搜索

x

留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

基于超声RF信号熵分析的声空化时空监测方法

宋人杰 袁紫燕 张琪 于洁 薛洪惠 屠娟 章东

引用本文:
Citation:

基于超声RF信号熵分析的声空化时空监测方法

宋人杰, 袁紫燕, 张琪, 于洁, 薛洪惠, 屠娟, 章东

Method of spatiotemporally monitoring acoustic cavitation based on radio frequency signal entropy analysis

Song Ren-Jie, Yuan Zi-Yan, Zhang Qi, Yu Jie, Xue Hong-Hui, Tu Juan, Zhang Dong
PDF
HTML
导出引用
  • 高强度聚焦超声(HIFU)治疗过程中剧烈的空化效应可能损伤靶区周围健康组织, 因此, 亟需开发可对生物组织内部声空化效应进行高精度时空定量监测的新型技术手段, 方能确保临床安全和有效. 相对于传统的商用超声灰度值信号, 超声射频(RF)信号可以更好地保留声波散射信号更多的细节信息. 而信息熵作为非基于数学函数模型的统计参数, 可以表征由声空化效应引发的组织内部散射体无序度演变状态. 因此, 本文提出了一种基于超声RF信号熵分析的声空化实时监测成像系统, 在此基础上实时评估HIFU引发的超声空化区域时空演化行为. 首先, 通过改制后的B超系统获取凝胶生物仿体内部由HIFU引发的空化泡群产生的散射回波原始RF信号, 利用二维均值滤波方法抑制HIFU强声束对声空化监测成像回波信号的干扰后, 通过数据标准化处理扩展RF信号的动态变化范围, 再基于滑动窗信息熵分析重建熵值图像, 经过二值化处理后即可实现对HIFU作用下组织内部声空化区域的时空监测. 实验结果表明, 相比于传统B超灰度成像法, 基于RF信号熵分析的声空化监测成像算法可以更灵敏且精确地确定空化发生的起始时间和空间位置, 有助于更好地保障HIFU临床治疗的安全性和有效性. 本文的工作为HIFU治疗过程中组织内部声空化区域的时空监测提供一种具有极大应用前景的技术手段, 为声空化生物效应量-效评估体系的建立奠定了良好的理论和实验基础.
    The violent inertial cavitation effect generated during high intensity focused ultrasound (HIFU) treatment may damage healthy tissues around the target area. Therefore, it is urgent to develop new technical approaches that can quantitatively monitor the acoustic cavitation motions in biological tissues with high precision in space and time, so as to ensure clinical safety and effectiveness. Compared with the traditional commercial ultrasonic gray value signal, the ultrasonic radio frequency (RF) signal can well retain more detailed information about the acoustic scattering signal. As a statistical parameter not based on mathematical function model, the information entropy can characterize the spatiotemporal evolution state of disorder of scatters inside tissues resulting from acoustic cavitation. Therefore, this paper proposes a real-time monitoring system for spatiotemporal evolution of acoustic cavitation based on the entropy analysis of ultrasonic RF signals. First, the original RF signal of scattered echoes generated by HIFU-induced cavitation bubbles inside the gel phantom is obtained by using a modified B-ultrasound system, and the two-dimensional mean filtering method is used to suppress the HIFU-induced strong interferences overlapping with cavitation monitoring imaging signals. Then, the dynamic variation range of the RF signal is expanded through data standardization processing, and the entropy image is reconstructed based on the sliding window information entropy analysis to demonstrate the spatiotemporal evolution status of the HIFU-induced cavitation behanviors. The experimental results indicate that the acoustic cavitation imaging algorithm based on RF signal entropy analysis should be more sensitive and accurate than the B-model gray scale imaging method for determining the onset time and spatial position of cavitation activities, which is helpful in ensuring the safety and efficacy of HIFU clinical treatment. Thepresent work will provide a useful tool for the spatiotemporal monitoring of the acoustic cavitation generated in tissues during HIFU treatment, and lays a solid theoretical and experimental foundation to establish an effective quantity-effect evaluation system for the cavitation related biological effect.
      通信作者: 屠娟, juantu@nju.edu.cn
    • 基金项目: 国家自然科学基金(批准号: 11774166, 11774168)和声场声信息国家重点实验室开放课题(批准号: SKLA202212)资助的课题
      Corresponding author: Tu Juan, juantu@nju.edu.cn
    • Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 11774166, 11774168) and the State Key Laboratory of Acoustics, Institute of Acoustics, Chinese Academy of Sciences (Grant No. SKLA202212).
    [1]

    Kennedy J E 2005 Nat. Rev. Cancer 5 321Google Scholar

    [2]

    Izadifar Z, Izadifar Z, Chapman D, Babyn P 2020 J. Clin. Med. 9 460Google Scholar

    [3]

    秦对, 邹青钦, 李章勇, 王伟, 万明习, 冯怡 2021 物理学报 70 154701Google Scholar

    Qin D, Zou Q Q, Li Z Y, Wang W, Wan M X, Feng Y 2021 Acta Phys. Sin. 70 154701Google Scholar

    [4]

    Yang Y Y, Li Q, Guo X S, Tu J, Zhang D 2020 Ultrason. Sonochem. 67 105096Google Scholar

    [5]

    于洁, 郭霞生, 屠娟, 章东 2015 物理学报 64 094306Google Scholar

    Yu J, Guo X S, Tu J, Zhang D 2015 Acta Phys. Sin. 64 094306Google Scholar

    [6]

    Valle L F, Lehrer E J, Markovic D, Elashoff D, Levin-Epstein R, Karnes R J, Reiter R E, Rettig M, Calais J, Nickols N G, Dess R T, Spratt D E, Steinberg M L, Nguyen P L, Davis B J, Zaorsky N G, Kishan A U 2021 Eur. Urol. 80 280Google Scholar

    [7]

    Yoshizawa S, Ikeda T, Ito A, Ota R, Takagi S, Matsumoto Y 2009 Med. Biol. Eng. Comput. 47 851Google Scholar

    [8]

    Zderic V, Keshavarzi A, Noble M L, Paun M, Sharar S R, Crum L A, Martin R W, Vaezy S 2006 Ultrasonics 44 46Google Scholar

    [9]

    Ilyas A, Chen C J, Ding D, Romeo A, Buell T J, Wang T R, Kalani M Y S, Park M S 2018 Neurosurg Focus 44 E12Google Scholar

    [10]

    Bader K B, Vlaisavljevich E, Maxwell A D 2019 Ultrasound Med. Biol. 45 1056Google Scholar

    [11]

    耿昊, 范庭波, 张喆, 屠娟, 郭霞生, 李发琪, 章东 2014 物理学报 63 044301Google Scholar

    Geng H, Fan T B, Zhang Z, Tu J, Guo X S, Li F Q, Zhang D 2014 Acta Phys. Sin. 63 044301Google Scholar

    [12]

    Yang D X, Ni Z Y, Yang Y Y, Xu G Y, Tu J, Guo X S, Huang P T, Zhang D 2018 Ultrason. Sonochem. 49 111Google Scholar

    [13]

    Tu J, Swalwell J E, Giraud D, Cui W C, Chen W Z, Matula T J 2011 IEEE Trans. Ultrason. Ferroelectr. Freq. Control 58 955Google Scholar

    [14]

    Song R J, Zhang C B, Teng F M, Tu J, Guo X S, Fan Z, Zheng Y F, Zhang D 2021 Ultrason. Sonochem. 79 105790

    [15]

    Fan P F, Yu J, Yang X, Tu J, Guo X S, Huang P T, Zhang D 2017 Chin. Phys. B 26 054301Google Scholar

    [16]

    钱骏, 谢伟, 周小伟, 谭坚文, 王智彪, 杜永洪, 李雁浩 2022 物理学报 71 037201Google Scholar

    Qian J, Xie W, Zhou X W, Tan J W, Wang Z B, Du Y H, Li Y H 2022 Acta Phys. Sin. 71 037201Google Scholar

    [17]

    Liu T, Yu D, Beitler J, Tridandapani S, Bruner D, Curran W, Yang X 2013 Med. Phys. 40 495Google Scholar

    [18]

    Zhang S, Li C, Zhou F Y, Wan M X, Wang S P 2014 J. Ultrasound Med. 33 959Google Scholar

    [19]

    Tsui P H, Chen C K, Kuo W H, Chang K J, Fang J, Ma H Y, Chou D 2017 Sci. Rep. 7 41004Google Scholar

    [20]

    Shankar P M 2000 IEEE Trans. Ultrason. Ferroelectr. Freq. Control 47 727Google Scholar

    [21]

    Tsui P H 2015 Entropy 17 6598Google Scholar

    [22]

    Hughes M S, Marsh J N, Wallace K D, Donahue T A, Connolly A M, Lanza G M, Wickline S A 2007 Ultrasound Med. Biol. 33 1236Google Scholar

    [23]

    Zhou Z H, Huang C C, Shung K K, Tsui P H, Fang J, Ma H Y, Wu S C, Lin C C 2014 PLoS One 9 e96195Google Scholar

    [24]

    Xu Z, Hall T L, Fowlkes J B, Cain C A 2007 J. Acoust. Soc. Am. 122 229Google Scholar

    [25]

    张玫玫, 高凡, 屠娟, 吴意赟, 章东 2021 物理学报 70 084302Google Scholar

    Zhang M M, Gao F, Tu J, Wu Y Y, Zhang D 2021 Acta Phys. Sin. 70 084302Google Scholar

    [26]

    Tuthill T A, Sperry R H, Parker K J 1988 Ultrasonic Imaging 10 81Google Scholar

    [27]

    Fan T B, Tu J, Luo L J, Guo X S, Huang P T, Zhang D 2016 Chin. Phys. Lett. 33 084302Google Scholar

    [28]

    陈楚怡, 于洁, 陈功, 马勇, 郭霞生, 屠娟, 章东 2015 声学学报 40 563Google Scholar

    Chen C Y, Yu J, Chen G, Ma Y, Guo X S, Tu J, Zhang D 2015 Acta Acustica 40 563Google Scholar

    [29]

    Yu J, Chen C Y, Chen G, Guo X S, Ma Y, Tu J, Zhang D 2014 Chin. Phys. Lett. 31 034302Google Scholar

    [30]

    Lee J S 1980 IEEE Trans. Pattern Anal. Mach. Intell. 2 165Google Scholar

    [31]

    Liao P S, Chew T S, Chung P C 2001 J. Inf. Sci. Eng. 17 713

    [32]

    吴俊, 汪源源, 陈悦, 余锦华, 庞芸 2014 光学精密工程 22 1312Google Scholar

    Wu J J, Wang Y Y, Chen Y, Yu J H, Pang Y 2014 Opt. and Precision Eng. 22 1312Google Scholar

    [33]

    Tsui P H, Chang C C 2007 Ultrasound Med. Biol. 33 608Google Scholar

    [34]

    Tsui P H, Wan Y L 2016 Entropy 18 341Google Scholar

    [35]

    Bailey M R, Khokhlova V A, Sapozhnikov O A, Kargl S G, Crum L A 2003 Acoust. Phys. 49 369Google Scholar

    [36]

    Vaezy S, Shi X G, Martin R W, Chi E, Nelson P I, Bailey M R, Crum L A 2001 Ultrasound Med. Biol. 27 33Google Scholar

  • 图 1  实验原理图

    Fig. 1.  Diagram of experimental schematic.

    图 2  基于B超灰度图像与RF信号熵分析监测HIFU空化区域算法示意图

    Fig. 2.  The algorithmic scheme designed for cavitation monitoring imaging based on B-mode and RF entropy images.

    图 3  不同时刻治疗区域的图像 (a) 初步B模式图像; (b) 去干扰后初步B模式图像; (c) 熵值图像; (d) 经二值化处理后的熵值图像

    Fig. 3.  Images at different treatment moments: (a) Preliminary B-mode images; (b) preliminary B-mode images after de-interference; (c) entropy images; (d) binary images at different treatment moments.

    图 4  标准化操作前后熵值图像及幅值分布图 (a) 未经标准化处理得到的熵值图像; (b) 未经标准化得到的熵值分布直方图; (c) 经过标准化处理得到的熵值图像; (d) 经过标准化得到的熵值分布直方图

    Fig. 4.  Entropy image and amplitude distribution before and after standardization: (a) Entropy image obtained without normalization; (b) histogram of entropy distribution obtained without normalization; (c) entropy image obtained with normalization; (d) histogram of entropy distribution obtained with normalization

    图 5  不同声压下分别基于灰度值法与熵值法得到的实时空化范围趋势图

    Fig. 5.  Real-time cavitation range trend based on gray value method and entropy value method respectively under different sound pressure.

    图 6  原始BFRF数据与检波后BFRF数据的频谱对比 (a) 初步B模式图像; (b) 检波前后数据频谱

    Fig. 6.  Comparison of frequency spectrum of the raw BFRF data and the BFRF data after demodulation: (a) Preliminary B-mode image; (b) data frequency spectrum pre- and post- demodulation

    图 7  一帧B超影像与熵值图像反映空化范围的典型例子 (a) 一帧B超影像; (b) 去干扰后B超影像; (c) 同一帧基于BFRF的初步B模式图像; (d) 同一帧熵值图像

    Fig. 7.  A typical example of a frame of ultrasound image and entropy image reflecting the range of cavitation: (a) A frame of ultrasound image; (b) the de-interfered ultrasound image; (c) the same frame of BFRF-based preliminary B-mode image; (d) the same frame of entropy image.

  • [1]

    Kennedy J E 2005 Nat. Rev. Cancer 5 321Google Scholar

    [2]

    Izadifar Z, Izadifar Z, Chapman D, Babyn P 2020 J. Clin. Med. 9 460Google Scholar

    [3]

    秦对, 邹青钦, 李章勇, 王伟, 万明习, 冯怡 2021 物理学报 70 154701Google Scholar

    Qin D, Zou Q Q, Li Z Y, Wang W, Wan M X, Feng Y 2021 Acta Phys. Sin. 70 154701Google Scholar

    [4]

    Yang Y Y, Li Q, Guo X S, Tu J, Zhang D 2020 Ultrason. Sonochem. 67 105096Google Scholar

    [5]

    于洁, 郭霞生, 屠娟, 章东 2015 物理学报 64 094306Google Scholar

    Yu J, Guo X S, Tu J, Zhang D 2015 Acta Phys. Sin. 64 094306Google Scholar

    [6]

    Valle L F, Lehrer E J, Markovic D, Elashoff D, Levin-Epstein R, Karnes R J, Reiter R E, Rettig M, Calais J, Nickols N G, Dess R T, Spratt D E, Steinberg M L, Nguyen P L, Davis B J, Zaorsky N G, Kishan A U 2021 Eur. Urol. 80 280Google Scholar

    [7]

    Yoshizawa S, Ikeda T, Ito A, Ota R, Takagi S, Matsumoto Y 2009 Med. Biol. Eng. Comput. 47 851Google Scholar

    [8]

    Zderic V, Keshavarzi A, Noble M L, Paun M, Sharar S R, Crum L A, Martin R W, Vaezy S 2006 Ultrasonics 44 46Google Scholar

    [9]

    Ilyas A, Chen C J, Ding D, Romeo A, Buell T J, Wang T R, Kalani M Y S, Park M S 2018 Neurosurg Focus 44 E12Google Scholar

    [10]

    Bader K B, Vlaisavljevich E, Maxwell A D 2019 Ultrasound Med. Biol. 45 1056Google Scholar

    [11]

    耿昊, 范庭波, 张喆, 屠娟, 郭霞生, 李发琪, 章东 2014 物理学报 63 044301Google Scholar

    Geng H, Fan T B, Zhang Z, Tu J, Guo X S, Li F Q, Zhang D 2014 Acta Phys. Sin. 63 044301Google Scholar

    [12]

    Yang D X, Ni Z Y, Yang Y Y, Xu G Y, Tu J, Guo X S, Huang P T, Zhang D 2018 Ultrason. Sonochem. 49 111Google Scholar

    [13]

    Tu J, Swalwell J E, Giraud D, Cui W C, Chen W Z, Matula T J 2011 IEEE Trans. Ultrason. Ferroelectr. Freq. Control 58 955Google Scholar

    [14]

    Song R J, Zhang C B, Teng F M, Tu J, Guo X S, Fan Z, Zheng Y F, Zhang D 2021 Ultrason. Sonochem. 79 105790

    [15]

    Fan P F, Yu J, Yang X, Tu J, Guo X S, Huang P T, Zhang D 2017 Chin. Phys. B 26 054301Google Scholar

    [16]

    钱骏, 谢伟, 周小伟, 谭坚文, 王智彪, 杜永洪, 李雁浩 2022 物理学报 71 037201Google Scholar

    Qian J, Xie W, Zhou X W, Tan J W, Wang Z B, Du Y H, Li Y H 2022 Acta Phys. Sin. 71 037201Google Scholar

    [17]

    Liu T, Yu D, Beitler J, Tridandapani S, Bruner D, Curran W, Yang X 2013 Med. Phys. 40 495Google Scholar

    [18]

    Zhang S, Li C, Zhou F Y, Wan M X, Wang S P 2014 J. Ultrasound Med. 33 959Google Scholar

    [19]

    Tsui P H, Chen C K, Kuo W H, Chang K J, Fang J, Ma H Y, Chou D 2017 Sci. Rep. 7 41004Google Scholar

    [20]

    Shankar P M 2000 IEEE Trans. Ultrason. Ferroelectr. Freq. Control 47 727Google Scholar

    [21]

    Tsui P H 2015 Entropy 17 6598Google Scholar

    [22]

    Hughes M S, Marsh J N, Wallace K D, Donahue T A, Connolly A M, Lanza G M, Wickline S A 2007 Ultrasound Med. Biol. 33 1236Google Scholar

    [23]

    Zhou Z H, Huang C C, Shung K K, Tsui P H, Fang J, Ma H Y, Wu S C, Lin C C 2014 PLoS One 9 e96195Google Scholar

    [24]

    Xu Z, Hall T L, Fowlkes J B, Cain C A 2007 J. Acoust. Soc. Am. 122 229Google Scholar

    [25]

    张玫玫, 高凡, 屠娟, 吴意赟, 章东 2021 物理学报 70 084302Google Scholar

    Zhang M M, Gao F, Tu J, Wu Y Y, Zhang D 2021 Acta Phys. Sin. 70 084302Google Scholar

    [26]

    Tuthill T A, Sperry R H, Parker K J 1988 Ultrasonic Imaging 10 81Google Scholar

    [27]

    Fan T B, Tu J, Luo L J, Guo X S, Huang P T, Zhang D 2016 Chin. Phys. Lett. 33 084302Google Scholar

    [28]

    陈楚怡, 于洁, 陈功, 马勇, 郭霞生, 屠娟, 章东 2015 声学学报 40 563Google Scholar

    Chen C Y, Yu J, Chen G, Ma Y, Guo X S, Tu J, Zhang D 2015 Acta Acustica 40 563Google Scholar

    [29]

    Yu J, Chen C Y, Chen G, Guo X S, Ma Y, Tu J, Zhang D 2014 Chin. Phys. Lett. 31 034302Google Scholar

    [30]

    Lee J S 1980 IEEE Trans. Pattern Anal. Mach. Intell. 2 165Google Scholar

    [31]

    Liao P S, Chew T S, Chung P C 2001 J. Inf. Sci. Eng. 17 713

    [32]

    吴俊, 汪源源, 陈悦, 余锦华, 庞芸 2014 光学精密工程 22 1312Google Scholar

    Wu J J, Wang Y Y, Chen Y, Yu J H, Pang Y 2014 Opt. and Precision Eng. 22 1312Google Scholar

    [33]

    Tsui P H, Chang C C 2007 Ultrasound Med. Biol. 33 608Google Scholar

    [34]

    Tsui P H, Wan Y L 2016 Entropy 18 341Google Scholar

    [35]

    Bailey M R, Khokhlova V A, Sapozhnikov O A, Kargl S G, Crum L A 2003 Acoust. Phys. 49 369Google Scholar

    [36]

    Vaezy S, Shi X G, Martin R W, Chi E, Nelson P I, Bailey M R, Crum L A 2001 Ultrasound Med. Biol. 27 33Google Scholar

  • [1] 汪亭亭, 梁宗文, 张若曦. 基于信息熵与迭代因子的复杂网络节点重要性评价方法. 物理学报, 2023, 72(4): 048901. doi: 10.7498/aps.72.20221878
    [2] 张玫玫, 高凡, 屠娟, 吴意赟, 章东. 非线性超声射频信号熵对乳腺结节良恶性的定征. 物理学报, 2021, 70(8): 084302. doi: 10.7498/aps.70.20201919
    [3] 刘备, 胡伟鹏, 邹孝, 丁亚军, 钱盛友. 基于变分模态分解与多尺度排列熵的生物组织变性识别. 物理学报, 2019, 68(2): 028702. doi: 10.7498/aps.68.20181772
    [4] 吴文华, 翟薇, 胡海豹, 魏炳波. 液体材料超声处理过程中声场和流场的分布规律研究. 物理学报, 2017, 66(19): 194303. doi: 10.7498/aps.66.194303
    [5] 郭各朴, 宿慧丹, 丁鹤平, 马青玉. 基于电阻抗层析成像的高强度聚焦超声温度监测技术. 物理学报, 2017, 66(16): 164301. doi: 10.7498/aps.66.164301
    [6] 赵福泽, 朱绍珍, 冯小辉, 杨院生. 高能超声制备碳纳米管增强AZ91D复合材料的声场模拟. 物理学报, 2015, 64(14): 144302. doi: 10.7498/aps.64.144302
    [7] 卢璐, 吉鸿飞, 郭各朴, 郭霞生, 屠娟, 邱媛媛, 章东. 超声增强藻酸钙凝胶支架材料孔隙率的研究. 物理学报, 2015, 64(2): 024301. doi: 10.7498/aps.64.024301
    [8] 耿昊, 范庭波, 张喆, 屠娟, 郭霞生, 李发琪, 章东. 球形集声器在生物组织中形成的组织损伤. 物理学报, 2014, 63(4): 044301. doi: 10.7498/aps.63.044301
    [9] 李先锐, 朱彦丽. DC-DC变换器的信息熵分析. 物理学报, 2014, 63(23): 238401. doi: 10.7498/aps.63.238401
    [10] 孙健明, 于洁, 郭霞生, 章东. 基于分数导数研究高强度聚焦超声的非线性声场. 物理学报, 2013, 62(5): 054301. doi: 10.7498/aps.62.054301
    [11] 龚凯, 唐明, 尚明生, 周涛. 在线热点事件的时空演变规律. 物理学报, 2012, 61(9): 098901. doi: 10.7498/aps.61.098901
    [12] 谢文贤, 蔡力, 岳晓乐, 雷佑铭, 徐伟. 两种群随机动力系统的信息熵和动力学研究. 物理学报, 2012, 61(17): 170509. doi: 10.7498/aps.61.170509
    [13] 冯爱霞, 龚志强, 黄琰, 王启光. 全球温度场信息熵的时空特征分析. 物理学报, 2011, 60(9): 099204. doi: 10.7498/aps.60.099204
    [14] 郭永峰, 徐伟, 李东喜, 王亮. 准单色噪声驱动的耗散动力系统的信息熵演化. 物理学报, 2010, 59(4): 2235-2239. doi: 10.7498/aps.59.2235
    [15] 张春涛, 马千里, 彭宏. 基于信息熵优化相空间重构参数的混沌时间序列预测. 物理学报, 2010, 59(11): 7623-7629. doi: 10.7498/aps.59.7623
    [16] 徐丰, 陆明珠, 万明习, 方飞. 256阵元高强度聚焦超声相控阵系统误差与多焦点模式精确控制. 物理学报, 2010, 59(2): 1349-1356. doi: 10.7498/aps.59.1349
    [17] 郭培荣, 徐伟, 刘迪. 非高斯噪声驱动的双奇异随机系统的熵流与熵产生. 物理学报, 2009, 58(8): 5179-5185. doi: 10.7498/aps.58.5179
    [18] 方小玲, 姜宗来. 基于脑电图的大脑功能性网络分析. 物理学报, 2007, 56(12): 7330-7338. doi: 10.7498/aps.56.7330
    [19] 郭永峰, 徐 伟, 李东喜. 色噪声驱动的双奇异随机系统随时间演化的熵变化率上界. 物理学报, 2007, 56(10): 5613-5617. doi: 10.7498/aps.56.5613
    [20] 谢文贤, 徐 伟, 蔡 力. 色噪声驱动的双奇异随机系统的熵流与熵产生. 物理学报, 2006, 55(4): 1639-1643. doi: 10.7498/aps.55.1639
计量
  • 文章访问数:  3111
  • PDF下载量:  68
  • 被引次数: 0
出版历程
  • 收稿日期:  2022-03-27
  • 修回日期:  2022-05-01
  • 上网日期:  2022-08-25
  • 刊出日期:  2022-09-05

/

返回文章
返回