A 3-D constrained mixture model for mechanically mediated vascular growth and remodeling

In contrast to the widely applied approach to model soft tissue remodeling employing the concept of volumetric growth, microstructurally motivated models are capable of capturing many of the underlying mechanisms of growth and remodeling; i.e., the production, removal, and remodeling of individual constituents at different rates and to different extents. A 3-dimensional constrained mixture computational framework has been developed for vascular growth and remodeling, considering new, microstructurally motivated kinematics and constitutive equations and new stress and muscle activation mediated evolution equations. Our computational results for alterations in flow and pressure, using reasonable physiological values for rates of constituent growth and turnover, concur with findings in the literature. For example, for flow-induced remodeling, our simulations predict that, although the wall shear stress is restored completely, the circumferential stress is not restored employing realistic physiological rate parameters. Also, our simulations predict different levels of thickening on inner versus outer wall locations, as shown in numerous reports of pressure-induced remodeling. Whereas the simulations are meant to be illustrative, they serve to highlight the experimental data currently lacking to fully quantify mechanically mediated adaptations in the vasculature.     

Theoretical study on the effects of pressure-induced remodeling on geometry and mechanical non-homogeneity of conduit arteries

A structure-based mathematical model for the remodeling of arteries in response to sustained hypertension is proposed. The model is based on the concepts of volumetric growth and constitutive modeling of the arterial tissue within the framework of the constrained mixture theory. The major novel result of this study is that remodeling is associated with a local change in the mass fractions of the wall constituents that ultimately leads to mechanical non-homogeneity of the arterial wall. In the new homeostatic state that develops after a sustained increase in arterial pressure, the mass fraction of elastin decreases from the intimal side to the adventitial side of arteries, while the collagen fraction manifests an opposite trend. The results obtained are supported by some experimental observations reported in the literature.     

A 2-D model of flow-induced alterations in the geometry, structure, and properties of carotid arteries

Evidence from diverse investigations suggests that arterial growth and remodeling correlates well with changes in mechanical stresses from their homeostatic values. Ultimately, therefore, there is a need for a comprehensive theory that accounts for changes in the 3-D distribution of stress within the arterial wall, including residual stress, and its relation to the mechanisms of mechanotransduction. Here, however, we consider a simpler theory that allows competing hypotheses to be tested easily, that can provide guidance in the development of a 3-D theory, and that may be useful in modeling solid-fluid interactions and interpreting clinical data. Specifically, we present a 2-D constrained mixture model for the adaptation of a cylindrical artery in response to a sustained alteration in flow. Using a rule-of-mixtures model for the stress response and first order kinetics for the production and removal of the three primary load-bearing constituents within the wall, we illustrate capabilities of the model by comparing responses given complete versus negligible turnover of elastin. Findings suggest that biological constraints may result in suboptimal adaptations, consistent with reported observations. To build upon this finding, however, there is a need for significantly more data to guide the hypothesis testing as well as the formulation of specific constitutive relations within the model.     

A potential role of smooth muscle tone in early hypertension: a theoretical study

A conspicuous long-term consequence of hypertension is a thickening of the arterial wall, which many suggest returns the circumferential wall stress toward its normal value. This thickening results from an increase in smooth muscle and extracellular matrix, with the associated growth and remodeling processes depending on a host of regulatory signals that likely include the altered mechanical environment. Although the precise mechanotransduction pathways remain unknown, we propose that vasoconstriction may be an early response of the arterial wall to a step-change in pressure. In particular, computations suggest that such a response can decrease the magnitude and transmural gradients of the pressure-induced wall stresses and return the mean wall shear stress toward its homeostatic value. Such an initial 'compensatory vasoconstriction' could also help set into motion subsequent growth and remodeling responses due to growth regulatory characteristics of the vasoactive molecules (e.g., nitric oxide, endothelin-1, angiotensin-II). Although the consequences of growth and remodeling have been the focus of prior biomechanical and histological studies, early responses dictate subsequent developments and therefore deserve increased attention in vascular biomechanics and mechanobiology.     

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.     

Exercise-mediated changes in conduit artery wall thickness in humans: role of shear stress

Episodic increases in shear stress have been proposed as a mechanism that induces training-induced adaptation in arterial wall remodeling in humans. To address this hypothesis in humans, we examined bilateral brachial artery wall thickness using high-resolution ultrasound in healthy men across an 8-wk period of bilateral handgrip training. Unilaterally, shear rate was attenuated by cuff inflation around the forearm to 60 mmHg. Grip strength, forearm volume, and girth improved similarly between the limbs. Acute bouts of handgrip exercise increased shear rate (P < 0.005) in the noncuffed limb, whereas cuff inflation successfully decreased exercise-induced increases in shear. Brachial blood pressure responses similarly increased during exercise in both the cuffed and noncuffed limbs. Handgrip training had no effect on baseline brachial artery diameter, blood flow, or shear rate but significantly decreased brachial artery wall thickness after 6 and 8 wk (ANOVA, P < 0.001) and wall-to-lumen ratio after week 8 (ANOVA, P = 0.005). The magnitude of decrease in brachial artery wall thickness and wall-to-lumen ratio after exercise training was similar in the noncuffed and cuffed arms. These results suggest that exercise-induced changes in shear rate are not obligatory for arterial wall remodeling during a period of 8 wk of exercise training in healthy humans.     

Mechanisms of blood flow-induced vascular enlargement

Chronic changes in wall shear stress lead to vascular remodeling, characterized by increased vascular wall diameter and thickness, to restore wall shear stress values to baseline. Release of nitric oxide from endothelial cells exposed to excessive shear is a fundamental step in the remodeling process, and potentially triggers a cascade of events, including growth factor induction and matrix metalloproteinase activation, that together contribute to restructuralization of the vessel wall. Understanding these processes could help explain how changes in blood vessel wall structure occur in the context of atherosclerosis or aortic aneurisms.     

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.     

A constrained mixture model for developing mouse aorta

Mechanical stresses influence the structure and function of adult and developing blood vessels. When these stresses are perturbed, the vessel wall remodels to return the stresses to homeostatic levels. Constrained mixture models have been used to predict remodeling of adult vessels in response to step changes in blood pressure, axial length and blood flow, but have not yet been applied to developing vessels. Models of developing blood vessels are complicated by continuous and simultaneous changes in the mechanical forces. Understanding developmental growth and remodeling is important for treating human diseases and designing tissue-engineered blood vessels. This study presents a constrained mixture model for postnatal development of mouse aorta with multiple step increases in pressure, length and flow. The baseline model assumes that smooth muscle cells (SMCs) in the vessel wall immediately constrict or dilate the inner radius after a perturbation to maintain the shear stress and then remodel the wall thickness to maintain the circumferential stress. The elastin, collagen and SMCs have homeostatic stretch ratios and passive material constants that do not change with developmental age. The baseline model does not predict previously published experimental data. To approximate the experimental data, it must be assumed that the SMCs dilate a constant amount, regardless of the step change in mechanical forces. It must also be assumed that the homeostatic stretch ratios and passive material constants change with age. With these alterations, the model approximates experimental data on the mechanical properties and dimensions of aorta from 3- to 30-day-old mice.     

壁剪应力变化对动脉重建影响的在体研究

为探讨动脉血流受阻后壁剪应力（Wall shear stress,WSS)变化对动脉适应性重建的影响,在60只实验兔建立动脉血流减小模型,术后0－30天8个不同时相点,检测动脉样本的壁厚及内径,单位面积（mm^2),动脉内皮细胞（Artereial endothelial cell,AEC）核数目和平滑肌细胞核数目。结果显示WSS变化通过调节动脉的舒缩而致使动脉管径适应性缩减,动脉壁腔比（WT／LD）保持恒定。动脉壁细胞成分中AEC受WSS变化的影响,而平滑肌细胞则不受影响。在术后3天、7天、AEC密度较正常对照显著降低（P＜0．01）;而在术后14天、30天,AEC密度显著增高（P＜0．01）。说明WSS对动脉适应性重建的影响,是通过调节动脉的舒缩所致,而非壁腔比的改变,WSS的变化在AEC的适应性重建过程中可能起着重要调节作用。     

Automatic detection of the carotid artery boundary on cross-sectional MR image sequences using a circle model guided dynamic programming

Background  

Systematic aerobe training has positive effects on the compliance of dedicated arterial walls. The adaptations of the arterial structure and function are associated with the blood flow-induced changes of the wall shear stress which induced vascular remodelling via nitric oxide delivered from the endothelial cell. In order to assess functional changes of the common carotid artery over time in these processes, a precise measurement technique is necessary. Before this study, a reliable, precise, and quick method to perform this work is not present.     

The role of deformability of endothelial cells in the arterial response to shear tension

Treatment of the femoral artery luminal surface with glutaraldehyde dimere or dithiosuccinimidyl propionate reduced or eliminated flow-induced dilation, the responses to acetylcholine and the ATP being preserved. The findings suggest that the endothelial cells perceive changes in shear stress and that the cell stiffness is a factor subject to the influence of the magnitude of flow-induced arterial dilation.     

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.     

Fluid shear stress and the vascular endothelium: for better and for worse

As blood flows, the vascular wall is constantly subjected to physical forces, which regulate important physiological blood vessel responses, as well as being implicated in the development of arterial wall pathologies. Changes in blood flow, thus generating altered hemodynamic forces are responsible for acute vessel tone regulation, the development of blood vessel structure during embryogenesis and early growth, as well as chronic remodeling and generation of adult blood vessels. The complex interaction of biomechanical forces, and more specifically shear stress, derived by the flow of blood and the vascular endothelium raise many yet to be answered questions:How are mechanical forces transduced by endothelial cells into a biological response, and is there a "shear stress receptor"?Are "mechanical receptors" and the final signaling pathways they evoke similar to other stimulus-response transduction systems?How do vascular endothelial cells differ in their response to physiological or pathological shear stresses?Can shear stress receptors or shear stress responsive genes serve as novel targets for the design of diagnostic and therapeutic modalities for cardiovascular pathologies?The current review attempts to bring together recent findings on the in vivo and in vitro responses of the vascular endothelium to shear stress and to address some of the questions raised above.     

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.     

Expression of TGF-β1 and β3 but not apoptosis factors relates to flow-induced aortic enlargement

Background  

Cell proliferation and apoptosis are both involved in arterial wall remodeling. Increase in blood flow induces arterial enlargement. The molecular basis of flow-induced remodeling in large elastic arteries is largely unknown.     

Disruption of TGF-β signaling in smooth muscle cell prevents flow-induced vascular remodeling

Transforming growth factor-β (TGF-β) signaling has been prominently implicated in the pathogenesis of vascular remodeling, especially the initiation and progression of flow-induced vascular remodeling. Smooth muscle cells (SMCs) are the principal resident cells in arterial wall and are critical for arterial remodeling. However, the role of TGF-β signaling in SMC for flow-induced vascular remodeling remains unknown. Therefore, the goal of our study was to determine the effect of TGF-β pathway in SMC for vascular remodeling, by using a genetical smooth muscle-specific (SM-specific) TGF-β type II receptor (Tgfbr2) deletion mice model. Mice deficient in the expression of Tgfbr2 (MyhCre.Tgfbr2^f/f) and their corresponding wild-type background mice (MyhCre.Tgfbr2^WT/WT) underwent partial ligation of left common carotid artery for 1, 2, or 4 weeks. Then the carotid arteries were harvested and indicated that the disruption of Tgfbr2 in SMC provided prominent inhibition of vascular remodeling. And the thickening of carotid media, proliferation of SMC, infiltration of macrophage, and expression of matrix metalloproteinase (MMP) were all significantly attenuated in Tgfbr2 disruption mice. Our study demonstrated, for the first time, that the TGF-β signaling in SMC plays an essential role in flow-induced vascular remodeling and disruption can prevent this process.     

Spatiotemporal analysis of flow-induced intermediate filament displacement in living endothelial cells

The distribution of hemodynamic shear stress throughout the arterial tree is transduced by the endothelium into local cellular responses that regulate vasoactivity, vessel wall remodeling, and atherogenesis. Although the exact mechanisms of mechanotransduction remain unknown, the endothelial cytoskeleton has been implicated in transmitting extracellular force to cytoplasmic sites of signal generation via connections to the lumenal, intercellular, and basal surfaces. Direct observation of intermediate filament (IF) displacement in cells expressing green fluorescent protein-vimentin has suggested that cytoskeletal mechanics are rapidly altered by the onset of fluid shear stress. Here, restored images from time-lapse optical sectioning fluorescence microscopy were analyzed as a four-dimensional intensity distribution function that represented IF positions. A displacement index, related to the product moment correlation coefficient as a function of time and subcellular spatial location, demonstrated patterns of IF displacement within endothelial cells in a confluent monolayer. Flow onset induced a significant increase in IF displacement above the nucleus compared with that measured near the coverslip surface, and displacement downstream from the nucleus was larger than in upstream areas. Furthermore, coordinated displacement of IF near the edges of adjacent cells suggested the existence of mechanical continuity between cells. Thus, quantitative analysis of the spatiotemporal patterns of flow-induced IF displacement suggests redistribution of intracellular force in response to alterations in hemodynamic shear stress acting at the lumenal surface.     

Flow-induced control of arterial lumen

Blood flow velocity is a factor that affects the diameter of arteries. In order to investigate the flow-induced arterial dilatation, the outer diameter of the femoral, common carotid or renal arteries of anaesthetized cats was measured during perfusion of these arteries with blood or plasma-substituting solutions under conditions of stabilized perfusion pressure. It has been shown that, whatever the perfusate, blood or a substituent, an increase in flow makes the artery to dilate. Consequently, the flow-induced dilatation is not due to any blood-borne humoral factor. As an increase in the solution's viscosity causes dilatation even at constant flow-rate and pressure in the artery, the effect is to be ascribed to the ability of the vascular wall to perceive shear stress. As far as removal of endothelium eliminates the dilatation evoked by increasing flow or fluid viscosity, it may be concluded that the flow-induced dilatation is due to the sensitivity to shear stress of the endothelium.     

Haemodynamics and wall remodelling of a growing cerebral aneurysm: a computational model

We have developed a computational simulation model for investigating an often postulated hypothesis connected with aneurysm growth. This hypothesis involves a combination of two parallel and interconnected mechanisms: according to the first mechanism, an endothelium-originating and wall shear stress-driven apoptotic behavior of smooth muscle cells, leading to loss of vascular tone is believed to be important to the aneurysm behavior. Vascular tone refers to the degree of constriction experienced by a blood vessel relative to its maximally dilated state. All resistance and capacitance vessels under basal conditions exhibit some degree of smooth muscle contraction that determines the diameter, and hence tone, of the vessel. The second mechanism is connected to the arterial wall remodeling. Remodeling of the arterial wall under constant tension is a biomechanical process of rupture, degradation and reconstruction of the medial elastin and collagen fibers. In order to investigate these two mechanisms within a computationally tractable framework, we devise mechanical analogues that involve three-dimensional haemodynamics, yielding estimates of the wall shear stress and pressure fields and a quasi-steady approach for the apoptosis and remodeling of the wall. These analogues are guided by experimental information for the connection of stimuli to responses at a cellular level, properly averaged over volumes or surfaces. The model predicts aneurysm growth and can attribute specific roles to the two mechanisms involved: the smooth muscle cell-related loss of tone is important to the initiation of aneurysm growth, but cannot account alone for the formation of fully grown sacks; the fiber-related remodeling is pivotal for the latter.