Strain Imaging for Arterial Wall with Translational Motion
Compensation and Center Frequency Estimation
Hideyuki Hasegawa and Hiroshi Kanai
Dept. of Electronic Engineering, Graduate School of Engineering, Tohoku University, Sendai 980-8579, Japan

1. Introduction
We have developed a phase-sensitive correlation method, namely, phased-tracking method, for estimating
the displacement distribution in the arterial wall for strain imaging [1]. In such methods, ultrasonic pulses
with finite frequency bandwidths are used. Therefore, the apparent change in center frequency occurs due tothe interference of echoes from scatterers in the wall. Under such a condition, the displacement estimates arebiased because it is obtained using the phase change and center frequency of received RF echo. An
autocorrelation-based method was proposed to compensate for this apparent change in center frequency [2].
However, the performance of this method is limited because the autocorrelation technique prefers the narrow
band signals [3]. To reduce the influences of the change in center frequency, the large translational motion of
the arterial wall should be compensated because the error due to the change in center freqeucy depends onthe magnitude of the displacement ( = phase change) and the translational motion of the arterial wall is muchlarger than strain. In this study, the displacement distribution of a phantom mimicking an artery wasestimated using the autocorrelation technique with the translational motion compensation and center
frequency estimation.
2. Methods and Materials
2.1. Displacement estimation using conventional autocorrelation methods including phased-tracking method
The phases of echoes from a moving target, which is located at depth d in the initial frame, are different in
two consecutive n-th and (n+1)-th frames. This phase shift, Δθd (n), depends on the displacement of the target.
Therefore, the instantaneous displacement, Δxd (n), between these two consecutive frames is estimated asfollows:

Δx d (n) =c 0 Δθ d (n),4π f 0(1)where c0 and f0 are the speed of sound and center frequency of RF echo, respectively. The accumulated
displacement is obtained by integrating the instantaneous displacement with respect to time, and thedisplacement distribution is obtained by estimating the accumulated displacement at each depth d whichcorresponds to the arterial radial direction. Finally, strain distribution is obtained by the spatial differentiationof displacements with respect to the arterial radial direction.
2.2. Center frequency estimation based on autocorrelation
As shown by Eq. (1), in conventional phase-sensitive autocorrelation method, the knowledge of center
frequency is required to obtain the unbiased displacement estimates. Rabben, et al. introduced the center
frequency estimation based on autocorrelation technique to obtain the unbiased displacement estimates [2].

2.3. Displacement estimation with translational motion compensation
To further reduce the influence of the change incenter frequency, the translational motion of thearterial wall should be compensated. Figures
1(a) and 1(b) shows the RF echoes from thephantom used in this study before and after theincrease in the internal pressure, respectively.
The translational motion of the wall iscompensated by tracking the echo from theluminal interface because it is dominant and isFig. 1 Translational motion compensation.

less influenced by the interference from other echoes from scatterers in the wall. After compensating for thetranslational motion (Figs. 1(c) and 1(d)), the phase shift of echoes before and after the increase of internalpressure is estimated at each depth d along the radial direction of the phantom. In this case, the estimatedphase shift contains only the phase shift due to strain. Therefore, the error due to the translational motion canbe reduced.
3.

Basic Experiments Using a Phantom

In this study, the phantom was scanned in its longitudinal
direction with a 10-MHz linear array probe. RF echoes were
sampled at 40 MHz. Figure 2(a) shows the strain distribution
along the ultrasonic beam estimated by the conventional
autocorrelation method. Plots and vertical bars show means andstandard deviations of 46 ultrasonic beams. Mean values follow
the theoretical strain profile, which obtained by the measured
internal pressure and elastic modulus (749 kPa) of wall. However,standard deviations are large. In Fig. 2(b), the center frequency
estimation was applied to the conventional method. However, thestrain estimates are not improved so much. Figure 2(c) shows thestrain distribution obtained by the proposed method. Strain
estimates were improved significantly by translational motion
compensation and center frequency estimation.
4.

Conclusions

This study addressed that the apparent change in center
frequency leads significant error in strain estimation. The
proposed method with translational motion compensation andcenter frequency estimation reduces this error significantly.
References

1. H. Kanai, M. Sato, N. Chubachi, and Y. Koiwa: IEEE Trans.

Fig. 2 Estimated strain distribution. (a)Conventional method. (b) Conventional
method with center frequency estimation.
(c) Proposed method with translationalmotion compensation and center frequency
estimation.

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3. H. Hasegawa and H. Kanai: IEEE Trans. Ultrason. Ferroelect. Freq. Contr. 53 (2006) 52.