A new model for blood flow through an artery with axisymmetric stenosis

Tandon, Pushkar; Rana, U.V.S.

doi:10.1016/s0020-7101(05)80008-x

Cited by 17 publications

(7 citation statements)

References 17 publications

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“…Discretization of the Navier-Stokes equations of motion for steady flow through stenoses was carried out by a number of authors for a Newtonian fluid [10][11][12][13][14][15][16]. Non-Newtonian models were considered numerically in [17][18][19] to name a few. All but [19] used the no-slip boundary condition.…”

Section: Introductionmentioning

confidence: 99%

Quantifying Compressibility and Slip in Multiparticle Collision (MPC) Flow Through a Local Constriction

Akhter

Rohlf

2014

Entropy

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The flow of a compressible fluid with slip through a cylinder with an asymmetric local constriction has been considered both numerically, as well as analytically. For the numerical work, a particle-based method whose dynamics is governed by the multiparticle collision (MPC) rule has been used together with a generalized boundary condition that allows for slip at the wall. Since it is well known that an MPC system corresponds to an ideal gas and behaves like a compressible, viscous flow on average, an approximate analytical solution has been derived from the compressible Navier-Stokes equations of motion coupled to an ideal gas equation of state using the Karman-Pohlhausen method. The constriction is assumed to have a polynomial form, and the location of maximum constriction is varied throughout the constricted portion of the cylinder. Results for centerline densities and centerline velocities have been compared for various Reynolds numbers, Mach numbers, wall slip values and flow geometries.

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Section: Introductionmentioning

confidence: 99%

Quantifying Compressibility and Slip in Multiparticle Collision (MPC) Flow Through a Local Constriction

Akhter

Rohlf

2014

Entropy

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“…If the disturbances caused by these diseases can be identified and quantified at common pulse sites (arteries that are easily accessible), this may enable detection of these diseases [15]. Extensive research has been carried out on blood flow in multidimensional stenotic vessels [16][17][18][19][20][21][22][23][24][25][26] and aneurysmal vessels [27][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42], focusing on the local velocity field and wall shear stress. Only a very limited number of studies are available for the analysis of stenoses or aneurysms in arterial network models.…”

Section: Introductionmentioning

confidence: 99%

An improved baseline model for a human arterial network to study the impact of aneurysms on pressure‐flow waveforms

Low

Loon

Sazonov

et al. 2012

Numer Methods Biomed Eng

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In this study, an improved and robust one-dimensional human arterial network model is presented. The one-dimensional blood flow equations are solved using the Taylor-locally conservative Galerkin finite element method. The model improvements are carried out by adopting parts of the physical models from different authors to establish an accurate baseline model. The predicted pressure-flow waveforms at various monitoring positions are compared against in vivo measurements from published works. The results obtained show that wave shapes predicted are similar to that of the experimental data and exhibit a good overall agreement with measured waveforms. Finally, computational studies on the influence of an abdominal aortic aneurysm are presented. The presence of aneurysms results in a significant change in the waveforms throughout the network.

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“…Next, we present the simulation of a simplified model of arterial blood flow in the presence of a symmetric stenotic region on the vessel wall (see e.g. [42,47]). We are only interested in the laminar regime, so (1.4a)−(1.4c) (with a simple Newtonian model for the blood) will suffice to describe the main components of the flow.…”

Section: Blood Flow Through An Axisymmetric Stenosed Arterymentioning

confidence: 99%

Stabilized mixed approximation of axisymmetric Brinkman flows

et al. 2015

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This paper is devoted to the numerical analysis of an augmented finite element approximation of the axisymmetric Brinkman equations. Stabilization of the variational formulation is achieved by adding suitable Galerkin least-squares terms, allowing us to transform the original problem into a formulation better suited for performing its stability analysis. The sought quantities (here velocity, vorticity, and pressure) are approximated by Raviart−Thomas elements of arbitrary order k ≥ 0, piecewise continuous polynomials of degree k + 1, and piecewise polynomials of degree k, respectively. The wellposedness of the resulting continuous and discrete variational problems is rigorously derived by virtue of the classical Babuška-Brezzi theory. We further establish a priori error estimates in the natural norms, and we provide a few numerical tests illustrating the behavior of the proposed augmented scheme and confirming our theoretical findings regarding optimal convergence of the approximate solutions.Mathematics Subject Classification. 65N30, 65N12, 76D07, 65N15, 65J20.

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A new model for blood flow through an artery with axisymmetric stenosis

Cited by 17 publications

References 17 publications

Quantifying Compressibility and Slip in Multiparticle Collision (MPC) Flow Through a Local Constriction

Quantifying Compressibility and Slip in Multiparticle Collision (MPC) Flow Through a Local Constriction

An improved baseline model for a human arterial network to study the impact of aneurysms on pressure‐flow waveforms

Stabilized mixed approximation of axisymmetric Brinkman flows

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