scholarly journals Non-Invasive Assessment of Intravascular Pressure Gradients: A Review of Current and Proposed Novel Methods

Diagnostics ◽  
2018 ◽  
Vol 9 (1) ◽  
pp. 5 ◽  
Author(s):  
Tin-Quoc Nguyen ◽  
Kristoffer Hansen ◽  
Thor Bechsgaard ◽  
Lars Lönn ◽  
Jørgen Jensen ◽  
...  
Keyword(s):  
Stokes Equations ◽  
Imaging Techniques ◽  
Navier Stokes ◽  
Pressure Gradients ◽  
Bernoulli Equation ◽  
Strong Correlations ◽  
Navier Stokes Equations ◽  
Non Invasive ◽  
Invasive Techniques

Invasive catheterization is associated with a low risk of serious complications. However, although it is the gold standard for measuring pressure gradients, it induces changes to blood flow and requires significant resources. Therefore, non-invasive alternatives are urgently needed. Pressure gradients are routinely estimated non-invasively in clinical settings using ultrasound and calculated with the simplified Bernoulli equation, a method with several limitations. A PubMed literature search on validation of non-invasive techniques was conducted, and studies were included if non-invasively estimated pressure gradients were compared with invasively measured pressure gradients in vivo. Pressure gradients were mainly estimated from velocities obtained with Doppler ultrasound or magnetic resonance imaging. Most studies used the simplified Bernoulli equation, but more recent studies have employed the expanded Bernoulli and Navier–Stokes equations. Overall, the studies reported good correlation between non-invasive estimation of pressure gradients and catheterization. Despite having strong correlations, several studies reported the non-invasive techniques to either overestimate or underestimate the invasive measurements, thus questioning the accuracy of the non-invasive methods. In conclusion, more advanced imaging techniques may be needed to overcome the shortcomings of current methods.

A Calculation Scheme for Three-Dimensional Viscous Incompressible Flows

1987 ◽  
Vol 109 (4) ◽  
pp. 345-352 ◽  
Author(s):  
M. Reggio ◽  
R. Camarero
Keyword(s):  
Incompressible Flows ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Numerical Procedure ◽  
Numerical Data ◽  
Momentum Balance ◽  
Navier Stokes ◽  
Test Cases ◽  
Pressure Gradients ◽  
Navier Stokes Equations

A numerical procedure to solve three-dimensional incompressible flows in arbitrary shapes is presented. The conservative form of the primitive-variable formulation of the time-dependent Navier-Stokes equations written for a general curvilinear coordiante system is adopted. The numerical scheme is based on an overlapping grid combined with opposed differencing for mass and pressure gradients. The pressure and the velocity components are stored at the same location: the center of the computational cell which is used for both mass and the momentum balance. The resulting scheme is stable and no oscillations in the velocity or pressure fields are detected. The method is applied to test cases of ducting and the results are compared with experimental and numerical data.

scholarly journals A Bright Future for Fluorescence Imaging of Fungi in Living Hosts

2019 ◽  
Vol 5 (2) ◽  
pp. 29 ◽  
Author(s):  
Ambre Chapuis ◽  
Elizabeth Ballou ◽  
Donna MacCallum
Keyword(s):  
Mouse Models ◽  
Fluorescent Proteins ◽  
Imaging Techniques ◽  
Post Mortem ◽  
New Techniques ◽  
Ethical Concerns ◽  
Non Invasive ◽  
Reporter Proteins ◽  
Invasive Techniques

Traditional in vivo investigation of fungal infection and new antifungal therapies in mouse models is usually carried out using post mortem methodologies. However, biomedical imaging techniques focusing on non-invasive techniques using bioluminescent and fluorescent proteins have become valuable tools. These new techniques address ethical concerns as they allow reduction in the number of animals required to evaluate new antifungal therapies. They also allow better understanding of the growth and spread of the pathogen during infection. In this review, we concentrate on imaging technologies using different fungal reporter proteins. We discuss the advantages and limitations of these different reporters and compare the efficacy of bioluminescent and fluorescent proteins for fungal research.

Calculation of Turbulent Flows in a Hydraulic Turbine Draft Tube

1990 ◽  
Vol 112 (3) ◽  
pp. 257-263 ◽  
Author(s):  
M. Agouzoul ◽  
M. Reggio ◽  
R. Camarero
Keyword(s):  
Turbulent Flows ◽  
Stokes Equations ◽  
Draft Tube ◽  
Three Dimensional ◽  
Hydraulic Turbine ◽  
Navier Stokes ◽  
Pressure Gradients ◽  
Navier Stokes Equations ◽  
Conservative Form ◽  
Hydraulic Turbine Draft Tube

A numerical method to simulate three-dimensional incompressible turbulent flows has been developed and applied to the calculation of various flow situations in a draft tube. The conservative form of the primitive-variable formulation of the Reynolds averaged Navier-Stokes equations, written for a general curvilinear co-ordinate system, is employed. An overlapping grid combined with opposed differencing for mass and pressure gradients is used. All the properties are stored at the center of the same computational cell which is used for mass and transport balances. The k–ε model is used to describe the turbulent flow. The boundary conditions for the turbulent properties are treated with a particular attention.

Modeling of Three-Dimensional Flow in Turning Channels

1984 ◽  
Vol 106 (3) ◽  
pp. 682-691 ◽  
Author(s):  
I. M. Khalil ◽  
H. G. Weber
Keyword(s):  
Stokes Equations ◽  
Reverse Flow ◽  
Three Dimensional ◽  
Solution Procedure ◽  
Three Dimensions ◽  
Navier Stokes ◽  
Pressure Gradients ◽  
Dean Number ◽  
Navier Stokes Equations ◽  
Curved Channels

The structure of developing flows inside curved channels has been investigated numerically using the time-averaged Navier Stokes equations in three dimensions. The equations are solved in primitive variables using finite difference techniques. The solution procedure involves a combination of repeated space-marching integration of the governing equations and correction for elliptic effects between two marching sweeps. Type-dependent differencing is used to permit downstream marching even in the reverse-flow regions. The procedure is shown to allow efficient calculations of turbulent flow inside strongly curved channels as well as laminar flow inside a moderately curved passage. Results obtained in both cases indicate that the flow structure is strongly controlled by local imbalance between centrifugal forces and pressure gradients. Furthermore, distortion of primary flow due to migration of low momentum fluid caused by secondary flow is found to be largely dependent on the Reynolds number and Dean number. Comparison with experimental data is also included.

scholarly journals Investigation of the Onset of Turbulence in Boundary Layers and the Implications for Solutions of the Navier-Stokes Equations.

2020 ◽  
Author(s):  
Andrew Logan
Keyword(s):  
Boundary Layer ◽  
Fluid Flow ◽  
Flat Plate ◽  
Stokes Equations ◽  
Analytic Solutions ◽  
Navier Stokes ◽  
Pressure Gradients ◽  
Navier Stokes Equations ◽  
Viscous Fluid Flow ◽  
Onset Of Turbulence

This paper investigates the onset of turbulence in incompressible viscous fluid flow over a flat plate by looking at the pressure gradients implied by the Blasius solution for laminar fluid flow and adjusting the predicted flow, leading to a mathematically predictable flow separation in the boundary layer and the onset of turbulence (including both transition and fully turbulent regions - both with and without the presence of a flat plate). It then considers the implications for potential analytic solutions to the Navier-Stokes Equations of the fact that it is possible to predict turbulence and a singularity for many flows (at any velocity).

scholarly journals In vivo measurements of blood viscosity and wall stiffness in the carotid using PC-MRI

2009 ◽  
Author(s):  
Stephane Avril ◽  
Jonathan M. Huntley ◽  
Rhodri Cusack
Keyword(s):  
Blood Viscosity ◽  
Phase Contrast ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Phase Contrast Mri ◽  
Cylindrical Pipe ◽  
Navier Stokes Equations ◽  
Linear Elastic ◽  
Wall Stiffness

A method is proposed for deducing blood viscosity and wall stiffness in the carotid from Phase-Contrast MRI data. The approach is based on Womersley’s model of blood flow derived from the resolution of the Navier-Stokes equations, assuming blood as a Newtonian fluid and the artery as a linear elastic cylindrical pipe. After presenting its principle, the approach is applied to the experimental data obtained on a single volunteer. Promising results are obtained.

Conditioned Navier-Stokes and k–ϵ–γ Equations to Model Transition in Pressure Gradient Flow

1995 ◽  
Author(s):  
J. Steelant ◽  
E. Dick
Keyword(s):  
Pressure Gradient ◽  
Stokes Equations ◽  
Gradient Flow ◽  
Transitional Flow ◽  
Navier Stokes ◽  
Pressure Gradients ◽  
Navier Stokes Equations ◽  
Intermittency Factor ◽  
Conditional Averaging ◽  
Model Transition

Conditionally averaged Navier-Stokes equations are derived to describe transitional flow. The averages are taken during the fraction of time the flow is laminar or turbulent, respectively. Conditional averaging leads both for the laminar and turbulent parts to a set of equations for mass, momentum and energy. The conditioned equations differ from the original Navier-Stokes equations by the presence of source terms which are functions of the intermittency factor, γ. This factor is the extra unknown and is determined by a transport equation. The evolution of γ depends mainly on the turbulence level, pressure gradient and Reynolds-number. The turbulence is described by the classical k-ϵ model. The approach is verified against several test cases, with and without pressure gradients.

scholarly journals ANALYTICAL SOLUTION FOR TRANSIENT ONEDIMENSIONAL COUETTE FLOW CONSIDERING CONSTANT AND TIME-DEPENDENT PRESSURE GRADIENTS

2009 ◽  
Vol 8 (2) ◽  
pp. 92 ◽  
Author(s):  
A. A. Mendiburu ◽  
L. R. Carrocci ◽  
J. A. Carvalho
Keyword(s):  
Pressure Gradient ◽  
Couette Flow ◽  
Stokes Equations ◽  
Transient State ◽  
Integral Transforms ◽  
Time Dependent ◽  
Navier Stokes ◽  
Pressure Gradients ◽  
Navier Stokes Equations ◽  
The One

This paperaims to determine the velocity profile, in transient state, for a parallel incompressible flow known as Couette flow. The Navier-Stokes equations were applied upon this flow. Analytical solutions, based in Fourier series and integral transforms, were obtained for the one-dimensional transient Couette flow, taking into account constant and time-dependent pressure gradients acting on the fluid since the same instant when the plate starts it´s movement. Taking advantage of the orthogonality and superposition properties solutions were foundfor both considered cases. Considering a time-dependent pressure gradient, it was found a general solution for the Couette flow for a particular time function. It was found that the solution for a time-dependent pressure gradient includes the solutions for a zero pressure gradient and for a constant pressure gradient.

Turbulent Flow in a Channel With a Wavy Wall

1991 ◽  
Vol 113 (4) ◽  
pp. 579-586 ◽  
Author(s):  
V. C. Patel ◽  
J. Tyndall Chon ◽  
J. Y. Yoon
Keyword(s):  
Numerical Method ◽  
Turbulence Model ◽  
Stokes Equations ◽  
Separated Flow ◽  
Navier Stokes ◽  
Pressure Gradients ◽  
Wavy Wall ◽  
Navier Stokes Equations ◽  
Law Of The Wall ◽  
Logarithmic Law

A numerical method for the solution of the Reynolds-averaged Navier-Stokes equations, together with a two-layer turbulence model, has been used to describe steady flow in a two-dimensional channel with a wavy wall. Comparisons of calculations with experiments demonstrate the effects of alternating pressure gradients induced by alternating surface curvatures, and multiple separations and reattachments. The numerical method and the turbulence model are shown to capture the overall features of such a flow, including the breakdown of the logarithmic law of the wall in strong pressure gradients and in separated flow.

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