Mathematical Evaluation of Steady, Laminar Flow by the Use of ContinuousWave (cw) Doppler and Pitot Tube System.
Abstract
Investigation, as to the usefulness of spectral analysis of the acoustical signal from the Doppler ultrasonic flowmeter, is being conducted. The hypothesis was that both hematocrit ((')H) and pressure head (H) influence the amplitude of the spectrum (A). Experiments were designed to: (a) evaluate their roles on amplitude; (b) derive the associated functional relationship. Preliminary experiments revealed that: (a) the accuracy of our Doppler flowmeter was satisfactory; (b) the relative weight of (')H on flow velocity was twice that of H. A pitot tube system whose bent tube component was capable of radial movement was developed to measure the instantaneous blood 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 second degree polynomial fit was good ((xi) = .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 measure the particle profile. The profile was parabolic and (')H, as a function of radius, was expressible in terms of a second degree polynomial. 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 amplitude corresponding to each given hematocrit was calculated by evaluating the area under the curve fitted to the transformed data. A((')H) was found to be a linear function of hematocrit. A generalized Doppler amplitude function A(H,(')H) was also derived. It was hypothesized that blood viscosity ((mu)) is an exponential function of hematocrit, that is, (mu) = A exp (B(.)(')H). Experimental results using a Falling ball type viscosimeter supported the theory with a high correlation between the data and the fitted curve ((xi) = .99). 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 is an exponentially decreasing function of (')H.
 Publication:

Ph.D. Thesis
 Pub Date:
 1983
 Bibcode:
 1983PhDT.......130S
 Keywords:

 Mathematics; Physics: Acoustics