2Pb5-5
Blood flow imaging of thyroid and carotid artery using
singular value decomposition filter
特異値分解フィルタを用いた甲状腺および頸動脈の血流イメージング
Hayato Ikeda1†, Takuro Ishii2, and Yoshifumi Saijo3 (1Tohoku Univ. Graduate School of
Biomedical Engineering; 2Frontier Research Institute for Interdisciplinary Sciences;)
池田 隼人 1†，石井 琢郎 2，西條 芳文 3
(1 東北大学大学院医工学研究科, 2 東北大学学際科学フロンティア研究所）

1. Introduction
Ultrafast ultrasonic imaging based on plane ordiverging waves transmissions can acquire rich twodimensional blood flow signals at very high framerates. To visualize the blood flow signal clearly, thesingular value decomposition (SVD) filter is applied
to effectively suppress tissue clutter signal using
differences in spatiotemporal characteristics andsignal amplitude, and is known to outperformconventional clutter filters, i.e., high-pass temporal
filtering in the removal performance of tissue
signals1-2). In order to improve the accuracy of bloodflow detection, this study investigated theperformance of the SVD filter using the periodicity
of beats with a larger ensemble size. The proposed
method was validated by in vivo measurement of the
carotid artery and thyroid.
2. Materials and Methods
2.1 Experimental set up
A liner array ultrasound probe with a center
frequency of 7.6 MHz (Verasonics Inc, L11-5v) wasconnected to a programable ultrasound scanner(Verasonics Vantage 256) to acquire RF data for
ultrasound ultrasonic imaging. Carotid artery andthyroid were imaged in order to acquire ultrasonicdata of beating tissue and blood flow.
2.2 Acquisition of signals
Fig.1 shows a schematic of the sequence ofultrafast ultrasound imaging. Plane waves weretransmitted at a PRF of 5.0 kHz at steering angles of-9, -4.5, 0, 4.5, 9 degrees for compounding operation.
Hence, the frame rate of imaging was 1.0 kHz. Image
data can be expressed as a complex variable
𝐒(𝑧, 𝑥, 𝑡), which is an analytical signal at a spatialposition (depth 𝑧, lateral dimension 𝑥 ) in a frame attime 𝑡. In this paper, the analytical data were named
IQ data. The IQ data of 2000 frames (= 2.0 s) wereacquired for pulsatile flow imaging. The size of theIQ data 𝐒(𝑧, 𝑥, 𝑡) was 300 pixels × 128 pixels × 2000pixels (𝑛𝑧 × 𝑛𝑥 ×𝑛𝑡 ).

Fig. 1 Sequence of ultrafast ultrasound imaging.

2.3 Singular value decomposition
Three-dimensional
data𝐒(𝑧, 𝑥, 𝑡)wererearranged as two-dimensional data 𝐌(𝑚, 𝑛), where𝑚 and 𝑛 are the numbers of a column and a row,respectively. The covariance matrix 𝐂M (𝑛, 𝑛) of𝐌(𝑚, 𝑛) is presented here in magnitude and is ofdimension 𝑛𝑡 × 𝑛𝑡 as expressed in Eq.1,1
𝐂M (𝑖, 𝑗) = 𝑛 ∙𝑛 ∑𝑚∙𝑛(|𝐌𝑖 | − 〈|𝐌𝑖 |〉) ×𝑚𝑛(|𝐌𝑗 | − 〈|𝐌𝑗 |〉). (1)The value of 𝐂M (𝑛, 𝑛) fluctuates according to thepulsation cycle. SVD of the matrix 𝐌(𝑚, 𝑛)provides a diagonal matrix ∆ containing singularvalues 𝜆𝑖 , unitary matrix 𝐔(𝑚, 𝑚) of spatial singular
vectors, and unitary matrix 𝐕(𝑛, 𝑛) of temporal
singular vectors as expressed in Eq.2,𝐌(𝑚, 𝑛) = 𝐔 ∙ ∆ ∙ 𝐕 ∗ .
(2)The singular values 𝜆𝑖 are arranged from the mostenergetic to the least ( 𝜆1 → 𝜆2000 ). Boundary
singular vector numbers #𝑝 was chosen to obtain
SVD-filtered blood flow signals 𝐒𝑏𝑙𝑜𝑜𝑑 (𝑧, 𝑥, 𝑡) andits power integral 𝐏𝐖(𝑧, 𝑥) as expressed in Eq.(3)and Eq.(4),𝐒𝑏𝑙𝑜𝑜𝑑 (𝑧, 𝑥, 𝑡) = ∑2000
𝑖=𝑝 𝜆𝑖 ∙ 𝐔𝑖 (𝑧, 𝑥) ∙ 𝐕𝑖 (𝑡), (3)|𝐒𝐏𝐖(𝑧, 𝑥) = ∫ 𝐛𝐥𝐨𝐨𝐝 (𝑧, 𝑥, 𝑡)|2 𝑑𝑡,(4)where 𝐔𝑖 and 𝐕𝑖 are the 𝑖 th columns of 𝐔 and 𝐕 ,respectively. The choice of # 𝑝 to determine theboundary between the tissue and the blood flow
signal is achieved by using the covariance matrix of
spatial singular matrix 𝐔3).

3. Result and Discussion
Fig.2 shows B-mode images of carotid arteryand thyroid, and covariance matrix of B-mode
images from 1 to 2000 frame. It was confirmed thatthe value of the covariance matrix changed with thepulsation cycle.
Fig.3 shows set of spatiotemporal singularvectors of carotid artery (a) #2-#200, (b) #200-2000,(c) #1980-#2000. The spatial singular vectors
correspond to the spatial information of each signal,and the temporal singular vectors correspond to thetemporal change between frames. The spatial
distribution of the blood vessel wall (#2-200) has atemporal change with pulsation. The signal intensityof the spatial distribution of blood flow (#200-2000)
decreases at the timing of beating. In the other hand,the blood flow signal component contained in noise(#1980-#2000) increases. In other words, the bloodflow component shifts to the higher-order side of thesingular value during beating.
Fig.4 shows set of spatiotemporal singular
vectors of thyroid (a) #2-#150, (b) #150-2000, (c)#1980-#2000. Even in the thyroid gland, which isless affected by pulsation than the carotid artery, it
was confirmed that the spatial distribution of bloodflow decreased at the time of pulsation.
Fig.5 shows Power doppler images of blood flowof carotid artery and thyroid, respectively. Noisedepending on the depth direction could be confirmed.

Fig. 3 Set of spatiotemporal singular value vectors ofcarotid artery.

Fig. 4 Set of spatiotemporal singular value vectorsof thyroid.

4. Conclusion
In this study, the SVD filter using the periodicity
of beats with larger ensemble size was proposed toapply detecting blood vessel beating and blood flow
selectively. The proposed method was verified by invivo measurement of the carotid artery and thyroid.

Fig. 5 Power doppler images of blood flow
carotid artery and thyroid, respectively.

ofAcknowledgment
This work was supported by a Grant-in-Aid for
JSPS Research Fellow, 20J11155.
References
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3. J. Baranger, B. Arnal and C.Demene: IEEE
Trans. Med. Imaging 37, 1574 (2018)

Fig. 2 B-mode images of carotid artery and thyroid,and covariance matrix of B-mode images from 1 to2000 frame.