Modeling water flow through arterial tissue

A simple model of, water flow through deformable porous media has been developed with emphasis on application to arterial walls. The model incorporates a strain-dependent permeability function into Darcy's Law which is coupled, to the force balance for the bulk material. A simple analytical expression relating water flux (volume flux) to pressure differential is developed which shows how strain-dependent permeability can lead to a reduction in hydraulic conductivity with increasing differential pressure as observed in experiments with arteries. The variation of permeability with position in the wall, which may influence the convective diffusion of macromolecules, is determined for both cylindrical and planar segments and a marked influence of geometry is noted.     

Regional distribution of layer-specific circumferential residual deformations and opening angles in the porcine aorta

Information on the layer-specific residual deformations of aortic tissue and how these vary throughout the vessel is important for understanding the regionally-varying aortic functions and pathophysiology, but not so much can be found in the literature. Toward this end, porcine aortas were sectioned into eighteen rings, with one ring from each anatomical position radially cut to obtain the zero-stress state for the intact wall and the other ring dissected into intimal-medial and adventitial layers; these rings were then radially cut to reach the zero-stress state for the intima-media and adventitia. Peripheral variations in internal/external circumferences, thickness, and opening angle of the intact wall and its layers were measured through image analysis at the no-load and zero-stress states. Intact wall and layer circumferences at both states significantly declined along the aorta, as did intact wall and intimal-medial but not adventitial thickness. Adventitia exhibited the greatest opening angles, approaching 180 deg all over the aorta. The opening angles of the intima-media and intact wall were quite similar, with the highest values in the ascending aorta, the lowest at the diaphragm, and increasing subsequently. Bending-related residual stretches were released by radial cutting that were compressive internally and tensile externally, displaying distinct axial variation for the intima-media and intact wall, and non-significant variation for the adventitia. Evidence is provided for the release upon layer separation of compressive stretches in the intima-media and of tensile stretches in the adventitia, whose values were smallest in the descending thoracic aorta and highest near the iliac artery bifurcation.     

Stress-modulated growth, residual stress, and vascular heterogeneity.

A simple phenomenological model is used to study interrelations between material properties, growth-induced residual stresses, and opening angles in arteries. The artery is assumed to be a thick-walled tube composed of an orthotropic pseudoelastic material. In addition, the normal mature vessel is assumed to have uniform circumferential wall stress, which is achieved here via a mechanical growth law. Residual stresses are computed for three configurations: the unloaded intact artery, the artery after a single transmural cut, and the inner and outer rings of the artery created by combined radial and circumferential cuts. The results show that the magnitudes of the opening angles depend strongly on the heterogeneity of the material properties of the vessel wall and that multiple radial and circumferential cuts may be needed to relieve all residual stress. In addition, comparing computed opening angles with published experimental data for the bovine carotid artery suggests that the material properties change continuously across the vessel wall and that stress, not strain, correlates well with growth in arteries.     

Alternate method for the analysis of residual strain in the arterial wall

If an artery is cut transversely into rings, and the rings are then cut radially, they spring open into sectors. This phenomenon implies the existence of residual stresses and strains in the arterial wall in the non-loaded state. In the present paper, we propose a new method to calculate the residual strain from the measured wall dimensions and a polar angle of a specimen in the stress-free state, assuming that the wall is homogeneous and incompressible, and that a radially cut, stress-free specimen forms a circular sector. For this analysis, edge angles were measured at the edges of the opened-up specimen. Residual strains were obtained for the descending thoracic aorta, the common carotid artery, and the femoral artery in the rabbit. The results obtained indicated that the magnitude of residual strain was largest in the femoral artery and smallest in the aorta among the three arteries. The opening angle did not depend upon the length of a ring specimen if the ratio of the length to the diameter was ≤ 3.     

A study on large radial motion of arteries in vivo

This study analyses the radial periodic motion of an artery which is modelled as a thin cylinder of uniform cross-section subjected to dynamic inner pressure using the theory of finite deformation of elastic materials. The arterial tissue properties (anisotropy, homogeneity and incompressibility) are taken into account in an analysis based on the use of the strain energy function. The validity of the mathematical analysis is illustrated through numerical computation applying the available in vivo data for elastic constants of the canine middle descending thoracic aorta to the expressions for the intramural pressure and circumferential stresses obtained by solving the necessary equation of motion together with the boundary conditions. Results obtained in this study indicate very low stresses which suggest that the arteriosclerosis resulting from high stress gradients is effectively ruled out in this model.     

Assessment of spatial inhomogeneities in intima media thickness along an arterial segment using its dynamic behavior

To assess locally deviating structural and mechanical properties of arterial walls, the spatial variance in end-diastolic intima media thickness (IMT) and the change in IMT during the cardiac cycle (DeltaIMT) were determined along a short segment of the common carotid artery (15.86 mm), at 16 positions simultaneously. Intrasubject spatial inhomogeneities along the artery were revealed by a spatial variance significantly larger than the temporal variance over several beats. If differences between positions were confirmed, the extent of the inhomogeneity was obtained by comparison of IMT and DeltaIMT at each position with their spatial medians +/- the least-significant difference. Because no intersubject comparisons were necessary, a single session of several measurements was sufficient to assess inhomogeneities in the arterial wall properties of a subject, making the method independent of biological variability between subjects. The method was evaluated on 47 presumed healthy subjects (age range 21-75 yr). In 22 subjects, spatial inhomogeneities in DeltaIMT occurred (P < 0.05). In young subjects, DeltaIMT was locally decreased, i.e., in systole inhomogeneities were less compressed than their surrounding tissue. In older subjects, DeltaIMT was locally increased, i.e., the inhomogeneity was locally more compressed than its surrounding wall tissue.     

Changes of opening angle in hypertensive and hypotensive arteries in 3-day organ culture

To study the effect of pressure changes on the opening angle of arteries in organ culture, tubular segments of porcine common carotid arteries were cultured with pulsatile flow perfusion under hypertensive (150+/-20 mmHg), normotensive (100+/-20 mmHg), or hypotensive (30+/-10 mmHg) pressure while maintaining the arteris at a physiological wall shear stress of approximately 15 dyn/cm(2) for up to 3 days. Arteries were then cut into short ring segments by sections perpendicular to the axis and then cut open radially to observe the opening angle in aerated phosphate buffered saline solution (37 degrees C). Norepinephrine (NE, 10 microM), carbacol (CCh, 100 microM), and sodium nitroprusside (SNP, 10 microM) were added after the radial cut at 30, 20, and 30 min intervals, the opening angles were measured, respectively. Results show that hypertensive arteries developed a significantly larger opening angle than normotensive and hypotensive arteries, associated with a significant increase in cell proliferation. In addition, with smooth muscle contraction activated by NE, the opening angle decreases significantly in hypertensive arteries but has little change in hypotensive and normotensive arteries, indicating an enhancement of smooth muscle contraction on the lumen side of the hypertensive arterial wall. In comparison, hypotensive pressure has little effect on arterial opening angle and cell proliferation.     

Towards early diagnosis of atherosclerosis: the finite volume method for fluid-structure interaction

Blood flow through arteries represents a very complex, fluid-structure interaction (FSI) problem. Strong coupling between the blood and artery is due to the relatively low stiffness of the artery compared to that of blood. Hence, the pressure exerted by the flowing blood on the artery wall can result in considerable deformations of the artery, and vice-versa, arterial deformations can in turn affect the blood flow. In the present work, the finite volume method is employed to solve the problem where compressible fluid, representing blood, flows in healthy arteries as well as in unhealthy, i.e., partly stiffened arteries. The stiffening of the arterial wall is assumed to be the first key stage in the development of atherosclerosis. The comparison between various deformation profiles of healthy and unhealthy arteries demonstrates significant and measurable differences, in particular in the radial direction. This is hoped to help toward establishing procedures for early diagnosis of the disease.     

Usefulness of Speckle Tracking Imaging to Assess Myocardial Contractility in Intra-Abdominal Hypertension: Study in a Mini-Pig Model

This study evaluated the usefulness of speckle tracking imaging (STI) in assessment of myocardial contractility in intra-abdominal hypertension experimentally induced in mini-pigs. To this effect, 12 mini-pigs were anesthetized with intravenous injection of 3?% sodium pentobarbital, hemorrhaged to reach the shock status, and resuscitated with excessive volume of lactated Ringer??s solution. The animals were either sham-operated (study group 1) or underwent treatment with intra-abdominal volume increment (study group 2). Observations were made prior to induction of shock, 1?h after shock, 2?h after induction of intra-abdominal hypertension, and 8 and 12?h after treatment. The heart rate and mean artery pressure were conventionally measured. STI was used to assess radial and circumferential strains of segmental ventricular wall. The results obtained demonstrated that myocardial contractility, as manifested by radial and circumferential strains of different ventricular wall segments, was decreased after induction of intra-abdominal hypertension. Treatment with intra-abdominal volume increment was able to decrease heart rate and intra-bladder pressure (indicator of effectiveness of treatment) and significantly improved myocardial contractility of involved ventricular wall segments. In conclusion, STI is a useful method to assess myocardial regional functions.     

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.     

犬不同血管搭桥方法及搭桥血管内流场的计算机数值模拟

目的血管搭桥术后的内膜增生往往导致手术失败,而内膜增生与搭桥血管内的流场密切相关,为改善搭桥血管中的流场结构,作者设计了偏心搭桥手术方法,利用计算机数值模拟技术,探索偏心搭桥和传统搭桥血管中流场的变化,为血管搭桥方法提供优化设计方案。方法16只犬随机分为偏心搭桥组和传统搭桥组进行血管搭桥,测定搭桥前后血管几何数据,搭桥后近心端及远心端吻合口血流量和血压。按测定的血管几何数据,FLUENT 6.2模拟搭桥血管内的流场。结果偏心搭桥近心端和远心端吻合口不在同一平面。传统搭桥中,主体动脉远心端吻合口对应面处存在一个较低壁面剪切应力（WSS）区域及流体停滞点,离脚跟较近的一部分流体会形成涡漩,血流进入主体动脉后,还会表现出迪恩涡二次流;偏心搭桥中,主体动脉吻合口对应面上的低WSS区域和流体停滞点消失,血流接触到吻合口底面后,以切向旋转的方式改变其流动方向,不会形成涡漩,且当血流进入主体动脉后,立即发生螺旋流态且能持续很长一段。结论偏心搭桥能够产生血液旋动流,显著增加远心端血流量、提高WSS。     

Heart rate,arterial distensibility,and optimal performance of the arterial tree

In this study we explore the ability of a previously developed model of pulsatile flow for explaining the observed reduction of arterial distensibility with heart rate. The parameters relevant for the analysis are arterial wall distensibility together with permeability and reflection coefficients of the end capillaries. A non-specific artery and the ensemble of tissues supplied by that artery were considered in the model. The blood current within that artery was equalized to the sum of all micro currents in the tissues supplied by that artery. A formula emerged that relates changes in arterial distensibility with heart rate, and also with some particular aspects of microcirculation. Then, that formula was tested with data of distensibilities of the radial and carotid arteries observed at the heart rates of 63, 90, and 110 b.p.m. The formula correctly predicted the trend of decreased distensibility with heart rate for both arteries. Moreover, due to the fact that the carotid artery supplies the brain, and because the Blood–Brain barrier is highly restrictive to colloids in the blood, for the carotid artery the formula predicted a less marked decrease in distensibility than in the case of the radial artery feeding muscle tissue, which has a greater permeability to colloids, a trend that was confirmed by data. It was found that reduction of arterial distensibility with heart rate was greater in arteries that supply end capillaries with high permeability and low reflection coefficients.     

Coupled computational analysis of arterial LDL transport -- effects of hypertension

Hypertension, a risk factor for atherosclerosis, increases the uptake of low density lipoproteins (LDL) by the arterial wall. Our objective in this work was to use computational modeling to identify physical factors that could be partially responsible for this effect. Fluid flow and mass transfer patterns in the lumen and wall of an arterial model were computed in a coupled manner, replicating as closely as possible previous experimental studies in which LDL uptake into the artery wall was measured in straight, excised arterial segments. Under conditions of both flow and no-flow, simulations predicted an increase in concentration polarization of LDL at the artery wall when arterial pressure was increased from 120 to 160 mmHg. However, this led to only a slight increase in mean LDL concentration within the arterial wall. However, if the permeability of the endothelium to LDL was allowed to vary with intra-arterial pressure, then the simulations predicted that the uptake of LDL would be enhanced 1.9-2.6 fold at higher pressure. The magnitude of this increase was consistent with experimental data. We conclude that the concentration polarization effects, enhanced by elevated intra-arterial pressure, cannot explain the increase in LDL uptake seen under hypertensive conditions. Instead, the data are most consistent with a pressure-linked increase in endothelial permeability to LDL.     

Residual stress and strain in the lamellar unit of the porcine aorta: experiment and analysis

The opened-up configuration of the artery wall has long been assumed to be stress-free. This is questionable in a microscopic level. The aortic media is made of concentric layers whose unit is called a lamellar unit, a pair of elastic lamina (EL) and a smooth muscle-rich layer (SML). Recently, we found that the EL was about 2.5 times stiffer than the SML. If the circumferential stress in the in vivo condition is the same between the two layers, residual stress of each layer should be different because the stress-strain relationships differ. Such residual stress is not released fully by radial cutting, but is released in the area close to the cut surface, causing hills and valleys on the surface due to residual stress. To check this hypothesis, we have developed a scanning micro indentation tester, a scaled-up version of the atomic force microscope, and measured the topography and the stiffness distribution of the cut surface. The surface of the section of porcine thoracic aortas shows hill and valley pattern corresponding with their histology. The hills were more than three times stiffer than the valleys, indicating that the hills are the ELs and the valleys the SMLs, and the ELs are compressed and the SMLs stretched in the lamellar unit. A finite element analysis showed that the residual stress in the EL and the SML is much higher than those estimated in the unloaded ring-like segments. Fairly large stress may still reside in the opened-up aortic wall.     

Vascular metabolic dissipation in Murray's law

The metabolic dissipation in Murray's minimum energy hypothesis includes only the blood metabolism. The metabolic dissipation of the vascular tree, however, should also include the metabolism of passive and active components of the vessel wall. In this study, we extend the metabolic dissipation to include blood metabolism, as well as passive and active components of the vessel wall. The analysis is extended to the entire vascular arterial tree rather than a single vessel as in Murray's formulation. The calculations are based on experimentally measured morphological data of coronary artery network and the longitudinal distribution of blood pressure along the tree. Whereas the model includes multiple dissipation sources, the total metabolic consumption of a complex vascular tree is found to remain approximately proportional to the cumulative arterial volume of the unit. This implies that the previously described scaling relations for the various morphological features (volume, length, diameter, and flow) remain unchanged under the generalized condition of metabolic requirements of blood and blood vessel wall.     

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.     

Passive elastic properties of the rat aorta

The passive anisotropic elastic properties of rat's aorta were studied in vitro by subjecting cylindrical segments of thoracic and abdominal aorta to a wide range of deformations. Using data on pressure, axial stretch, outer diameter, axial force and wall thickness, incremental moduli of elasticity in the circumferential, axial and radial directions were computed. Results indicate that while the elastic behavior of the aortic wall is globally anisotropic, there exists a state of deformation at which the vessel displays incremental isotropy. This state of deformation corresponds approximately to the loading conditions to which the aorta is exposed in situ. Values of the moduli, analyzed as a function of transmural pressure, show that the stiffness of the aortic wall is fairly constant at low pressures but raises steeply for pressures higher than physiological. For axial stretches as occurring in situ, the magnitudes of the circumferential and radial moduli do not differ significantly for the thoracic aorta; hence this vessel can be regarded as transversely isotropic over a wide range of pressures. The same observation is valid also for the abdominal aorta when pressures equal or smaller than physiological are considered. For both the thoracic and abdominal segments of the aorta, the circumferential and radial moduli are smaller than the axial modulus at low pressures, while the reverse is true for large pressures.     

In-situ characterization of the uncrimping process of arterial collagen fibers using two-photon confocal microscopy and digital image correlation

Uncrimping of collagen fibers in the arterial wall is an integral process in regulating the macro-level mechanical response of arteries. Uncrimping of collagen fibers leads to a gradual, but significant strain-stiffening response of the artery at physiological pressures and prevents overdistention at elevated pressures. In this study, we imaged adventitial collagen fibers from fresh primate arteries using two-photon excitation microscopy while subjecting the arteries to physiological inflation pressures and axial stretches. The imaging focal plane was fixed at a constant radial location in the adventitial wall by adjusting the focal distance as the arteries inflated, allowing for the continuously monitoring of the uncrimping process of a single region of collagen fibers. Digital image correlation was then applied to the sequential images to assess and correlate the local displacements to manual traces of selected reference fibers and their engagements. We found that the collagen fibers of interest became fully engaged at a luminal pressure of 20 mmHg, this was then followed by rotation of these fibers as the bulk artery continued to dilate. This technique helps to further the understanding of the uncrimping process of collagen fibers under physiological loads, which can aid in the development of more accurate microstructural constitutive models.     

Biomechanics of the venous wall under simulated arterial conditions

The failure of vein graft conduits implanted in the arterial circulation has been hypothesized to occur in part due to the exposure of the graft to altered biomechanical and fluid shearing forces. In the present study, these forces are characterized for canine internal jugular veins (IJV) exposed to realistic arterial flow dynamics. Freshly excised vein segments were mounted into a pulsatile perfusion apparatus and exposed to arterial flow conditions (P = 115/75 mmHg and Q = 110 ml min-1) for 2 h. Dynamic measurements of intraluminal pressure and flow rate and vessel wall radial distension were acquired to accurately quantitate the incremental modulus of elasticity; hoop, axial and radial wall stresses; and fluid shearing forces within the vessel. Identical measurements were performed on canine carotid arteries (CCA) to serve as a comparison. Under arterial conditions, IJV segments demonstrated a significant elevation (p less than 0.05) over the CCA in the incremental elasticity modulus, along with a corresponding elevation in hoop and axial wall stresses. Additionally the average wall shearing rate to which the IJV endothelial surface was exposed was a factor of six less than that observed in the CCA. These results are discussed in relationship to the clinical situation of vein graft adaptation to arterial hemodynamics.