Accuracy of the inverse womersley method for the calculation of hemodynamic variables

Cezeaux, J.L.; Grondelle, Albertus van

doi:10.1007/bf02684193

Cited by 17 publications

(14 citation statements)

References 17 publications

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“…1) was proposed to analyze the effects of local and global factors on the CS and/or WSS. The 2D(3D) fluid-solid coupling problem in the straight artery was decoupled to calculate the CS and WSS with consideration of the characteristics of pulsatile flows in straight arteries [26,27]. In order to obtain the wall circumferential stress, the arterial wall was treated as a nonlinear, anisotropic, incompressible, psuedoelastic material, of which the mechanical property can be expressed as the widely used Fung exponential strain energy density function [25].…”

Section: Discussionmentioning

confidence: 99%

“…According to the characteristic of pulsatile blood flow in a straight artery, the equations governing the pulsatile blood flow can be simplified as follows [26,27] ∂u ∂t…”

Section: Determination Of the Wall Shear Stressmentioning

confidence: 99%

“…to overcome the difficulty due to the moving boundary, and Ling & Atabek's "local flow" assumption [24,26,27] ∂u ∂x = f (x, t)|u|.…”

Section: Determination Of the Wall Shear Stressmentioning

confidence: 99%

“…If the blood viscosity η, blood pressure p(t), radius r i (t) and flow rate q(t) are known, the velocities u and v, and wall shear stress τ -will be obtained [24,26,27]. …”

Section: Determination Of the Wall Shear Stressmentioning

confidence: 99%

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A multiscale model for analyzing the synergy of CS and WSS on the endothelium in straight arteries

et al. 2006

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A multiscale model was proposed to calculate the circumferential stress (CS) and wall shear stress (WSS) and analyze the effects of global and local factors on the CS, WSS and their synergy on the arterial endothelium in large straight arteries. A parameter pair [Zs, SP A] (defined as the ratio of CS amplitude to WSS amplitude and the phase angle between CS and WSS for different harmonic components, respectively) was proposed to characterize the synergy of CS and WSS. The results demonstrated that the CS or WSS in the large straight arteries is determined by the global factors, i.e. the preloads and the afterloads, and the local factors, i.e. the local mechanical properties and the zero-stress states of arterial walls, whereas the Zs and SP A are primarily determined by the local factors and the afterloads. Because the arterial input impedance has been shown to reflect the physiological and pathological states of whole downstream arterial beds, the stress amplitude ratio Zs and the stress phase difference SP A might be appropriate indices to reflect the influences of the states of whole downstream arterial beds on the local blood flow-dependent phenomena such as angiogenesis, vascular remodeling and atherosgenesis.

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Section: Discussionmentioning

confidence: 99%

“…According to the characteristic of pulsatile blood flow in a straight artery, the equations governing the pulsatile blood flow can be simplified as follows [26,27] ∂u ∂t…”

Section: Determination Of the Wall Shear Stressmentioning

confidence: 99%

“…to overcome the difficulty due to the moving boundary, and Ling & Atabek's "local flow" assumption [24,26,27] ∂u ∂x = f (x, t)|u|.…”

Section: Determination Of the Wall Shear Stressmentioning

confidence: 99%

“…If the blood viscosity η, blood pressure p(t), radius r i (t) and flow rate q(t) are known, the velocities u and v, and wall shear stress τ -will be obtained [24,26,27]. …”

Section: Determination Of the Wall Shear Stressmentioning

confidence: 99%

See 2 more Smart Citations

A multiscale model for analyzing the synergy of CS and WSS on the endothelium in straight arteries

et al. 2006

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“…Accordingly, for the Poiseuille approximation, the measured velocity profile was approximated by a parabolic velocity profile with a maximum velocity equal to the measured maximum velocity. For the Womersley approximation, the inverse Womersley method (Cezeaux and Grondelle 1997) was applied to determine the flow rate from the measured maximum velocity. All three flow approximations were compared to the flow as assessed directly during the measurement.…”

Section: Flow Estimationmentioning

confidence: 99%

Perpendicular ultrasound velocity measurement by 2D cross correlation of RF data. Part B: volume flow estimation in curved vessels

et al. 2010

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A novel axial velocity profile integration method, obtained from ultrasonic perpendicular velocimetry, for flow estimation in curved tubes was validated. In an experimental set-up, physiologically relevant curved geometries and flows were considered. Axial velocity profile measurements were taken by applying particle imaging velocimetry-based methods to ultrasound data acquired by means of a linear array transducer positioned perpendicular to the axial velocity component. Comparison of the assessed asymmetric velocity profiles to computational fluid dynamics calculations showed excellent agreement. Subsequently, the recently introduced cos hintegration method for flow estimation was compared to the presently applied Poiseuille and Womersley models. The average deviation between the cos h-integration-based unsteady flow estimate and the reference flow was about 5%, compared to an average deviation of 20% for both the Poiseuille and Womersley approximation. Additionally, the effect of off-centre measurement was analysed for the three models. It was found that only for the cos h-integration method, an accurate flow estimation is feasible, even when it is measured off centre.

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Numerical investigation of biomagnetic fluids in circular ducts

Tzirakis

Papaharilaou

Giordano

et al. 2013

Numer Methods Biomed Eng

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A mathematical model for the description of biomagnetic fluid flow exposed to a magnetic field that accounts for both electric and magnetic properties of the biofluid is presented. This is achieved by adding the Lorentz and magnetization forces in the Navier-Stokes equations. To demonstrate the effects of magnetic fields, we consider the case of laminar, incompressible, viscous, the steady flow of a Newtonian biomagnetic fluid (i) between two parallel plates; and (ii) through a straight rigid tube with a 60% in diameter, 84% on area, axisymmetric stenosis. Two external magnetic fields were investigated: one produced by an infinite wire carrying constant current, and a dipole-like field. We show, numerically and analytically, that the wire produces an irrotational force that, independent of its intensity, only alters the pressure leaving the velocity field unaffected. In contrast, when the fluid is exposed to the dipole-like field, which generates a rotational force, then both pressure and velocity can be strongly influenced even at moderate field strengths. Similar trends were obtained when a time varying flow is simulated through the axisymmetric stenosis in the presence of the dipole-like rotational magnetic field. It is expected that our findings could have important applications in blood flow control.

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Accuracy of the inverse womersley method for the calculation of hemodynamic variables

Cited by 17 publications

References 17 publications

A multiscale model for analyzing the synergy of CS and WSS on the endothelium in straight arteries

A multiscale model for analyzing the synergy of CS and WSS on the endothelium in straight arteries

Perpendicular ultrasound velocity measurement by 2D cross correlation of RF data. Part B: volume flow estimation in curved vessels

Numerical investigation of biomagnetic fluids in circular ducts

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