Effect of vessel curvature on Doppler derived velocity profiles and fluid flow

Krams, Rob; Bambi, G.; Guidi, Francesco; Helderman, Frank; Steen, A.F.W. van der; Tortoli, Piero

doi:10.1016/j.ultrasmedbio.2005.01.011

Cited by 29 publications

(22 citation statements)

References 41 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Since angle correction is performed under the assumption that velocity vectors point in the axial direction only, the presence of secondary flow (i.e. radial and/or circumferential velocity components) may confound measurement of axial velocity [36] and thereby contribute positive or negative bias in calculated WSS. Another consequence of secondary flow is that the WSS vectors may contain in-plane components (Fig.…”

Section: Discussionmentioning

confidence: 99%

Errors in the estimation of wall shear stress by maximum Doppler velocity

2013

View full text Add to dashboard Cite

Objective Wall shear stress (WSS) is an important parameter with links to vascular (dys)function. Difficult to measure directly, WSS is often inferred from maximum spectral Doppler velocity (Vmax) by assuming fully-developed flow, which is valid only if the vessel is long and straight. Motivated by evidence that even slight/local curvatures in the nominally straight common carotid artery (CCA) prevent flow from fully developing, we investigated the effects of velocity profile skewing on Vmax-derived WSS. Methods Velocity profiles, representing different degrees of skewing, were extracted from the CCA of image-based computational fluid dynamics (CFD) simulations carried out as part of the VALIDATE study. Maximum velocities were calculated from idealized sample volumes and used to estimate WSS via fully-developed (Poiseuille or Womersley) velocity profiles, for comparison with the actual (i.e. CFD-derived) WSS. Results For cycle-averaged WSS, mild velocity profile skewing caused ±25% errors by assuming Poiseuille or Womersley profiles, while severe skewing caused a median error of 30% (maximum 55%). Peak systolic WSS was underestimated by ~50% irrespective of skewing with Poiseuille; using a Womersley profile removed this bias, but ±30% errors remained. Errors were greatest in late systole, when skewing was most pronounced. Skewing also introduced large circumferential WSS variations: ±60%, and up to ±100%, of the circumferentially averaged value. Conclusion Vmax-derived WSS may be prone to substantial variable errors related to velocity profile skewing, and cannot detect possibly large circumferential WSS variations. Caution should be exercised when making assumptions about velocity profile shape to calculate WSS, even in vessels usually considered long and straight.

show abstract

Section: Discussionmentioning

confidence: 99%

Errors in the estimation of wall shear stress by maximum Doppler velocity

2013

View full text Add to dashboard Cite

show abstract

“…However, most arteries are tapered, curved, and bifurcated, causing the axial velocity distribution to be altered by transversal velocities, resulting in asymmetrical axial velocity profiles and consequently in inaccurate flow estimations. 7 To perform the velocity measurements, the ultrasound beam needs to be positioned, not perpendicular, but at a certain angle with respect to the centerline of the artery ͑the insonation angle͒. The uncertainty in this angle influences the error of the Doppler measurement.…”

Section: A Motivation and Aimmentioning

confidence: 99%

Estimation of volume flow in curved tubes based on analytical and computational analysis of axial velocity profiles

et al. 2009

View full text Add to dashboard Cite

To monitor biomechanical parameters related to cardiovascular disease, it is necessary to perform correct volume flow estimations of blood flow in arteries based on local blood velocity measurements. In clinical practice, estimates of flow are currently made using a straight-tube assumption, which may lead to inaccuracies since most arteries are curved. Therefore, this study will focus on the effect of curvature on the axial velocity profile for flow in a curved tube in order to find a new volume flow estimation method. The study is restricted to steady flow, enabling the use of analytical methods. First, analytical approximation methods for steady flow in curved tubes at low Dean numbers (Dn) and low curvature ratios (δ) are investigated. From the results a novel volume flow estimation method, the cos θ-method, is derived. Simulations for curved tube flow in the physiological range (1≤Dn≤1000 and 0.01≤δ≤0.16) are performed with a computational fluid dynamics (CFD) model. The asymmetric axial velocity profiles of the analytical approximation methods are compared with the velocity profiles of the CFD model. Next, the cos θ-method is validated and compared with the currently used Poiseuille method by using the CFD results as input. Comparison of the axial velocity profiles of the CFD model with the approximations derived by Topakoglu [J. Math. Mech. 16, 1321 (1967)] and Siggers and Waters [Phys. Fluids 17, 077102 (2005)] shows that the derived velocity profiles agree very well for Dn≤50 and are fair for 50<Dn≤100, and this result applies for 0.01≤δ≤0.16, while Dean’s [Philos. Mag. 5, 673 (1928)] approximation only coincides for δ=0.01. For higher Dean numbers (Dn>100), no analytical approximation method exists. In the position of the maximum axial velocity, a shift toward the inside of the curve is observed for low Dean numbers, while for high Dean numbers, the position of the maximum velocity is located at the outer curve. When the position of the maximum velocity of the axial velocity profile is given as a function of the Reynolds number, a “zero-shift point” is found at Re=21.3. At this point the shift in the maximum axial velocity to the outside of the curve, caused by the difference in axial pressure gradient, balances the shift to the inside of the curve, caused by the centrifugal forces (radial pressure gradient). Comparison of the volume flow estimation of the cos θ-method with the Poiseuille method shows that for Dn≤100 the Poiseuille method is sufficient, but for Dn≥100 the cos θ-method estimates the volume flow nearly three times better. For δ=0.01 the maximum deviation from the exact flow is 4% for the cos θ-method, while this is 12.7% for the Poiseuille method in the plane of symmetry. The axial velocity profile measured at a certain angle from the symmetry plane results in a maximum estimation error of 6.2% for Dn=1000 and δ=0.16. The results indicate that the estimation of the volume flow through a curved tube from a given asymmetrical axial velocity profile is more precise with the cos θ-method than the Poiseuille method, which is currently used in clinical practice.

show abstract

“…This renders a simultaneous measurement of velocity by Doppler ultrasound and wall position impossible, hampering an accurate flow assessment. Furthermore, most arteries are tapered, curved and bifurcating, causing the axial velocity distribution to be altered by transversal velocities, resulting in asymmetrical axial velocity profiles and consequently in inaccurate flow estimations (Krams et al 2005). For volume flow estimation in curved vessels, the reader is referred to part B of this article (Beulen et al 2010).…”

Section: Introductionmentioning

confidence: 99%

Perpendicular ultrasound velocity measurement by 2D cross correlation of RF data. Part A: validation in a straight tube

et al. 2010

View full text Add to dashboard Cite

An ultrasound velocity assessment technique was validated, which allows the estimation of velocity components perpendicular to the ultrasound beam, using a commercially available ultrasound scanner equipped with a linear array probe. This enables the simultaneous measurement of axial blood velocity and vessel wall position, rendering a viable and accurate flow assessment. The validation was performed by comparing axial velocity profiles as measured in an experimental setup to analytical and computational fluid dynamics calculations. Physiologically relevant pulsating flows were considered, employing a blood analog fluid, which mimics both the acoustic and rheological properties of blood. In the core region (|r|/a \ 0.9), an accuracy of 3 cm s -1 was reached. For an accurate estimation of flow, no averaging in time was required, making a beat to beat analysis of pulsating flows possible.

show abstract

Effect of vessel curvature on Doppler derived velocity profiles and fluid flow

Cited by 29 publications

References 41 publications

Errors in the estimation of wall shear stress by maximum Doppler velocity

Errors in the estimation of wall shear stress by maximum Doppler velocity

Estimation of volume flow in curved tubes based on analytical and computational analysis of axial velocity profiles

Perpendicular ultrasound velocity measurement by 2D cross correlation of RF data. Part A: validation in a straight tube

Contact Info

Product

Resources

About