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

为了分析软质生物组织中的超声波，我使用了有限差分法中的跳跃蛙算法。该方法可以明确、简单地表述，边界条件易于设置，对瞬态分析具有优势。结果发现，与传统超声诊断设备通常使用的纵波频率相比，剪切波和表面波可以在更低的频率（大约10千赫）下产生和传播。如果我们能够使用剪切波和表面弹性波，医用超声系统的发展是可以预期的。但计算是在近似组织为齐次而非非线性的情况下进行的。因此，数值结果与实验结果是一致的。为此，采用激光多普勒振动仪测量了明胶凝胶表面波的速度和衰减系数。测量速度为1-2 [m/s]，频率范围为100 [Hz] ~ 800 [Hz]。在100 [Hz]和300 [Hz]频率下，衰减约为0.1 [1/mm]。由于测量系统的灵敏度和波的非线性畸变，我无法使用数值分析测量高频值。但在粘弹性软质材料中，表面波的产生和传播证明了剪切波的存在。接下来，我将用同样的时域数值方法制作软件，用于分析超声诊断设备，了解设备发出的超声波波形，以及超声波显微镜，准确测量组织的性质。目前，该系统已经可以对具有烘烤材料和匹配层的超声波换能器进行二维分析。研究了二维线聚焦超声光束测量样品的反射特性。

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.