Microwave induced thermoacoustic tomography (TAT) images usually suffer from distortions arising from the microwave polarization effect and standing wave effect. The microwave polarization effect, resulting from linearly polarized microwave illumination, splits the image of the object along the polarization direction, while the standing wave effect, when the object size is larger than the microwave wavelength within the object, modulates the image of the object. Both effects cause non-uniform energy distribution in a uniformly absorbing object and create artifacts in the reconstructed images. To address these problems in TAT, we propose an image reconstruction method that combines multi-view Hilbert transformation with the back-projection algorithm. We experimentally validate this method by imaging breast and brain tumor phantoms, showing that the aforementioned distortions are significantly suppressed. We anticipate that this method will contribute to clinical tumor diagnosis

He, Yu

Liu, Changjun

Shen, Yuecheng

Wang, Lihong V.

Caltech Authors - Main

Appl. Phys. Lett. 110, 053701 (2017); https://doi.org/10.1063/1.4975204 110, 053701
© 2017 Author(s).
Suppressing excitation effects in microwave
induced thermoacoustic tomography by
multi-view Hilbert transformation
Cite as: Appl. Phys. Lett. 110, 053701 (2017); https://doi.org/10.1063/1.4975204
Submitted: 15 December 2016 . Accepted: 18 January 2017 . Published Online: 30 January 2017
Yu He, Yuecheng Shen , Changjun Liu , and Lihong V. Wang
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Suppressing excitation effects in microwave induced thermoacoustic
tomography by multi-view Hilbert transformation
Yu He,1,2 Yuecheng Shen,1 Changjun Liu,2,a) and Lihong V. Wang1,a)
1Optical Imaging Laboratory, Department of Biomedical Engineering, Washington University in St. Louis,
St. Louis, Missouri 63130, USA
2School of Electronics and Information Engineering, Sichuan University, Chengdu 610041, China
(Received 15 December 2016; accepted 18 January 2017; published online 30 January 2017)
Microwave induced thermoacoustic tomography (TAT) images usually suffer from distortions
arising from the microwave polarization effect and standing wave effect. The microwave
polarization effect, resulting from linearly polarized microwave illumination, splits the image of
the object along the polarization direction, while the standing wave effect, when the object size is
larger than the microwave wavelength within the object, modulates the image of the object. Both
effects cause non-uniform energy distribution in a uniformly absorbing object and create artifacts
in the reconstructed images. To address these problems in TAT, we propose an image reconstruc-
tion method that combines multi-view Hilbert transformation with the back-projection algorithm.
We experimentally validate this method by imaging breast and brain tumor phantoms, showing that
the aforementioned distortions are significantly suppressed. We anticipate that this method will
contribute to clinical tumor diagnosis. Published by AIP Publishing.
[http://dx.doi.org/10.1063/1.4975204]
Microwave induced thermoacoustic tomography (TAT),
combining the high contrast of microwave imaging and high
resolution of ultrasound imaging, is a potential nonionizing
candidate for breast tumor diagnosis.1–8 There are consider-
able differences in the microwave dielectric properties of
malignant tissue and normal adipose-dominant tissue in the
breast.9 When a morbid breast is irradiated by a microwave
pulse, the malignant tissue, which has a higher dielectric
loss, absorbs more energy and creates stronger thermoacous-
tic waves than the surrounding healthy tissue. The generated
thermoacoustic waves carrying information about the micro-
wave absorption distribution of the breast can be measured
by a single-element ultrasonic transducer or a transducer
array. Besides its application in breast imaging, TAT also
shows potential for brain imaging,10–12 and it is a candidate
for brain tumor detection.
The absorbed microwave power density is proportional
to the product of the local tissue loss and the squared ampli-
tude of the electric field within the irradiated medium.13
Since the reconstructed images in TAT are expected to repre-
sent the real structure of the tissue, i.e., the distribution of
dielectric loss, the tissue should be homogeneously illumi-
nated; otherwise, the images will reveal not only the differ-
ent dielectric properties but also the inhomogeneous electric
field. However, homogenous illumination is difficult to
achieve in practice. In the conventional TAT reconstruction
process,14 non-uniform microwave energy deposition in the
object distorts the TAT images for two reasons.15–17 One is
the microwave polarization effect, which occurs when the
object is under linearly polarized microwave illumination
(e.g., microwave from a pyramidal horn antenna); the other
is the microwave standing wave effect inside the object,
which arises when the object is larger than the microwave
wavelength within the object, and there is high contrast
between the object and background. Both factors cause
ambiguities in image interpretation.
Another challenge in the conventional TAT reconstruc-
tion process is that the reconstructed images present bipolar
(i.e., both positive and negative) pixel values due to the
band-pass response of the ultrasonic transducer.18 We want
to quantify the microwave energy deposition, so non-
negative pixel values are desired. Bipolar images are difficult
to interpret because both positive and negative peak values
indicate strong microwave absorption. Unipolar images can
be obtained by deconvolving the transducer’s electrical
impulse response.19,20 However, this process is usually com-
putationally time consuming.
In order to address the aforementioned problems in
conventional TAT reconstruction, we propose an image
reconstruction method combining multi-view Hilbert trans-
formation with the back-projection algorithm. After recon-
struction, the images become unipolar, and the artifacts
created by the polarization effect and standing wave effect
are significantly suppressed.
The experimental setup is shown in Fig. 1(a).
Microwave pulses transmitted from a microwave generator
(peak power: 60 kW, pulse width: 0.6 ls, frequency: 3GHz,
and repetition rate: 10Hz) were delivered to the target
through a pyramidal horn antenna (10.8 7.2 cm2). The tar-
get absorbed microwave energy and created thermoacoustic
waves. The actual averaged microwave power density at
the phantom surface was 4.7mW/cm2, which is below the
IEEE safety standard (10mW/cm2 at 3GHz).21 An ultrasonic
transducer (2.25MHz) points horizontally to the rotation
center and scans step by step around the phantom. At each
step, the induced thermoacoustic signals are received by
the transducer, amplified, and transferred to a computer for
a)Authors to whom correspondence should be addressed. Electronic addresses:
cjliu@ieee.org and lhwang@wustl.edu.
0003-6951/2017/110(5)/053701/5/$30.00 Published by AIP Publishing.110, 053701-1
APPLIED PHYSICS LETTERS 110, 053701 (2017)
image reconstruction. Details of our TAT system have been
reported in our previous work.17
In this work, multi-view Hilbert transformation is applied
to recover the envelope of the image, which converts bipolar
images into unipolar images18 and effectively suppresses the
polarization and standing wave effects. Since Hilbert transfor-
mation must be performed along the axis of the time of
arrival, i.e., the acoustic axis in the system, the direction of
the transformation needs to be altered at each scanning step.
Otherwise, the mismatch between the Hilbert transformation
direction and the acoustic axis will cause artifacts. Since the
transducer rotates around the object, the acoustic axis rotates
accordingly. Therefore, two coordinate systems are used dur-
ing the reconstruction process. As shown in Fig. 1(b), one is
the fixed global coordinates (x, y), where ai denotes the azi-
muth angle of the transducer with respect to the center. The
other one is the rotating local coordinates (xi, yi).
Here, we describe the general scheme of the reconstruc-
tion process:
1. At each rotation angle ai, we reconstruct the measured
acoustic pressure signal pið~r ; tÞ by using the filtered back-
projection (FBP) algorithm22 and thereby obtain the
reconstructed TA pressure pi0ð~rÞ. The reconstruction for-
mula is as follows:
pi0ð~rÞ ¼
ð
X
2pið~r; tÞ  2t@pið~r ; tÞ=@tdX=X;

(1)
where pið~r; tÞ is the acoustic pressure measured by the
transducer at the position ~r and time t, and the transducer
is at the angle ai. The term dX=X is a weighting factor.
Here, we note that pi0ð~rÞ presents bipolar pixel values.
2. By rotating pi0ð~rÞ by an angle of ai, we change the
global coordinates to the local coordinates. Specifically,
the pixel coordinates in these two coordinate systems are
connected by the following matrix equation:
xi
yi
 
¼ cos ai sin aisin ai cos ai
 
x
y
 
: (2)
After transforming all the pixel coordinates, the image
must be resampled using a square grid of pixel values.
We apply bilinear interpolation, which determines the
value based on the weight of the four nearest pixels and
thereby acquire pi1ð~rÞ: pi1ð~rÞ ¼ Rai ½pi0ð~rÞ, where R is the
rotating operator.
3. By taking the absolute value of the Hilbert transform of
the signal pi1ð~rÞ, we recover the envelope of the signals
and acquire pi2ð~rÞ: pi2ð~rÞ ¼ AbsfH½pi0ð~rÞg, where Abs is
the absolute value operator and H is the Hilbert transform
operator. The pixel values change from bipolar to
unipolar.
4. By rotating the signal pi2ð~rÞ back by an angle of ai, the local
coordinate system is transformed back to the global coordi-
nate system, and we acquire pi3ð~rÞ: pi3ð~rÞ ¼ Rai ½pi2ð~rÞ.
5. We repeat steps 1 to 4 for all angles and average all the
acquired images to obtain the final reconstructed image
pð~rÞ. The flow chart of the reconstruction process is shown
in Fig. 2, and the whole process can be formulated as
p ~rð Þ ¼ 1
N
XN
i¼1
Rai Abs H Rai p
i
0 ~rð Þ
    
: (3)
To reconstruct an image with 250 250 pixels, we esti-
mated that the proposed algorithm with multi-view Hilbert
transformation took about 9.2 s on our personal computer,
which was about 3 times the computational time required by
the conventional FBP (3.3 s on the same computer). We note
that the extra time consumed was mainly occupied by proc-
essing the interpolation during matrix rotation.
Using this reconstruction scheme, we validated our pro-
posed method by imaging tumor phantoms. The breast
tumor phantoms were made of porcine fat with a central
hole filled with a water-based gel, as shown in Fig. 3. The
gel, made of 3% agar and 97% water, mimicked a breast
tumor, and the surrounding porcine fat mimicked normal
breast tissue. Considering that the wavelength of a 3GHz
microwave within the tumor phantom is about 12mm, we
prepared two 10mm tall cylindrical tumor phantoms with
diameters of 10mm and 15mm to illustrate the polarization
and standing wave distortions, respectively.
We first studied the suppression of the microwave polar-
ization effect by applying our proposed multi-view Hilbert
transformation. We used a pyramidal horn antenna, radiating
linearly polarized microwaves, to illuminate the tumor
FIG. 1. (a) Experimental setup. (b) Scanning configuration. The acoustic axis changes with the rotation angle.
053701-2 He et al. Appl. Phys. Lett. 110, 053701 (2017)
phantom in Fig. 3(a). The polarization direction of the horn
antenna was along the y direction. The microwave absorption
of the tumor phantom was simulated by COMSOL finite ele-
ment software, with the result shown in Fig. 4(a). The micro-
wave absorption in the phantom is not homogeneously
distributed: it is stronger along the polarization direction and
weaker normal to the polarization direction. In the original
FBP algorithm, the reconstructed image is a direct reflection
of the microwave energy absorption in the object. Therefore,
like the simulated results, the tumor phantom splits into two
parts in the reconstructed image, as shown in Fig. 4(b). After
applying the multi-view Hilbert transformation, the “split”
pattern in the reconstructed image is well suppressed, as
shown in Fig. 4(c), which makes the image more realistic.
Another image distortion in TAT results from the micro-
wave standing wave effect. As shown in Fig. 3(b), when the
diameter of the tumor (here, 15mm) is larger than the micro-
wave wavelength in the tumor (12mm), the large dielectric
constant of the tumor causes a standing wave effect,23 giving
a non-uniform microwave absorption distribution. Fig. 5
presents the simulated microwave absorption and recon-
structed results of both linearly and circularly polarized cases.
In the linearly polarized case, the simulated microwave
absorption and the reconstructed image both show periodical
patterns along the x direction. In the circularly polarized case,
we used a helical antenna to illuminate the tumor phantom.
Unlike the pyramidal horn antenna, in which the electric field
at a fixed point in space remains pointing in a fixed direction,
the helical antenna radiates microwaves in both the x direction
and y direction, as well as in every plane in between. Although
the boundaries of the tumor are homogeneous in the simulated
microwave absorption and the reconstructed image, the micro-
wave absorption at the center of tumor is heterogeneous and
looks like three concentric circles. After applying multi-view
FIG. 3. Experimental breast tumor phantoms made of porcine fat with a
small hole at the center filled with either a 10mm (a) or a 15mm (b) diame-
ter cylindrical agar gel.
FIG. 4. Tumor phantom made of a 10mm diameter cylindrical agar gel
under linearly polarized illumination. (a) Simulated microwave absorption
of the tumor phantom. (b) Bipolar image reconstructed by using the FBP
algorithm. (c) Unipolar image reconstructed by applying the multi-view
Hilbert transformation.
FIG. 5. Tumor phantom made of a 15mm diameter cylindrical agar gel
inside porcine fat under (a) linearly polarized illumination and (b) circu-
larly polarized illumination. The left panel shows the simulated micro-
wave absorption of the tumor phantom. The middle panel shows bipolar
images reconstructed by using the FBP algorithm. The right panel shows
unipolar images reconstructed by applying the multi-view Hilbert
transformation.
FIG. 2. Flow chart of the reconstruction process.
053701-3 He et al. Appl. Phys. Lett. 110, 053701 (2017)
Hilbert transformation, the boundaries of the tumor are
strengthened, while the artifacts induced by the standing wave
effect are significantly suppressed.
In the breast tumor phantom, the dielectric contrast
between the tumor (conductivity r 3 S/m and relative
permittivity er 70) and the porcine fat (r 0.2 S/m and
er 5) is high. Thus, the porcine fat absorbs much less
microwave energy than the tumor does. Although the
absorbed microwave energy perpendicular to the microwave
polarization direction is weak, the boundaries along the
x direction can still be distinguished from the porcine fat
background in Fig. 4(b).
However, using TAT to detect brain tumors poses a
different problem: the dielectric contrast between the
tumor and the normal brain tissue (r 2.3 S/m and er 55)
is not high, which makes the boundaries of the tumor per-
pendicular to the polarization direction indiscernible. To
address this concern, we did another experiment with a
monkey brain tumor phantom. A 10mm diameter agar gel
mimicking a tumor was placed inside an ex vivo monkey
brain, as shown in Fig. 6(a). In the conventional FBP
reconstructed result, the boundaries of the tumor along the
x direction cannot be distinguished from the normal brain
tissue. The image of the tumor splits into two parts along
the polarization direction, and the shape is totally distorted,
as shown in Fig. 6(b). When the proposed multi-view
Hilbert transformation was performed, the boundaries of
the tumor were well revealed, and the shape and size of the
tumor were better presented, as shown in Fig. 6(c).
Further, in the unipolar image, the amplitude of the signals
from normal brain tissue is weakened, and the tumor
becomes more noticeable in the unipolar image due to its
stronger microwave absorption.
We note that the microwave polarization effect may also
be suppressed by using a circular polarized antenna,17 e.g., a
helical antenna, to illuminate the tumor, or by near-field imag-
ing using magnetically resonant coils.24–26 Since the standing
wave effect occurs due to the comparable size of the tumor
size and the microwave wavelength, increasing the microwave
wavelength is another way to suppress the standing wave
effect. However, the dimensions of the antenna would
increase accordingly, which would enlarge the TAT system.
To conclude, in this work, we proposed a multi-view
Hilbert transformation method combined with the back pro-
jection algorithm to suppress the microwave polarization
effect and standing wave effect in microwave induced ther-
moacoustic tomography. Moreover, unipolar images are
obtained with strengthened tumor boundaries in the images.
Thus, images reconstructed using the proposed multi-view
Hilbert transformation can potentially help physicians locate
the position and determine the size of a tumor more accu-
rately. Our method represents an important step towards clin-
ical tumor detection in the breast and brain.
This work was supported in part by the China 973
program 2013CB328902 and the China Scholarship Council.
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Suppressing excitation effects in microwave induced thermoacoustic tomography by multi-view Hilbert transformation

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Suppressing excitation effects in microwave induced thermoacoustic tomography by multi-view Hilbert transformation

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