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.

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.

scholarly journals Exact and limiting solutions of fluid flow for axially oscillating cylindrical pipe and annulus

2021 ◽  
Vol 3 (3) ◽  
Author(s):  
U. K. Sarkar ◽  
Nirmalendu Biswas
Keyword(s):  
Velocity Distribution ◽  
High Frequency ◽  
Oscillatory Flow ◽  
Stokes Equations ◽  
Low Frequency ◽  
Navier Stokes ◽  
Cylindrical Pipe ◽  
Navier Stokes Equations ◽  
Cylindrical Annulus

AbstractThe Navier–Stokes equations have been solved to derive the expressions of the velocity distributions for two cases: (1) oscillatory flows inside and outside of an axially oscillating cylindrical pipe, and (2) oscillatory flow inside an axially oscillating cylindrical annulus. In both the cases, in addition to the exact expressions for the velocity profiles, particular emphasis has been given for the determination of approximate velocity distributions for the high frequency and low frequency or quasi-static limits. It is shown that, for sufficiently large value of an appropriate frequency parameter, the velocity distribution inside the axially or longitudinally oscillating cylindrical annulus can be approximated as a superposition of the velocity distribution inside an axially oscillating cylindrical pipe of radius $${\bar R_o}$$ R ¯ o and the velocity distribution outside an axially oscillating cylindrical pipe of radius $${\bar R_i}$$ R ¯ i , where $${\bar R_i}$$ R ¯ i and $${\bar R_o}$$ R ¯ o are the inner and outer radii of the axially oscillating annulus, respectively.

Wall Shear Stress Estimates in Coronary Artery Constrictions

1992 ◽  
Vol 114 (4) ◽  
pp. 515-520 ◽  
Author(s):  
L. H. Back ◽  
D. W. Crawford
Keyword(s):  
Shear Stress ◽  
Coronary Artery ◽  
Wall Shear Stress ◽  
Shape Function ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Simple Method ◽  
Navier Stokes Equations ◽  
Wall Shear

Wall shear stress estimates from laminar boundary layer theory were found to agree fairly well with the magnitude of shear stress levels along coronary artery constrictions obtained from solutions of the Navier Stokes equations for both steady and pulsatile flow. The relatively simple method can be used for in vivo estimates of wall shear stress in constrictions by using a vessel shape function determined from a coronary angiogram, along with a knowledge of the flow rate.

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