Design of HIFU Transducers for Generating Specified Nonlinear Ultrasound Fields

Abstract

Various clinical applications of high intensity focused ultrasound (HIFU) have different requirements for the pressure levels and degree of nonlinear waveform distortion at the focus. The goal of this work was to determine transducer design parameters that produce either a specified shock amplitude in the focal waveform or specified peak pressures while still maintaining quasilinear conditions at the focus. Multi-parametric nonlinear modeling based on the KZK equation with an equivalent source boundary condition was employed. Peak pressures, shock amplitudes at the focus, and corresponding source outputs were determined for different transducer geometries and levels of nonlinear distortion. Results are presented in terms of the parameters of an equivalent single-element, spherically shaped transducer. The accuracy of the method and its applicability to cases of strongly focused transducers were validated by comparing the KZK modeling data with measurements and nonlinear full-diffraction simulations for a single-element source and arrays with 7 and 256 elements. The results provide look-up data for evaluating nonlinear distortions at the focus of existing therapeutic systems as well as for guiding the design of new transducers that generate specified nonlinear fields.

Dependence of Boiling Histotripsy Treatment Efficiency on HIFU Frequency and Focal Pressure Levels

“…2, blue lines ) or the condition of saturated shocks, in which shock amplitude is equal to the sum of peak negative and peak positive pressures. Again, in accordance with theoretical predictions, at these output levels the shock amplitude for each frequency increased by 41%–48% compared with the condition of the developed shock (Rosnitskiy et al 2015, 2017). The output level corresponding to the shock amplitude in the middle between “low” and “high” levels will be referred to as “intermediate.”…”

Inactivation of Planktonic Escherichia coli by Focused 1-MHz Ultrasound Pulses with Shocks: Efficacy and Kinetics Upon Volume Scale-Up

“…The maximum shock amplitude in the single pulse measurements was equal to the maximum peak positive pressure, which corresponds to the level of non-linear waveform distortion, defined as a developed shock front (Rosnitskiy et al 2015). As has been shown in recent studies, the peak pressure levels, which correspond to the formation of the developed shock, are mainly determined by the F-number of the transducer and are practically independent of its frequency or dimensions (Rosnitskiy et al 2015, 2017). Indeed, the same peak pressures were measured for such waveforms in the field of transducers of the same dimensions but different frequency of 2 MHz (Canney et al 2008) and of the same frequency and F-number but larger dimensions (Rosnitskiy et al 2017).…”

For Whom the Bubble Grows: Physical Principles of Bubble Nucleation and Dynamics in Histotripsy Ultrasound Therapy

“…Spherically focused sources produce a focal region of high pressure amplitude, where the ratio of amplitudes between the focal peak and transducer surface is defined by the focal gain, G. For most histotripsy applications, large-aperture transducers with short focal distances are used to ensure G is greater than »30 (Hall et al 2009;Maxwell et al 2009Maxwell et al , 2017Xu et al 2004). The focus forms as a prolate ellipsoidal volume, with typical À6-dB dimensions of »10 mm along the acoustic axis and 1-to 2-mm width lateral to the acoustic axis in a linear (lowamplitude) regime (Rosnitskiy et al 2017).…”

“…The focal volume decreases with a reduction in the f-number of the source, thereby refining the region over which bubble activity is generated. The smaller focal volume has the added effect of reducing the waveform non-linearity for a given peak negative pressure (Rosnitskiy et al 2017). That is, bubbles can be nucleated before the onset of strong non-linearities for intrinsic threshold pulses.…”