Tuesday afternoon, 11 November - The Acoustical Society of America

ection of the resonance frequency shift is determined by the efficiency of
second-harmonic generation in modes having natural frequencies below versus
above the frequency of the second harmonic, and how the net effect of
this coupling compares with the frequency shifts due to cubic nonlinearity
and static deformation.
2:15
2pPA6. Prediction and measurement of particle velocities in ultrasonic
standing waves. Bart Lipkens, Jason Dionne, Alex Trask, Brian Szczur
Dept. of Mech. Eng., Western New England College, 1215 Wilbraham Rd.,
Springfield, MA 01119, and Ed Rietman Physical Sci. Inc., Andover, MA
01810
A numerical model has been developed to predict particle trajectories in
ultrasonic standing waves. The model includes an electroacoustic model that
calculates the characteristics of the one-dimensional standing wave as a
function of the input voltage to the piezoelectric transducer driving the
cavity. Next, the acoustic radiation force is calculated for particles residing
within the water filled cavity. Finally, the particle trajectories are calculated
through integration of the equations of motion of the particles. Particle
translation is achieved through a periodic sweeping of the excitation
frequency. Translational velocities of 6-µm-diameter polystyrene spheres are
calculated for a 2-MHz standing wave driven by a PZT-4 transducer. In the
experiment a cavity is filled with water and polystyrene particles. A PZT-4
transducer operates near its resonance frequency of 2 MHz. Through a periodic
sweeping of the frequency the particles are translated away from the
transducer face and ultimately clump together near the rigid reflector at the
opposite end. The particle translational velocity is a function of the sweep
parameters, i.e., frequency range and sweep period. The calculated particle
velocities are then compared to the measured velocities. Needle hydrophone
measurements are used to characterize the acoustic standing wave.
2:30
2pPA7. Computation of three-dimensional, pulsed, nonlinear acoustic
wavefields from medical phased array transducers in very large
domains. Jacob Huijssen, Martin D. Verweij Lab. of Electromagnetic Res.,
Fac. of Elec. Eng., Mathematics and Comput. Sci., Delft Univ. of Technol.,
Mekelweg 4, 2628 CD Delft, The Netherlands, j.huijssen@tudelft.nl, and
Nico De Jong Erasmus Medical Ctr., 3015 GR Rotterdam, The
Netherlands
For the optimization and development of medical ultrasound transducers
and imaging modalities, the iterative nonlinear contrast source INCS
method has been developed. This numerical method predicts the nonlinear
acoustic pressure field generated by a pulsed plane source with an arbitrary
aperture and propagating in a three-dimensional tissuelike medium that extends
over a very large domain of interest. The INCS method obtains the
acoustic pressure from the nonlinear acoustic wave equation by treating the
nonlinear term as a contrast source. The full nonlinear wave field is then
found by iteratively solving the linearized wave problem using a Green’s
function method. By employing the filtered convolution method discussed in
a companion paper, accurate field predictions are obtained at a discretization
approaching two points per wavelength or period of the highest frequency of
interest. In this paper, very large-scale nonlinear field profiles are presented
for transducers with cylindrical as well as phased array geometries excited
with a pulsed waveform having a center frequency of 1–2 MHz. Comparison
with the results obtained from models of reduced complexity shows that
in all cases the INCS method accurately predicts the nonlinear field. Work
supported by the STW and the NCF.
2:45
2pPA8. A filtered convolution method for the numerical evaluation of
very large-scale ultrasound problems. Martin Verweij, Jacob Huijssen
Lab. of Electromagnetic Res., Fac. of Elec. Eng., Mathematics and
Comput. Sci., Delft Univ. of Technol., Mekelweg 4, 2628 CD Delft, The
Netherlands, m.d.verweij@tudelft.nl, and Nico de Jong Erasmus Medical
Ctr., 3015 GR Rotterdam, The Netherlands
The pulsed ultrasound field in nonlinear biomedical tissue may be computed
by the recurrent evaluation of the field of a distributed contrast source
in a linear homogeneous background medium. For human organs, the computational
domain may easily measure hundreds of wavelengths or periods
in each spatiotemporal dimension. Even with today’s supercomputers, the
evaluation of the transient field from the contrast sources in these very large
inhomogeneous domains is a big challenge, and is only feasible if the applied
numerical method is extremely efficient in terms of memory usage and
computational speed. Using a Green’s function method, the critical operation
is a spatiotemporal convolution over the entire computational domain. It
is shown how a systematic filtering and windowing of the involved functions
yield accurate numerical convolutions with a discretization approaching
the Nyquist limit of two points per wavelength or period of the highest
frequency. This minimizes the storage requirement. Application of fast Fourier
transforms for evaluation of the discrete convolution sum renders a
method that is also computationally fast. The performance of a Neumann
method equipped with these numerical convolutions is shown by presenting
the computed transient wave field that traverses a very large inhomogeneous
domain. Work supported by the STW and the NCF.
2492 J. Acoust. Soc. Am., Vol. 124, No. 4, Pt. 2, October 2008 156th Meeting: Acoustical Society of America
2492