Study Of Certain Nonlinear Problems In Biomedical Ultrasound

In theory and application of biomedical ultrasound, the study of nonlinear phenomena is one of the highlights and difficulties during the last several years. Better resolution and contrast can be obtained by employing nonlinear principles in ultrasonic imaging. Ultrasound images with higher quality then can be constructed to describe the imaging objects more clearly and truly. It has shown us remarkable advantages and an attractive future.All research work introduced in this thesis follows the rigorous,feasible and effective principle, and offers systematic theory,modeling,numerical computation and simulation methods in solving some important problems in the principle and application of nonlinear ulteasound. The research achievements presented in this doctoral dissertation has following features:1. A new method based on the Fourier-Bessel series is proposed to calculate the higher-order harmonic components of a nonlinear ultrasound field in absorbing medium and an analytical solution of a series form is obtained. A closed analytical solution of the higher-order harmonics in the zeroth-order Bessel ultrasound field and the focused Gaussian ultrasound field is deduced to study the field property, especially the near-field property.2. The fundamental and higher-order harmonic ultrasound fields of a zeroth-order Bessel ultrasound field and focused Gaussian field in absorbing medium are computed and simulated by solving the KZK equation using a frequency domain finite difference method. The computation and simulation results verified the theoretical conclusion.3. A preliminary study of the harmonic imaging theory and model is introduced, and a simple computation model frame is proposed.This research is sponsored by the National Science Foundation of China project "Study on high resolution and high frame rate ultrasonic imaging system" (No. 60471057) and the Youth Foundation of the University of Science and Technology of China "Study of the property of nonlinear non-diffraction beam and its application in medical ultrasound" (No. KA2100230001).