Flow-tissue interaction with compliance mismatch in a model stented artery

The insertion of an endovascular prosthesis is known to have a thrombogenic effect that is also a consequence of the interaction between the flowing blood and the stented arterial segment; in fact the prosthesis induces a compliance mismatch and a possible small expansion along the vessel that eventually gives rise to an anomalous distribution of wall shear stresses. The fluid dynamics inside a rectilinear elastic vessel with compliance and section variation is studied here numerically. A recently introduced perturbative approach is employed to model the interaction between the fluid and the elastic tissue; this approximate technique is first validated by comparison with a complete solution within a simple one-dimensional model of the same system. Then it is applied to an axisymmetric model in order to evaluate the flow dynamics and the distribution of wall shear stress in the stented vessel. Compliance mismatch is shown to produce more intense negative wall shear stresses in the stented segment while rapid variations of wall shear stress are found at the stent ends. These effects are enhanced when the prosthesis is accompanied by a small increase of the vessel lumen.     

A Green's function method for analysis of oxygen delivery to tissue by microvascular networks

A theoretical model is formulated for analyzing oxygen delivery from an arbitrary network configuration of cylindrical microvessels to a finite region of tissue. In contrast to models based on the classical Krogh cylinder approach, this model requires no a priori assumptions concerning the extent of the tissue region supplied with oxygen by each vessel segment. Steady-state conditions are assumed, and oxygen consumption in the tissue is assumed to be uniform. The nonlinear dissociation characteristics of oxyhemoglobin are taken into account. A computationally efficient Green's function approach is used, in which the tissue oxygen field is expressed in terms of the distribution of source strengths along each segment. The utility of the model is illustrated by analyses of oxygen delivery to a cuboidal tissue region by a single segment and by a six-segment network. It is found that the fractional contribution of the proximal segments to total oxygen delivery increases with decreasing flow rate and metabolic rate.     

Effects of vessel compliance on flow pattern in porcine epicardial right coronary arterial tree

The compliance of the vessel wall affects hemodynamic parameters which may alter the permeability of the vessel wall. Based on experimental measurements, the present study established a finite element (FE) model in the proximal elastic vessel segments of epicardial right coronary arterial (RCA) tree obtained from computed tomography. The motion of elastic vessel wall was measured by an impedance catheter and the inlet boundary condition was measured by an ultrasound flow probe. The Galerkin FE method was used to solve the Navier–Stokes and Continuity equations, where the convective term in the Navier–Stokes equation was changed in the arbitrary Lagrangian–Eulerian (ALE) framework to incorporate the motion due to vessel compliance. Various hemodynamic parameters (e.g., wall shear stress—WSS, WSS spatial gradient—WSSG, oscillatory shear index—OSI) were analyzed in the model. The motion due to vessel compliance affects the time-averaged WSSG more strongly than WSS at bifurcations. The decrease of WSSG at flow divider in elastic bifurcations, as compared to rigid bifurcations, implies that the vessel compliance decreases the permeability of vessel wall and may be atheroprotective. The model can be used to predict coronary flow pattern in subject-specific anatomy as determined by noninvasive imaging.     

Melatonin restores diminished neurogenic reactivity of the juvenile rat tail artery

The effect of melatonin on neurogenic reactivity of the juvenile rat tail artery segment was studied. The electrical field stimulation-evoked contraction of the segment decreased in the course of the experiment. Melatonin (0.1 microM) applied at different time points of the experiment produced an increase in the contraction, which directly correlated with a spontaneous decrease in the electrical field stimulation-evoked response. The increase in the potentiating effect of melatonin in the course of the experiment was not due to sensitization of the segment to this substance. Noradrenaline-evoked contraction of the vessel segment was not changed by melatonin. The data indicate that melatonin restores the diminished neurogenic reactivity of the juvenile rat tail artery probably by potentiation of the contractile response of the vessel, but this effect is hardly due to a change in sensitivity of the postjunctional membrane to noradrenaline.     

Flow of aqueous humor in the canal of Schlemm

A mathematical model is presented for the flow of aqueous humor in Schlemm's canal in the eye. The model introduces a canal segment between two collector channels as a rectangular channel with porous upper wall. Two cases have been considered in the model: (I) the inner porous wall of the canal is rigid; (II) the inner wall is collapsible. Analytical solution of the governing equation in case I is straightforward, whereas the nonlinear equation in case II is solved by an iterative procedure. Aqueous fluid pressure and flow profiles in the proposed model are drawn, and the effects of important parameters on these profiles are brought out and discussed. It is concluded that for case I, resistance to aqueous flow is influenced by the filtration constant of the trabecular and endothelial meshwork and that narrowing of the canal reduces outflow. In case II, an increase in intraocular pressure (IOP) or compliance coefficient of the canal inner wall increases the collapse of the canal, which offers increased resistance to flow resulting in the decreased flow whereas increasing filtration constant facilitates aqueous outflow. These theoretical results suggest that increased IOP or decreased rigidity of the inner wall may contribute to the development of increased resistance as observed in some cases of glaucoma and that increasing values of filtration constant may contribute to the facility of outflow increase.     

Heterogeneous mechanics of the mouse pulmonary arterial network

Individualized modeling and simulation of blood flow mechanics find applications in both animal research and patient care. Individual animal or patient models for blood vessel mechanics are based on combining measured vascular geometry with a fluid structure model coupling formulations describing dynamics of the fluid and mechanics of the wall. For example, one-dimensional fluid flow modeling requires a constitutive law relating vessel cross-sectional deformation to pressure in the lumen. To investigate means of identifying appropriate constitutive relationships, an automated segmentation algorithm was applied to micro-computerized tomography images from a mouse lung obtained at four different static pressures to identify the static pressure–radius relationship for four generations of vessels in the pulmonary arterial network. A shape-fitting function was parameterized for each vessel in the network to characterize the nonlinear and heterogeneous nature of vessel distensibility in the pulmonary arteries. These data on morphometric and mechanical properties were used to simulate pressure and flow velocity propagation in the network using one-dimensional representations of fluid and vessel wall mechanics. Moreover, wave intensity analysis was used to study effects of wall mechanics on generation and propagation of pressure wave reflections. Simulations were conducted to investigate the role of linear versus nonlinear formulations of wall elasticity and homogeneous versus heterogeneous treatments of vessel wall properties. Accounting for heterogeneity, by parameterizing the pressure/distention equation of state individually for each vessel segment, was found to have little effect on the predicted pressure profiles and wave propagation compared to a homogeneous parameterization based on average behavior. However, substantially different results were obtained using a linear elastic thin-shell model than were obtained using a nonlinear model that has a more physiologically realistic pressure versus radius relationship.     

The quantitative estimation of microvessels in microvascular networks

A novel method is presented that greatly facilitates the determination of vessel segment number and density in both simple and complex microvascular networks. This approach was applied to microvascular networks represented by the Bra-Ket operator technique and accurately predicted the number of vessel segments in both tree-branched and loop-branched (arcade) networks. The method was then applied to the complex hexagonal array network described by Engelson et al. for gastrointestinal mucosa and accurately yielded an average vessel segment number of three around each hexagonal loop. This new method may be used for conveniently estimating tissue microvascular densities, such as vessel rarefaction or proliferation, and for the modelling of microvascular networks.     

Why is the subendocardium more vulnerable to ischemia? A new paradigm

Myocardial ischemia is transmurally heterogeneous where the subendocardium is at higher risk. Stenosis induces reduced perfusion pressure, blood flow redistribution away from the subendocardium, and consequent subendocardial vulnerability. We propose that the flow redistribution stems from the higher compliance of the subendocardial vasculature. This new paradigm was tested using network flow simulation based on measured coronary anatomy, vessel flow and mechanics, and myocardium-vessel interactions. Flow redistribution was quantified by the relative change in the subendocardial-to-subepicardial perfusion ratio under a 60-mmHg perfusion pressure reduction. Myocardial contraction was found to induce the following: 1) more compressive loading and subsequent lower transvascular pressure in deeper vessels, 2) consequent higher compliance of the subendocardial vasculature, and 3) substantial flow redistribution, i.e., a 20% drop in the subendocardial-to-subepicardial flow ratio under the prescribed reduction in perfusion pressure. This flow redistribution was found to occur primarily because the vessel compliance is nonlinear (pressure dependent). The observed thinner subendocardial vessel walls were predicted to induce a higher compliance of the subendocardial vasculature and greater flow redistribution. Subendocardial perfusion was predicted to improve with a reduction of either heart rate or left ventricular pressure under low perfusion pressure. In conclusion, subendocardial vulnerability to a acute reduction in perfusion pressure stems primarily from differences in vascular compliance induced by transmural differences in both extravascular loading and vessel wall thickness. Subendocardial ischemia can be improved by a reduction of heart rate and left ventricular pressure.     

A new method to model change in cutaneous blood flow due to mechanical skin irritation part II: parameter identification procedure

Mechanical skin irritation, for example a light scratch with a needle, induces histamine and neuropeptide release on the line of stroke and in the surrounding tissue. Both histamine and neuropeptides are vasodilators. They cause vasodilation by changing the contraction state of the vascular smooth muscles and hence vessel compliance. Smooth muscle contraction state is very difficult to measure in vivo. For that reason we propose in this article an identification procedure to establish an irritation law. The law gives change in vessel compliance as a function of space, time and the intensity of the stroke. We have showed that vessel compliance increases immediately after the stroke not only on the line of stroke, but also in the surrounding tissue. Then, after a short delay, vessel compliance starts decreasing in the surrounding tissue, whereas vessel compliance on the line of stroke keeps increasing. Hence, blood is transported from the surrounding tissue to the line of stroke. In this way, higher blood volume on the line of stroke can be obtained than by only changing vessel compliance locally.     

Theoretical analysis of pressure pulse propagation in arterial vessels.

An original mathematical model of viscous fluid motion in a tapered and distensible tube is presented. The model equations are deduced by assuming a two-dimensional flow and taking into account the nonlinear terms in the fluid motion equations, as well as the nonlinear deformation of the tube wall. One distinctive feature of the model is the formal integration with respect to the radial coordinate of the Navier-Stokes equations by power series expansion. The consequent computational frame allows an easy, accurate evaluation of the effects produced by changing the values of all physical and geometrical tube parameters. The model is employed to study the propagation along an arterial vessel of a pressure pulse produced by a single flow pulse applied at the proximal vessel extremity. In particular, the effects of the natural taper angle of the arterial wall on pulse propagation are investigated. The simulation results show that tapering considerably influences wave attenuation but not wave velocity. The substantially different behavior of pulse propagation, depending upon whether it travels towards the distal extremity or in the opposite direction, is observed: natural tapering causes a continuous increase in the pulse amplitude as it moves towards the distal extremity; on the contrary, the reflected pulse, running in the opposite direction, is greatly damped. For a vessel with physical and geometrical properties similar to those of a canine femoral artery and 0.1 degree taper angle, the forward amplification is about 0.9 m-1 and the backward attenuation is 1.4 m-1, so that the overall tapering effect gives a remarkably damped pressure response. For a natural taper angle of 0.14 degrees the perturbation is almost extinct when the pulse wave returns to the proximal extremity.     

木本植物导管长度分布规律研究新方法

从理论上推导出以着色导管数计算导管长度的关系式,为注入颜料法测定植物导管长度分布规律了理论基础,并推导了导管长度分布规律,以及着色导管数与样品长度关系。以香梓、梧桐为试材,研究了导管长主工分布规律,实验结果与理论结果完全一致,表明理论推导和实验结果是可靠的。     

The effect of incorporating vessel compliance in a computational model of blood flow in a total cavopulmonary connection (TCPC) with caval centerline offset

BACKGROUND: The total cavopulmonary connection (TCPC), a palliative correction for congenital defects of the right heart, is based on the corrective technique developed by Fontan and Baudet. Research into the TCPC has primarily focused on reducing power loss through the connection as a means to improve patient longevity and quality of life. The goal of our study is to investigate the efficacy of including a caval offset on the hemodynamics and, ultimately, power loss of a connection. As well, we will quantify the effect of vessel wall compliance on these factors and, in addition, the distribution of hepatic blood to the lungs. METHODS: We employed a computational fluid dynamic model of blood flow in the TCPC that includes both the non-Newtonian shear thinning characteristics of blood and the nonlinear compliance of vessel tissue. RESULTS: Power loss in the rigid-walled simulations decayed exponentially as caval offset increased. The compliant-walled results, however, showed that after an initial substantial decrease in power loss for offsets up to half the caval diameter, power loss increased slightly again. We also found only minimal mixing in both simulations of all offset models. CONCLUSIONS: The increase in power loss beyond an offset of half the caval diameter was due to an increase in the kinetic contribution. Reduced caval flow mixing, on the other hand, was due to the formation of a pressure head in the offset region which acts as a barrier to flow.     

Liver vessel segmentation based on extreme learning machine

Liver-vessel segmentation plays an important role in vessel structure analysis for liver surgical planning. This paper presents a liver-vessel segmentation method based on extreme learning machine (ELM). Firstly, an anisotropic filter is used to remove noise while preserving vessel boundaries from the original computer tomography (CT) images. Then, based on the knowledge of prior shapes and geometrical structures, three classical vessel filters including Sato, Frangi and offset medialness filters together with the strain energy filter are used to extract vessel structure features. Finally, the ELM is applied to segment liver vessels from background voxels. Experimental results show that the proposed method can effectively segment liver vessels from abdominal CT images, and achieves good accuracy, sensitivity and specificity.     

Measuring vessel length in vascular plants: can we divine the truth? History,theory, methods,and contrasting models

Key message

The Cohen method of measuring vessel-length distributions is much more accurate than the DD algorithm on integer values, which should be abandoned. More research is needed to get the real distribution of vessel length.

Abstract

Scientists have been measuring the vessel length of plants for more than 50 years. The method involves infusing stem or segments with a visible substance that completely fills vessels cut open at the infusion surface. The number of infused vessels is then quantified versus distance from the infusion surface. A theoretical model is then used to convert the counts of infused vessels to a vessel length distribution. Over the years the methods and theory have changed greatly. The purpose of this review is to give the reader an understanding of why vessel length is important and to provide a theoretical basis for selection of the best method and theory to arrive at vessel length data.     

Fast blood-flow simulation for large arterial trees containing thousands of vessels

Blood flow modelling has previously been successfully carried out in arterial trees to study pulse wave propagation using nonlinear or linear flow solvers. However, the number of vessels used in the simulations seldom grows over a few hundred. The aim of this work is to present a computationally efficient solver coupled with highly detailed arterial trees containing thousands of vessels. The core of the solver is based on a modified transmission line method, which exploits the analogy between electrical current in finite-length conductors and blood flow in vessels. The viscoelastic behaviour of the arterial-wall is taken into account using a complex elastic modulus. The flow is solved vessel by vessel in the frequency domain and the calculated output pressure is then used as an input boundary condition for daughter vessels. The computational results yield pulsatile blood pressure and flow rate for every segment in the tree. This solver is coupled with large arterial trees generated from a three-dimensional constrained constructive optimisation algorithm. The tree contains thousands of blood vessels with radii spanning ~1 mm in the root artery to ~30 μm in leaf vessels. The computation takes seconds to complete for a vasculature of 2048 vessels and less than 2 min for a vasculature of 4096 vessels on a desktop computer.     

Effects of extracellular pH on the response of the isolated rat mesenteric artery to electrical field stimulation

In experiments on isolated segments of the rat mesenteric artery, effects of changes in solution pH on the response of the segments to noradrenaline (10 microM) or electrical field stimulation (EFS) were studied. The pH 7.8 solution slightly increased (from 0.48 +/- 0.07 mN at pH 7.4 to 0.67 +/- 0.12 mN or by 41%). while the pH 7.0 and 6.6 solutions significantly decreased (to 0.16 +/- 0.05 and 0.08 +/- 0.04 mN or by 66 and 83%, respectively) the EFS-evoked response of the vessel prestretched to the value corresponding to the intravascular pressure of about 100 mm Hg. A pH shift either to the alkaline or acidic range did not change the resting tension (15.65 +/- 0.74 mN at pH 7.4) of the vessel without precontraction. The pH 6.6 solution reduced the response to noradrenaline twofold. Dilation produced by EFS of noradrenaline-precontracted segment was inhibited and the constrictor responses appeared in the pH 6.6 solution. In the vessel pretreated with N(G)-nitro-L-arginine (100 microM), the acidification of the solution (pH 6.6) inhibited the response of the vascular segment to EFS to a lower extent and did not change its response to noradrenaline. The data obtained demonstrate an inhibitory effect of acidosis on reactivity of the rat mesenteric artery as well as a modification of this effect under a high initial tone of the vessel studied.     

Determination of constitutive equations for human arteries from clinical data

Stress-strain analyses of vessel walls require appropriate constitutive equations. Determination of constitutive equations is based on experimental data of (i) diameter and length of a vessel segment subject to internal pressure and external axial force, and (ii) the load-free reference geometry. Typical clinical data, however, provide only pressure-diameter relations in the diastolic-systolic pressure range. In order to overcome this problem, an approach is proposed allowing the determination of constitutive equations from clinical data by means of reasonable assumptions regarding in situ configurations and stress states of arterial walls. The approach is based on a two-dimensional Fung-type stored-energy function capturing the characteristic nonlinear and anisotropic responses of arteries. Examples concerning human aortas from a normotensive and a hypertensive subject illustrate the potential of the approach.     

Effects of compliance mismatch on blood flow in an artery with endovascular prosthesis

The objective of this paper is to study the mechanical effects caused by the local stiffening of an artery (due to the vascular prosthesis, for instance). At the junction of the host artery and the more rigid implantant, the abrupt change in compliance creates an abnormal stress concentration that initiates an adaptive response in the vascular tissue. The roles of both fluid and solid mechanical phenomena must be considered in the prosthesis design optimization. In this context, even the simple models could provide helpful tools for designing process. We present here a model of blood flow in compliant vessel. The artery is supposed to be an orthotropical thin elastic shell. We obtain the solution by matched asymptotic expansions. The results prove the high flexure concentration close to the compliance jump. It is shown that the use of orthotropical graft may reduce the peak value of these shear forces to a remarkable extent. Waves reflected from the suture and pressure increase in the prosthesis are discussed. Compliance mismatch is shown to reduce the peak value of maximal wall shear stress.     

Biomechanical properties of the human umbilical cord

The umbilical cord is a complex and fascinating structure that connects the fetus to the placenta and encases the umbilical vessels. The response of its tissues to mechanical loading due to fetal movements and uterine contractions is not well understood. The aim of this study is the evaluation of the mechanical properties of the main components of the human umbilical cord. Fresh umbilical cord specimens were collected from neonates born at term of the gestation and submitted to compliance tests. Furthermore, uniaxial tensile and stress-relaxation tests were performed on samples of umbilical vein and Wharton's jelly. Both materials exhibited nonlinear stress-strain response with increasing strain, increasing the elastic modulus (E(high) about 10-20 times E(low)) and significant viscoelastic behavior. In addition, anisotropy of the vein was observed. Although the circumferential properties of the vein (mean E(high) about 2.4 MPa) were similar to those after birth, the longitudinal stiffness of both materials was higher (mean E(high) over 10 MPa) and comparable to that of the ligaments. These findings suggest a mechanism of protection acting against excessive elongations of the cord, which could cause undue restriction of the umbilical vessel area and interference with the fetal blood circulation.