In many domains of acoustic field propagation, such as medical ultrasound imaging, lithotripsy shock treatment, and underwater sonar, a realistic calculation of beam patterns requires treatment of the effects of diffraction from finite sources. Also, the mechanisms of loss and nonlinear effects within the medium are typically nonnegligible. The combination of diffraction, attenuation, and nonlinear effects has been treated by a number of formulations and numerical techniques. A novel model that incrementally propagates the field of baffled planar sources with substeps that account for the physics of diffraction, attenuation, and nonlinearity is presented. The model accounts for the effect of refraction and reflection (but not multiple reflections) in the case of propagation through multiple, parallel layers of fluid medium. An implementation of the model for axis symmetric sources has been developed. In one substep of the implementation, a new discrete Hankel transform is used with spatial transform techniques to propagate the field over a short distance with diffraction and attenuation. In the other substep, the temporal frequency domain solution to Burgers' equation is implemented to account for the nonlinear accretion and depletion of harmonics. This approach yields a computationally efficient procedure for calculating beam patterns from a baffled planar, axially symmetric source under conditions ranging from quasilinear through shock. The model is not restricted by the usual parabolic wave approximation and the field's directionality is explicitly accounted for at each point. Useage of a harmonic-limiting scheme allows the model to propagate some previously intractable high-intensity nonlinear fields. Results of the model are shown to be in excellent agreement with measurements performed on the nonlinear field of an unfocused 2.25-MHz piston source, even in the near field where the established parabolic wave approximation model fails. Next, the model is used to compare the water path and in situ fields of a medical ultrasound device. Finally, the model is used to calculate the spatial heating rate associated with a nonlinear field and to simulate the phenomenon of saturation-induced beam broadening.

New algorithms are described that provide insight into linear field propagation and offer significant reductions in computational complexity. The developments presented here include the usage of a recently developed discrete Hankel transform to implement two single step, planar propagation algorithms for baffled, radially symmetric, acoustic pressure or velocity fields; an update on the single step approaches that reduce computational complexity through geometrically determined spatial frequency limitations; and algorithms for extending to multistep propagation. Two equivalent means of introducing arbitrary medium attenuation into the above schemes are presented. Finally, a planar boundary crossing algorithm that accounts for refraction and reflection (but not multiple reflections) is added to one of the multistep propagating algorithms. The resulting algorithm is then used to examine the differences between the corresponding fields of a focused piston source operating in water and in a layered fat/liver (biomedical imaging) medium. The results yield computationally efficient algorithms that can be used for linear propagation of focused or unfocused beams in attenuating, multilayer media, and also provide the basis for a novel nonlinear propagation algorithm.

A new algorithm for nonlinear plane-wave propagation is presented. The algorithm uses a novel time domain representation to account for nonlinearity, while accounting for absorption in the frequency domain. The new algorithm allows for accurate representations of diffractive shockwave propagation in the framework of an existing nonlinear beam propagation model using far fewer harmonics (and thus time) than alternative algorithms based on a frequency domain solution to Burgers' equation. The new algorithm is tested against the frequency domain solution to Burgers' equation in a variety of cases and then used to model a focused ultrasonic piston transducer operating at very high source intensities.

Recent work has established an analytical formulation of broadband fields which extend in the axial direction and converge to a narrow concentrated line. Those unique (needle) fields have their origins in an angular spectrum configuration in which the forward propagating wavenumber of the field ( ) is constant across any plane for all of the propagated frequencies. A 3 MHz-based, finite amplitude distorted simulation of such a field is considered here in a water path scenario relevant to medical imaging. That nonlinear simulation had its focal features compared to those of a comparable Gaussian beam. The results suggest that the unique convergence of the needle pulse to a narrow but extended axial line in linear propagation is also inherited by higher harmonics in nonlinear propagation. Furthermore, the linear needle field's relatively short duration focal pulses, and the asymptotic declines of its radial profiles, also hold for the associated higher harmonics. Comparisons with the Gaussian field highlight some unique and potentially productive features of needle fields.

Recent advances in the computation of shock wave front propagation [P. T. Christopher and K. J. Parker, J. Acoust. Soc. Am. 90, 488–499 (1991)] have allowed the prediction of spark-gap lithotripter waveforms both on and off-axis for a variety of geometries and conditions. Since in both urinary and biliary lithotripsy, shock pulses must propagate through layered human tissues (e.g., fat, muscle, and other soft tissues) it is especially important to understand how waveforms evolve in layered media. Comparisons of computational predictions and experimental results are presented for a laboratory lithotripter of our own construction whose axis of symmetry is vertical. Measurements of waveforms were made using a novel PVDF membrane hydrophone [E. C. Everbach, J. Acoust. Soc. Am. Suppl. 1 87, S128 (1990)] immersed in oil–water layers horizontally stratified by buoyancy forces. The comparisons show sufficient agreement to allow the possibility of optimizing lithotripter reflector geometries so that waveforms could be tailored to accommodate tissue configurations of individual patients.