| Summary: | 碩士 === 淡江大學 === 機械與機電工程學系碩士班 === 97 === In this study, Biot’s poroelastic theory is used to derive the pulse echo responses and phase velocities of fast and slow waves of cancellous bones. First, Biot’s equations were transformed to Laplace domain. By specifying the boundary conditions for the pulse echo simulation and the relation between the Laplace transform parameter and the angular frequency(s=iω), the theoretical frequency response functions of phase velocities and the displacement of the driving surface of the cancellous bone were obtained. In time domain, phase velocities of cancellous bone were analyzed using the displacement frequency response function obtained and flat top windows, and were calculated from the rate at which the phase of the wave propagates. In the end of this study, the influences of dimensionless material parameters on the dimensionless phase velocities of fast and slow waves were discussed.
Using the phase velocity results derived the influences of bone properties on the phase velocities were numerically analyzed. The predicted results were validated by ultrasonic experimental results and a good agreement was observed. The phase velocities, which were calculated from the phase propagation rate, also agreed well with the results derived. After the influence analyses of bone properties on the phase velocities, it was found that the density the solid, the bulk modulus of the frame, the shear modulus of the frame affect the phase velocity of the fast wave. The bulk modulus the fluid affect the phase velocity of the slow wave. The porosity and tortuosity of the bone affect both waves. The only one parameter that has minor effects is the bulk modulus of the solid.
After the analyses of the dimensionless bone properties on the phase velocities, it was found that the dimensionless Biot’s coefficients R* and P* have major effects on the phase velocity of the fast wave in low frequency and high frequency regions, respectively. Moreover, the dimensionless Biot’s coefficient R* affect the phase velocity of the slow wave. Furthermore, the dimensionless total effective mass density of the solid affects the phase velocity of the fast wave. The increase of the dimensionless total effective mass density of the fluid has no effect on the phase velocity of the fast wave above the low frequency region, but will decrease the initial value of the phase velocity of the slow wave. Increasing the value of the coupling mass density will also increase the value of the phase velocities accordingly. Nevertheless, enlarging the value of the dimensionless dissipation coefficient will move the phase velocity curve toward the high frequency side but makes no change to the shape of the curve.
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