Theory Of Oscillatory Flow Research Articles

A new formula for predicting the position of severe arterial stenosis

Noninvasive location of an occlusion or a severe stenosis in the arterial system is of a great interest for surgical interventions. Here, we present a new method to determine the location of arterial 99% stenosis in the arterial (sub) system. The method requires a measurement of propagation constant and the instantaneous flow rate or velocity at two sites of an arterial tree. The method was successfully tested using Womersley’s oscillatory flow theory and the data obtained by a simulation of Fluid structure interaction (FSI). The effect of noise has been investigated to simulate experimental conditions. The results demonstrate that location of 99% severe stenosis could be accurately obtained. The spatial resolution was approximately a few centimeters and the differences between exact and computed values didn’t exceed 13%. However, the identifications of stenotic sites decreased with the distance. Further investigation of the developed method in vivo and in vitro is required.

Abnormal arterial flows by a distributed model of the fetal circulation

Modeling the propagation of blood pressure and flow along the fetoplacental arterial tree may improve interpretation of abnormal flow velocity waveforms in fetuses. The current models, however, either do not include a wide range of gestational ages or do not account for variation in anatomical, vascular, or rheological parameters. We developed a mathematical model of the pulsating fetoumbilical arterial circulation using Womersley's oscillatory flow theory and viscoelastic arterial wall properties. Arterial flow waves are calculated at different arterial locations from which the pulsatility index (PI) can be determined. We varied blood viscosity, placental and brain resistances, placental compliance, heart rate, stiffness of the arterial wall, and length of the umbilical arteries. The PI increases in the umbilical artery and decreases in the cerebral arteries, as a result of increasing placental resistance or decreasing brain resistance. Both changes in resistance decrease the flow through the placenta. An increased arterial stiffness increases the PIs in the entire fetoplacental circulation. Blood viscosity and peripheral bed compliance have limited influence on the flow profiles. Bradycardia and tachycardia increase and decrease the PI in all arteries, respectively. Umbilical arterial length has limited influence on the PI but affects the mean arterial pressure at the placental cord insertion. The model may improve the interpretation of arterial flow pulsations and thus may advance both the understanding of pathophysiological processes and clinical management.

Equivalent viscosity of plasma and plasma substitutes in oscillatory flow.

Womersley's theory of oscillatory flow has been used to determine the equivalent viscosity (analogous to the apparent viscosity under steady flow conditions) of plasma and plasma substitutes (dextrans) of various molecular weights in rigid cylindrical tubes of radii ranging from 0.0304 to 0.162 cm. It is shown that the equivalent viscosity of dextran solutions is radius independent and is higher than that of plasma, at all frequencies. The continuum theory of suspensions, developed by Kline and Allen, is shown to be in good agreement with these findings.

Frequency dependence of blood viscosity in oscillatory flow1

Womersley’s theory of oscillatory flow is used to derive a parameter, the equivalent viscosity, which characterizes the rheological state of a non-Newtonian fluid under oscillatory conditions. The equivalent viscosity so obtained is analogous to the

Non-Newtonian Behavior of Blood in Oscillatory Flow

Sinusoidal oscillatory flow of blood and of aqueous glycerol solutions was produced in rigid cylindrical tubes. For aqueous glycerol, the amplitude of the measured pressure gradient wave form conformed closely to that predicted by Womersley's theory of oscillatory flow, up to Reynolds numbers approaching 2000. Blood differed significantly from aqueous glycerol solutions of comparable viscosity, especially at low frequencies and high hematocrits. As frequency increased, the hydraulic impedance of blood decreased to a minimum at a frequency of about 1-2 CPS, increasing monotonically at higher frequencies. The dynamic apparent viscosity of blood, calculated from Womersley's theory, decreased with increasing flow amplitude. The reactive component of the hydraulic impedance increased with frequency as predicted by theory; the resistive component decreased with increasing frequency, differing from the resistance of a Newtonian fluid which increased with frequency.