A lumped model for blood flow and pressure in the systemic arteries
based on an approximate velocity profile function

A nonlinear differential equation describing the Doppler velocity profile for blood flow through the mitral valve has been derived. This equation is based on fluid dynamics and a simple, but comprehensive model of atrial and ventricular mechanics. A numerical solution to the equation is described and provides excellent agreement with Doppler velocity curves obtained clinically. One important result of the theory is that in patients with mitral stenosis, the slope of the clinically observed straight-line descent of the velocity profile is proportional to the mitral orifice area and inversely proportional to the atrioventricular compliance.

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Biphasic Cerebral Blood Flow Velocity Profile in Patients With Aneurysmal Subarachnoid Hemorrhage

Neurocritical Care ◽

10.1385/ncc:1:4:455 ◽

2004 ◽

Vol 1 (4) ◽

pp. 455-460 ◽

Cited By ~ 1

Author(s):

Andreas R. Luft ◽

Manuel M. Buitrago ◽

Michel Torbey ◽

Anish Bhardwaj ◽

Alexander Razumovsky

Keyword(s):

Blood Flow ◽

Cerebral Blood Flow ◽

Subarachnoid Hemorrhage ◽

Velocity Profile ◽

Flow Velocity ◽

Blood Flow Velocity ◽

Cerebral Blood Flow Velocity ◽

Aneurysmal Subarachnoid Hemorrhage ◽

Flow Velocity Profile

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Three Dimensional Simulation of Blood Flow in the Small Arteries of a Truncated Vascular System With Three Levels of Bifurcation

Volume 1A, Symposia: Advances in Fluids Engineering Education; Turbomachinery Flow Predictions and Optimization; Applications in CFD; Bio-Inspired Fluid Mechanics; Droplet-Surface Interactions; CFD Verification and Validation; Development and Applications of Immersed Boundary Methods; DNS, LES, and Hybrid RANS/LES Methods ◽

10.1115/fedsm2014-22240 ◽

2014 ◽

Author(s):

Kamil Kahveci ◽

Bryan R. Becker

Keyword(s):

Boundary Condition ◽

Blood Flow ◽

Blood Vessel ◽

Velocity Profile ◽

Flow Velocity ◽

Blood Flow Velocity ◽

Vascular System ◽

Three Dimensional ◽

Simulation Software ◽

Small Arteries

Three dimensional blood flow in a truncated vascular system is investigated numerically using a commercially available finite element analysis and simulation software. The vascular system considered in this study has three levels of symmetric bifurcation. Geometric parameters for daughter vessels, such as their diameters and their angles of bifurcation, are specified according to Murray’s law based on the principle of minimum work. The ratio of blood vessel length to diameter is based upon experimental data found in the literature. An experimentally obtained velocity profile, available in the literature, is used as the inlet boundary condition. An outflow boundary model, consisting of a contraction tube to represent the pressure drop of the small arteries, arterioles, and capillaries that would follow the truncated vascular system, is used to specify the boundary condition at the eight outlets. The results show that although the blood flow velocity experiences a sudden decrease after the bifurcation points due to the higher total cross-sectional area of the daughter vessels as compared to the parent vessel, this decrease in velocity is partially recovered due to the tapering of the blood vessels as they approach the next bifurcation point. The results also show that the secondary flow which is typical after the bifurcation of large arteries does not develop after the bifurcation of small arteries due to the presence of laminar blood flow with very low Reynolds number in the small arteries. The numerical model yields pressure distributions and pressure drops along the vascular system that agree quite well with the physiological data found in the literature. Finally, the results show that, immediately following a bifurcation, the blood flow velocity profile is not symmetrical about the longitudinal axes of blood vessel. However, symmetry is recovered as the blood flow proceeds down the vessel.

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Persistence of Asymmetry in Nonaxisymmetric Entry Flow in a Circular Cylindrical Tube and Its Relevance to Arterial Pulse Wave Diagnosis

Journal of Biomechanical Engineering ◽

10.1115/1.3168337 ◽

1989 ◽

Vol 111 (1) ◽

pp. 37-41 ◽

Cited By ~ 4

Author(s):

H. Xue ◽

Y. C. Fung

Keyword(s):

Blood Flow ◽

Chinese Medicine ◽

Traditional Chinese Medicine ◽

Velocity Profile ◽

Radial Artery ◽

Pulse Wave ◽

Arterial Blood Flow ◽

Arterial Pulse ◽

Entry Length ◽

Arterial Pulse Wave

In an experiment motivated by the study of arterial blood flow along the lines suggested by the traditional Chinese medicine, the flow in a pipe whose lumen was blocked by a semi-circular plug two tube-diameters long was visualized by suspended particles, recorded by cinematography, and analyzed digitally. The Reynolds number was in the range of 100 to 450 based on the pipe diameter, similar to that of blood flow in the radial artery in the arms of man. The blockage was found to have a profound effect on the velocity profile of the flow in the wake, but it had little influence on the symmetry of the velocity profile upstream of the block, except in its immediate neighborhood. When the end conditions far away from the block were steady, the flow in the wake was steady. The asymmetry of the flow in the wake can be judged by the deviation of the location of the maximum axial velocity from the center line of the pipe as seen in the plane of symmetry of the blockage. Our results show that the deviation can be described as the sum of two components. The first is a strong one which decays exponentially in an entry length which is about twice as long as the classical Boussinesq entry length of axisymmetric flow. The second is a weaker component which is wavy spatially and persists far downstream (many times the entry length). The separated flow and vortex system behind the blockage are sensitive to the flow rate. The relevance of these findings to the arterial pulse wave diagnosis methods used in the traditional Chinese medicine is discussed. We show that the human arteries are shorter than the entry length, hence nonaxisymmetric disturbances can be propagated throughout the circulation system. We propose that the propagation of the persistent, small, wavy asymmetric wave is relevant to the “localization” of the spheres of influence of internal and external organs in a two-inch region of the radial artery. We propose further that the method of pressing hard on the artery to “feel” the pulse is to amplify the signal by creating a wake that is very sensitive to velocity of flow.

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The mechanism of cardiac shunting in reptiles: a new synthesis.

Journal of Experimental Biology ◽

10.1242/jeb.199.6.1435 ◽

1996 ◽

Vol 199 (6) ◽

pp. 1435-1446 ◽

Cited By ~ 5

Author(s):

J W Hicks ◽

A Ishimatsu ◽

S Molloi ◽

A Erskin ◽

N Heisler

Keyword(s):

Blood Flow ◽

Digital Subtraction Angiography ◽

Diastolic Pressure ◽

Systolic Pressure ◽

Digital Subtraction ◽

New Synthesis ◽

Vagal Nerves ◽

The Common ◽

The Difference ◽

Systemic Arteries

The mechanism of cardiac shunting in reptiles is controversial. Recent evidence suggests that a right-to-left shunt in turtles results primarily from a washout mechanism. The mechanism that accounts for left-to-right (L-R) shunting is unresolved. This study used haemodynamic analysis and digital subtraction angiography to determine the mechanism of L-R cardiac shunting in the turtle Trachemys (Pseudemys) scripta. Animals were instrumented with ultrasonic blood flow probes (Transonic Systems, Inc.) for the measurement of total pulmonary blood flow and total systemic blood flow. In addition, catheters were inserted into the common pulmonary artery (PA), the systemic arteries, the left atrium and right atrium. These catheters were used for the measurement of blood pressure or for the infusion of radio-opaque material. Haemodynamic conditions were altered by electrical stimulation of the afferent (VAF) or efferent vagal nerves or by infusion of vasoactive drugs. Under control conditions, the peak systolic pressure in the systemic arteries was slightly higher than that in the PA (30.6 versus 28.3 mmHg; 4.08 versus 3.77 kPa), whereas diastolic pressure in the PA was significantly less than that in the systemic arteries (9.8 versus 24.4 mmHg; 1.31 versus 3.25 kPa). During VAF stimulation, the peak systolic pressures in the PA and aortae almost doubled. Diastolic pressure in the systemic arteries also doubled, but it increased by only 45% in the PA. Ejection of blood into the PA preceded that into the left aorta by 53 ms under control conditions. This difference increased (by as much as 200 ms) as the difference in the diastolic pressures between the two circulations increased during VAF stimulation. This resulted in the development of a large net L-R shunt. Under these conditions, digital subtraction angiography showed that the L-R shunt resulted from a combination of both washout and pressure mechanisms.

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