Mathematical model of wall shear stress-dependent vasomotor response based on physiological mechanisms

2014 ◽  
Vol 45 ◽  
pp. 126-135 ◽  
Author(s):  
Yoichi Yamazaki ◽  
Yoshimi Kamiyama
Keyword(s):  
Mathematical Model ◽  
Shear Stress ◽  
Wall Shear Stress ◽  
Vasomotor Response ◽  
Physiological Mechanisms ◽  
Wall Shear ◽  
Stress Dependent

scholarly journals Branching exponent heterogeneity and wall shear stress distribution in vascular trees

2001 ◽  
Vol 280 (3) ◽  
pp. H1256-H1263 ◽  
Author(s):  
Kelly L. Karau ◽  
Gary S. Krenz ◽  
Christopher A. Dawson
Keyword(s):  
Shear Stress ◽  
Wall Shear Stress ◽  
Coefficient Of Variation ◽  
Vessel Diameter ◽  
Mean Value ◽  
Heterogeneous Distribution ◽  
Uniform Shear ◽  
The Mean ◽  
Wall Shear ◽  
Stress Dependent

A bifurcating arterial system with Poiseuille flow can function at minimum cost and with uniform wall shear stress if the branching exponent ( z) = 3 [where z is defined by ( D 1) z = ( D 2) z + ( D 3) z ; D 1 is the parent vessel diameter and D 2 and D 3 are the two daughter vessel diameters at a bifurcation]. Because wall shear stress is a physiologically transducible force, shear stress-dependent control over vessel diameter would appear to provide a means for preserving this optimal structure through maintenance of uniform shear stress. A mean z of 3 has been considered confirmation of such a control mechanism. The objective of the present study was to evaluate the consequences of a heterogeneous distribution of z values about the mean with regard to this uniform shear stress hypothesis. Simulations were carried out on model structures otherwise conforming to the criteria consistent with uniform shear stress when z = 3 but with varying distributions of z. The result was that when there was significant heterogeneity in z approaching that found in a real arterial tree, the coefficient of variation in shear stress was comparable to the coefficient of variation in z and nearly independent of the mean value of z. A systematic increase in mean shear stress with decreasing vessel diameter was one component of the variation in shear stress even when the mean z = 3. The conclusion is that the influence of shear stress in determining vessel diameters is not, per se, manifested in a mean value of z. In a vascular tree having a heterogeneous distribution in zvalues, a particular mean value of z (e.g., z = 3) apparently has little bearing on the uniform shear stress hypothesis.

A New Ultrasonographic Instrument for Measuring Vessel Wall Shear Stress: Comparison to a Mathematical Model in Essential Hypertensives

1996 ◽  
pp. 403-407 ◽  
Author(s):  
Moreno Bardelli ◽  
Renzo Carretta ◽  
Domenico Dotti ◽  
Bruno Fabris ◽  
Fabio Fischetti ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Shear Stress ◽  
Wall Shear Stress ◽  
Vessel Wall ◽  
Measuring Vessel ◽  
Wall Shear

Numerical Simulation of Flow-Induced Wall Shear Stress of a One Strand Tundish Design

2011 ◽  
Vol 402 ◽  
pp. 85-89 ◽  
Author(s):  
Zhi Bing Tian ◽  
Yan Jin ◽  
Hong Yu Li
Keyword(s):  
Numerical Simulation ◽  
Mathematical Model ◽  
Shear Stress ◽  
Service Life ◽  
Wall Shear Stress ◽  
Design Parameters ◽  
Horizontal Distance ◽  
Wall Shear

In this paper, the flow-induced wall shear stress on the wall of a one Strand tundish has been computed by a 3-D mathematical model. Different design parameters of the tundish such as HB(the height of the dam) and DB(the horizontal distance between the dam and the outlet of the tundish) are studied by analyzing the flow-induced wall shear stress. After a series of calculation, A modification in design parameters (DB and HB )of the tundish can reduce the wall shear stress, thus may help to improve the service life of the tundish.

FLOW OF MICROPOLAR FLUID THROUGH CATHETERIZED ARTERY — A MATHEMATICAL MODEL

2012 ◽  
Vol 05 (02) ◽  
pp. 1250019 ◽  
Author(s):  
D. SRINIVASACHARYA ◽  
D. SRIKANTH
Keyword(s):  
Mathematical Model ◽  
Shear Stress ◽  
Wall Shear Stress ◽  
Micropolar Fluid ◽  
Outer Wall ◽  
Shear Stresses ◽  
Closed Form Solutions ◽  
Catheterized Artery ◽  
Wall Shear ◽  
Coupling Number

In this paper, the flow of blood through catheterized artery with mild constriction at the outer wall is considered. The closed form solutions are obtained for velocity and microrotation components. The impedance (resistance to the flow) and wall shear stress are calculated. The effects of catheterization, coupling number, micropolar parameter, and height of the stenosis on impedance and wall shear stresses are discussed.

scholarly journals Assessment with clinical data of a coupled bio-hemodynamics numerical model to predict leukocyte adhesion in coronary arteries

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Umberto Ciri ◽  
Ruth L. Bennett ◽  
Rita Bhui ◽  
David S. Molony ◽  
Habib Samady ◽  
...  
Keyword(s):  
Shear Stress ◽  
Numerical Model ◽  
Wall Shear Stress ◽  
Coronary Arteries ◽  
Clinical Data ◽  
Leukocyte Adhesion ◽  
Three Dimensional ◽  
High Adhesion ◽  
Wall Shear ◽  
Stress Dependent

AbstractNumerical simulations of coupled hemodynamics and leukocyte transport and adhesion inside coronary arteries have been performed. Realistic artery geometries have been obtained for a set of four patients from intravascular ultrasound and angiography images. The numerical model computes unsteady three-dimensional blood hemodynamics and leukocyte concentration in the blood. Wall-shear stress dependent leukocyte adhesion is also computed through agent-based modeling rules, fully coupled to the hemodynamics and leukocyte transport. Numerical results have a good correlation with clinical data. Regions where high adhesion is predicted by the simulations coincide to a good approximation with artery segments presenting plaque increase, as documented by clinical data from baseline and six-month follow-up exam of the same artery. In addition, it is observed that the artery geometry and, in particular, the tortuosity of the centerline are a primary factor in determining the spatial distribution of wall-shear stress, and of the resulting leukocyte adhesion patterns. Although further work is required to overcome the limitations of the present model and ultimately quantify plaque growth in the simulations, these results are encouraging towards establishing a predictive methodology for atherosclerosis progress.

Mass Transfer of LDL Based on Wall Shear Stress From FSI Simulation in Atherosclerotic Human Carotid Artery

2010 ◽  
Author(s):  
Sungho Kim ◽  
Don P. Giddens
Keyword(s):  
Shear Stress ◽  
Carotid Artery ◽  
Wall Shear Stress ◽  
Low Density Lipoprotein ◽  
Density Lipoprotein ◽  
High Mass ◽  
Black Blood ◽  
Ldl Particles ◽  
Wall Shear ◽  
Stress Dependent

Wall shear stress (WSS) distribution and low density lipoprotein (LDL) mass flux are simulated using a fluid-structure interaction (FSI) approach. T2 weighted black blood MRI images of a human left carotid artery are used for the arterial model construction, and the boundary conditions for FSI simulation are derived from phase contrast (PC) MR data. The endothelium is treated as a shear stress dependent, three pathways pore model for LDL particles. The computational results demonstrate that the region distal to an atherosclerotic plaque in the internal carotid artery experiences both low WSS and high mass and volume flux, which are hypothesized to be essential factors in progression of atherosclerosis.

Endothelial NOS is main mediator for shear stress-dependent angiogenesis in skeletal muscle after prazosin administration

2004 ◽  
Vol 287 (5) ◽  
pp. H2300-H2308 ◽  
Author(s):  
Oliver Baum ◽  
Luis Da Silva-Azevedo ◽  
Gregor Willerding ◽  
Achim Wöckel ◽  
Gerit Planitzer ◽  
...  
Keyword(s):  
Skeletal Muscle ◽  
Shear Stress ◽  
Wall Shear Stress ◽  
Knockout Mice ◽  
Skeletal Muscles ◽  
Capillary Density ◽  
Enos Expression ◽  
Wall Shear ◽  
Stress Dependent ◽  
Endothelial Nitric Oxide

The increase of wall shear stress in capillaries by oral administration of the α1-adrenergic receptor antagonist prazosin induces angiogenesis in skeletal muscles. Because endothelial nitric oxide synthase (eNOS) is upregulated in response to elevated wall shear stress, we investigated the relevance of eNOS for prazosin-induced angiogenesis in skeletal muscles. Prazosin and/or the NOS inhibitor Nω-nitro-l-arginine methyl ester (l-NAME) were given to C57BL/6 wild-type mice and eNOS-knockout mice for 14 days. The capillary-to-fiber (C/F) ratio and capillary density (CD; no. of capillaries/mm2) were determined in frozen sections from extensor digitorum longus (EDL) muscles of these mice. Immunoblotting was performed to quantify eNOS expression in endothelial cells isolated from skeletal muscles, whereas VEGF (after precipitation with heparin-agarose) and neuronal NOS (nNOS) concentrations were determined in EDL solubilizates. In EDL muscles of C57BL/6 mice treated for 14 days, the C/F ratio was 28% higher after prazosin administration and 11% higher after prazosin and l-NAME feeding, whereas the CD increased by 21 and 13%, respectively. The C/F ratio was highest after day 4 of prazosin treatment and decreased gradually to almost constant values after day 8. Prazosin administration led to elevation of eNOS expression. VEGF levels were lowest at day 4, whereas nNOS values decreased after day 8. In EDL muscles of eNOS-knockout mice, no significant changes in C/F ratio, CD, or VEGF and nNOS expression were observed in response to prazosin administration. Our data suggest that the presence of eNOS is essential for prazosin-induced angiogenesis in skeletal muscle, albeit other signaling molecules might partially compensate for or contribute to this angiogenic activity. Furthermore, subsequent remodeling of the capillary system accompanied by sequential downregulation of VEGF and nNOS in skeletal muscle fibers characterizes shear stress-dependent angiogenesis.

scholarly journals A Mathematical Model on the Feedback Between Wall Shear Stress and Intimal Hyperplasia

2016 ◽  
Vol 08 (07) ◽  
pp. 1640011 ◽  
Author(s):  
Martin E. Goodman ◽  
X. Y. Luo ◽  
N. A. Hill
Keyword(s):  
Mathematical Model ◽  
Blood Flow ◽  
Shear Stress ◽  
Wall Shear Stress ◽  
Arterial Wall ◽  
Endothelial Permeability ◽  
Feedback Mechanism ◽  
Fast Time ◽  
Time Step ◽  
Wall Shear

In this paper, we present a mathematical model linking blood flow, shear-dependent endothelium permeability and intimal thickening (hyperplasia) of the arterial wall, which is an initial stage in the development of atherosclerosis. The key concepts are that the intimal layer swells in response to the presence of excess oxidised LDL (OxLDL) in foam cells. The hyperplasia disturbs blood flow, affecting endothelial permeability via the wall shear stress (WSS). These changes produce a feedback mechanism. LDL is transported through the arterial wall by advection and diffusion, and the concentration of LDL at each time step is assumed to be quasi-steady since it equilibrates on a fast time scale. The process is controlled by the slow timescale of the increase in concentration of OxLDL. We consider a section of uniform axisymmetric artery, and impose an initial local injury or ‘hotspot’ of relatively high permeability that enhances the influx of LDL, triggering the development of a bump-shaped lesion. In the absence of further inflammatory processes, the lesion eventually decays back to the homeostatic state. The model is used to explore how the shape of the lesion changes over time, its effect on WSS, influx rates of LDL and the sensitivity of these processes to oxidation parameters. The lesion is shown to propagate downstream driven by regions of high and low WSS on either side of the bump, and it persists for some time after the hotspot has vanished, leaving ample time for further pro-atherogenic processes to develop.

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