High-intensity focused ultrasound (HIFU) is a treatment modality that relies on the delivery of acoustic energy to remote tissue sites to induce thermal and/or mechanical tissue ablation. To ensure the safety and efficacy of this medical technology, standard approaches are needed for accurately characterizing the acoustic pressures generated by clinical ultrasound sources under operating conditions. Characterization of HIFU fields is complicated by nonlinear wave propagation and the complexity of phased-array transducers. Previous work has described aspects of an approach that combines measurements and modeling, and here we demonstrate this approach for a clinical phased array transducer. First, low-amplitude hydrophone measurements were performed in water over a scan plane between the array and the focus. Second, these measurements were used to holographically reconstruct the surface vibrations of the transducer and to set a boundary condition for a 3-D acoustic propagation model. Finally, nonlinear simulations of the acoustic field were carried out over a range of source power levels. Simulation results were compared to pressure waveforms measured directly by hydrophone at both low and high power levels, demonstrating that details of the acoustic field including shock formation are quantitatively predicted.
A novel numerical model was developed to simulate three-dimensional nonlinear fields generated by high intensity focused ultrasound (HIFU) arrays. The model is based on the solution to the Westervelt equation; the developed algorithm makes it possible to model nonlinear pressure fields of periodic waves in the presence of shock fronts localized near the focus. The role of nonlinear effects in a focused beam of a two-dimensional array was investigated in a numerical experiment in water. The array consisting of 256 elements and intensity range on the array elements of up to 10 W/cm2 was considered. The results of simulations have shown that for characteristic intensity outputs of modern HIFU arrays, nonlinear effects play an important role and shock fronts develop in the pressure waveforms at the focus.
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.
The propagation of nonlinear spherically diverging N-waves in homogeneous air is studied experimentally and theoretically. A spark source is used to generate high amplitude (1.4 kPa) short duration (40 μs) N-waves; acoustic measurements are performed using microphones (3 mm diameter, 150 kHz bandwidth). Numerical modeling with the generalized Burgers equation is used to reveal the relative effects of acoustic nonlinearity, thermoviscous absorption, and oxygen and nitrogen relaxation on the wave propagation. The results of modeling are in a good agreement with the measurements in respect to the wave amplitude and duration. However, the measured rise time of the front shock is ten times longer than the calculated one, which is attributed to the limited bandwidth of the microphone. To better resolve the shock thickness, a focused shadowgraphy technique is used. The recorded optical shadowgrams are compared with shadow patterns predicted by geometrical optics and scalar diffraction model of light propagation. It is shown that the geometrical optics approximation results in overestimation of the shock rise time, while the diffraction model allows to correctly resolve the shock width. A combination of microphone measurements and focused optical shadowgraphy is therefore a reliable way of studying evolution of spark-generated shock waves in air.
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