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Accuracy of backscatter coefficient estimation in
aberrating media using different phase aberration
correction strategies – A simulation study
Eduardo González1, Niral Sheth2, Benjamín Castañeda1, Jeremy Dahl2 and Roberto Lavarello1
1Laboratorio de Imágenes Médicas, Depto. de Ingeniería, Pontificia Universidad Católica del Perú, Lima, Perú.
2Biomedical Engineering Department, Duke University, Durham, USA.
Abstract—Phase aberration is the distortion of the diffraction
pattern when a w ave propagates in a medium with an
inhomogeneous sound speed. In this study, the accuracy of the
estimation of backscatter coefficients (BSCs) in the presence of
near-field phase aberrations was studied through simulations.
Further, the accuracy was also evaluated when using two
different phase aberration correction strategies prior to BSC
estimation. Simulations were performed using the FIELD II
software for pulsed ultrasound field calculation. The simulation
utilized a 45 element, 3.5 MHz linear array with 70% bandwidth.
The imaging medium consisted of randomly positioned circular
scatterers having a diameter of 176 microns. Near field phase
aberrators were applied to the transmit and receive signals of the
simulation having 50, 75, and 100 ns RMS strength and a 3 mm
correlation length. Phase aberrations were estimated using a
multi-lag least squares estimation technique. BSCs were
estimated using the reference phantom method and
radiofrequency data segments with a length of 14 wavelengths
and centered around the transducer transmit focus. BSC
estimation accuracy was quantified using the average difference
in dB between the theoretical and estimated curves within the -10
dB bandwidth of the transducer. The mean BSC estimation
errors were -9.31, -12.82 and -15.58 dB in the presence of the 50,
75 and 100 ns aberrators, respectively. The use of aberration
correction on receive was inadequate for the BSC accuracy for
all three cases. The estimation errors for the 50 ns, 75 ns and 100
ns aberrators were -7.24, -12.66 dB and -14.68 dB, respectively.
In contrast, the use of aberration correction on transmit-receive
allowed an accurate BSC estimation, with estimation errors
lower than 0.7 dB for the first two cases. These results suggest
that phase aberration effects may adversely influence the
performance of BSC estimation, and that a robust BSC-based
tissue characterization may require compensating for the effects
of aberration on both transmit and receive beams.
Keywords—Phase aberration; Backscatter coefficient;
Aberration correction; Quantitative Ultrasound;
I. INTRODUCTION
The backscatter coefficient (BSC) is a fundamental
parameter that quantifies the frequency-dependent reflectivity
of a medium. A large number of quantitative ultrasound
(QUS) imaging methods use the BSC as a tool to retrieve
crucial information about the material microstructure and have
showed favorable results in tissue characterization [1].
Backscatter coefficient estimation requires compensating
for the transducer diffraction pattern. Current methods for
diffraction compensation are based on the assumption that
ultrasound propagates in a homogeneous medium at a constant
sound speed [1, 2]. However, real sound velocities in human
tissues deviate from the nominal value of 1540 m/s depending
on the tissue type (i.e., 1470 m/s for fat and 1610 m/s for
muscle [3, 4]). As a consequence, local sound speed variations
distort the wavefront patterns and degrade the beamforming
process (i.e. image defocusing and spatial resolution and
contrast reduction) as it has been extensively reported in the B-
mode imaging literature. This phenomenon is known as phase
aberration.
Hinkelman et al. estimated arrival time fluctuations in
human chest wall that varied from 12.9 ns to 29.7 ns [5] and in
the abdominal wall, were delay differences fluctuated around
40 ns [6]. Similarly, Gauss et al. measured the phase aberration
in the human breast that ranged from 8 ns to 67 ns [7]. It can be
observed from these studies that the severity of phase
aberration can vary significantly among different tissues.
Therefore, it is important to assess how different levels of
aberration may affect different QUS methods for tissue
characterization tasks. Unfortunately, the amount of reports in
the literature on this issue is scarce, but they suggest that the
sensitivity to phase aberration is dependent on the actual QUS
parameter. For instance, Amador et al. showed that phase
aberration affects tissue elasticity imaging by decreasing the
shear waves amplitudes [8], whereas Gerig and Zagzebski
found that phase aberration had minimum repercussions for
typical phase aberration decorrelation lengths in the estimation
of scatterer sizes derived from BSCs [9].
Moreover, several phase aberration correction techniques
have been developed over the past decades for the purpose of
improving the quality of echographic imaging [PP,QQ].
However, in spite of the wide availability of these methods,
phase aberration correction has not yet been applied to the
estimation of QUS parameters, and specifically to the
estimation of backscatter coefficients.
The goal of this study is to examine through simulations the
effects of phase aberration on BSC estimation using the
reference phantom method. The usefulness of phase aberration
correction on receive and transmit/receive was explored for
reducing the effects of phase aberration on BSC estimates.
II. METHODS
A. Multi-lag least square aberration estimation
In order to properly correct phase aberration present in a
medium, time shift delays on each transducer element must be
estimated and then cancelled or reduced during beamforming.
2438978-1-4799-7049-0/14/$31.00 ©2014 IEEE 2014 IEEE International Ultrasonics Symposium Proceedings
10.1109/ULTSYM.2014.0608
In this work, a wavefront estimation method was used based on
the theoretical framework proposed by Liu and Waag [10].
Arrival time differences in the aperture were assumed to follow
phase closure, i.e., the aberration time delay between any two
elements was assumed to be the sum of the aberration time
delays of the elements in between. Aberration time delays were
estimated using the peak position of the cross-correlation of the
radio frequency (RF) signals between two elements in the
array. Multiple estimates of the aberration delays at each
element (or group of elements) were obtained by computing
aberration delays over multiple lags (distance between
elements) and selecting a reference element with an aberration
delay value of zero.
Following the work of Dahl et al. [11], a linear array of N
elements where the RF signals from each element have been
delayed to compensate for path-length differences was
considered. An overdetermined system of equations was
obtained corresponding to estimates of the arrival-time
differences d(i,k) between element i and its ten neighboring
elements (see Fig. 1) estimated using cross-correlation, i.e.,
ݐା െݐ
ൌ݀
ሺǡሻ ǡ (1)
where ݇ א ሾെͷǡെͶǡǥǡെͳǡͳǡǥǡͶǡͷ
ሿ and ti is the unknown
arrival time corresponding to the i-th element. The system of
equations can be described in matrix form as
ܣݔ ൌ ܦǡ (2)
where A is the model matrix obtained from the coefficients of
the arrival times in (1), x is a vector containing the unknown
arrival times of the elements, and D is a vector containing the
estimated delay values. Then, using the least square error
algorithm, the solution for x is
ݔൌሺܣ
்ܣሻିଵܣ்ܦ. (3)
This approach is known as the multi-lag cross-correlation
technique. The estimated time delay values are used to
compensate for aberration and to improve the beamformed
data. In an ideal situation, the estimated individual times match
the delays from the aberration profile over the isoplanatic patch
(i.e., the sector of constant aberration profile) and the
aberration is completely nullified.
Fig.1. Correlation maps for a 1-D array transducer of N elements. Echoes from
the dark-gray element are cross-correlated with those of the light-gray elements
on each basic cell for the generation of the transition matrix.
B. Backscatter coefficient estimation
The reference phantom method by Yao et al [12] was used
for backscatter coefficient estimation. First, a gated window of
length t0 was applied around the focal depth to obtain
segmented data of both the sample and reference media. Then,
the ratio between the average spectra of the sample and the
reference satisfy
ܫௌሺ߱ǡ ݖሻ
ܫோሺ߱ǡ ݖሻ ൌܴܤ
ሺ߱ሻሺെͶοߙሺ߱ሻݖሻǡ ሺͶሻ
where ܫௌሺ߱ǡ ݖሻand ܫோሺ߱ǡݖሻ are the spectra of the sample and
reference phantoms at angular frequency ߱ and depth z,
respectively, and ܴܤሺ߱ሻ and οߙሺ߱ሻ are the backscatter
coefficient ratio and attenuation coefficient difference between
reference and sample media, respectively. In this study the
media were considered to be lossless. Therefore, the
attenuation compensation term was set to 1. The reference BSC
was calculated using a fluid sphere model [13]. The BSC of the
sample was estimated using (4) within the -10 dB bandwidth of
the transducer.
C. Simulation Setup
Two homogeneous phantoms of size 35 mm x 4 mm x 30
mm were simulated and located at 25 mm from the transducer
along the axial direction. The sample and reference data was
obtained by processing the phantoms with and without phase
aberration, respectively. The scatterer density was set to 8
scatters per resolution cell. For backscatter estimation, the
region of analysis was considered to contain circular scatters
with a diameter of 176 microns.
Aberration was modeled as a set of time delays placed at
the transducer aperture, commonly called the near-field phase-
screen aberration. The aberration profile remained constant on
both transmit and receive apertures of the transducer, and the
root-mean-square (RMS) time values were scaled for 50, 75
and 100 ns for phase aberration correction analysis. Next, the
FIELD II ultrasonic wave-propagation software [14, 15] was
used to simulate pulsed-echo data from a 3.5 MHz linear array
transducer with a 70% bandwidth. The array utilized 45
elements which, for the purpose of aberration simulation, were
divided in 4 and 10 mathematical elements in the lateral and
elevation direction, respectively. The element width was 0.44
mm and the element height was 10 mm. The azimuthal and
fixed-elevation lens focus were set to 40 mm, resulting in focal
numbers of 2 and 4, respectively. Pre-beamformed data were
obtained for each aberration simulation and a 1 mm window
was used from the RF echoes of the individual channels to
estimate the profile of the aberrator. For backscatter estimation,
data segments were 14 wavelengths long (6.16 mm). Finally,
signals at 40 mm depth were processed, matching the
transducer azimuthal and elevation focus.
A series of strategies were implemented for phase
aberration correction. Each aberration profile was processed by
the following steps. First, aberrations where estimated from the
time delayed element signals. Phase aberration correction
(PAC) was performed on the receive aperture (RX PAC) by
compensating the receive delays with the inverted, estimated
aberration profile. Next, the new estimated aberration profile
was subtracted from the near-field phase aberration applied to
the transmit aperture, and a second simulation was performed,
keeping the receive aberration unchanged. The resulting
element data obtained from the simulation represented
transmit-only phase aberration correction (TX PAC). After
2439 2014 IEEE International Ultrasonics Symposium Proceedings
22.5 33.5 44. 5
0
0.5
1
1.5
2
2.5
3
3.5
Backscatter Coefficient [Sr
-1cm-1]
Fr
eque
n
cy
[
MHz
]
p
Ideal
No PAC
RX PAC
TX/RX IT3
22.5 33.5 44. 5
0
0.5
1
1.5
2
2.5
3
3.5
Backscatter Coefficient [Sr
-1cm
-1
]
Frequency [ MHz]
p
Ideal
No PAC
RX PAC
TX/RX IT3
22.5 33.5 44. 5
0
0.5
1
1.5
2
2.5
3
3.5
Backscatter Coefficient [Sr
-1cm
-1
]
Frequency [ MHz]
p
Ideal
No PAC
RX PAC
TX/RX IT3
running the multi-lag least square algorithm, PAC on transmit
and receive (TX/RX PAC) was achieved. Additionally, in
order to analyze further improvement of the correction
algorithm, additional iterations of TX/RX PAC
(transmit/receive) were computed. A quantitative comparison
of BSC estimation was based on the average difference
measured in dB between the theoretical and estimated curves
within the analysis bandwidth.
III. RESULTS
The backscatter coefficient estimation improvements
through PAC processes are shown in Figure 2, starting with the
initial aberrated data without correction (No PAC), aberration
correction on receive (RX PAC), and the final estimate after a
third iteration of the transmit/receive phase aberration
correction (TX/RX IT3). The comparative analysis of BSC
estimation errors for No PAC, RX PAC and TX/RX PAC IT 1-
3 at 50 ns, 75 ns and 100 ns aberration strength is shown in
Table 1.
The iterative PAC methods allowed estimating BSCs that
followed closely on the ideal BSC curve for both the 50 ns and
75 ns aberration strengths. For the 50 ns aberration strength,
the BSC error was largely reduced immediately after the first
TX/RX PAC iteration (i.e., the mean estimation error was
reduced from -9.31 dB to 0.14 dB). In contrast, three TX/RX
PAC iterations were needed in order to reduce the mean BSC
estimation error below 1 dB. Finally, the mean BSC estimation
error for the 100 ns aberration strength was not significantly
improved and remained above 10dB even after the third
aberration correction iteration. Although the mean value for
each simulation improved through each step of the correction
process, the standard deviation of the BSC estimates was
relatively constant throughout all studied cases.
TABLE I. BACKSCATTER ESTIMATION ERROR
50 ns R.M.S.
75 ns R.M.S.
100 ns R.M.S.
Aberrator
Mean*
STD*
Mean*
STD*
Mean*
STD*
No PAC -
9.31
2.77
-12.82
2.00
-15.58
2.42
RX PAC
-
7.24
3.51
-12.66
2.54
-14.63
2.24
TX/RX
PAC
IT 1
-
0.14
2.09
-
7.13
3.11
-12.04
1.87
IT 2
0.67
2.10
-
1.80
2.17
-11.34
2.10
IT 3
0.67
2.10
-
0.58
2.09
-10.77
2.40
*Values expressed in dB
IV. DISCUSSION
The results of this study confirm that the accuracy of BSC
estimation is dependent on the phase aberration strength. In
particular, the mean BSC estimation error ranged from -9.31
dB for the 50 ns aberration strength to -15.58 dB for the 100 ns
aberration strength. As reported in Section I, typical aberration
strengths in human soft tissues have been measured to range up
to 70 ns. However, larger aberration strengths may be observed
in particular cases, such as abdominal imaging of obese
patients. Therefore, the results of the present study are relevant
towards understanding the effects of aberration when
estimating BSCs in vivo.
Fig. 2. Backscatter coefficient estimation for (a) 50 ns (b) 75 ns and (c) 100 ns
R.M.S. aberration strength with different aberration correction strategies.
(a)
(b)
(c)
2440 2014 IEEE International Ultrasonics Symposium Proceedings
Further, the results suggest that the degree of improvement
on BSC estimation accuracy is dependent on the aberration
correction strategy as well as the aberration strength. In
particular, receive-only phase aberration correction did not
provide a significant improvement on the BSC estimation
accuracy for any of the investigated aberration strength values.
This result is particularly important because despite the success
of this approach for improving echographic imaging, receive-
only phase aberration correction may not prove beneficial for
BSC estimation.
In contrast, it was observed that transmit/receive phase
aberration correction successfully reduced the BSC estimation
error for aberration strengths up to 75 ns. As noted in Section
III, the number of iterations required for the error to converge
within a given threshold was dependent on the aberration
strength. The lack of improvement at larger aberration
strengths (e.g., 100 ns strength) was likely a limitation of the
delay estimation technique imposed by jitter and aberration
integration error.
Although the results suggest that the iterative TX/RX PAC
might be needed for improving the accuracy of BSC
estimation, several issues may be found in practice. First, in
this study the aberration compensation using the estimated time
delays was feasible with infinitesimal accuracy. In practice,
hardware limitations will result in quantization errors in the
delays that can be applied to the transducer elements on
transmit. Therefore, the effectiveness of TX/RX PAC for
improving BSC estimation may be reduced in experiments.
Second, practical implementations of RX PAC demand
significant computational resources but can be accomplished
with hardware enhancements. In contrast, TX/RX PAC with
multiple iterations require repeated transmit events, which
affects the data acquisition and imaging performance by
lowering the frame rate. Therefore, although increasing the
number of iterations may further reduce the BSC estimation
bias, in practice a trade-off between estimation accuracy and
frame rate will exist.
V. CONCLUSIONS
Several phase aberration correction strategies using a multi-
lag cross correlation method were evaluated to assess the
performance of BSC estimation in simulations. The results
indicate that phase aberration adversely affects BSC-based
tissue characterization. Phase aberration correction on receive
did not provide significant improvements of BSC estimates
while iterative corrections on transmit/receive were able to
successfully compensate for the effects of aberration strengths
up to 75 ns. Therefore, a robust estimation of BSCs in vivo
may require compensating for the effects of aberration both on
transmit and receive. Further, currently available methods for
phase aberration compensation may prove to be valuable for
improving the applicability of BSC-based quantitative
ultrasound tissue characterization.
VI. ACKNOWLEDGEMENTS
This work was supported by projects PUCP DGI 2013-
0131 and 205-FinCYT-IA-2013 funded by the Peruvian
government.
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2441 2014 IEEE International Ultrasonics Symposium Proceedings
