Phase shift migration based plane-wave imaging of cortical bone

Zhang Yun-Yun; Li Yi-Fang; Shi Qin-Zhen; Xu Le-Xiu; Dai Fei; Xing Wen-Yu; Ta De-An

doi:10.7498/aps.72.20230581

Abstract

Cortical bone, a highly attenuated, anisotropic, and multilayered biological medium with high acoustic impedance, presents significant challenges for high-frequency ultrasound to penetrate its complex structure and acquire high-quality images. The traditional method of using uniform sound velocity in ultrasonic dynamic focusing imaging is limited by emission energy and frame rate, which hinders the accurate and rapid reconstruction of multi-layer structures and clinical applications. In order to meet these challenges, this study proposes a novel method, called the phase shift migration-based plane-wave bone imaging via velocity inversion (PSM-PW-VI), that can accurately and quickly image the multi-layer structure of cortical bone. In the PSM-PW-VI method, two identical linear array probes are arranged in parallel on both sides of the cortical bone for data acquisition. First, the ultrasound velocity distribution in the imaging region is obtained by using ultrasound travel time inversion. Next, two images corresponding to the upper probe and lower probe are acquired in parallel in the frequency domain by employing a phase shift migration-based coherent plane-wave compounding method. Finally, the two images are merged to generate a complete ultrasound image of the cortical bone. Wave propagation in cortical bone is simulated by using the open source toolbox k-wave in MATLAB. Ex-vivo experiments are conducted on 2.5-mm-thick sawbones phantom and 2.45-mm-thick bovine bone plates to evaluate the feasibility of the proposed method, by using the Verasonics platform. Simulation, phantom (Sawbones), and ex-vivo experiments validate the effectiveness of the method. Notably, the average error of the thickness is less than 0.2 mm, and the relative error is less than 7% for both three-layer and five-layer cortical bone. The influence of the number of plane wave compounding angles on imaging quality is investigated, revealing that only 15 angles are sufficient to produce high-quality images. The influence of the velocity model on imaging accuracy is also examined since accurate sound velocity estimation is crucial for obtaining high-quality images of cortical bone. Finally, the performances of PSM-PW-VI and PSM-SA in imaging depth and efficiency are compared. The results demonstrate that the proposed PSM-PW-VI method offers significant improvements in temporal resolution, data storage and processing quantity, emission energy, and imaging depth. The experimental findings validate the effectiveness of the proposed method as an accurate and efficient ultrasound imaging tool for cortical bone, and its substantial role in promoting ultrasound bone imaging technology and clinical applications.

Keywords:

Authors and contacts

1.
Center for Biomedical Engineering, School of Information Science and Technology, Fudan University, Shanghai 200438, China
2.
Academy for Engineering and Technology, Fudan University, Shanghai 200438, China

Corresponding author: Li Yi-Fang, yifangli@fudan.edu.cn ; Ta De-An, tda@fudan.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 11827808, 12034005, 12274094) and the China Postdoctoral Science Foundation Project (Grant No. 2022M720814)

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References

[1]	Compston J E, McClung M R, Leslie W D 2019 Lancet 393 364 Google Scholar
[2]	杨慧林 2022 中华骨与关节外科杂志 15 652 Google Scholar Yang H L 2022 Chin. J. Bone Joint Surg. 15 652 Google Scholar
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Cited By

图 1 PSM-PW-VI成像原理图

Figure 1. Schematic diagram of PSM-PW-VI.

DownLoad: Full-Size Img PowerPoint

图 2 皮质骨声速模型　(a) 三层模型皮质骨声速模型; (b) 五层模型皮质骨声速模型

Figure 2. Velocity model of cortical bone: (a) Velocity model of cortical bone with three-layer model; (b) velocity model of cortical bone with five-layer model.

DownLoad: Full-Size Img PowerPoint

图 3 实验装置示意图

Figure 3. Schematic diagram of the experimental setup.

DownLoad: Full-Size Img PowerPoint

图 4 仿真重建结果　(a)三层模型皮质骨重建结果; (b)五层模型皮质骨重建结果. 橙线为从模型提取的结构和边缘

Figure 4. Simulated reconstructed results: (a) Reconstructed result of cortical bone with three-layer model; (b) reconstructed result of cortical bone with five-layer model. Orange lines are the structure and edge extracted from the model

DownLoad: Full-Size Img PowerPoint

图 5 仿体重建结果, 其中橙线为从真实模型中提取的结构和边缘

Figure 5. Reconstructed result of phantom experiment. Orange lines are the structure and edge extracted from the true model.

DownLoad: Full-Size Img PowerPoint

图 6 离体实验结果　(a)三层模型皮质骨重建结果; (b)五层模型皮质骨重建结果. 橙线为从真实模型中提取的结构和边缘

Figure 6. Results of ex-vivo experiment: (a) Reconstructed result of three-layer model cortical bone; (b) reconstructed result of five-layer model cortical bone. Orange lines are the structure and edge extracted from the true model.

DownLoad: Full-Size Img PowerPoint

图 7 复合角度数量对CNR的影响

Figure 7. Effect of the number of compounding angles on the contrast-to-noise ratio.

DownLoad: Full-Size Img PowerPoint

图 8 五层模型皮质骨均匀声速重建结果, 其中橙线为从真实模型中提取的结构和边缘

Figure 8. Experiment reconstructed result of cortical bone with five-layer model using uniform velocity model; Orange lines are the structure and edge extracted from the true model

DownLoad: Full-Size Img PowerPoint

图 9 重建结果对比　(a) 合成孔径重建结果; (b) 平面波重建结果

Figure 9. Comparison of reconstructed results: (a) Reconstruction result using synthetic aperture method; (b) reconstruction result using plane wave method.

DownLoad: Full-Size Img PowerPoint

表 1 模型参数设置

Table 1. Model parameter setting.

	参数名称	参数值
仿真骨板模型	纵波声速V_L⊥/(m·s^–1)	2900
仿真骨板模型	质量密度/(kg·m^–3)	1850
Sawbones仿体	纵波声速V_L⊥/(m·s^–1)	2910^[34]
	质量密度/(kg·m^–3)	1850^[34]
	厚度/mm	2.50
	外径/mm	10
牛骨板	#1纵波声速V_L⊥/(m·s^–1)	3037
	#2纵波声速V_L⊥/(m·s^–1)	3159
	质量密度/(kg·m^–3)	1850
	厚度/mm	2.45

DownLoad: CSV

表 2 仿真和实验设置

Table 2. Simulation and experiment setup.

设置	仿真研究	实验研究
中心频率/MHz	3.5	3.5
脉冲周期数	2	2
采样率/MHz	25	25
相邻阵元中心/mm	0.3	0.3
外推步长/mm	0.044	0.044
–6 dB带宽/MHz	2.3—4.7	2.3—4.7
阵元间距/mm	0.1	0.1
有效孔径长度/mm	38.4	38.4
网格尺寸	0.02 mm×0.02 mm	—
时间步长/s	4×10^–9	—

DownLoad: CSV

表 3 PSM-SA与PSM-PW-VI方法计算复杂度

Table 3. Computational complexity of PSM-SA and PSM-PW-VI algorithms.

操作	PSM-SA复杂度	PSM-PW-VI复杂度
2维插值	${N_{\text{e}}}{N_x}{N_z}$	${N_{\text{p}}}{N_x}{N_z}$
${\mathscr{F} }_{x, t}\{\cdot\}$	$2{N_{\text{e}}}{N_{\text{t}}}{\log _2}({N_{\text{e}}}{N_{\text{t}}})$	${N_{\text{t}}}{\log _2}({N_{\text{t}}}) + {N_{\text{p}}}{N_{\text{e}}}{\log _2}({N_{\text{e}}})$
${\mathscr{F} }_{x}^{-1}\{\cdot\}$	$2{N_{\text{e}}}{N_x}{N_z}{\log _2}({N_x})$	${N_{\text{p}}}{N_x}{N_z}{\log _2}({N_x})$

DownLoad: CSV

表 4 PSM-SA与PSM-PW-VI方法运行时间

Table 4. Running time of PSM-SA and PSM-PW-VI imaging algorithms.

成像深度/mm	PSM-SA时间/s	PSM-PW-VI时间/s
7.5	158.37	8.26
25.0	208.27	9.79

DownLoad: CSV

[1]	Compston J E, McClung M R, Leslie W D 2019 Lancet 393 364 Google Scholar
[2]	杨慧林 2022 中华骨与关节外科杂志 15 652 Google Scholar Yang H L 2022 Chin. J. Bone Joint Surg. 15 652 Google Scholar
[3]	Langton C M, Njeh C F 2008 IEEE Trans. Ultrason. Ferroelectr. Freq. Control 55 1546 Google Scholar
[4]	东蕊, 刘成成, 蔡勋兵, 邵留磊, 李博艺, 他得安 2019 物理学报 68 150 Google Scholar Dong R, Liu C C, Cai X B, Shao L L, Li B Y, Ta D A 2019 Acta Phys. Sin. 68 150 Google Scholar
[5]	Moilanen P, Nicholson Patrick H F, Kilappa V, Cheng, Timonen 2007 Ultrasound Med. Biol. 33 254 Google Scholar
[6]	Minonzio J G, Talmant M, Laugier P 2010 J. Acoust. Soc. Am. 127 2913 Google Scholar
[7]	Manes G, Tortoli P, Andreuccetti F, Avitabile G, Atzeni C 1988 IEEE Trans. Ultrason. Ferroelectr. Freq. Control 35 14 Google Scholar
[8]	Adams R B 2022 Surg. Open Sci. 10 182 Google Scholar
[9]	Weismann C, Mayr C, Egger H, Auer A 2011 Breast Care 6 98 Google Scholar
[10]	Zu Siederdissen C H, Potthoff A 2020 Internist 61 115 Google Scholar
[11]	Nguyen Minh H, Du J, Raum K 2020 IEEE Trans. Ultrason. Ferroelectr. Freq. Control 67 568 Google Scholar
[12]	Nowicki A, Gambin B 2014 Arch. Acoust. 39 427 Google Scholar
[13]	孙宝申, 沈建中 1993 应用声学 3 43 Google Scholar Sun B S, Shen J Z 1993 Appl. Acoust. 3 43 Google Scholar
[14]	Renaud G, Kruizinga P, Cassereau D, Laugier P 2018 Phys. Med. Biol. 63 125010 Google Scholar
[15]	李云清, 江晨, 李颖, 徐峰, 许凯亮, 他得安, 黎仲勋 2019 物理学报 68 184302 Google Scholar Li Y Q, Jiang C, Li Y, Xu F, Xu K L, Ta D A, Li Z X 2019 Acta Phys. Sin. 68 184302 Google Scholar
[16]	Jiang C, Li Y, Li B, Liu C, Xu F, Xu K, Ta D 2019 IEEE Access 7 163013 Google Scholar
[17]	Jiang C, Li Y, Xu K L, Ta D A 2021 IEEE Trans. Ultrason. Ferroelectr. Freq. Control 68 72 Google Scholar
[18]	Li Y F, Shi Q Z, Liu Y, Gu M L, Liu C C, Song X J, Ta D A, Wang W Q 2021 IEEE Trans. Ultrason. Ferroelectr. Freq. Control 68 2619 Google Scholar
[19]	Montaldo G, Tanter M, Bercoff J, Benech N, Fink M 2009 IEEE Trans. Ultrason. Ferroelectr. Freq. Control 56 489 Google Scholar
[20]	Bercoff J, Montaldo G, Loupas T, Savery D, Meziere F, Fink M, Tanter M 2011 IEEE Trans. Ultrason. Ferroelectr. Freq. Control 58 134 Google Scholar
[21]	Tanter M, Fink M 2014 IEEE Trans. Ultrason. Ferroelect. Freq. Control 61 102 Google Scholar
[22]	Mace E, Montaldo G, Osmanski B F, Cohen I, Fink M, Tanter M 2013 IEEE Trans. Ultrason. Ferroelectr. Freq. Control 60 492 Google Scholar
[23]	Song P F, Trzasko J D, Manduca A, Huang R Q, Kadirvel R, Kallmes D F, Chen S G 2018 IEEE Trans. Ultrason. Ferroelect. Freq. Control 65 149 Google Scholar
[24]	Rachev R K, Wilcox P D, Velichko A, McAughey K L 2020 IEEE Trans. Ultrason. Ferroelect. Freq. Control 67 1303 Google Scholar
[25]	Lu J Y 1998 IEEE Trans. Ultrason. Ferroelect. Freq. Control 45 84 Google Scholar
[26]	Cheng J, Lu J Y 2006 IEEE Trans. Ultrason. Ferroelect. Freq. Control 53 880 Google Scholar
[27]	Garcia D, Tarnec L L, Muth S, Montagnon E, Poree J, Gloutier G 2013 IEEE Trans. Ultrason. Ferroelect. Freq. Control 60 1853 Google Scholar
[28]	Le Jeune L, Robert S, Prada C 2016 AIP Conference Proceedings 1706 020010 Google Scholar
[29]	Rakhmatov D 2021 IEEE International Symposium on Circuits and Systems (ISCAS) Daegu, South Korea, May 22–28, 2021 p22
[30]	Lukomski T 2016 Ultrasonics 70 241 Google Scholar
[31]	Gazdag J 1978 Geophysics 43 1342 Google Scholar
[32]	Treeby B E, Jaros J, Rohrbac D, Cox B T 2014 IEEE International Ultrasonics Symposium (IUS) Chicago, IL, Sep 03–06, 2014 p146
[33]	Peralta L, Cai X, Laugier P, Grimal Q 2017 Ultrasonics 80 119 Google Scholar
[34]	Li Y F, Xu K L, Li Y, Xu F, Ta D A, Wang W Q 2021 IEEE Trans. Ultrason. Ferroelectr. Freq. Control 68 935 Google Scholar
[35]	van Wijk M C, Thijssen J M 2002 Ultrasonics 40 585 Google Scholar
[36]	Li H J, Le L H, Sacchi M D, Lou E H M 2013 Ultrasound Med. Biol. 39 1482 Google Scholar
[37]	Merabet L, Robert S, Prada C 2019 IEEE Trans. Ultrason. Ferroelectr. Freq. Control 66 772 Google Scholar
[38]	Zhuang Z Y, Zhang J, Lian G X, Drinkwater B W 2020 Sensors 20 4951 Google Scholar

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