Determination of the parameters of a high power ultrasound transducer to provide certain shock amplitude at the focus

Many modern medical applications of high intensity focused ultrasound rely on nonlinear acoustic effect of shock formation in the pressure waveform at the focus. The problem arises to determine parameters of the transducer that allow to obtain a certain value of the shock amplitude at the focus required for a specific application. It was proposed that the main transducer parameter, which determines the shock amplitude, is the transducer F-number. This hypothesis was tested using multi parameter numerical calculations of nonlinear ultrasound fields generated by such transducers. Khokhlov-Zabolotskaya-Kuznetsov equation was used in the modeling. The method to determine characteristic focal waveform with fully developed shock front was proposed. The approach was developed for calculating the shock amplitude between the time points at the specified level of the waveform time derivative. The magnitude of this level as relative to the maximum value of the derivative was determined by comparing heat deposition at the focus, calculated numerically and analytically using the weak shock theory. Characteristic shock amplitudes in the focal waveforms were calculated for transducers operating at 1 MHz frequency within the range of F-numbers from 0.8 to 2. It was shown that fully developed shock fronts of 80 MPa amplitudes correspond to transducers with F-number close to unity, which is a typical value for therapeutic transducers.