Ferrari L, Jones J P
Ultrasound Med Biol. 1985 Mar-Apr;11(2):299-305. doi: 10.1016/0301-5629(85)90129-2.
The interrogating pulse used in most conventional medical ultrasonic imaging systems can be approximated as a band-limited Gaussian modulated pulse. In this paper we analyze the propagation of such a pulse in an attenuating media such as tissue. We show that an initially Gaussian pulse retains its Gaussian shape during propagation provided that the medium has attenuation with a power-law dependence on frequency of between zero and two. That is, if the attenuation factor is e- alpha x, where alpha is the attenuation coefficient and x is the distance over which the pulse has traveled, then the pulse will remain Gaussian provided alpha = afp, where a is a constant, f is the frequency, and 0 less than p less than or equal to 2. This condition is certainly valid for soft tissue (p approximately 1) as well as for all other attenuating materials with which we are familiar. Although a Gaussian pulse retains its Gaussian shape in an attenuating media, it does suffer a shift in its mean frequency as well as a broadening in its shape. Here we also obtain analytical expressions relating the mean frequency shift and the pulse broadening to the attenuating properties of the medium. In contrast to other studies recently published in the literature, we consider propagation in a medium which has velocity dispersion as well as frequency dependent loss.
大多数传统医学超声成像系统中使用的探测脉冲可近似为带限高斯调制脉冲。在本文中，我们分析了这种脉冲在诸如组织等衰减介质中的传播情况。我们表明，只要介质的衰减与频率呈幂律依赖关系，幂指数在零到二之间，初始高斯脉冲在传播过程中就会保持其高斯形状。也就是说，如果衰减因子为e-αx，其中α是衰减系数，x是脉冲传播的距离，那么当α = afp时，脉冲将保持高斯形状，其中a是常数，f是频率，且0 < p ≤ 2。这个条件对于软组织（p约为1）以及我们熟悉的所有其他衰减材料肯定是有效的。尽管高斯脉冲在衰减介质中保持其高斯形状，但它的平均频率确实会发生偏移，形状也会变宽。在这里，我们还得到了将平均频率偏移和脉冲展宽与介质的衰减特性相关联的解析表达式。与最近文献中发表的其他研究不同，我们考虑的是在具有速度色散以及频率相关损耗的介质中的传播。
