Fundamental Investigation of Ultrasonic properties in Biological Tissues by Numerical Analysis.

为了分析生物软组织中的超声波，本文采用有限差分法中的蛙跳算法。它具有瞬态分析的优势，因为显式和简单的列式的可能性和容易设置的边界条件。结果，认识到剪切波和表面波可以以比常规超声诊断设备通常使用的纵波的频率（几MHz）更低的频率（几十kHz）产生和传播。如果我们能够负担得起横波和表面弹性波的使用，医学超声系统的发展是可以预期的，但计算是在组织是均匀的，没有非线性的近似下进行的。数值计算结果与实验结果吻合较好。为此，本文用激光多普勒测振仪测量了明胶凝胶表面表面波的速度和衰减系数。在100 [Hz]至800 [Hz]频率范围内测量的速度为1-2 [m/s]。在频率100 [Hz]和300 [Hz]下衰减约为0.1 [1/mm]。由于测量系统的灵敏度和非线性引起的波的失真，我无法通过数值分析测量高频值。但在粘弹性软材料中表面波的产生和传播，即剪切波的存在已被证实。接下来，我打算用同样的时域数值方法编制软件，用于分析超声诊断设备，了解设备发射的超声波波形，以及超声显微镜，以准确测量组织的性质。现在，它可以分析一个具有烧结材料和匹配层的超声换能器的二维。以及二维线聚焦超声束在被测样品上的反射特性。

To analyze the ultrasonic waves in soft biologicasl tissues, I used the leap frog algorithm of finite difference method. It has advantage for transient analysis because of the possibility of explicit and simple formulation and easy setting of boundary conditions. In result, it's realized that shear and surface waves can be generated and propagate at lower frequencies (some decade kHz) than the frequencies (some MHz) at which longitudinal wave is commonly used by a conventional ultrasonic diagnosis equipment. If we can afford to employ the shear and surface elastic waves, the development of medical ultrasonic systems can be expected.But the calculation was done with the approximation that the tissue is homogenous and not has nonlinearity. So the numerical result is confirmed by experimental one. So, the velocity and the attenuation coefficient of the surface wave on gelatin gel were measured by the laser Doppler vibromater. The measured velocity was 1-2 [m/s] from100 [Hz] to 800 [Hz] frequency range. The attenuation was about 0.1 [1/mm] at frequencies 100 [Hz] and 300 [Hz]. Because of the sensitivity of the measuring system and the distortion of waves by nonlinearity, I could not measure the values at high frequencies using by the numerical analysis. But the generation and propagation of surface waves, which shown the existence of shear waves, in vgiscoelastic soft materials were confirmed.Next, I was going to make software by the same numerical method in time domain for analyzing ultrasonic diagnosis equipment to know the ultrasonic wave form emitted by the equipment, and ultrasonic microscope to measure the tissue's properties exactly. Now, it can analyze a ultrasonic transducer with a baking material and matching layrs in two dimension. And the reflection characteristics from measuring samples of a two dimensional line focus ultrasonic beam.