Nonlinearity is one of the phenomena that affect the ultrasonic wave during its propagation in a given medium. In the time domain the nonlinearity is seen as a variation of the phase velocity which leads to a distortion of the waveform. This corresponds in the frequency domain to energy transfer from the fundamental frequency to the harmonic and among the harmonic themselves. Our purpose in this paper is to introduce a SPICE implementation of the computational model of the nonlinear ultrasound propagation. We first study the plane wave distortion based on the Burgers’ equation. Our SPICE model allowed studying the temporal profile of the ultrasonic wave during its propagation. The simulation results are compared to the analytical solution of the Burgers’ equation showing the validity of the model. An experimental device based on ultrasonic transmission mode is used to carry out measurements and the comparison with the simulation results shows a good agreement.

References

1.
Alton Everest
,
F.
, 2001, “
Absorption of Sound
,” in
The Master Handbook of Acoustics
, 4th ed.,
McGraw-Hill
,
New York
.
2.
Pierce
,
A. D.
, 2007, “
Basic Linear Acoustics
,” in
Springer Handbook of Acoustics
,
Springer
,
New York
.
3.
Enflo
,
B. O.
, and
Hedberg
,
C. M.
, 2004, “
Physical Theory of Nonlinear Acoustics
,” in
Theory of Nonlinear Acoustics in Fluids
, Fluid Mechanics and its Applications, Vol.
67
,
Kluwer Academic
,
Dordrecht, Netherlands.
4.
Zhou
,
Y.
,
Kargl
,
S.
,
Kim
,
K.
, and
Hwang
,
J. H.
, 2008, “
Comparison of Pathway in High Intensity Focused Ultrasound (HIFU) Lesion Production
,”
Proc. Meet. Acoust.
,
2
, p.
020002
.
5.
Liu
,
Y.
,
Maruvada
,
S.
,
King
,
R. L.
,
Herman
,
B. A.
, and
Wear
,
K. A.
, 2008, “
Development and Characterization of a Blood Mimicking Fluid for High Intensity Focused Ultrasound
,”
J. Acoust. Soc. Am.
,
124
(
1
), pp.
1803
1810
.
6.
Zaitsev
,
A. V.
,
Sanghvi
,
N. T.
,
Ikenberry
,
S.
,
Worzalla
,
J. F.
,
Schultz
,
R. M.
, and
Self
,
T. D.
, 1996, “
High Intensity Focused Ultrasound (HIFU) Treatment of Human Pancreatic Cancer
,”
Proc. Ultrasin. Symp.
,
2
, pp.
1295
1298
.
7.
Rabkin
,
M. A.
,
Zderic
,
V.
, and
Vaezy
,
S.
, 2004, “
Involvement of Cavitation in the Appearance of Hyperechoic Regions in Ultrasound Image Visualization of High Intensity Focused Ultrasound Therapy: In-Vivo Results
,”
Proc. Ultrasin. Symp.
,
2
, pp.
1469
1472
.
8.
Ensminger
,
D.
, 1988,
Ultrasonics: Fundamentals, Technology, Applications
, 2nd ed.,
Marcel Dekker
,
New York
.
9.
Kuznetsov
,
V. P.
, 1971, “
Equation of Nonlinear Acoustics
,”
Sov. Phys. Acoust.
,
16
(
4
), pp.
467
470
.
10.
Zabolotskaya
,
E. A.
, and
Khokhlov
,
R. V.
, 1969, “
Quasi-Plane Waves in the Nonlinear Acoustics of Confined Beams
,”
Sov. Phys. Acoust.
,
15
(
1
), pp.
35
40
.
11.
Aanonsen
,
S. I.
,
Barkve
,
T.
, and
Tjotta
,
J. N.
, 1984, “
Distortion and Harmonic Generation in the Nearfield of a Finite Amplitude Sound Beam
,”
J. Acoust. Soc. Am.
,
75
, pp.
749
768
.
12.
Lee
,
Y. S.
, and
Hamilton
,
M. F.
, 1995, “
Time-Domain Modeling of Pulsed Finite-Amplitude Sound Beams
,”
J. Acoust. Soc. Am.
,
97
, pp.
906
917
.
13.
Christopher
,
P. T.
, and
Parker July
,
K. J.
, 1991, “
New Approaches to Nonlinear Diffractive Field Propagation
,”
J. Acoust. Soc. Am.
,
90
(
1
), pp.
488
499
.
14.
Fjellestad
,
H.
, 2000, “
Simulation of Nonlinear Ultrasound Fields Mathematical Modelling
,” Cand. Scient. thesis, University of Oslo.
15.
Leach
,
W. M.
, 1994, “
Controlled-Source Analogous Circuits and SPICE Models for Piezoelectric Transducers
,”
IEEE. Trans. Ultrason. Ferroelecr. Freq. Control
,
41
(
1
), pp.
60
66
.
16.
Püttmer
,
A.
,
Hauptmann
,
P.
,
Lucklum
,
R.
,
Krause
,
O.
, and
Henneing
,
B.
, 1997, “
SPICE Model for Lossy Piezoceramic Transducer
,”
IEEE Trans. Ultrason. Ferroelectr. Freq. Control
,
44
(
1
), pp.
60
66
.
17.
Van Deventer
,
J.
,
Löfqvist
,
T.
, and
Delsing
,
J.
, 2000, “
Pspice Simulation of Ultrasonic Systems
,”
IEEE Trans.Ultrason. Ferroelectr. Freq. Control
,
47
(
4
), pp.
1014
1024
.
18.
Johansson
,
J.
, and
Delsing
,
J.
, 2003, “
Effects of Parasitic Electrical Components on an Ultrasound System—Measurements and Simulations Using SPICE Models
,”
Trans. Mater. Devices
,
4946
, pp.
174
182
.
19.
Johansson
,
J.
, 2001, “
Optimisation of a Piezoelectric Crystal Driver Stage Using System Simulations
,”
IEEE Ultrason. Symp.
,
2
, pp
1049
1054
.
20.
Johansson
,
J.
, and
Martinsson
,
P.
, 2001, “
Incorporation of Diffraction Effects in Simulations of Ultrasonic Systems Using Pspice Models
,”
IEEE Ultrason. Symp.
,
1
, pp.
405
410
.
21.
Aouzale
,
N.
,
Chitnalah
,
A.
,
Jakjoud
,
H.
, and
Kourtiche
,
D.
, 2009, “
Experimental Validation of PSpice Modelling Diffraction Effects in Pulse Echo Ultrasonic System
,”
IEEE Trans. Circ. Syst. II
,
56
(
12
), pp.
911
915
.
22.
Aouzale
,
N.
,
Chitnalah
,
A.
,
Jakjoud
,
H.
, and
Kourtiche
,
D.
, 2008, “
PSpice Modelling of an Ultrasonic Setup for Materials Characterization
,”
Ferroelectrics
,
372
, pp.
107
114
.
23.
Blackstock
,
D. T.
, 1985, “
Generalized Burgers Equation for Plane Waves
,”
J. Acoust. Soc. Am.
,
77
(
6
), pp.
2050
2053
.
24.
Hamilton
,
M. F.
, and
Blackstock
,
D. T.
, 1998, “
History of Nonlinear Acoustics: 1750s–1930s
,” in
Nonlinear Acoustics
,
Academic
,
New York
, pp.
1
22
.
You do not currently have access to this content.