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，我使用了有限差分方法中的跳蛙算法。该方法具有显式形式简单、边界条件设置容易等优点，对暂态分析具有一定的优势。结果，实现了横波和面波的产生和传播的频率可以比传统超声诊断设备通常使用的纵波的频率(一些MHz)更低(大约10 kHz)。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，但计算是在组织是均匀的而不是非线性的近似下进行的。因此，数值计算结果与实验结果相吻合。为此，利用激光多普勒测振仪测量了明胶表面波的传播速度和衰减系数。在100~800赫兹频率范围内，测得的速度为1~2[m/S]。在100[赫兹]和300[赫兹]频率下，衰减约为0.1[1/mm]。由于测量系统的敏感性和非线性引起的波形失真，我无法用数值分析的方法测量高频下的数值。但证实了粘弹性软材料中表面波的产生和传播，表明了剪切波的存在。接下来，我将用同样的时间域数值方法编制软件来分析超声诊断设备，以了解设备发出的超声波波形，并用超声显微镜准确地测量组织的特性。现在，它可以对具有烘烤材料和匹配层的超声换能器进行二维分析。以及二维线聚焦超声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.