Content uploaded by Michalakis A Averkiou
Author content
All content in this area was uploaded by Michalakis A Averkiou on Jan 11, 2016
Content may be subject to copyright.
A NEW IMAGING TECHNIQUE BASED ON THE NONLINEAR PROPERTIES
OF TISSUES
Michalakis A. Averkiou, David N. Roundhill, and Jeffry E. Powers
ATL Ultrasound, Post Office Box 3003
Bothell, Washington, 98041-3003
ABSTRACT
Finite amplitude sound propagating in a medium
undergoes distortion due to the nonlinear properties of
the medium. The nonlinear distortion produces har-
monic (and subharmonic) energy in the propagating
signal. The amplitudes used by commercial medical
scanners during routine diagnostic scanning are in most
cases finite and thus within the range that produces
nonlinear distortion. Thermoviscous absorption of tis-
sue which is frequency dependent rapidly dissipates this
harmonic energy. This has led to the widely held as-
sumption that nonlinear distortion was not a signifi-
cant factor in medical diagnostic imaging. However,
the wide dynamic range, digital architecture, and the
signal processing capabilities of modern diagnostic ul-
trasound systems make it possible to utilize this tis-
sue generated harmonic energy for image formation.
These images often demonstrate reduced nearfield arti-
facts and improved tissue structure visualization. Pre-
viously, those images were believed to be the result of
transmitted second harmonic energy. It is shown that
the nonlinear properties of tissue are the major contri-
bution of harmonic images.
INTRODUCTION
Medical ultrasound scanners are widely used in hospi-
tals all over the world for diagnostic purposes. While
many technological improvements have been achieved
over the years that resulted in better images, a large
number of patients are still difficult to image due to
problems such as tough windows, inhomogeneous skin
layers, and limited penetration.
In the recent years contrast agents have been intro-
duced to enhance ultrasound images. Contrast agents
are gas filled microbubbles with typical diameters of a
few microns that are injected into the blood and os-
cillate under insonification and thus enhance the ul-
trasonic images. The nonlinear nature of bubble dy-
namics lends itself to harmonic imaging, a procedure
by which energy is being transmitted in a fundamen-
tal frequency fand an image is formed with energy
at the second harmonic 2f. One of the original as-
sumptions in attempting harmonic imaging was that
tissue may be modeled as linear and thus only the con-
trast microbubbles in the blood would produce second
harmonic signals. The harmonic images before con-
trast microbubble injection were originally believed to
be the result of transmitted second harmonic energy
from the transducer or incomplete filtering out of the
fundamental.
Propagation of sound beams in water is known to be
nonlinear, giving rise to waveform distortion, harmonic
generation, and eventually shock formation. Water is
quite unique in terms of harmonic generation because,
while it has a nonlinearity coefficient that is very simi-
lar to the vast majority of fluids and more importantly
biological tissues, it has an extremely low absorption
coefficient (in most cases may be modeled as lossless)
and thus the shifting of energy to higher frequency
bands (due to distortion) is easily observed. Tissue,
on the other hand, has a very similar nonlinearity co-
efficient to water but a considerably higher absorption
coefficient and thus any harmonic generation is accom-
panied by excessive absorption and is not easily ob-
served.
Some of the characteristics of the nonlinearly gen-
erated second harmonic beams are a narrower beam,
lower sidelobes than the fundamental,[1] and beam for-
mation in a cumulative process–the second harmonic is
drawing energy continually along propagation from the
fundamental. These characteristics are contributing to
axial resolution improvements, reduction of multiple re-
flections due to tough windows, and clutter reduction
due to inhomogeneities in the tissue and skin layers.
The sound beams used in diagnostic ultrasound sys-
tems may be modeled with the Khokhlov-Zabolotskaya-
Kuznetsov (KZK) equation.[2, 3] This model accounts
for diffraction, absorption and nonlinearity. Since the
properties of tissue are readily available in literature,
including the coefficient of nonlinearity, nonlinear prop-
agation through tissue can be modeled with the KZK
0-7803-4153-8/97/$10.00 (C)1997 IEEE. 1997 IEEE ULTRASONICS SYMPOSIUM0-7803-4153-8/97/$10.00 (c)1997 IEEE. 1997 IEEE ULTRASONICS SYMPOSIUM
equation. In doing so we can get an estimate of the de-
gree of harmonic generation that takes place in biolog-
ical tissues. This would be an indicator as to whether
there would be enough energy in the second harmonic
band to form an image.
In this paper we first discuss the basics of nonlin-
ear beam propagation and present a theoretical model.
Experiments of harmonic generation in water and beef
tissue using an ATL HDI-3000 medical scanner are pre-
sented next. The implementation of harmonic imaging
on the ATL HDI-3000 is discussed. Radio-frequency
data of backscattered signals from cardiac and abdom-
inal images are shown to indicate the level of second
harmonic signal available for imaging. The method of
frequency compounding and its application to second
harmonic imaging is discussed. Images are shown that
emphasize the benefits of harmonic imaging.
THEORY
The combined effects of diffraction, absorption, and
nonlinearity in directive sound beams are modeled by
the KZK nonlinear parabolic wave equation:
∂2p
∂z∂t0=c0
2∇2
rp+δ
2c3
0
∂3p
∂t03+β
2ρ0c3
0
∂2p2
∂t02,(1)
where pis the sound pressure, zthe coordinate along
the axis of the beam, ∇2
r=∂2/∂r2+r−1(∂/∂r), ris
the transverse radial coordinate (the sound beam is as-
sumed to be axisymmetric for simplicity), t0=t−z/c0
the retarded time, and c0the sound speed. The first
term on the right-hand side of Eq. (1) accounts for
diffraction. The second term accounts for thermovis-
cous dissipation (δis the diffusivity of sound,[4] which
accounts for losses due to shear viscosity, bulk viscos-
ity, and heat conduction) and is proportional to the
absorption coefficient α. The third term accounts for
quadratic nonlinearity of the fluid (βis the coefficient
of nonlinearity,[5] β= 1+B/2A,andρ
0is the ambient
density of the fluid). In general, Eq. (1) is an accurate
model of the sound field produced by directive sound
sources (ka À1, where kcharacterizes the wavenum-
ber and athe radius of the source) at distances beyond
a few source radii and in regions close to the axis of the
source, the paraxial region (up to about 20◦off the z
axis in the farfield). These restrictions are satisfied in
most practical applications of directive sound beams,
including diagnostic ultrasound. The KZK equation
has been used by many researchers and was found to
be in excellent agreement with experiments.[6, 7, 8]
Nonlinear waveform distortion in water is easily ob-
served due to its low thermoviscous absorption coeffi-
cient. Tissue has similar nonlinear properties with wa-
ter but it also has a much higher absorption coefficient
which results in a faster dissipation of the harmonic
energy. This has led researchers to believe that tissue
may be modeled as linear. Table 1 shows the coefficient
of nonlinearity for various fluids and tissues.[9]
Material Coeff. of Nonlin., β=1+B/2A
water 3.5
amniotic fluid 3.6
kidney 5.5
liver 4.5
spleen 5.0
muscle 3.9
lymph node 5.1
brain 4.3
fat 6.5
Table 1: Coefficient of nonlinearity (β) for various flu-
ids and tissues.
Equation(1) is used here to model propagation of
an imaging ultrasound beam in tissue. The tissue and
source parameters are discussed first. The model as-
sumes a circular source and we use a radius of a=1cm
which has roughly the same area as the P3-2 phased ar-
ray of an ATL HDI-3000. The frequency used is f=2
MHz. For focal length we use d= 10 cm. The as-
sumed speed of sound is c= 1550 cm/s, the density is
ρ= 1050 kg/m3, and the coefficient of nonlinearity is
β= 5, which is higher than water (βwater =3.5) as is
the case for almost all kinds of tissues. For absorption
we use 0.3 dB/cm at 1 MHz with a frequency depen-
dence f1.1.Atf= 2 MHz the absorption is α0=6.4
dB/cm.
The source pressure very close to the P3-2 phased
array was measured with a Marconi membrane hydro-
phone for various system settings. During those mea-
surements we have observed that the second harmonic
level at about 5 mm away from the source is 30 dB down
from the fundamental. Since this measurement is taken
very close to the source, the edge wave (diffracted) and
the center wave (direct) are well separated and no fo-
cusing has taken place yet. For a setting where the Me-
chanical Index (MI)is1.0 the measured source pres-
sure is about 0.5 MPa. In our modeling here we use
p0= 372 kPa, a value that is even less than measured
to emphasize that nonlinear propagation takes place at
even lower amplitudes. We used a numerical code that
solves Eq.(1) in the frequency domain. The numerical
code uses three nondimensional parameters:
•An absorption parameter, A=α0d
•A nonlinearity parameter, N=d/lp, where lp=
0-7803-4153-8/97/$10.00 (C)1997 IEEE. 1997 IEEE ULTRASONICS SYMPOSIUM0-7803-4153-8/97/$10.00 (c)1997 IEEE. 1997 IEEE ULTRASONICS SYMPOSIUM
ρ0c3/βωp0is the plane wave shock formation dis-
tance, and
•The focusing gain, G=ka2/2d
According to the tissue and source parameters listed
above the nondimensional parameters were A=0.74,
N=0.60, and G=4.23.
In Fig. 1 the numerical results for propagation curves
for the first three harmonic components in tissue are
shown. The second harmonic component maximum is
0.50.0 1 1.5 2
0.001
0.01
0.1
1
10.
p/p0
z/d
Figure 1: Numerical results for propagation curves for
the first three harmonic components in tissue for A=
0.74, N=0.60, and G=4.23.
shifted by about 15% away from the transducer. This
is expected because the second harmonic component
is built from the fundamental in a cumulative pro-
cess. We may think of it as being created by a virtual
source which is a volume beginning in front of the ac-
tual source and extending along the propagation path.
The extend of this virtual source is limited by thermo-
viscous losses (attenuation) and in most practical tissue
related cases may extend up to the focal region. It is
also a more focused beam. Since near the transducer
it is still in an early development state it will not inter-
fere with path obstacles that may cause clutter. Here
we are reminded that the actual transducers are rect-
angular (and not circular as the model assumes) and
at times source apodization is used. Thus, the struc-
ture shown here for a circular source with deep nulls is
overemphasized. However, the general trends are still
the same.
In Fig. 2 the numerical results for beam patterns
at various ranges for the first three harmonic compo-
nents in tissue are shown. At all ranges it is observed
that the second (and third) harmonic beam patterns
are narrower than the fundamental as expected. In ad-
dition, the sidelobes of the harmonic beams are lower
than those of the fundamental. Even though a very
-1 -.6 -.2 .2 1.6
0.001
0.01
0.1
1
10.
0.001
0.01
0.1
1
10.
p/p0p/p0
z/d=0.5
z/d=0.7
z/d=1.0
z/d=1.4
r/a
-1 -.6 -.2 .2 1.6
r/a
(a) (b)
(c) (d)
Figure 2: Numerical results for beam patterns for the
first three harmonic components in tissue for A=0.74,
N=0.60, and G=4.23.
typical tissue absorption is used in the model, there
is still a considerable amount of second harmonic en-
ergy at the focus where the second harmonic is only 9
dB down. The beam pattern at the focus (z/d =1.0)
shows the classic Bessel directivity for the fundamen-
tal. We note that the second harmonic beam pattern
has extra sidelobes at locations where the fundamental
has nulls. These extra sidelobes are often called “fin-
gers” and have been observed in previously published
experiments.[10, 11]
EXPERIMENTS
In this section we show measurements of the beam pro-
duced by an ATL HDI-3000 P3-2 phased array in water
and beef tissue. In these measurements we address the
question of whether the second harmonic present is due
to nonlinear propagation or direct transmit at twice the
fundamental frequency.
In Fig. 3 the measured fundamental and second har-
monic beam patterns at the focus in the elevation and
transverse direction, respectively, are shown. All mea-
surements presented here were taken with a Marconi
membrane hydrophone. The output of the ultrasound
system was such that MI =0.3 (this would be the MI
reading in tissue) anda3cycletoneburst at 2 MHz
was used. The second harmonic beam patterns are
narrower beams than their corresponding fundamen-
tal beam patterns, as expected. In general, an increase
in frequency while keeping all other parameters con-
stant results in a narrower beam. However, the second
harmonic beam patterns shown in Fig. 3 show better
sidelobe suppression. The fundamental sidelobes in the
elevation plane are at about 10 dB down from the main
lobe and 14 dB in the scanplane, whereas the second
0-7803-4153-8/97/$10.00 (C)1997 IEEE. 1997 IEEE ULTRASONICS SYMPOSIUM0-7803-4153-8/97/$10.00 (c)1997 IEEE. 1997 IEEE ULTRASONICS SYMPOSIUM
0
0.2
0.4
0.6
0
0.05
0.1
0.15
0.2
50 10 15 20 25
0
0.3
0.6
0.9
1.2
p [MPa] p [MPa]p/pmax
x [mm] 50 10 15 20 25
y [mm]
scan-planeelevation-plane
fund. fund.
sec. harm. sec. harm.
Figure 3: Measurements of focal beam patterns of a
P3-2 phased array.
harmonic sidelobes are 16 dB and 20 dB down, respec-
tively.
Extra sidelobes or fingers appear at transverse po-
sitions where the fundamental has a null as in Fig. 2.
Figure 4 shows beam patterns in dB scale for a slightly
higher output setting, MI =0.6. We note the similar-
ity with Fig. 2b. If direct transmit from the transducer
50 10 15 20 25
0.001
0.01
0.1
1
y [mm]
p [MPa]
Figure 4: Measurements of focal beam patterns in dB
scale of a P3-2 phased array.
at a frequency twice the fundamental was the cause of
the second harmonic component, the finger-structure
would not be present.
Harmonic generation in beef tissue was also mea-
sured. The set-up in Fig. 5 was used. The beef tis-
sue was only 5 mm away from the transducer or the
hydrophone. A 3-cycle tone burst was used and the
output setting of the ultrasound system was such that
MI =0.5. The focus was at 8 cm and the hydrophone
was placed at 10 cm.
P3-2 phased array
beef
Marconi
hydrophone water tank
Figure 5: Experimental set-up for measurement of har-
monic generation in beef tissue.
Before the beef tissue was placed in the tank we
measured the waveform very close to the transducer (5
mm away). As shown in Fig. 6(a) the second harmonic
was 30 dB below the fundamental at this range. Next
-1
-0.5
0
0.5
1
-40
-20
0
-4
0
4
8
-40
-20
0
10 2 3 4
-1
-0.5
0
0.5
1
40 8 12 16
-80
-40
0
water
z=10 cm
beef
z=10 cm
water
z=5 mm
f [MHz]
p [MPa]p [MPa]p [MPa]
S [dB]S [dB] S [dB]
t [µs]
waveforms spectra
(a)
(b)
(c)
Figure 6: Measured waveforms at the transducer sur-
face (a), and at 10 cm away from the transducer after
propagation through beef tissue (b) and water (c).
we measured the waveform at the beef exit plane (10
cm away from the transducer), as shown in Fig. 6(b).
Finally, we removed the tissue and we measured the
waveform in Fig. 6(c). In the spectrum for the beef
waveform we see a strong second harmonic present, and
even the 4th harmonic is within 40 dB. Comparing the
0-7803-4153-8/97/$10.00 (C)1997 IEEE. 1997 IEEE ULTRASONICS SYMPOSIUM0-7803-4153-8/97/$10.00 (c)1997 IEEE. 1997 IEEE ULTRASONICS SYMPOSIUM
beef and water spectra we also calculated the attenua-
tion coefficient to be 0.8 dB/cm at 2 MHz, 1.6 dB/cm
at 4, and 2.4 dB/cm at 8, or 0.4 dB/cm/MHz.
Beam patterns at the exit plane of tissue were mea-
sured next as shown in Fig. 7. Harmonic generation
down to three harmonic components is observed for a
power setting of MI =1.0 (a setting higher than the
one used in Fig. 6). The fourth harmonic component
was also measured but it is not shown here. The fin-
ger structure, a feature very prominent of nonlinear
generation is seen in both the 2nd and 3rd harmon-
ics. The asymmetry in the beam patterns comes from
the asymmetry of the sample (not perfectly rectangu-
lar) and from the movement in the hydrophone (not
perfectly aligned).
2.50 5 7.5 10 12.5 15 17.5 20
0.01
0.005
0.001
0.05
0.1
0.5
1
p [MPa]
y [mm]
Figure 7: Beam patterns of the first three harmonic
components after propagation through beef tissue.
APPLICATION TO MEDICAL IMAGING
The implementation of harmonic imaging on an ATL
HDI-3000 is discussed here. For the cardiology appli-
cation a 4-cycle tone burst at 1.67 MHz is used. This is
at a lower frequency than what is used in conventional
imaging in order to accommodate both the transmit
and receive bands within the band width of the P3-2
phased array. It is also a longer pulse to enable separa-
tion of the received fundamental and second harmonic
bands. A similar approach is used in radiology. In
Fig. 8 we show the spectrum of typical RF-signals that
are collected back at the transducer. This is the average
spectrum of 30 scanlines (out of 128-line sector) that
pass through the myocardium. The total range of this
data is 2 cm. For this example the second harmonic
level received is 30 dB down from the fundamental.
Here we are reminded that the transducer has different
sensitivity at the fundamental and second harmonic.
The speckle artifact associated with ultrasound ima-
ging may be reduced by various frequency compound-
0246810
-60
-40
-20
0
f [MHz]
S [dB]
fundamental
2nd harm.
Figure 8: Spectrum of RF-signals from a cardiac image.
ing (or diversity) approaches.[12] These compounding
methods involve averaging signals from the same sam-
ple region that have partially decorrelated speckle pat-
terns. One approach to achieving decorrelation of spe-
ckle is to form detected signals form two or more fre-
quency bands. When these detected signals are aver-
aged, the speckle artifact is reduced.
Tissue harmonic imaging has been applied for both
cardiology and radiology settings. In both cases the im-
provement of images was in terms of clutter and haze
reduction from multipath reflection in the nearfield in
patients with tough windows and tough skin layer aber-
ration. The endocardial boarders are delineated better
in harmonic mode and the chambers are easier to see.
The presence of a fluid path like the left ventricle in car-
diology, or the aorta and the gal bladder in radiology,
seem to help the enhancement of surrounding borders
and supplied better tissue definition.
In Fig. 9 a renal cyst is imaged in conventional (fun-
damental) mode and in Fig. 10 in harmonic mode.
The cyst is better defined in harmonic mode. In addi-
tion, the haze present in conventional mode (a problem
typically encountered with 30% of the patients in radi-
ology) is removed in the harmonic mode. This obser-
vation was made repeatedly with many patients during
clinical evaluations of harmonic imaging.
CONCLUSION
A new imaging technique, Tissue Harmonic Imaging,
has been presented where the images are formed from
the second harmonic energy that results from nonlin-
ear propagation through tissue. A diagnostic ultra-
sound beam was modeled with the KZK equation and
the level of harmonic generation was predicted first.
Hydrophone measurements of a diagnostic ultrasound
beam in water and in beef tissue were used to prove that
0-7803-4153-8/97/$10.00 (C)1997 IEEE. 1997 IEEE ULTRASONICS SYMPOSIUM0-7803-4153-8/97/$10.00 (c)1997 IEEE. 1997 IEEE ULTRASONICS SYMPOSIUM
Figure 9: Renal cyst in fundamental mode.
Figure 10: Renal cyst in harmonic mode.
the second harmonic signals that are present and used
for imaging are due to nonlinear propagation and not
due to direct transmit of the harmonic frequency. The
extra sidelobes shown in the literature in the past as
an indicator of harmonic generation were also measured
in the field of a diagnostic beam. The harmonic beams
generated are narrower than the fundamental beams
that are originally transmitted, have lower sidelobes,
and suffer less aberration. The images that are formed
with this technique offer better border definition, give
better tissue contrast, and show clear improvements in
cases where tough windows and highly inhomogeneous
paths are encountered.
References
[1] T. Christopher, “Finite amplitude distortion-
based inhomogeneous pulse echo ultrasonic imag-
ing,” IEEE Trans. Ultrason. Ferr. Freq. Control
44, 125–130 (1997).
[2] E. A. Zabolotskaya and R. V. Khokhlov, “Quasi-
plane waves in the nonlinear acoustics of confined
beams,” Sov. Phys. Acoust. 15, 35–40 (1969).
[3] V. P. Kuznetsov, “Equation of nonlinear acous-
tics,” Sov. Phys. Acoust. 16, 467–470 (1970).
[4] J. Lighthill, Waves in Fluids (Cambridge Univer-
sity Press, Cambridge, 1980), pp. 78–83.
[5] R. T. Beyer, “Parameter of nonlinearity in fluids,”
J. Acoust. Soc. Am. 32, 719–721 (1960).
[6] M. A. Averkiou and M. F. Hamilton, “Nonlin-
ear distortion of short pulses radiated by plane
and focused circular pistons,” J. Acoust. Soc. Am.
102,(1997).
[7] A. C. Baker and V. F. Humphrey, “Nonlinear
propagation of short ultrasonic pulses in focused
fields,” in Frontiers of Nonlinear Acoustics: Pro-
ceedings of 12th ISNA, edited by M. F. Hamilton
and D. T. Blackstock (Elsevier Applied Science,
London, 1990), pp. 185–190.
[8] A. C. Baker, A. M. Berg and J. N. Tjøtta, “The
nonlinear pressure field of plane,rectangular aper-
tures: Experimental and theoretical results,” J.
Acoust. Soc. Am. 97, pp. 3510–3517 (1997).
[9] Francis A. Duck, Physical properties of tissue: a
comprehensive reference book (Academic Press,
London, San Diego, 1990), p. 98.
[10] M. A. Averkiou and M. F. Hamilton, “Measure-
ments of harmonic generation in a focused finite-
amplitude sound beam,” J. Acoust. Soc. Am. 98,
3439–3442 (1995).
[11] J. A. TenCate, “An experimental investigation of
the nonlinear pressure field produced by a plane
circular piston,” J. Acoust. Soc. Am. 94, 1084–
1089 (1993).
[12] Frederic L. Lizzi, Marek Elbaum, Ernest Feleppa,
“Frequency diversity for image enhancement,”
United States Patent 4,561,019, Dec. 1985
0-7803-4153-8/97/$10.00 (C)1997 IEEE. 1997 IEEE ULTRASONICS SYMPOSIUM0-7803-4153-8/97/$10.00 (c)1997 IEEE. 1997 IEEE ULTRASONICS SYMPOSIUM
