Mathematical Evaluation of Steady, Laminar Flow by the use of Continuous-Wave (CW) Doppler and Pitot Tube System

<p>Investigation, as to the usefulness of spectral analysis of the acoustical signal from the Doppler ultrasonic flowmeter, is being conducted. The purpose was to determine some of the hemodynamic influences on the spectrum. The hypothesis was that both hematocrit and pressure head influence the amplitude of the spectrum. Experiments were designed to: a) evaluate their roles on amplitude; b) derive the associated functional relationship.</p> <p>Preliminary experiments revealed that: a) the accuracy of our Doppler flowmeter was satisfactory, since a very good linear relation was found between electromagnetically and Doppler derived flow; b) the relative weight of the hematocrit parameter on flow velocity was twice that of the pressure.</p> <p>Experiments were carried out to determine the distribution of velocities and the particle profile within the tube prior to investigation of functional dependence of Doppler amplitude on hematocrit and pressure head. A pitot tube system whose bent tube component was capable of radial movement was developed to measure the instantaneous blood (or particle) velocity. The bent tube was moved across the lumen of the vessel in steps of 0.1 mm., and particle velocity was measured at each sampling point. The distribution of velocity was parabolic and the agreement between experimental data and the 2nd degree polynomial least squares fitting was good (ξ = .94). An array of small bent tubes, each placed successively deeper within the lumen of the rubber tubing and connected to a small syringe, was constructed to measured the distribution of red cells. Small uniform samples were taken from the flowing stream. The particle profile was parabolic and the hematocrit, as a function of radius, was expressible in terms of a 2nd degree polynomial. A mapping of particle velocities onto the set of hematocrit values is also parabolic.</p> <p>To determine the dependency of ultrasonic energy backscattering on hematocrit, Doppler signals were recorded, digitized, and frequency resolved via the fast Fourier transform, for hematocrits ranging from 4.5% to 46.5%. The mean amplitude corresponding to each given hematocrit was calculated by evaluating the area under the curve fitted to the transformed data. The Doppler amplitude was found to be a linear function of hematocrit for all cases of applied pressure heads. A generalized Doppler amplitude function of double variables was also derived in terms of hematocrit and pressure head.</p> <p>It was hypothesized that blood viscosity (μ) is an exponential function of hematocrit (Ĥ), that is, μ = A exp (B Ĥ). Experimental results using a Falling ball type viscosimeter supported the theory with a high correlation between the data and the fitted curve (ξ=.99).</p> <p>The constant A has the dimensions of viscosity and is dependent on temperature, whereas, B is dimensionless and a linear function of hematocrit. A consequence of this hypothesis is that flow velocity decreases exponentially as a function of hematocrit. It can be hypothesized that viscosity influences the power content of the Doppler signal, which requires further work and research.</p>

Name thesis:degree_name

Doctor of Philosophy (PhD)

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mathematical Sciences

Year

1983

Author dc:creator

• Sharif, Malek Mansoor

Contributors dc:contributor

• S. Andrew Yakush
• Ramon R. Gonzalez, Jr.
• Raymond G. Hall, Jr.
• George Maeda
• C. Duane Zimmerman

• Applied Mathematics
• Blood Flow Velocity; Ultrasonics; Flowmeters

Statement dc:rights

• This title appears here courtesy of the author, who has granted Loma Linda University a limited, non-exclusive right to make this publication available to the public. The author retains all other copyrights.

Language dc:language

English

Repository record dc:identifier

https://scholarsrepository.llu.edu/etd/1348

OAI identifier oai:identifier

oai:scholarsrepository.llu.edu:etd-2120