Velocity profiles of oscillating arterial flow, with some calculations of viscous drag and the Reynolds number

Hale, J. F.; McDonald, D. A.; Womersley, J. R.

doi:10.1113/jphysiol.1955.sp005330

Cited by 133 publications

(61 citation statements)

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“…The red blood cell velocity distribution in a conduit artery at rest varies between the cardiosystolic and the cardiodiastolic phase [1][2][3][4]. In the carotid and femoral arteries at rest, it has previously been demonstrated that the blood velocity profile during the cardiosystolic phase is less "steep" and somewhat more "flat" compared to the "steeper" parabolic velocity profile during the cardiodiastolic phase [4][5][6].…”

mentioning

confidence: 99%

Alterations in the Blood Velocity Profile Influence the Blood Flow Response during Muscle Contractions and Relaxations

Osada

Rådegran

2006

J. Physiol. Sci

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Abstract:The present study examined the influences of the muscle contraction (MCP) and relaxation (MRP) phases, as well as systole and diastole, on the blood velocity profile and flow in the conduit artery at different dynamic muscle contraction forces. Eight healthy volunteers performed one-legged dynamic knee-extensor exercise at work rates of 5, 10, 20, 30, and 40 W at 60 contractions per minute. The time-and space-averaged, amplitude-weighted, mean (V mean ) and maximum (V max ) blood flow velocities were continuously measured in the common femoral artery during the cardiosystolic (CSP) and cardiodiastolic (CDP) phases during MCP and MRP, respectively. The V max / V mean ratio was used as a flow profile index where a ratio of approximately (~) 1 indicates a "flat" velocity profile, and a ratio significantly greater than (>>) 1 indicates a "parabolic" velocity profile. At rest, a "steeper" parabolic velocity profile was found during the CDP (ratio: 1.75 ± 0.06) than during the CSP (ratio: 1.31 ± 0.02). During the MRP of exercise, the V max /V mean ratio shifted to be less steep (p < 0.05) than at rest during the CDP (ratio: 1.41-1.54) at 5, 10, 20, 30, and 40 W; whereas it was slightly higher (p < 0.05) at 30 and 40 W than at rest during the CSP (ratio: 1.43-1.46). During the MCP, the parabolic blood velocity profile was enhanced (p < 0.05) at higher contraction forces, ≥20 W during the CDP (ratio: 2.15-2.52) and ≥30 W during the CSP (ratio: 1.49-1.77), potentially because of a greater retrograde flow component. A higher blood flow furthermore appeared during the MRP compared to during the MCP, coinciding with a greater uniformity of the red blood cells moving at higher blood velocities during the MRP. Thus part of the difference in the magnitude of blood flow during the MRP vs. MCP may be due to the alterations of the blood velocity flow profile.

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confidence: 99%

Alterations in the Blood Velocity Profile Influence the Blood Flow Response during Muscle Contractions and Relaxations

Osada

Rådegran

2006

J. Physiol. Sci

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“…For the capillary tube model, pulsatile flow has been characterized using the Womersley model to calculate shear stress [20,68]. However, some have reported values for FSS in unsteady flow regimes without including their methods of calculation [18].…”

Section: Huvec Protein Expression (Properdin)mentioning

confidence: 99%

“…When unsteady flows are outside this regime, they showed that FSS can be calculated using a similar derivation to Womersley's solution for unsteady flow in a rigid tube [10,20]. Hsiai et al demonstrated another approach: measuring heat transfer at the wall directly by using MEMS sensors, then calculating the FSS based on heat transfer principles [21].…”

Section: Introductionmentioning

confidence: 99%

Device-Based In Vitro Techniques for Mechanical Stimulation of Vascular Cells: A Review

Davis

Zambrano

Anumolu

et al. 2015

Journal of Biomechanical Engineering

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The most common cause of death in the developed world is cardiovascular disease. For decades, this has provided a powerful motivation to study the effects of mechanical forces on vascular cells in a controlled setting, since these cells have been implicated in the development of disease. Early efforts in the 1970 s included the first use of a parallel-plate flow system to apply shear stress to endothelial cells (ECs) and the development of uniaxial substrate stretching techniques (Krueger et al., 1971, "An in Vitro Study of Flow Response by Cells," J. Biomech., 4(1), pp. 31-36 and Meikle et al., 1979, "Rabbit Cranial Sutures in Vitro: A New Experimental Model for Studying the Response of Fibrous Joints to Mechanical Stress," Calcif. Tissue Int., 28(2), pp. 13-144). Since then, a multitude of in vitro devices have been designed and developed for mechanical stimulation of vascular cells and tissues in an effort to better understand their response to in vivo physiologic mechanical conditions. This article reviews the functional attributes of mechanical bioreactors developed in the 21st century, including their major advantages and disadvantages. Each of these systems has been categorized in terms of their primary loading modality: fluid shear stress (FSS), substrate distention, combined distention and fluid shear, or other applied forces. The goal of this article is to provide researchers with a survey of useful methodologies that can be adapted to studies in this area, and to clarify future possibilities for improved research methods.

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“…It is concluded that the Womersley number, a, a dimensionless expression of the pulsatile flow frequency in relation to viscous effects, is the only parameter that governs the behaviour of oscillatory flow and that the wave speed increases with the Womersley number tending to an asymptotic value obtained by Lamb (1898). The model predicts the phase lag between the pressure gradient and the flow as well as flow reversal initiating at the walls (Hale et al, 1955). A second two-dimensional algorithm was proposed by Branson (1945).…”

Section: Introductionmentioning

confidence: 99%

Nonlinear and viscous effects on wave propagation in an elastic axisymmetric vessel

Park

Payne

2011

Journal of Fluids and Structures

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Velocity profiles of oscillating arterial flow, with some calculations of viscous drag and the Reynolds number

Cited by 133 publications

References 4 publications

Alterations in the Blood Velocity Profile Influence the Blood Flow Response during Muscle Contractions and Relaxations

Alterations in the Blood Velocity Profile Influence the Blood Flow Response during Muscle Contractions and Relaxations

Device-Based In Vitro Techniques for Mechanical Stimulation of Vascular Cells: A Review

Nonlinear and viscous effects on wave propagation in an elastic axisymmetric vessel

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