Effect of the angular aperture of medical ultrasound transducers on the parameters of nonlinear ultrasound field with shocks at the focus

Abstract

Certain modern applications of high-intensity focused ultrasound (HIFU) in medicine use the nonlinear effect of shock front formation in the focal waveform. However, an important problem remains unsolved: determination of transducer parameters that provide the given pressure levels of the shock wave field at the focus required for a specific application. In this paper, simulations based on the Khokhlov-Zabolotskaya equation are performed to test and confirm the hypothesis that angular aperture of the transducer is the main parameter that determines the characteristic amplitude of the shock front and corresponding values for the peak positive and negative pressures at the focus. A criterion for formation of a developed shock in the acoustic waveform, as well as a method for determining its amplitude is proposed. Quantitative dependences of the amplitude of the developed shock and the peak pressures in the wave profile on the angular aperture of the transducer are calculated. The effects of saturation and the range of changes of the shock waveform parameters at the focus are analyzed for a typical HIFU transducer.