The propagation of Gaussian modulated pulses in dissipative and/or dispersive media such as tissue.
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.
D000818:Animals; D006801:Humans; D008433:Mathematics; D008954:Models, Biological; D014465:Ultrasonics