Diffraction of nonlinear acoustic waves in inhomogeneous moving media

The combined effects of acoustic nonlinearity and diffraction on the propagation of intense acoustic waves in an inhomogeneous moving medium are investigated. A nonlinear parabolic equation that accounts for scalar inhomogeneity (spatial distribution of sound speed and density) and vector inhomogeneity (spatial distribution of medium velocity) is employed. Numerical solutions are obtained in two-dimensions using a frequency domain algorithm for both scalar and vector inhomogeneities. The results are compared with those obtained using ray theory (within the paradigm of nonlinear geometrical acoustics) in order to investigate the impact of diffraction on focusing in inhomogeneous media. It is shown that the prediction of caustics and shadow zones by nonlinear geometrical acoustics only partially corresponds to the regions of high and low pressure levels predicted with the nonlinear parabolic wave equation. The discrepancy between the results of the models increases for smaller size of inhomogeneities and for longer distances in randomly inhomogeneous media. When nonlinearity is present distorted waveforms are obtained in the diffraction field even in the shadow zones of decreased pressure due to scattering of higher frequencies for the areas of focusing

Propagation of nonlinear acoustic signals through inhomogeneous moving media

Nonlinear propagation of intense acoustic waves through inhomogeneous medium is an important problem for many modern applications including sonic booms in a turbulent atmosphere, explosive waves in a fluctuating ocean, and intense ultrasound and shock waves in biological tissue. In this work, a nonlinear parabolic wave equation with inclusion of scalar and vectorial inhomogeneities is presented. Results are presented in the case of the initially harmonic wave propagation through a 2D random velocity field. © 2004 IEEE

Numerical simulations of heating patterns and tissue temperature response due to high-intensity focused ultrasound.

The results of this paper show-for an existing high intensity, focused ultrasound (HIFU) transducer-the importance of nonlinear effects on the space/time properties of wave propagation and heat generation in perfused liver models when a blood vessel also might be present. These simulations are based on the nonlinear parabolic equation for sound propagation and the bio-heat equation for temperature generation. The use of high initial pressure in HIFU transducers in combination with the physical characteristics of biological tissue induces shock formation during the propagation of a therapeutic ultrasound wave. The induced shock directly affects the rate at which heat is absorbed by tissue at the focus without significant influence on the magnitude and spatial distribution of the energy being delivered. When shocks form close to the focus, nonlinear enhancement of heating is confined in a small region around the focus and generates a higher localized thermal impact on the tissue than that predicted by linear theory. The presence of a blood vessel changes the spatial distribution of both the heating rate and temperature

Effect of overpressure and pulse repetition frequency on cavitation in shock wave lithotripsy.

Cavitation appears to contribute to tissue injury in lithotripsy. Reports have shown that increasing pulse repetition frequency [(PRF) 0.5-100 Hz] increases tissue damage and increasing static pressure (1-3 bar) reduces cell damage without decreasing stone comminution. Our hypothesis is that overpressure or slow PRF causes unstabilized bubbles produced by one shock pulse to dissolve before they nucleate cavitation by subsequent shock pulses. The effects of PRF and overpressure on bubble dynamics and lifetimes were studied experimentally with passive cavitation detection, high-speed photography, and B-mode ultrasound and theoretically. Overpressure significantly reduced calculated (100-2 s) and measured (55-0.5 s) bubble lifetimes. At 1.5 bar static pressure, a dense bubble cluster was measured with clinically high PRF (2-3 Hz) and a sparse cluster with clinically low PRF (0.5-1 Hz), indicating bubble lifetimes of 0.5-1 s, consistent with calculations. In contrast to cavitation in water, high-speed photography showed that overpressure did not suppress cavitation of bubbles stabilized on a cracked surface. These results suggest that a judicious use of overpressure and PRF in lithotripsy could reduce cavitation damage of tissue while maintaining cavitation comminution of stones