Thompson R S, Aldis G K
School of Mathematics and Statistics, University of Sydney, Australia.
IEEE Trans Biomed Eng. 1996 May;43(5):451-9. doi: 10.1109/10.488793.
The insonation of axisymmetric flow in a tube by an ultrasound beam which is refracted at the tube surface is considered. A three-dimensional (3-D) model for refraction at a cylindrical interface is developed. The incident beam, which is planar but otherwise arbitrary, is refracted at a single acoustic impedance interface between the medium within the tube and the surrounding medium. A ray approximation is used as the ultrasonic wavelength is small compared to the radius of curvature of the tube. A parametric form for the ray paths is obtained and used to derive an expression for the intensity. The intensity depends on the specific position within the tube, as well as the ratio of sound speeds, N, and the Doppler angle thetaD. A diverging (N = 1.2, thetaD = 45 degrees) and a converging (N = 0.8, thetaD = 45 degrees) case are presented in detail. The converging interface results in more extreme intensity distortion. The regions of maximum and minimum intensity over a tube slice are immediately adjacent in both diverging and converging cases. Once the intensity distribution across a tube slice is known, the previously reported volume integral method for the calculation of continuous wave (CW) Doppler spectral power density (spd) functions may be used. The effect of refraction of the incident beam on the spd function is shown for both an infinite beam and a circular beam with radius equal to the tube radius. A curved acoustic impedance interface, as may be encountered in vitro in flow phantoms or in vivo in vascular disease, leads to nonuniform insonation and spectral distortion which depends on transducer orientation.
研究了超声束在管表面折射时对管内轴对称流的声呐作用。建立了圆柱界面折射的三维（3 - D）模型。入射束是平面的，但在其他方面是任意的，在管内介质与周围介质之间的单个声阻抗界面处发生折射。由于超声波长与管的曲率半径相比很小，因此采用射线近似法。得到了射线路径的参数形式，并用于推导强度表达式。强度取决于管内的特定位置，以及声速比N和多普勒角θD。详细介绍了发散情况（N = 1.2，θD = 45度）和会聚情况（N = 0.8，θD = 45度）。会聚界面会导致更极端的强度畸变。在发散和会聚情况下，管切片上强度最大和最小的区域紧邻。一旦知道了管切片上的强度分布，就可以使用先前报道的用于计算连续波（CW）多普勒频谱功率密度（spd）函数的体积积分方法。对于无限束和半径等于管半径的圆形束，都显示了入射束折射对spd函数的影响。在体外流动模型或体内血管疾病中可能遇到的弯曲声阻抗界面会导致不均匀的声呐作用和频谱畸变，这取决于换能器的方向。
