Modeling and Analysis of Ultrasound Propagation in Layered Medium

Abstract

For many medical applications of ultrasonic devices, it is often of interest to determine the distortion of ultrasound waves due to tissue layers of fat and muscle. Bending of the acoustic rays due to refraction at intermediate layers degrades image resolution, causes distortion and other artifacts in ultrasound images. In this work, ultrasound propagation in layered media is modeled analytically. Closed-form expressions are presented for the eld amplitude of spherical waves for the following cases: (1) transmission through a three- layered media, (2) extension to transmission through multi-layered medium, (3) a special case of modeling received echoes from an interface through two layers. In our derivations, ray-acoustic approximations have been assumed. We show that ray-acoustic approximations are valid for wavelengths (relative to medium layer dimensions) of interest. The eld amplitude is calculated by taking di erentials of the rays to form ux tubes and algebraically calcu- lating the ratios of ux-tube areas. We also take into account the frequency dependent attenuation due to absorption and backscattering loss in the me- dia. The interfaces between media are assumed to be arbitrary shaped, but can be broken up into small planar segments. The resulting response can be extended to di erent aperture geometries and di erent beam formations by delaying and summing the result for the Huygen waves emanating from the points forming the aperture. We have considered the inversion problem for the case of two layers on a re ective interface, where the layers are planar and parallel to the aperture. We showed that it is better to use demodulated versions of signal ouputs than use the raw signals themselves to avoid local minima at regular intervals around the global minimum. Validation experiments were performed using custom made tissue mimick- ing phantoms of fat and muscle and a steel-block. We t the forward-model to the experimental data using Levenberg-Marquardt inversion and show results of the parameter recovery and the simulation results with the nal parameters. For a 3 mm circular aperture transducer operating at 7 MHz, we obtained the RMS ratio of the experimental to the simulated echoes from two interfaces as 1:03 and 0:95 respectively.