J Med Ultrasonics (2014) 41:151–153
DOI 10.1007/s10396-013-0496-6

TECHNICAL NOTE

Expanding aliasing limit in measurement of tissue velocity
using autocorrelation method
Hideyuki Hasegawa • Hiroshi Kanai

Received: 21 June 2013 / Accepted: 27 August 2013 / Published online: 3 October 2013
Ó The Japan Society of Ultrasonics in Medicine 2013

Abstract Autocorrelation using in-phase and quadrature(IQ) signals suffers from aliasing when the velocity ofrapidly moving tissue, such as the heart wall, is measured.
In the present study, a simple method was proposed toexpand the aliasing limit. In the proposed method, thevelocity difference between two successive frames (corresponding to acceleration) of tissue was also estimateddirectly from IQ signals. When aliasing occurs in thevelocity in the current frame, which was estimated from IQ
signals, the velocity in the current frame was corrected byadding the velocity difference to the velocity in the previous frame. Using this procedure, the velocity can be
estimated if the difference between velocities in the current
and previous frames is less than the aliasing limit. Thevelocity of the posterior heart wall in the longitudinal-axis
view of about 0.08 m/s could be estimated under the aliasing limit of the conventional autocorrelation method of
0.047 m/s. Myocardial velocity over the conventional aliasing limit could be measured by the proposed method.
Keywords Autocorrelation method  Aliasing Tissue velocity  Velocity difference

Introduction
It has already been shown that the measurement of tissue
motion is of great benefit for assessment of functional
imaging of tissues [1]. For this purpose, autocorrelation
using in-phase and quadrature (IQ) signals [2] is widelyused for the measurement of tissue velocity. This method
can estimate slight tissue motion accurately using the phaseshift of the IQ signal [3]. On the other hand, it suffers fromaliasing when the velocity of rapidly moving tissue, such as
the heart wall, is measured because the phase shift can be
estimated correctly between ±p. Also, the aliasing limit in
the velocity estimation depends on the ultrasonic frequency
and frame rate. In the present study, a simple method wasproposed for expanding the aliasing limit by evaluating thevelocity difference between consecutive frames.

Materials and methods
Method for expanding the aliasing limit
The velocity of a target v(z; n) at an axial position z in then-th frame can be estimated using the complex correlation
function r(z; n) of IQ signals {gn(z)} obtained from thereceived ultrasonic radio-frequency (RF) signals as follows[3]:

H. Hasegawa  H. Kanai
Graduate School of Biomedical Engineering, Tohoku University,
6-6-05 Aramaki-aza-Aoba, Aoba-ku,Sendai 980-8579, Miyagi, Japan
H. Hasegawa (&)  H. Kanai
Graduate School of Engineering, Tohoku University, 6-6-05
Aramaki-aza-Aoba, Aoba-ku, Sendai 980-8579, Miyagi, Japane-mail: hasegawa@ecei.tohoku.ac.jpv^1 ðz; nÞ ¼ c0
 \^r ðz; nÞ;
4pf0 Tð1Þ

where v^1 ðz; nÞ denotes the velocity estimated by theconventional autocorrelation method, and c0, f0, T, and \are the speed of sound in the medium, ultrasonic centerfrequency, frame interval, and phase angle, respectively.
Complex correlation function r(z; n) is defined as follows:

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Pg ðzÞ  gnþ1 ðzÞ;r^ðz; nÞ ¼ Pz2W nz2W gn ðzÞ  gnþ1 ðzÞJ Med Ultrasonics (2014) 41:151–153

ð2Þ

where W and * denote the correlation kernel and complex
conjugate, respectively. The aliasing limit vmax of theconventional autocorrelation method corresponds to themagnitude of velocity at \r (z; n) = p given by
pc0vmax ¼:
ð3Þ
4pf0 T
Figure 1a illustrates correlation functions, r(z; n-1) andr(z; n) (their phase values correspond to velocities in the(n-1)-th and n-th frames), under the presence of thealiasing effect. Even under such a condition, the change invelocity, Dv(z; n) = v(z; n)-v(z; n-1) (corresponding toacceleration), from the n-th frame to (n ? 1)-th frame canbe estimated as long as |Dv(z; n)| \ vmax. Figure 1b shows
the range of velocity satisfying this condition. Thiscondition would be valid in most cases because the heart
wall moves continuously and, thus, the change in velocity(acceleration) would be lower than the velocity itself.
Therefore, in the present study, the change in velocity wasemployed for the estimation of velocity.
Using the complex correlation functions r(z; n-1) andr(z; n) in two consecutive frames, the change in velocity
Dv(z; n) from the (n-1)-th frame to n-th frame is estimatedas follows:c0D^vðz; nÞ ¼ 
 \fr^ ðz; n  1Þ  r^ðz; nÞg:ð4Þ
4pf0 T
Instead of Eq. (1), velocity v (z; n) in the n-th frame isestimated using D^vðz; nÞ as follows:v^2 ðz; nÞ ¼ v^ðz; n  1Þ þ D^vðz; nÞ;ð5Þ

where velocity v^ðz; nÞ estimated using D^vðz; nÞ is denotedby v^2 ðz; nÞ:However, accumulation of the changes in velocity{D^vðz; nÞ} may cause an undesirable drift in the estimatedvelocity. Therefore, in the present study, velocity v(z; n) isFig. 1 a Illustration of thephase shift of IQ signals owing
to tissue motion. b Illustrationof the range of velocities
satisfying the envisioned
condition

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estimated using v^1 ðz; nÞ without the aliasing effect as muchas possible. To realize this strategy, velocity v(z; n) in then-th frame is estimated as follows:v^1 ðz; nÞ ðif jv^ðz; n  1Þ  v^1 ðz; nÞj\vmax Þ;v^ðz; nÞ ¼v^2 ðz; nÞ ðif jv^ðz; n  1Þ  v^1 ðz; nÞj  vmax Þ;ð6Þ
where v^ðz; 0Þ ¼ v^1 ðz; 0Þ and, also, the magnitude ofvelocity in the initial frame v(z; 0) should be under thealiasing limit vmax of the conventional autocorrelation
method of Eq. (1). Under such conditions, the aliasing limit
can be expanded if the acceleration of tissue is not extremely large (|v(z; n)-v(z; n-1)| \ vmax).
Experimental system
In the present study, a modified ultrasound diagnosticsystem (Aloka, SSD-6500) was used with a 3.75-MHz
phased array probe. RF signals obtained by conventionaltransmit-receive beamforming were sampled at 15 MHz at
16-bit resolution. The number of scan lines was reduced to
9 to realize a high frame rate of 445 Hz. The RF signal
along a scan line was analyzed in the M-mode format.
In vivo experimental results
In the present study, RF signals from the heart of a 26-yearold healthy male measured in vivo were analyzed. The RF
signals from the posterior wall were acquired in the parasternal long-axis view. Figure 2(1-a) and (2-a) show thesame M-mode images, and the tracking lines (red curves)
estimated by the conventional autocorrelation method [3]and the proposed method are overlaid on the M-mode
images in Fig. 2(1-a) and (2-a), respectively. Figure 2(1-b)
and (2-b) show the same electrocardiogram andphonocardiogram.
Figure 2(1-c) and (2-c) show velocities on the tracking
lines in Fig. 2(1-a) and (2-a) estimated by the conventional

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Fig. 2 In vivo experimental
results from a 26-year-old
healthy male obtained by the 1conventional autocorrelation
method and 2 proposed method.
(a) M-mode image of theposterior heart wall measured in
the parasternal long-axis viewand tracking lines (red curves).
(b) Electrocardiogram andphonocardiogram. (c) Estimatedvelocities on the red curves in(a)autocorrelation method and the proposed method, respectively. As can be seen in Fig. 2(1-a) and (1-c), on theendocardial side of the posterior wall, aliasing is found in
the velocities estimated by the conventional autocorrelation
method during the rapid filling phase due to the rapid
expansion of the left ventricle, and significant tracking
errors are also found. In that case, the aliasing limit vmax ofthe conventional autocorrelation method was 0.047 m/s (atf0 of 3.75 MHz). Using the proposed method, as shown inFig. 2(2-a) and (2-c), the aliased velocity estimates andtracking errors are corrected and the velocity of about
0.08 m/s, which is over the aliasing limit of the conventional autocorrelation method, can be estimated by theproposed method.

Conclusions
In the present study, a simple method has been proposed toexpand the aliasing limit of the autocorrelation method for theestimation of tissue motion. The proposed method utilized thevelocity difference between two consecutive frames, which wasdirectly estimated using the IQ signals. By analyzing in vivo
experimental data from a human heart, it was shown that thealiasing limit could be expanded using the proposed method.
The proposed method would be useful for measurement ofvelocity of rapidly moving tissue, such as the heart wall, as
shown in the present study. Also, the method is very simple andcan be incorporated into any type of diagnostic system.
Conflict of interest

Discussion
O’Donnell et al. [4] also tried to expand the aliasing limit
by estimating and accumulating velocity difference
between two nearest spatial points. However, in this case,
all the spatial points in the accumulation path are influenced when a spatial point with an erroneous velocity
estimate (due to various reasons such as a low signal-tonoise ratio) is included. Therefore, as discussed in theirreport [4], it is necessary to identify an appropriate accumulation path in a 2D data set (B-mode). However, in thecase of a 1D data set (M-mode), there is only one spatialaccumulation path and, thus, the proposed method is suitable because accumulation is performed in the frame
direction and a spatial point with an erroneous velocity
estimate does not affect other spatial points.

None.

Ethical considerations This study was in accordance with theinstitutional committee on human experimentation and with theHelsinki Declaration of 1975, as revised in 2008 (5). Informed consent was obtained from the subject.

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