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Chin. Phys. B, 2022, Vol. 31(7): 074301    DOI: 10.1088/1674-1056/ac3eca

Nonlinear inversion of ultrasonic guided waves for in vivo evaluation of cortical bone properties

Xiaojun Song(宋小军)1,2, Tiandi Fan(樊天地)2, Jundong Zeng(曾俊冬)2, Qin-Zhen Shi(石勤振)1, Qiong Huang(黄琼)2, Meilin Gu(顾美琳)1, Petro Moilanen3, Yi-Fang Li(李义方)4,†, and Dean Ta(他得安)1,4,‡
1 Center for Biomedical Engineering, Fudan University, Shanghai 200433, China;
2 College of Electronics and Information engineering, Shanghai University of Electric Power, Shanghai 200090, China;
3 Department of Physics, University of Helsinki, Helsinki, Finland;
4 Academy for Engineering and Technology, Fudan University, Shanghai 200433, China
Abstract  Ultrasonic guided waves (UGWs), which propagate throughout the entire thickness of cortical bone, are attractive for the early diagnosis of osteoporosis. However, this is challenging due to the impact of soft tissue and the inherent difficulties related to multiparametric inversion of cortical bone quality factors, such as cortical thickness and bulk wave velocity. Therefore, in this research, a UGW-based multi-parameter inversion algorithm is developed to predict strength-related factors. In simulation, a free plate (cortical bone) and a bilayer plate (soft tissue and cortical bone) are used to validate the proposed method. The inversed cortical thickness (CTh), longitudinal velocity (VL) and transverse velocity (VT) are in accordance with the true values. Then four bovine cortical bone plates were used in in vitro experiments. Compared with the reference values, the relative errors for cortical thickness were 3.96%, 0.83%, 2.87%, and 4.25%, respectively. In the in vivo measurements, UGWs are collected from the tibias of 10 volunteers. The theoretical dispersion curves depicted by the estimated parameters (VT, VL, CTh) match well with the extracted experimental ones. In comparison with dual-energy x-ray absorptiometry, our results show that the estimated transverse velocity and cortical thickness are highly sensitive to osteoporosis. Therefore, these two parameters (CTh and VT) of long bones have potential to be used for diagnosis of bone status in clinical applications.
Keywords:  ultrasonic guided waves      inversion algorithm      transverse velocity      bone evaluation  
Received:  27 October 2021      Revised:  30 November 2021      Accepted manuscript online:  01 December 2021
PACS:  43.25.Ba (Parameters of nonlinearity of the medium)  
  43.60.Ek (Acoustic signal coding, morphology, and transformation)  
  43.80.Ev (Acoustical measurement methods in biological systems and media) (Fatigue)  
Fund: Project supported by the National Natural Science Foundation of China (Grant No. 12034005), in part by the Program of Shanghai Academic Research Leader (Grant No. 19XD1400500), and in part by the China Postdoctoral Science Foundation (Grant No. 2019M661334).
Corresponding Authors:  Yi-Fang Li, Dean Ta     E-mail:;

Cite this article: 

Xiaojun Song(宋小军), Tiandi Fan(樊天地), Jundong Zeng(曾俊冬), Qin-Zhen Shi(石勤振), Qiong Huang(黄琼), Meilin Gu(顾美琳), Petro Moilanen, Yi-Fang Li(李义方), and Dean Ta(他得安) Nonlinear inversion of ultrasonic guided waves for in vivo evaluation of cortical bone properties 2022 Chin. Phys. B 31 074301

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