2Pa5-7
3D Ultrasound Imaging by Synthetic Transmit Aperture
Beamforming Obtained with a Spherically Curved ArrayTransducer
半球型アレイトランスデューサの送信開口合成による３次元
超音波イメージング
Eiki Hayashi1‡, Naoya Kanno1, Ryo Shintate1, Takuro Ishii1, Ryo Nagaoka2,and Yoshifumi Saijo1(1Graduate School of Biomedical Engineering, Tohoku
2
Univ; Graduate School of Science and Engineering for Research, Univ. of Toyama.)
林瑛己 1‡，菅野尚哉 1，新楯諒 1 , 石井琢郎 1, 長岡亮 2, 西條芳文 1 (1 東北大院 医工, 2 富山大院 理工）

1. Introduction
Imaging of micro-structures in the skin is
important for elucidating the detailed properties of
the tissue altered due to skin diseases and aging. On
this topic, photoacoustic (PA) imaging has attracted
much attention in recent years as a modality that canprovide high-contrast micro vascular images in theskin layers. Essentially, the imaging modality
acquires photoacoustic (PA) waves generated atparticles that are irradiated with laser pulses and emit
acoustic waves based on the "photoacoustic effect"[1],and has an ability to selectively visualize theparticles. We have developed a PA imaging systemequipped with a custom spherically curved arraytransducer to achieve three-dimensional PA images
with both high spatial and temporal resolution, andhave successfully visualized skin microvessels[2].
However, the obtained images lacked morphologicalinformation around the vessels. Since ultrasound(US) imaging has the potential to complement thelimitation, the optimal US imaging sequence for the
spherically curved array transducer has to bedetermined. In this study, we designed a US imaging
method for the spherical transducer using thesynthetic transmission aperture (STA) scheme andevaluated the imaging quality of the proposed
method.
2. Materials and Methods
2.1 Spherically curved array transducer
A 256-ch spherically curved arraytransducer was custom-designed and fabricated.
As shown in Fig. 1! the transducer was 42.4 mm indiameter with an opening angle of 90° and aspherical radius of 30 mm. It also had a hole of 10.4mm in diameter at the center for laser irradiation.
Each element was a square shape of approximately
2.2 × 2.2 mm. From a preliminary experiment thateiki.hayashi.p5@dc.tohoku.ac.jp

Fig. 1. Dimensions of the spherically curved
array transducer. SR: spherical radius.
transmits acoustic pulses to a metal plate, the center
frequency of the transducer was measured to be 11.5
MHz with a fractional bandwidth of approximately
62 % (8-15.5 MHz). It is noted that the specificationof the transducer was originally designed for
maximizing its sensitivity for the PA waves and thisstudy used the same transducer for US imaging inorder to achieve duplex PA-US images as a goal of
our project.
2.2 Synthetic transmit aperture (STA) method
As a scheme of ultrasound transmissions,
STA method [3] was used to! enhance image
resolution. Because of the hemispherical geometryof the transducer surface, each element transmits abeam that intersects the geometric focus of the array(Fig. 2), and the echoes are received by all theelements. This process is repeated for all N elements,
resulting in N x N echoes. Focusing is corrected by
calculating the delay time, which depends on thegeometric distance from the transmitting element tothe imaging point and the distance back to thereceiving element. The round trip delay is then1𝜏𝑚,𝑛 = [(𝑟 − 𝑟𝑚 ) + (𝑟 − 𝑟𝑛 )]
(1)
𝑐2

2

𝜏𝑖 = !"𝑥𝑝 − 𝑥𝑖# + $𝑦𝑝 − 𝑦𝑖 % + "𝑧𝑝 − 𝑧𝑖#2

𝑖 = 𝑚, 𝑛 (2)where r is the focal length (distance from eachelement to the geometric focal point), 𝑟! and 𝑟" arethe distances from the image points to the transmitterand receiver elements, respectively, c is the speed ofsound, and (𝑥# , 𝑦# , 𝑧# ), (𝑥! , 𝑦! , 𝑧! ) and (𝑥" , 𝑦" , 𝑧" ) are
the coordinates of the image pixels and transmitterand receiver elements, respectively. In the case of anarray of N elements, the image pixels of (𝑥# , 𝑦# , 𝑧# )can be expressed by
𝑀 𝑁
2𝑟(3)
𝐴𝑆𝑇𝐴 0𝑥𝑝 , 𝑦𝑝 , 𝑧𝑝 1 = 2 2 𝑦𝑚,𝑛 3 − 𝜏𝑚,𝑛 4𝑐
𝑚=1 𝑛=1
where 𝑦!," is the echo signal and 𝜏!," is the delay
time calculated in Eq. (1).

(MathWorks, Natick, USA). C-mode and B-mode
images were generated from both methods and theaxial and lateral resolutions were evaluated by
calculating full width at half maximum (FWHM) of
the copper wire in the images.
3. Result and Discussion"Fig. 3 shows the imaging result of thecopper wire in C-mode (Fig.3 (a, c)) and B-mode(Fig. 3 (b, d)) images to compare with theconventional and the STA methods. These results
showed that STA method could image the wire more
uniformly and smoothly than the conventional
method. Also, the lateral (Fig. 4(e)) and axial (Fig.
4(f)) profiles were compared between the twomethods. The FWHM in the axial and lateral
directions of the conventional methods were 128 and172 μm, respectively, while those values of STA
methods were 155 and 184 μm, respectively.
4. Conclusion

Fig. 2 Synthetic transmit aperture (STA) method
2.3 Wire phantom experiment
To investigate the spatial resolution and theeffect of artifacts, we imaged a copper wire with adiameter of 100 μm placed in water at a depth of 30mm, which is the geometrical focal point of thetransducer. The US signals were collected by aprogrammable acquisition system (Vantage 256systems, Verasonics). The transmission frequency
was 12.5 MHz and the sampling frequency was 62.5
MHz. Two methods of US imaging scheme wereused: 1)conventional method (transmitting from asingle element and receiving at all elements), 2) STA
method described in 2.2. The acquired US signals
were processed and analyzed in MATLAB

In this paper, we introduced a STA
approach for US imaging using a spherically curved
array transducer, and the imaging quality wascompared with the single element transmission
method. While the axial and lateral resolutions of
STA images were relatively low compared with theconventional method, the proposed method achieved
uniform and smooth images. It was suggested that
the STA method would be effective for US imaging
using the spherically curved array transducer.
References1. A. G. Bell: Am. J. Sci. 20 (1880) 305.
2. R. Nagaoka: IEEE Trans. Ultrason. Ferroelectr.
Freq. Control. 64 (2017) 1223
3. Y. Tasinkevych : Ultrasonics 52 (2012) 333

Fig. 3 US Imaging result of cooper wire, (a), (b) C-mode and B-mode image by conventional method. (c), (d) C-mode andB-mode image by STA method. (e), (f) The comparison of the envelope along the dotted line in C-mode image and B-modeimage.