Fast Calculation And Study On Nonlinear Field Of Limited Ultrasound Beam

The higher-order harmonics of nonlinear ultrasound can improve the quality of medical ultrasonic imaging. The study of nonlinear ultrasound characteristics can provide theoretical basis for its applications in various fields,it will help to improve the level of ultrasonic diagnosis. In the study of ultrasonic imaging and treatment, KZK equation is widely used to research the nonlinear field of limited ultrasound beam under the parabolic approximation. KZK equation is a higher-order nonlinear partial differential equation and the explicit analytical solution is difficult to be derived. In most cases it can only be solved by a numerical method. At present, we could use frequency-domain method and time-domain numerical method to solve KZK equation. Frequency-domain method is widely used because the frequency-dependent absorption can be easily processed with it. The time-domain method is suitable for the sound field with short pulse excitation.The research works in this paper focused on the following two aspects:1,In order to improve the time and memory efficiency in frequency-domain finite difference method, we proposed a parallel computation model. Theoretical study shows that there are multiple couplings in nonlinear finite sound beam: full coupling between the harmonics, recursive coupling between the field points along the axial direction, and local coupling along the radial direction. Therefore, the radial sound field can be divided into several sub-regional, and can use multi-threads parallel computing to improve computational efficiency. The method may be achieved through multi-threads parallel computation. The calculation results of nonlinear focused Gaussian continuous wave under single transducer show that: When the problem size and the number of threads realize a reasonable match, this algorithm can significantly improve the calculation speed while ensuring calculation accuracy. The calculation results are compared with the theoretical analysis.2,In order to study the nonlinear field of the focused Gaussian beam radiated from array transducers with a pulse excitation, the KZK equation was solved by time-domain finite difference method. The characteristics include the distribution of the fundamental and second harmonic field in the space. The results indicate that the distribution of the fundamental and second harmonic field is approximate in the space. They follow a law of Gaussian function approximately along the radial direction and the second harmonic has narrower beam-width. The calculation results are consistent with the theoretical study. In addition, the study is also a basis for modeling harmonic imaging.