model the role of the evolving transmural stress distribution.     

Effects of a sustained extension on arterial growth and remodeling: a theoretical study

Three recent studies reveal that the unloaded length of a carotid artery increases significantly and rapidly in response to sustained increases in axial extension. Moreover, such lengthening involves an "unprecedented" increase in the rate of turnover of cells and matrix. Although current data are not sufficient for detailed biomechanical analyses, we present general numerical simulations that are consistent with the reported observations and support the hypothesis that rates of turnover correlate with the extent that stresses are perturbed from normal. In particular, a 3-D analysis of wall stress suggests that moderate (15%) increases in axial extension can increase the axial stress to a much greater extent than marked (50%) increases in blood pressure increase the circumferential stress. Furthermore, such increases in axial stress can occur without inducing significant gradients in stress within the wall. Consequently, we use a new, 2-D constrained mixture model to study evolving changes in the geometry, structure, and properties of carotid arteries in response to a sustained increase in axial extension. These simulations are qualitatively similar to the reports in the literature and support the notion that the stress-free lengths of individual constituents evolve during growth and remodeling.     

Radial artery wall shear stress evaluation in patients with arteriovenous fistula for hemodialysis access

It has been extensively documented that changes in blood flow induce vascular remodeling and this phenomenon seems to be correlated to the shear forces imposed on the vessel wall by motion of blood. Wall shear stress, the tractive force that acts on the endothelium, has been shown to influence endothelial cell function. To study changes in wall shear stress that develop on the vessel wall upon changes of blood flow, we set up a technique that allows estimation of shear stress in the radial artery of patients on chronic hemodialysis therapy. The technique is based on color-flow Doppler examination of the radial artery before and after surgical creation of radiocephalic fistula for hemodialysis. Calculation of time function wall shear stress and blood flow rate in the radial artery is performed on the basis of arterial diameter, center-line velocity waveform and blood viscosity, using a numerical method developed according to Womersley's theory for pulsatile flow in tubes. The results presented confirm that the model developed is suitable for calculation of the wall shear stress that develops in the radial artery of patients before and after surgical creation of an arteriovenous fistula for hemodialysis. This methodology was developed for characterization of wall shear stress in the radial artery but may be well applied to other vessels that can be examined by echo-Doppler technique.     

Adaptation of active tone in the mouse descending thoracic aorta under acute changes in loading

Arteries can adapt to sustained changes in blood pressure and flow, and it is thought that these adaptive processes often begin with an altered smooth muscle cell activity that precedes any detectable changes in the passive wall components. Yet, due to the intrinsic coupling between the active and passive properties of the arterial wall, it has been difficult to delineate the adaptive contributions of active smooth muscle. To address this need, we used a novel experimental–computational approach to quantify adaptive functions of active smooth muscle in arterial rings excised from the proximal descending thoracic aorta of mice and subjected to short-term sustained circumferential stretches while stimulated with various agonists. A new mathematical model of the adaptive processes was derived and fit to data to describe and predict the effects of active tone adaptation. It was found that active tone was maintained when the artery was adapted close to the optimal stretch for maximal active force production, but it was reduced when adapted below the optimal stretch; there was no significant change in passive behavior in either case. Such active adaptations occurred only upon smooth muscle stimulation with phenylephrine, however, not stimulation with KCl or angiotensin II. Numerical simulations using the proposed model suggested further that active tone adaptation in vascular smooth muscle could play a stabilizing role for wall stress in large elastic arteries.     

Model of geometrical and smooth muscle tone adaptation of carotid artery subject to step change in pressure

Recent experimental studies have shown significant alterations of the vascular smooth muscle (VSM) tone when an artery is subjected to an elevation in pressure. Therefore, the VSM participates in the adaptation process not only by means of its synthetic activity (fibronectins and collagen) or proliferative activity (hypertrophy and hyperplasia) but also by adjusting its contractile properties and its tone level. In previous theoretical models describing the time evolution of the arterial wall adaptation in response to induced hypertension, the contribution of VSM tone has been neglected. In this study, we propose a new biomechanical model for the wall adaptation to induced hypertension, including changes in VSM tone. On the basis of Hill's model, total circumferential stress is separated into its passive and active components, the active part being the stress developed by the VSM. Adaptation rate equations describe the geometrical adaptation (wall thickening) and the adaptation of active stress (VSM tone). The evolution curves that are derived from the theoretical model fit well the experimental data describing the adaptation of the rat common carotid subjected to a step increase in pressure. This leads to the identification of the model parameters and time constants by characterizing the rapidity of the adaptation processes. The agreement between the results of this simple theoretical model and the experimental data suggests that the theoretical approach used here may appropriately account for the biomechanics underlying the arterial wall adaptation.     

Adaptive regulation of wall shear stress optimizing vascular tree function

The branching structure of the mammalian arterial tree has been known to be close to that of an optimal conduit system of the minimum work model characterized as the branch system of constant wall shear rate. The physiological mechanism producing such construction was considered to be based on the local response of arterial caliber induced by the wall shear stress (shear rate × blood viscosity) and thereby maintaining this stress constant, which was previously observed at the canine common carotid artery shunted to the external jugular vein. The stress levels at various parts of the arterial system estimated from available data fell within ±50% of the mean (15 dyn/cm²), which was consistent with the value predicted from the model. Theoretical analyses on the cost function of the model indicated that the suspected variation of shear rate levels in the arterial tree due to the anomalous changes in blood viscosity which might bring about 3- to 4-fold differences between the minimum and maximum shear rates would cause less than 10% increase in the total energy cost. It was concluded that a local adaptive response to wall shear stress is the mechanism which effectively optimizes the design of the arterial tree.     

Arterial remodeling in response to increased blood flow using a constituent-based model

Previous theoretical models of arterial remodeling in response to changes in blood flow were based on the assumption that material properties of the arterial wall remain unchanged during the remodeling process. According to experimental findings, however, remodeling due to increased flow is accompanied by alteration in the structural properties of elastin, which results in a decrease in its effective elastic stiffness. To account for these effects, we propose a predictive model of arterial remodeling hypothesizing that the variation in mechanical properties of elastin is initiated and driven by the deviation of the intimal shear stress from its baseline value. Geometrical remodeling restores the wall stress distribution as it was under normal flow conditions. A constrained mixture approach is followed. Artery is modeled as a thick-walled cylindrical tube made of non-linear, elastic, anisotropic and incompressible material. Data for a rabbit thoracic aorta have been employed. At the final adapted state, the model predicts a non-monotonic dependence of arterial compliance on the magnitude of flow. This result is in agreement with available experimental data in the literature.     

Uniform strain hypothesis and thin-walled theory in arterial mechanics

The authors (1987), and Chuong and Fung (1986) have shown that the strain and stress distributions in the arterial wall should be more uniform than those calculated on the basis of the conventional assumption that there is no stress over the cross-section of the arterial wall when all external force is removed (zero initial stress hypothesis). Instead of this assumption, the authors have proposed a new hypothesis that the circumferential strain uniformly distributes through the wall thickness at a physiologically normal loading, and named it 'uniform strain hypothesis'. Their results suggest the validity of the thin-walled theory in the vascular mechanics. This paper shows that if the uniform strain hypothesis is applied, the thin-walled theory can be used to accurately determine the constants included in the strain energy density function which describes the mechanical properties of the arterial wall. There were, however, significant differences in the values of the constants between the thin-walled theory and the thick-walled theory if assuming the conventional zero initial stress hypothesis.     

Origin of axial prestretch and residual stress in arteries

The structural protein elastin endows large arteries with unique biological functionality and mechanical integrity, hence its disorganization, fragmentation, or degradation can have important consequences on the progression and treatment of vascular diseases. There is, therefore, a need in arterial mechanics to move from materially uniform, phenomenological, constitutive relations for the wall to those that account for separate contributions of the primary structural constituents: elastin, fibrillar collagens, smooth muscle, and amorphous matrix. In this paper, we employ a recently proposed constrained mixture model of the arterial wall and show that prestretched elastin contributes significantly to both the retraction of arteries that is observed upon transection and the opening angle that follows the introduction of a radial cut in an unloaded segment. We also show that the transmural distributions of elastin and collagen, compressive stiffness of collagen, and smooth muscle tone play complementary roles. Axial prestresses and residual stresses in arteries contribute to the homeostatic state of stress in vivo as well as adaptations to perturbed loads, disease, or injury. Understanding better the development of and changes in wall stress due to individual extracellular matrix constituents thus promises to provide considerable clinically important insight into arterial health and disease.     

A boundary layer model for wall shear stress in arterial stenosis

This paper proposes a model for wall shear stress in arterial stenosis based on boundary layer theory. Wall shear stress estimates are obtained by solving the momentum integral equation using the method proposed by Walz and applying this method to various stenosis geometries for Reynolds numbers (Re) of Re = 59-1000. Elevated wall shear stress may be of importance when considering thrombosis and vascular erosion in stenosis, as well as the potential for debris from the stenotic area to 'break away' and cause further pathology. The values of shear stress obtained using the model in this study agree well with published values of wall shear stress. When compared to a previously published boundary layer model utilizing the Thwaites method (Reese and Thompson, 1998), the model proposed herein performs better at higher Re while the model utilizing the Thwaites method performs better at lower Re. Wall shear stresses are shown to increase with increasing stenosis (increased area reduction) for a given stenosis length, increase with increasing Re for a given stenosis geometry, and increase for steeper stenosis of the same constriction. The boundary layer model proposed can be easily implemented by clinical researchers to provide in vivo estimates of wall shear stress through arterial stenoses.     

Accurate prediction of wall shear stress in a stented artery: newtonian versus non-newtonian models

A significant amount of evidence linking wall shear stress to neointimal hyperplasia has been reported in the literature. As a result, numerical and experimental models have been created to study the influence of stent design on wall shear stress. Traditionally, blood has been assumed to behave as a Newtonian fluid, but recently that assumption has been challenged. The use of a linear model; however, can reduce computational cost, and allow the use of Newtonian fluids (e.g., glycerine and water) instead of a blood analog fluid in an experimental setup. Therefore, it is of interest whether a linear model can be used to accurately predict the wall shear stress caused by a non-Newtonian fluid such as blood within a stented arterial segment. The present work compares the resulting wall shear stress obtained using two linear and one nonlinear model under the same flow waveform. All numerical models are fully three-dimensional, transient, and incorporate a realistic stent geometry. It is shown that traditional linear models (based on blood's lowest viscosity limit, 3.5 Pa s) underestimate the wall shear stress within a stented arterial segment, which can lead to an overestimation of the risk of restenosis. The second linear model, which uses a characteristic viscosity (based on an average strain rate, 4.7 Pa s), results in higher wall shear stress levels, but which are still substantially below those of the nonlinear model. It is therefore shown that nonlinear models result in more accurate predictions of wall shear stress within a stented arterial segment.     

Effects of arterial wall stress on vasomotion

Smooth muscle and endothelial cells in the arterial wall are exposed to mechanical stress. Indeed blood flow induces intraluminal pressure variations and shear stress. An increase in pressure may induce a vessel contraction, a phenomenon known as the myogenic response. Many muscular vessels present vasomotion, i.e., rhythmic diameter oscillations caused by synchronous cytosolic calcium oscillations of the smooth muscle cells. Vasomotion has been shown to be modulated by pressure changes. To get a better understanding of the effect of stress and in particular pressure on vasomotion, we propose a model of a blood vessel describing the calcium dynamics in a coupled population of smooth muscle cells and endothelial cells and the consequent vessel diameter variations. We show that a rise in pressure increases the calcium concentration. This may either induce or abolish vasomotion, or increase its frequency depending on the initial conditions. In our model the myogenic response is less pronounced for large arteries than for small arteries and occurs at higher values of pressure if the wall thickness is increased. Our results are in agreement with experimental observations concerning a broad range of vessels.     

Physiological and cellular responses of the 2,4-D degrading bacterium,Burkholderia cepacia YK-2, to the phenoxyherbicides 2,4-D and 2,4,5-T

Our previous research has demonstrated that novel 43-kDa DnaK and 41-kDa GroEL proteins are synthesized in Burkholderia sp. YK-2 in response to sublethal concentrations of 2,4-D stress [Cho et al. (2000) Curr Microbiol 41:33-38]. In this study, we have extended this work to examine the cellular responses of strain YK-2 to stresses induced in response to the phenoxyherbicides 2,4-D or 2,4,5-T. Strain YK-2 exhibited a more sensitive response to 2,4,5-T stress than to 2,4-D stress, as shown in physiological and morphological changes, suggesting a greater cytotoxic effect of 2,4,5-T. SEM analyses revealed the presence of perforations and irregular rod forms with wrinkled surfaces for cells treated with either herbicide. These irregularities were found more frequently for 2,4,5-T-treated cells than for 2,4-D-treated cells. Analysis of cellular fatty acids showed similar effects in the shifts of total cellular fatty acid composition in response to 2,4-D and 2,4,5-T. Strain YK-2 could degrade 2.25 m M 2,4-D completely during 28 h of incubation with transient production of 2,4-dichlorophenol as a metabolite; however, 2,4,5-T was not catabolized at any of the concentrations tested. BIOLOG and 16S rDNA analyses revealed that strain YK-2 was 98% similar to the Burkholderia cepacia species cluster; therefore, we have designated this strain as B. cepacia YK-2.     

Structural analysis of two different stent configurations

Two different stent configurations (i.e. the well known Palmaz–Schatz (PS) and a new stent configuration) are mechanically investigated. A finite element model was used to study the two geometries under combining loads and a computational fluid dynamic model based on fluid structure interaction was developed investigating the plaque and the artery wall reactions in a stented arterial segment. These models determine the stress and displacement fields of the two stents under internal pressure conditions. Results suggested that stent designs cause alterations in vascular anatomy that adversely affect arterial stress distributions within the wall, which have impact in the vessel responses such as the restenosis. The hemodynamic analysis shows the use of new stent geometry suggests better biofluid mechanical response such as the deformation and the progressive amount of plaque growth.     

Heat-induced changes in the finite strain viscoelastic behavioir of a collaagenous tissue

Supra-physiological temperatures are increasingly being used to treat many different soft need for injuries. To identify improved clinical treatments, however, there is a need for better information on the effect of the mechanics on the thermal damage process as well as the effect of the incurred damage on the subsequent mechanical properties. In this paper we report the first biaxial data on the stress relaxation behavior of a collagenous tissue before and after thermal damage. Based on a two-dimensional finite strain viscoelastic model, which incorporates an exponential elastic response, it is shown that the thermal damage can significantly decrease the characteristic time for stress relaxation and the stress residual.     

A description of arterial wall mechanics using limiting chain extensibility constitutive models

Certain aspects of the mechanical response of arterial walls can be described using nonlinear elasticity theory. Uniaxial tests on vascular walls reveal nonlinear stress-strain behavior, with higher extensibility in the low stretch range and progressively lower extensibility with increasing stretch. This phenomenon is well known in the framework of rubber-like materials where it is called a strain-hardening or strain-stiffening effect. Constitutive models of incompressible hyperelasticity that take this into account include power-law models and limiting chain extensibility models. Our purpose in this paper is to bring to the attention of the biomechanics community some essential features of one such model of the latter type due to Gent. This model is compared with isotropic versions of biomechanical constitutive models by Takamizawa-Hayashi and Fung; the latter is a limiting version of a power-law material. Two particular problems are considered for which experimental data on arterial wall deformations are available. The first concerns small oscillations superposed on a large static stretch of a vertical string of arterial tissue. It is shown that the exponential model of Fung and the Gent model match well with the experimental data. The second problem is the extension of an internally pressurized circular cylindrical tube. It is shown that an inversion phenomenon observed experimentally for the human iliac artery can be described within a membrane theory by the Gent model whereas this cannot be described using the exponential model. The foregoing considerations are carried out for isotropic elastic materials in the absence of residual stress. Extensions to include anisotropy are also indicated.     

A multi-scale mechanobiological model of in-stent restenosis: deciphering the role of matrix metalloproteinase and extracellular matrix changes

Since their first introduction, stents have revolutionised the treatment of atherosclerosis; however, the development of in-stent restenosis still remains the Achilles' heel of stent deployment procedures. Computational modelling can be used as a means to model the biological response of arteries to different stent designs using mechanobiological models, whereby the mechanical environment may be used to dictate the growth and remodelling of vascular cells. Changes occurring within the arterial wall due to stent-induced mechanical injury, specifically changes within the extracellular matrix, have been postulated to be a major cause of activation of vascular smooth muscle cells and the subsequent development of in-stent restenosis. In this study, a mechanistic multi-scale mechanobiological model of in-stent restenosis using finite element models and agent-based modelling is presented, which allows quantitative evaluation of the collagen matrix turnover following stent-induced arterial injury and the subsequent development of in-stent restenosis. The model is specifically used to study the influence of stent deployment diameter and stent strut thickness on the level of in-stent restenosis. The model demonstrates that there exists a direct correlation between the stent deployment diameter and the level of in-stent restenosis. In addition, investigating the influence of stent strut thickness using the mechanobiological model reveals that thicker strut stents induce a higher level of in-stent restenosis due to a higher extent of arterial injury. The presented mechanobiological modelling framework provides a robust platform for testing hypotheses on the mechanisms underlying the development of in-stent restenosis and lends itself for use as a tool for optimisation of the mechanical parameters involved in stent design.